Minor experiment fixes

.gitignore

@@ -30,3 +30,7 @@ Manifest.toml
 .julia
 **/.ipynb_checkpoints/
 *.bkp
+
+*.sif
+
+data/hemera_temp

Project.toml

@@ -1,11 +1,12 @@
+authors = ["Anton Reinhard <anton.reinhard@proton.me>"]
 name = "MetagraphOptimization"
 uuid = "3e869610-d48d-4942-ba70-c1b702a33ca4"
-authors = ["Anton Reinhard <anton.reinhard@proton.me>"]
 version = "0.1.0"
 
 [deps]
 AccurateArithmetic = "22286c92-06ac-501d-9306-4abd417d9753"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 JuliaFormatter = "98e50ef6-434e-11e9-1051-2b60c6c9e899"
@@ -19,6 +20,7 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 
 [extras]
+CUDA_Runtime_jll = "76a88914-d11a-5bdc-97e0-2f5a05c973a2"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]

data/bench_results_32.csv

@@ -0,0 +1,9 @@
+process_name,graph_gen_time,optimization_time,function_generation_time,graph_nodes,graph_edges,graph_mem,cpu_threads,n_inputs,nflops_likwid,cpu_time,cpu_std,cpu_rate,cpu_gflops,gpu_name,gpu_time,gpu_std,gpu_rate,gpu_gflops
+QED Process: 'ke->ke' reduced,0.004851193,0.001290078,0.006093401,26,29,6948.0,32,10000000,0,0.2810178885,0.00909457898005121,3.5584923270818755e7,1.886000933353394,NVIDIA A100-SXM4-80GB,0.4060797745,0.0013320688448668838,2.462570319418851e7,1.305162269291991
+QED Process: 'ke->kke' reduced,0.001065397,0.010432606,0.014287271,59,77,16383.0,32,10000000,0,0.823029796,0.01692859562197734,1.2150228398292398e7,2.223491796887509,NVIDIA A100-SXM4-80GB,2.3333098275,0.0014037935241043983,4.285757460128814e6,0.784293615203573
+QED Process: 'ke->kkke' reduced,0.001348518,0.005210738,0.034243651,188,273,54426.0,32,10000000,0,2.9432864705,0.031053960614444084,3.397562588700793e6,2.497208502695083,NVIDIA A100-SXM4-80GB,10.340032588,0.0028660606476431714,967114.9403924877,0.7108294811884784
+QED Process: 'ke->kkkke' reduced,0.004413783,0.039469525,0.15704043,853,1295,243781.0,32,10000000,0,14.980394603,0.5162977440607073,667539.1580137269,2.4318451526440072,NVIDIA A100-SXM4-80GB,54.2063089555,0.006347197107681703,184480.371246258,0.672061992450118
+QED Process: 'ke->kkkkke' reduced,0.021871728,0.716956567,1.121625045,4982,7655,1.800816e6,32,10000000,0,82.035650126,0.3421310894344223,121898.22332901397,2.6545776094359375,NVIDIA A100-SXM4-80GB,321.789538108,NaN,31076.212293277757,0.6767466751107096
+ABC Process: 'AB->AB' reduced,0.000867035,0.002263493,0.007340721,34,37,9296.0,32,10000000,0,0.1877912925,0.0029540808349122686,5.325060532292784e7,2.8222820821151755,NVIDIA A100-SXM4-80GB,0.0016617045,1.5729813606955104e-5,6.01791714471496e9,318.9496086698929
+ABC Process: 'AB->ABBB' reduced,0.000547175,0.004720326,0.035918118,200,285,57156.0,32,10000000,0,0.257040364,0.007250633041861087,3.8904395575785905e7,28.59473074820264,NVIDIA A100-SXM4-80GB,0.003641165,3.2217340292524716e-5,2.74637375675093e9,2018.5847112119334
+ABC Process: 'AB->ABBBBB' reduced,0.019826198,0.258674017,1.136386232,4998,7671,1.507432e6,32,10000000,0,1.818710381,0.03353568966350073,5.498401562156146e6,119.7386908190744,NVIDIA A100-SXM4-80GB,0.492263776,0.0031065569742746986,2.031431213821429e7,442.38477543389257

data/bench_results_reduction_steps_gpu.csv

@@ -0,0 +1,346 @@
+threads,process,operations,cumulative_optimization_time,graph_nodes,graph_edges,graph_ce,graph_dt,graph_ci,gen_func_t,cpu_compile_t,cpu_st_t,cpu_mt_t,gpu_compile_t,gpu_t
+32,ke->ke,0,0.0,26,29,53.0,1728.0,0.030671296296296297,0.013232422,0.0,0.0,0.0,1.36799064,0.0025947596659751035
+32,ke->kke,0,0.0,77,101,252.0,6240.0,0.04038461538461539,0.020012756,0.0,0.0,0.0,1.231005025,0.015223909966666668
+32,ke->kke,1,3.517e-6,76,99,246.0,6240.0,0.03942307692307692,0.016084704,0.0,0.0,0.0,18.109718661,0.014950094794029853
+32,ke->kke,2,7.533999999999999e-6,75,97,240.0,6240.0,0.038461538461538464,0.016960479,0.0,0.0,0.0,17.864391615,0.013883601284931504
+32,ke->kke,3,9.557999999999999e-6,74,96,240.0,6144.0,0.0390625,0.015486889,0.0,0.0,0.0,16.552522724,0.013848918081967213
+32,ke->kke,4,1.2723e-5,73,95,229.0,6144.0,0.037272135416666664,0.015753696,0.0,0.0,0.0,16.557817835,0.013859916103825138
+32,ke->kke,5,1.7112e-5,72,94,229.0,6048.0,0.03786375661375661,0.015941096,0.0,0.0,0.0,16.536988,0.013445035575268818
+32,ke->kke,6,1.9076e-5,71,92,223.0,6048.0,0.036871693121693125,0.015080442,0.0,0.0,0.0,16.09385785,0.013467766330687829
+32,ke->kke,7,2.0048000000000002e-5,70,90,217.0,6048.0,0.03587962962962963,0.014148442,0.0,0.0,0.0,16.103422137,0.01238744493382353
+32,ke->kke,8,2.4046e-5,69,89,217.0,5952.0,0.036458333333333336,0.016461999,0.0,0.0,0.0,14.753563876,0.012332419892682927
+32,ke->kke,9,2.5729e-5,68,88,206.0,5952.0,0.03461021505376344,0.013755849,0.0,0.0,0.0,14.769888379,0.012313080251219513
+32,ke->kke,10,3.0839e-5,67,87,206.0,5856.0,0.0351775956284153,0.015436866,0.0,0.0,0.0,14.727667086,0.01235367271219512
+32,ke->kke,11,3.4586e-5,66,85,200.0,5856.0,0.03415300546448088,0.01455519,0.0,0.0,0.0,14.769188548,0.011115546662222224
+32,ke->kke,12,3.675e-5,65,84,200.0,5760.0,0.034722222222222224,0.013489783,0.0,0.0,0.0,13.318672311,0.011114837093333333
+32,ke->kke,13,3.8663e-5,64,83,189.0,5760.0,0.0328125,0.013254745,0.0,0.0,0.0,13.320692511,0.011133442756578946
+32,ke->kke,14,4.1058e-5,63,82,189.0,5664.0,0.03336864406779661,0.013846048,0.0,0.0,0.0,13.324213832,0.011126353173626374
+32,ke->kke,15,4.2990999999999995e-5,62,81,189.0,5568.0,0.03394396551724138,0.013539879,0.0,0.0,0.0,13.287594184,0.01110243711868132
+32,ke->kke,16,4.5545999999999994e-5,61,80,189.0,5472.0,0.03453947368421053,0.013225583,0.0,0.0,0.0,13.281132325,0.011124111786813187
+32,ke->kke,17,4.7498999999999994e-5,60,78,183.0,5472.0,0.03344298245614035,0.013304901,0.0,0.0,0.0,13.312699583,0.011084860098901101
+32,ke->kke,18,4.9962999999999996e-5,59,77,183.0,5376.0,0.03404017857142857,0.012726359,0.0,0.0,0.0,13.261357915,0.011093873620614035
+32,ke->kkke,0,0.0,356,493,1399.0,30528.0,0.0458267819706499,0.062291731,0.0,0.0,0.0,1.645480116,0.08758698800000002
+32,ke->kkke,1,4.108e-6,351,483,1369.0,30528.0,0.044844077568134175,0.134859557,0.0,0.0,0.0,104.631981481,0.08257773047692307
+32,ke->kkke,2,5.791e-6,346,473,1339.0,30528.0,0.04386137316561845,0.062112695,0.0,0.0,0.0,97.967784386,0.08185815223076924
+32,ke->kkke,3,7.063e-6,341,468,1339.0,30048.0,0.04456203407880724,0.061549271,0.0,0.0,0.0,97.192234091,0.08231506838461537
+32,ke->kkke,4,9.348e-6,336,458,1309.0,30048.0,0.0435636315228967,0.06061296,0.0,0.0,0.0,97.763394214,0.0814985204375
+32,ke->kkke,5,1.2934999999999999e-5,331,448,1279.0,30048.0,0.042565228966986154,0.059496056,0.0,0.0,0.0,97.355486672,0.07567312011111112
+32,ke->kkke,6,1.56e-5,326,438,1249.0,30048.0,0.04156682641107561,0.057610873,0.0,0.0,0.0,89.846992296,0.07547397385714287
+32,ke->kkke,7,1.7564e-5,321,428,1219.0,30048.0,0.04056842385516507,0.057330145,0.0,0.0,0.0,90.006688844,0.06945375210666667
+32,ke->kkke,8,1.8977e-5,316,423,1219.0,29568.0,0.04122700216450217,0.056788364,0.0,0.0,0.0,83.066104484,0.06917525456
+32,ke->kkke,9,2.086e-5,311,413,1189.0,29568.0,0.040212391774891776,0.055730943,0.0,0.0,0.0,82.785752198,0.0689315006
+32,ke->kkke,10,2.3866e-5,306,408,1189.0,29088.0,0.04087596259625963,0.056044542,0.0,0.0,0.0,82.521686254,0.06882199208
+32,ke->kkke,11,2.6381e-5,301,403,1189.0,28608.0,0.04156180089485459,0.054958499,0.0,0.0,0.0,82.510111584,0.06864414128
+32,ke->kkke,12,2.9186e-5,296,398,1134.0,28608.0,0.039639261744966445,0.05377484,0.0,0.0,0.0,82.352897134,0.06854103965333333
+32,ke->kkke,13,3.159e-5,291,393,1134.0,28128.0,0.040315699658703075,0.052597173,0.0,0.0,0.0,82.277192985,0.06860944045333334
+32,ke->kkke,14,3.5277e-5,286,388,1079.0,28128.0,0.0383603526734926,0.051911746,0.0,0.0,0.0,82.334653097,0.06860165869333334
+32,ke->kkke,15,4.1068e-5,281,383,1079.0,27648.0,0.03902633101851852,0.109366361,0.0,0.0,0.0,82.313609359,0.06861992726666667
+32,ke->kkke,16,4.4364e-5,280,381,1073.0,27648.0,0.03880931712962963,0.050948456,0.0,0.0,0.0,82.340420891,0.06715403988000002
+32,ke->kkke,17,4.6268e-5,275,376,1073.0,27168.0,0.039494994110718495,0.049457541,0.0,0.0,0.0,80.823424533,0.06712361076
+32,ke->kkke,18,4.8241999999999997e-5,274,374,1067.0,27168.0,0.03927414605418139,0.050028919,0.0,0.0,0.0,80.926294213,0.06644700734999999
+32,ke->kkke,19,5.0486e-5,273,372,1061.0,27168.0,0.03905329799764429,0.04969222,0.0,0.0,0.0,79.426824081,0.06518913086249999
+32,ke->kkke,20,5.2189e-5,272,371,1061.0,27072.0,0.03919178486997636,0.05022296,0.0,0.0,0.0,78.009270537,0.06507858397499999
+32,ke->kkke,21,5.4943999999999994e-5,271,370,1050.0,27072.0,0.0387854609929078,0.049509745,0.0,0.0,0.0,78.049841685,0.0651959106125
+32,ke->kkke,22,5.707799999999999e-5,270,369,1050.0,26976.0,0.038923487544483985,0.049194603,0.0,0.0,0.0,78.072865028,0.0650351303375
+32,ke->kkke,23,6.037399999999999e-5,269,367,1044.0,26976.0,0.03870106761565836,0.049468096,0.0,0.0,0.0,78.015114265,0.06368166115
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+32,ke->kkke,25,6.475199999999998e-5,267,365,1033.0,26880.0,0.038430059523809526,0.049233092,0.0,0.0,0.0,76.70857061,0.0638864341625
+32,ke->kkke,26,6.754699999999998e-5,266,364,1033.0,26784.0,0.03856780167264038,0.04945557,0.0,0.0,0.0,76.722101733,0.06370140345
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+32,AB->ABBBBB,705,2.0279186259999986,6199,9110,25185.0,291504.0,0.08639675613370656,1.448574101,0.0,0.0,0.0,12.715612246,0.002208990990728477
+32,AB->ABBBBB,710,2.0287382549999986,6194,9105,25185.0,291264.0,0.08646794660514173,1.439892089,0.0,0.0,0.0,12.851694614,0.0022228503146666666
+32,AB->ABBBBB,715,2.0309239919999986,6187,9098,25185.0,290928.0,0.0865678105923115,1.450127792,0.0,0.0,0.0,12.885176911,0.0022229451498226955
+32,AB->ABBBBB,720,2.0319220339999986,6181,9092,25163.0,290736.0,0.08654930933905673,1.437943464,0.0,0.0,0.0,12.856422709,0.002231291979064588
+32,AB->ABBBBB,725,2.0327114669999986,6176,9087,25141.0,290592.0,0.08651649047461733,1.416551309,0.0,0.0,0.0,12.827515503,0.002233883771428571
+32,AB->ABBBBB,730,2.0337705529999988,6168,9079,25086.0,290448.0,0.08637002148405222,1.411165422,0.0,0.0,0.0,12.966259211,0.002234555193850267
+32,AB->ABBBBB,735,2.0349641599999986,6162,9073,25075.0,290208.0,0.08640354504355496,1.422885775,0.0,0.0,0.0,12.993324369,0.0022326211566964286
+32,AB->ABBBBB,740,2.0365303419999985,6153,9064,25042.0,289920.0,0.08637555187637969,1.410504326,0.0,0.0,0.0,12.964384892,0.0022272366017817373
+32,AB->ABBBBB,745,2.0372326019999987,6148,9059,25020.0,289776.0,0.08634255424879907,1.401546615,0.0,0.0,0.0,12.871037704,0.002225257365777778
+32,AB->ABBBBB,750,2.0385480169999988,6138,9049,24954.0,289584.0,0.08617188794961048,1.4070123,0.0,0.0,0.0,12.994209352,0.0022340590772321435
+32,AB->ABBBBB,755,2.0402276399999986,6131,9042,24943.0,289296.0,0.08621965046181074,1.406919051,0.0,0.0,0.0,13.215688327,0.0023034128057090233
+32,AB->ABBBBB,760,2.0413350059999984,6126,9037,24921.0,289152.0,0.08618650398406374,1.398866293,0.0,0.0,0.0,13.111106793,0.002305295416129032
+32,AB->ABBBBB,765,2.0430572889999983,6116,9027,24888.0,288816.0,0.08617251121821505,1.380178623,0.0,0.0,0.0,13.206362271,0.002279012030979499
+32,AB->ABBBBB,770,2.044160666999998,6109,9020,24855.0,288624.0,0.08611549975054049,1.408393927,0.0,0.0,0.0,12.968425944,0.002248266290843806
+32,AB->ABBBBB,775,2.0446253239999983,6104,9015,24822.0,288528.0,0.08602977873897855,1.403474129,0.0,0.0,0.0,12.889392971,0.0022325058556149726
+32,AB->ABBBBB,780,2.054629998999998,5979,8890,24800.0,282624.0,0.08774909420289854,1.369198466,0.0,0.0,0.0,15.513933561,0.002395324302392344
+32,AB->ABBBBB,785,2.0562029739999983,5970,8881,24767.0,282336.0,0.08772172163663153,1.377730638,0.0,0.0,0.0,15.696071995,0.002403344021133526
+32,AB->ABBBBB,790,2.0567579989999984,5965,8876,24745.0,282192.0,0.08768852412541815,1.376537672,0.0,0.0,0.0,15.727161659,0.002399491918944844
+32,AB->ABBBBB,795,2.0574460919999984,5958,8869,24690.0,282096.0,0.08752339629062447,1.363230402,0.0,0.0,0.0,15.662599522,0.0023887196377088307
+32,AB->ABBBBB,800,2.0591366349999984,5951,8862,24668.0,281856.0,0.08751986830154405,1.311037642,0.0,0.0,0.0,15.709640431,0.0023779721073124405
+32,AB->ABBBBB,805,2.0603478839999982,5943,8854,24635.0,281616.0,0.08747727401852168,1.355314275,0.0,0.0,0.0,15.624383798,0.0024053574769230773
+32,AB->ABBBBB,810,2.0616614739999983,5934,8845,24591.0,281376.0,0.08739551347662913,1.354766478,0.0,0.0,0.0,15.70930316,0.0024099524009638562
+32,AB->ABBBBB,815,2.0631642969999984,5927,8838,24558.0,281184.0,0.08733782861044725,1.296472478,0.0,0.0,0.0,15.705746018,0.0023847287576190474
+32,AB->ABBBBB,820,2.064667347999998,5920,8831,24547.0,280896.0,0.08738821485532011,1.352393082,0.0,0.0,0.0,15.754419163,0.002445868796577017
+32,AB->ABBBBB,825,2.065718067999998,5915,8826,24525.0,280752.0,0.08735467601299367,1.358363183,0.0,0.0,0.0,15.420536669,0.002403251855427474
+32,AB->ABBBBB,830,2.067162020999998,5909,8820,24514.0,280512.0,0.08739020077572439,1.280680896,0.0,0.0,0.0,15.728023382,0.002415643942995169
+32,AB->ABBBBB,835,2.068858544999998,5896,8807,24448.0,280176.0,0.0872594369253612,1.341101369,0.0,0.0,0.0,15.941962612,0.0024475203388753058
+32,AB->ABBBBB,840,2.070637773999998,5889,8800,24415.0,279984.0,0.0872014115092291,1.29790371,0.0,0.0,0.0,15.861084988,0.002437718985888078
+32,AB->ABBBBB,845,2.0712105929999978,5884,8795,24393.0,279840.0,0.08716766723842195,1.335179797,0.0,0.0,0.0,15.808306824,0.002447385063049854
+32,AB->ABBBBB,850,2.0721890279999977,5879,8790,24371.0,279696.0,0.08713388822149763,1.330042746,0.0,0.0,0.0,15.723236372,0.0024326279635568516
+32,AB->ABBBBB,855,2.0731991519999977,5874,8785,24349.0,279552.0,0.0871000744047619,1.340141922,0.0,0.0,0.0,15.892609434,0.002441674606237817
+32,AB->ABBBBB,860,2.0742822419999976,5865,8776,24305.0,279312.0,0.0870173855759867,1.33660764,0.0,0.0,0.0,15.831107771,0.0024102259845783128
+32,AB->ABBBBB,865,2.0750848389999974,5857,8768,24272.0,279072.0,0.08697397087489966,1.31883023,0.0,0.0,0.0,15.833084169,0.0024507554701857287
+32,AB->ABBBBB,870,2.0764542829999972,5847,8758,24239.0,278736.0,0.08696042133057803,1.324416412,0.0,0.0,0.0,15.946636525,0.0024412372609756107
+32,AB->ABBBBB,875,2.077360392999997,5836,8747,24184.0,278448.0,0.08685284146411539,1.293134509,0.0,0.0,0.0,15.783997504,0.0024557449848039217
+32,AB->ABBBBB,880,2.078363443999997,5826,8737,24118.0,278256.0,0.08667557932263814,1.321427016,0.0,0.0,0.0,16.002625756,0.002451596862102689
+32,AB->ABBBBB,885,2.0800038039999973,5816,8727,24085.0,277920.0,0.08666162924582614,1.319821626,0.0,0.0,0.0,15.869988533,0.00246811017357002
+32,AB->ABBBBB,890,2.081413002999997,5809,8720,24052.0,277728.0,0.08660271920728195,1.322749328,0.0,0.0,0.0,15.751667466,0.0024396378209245746
+32,AB->ABBBBB,895,2.082161679999997,5804,8715,24030.0,277584.0,0.08656839010893999,1.315531842,0.0,0.0,0.0,15.796645945,0.00245316119117647
+32,AB->ABBBBB,900,2.092760783999997,5680,8591,23986.0,271824.0,0.08824092059567956,1.275305765,0.0,0.0,0.0,17.49622745,0.0024174821903381644
+32,AB->ABBBBB,905,2.094081176999997,5673,8584,23975.0,271536.0,0.08829400153202523,1.277309132,0.0,0.0,0.0,17.301963605,0.00241616681352657
+32,AB->ABBBBB,910,2.094740465999997,5668,8579,23942.0,271440.0,0.08820365458296493,1.290882361,0.0,0.0,0.0,17.401035411,0.0024252565515738493
+32,AB->ABBBBB,915,2.095970990999997,5661,8572,23909.0,271248.0,0.08814442871468177,1.241385252,0.0,0.0,0.0,17.436377541,0.002395173925978987
+32,AB->ABBBBB,920,2.097313114999997,5654,8565,23887.0,271008.0,0.08814130948163892,1.2775917,0.0,0.0,0.0,17.524830238,0.002444996668292683
+32,AB->ABBBBB,925,2.0982253869999967,5647,8558,23854.0,270816.0,0.08808194493678365,1.256303821,0.0,0.0,0.0,17.390458692,0.002388473591904761
+32,AB->ABBBBB,930,2.0993203999999968,5637,8548,23810.0,270528.0,0.0880130707357464,1.254361716,0.0,0.0,0.0,17.460836585,0.002419127783574879
+32,AB->ABBBBB,935,2.100076670999997,5632,8543,23788.0,270384.0,0.08797857861411917,1.242177769,0.0,0.0,0.0,17.55133577,0.002425685713801453
+32,AB->ABBBBB,940,2.1010204209999968,5622,8533,23722.0,270192.0,0.08779682596079824,1.229283041,0.0,0.0,0.0,17.534817665,0.0024144238120481928
+32,AB->ABBBBB,945,2.1025895179999967,5615,8526,23722.0,269856.0,0.08790614253527808,1.226642517,0.0,0.0,0.0,17.582716932,0.0024112452289156627
+32,AB->ABBBBB,950,2.1036800319999966,5610,8521,23700.0,269712.0,0.08787150738565581,1.223035762,0.0,0.0,0.0,17.544104775,0.002417941161352657
+32,AB->ABBBBB,955,2.1047202919999966,5603,8514,23667.0,269520.0,0.08781166518254675,1.213185959,0.0,0.0,0.0,17.613564227,0.0024441142439024393
+32,AB->ABBBBB,960,2.1074147579999964,5480,8272,22942.0,269376.0,0.08516720123544785,1.231149899,0.0,0.0,0.0,17.502789822,0.002447688212609971
+32,AB->ABBBBB,965,2.1096814159999964,5469,8261,22909.0,268992.0,0.08516610159409946,1.232054637,0.0,0.0,0.0,17.592947626,0.002409367888088376
+32,AB->ABBBBB,970,2.110843613999996,5463,8255,22898.0,268752.0,0.08520122640947789,1.219057813,0.0,0.0,0.0,17.566256478,0.002414121072771085
+32,AB->ABBBBB,975,2.111524052999996,5457,8249,22854.0,268656.0,0.08506789351438271,1.214007072,0.0,0.0,0.0,17.311929893,0.002405199301633045
+32,AB->ABBBBB,980,2.1127225479999963,5451,8243,22843.0,268416.0,0.0851029744873629,1.219959699,0.0,0.0,0.0,17.868461334,0.0024446314024449876
+32,AB->ABBBBB,985,2.123318061999996,5210,7883,22118.0,262608.0,0.08422439529641138,1.154656816,0.0,0.0,0.0,18.261849977,0.002228250951002227
+32,AB->ABBBBB,990,2.124466403999996,5200,7873,22074.0,262320.0,0.0841491308325709,1.151790098,0.0,0.0,0.0,18.452627216,0.002234809248882931
+32,AB->ABBBBB,995,2.125274701999996,5193,7866,22041.0,262128.0,0.08408487456509797,1.144860994,0.0,0.0,0.0,18.355816449,0.0022355378512064344
+32,AB->ABBBBB,1000,2.126074423999996,5188,7861,22030.0,261936.0,0.0841045140797752,1.151574205,0.0,0.0,0.0,18.244992588,0.0022196777043439714
+32,AB->ABBBBB,1005,2.127001131999996,5065,7738,22019.0,256080.0,0.08598484848484848,1.126015159,0.0,0.0,0.0,19.640969518,0.002282847320091324
+32,AB->ABBBBB,1010,2.1277870889999964,5058,7731,21975.0,255936.0,0.08586130907726931,1.111671033,0.0,0.0,0.0,19.778486854,0.002286495183561644
+32,AB->ABBBBB,1015,2.1289088109999965,5052,7725,21953.0,255744.0,0.08583974599599599,1.1012797,0.0,0.0,0.0,19.74738901,0.0022880000328767123
+32,AB->ABBBBB,1020,2.1309106249999967,5042,7715,21931.0,255360.0,0.0858826754385965,1.114773447,0.0,0.0,0.0,19.480380943,0.002266492517647059
+32,AB->ABBBBB,1025,2.132171787999997,5032,7705,21898.0,255024.0,0.08586642825773261,1.104269874,0.0,0.0,0.0,19.635432747,0.002294164430275229
+32,AB->ABBBBB,1030,2.132989973999997,5025,7698,21876.0,254784.0,0.08586096458176337,1.106994476,0.0,0.0,0.0,19.833955597,0.002268743923913044
+32,AB->ABBBBB,1035,2.133999587999997,5015,7688,21843.0,254448.0,0.0858446519524618,1.100426335,0.0,0.0,0.0,19.587691826,0.002265552461050725
+32,AB->ABBBBB,1040,2.134759034999997,5008,7681,21821.0,254208.0,0.08583915533736153,1.104290517,0.0,0.0,0.0,19.369010806,0.002261468618058691
+32,AB->ABBBBB,1045,2.136065942999997,4998,7671,21777.0,253920.0,0.0857632325141777,1.096264587,0.0,0.0,0.0,19.447834897,0.002260751829345372

data/evaluate.jl

@@ -0,0 +1,170 @@
+using CSV
+using DataFrames
+using Plots
+using StatsPlots
+using LaTeXStrings
+
+if (length(ARGS) < 1)
+    println("Please use with \"input_file.csv\"")
+end
+
+processes = [
+    "QED Process: 'ke->ke'",
+    "QED Process: 'ke->kke'",
+    "QED Process: 'ke->kkke'",
+    #"QED Process: 'ke->kkkke'",
+    #"QED Process: 'ke->kkkkke'",
+    #"QED Process: 'ke->kkkkkke'",
+    #"QED Process: 'ke->kkkkkkke'",
+    "ABC Process: 'AB->AB'",
+    "ABC Process: 'AB->ABBB'",
+    #"ABC Process: 'AB->ABBBBB'",
+]
+
+function proc_to_n(str::AbstractString)
+    parts = split(str, "'")
+    parts = split(parts[2], "->")
+    k_count = count(c -> c == 'k', parts[2])
+    return k_count
+end
+
+function beautify_title(str::AbstractString)
+    parts = split(str, "'")
+
+    preprefix = parts[1]
+    infix = parts[2]
+    sufsuffix = parts[3]
+
+    parts = split(infix, "->")
+
+    prefix = parts[1]
+    suffix = parts[2]
+
+    k_count = count(c -> c == 'k', suffix)
+    B_count = count(c -> c == 'B', suffix)
+
+    if k_count == 1 || B_count == 1
+        new_suffix = suffix
+    elseif k_count >= 1
+        new_suffix = replace(suffix, r"k+" => "k^$k_count")
+    elseif B_count >= 1
+        new_suffix = replace(suffix, r"B+" => "B^$B_count")
+    end
+
+    return preprefix * L"%$prefix \rightarrow %$new_suffix" * sufsuffix
+end
+
+input_file = ARGS[1]
+df = CSV.read(input_file, DataFrame)
+n_inputs = df[:, "n_inputs"][1]
+
+# plotting with threads as x axis
+for process_name in processes
+    title_string = "$(beautify_title(process_name)), $n_inputs samples"
+    println("$title_string")
+
+    process_no_opt = process_name * " not optimized"
+    process_red = process_name * " reduced"
+    process_tape_no_opt = process_name * " not optimized tape"
+    process_tape_red = process_name * " reduced tape"
+
+    df_no_opt = filter(:process_name => x -> x == process_no_opt, df)
+    df_red = filter(:process_name => x -> x == process_red, df)
+    df_tape_no_opt = filter(:process_name => x -> x == process_tape_no_opt, df)
+    df_tape_red = filter(:process_name => x -> x == process_tape_red, df)
+
+    @df df_no_opt scatter(:cpu_threads, :cpu_time, label = "unoptimized function", markershape = :circle)
+    @df df_red scatter!(:cpu_threads, :cpu_time, label = "reduced function", markershape = :rect)
+    @df df_tape_no_opt scatter!(:cpu_threads, :cpu_time, label = "unoptimized tape", markershape = :utriangle)
+    @df df_tape_red scatter!(:cpu_threads, :cpu_time, label = "reduced tape", markershape = :star)
+
+    plot!(
+        title = title_string,
+        yscale = :linear,
+        legend = :outerright,
+        legendcolumns = 1,
+        legend_font_pointsize = 10,
+        size = (800, 600),
+        ylabel = "execution time (s)",
+        xlabel = "threads (#)",
+    )
+
+    savefig("$(process_name)_time.pdf")
+
+
+    @df df_no_opt scatter(:cpu_threads, :cpu_rate, label = "unoptimized function", markershape = :circle)
+    @df df_red scatter!(:cpu_threads, :cpu_rate, label = "reduced function", markershape = :rect)
+    @df df_tape_no_opt scatter!(:cpu_threads, :cpu_rate, label = "unoptimized tape", markershape = :utriangle)
+    @df df_tape_red scatter!(:cpu_threads, :cpu_rate, label = "reduced tape", markershape = :star)
+
+    plot!(
+        title = "Sample rate, " * title_string,
+        yscale = :log10,
+        legend = :outerright,
+        legendcolumns = 1,
+        legend_font_pointsize = 10,
+        size = (800, 600),
+        ylabel = "rate (" * L"s^{-1}" * ")",
+        xlabel = "threads (#)",
+    )
+
+    savefig("$(process_name)_rate.pdf")
+
+
+    @df df_no_opt scatter(:cpu_threads, :cpu_gflops, label = "unoptimized function", markershape = :circle)
+    @df df_red scatter!(:cpu_threads, :cpu_gflops, label = "reduced function", markershape = :rect)
+    @df df_tape_no_opt scatter!(:cpu_threads, :cpu_gflops, label = "unoptimized tape", markershape = :utriangle)
+    @df df_tape_red scatter!(:cpu_threads, :cpu_gflops, label = "reduced tape", markershape = :star)
+
+    plot!(
+        title = "CPU performance, " * title_string,
+        yscale = :linear,
+        legend = :outerright,
+        legendcolumns = 1,
+        legend_font_pointsize = 10,
+        size = (800, 600),
+        ylabel = "CPU performance (GFLOPS)",
+        xlabel = "threads (#)",
+    )
+
+    savefig("$(process_name)_performance.pdf")
+
+end
+
+# plotting with process size as x axis
+THREADS = [1, 2, 4, 8, 16]
+
+for threads in THREADS
+    title_string = "$threads threads, $n_inputs samples"
+
+    df_filt = filter(:cpu_threads => x -> x == threads, df)
+    df_filt = filter(:process_name => x -> proc_to_n(x) >= 1, df_filt)
+
+    df_filt.process_size = @. proc_to_n(df_filt.process_name)
+
+    df_no_opt = filter(:process_name => x -> match(r" not optimized$", x) !== nothing, df_filt)
+    df_red = filter(:process_name => x -> match(r" reduced$", x) !== nothing, df_filt)
+    df_tape_no_opt = filter(:process_name => x -> match(r" not optimized tape$", x) !== nothing, df_filt)
+    df_tape_red = filter(:process_name => x -> match(r" reduced tape$", x) !== nothing, df_filt)
+
+
+    @df df_no_opt scatter(:process_size, :graph_gen_time, label = "graph generation time")
+    @df df_red scatter!(:process_size, :optimization_time, label = "optimization time")
+    @df df_no_opt scatter!(:process_size, :function_generation_time, label = "unoptimized function generation time")
+    @df df_tape_no_opt scatter!(:process_size, :function_generation_time, label = "unoptimized tape generation time")
+    @df df_red scatter!(:process_size, :function_generation_time, label = "reduced function generation time")
+    @df df_tape_red scatter!(:process_size, :function_generation_time, label = "reduced tape generation time")
+
+    plot!(
+        title = "function generation times, " * title_string,
+        yscale = :log10,
+        legend = :outerbottom,
+        legendcolumns = 2,
+        legend_font_pointsize = 10,
+        size = (800, 600),
+        ylabel = "time (s)",
+        xlabel = "process size (#)",
+    )
+
+    savefig("gen_times_$(threads)_threads.pdf")
+end

data/evaluate_cpu_gpu_exec.jl

@@ -0,0 +1,143 @@
+using CSV
+using DataFrames
+using Plots
+using StatsPlots
+using LaTeXStrings
+
+if (length(ARGS) < 1)
+    println("Please use with \"input_file.csv\"")
+end
+
+processes = [
+    "QED Process: 'ke->ke'",
+    "QED Process: 'ke->kke'",
+    "QED Process: 'ke->kkke'",
+    "QED Process: 'ke->kkkke'",
+    "QED Process: 'ke->kkkkke'",
+    #"QED Process: 'ke->kkkkkke'",
+    #"QED Process: 'ke->kkkkkkke'",
+    "ABC Process: 'AB->AB'",
+    "ABC Process: 'AB->ABBB'",
+    "ABC Process: 'AB->ABBBBB'",
+]
+
+function proc_to_n(str::AbstractString)
+    parts = split(str, "'")
+    parts = split(parts[2], "->")
+    k_count = count(c -> c == 'k', parts[2])
+    return k_count
+end
+
+function abc_proc_to_n(str::AbstractString)
+    parts = split(str, "'")
+    parts = split(parts[2], "->")
+    b_count = count(c -> c == 'B', parts[2])
+    return b_count
+end
+
+function beautify_title(str::AbstractString)
+    parts = split(str, "'")
+
+    preprefix = parts[1]
+    infix = parts[2]
+    sufsuffix = parts[3]
+
+    parts = split(infix, "->")
+
+    prefix = parts[1]
+    suffix = parts[2]
+
+    k_count = count(c -> c == 'k', suffix)
+    B_count = count(c -> c == 'B', suffix)
+
+    if k_count == 1 || B_count == 1
+        new_suffix = suffix
+    elseif k_count >= 1
+        new_suffix = replace(suffix, r"k+" => "k^$k_count")
+    elseif B_count >= 1
+        new_suffix = replace(suffix, r"B+" => "B^$B_count")
+    end
+
+    return preprefix * L"%$prefix \rightarrow %$new_suffix" * sufsuffix
+end
+
+input_file = ARGS[1]
+df = CSV.read(input_file, DataFrame)
+n_inputs = df[:, "n_inputs"][1]
+
+
+
+title_string = "QED N-Photon Compton Scattering\nCalculate 10,000,000 Matrix Elements"
+
+df_filt = filter(:process_name => x -> proc_to_n(x) >= 1, df)
+
+df_filt.process_size = @. proc_to_n(df_filt.process_name)
+
+df_red = filter(:process_name => x -> match(r" reduced$", x) !== nothing, df_filt)
+
+@df df_red scatter(
+    :process_size,
+    :cpu_time,
+    yerror = :cpu_std,
+    label = "CPU execution time, 32 threads (s)",
+    markersize = 6,
+)
+@df df_red scatter!(
+    :process_size,
+    :gpu_time,
+    yerror = :gpu_std,
+    label = "GPU execution time, A100 80GB (s)",
+    markersize = 6,
+)
+
+plot!(
+    title = title_string,
+    yscale = :log10,
+    legend = :outerbottom,
+    legendcolumns = 2,
+    legend_font_pointsize = 10,
+    size = (800, 600),
+    ylabel = "time (s)",
+    xlabel = "process size (#)",
+)
+
+savefig("cpu_vs_gpu_qed.pdf")
+
+
+
+
+title_string = "\$AB\\rightarrow AB^n\$ ABC Processes\nCalculate 10,000,000 Matrix Elements"
+
+df_filt = filter(:process_name => x -> abc_proc_to_n(x) >= 1, df)
+
+df_filt.process_size = @. abc_proc_to_n(df_filt.process_name)
+
+df_red = filter(:process_name => x -> match(r" reduced$", x) !== nothing, df_filt)
+
+@df df_red scatter(
+    :process_size,
+    :cpu_time,
+    yerror = :cpu_std,
+    label = "CPU execution time, 32 threads (s)",
+    markersize = 6,
+)
+@df df_red scatter!(
+    :process_size,
+    :gpu_time,
+    yerror = :gpu_std,
+    label = "GPU execution time, A100 80GB (s)",
+    markersize = 6,
+)
+
+plot!(
+    title = title_string,
+    yscale = :log10,
+    legend = :outerbottom,
+    legendcolumns = 2,
+    legend_font_pointsize = 10,
+    size = (800, 600),
+    ylabel = "time (s)",
+    xlabel = "process size (#)",
+)
+
+savefig("cpu_vs_gpu_abc.pdf")

data/evaluate_gen.jl

@@ -0,0 +1,232 @@
+using CSV
+using DataFrames
+using Plots
+using StatsPlots
+using LaTeXStrings
+
+if (length(ARGS) < 1)
+    println("Please use with \"input_file.csv\"")
+end
+
+function proc_to_n(str::AbstractString)
+    parts = split(str, "->")
+    k_count = count(c -> c == 'k', parts[2])
+    return k_count
+end
+
+input_file = ARGS[1]
+df = CSV.read(input_file, DataFrame)
+
+# plotting with process size as x axis
+THREADS = [1]
+
+for threads in THREADS
+    title_string = "n-photon Compton diagram generation"
+
+    df_filt = filter(:cpu_threads => x -> x == threads, df)
+    df_filt = filter(:process_name => x -> proc_to_n(x) >= 1, df_filt)
+
+    # ns -> s
+    df_filt.graph_gen_mean = @. df_filt.graph_gen_mean / 1e9
+    df_filt.graph_gen_std = @. df_filt.graph_gen_std / 1e9
+
+    # B -> MB (not MiB since the log scale is base 10)
+    df_filt.graph_mem = @. df_filt.graph_mem / 1e6
+    df_filt.graph_mem_reduced = @. df_filt.graph_mem_reduced / 1e6
+
+    df_filt.process_size = @. proc_to_n(df_filt.process_name)
+    l = length(df_filt.process_size)
+
+    println(df_filt[!, :process_size])
+    println(df_filt[!, :graph_mem])
+    println(df_filt[!, :graph_mem_reduced])
+
+
+    @df df_filt scatter(:process_size, :graph_mem, label = "unreduced graph", markersize = 7)
+    scatter!(
+        df_filt[!, :process_size],
+        df_filt[!, :graph_mem_reduced],
+        label = "reduced graph",
+        markershape = :square,
+        markersize = 7,
+    )
+
+    plot!(
+        title = "n-photon Compton diagram memory footprint",
+        yscale = :log10,
+        legend = :outerbottom,
+        minorgrid = true,
+        xticks = :process_size,
+        #yticks = [1e-3, 1e-1, 1e1, 1e3],
+        xgrid = false,
+        xminorticks = false,
+        legendcolumns = 1,
+        legend_font_pointsize = 12,
+        fontsize = 12,
+        size = (800, 600),
+        ylabel = "memory footprint (MB)",
+        xlabel = "process size (#)",
+    )
+
+    savefig("gen_memory_$(threads).pdf")
+
+    @df df_filt scatter(
+        :process_size,
+        :graph_gen_mean,
+        yerror = :graph_gen_std,
+        label = "graph generation time",
+        markersize = 7,
+    )
+    scatter!(
+        df_filt[!, :process_size],
+        df_filt[!, :graph_elapsed_reduce],
+        label = "graph reduction time",
+        markershape = :square,
+        markersize = 7,
+    )
+
+    plot!(
+        title = title_string,
+        yscale = :log10,
+        legend = :outerbottom,
+        minorgrid = true,
+        xticks = :process_size,
+        yticks = [1e-3, 1e-1, 1e1, 1e3],
+        xgrid = false,
+        xminorticks = false,
+        legendcolumns = 1,
+        legend_font_pointsize = 12,
+        fontsize = 12,
+        size = (800, 600),
+        ylabel = "time (s)",
+        xlabel = "process size (#)",
+    )
+
+    savefig("gen_times_$(threads)_threads.pdf")
+    exit(0)
+
+    # graph size
+    title_string = "n-photon Compton unreduced graph size"
+
+    @df df_filt scatter(:process_size, :graph_nodes, label = "nodes", markershape = :circle)
+    @df df_filt scatter!(:process_size, :graph_edges, label = "edges", markershape = :square)
+    @df df_filt scatter!(:process_size, :graph_u_nodes, label = "U-nodes", markershape = :star)
+    @df df_filt scatter!(:process_size, :graph_v_nodes, label = "V-nodes", markershape = :utriangle)
+    @df df_filt scatter!(:process_size[2:end], :graph_s1_nodes[2:end], label = "S1-nodes", markershape = :x)
+    @df df_filt scatter!(:process_size, :graph_s2_nodes, label = "S2-nodes", markershape = :diamond)
+
+    plot!(
+        title = title_string,
+        yscale = :log10,
+        legend = :outerbottom,
+        yminorgrid = true,
+        xticks = :process_size,
+        yticks = [1e1, 1e3, 1e5, 1e7],
+        xgrid = false,
+        xminorticks = false,
+        legendcolumns = 2,
+        legend_font_pointsize = 10,
+        size = (800, 600),
+        ylabel = "(#)",
+        xlabel = "process size (#)",
+    )
+
+    savefig("compton_graph_size_unreduced.pdf")
+
+
+    # graph size
+    title_string = "n-photon Compton reduced graph size"
+
+    @df df_filt scatter(:process_size, :graph_nodes_reduced, label = "nodes", markershape = :circle)
+    @df df_filt scatter!(:process_size, :graph_edges_reduced, label = "edges", markershape = :square)
+    @df df_filt scatter!(:process_size, :graph_u_nodes_reduced, label = "U-nodes", markershape = :star)
+    @df df_filt scatter!(:process_size, :graph_v_nodes_reduced, label = "V-nodes", markershape = :utriangle)
+    @df df_filt scatter!(:process_size[2:end], :graph_s1_nodes_reduced[2:end], label = "S1-nodes", markershape = :x)
+    @df df_filt scatter!(:process_size, :graph_s2_nodes_reduced, label = "S2-nodes", markershape = :diamond)
+
+    plot!(
+        title = title_string,
+        yscale = :log10,
+        legend = :outerbottom,
+        yminorgrid = true,
+        xticks = :process_size,
+        yticks = [1e1, 1e2, 1e3, 1e4, 1e5, 1e6],
+        xgrid = false,
+        xminorticks = false,
+        legendcolumns = 2,
+        legend_font_pointsize = 10,
+        size = (800, 600),
+        ylabel = "(#)",
+        xlabel = "process size (#)",
+    )
+
+    savefig("compton_graph_size_reduced.pdf")
+
+
+    # graph size versus
+    title_string = "n-photon Compton graph sizes"
+
+    @df df_filt scatter(:process_size, :graph_nodes, label = "nodes", markershape = :circle)
+    @df df_filt scatter!(:process_size, :graph_edges, label = "edges", markershape = :square)
+    @df df_filt scatter!(:process_size, :graph_nodes_reduced, label = "nodes (after reduction)", markershape = :star)
+    @df df_filt scatter!(
+        :process_size,
+        :graph_edges_reduced,
+        label = "edges (after reduction)",
+        markershape = :utriangle,
+    )
+
+    plot!(
+        title = title_string,
+        yscale = :log10,
+        legend = :outerbottom,
+        yminorgrid = true,
+        xticks = :process_size,
+        yticks = [1e1, 1e2, 1e3, 1e4, 1e5, 1e6],
+        xgrid = false,
+        xminorticks = false,
+        legendcolumns = 2,
+        legend_font_pointsize = 10,
+        size = (800, 600),
+        ylabel = "(#)",
+        xlabel = "process size (#)",
+    )
+
+    savefig("compton_graph_size_versus.pdf")
+
+end
+
+# for a specific process, plot times with threads as x
+process = "ke->kkkkkkkke"
+title_string = "n-photon Compton diagram generation times, $process"
+
+df_filt = filter(:process_name => x -> x == process, df)
+df_filt.graph_gen_mean = @. df_filt.graph_gen_mean / 1e9
+df_filt.graph_gen_std = @. df_filt.graph_gen_std / 1e9
+
+@df df_filt scatter(
+    :cpu_threads,
+    :graph_gen_mean,
+    yerror = :graph_gen_std,
+    label = "graph generation time",
+    markersize = 7,
+)
+
+plot!(
+    title = title_string,
+    yscale = :linear,
+    legend = :outerbottom,
+    minorgrid = true,
+    xticks = :cpu_threads,
+    #yticks = [1e-3, 1e-2, 1e-1, 1e-0, 1e1],
+    ylim = (0, max(df_filt[!, :graph_gen_mean]...) * 1.1),
+    xgrid = false,
+    xminorticks = false,
+    legendcolumns = 1,
+    legend_font_pointsize = 10,
+    size = (800, 600),
+    ylabel = "time (s)",
+    xlabel = "process size (#)",
+)
+
+savefig("gen_times_$(process).pdf")

data/evaluate_gen_one_sided_comparison.jl

@@ -0,0 +1,52 @@
+using CSV
+using DataFrames
+using Plots
+using StatsPlots
+using LaTeXStrings
+
+if (length(ARGS) < 2)
+    println("Please use with \"input_file.csv\" \"input_file_onesided.csv\"")
+end
+
+function proc_to_n(str::AbstractString)
+    parts = split(str, "->")
+    k_count = count(c -> c == 'k', parts[2])
+    return k_count
+end
+
+input_file = ARGS[1]
+input_file_onesided = ARGS[2]
+df = CSV.read(input_file, DataFrame)
+df2 = CSV.read(input_file_onesided, DataFrame)
+
+
+df_filt = filter(:process_name => x -> proc_to_n(x) >= 1 && proc_to_n(x) <= 7, df)
+df_filt.process_size = @. proc_to_n(df_filt.process_name)
+
+df_filt2 = filter(:process_name => x -> proc_to_n(x) >= 1 && proc_to_n(x) <= 7, df2)
+df_filt2.process_size = @. proc_to_n(df_filt2.process_name)
+
+
+# graph size
+title_string = "n-photon Compton reduced graph size"
+
+@df df_filt scatter(:process_size, :graph_nodes_reduced, label = "nodes, two-sided generation", markershape = :circle)
+@df df_filt2 scatter!(:process_size, :graph_nodes_reduced, label = "nodes, one-sided generation", markershape = :square)
+
+plot!(
+    title = title_string,
+    yscale = :log10,
+    legend = :outerbottom,
+    yminorgrid = true,
+    xticks = :process_size,
+    yticks = [1e1, 1e2, 1e3, 1e4, 1e5, 1e6],
+    xgrid = false,
+    xminorticks = false,
+    legendcolumns = 2,
+    legend_font_pointsize = 10,
+    size = (800, 600),
+    ylabel = "(#)",
+    xlabel = "process size (#)",
+)
+
+savefig("compton_diagram_gen_comparison.pdf")

data/evaluate_gpu.jl

@@ -0,0 +1,130 @@
+using CSV
+using DataFrames
+using Plots
+using StatsPlots
+using LaTeXStrings
+
+if (length(ARGS) < 1)
+    println("Please use with \"input_file.csv\"")
+end
+
+processes = [
+    "QED Process: 'ke->ke'",
+    "QED Process: 'ke->kke'",
+    "QED Process: 'ke->kkke'",
+    #"QED Process: 'ke->kkkke'",
+    #"QED Process: 'ke->kkkkke'",
+    "ABC Process: 'AB->AB'",
+    "ABC Process: 'AB->ABBB'",
+    #"ABC Process: 'AB->ABBBBB'",
+]
+
+function proc_to_n(str::AbstractString)
+    parts = split(str, "'")
+    parts = split(parts[2], "->")
+    k_count = count(c -> c == 'k', parts[2])
+    return k_count
+end
+
+function beautify_title(str::AbstractString)
+    parts = split(str, "'")
+
+    preprefix = parts[1]
+    infix = parts[2]
+    sufsuffix = parts[3]
+
+    parts = split(infix, "->")
+
+    prefix = parts[1]
+    suffix = parts[2]
+
+    k_count = count(c -> c == 'k', suffix)
+    B_count = count(c -> c == 'B', suffix)
+
+    if k_count == 1 || B_count == 1
+        new_suffix = suffix
+    elseif k_count >= 1
+        new_suffix = replace(suffix, r"k+" => "k^$k_count")
+    elseif B_count >= 1
+        new_suffix = replace(suffix, r"B+" => "B^$B_count")
+    end
+
+    return preprefix * L"%$prefix \rightarrow %$new_suffix" * sufsuffix
+end
+
+input_file = ARGS[1]
+df = CSV.read(input_file, DataFrame)
+n_inputs = df[:, "n_inputs"][1]
+gpu_name = df[:, "gpu_name"][1]
+if (gpu_name == "")
+    println("Results file did not execute everything on GPU! (or didn't write gpu name)")
+    exit(0)
+end
+
+# plotting with process size as x axis
+title_string = "GPU $gpu_name, $n_inputs samples"
+
+df_filt = filter(:process_name => x -> proc_to_n(x) >= 1, df)
+df_filt.gpu_rate = df_filt.gpu_rate .* 1e9
+df_filt.gpu_time = df_filt.gpu_time ./ 1e9
+df_filt.gpu_gflops = df_filt.gpu_gflops .* 1e9
+
+df_filt.process_size = @. proc_to_n(df_filt.process_name)
+
+df_no_opt = filter(:process_name => x -> match(r" no optimization$", x) !== nothing, df_filt)
+df_red = filter(:process_name => x -> match(r" reduced$", x) !== nothing, df_filt)
+
+@df df_no_opt scatter(:process_size, :gpu_rate, label = "unoptimized function execution rate", markersize = 7)
+@df df_red scatter!(:process_size, :gpu_rate, label = "reduced function execution rate", markersize = 7)
+
+plot!(
+    title = title_string * ", sample rate",
+    yscale = :log10,
+    legend = :outerbottom,
+    xticks = [1, 2, 3],
+    legendcolumns = 2,
+    legend_font_pointsize = 10,
+    size = (800, 600),
+    ylabel = "rate (" * L"s^{-1}" * ")",
+    xlabel = "process size (#)",
+)
+
+savefig("gpu_rate_$(gpu_name).pdf")
+
+
+
+@df df_no_opt scatter(:process_size, :gpu_time, label = "unoptimized function execution time", markersize = 7)
+@df df_red scatter!(:process_size, :gpu_time, label = "reduced function execution time", markersize = 7)
+
+plot!(
+    title = title_string * ", execution time",
+    yscale = :log10,
+    legend = :outerbottom,
+    xticks = [1, 2, 3],
+    legendcolumns = 2,
+    legend_font_pointsize = 10,
+    size = (800, 600),
+    ylabel = "time (s)",
+    xlabel = "process size (#)",
+)
+
+savefig("gpu_times_$(gpu_name).pdf")
+
+
+
+@df df_no_opt scatter(:process_size, :gpu_gflops, label = "unoptimized function", markersize = 7)
+@df df_red scatter!(:process_size, :gpu_gflops, label = "reduced function", markersize = 7)
+
+plot!(
+    title = title_string * ", GFLOPS",
+    yscale = :linear,
+    legend = :outerbottom,
+    xticks = [1, 2, 3],
+    legendcolumns = 2,
+    legend_font_pointsize = 10,
+    size = (800, 600),
+    ylabel = "performance (GFLOPS)",
+    xlabel = "process size (#)",
+)
+
+savefig("gpu_perf_$(gpu_name).pdf")

data/evaluate_reduce_bench.jl

@@ -0,0 +1,204 @@
+using Plots
+using StatsPlots
+using CSV
+using DataFrames
+using LaTeXStrings
+
+
+if (length(ARGS) < 2)
+    println("Please use with \"input_file.csv\" \"input_file_gpu.csv\"")
+end
+
+
+function proc_to_n(str::AbstractString)
+    parts = split(str, "'")
+    parts = split(parts[2], "->")
+    k_count = count(c -> c == 'k', parts[2])
+    return k_count
+end
+
+function beautify_title(str::AbstractString)
+    parts = split(str, "->")
+
+    prefix = parts[1]
+    suffix = parts[2]
+
+    k_count = count(c -> c == 'k', suffix)
+    B_count = count(c -> c == 'B', suffix)
+
+    if k_count == 1 || B_count == 1
+        new_suffix = suffix
+    elseif k_count >= 1
+        new_suffix = replace(suffix, r"k+" => "k^$k_count")
+    elseif B_count >= 1
+        new_suffix = replace(suffix, r"B+" => "B^$B_count")
+    end
+
+    return L"%$prefix \rightarrow %$new_suffix"
+end
+
+processes = ["ke->ke", "ke->kke", "ke->kkke", "ke->kkkke", "ke->kkkkke", "AB->AB", "AB->ABBB", "AB->ABBBBB"]
+
+input_file = ARGS[1]
+input_file_gpu = ARGS[2]
+df = CSV.read(input_file, DataFrame)
+df_gpu = CSV.read(input_file_gpu, DataFrame)
+n_inputs = 50_000
+
+for process in processes
+    df_filt = filter(:process => x -> x == process, df)
+    df_filt_gpu = filter(:process => x -> x == process, df_gpu)
+
+    # add dummy factors to get the numbers in similar orders of magnitude
+    df_filt.cumulative_optimization_time = df_filt.cumulative_optimization_time .* 1e4
+    df_filt_gpu.cumulative_optimization_time = df_filt_gpu.cumulative_optimization_time .* 1e4
+    df_filt_gpu.gpu_t = df_filt_gpu.gpu_t .* 1e1
+
+    cpu = !isempty(df_filt)
+    gpu = !isempty(df_filt_gpu)
+
+    ymax = 0.0
+
+    if cpu
+        @df df_filt scatter(
+            :operations,
+            :cumulative_optimization_time,
+            label = "Cumulative Optimization Time (x10000) (s)",
+            markersize = 4,
+        )
+        ymax = max(df_filt[!, :cpu_st_t]..., df_filt[!, :cumulative_optimization_time]...) * 1.1 * 1e4
+        @df df_filt scatter!(
+            :operations,
+            :cpu_st_t,
+            label = "Single-Threaded Execution (s)",
+            markersize = 4,
+            markershape = :square,
+        )
+    end
+
+    if gpu
+        if !cpu
+            @df df_filt_gpu scatter(
+                :operations,
+                :cumulative_optimization_time,
+                label = "Cumulative Optimization Time (x10000) (s)",
+                markersize = 4,
+            )
+            ymax = max(df_filt_gpu[!, :gpu_t]..., df_filt_gpu[!, :cumulative_optimization_time]...) * 1.1 * 1e4
+        end
+
+        @df df_filt_gpu scatter!(
+            :operations,
+            :gpu_t,
+            label = "GPU Execution (x10) (s)",
+            markersize = 4,
+            markershape = :diamond,
+        )
+    end
+
+    if cpu || gpu
+        plot!(
+            title = ("$(beautify_title(process)) Reduction Progression ($(n_inputs) Inputs)"),
+            xscale = :linear,
+            yscale = :linear,
+            #ylim = (0, ymax),
+            legend = :outerbottom,
+            minorgrid = true,
+            xticks = :process_size,
+            #yticks = [1e-3, 1e-1, 1e1, 1e3],
+            xgrid = false,
+            xminorticks = false,
+            legendcolumns = 1,
+            legend_font_pointsize = 12,
+            fontsize = 12,
+            size = (800, 600),
+            xlabel = "optimizer steps (#)",
+            ylabel = "time (s)",
+        )
+
+        savefig("$(String(process))_reduction_bench.pdf")
+    end
+end
+
+# ABC vs QED
+AB_process = "AB->ABBB"
+QED_process = "ke->kkkkke"
+
+df_filt_AB = filter(:process => x -> x == AB_process, df)
+df_filt_QED = filter(:process => x -> x == QED_process, df)
+
+max_AB = max(df_filt_AB[!, :operations]...)
+max_QED = max(df_filt_QED[!, :operations]...)
+
+df_filt_AB.reduction_progress = df_filt_AB.operations ./ max_AB .* 100.0
+df_filt_QED.reduction_progress = df_filt_QED.operations ./ max_QED .* 100.0
+
+df_filt_AB.relative_performance = df_filt_AB.cpu_st_t ./ df_filt_AB[!, :cpu_st_t][1] .* 100.0
+df_filt_QED.relative_performance = df_filt_QED.cpu_st_t ./ df_filt_QED[!, :cpu_st_t][1] .* 100.0
+
+@df df_filt_AB scatter(:reduction_progress, :relative_performance, label = AB_process, markersize = 4)
+@df df_filt_QED scatter!(:reduction_progress, :relative_performance, label = QED_process, markersize = 4)
+
+plot!(
+    title = ("Relative Performance of $(beautify_title(QED_process)) versus $(beautify_title(AB_process)) on CPU"),
+    xscale = :linear,
+    yscale = :linear,
+    #ylim = (0, ymax),
+    legend = :outerbottom,
+    minorgrid = true,
+    xticks = :process_size,
+    #yticks = [1e-3, 1e-1, 1e1, 1e3],
+    xgrid = false,
+    xminorticks = false,
+    legendcolumns = 1,
+    legend_font_pointsize = 12,
+    fontsize = 12,
+    size = (800, 600),
+    xlabel = "reduction progress (%)",
+    ylabel = "relative time taken (%)",
+)
+
+savefig("reduction_bench_relative.pdf")
+
+
+# ABC vs QED on GPU
+AB_process = "AB->ABBB"
+QED_process = "ke->kkke"
+
+df_filt_AB = filter(:process => x -> x == AB_process, df_gpu)
+df_filt_QED = filter(:process => x -> x == QED_process, df_gpu)
+
+max_AB = max(df_filt_AB[!, :operations]...)
+max_QED = max(df_filt_QED[!, :operations]...)
+
+df_filt_AB.reduction_progress = df_filt_AB.operations ./ max_AB .* 100.0
+df_filt_QED.reduction_progress = df_filt_QED.operations ./ max_QED .* 100.0
+
+df_filt_AB.relative_performance = df_filt_AB.gpu_t ./ df_filt_AB[!, :gpu_t][1] .* 100.0
+df_filt_QED.relative_performance = df_filt_QED.gpu_t ./ df_filt_QED[!, :gpu_t][1] .* 100.0
+
+@df df_filt_AB scatter(:reduction_progress, :relative_performance, label = AB_process, markersize = 4)
+@df df_filt_QED scatter!(:reduction_progress, :relative_performance, label = QED_process, markersize = 4)
+
+plot!(
+    title = (
+        "Relative Performance of $(beautify_title(QED_process)) versus $(beautify_title(AB_process)) on GPU (A100)"
+    ),
+    xscale = :linear,
+    yscale = :linear,
+    #ylim = (0, ymax),
+    legend = :outerbottom,
+    minorgrid = true,
+    xticks = :process_size,
+    #yticks = [1e-3, 1e-1, 1e1, 1e3],
+    xgrid = false,
+    xminorticks = false,
+    legendcolumns = 1,
+    legend_font_pointsize = 12,
+    fontsize = 12,
+    size = (800, 600),
+    xlabel = "reduction progress (%)",
+    ylabel = "relative time taken (%)",
+)
+
+savefig("reduction_bench_relative_gpu.pdf")

data/fwk8999_gpu_results_a198f37f8e02a3dfdc31679d0c7126633832ea84.csv

@@ -0,0 +1,13 @@
+process_name,graph_gen_time,optimization_time,function_generation_time,graph_nodes,graph_edges,graph_mem,cpu_threads,n_inputs,nflops_likwid,cpu_time,cpu_rate,cpu_gflops,gpu_name,gpu_time,gpu_rate,gpu_gflops
+QED Process: 'ke->ke' no optimization,0.021888338,0.0,0.143835415,26,29,6532.0,8,1000000,5631,1.880485659327354e8,0.0053177751983373165,2.9944392141837426e-8,NVIDIA A30,9.210393121686748e7,0.010857299865359762,6.113745554184082e-8
+QED Process: 'ke->ke' reduced,0.021888338,0.100014526,0.006987601,26,29,6948.0,8,1000000,5631,1.874650740045045e8,0.005334326968958344,3.0037595162204434e-8,NVIDIA A30,9.341787712903225e7,0.010704589214961101,6.027754186944596e-8
+QED Process: 'ke->kke' no optimization,0.011560896,0.0,0.166822706,77,101,19175.0,8,1000000,25082,5.1290228314606744e8,0.001949689117907892,4.890210245536574e-8,NVIDIA A30,6.011860777314286e8,0.001663378506324519,4.172085969563159e-8
+QED Process: 'ke->kke' reduced,0.011560896,0.067716005,0.014070132,59,77,16383.0,8,1000000,16835,4.00165268947644e8,0.0024989674956794813,4.207011778976407e-8,NVIDIA A30,4.5467275652879584e8,0.0021993840309116187,3.70266301603971e-8
+QED Process: 'ke->kkke' no optimization,0.032403395,0.0,0.082379401,356,493,85898.0,8,1000000,127663,2.047233999655914e9,0.0004884639470466364,6.235877287181474e-8,NVIDIA A30,2.53188631039759e9,0.0003949624419917049,5.042209023198702e-8
+QED Process: 'ke->kkke' reduced,0.032403395,0.183699028,0.031991448,148,221,43962.0,8,1000000,43407,8.954736112291666e8,0.00111672749197752,4.847379024426821e-8,NVIDIA A30,1.4135596722016807e9,0.0007074338775118397,3.0707582321156425e-8
+QED Process: 'ke->kkkke' no optimization,0.502179994,0.0,3.738385104,2183,3015,504653.0,8,1000000,830042,1.3143839308454546e10,7.608127096903622e-5,6.315065031768076e-8,NVIDIA A30,1.84391171835625e10,5.423253131074232e-5,4.5015278754231176e-8
+QED Process: 'ke->kkkke' reduced,0.502179994,5.320319119,0.113738175,543,885,166661.0,8,1000000,164502,3.096394581197183e9,0.0003229562556634375,5.31269499691468e-8,NVIDIA A30,5.367842921893617e9,0.0001862945720563726,3.064582969241741e-8
+ABC Process: 'AB->AB' no optimization,0.000433092,0.0,0.017023325,34,37,8624.0,8,1000000,41,8.381314010084033e7,0.011931303358839001,4.89183437712399e-10,NVIDIA A30,1.8635275427480917e7,0.05366166998129408,2.2001284692330575e-9
+ABC Process: 'AB->AB' reduced,0.000433092,0.065024113,0.007775533,34,37,9296.0,8,1000000,41,8.377098068354431e7,0.01193730802528896,4.894296290368474e-10,NVIDIA A30,1.8622735923664123e7,0.05369780273419915,2.2016099121021654e-9
+ABC Process: 'AB->ABBB' no optimization,0.000342619,0.0,0.055432922,280,385,69428.0,8,1000000,555,1.185642213930131e8,0.00843424760227818,4.681007419264389e-9,NVIDIA A30,1.7535707459770113e7,0.0570264987765204,3.164970682096882e-8
+ABC Process: 'AB->ABBB' reduced,0.000342619,0.124045849,0.040663336,200,285,57156.0,8,1000000,899,1.2518282353097345e8,0.00798831638233958,7.181496427723283e-9,NVIDIA A30,1.6718557076628352e7,0.059813774323739126,5.377258311704147e-8

data/fwk8999results.csv

@@ -0,0 +1,545 @@
+process_name,graph_gen_time,optimization_time,function_generation_time,graph_nodes,graph_edges,graph_mem,cpu_threads,n_inputs,nflops_likwid,cpu_time,cpu_rate,cpu_gflops,gpu_name,gpu_time,gpu_rate,gpu_gflops
+QED Process: 'ke->ke' not optimized,0.000416832,0.0,0.142191958,26,29,6532.0,1,1000000,5683,1.099657532,909374.0286407642,5.167972604765463,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000416832,0.000226336,0.007362257,26,29,6948.0,1,1000000,5683,1.093019605,914896.6728734934,5.199357791940063,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001429112,0.0,0.162321306,77,101,19175.0,1,1000000,23078,3.929152613,254507.80320708302,5.873531082413062,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001429112,0.053476821,0.014625596,61,79,16863.0,1,1000000,16308,2.71745083,367991.9389746603,6.00121254079876,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011559475,0.0,0.082647032,356,493,85898.0,1,1000000,120271,19.718061619,50714.924180803675,6.099534646149439,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011559475,0.005813488,0.032362166,148,221,43962.0,1,1000000,43511,7.009285762,142667.88856310863,6.207622499269419,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059642889,0.0,0.484053531,2183,3015,504653.0,1,1000000,749880,127.166558192,7863.7026449215455,5.896833339373769,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059642889,0.038744443,0.134278476,621,983,185533.0,1,1000000,189455,36.864168806,27126.611894128488,5.139272256402113,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.062327969,0.0,6.39553959,15866,21617,3.982352e6,1,1000000,5405897,944.871738203,1058.3447039085383,5.721302459825056,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.062327969,0.471654237,0.526469997,2234,3977,1.145088e6,1,1000000,648737,128.755149847,7766.679633306333,5.03853244527225,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,41.640690229,17.832311501,6.235837339,15033,27047,6.074251e6,1,1000000,4340484,888.270837833,1125.7827651300265,4.886442079522638,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000474433,0.0,0.016971529,34,37,8624.0,1,1000000,41,0.167961691,5.953738581972243e6,0.244103281860862,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000474433,0.000250697,0.0079372,34,37,9296.0,1,1000000,41,0.170930543,5.850329510741682e6,0.23986350994040895,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000391901,0.0,0.05897346,280,385,69428.0,1,1000000,555,0.500031125,1.9998755077496425e6,1.1099309068010517,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000391901,0.003088955,0.040907741,200,285,57156.0,1,1000000,899,0.544853754,1.8353548868087637e6,1.6499840432410786,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.008247368,0.0,2.347340066,7854,11241,1.982968e6,1,1000000,15833,38.190558541,26184.482191493382,0.4145789065379147,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.008247368,0.277489117,1.301354394,4998,7671,1.507432e6,1,1000000,27893,40.152697698,24904.926874933484,0.6946731253225197,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000403852,0.0,0.142253199,26,29,6532.0,2,1000000,5683,0.715233959,1.3981439044059708e6,7.945651808739132,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000403852,0.000333769,0.007473796,26,29,6948.0,2,1000000,5683,0.710643502,1.4071753237532594e6,7.996977364889774,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001427479,0.0,0.164651479,77,101,19175.0,2,1000000,23078,1.994241302,501443.8317956369,11.572320750179708,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001427479,0.001256415,0.014462799,61,79,16863.0,2,1000000,16308,1.395239134,716723.0158841,11.688318943037903,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011687372,0.0,0.083362074,356,493,85898.0,2,1000000,120271,10.079910039,99207.23460139206,11.931753312744025,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011687372,0.020481006,0.032324393,148,221,43962.0,2,1000000,43511,3.542087589,282319.3878958593,12.283998886736734,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.058450195,0.0,0.487866147,2183,3015,504653.0,2,1000000,749880,64.173043909,15582.866871922748,11.685280209917432,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.058450195,0.040989213,0.136890851,621,983,185533.0,2,1000000,189455,19.426389187,51476.370125910624,9.752455702204397,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.907366535,0.0,6.673265193,15866,21617,3.982352e6,2,1000000,5405897,476.620817192,2098.1039097106077,11.342133631192844,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.907366535,0.515813351,0.543554445,2234,3977,1.138176e6,2,1000000,648737,69.196827669,14451.529552531747,9.375241927320788,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,42.970869315,17.421805278,6.286650041,15033,27047,6.074251e6,2,1000000,4340484,469.142044286,2131.5505872468266,9.251961219135454,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000156505,0.0,0.016950324,34,37,8624.0,2,1000000,41,0.122152986,8.18645563031918e6,0.33564468084308635,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000156505,0.000394292,0.008227015,34,37,9296.0,2,1000000,41,0.123829122,8.075644758266153e6,0.33110143508891227,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000383511,0.0,0.06001645,280,385,69428.0,2,1000000,555,0.206061622,4.852917250161217e6,2.693369073839475,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000383511,0.003188985,0.042017264,200,285,57156.0,2,1000000,899,0.23257461,4.299695482666831e6,3.8654262389174816,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007379088,0.0,2.384403811,7854,11241,1.982968e6,2,1000000,15833,21.434312986,46654.16617986116,0.7386754131257417,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007379088,0.310597709,1.355576602,4998,7671,1.507432e6,2,1000000,27893,22.115403905,45217.35186459395,1.261247595559119,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000405703,0.0,0.142290644,26,29,6532.0,3,1000000,5683,0.618635998,1.616459441792781e6,9.186339007708375,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000405703,0.000293069,0.00749667,26,29,6948.0,3,1000000,5683,0.608292104,1.6439470337099757e6,9.342550992573791,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001477943,0.0,0.165342625,77,101,19175.0,3,1000000,23078,1.410915157,708759.8393416366,16.35675957232629,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001477943,0.001259767,0.014541245,61,79,16863.0,3,1000000,16308,0.956493062,1.0454858897868305e6,17.04978389064363,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011676933,0.0,0.083632557,356,493,85898.0,3,1000000,120271,6.599057066,151536.80139428575,18.225482640492142,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011676933,0.007060747,0.032375987,148,221,43962.0,3,1000000,43511,2.339197699,427497.0005431764,18.60082199063415,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059402986,0.0,0.604593404,2183,3015,504653.0,3,1000000,749880,42.229919926,23679.893349367274,17.757078424823533,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059402986,0.040831071,0.138829109,621,983,185533.0,3,1000000,189455,13.358083803,74861.03656389825,14.182797682213343,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.010801956,0.0,6.513001516,15866,21617,3.982352e6,3,1000000,5405897,314.28804148,3181.794621554622,17.200453999278267,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.010801956,0.520249361,0.55030339,2234,3977,1.145088e6,3,1000000,648737,48.109826326,20785.77447409262,13.484500974999424,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,43.577325507,17.370965212,6.417132285,15033,27047,6.074251e6,3,1000000,4340484,324.487561375,3081.7822284544577,13.376426454090918,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000165215,0.0,0.017266445,34,37,8624.0,3,1000000,41,0.10678774,9.36437085380775e6,0.3839392050061177,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000165215,0.000363811,0.008209255,34,37,9296.0,3,1000000,41,0.111947808,8.932734082653945e6,0.36624209738881175,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000432082,0.0,0.061304796,280,385,69428.0,3,1000000,555,0.16296477,6.136295593213183e6,3.4056440542333166,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000432082,0.003687795,0.043141496,200,285,57156.0,3,1000000,899,0.175522881,5.697262911266822e6,5.121839357228874,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007962198,0.0,2.402439353,7854,11241,1.982968e6,3,1000000,15833,15.293166704,65388.681059655566,1.0352989872175264,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007962198,0.278245766,1.363143846,4998,7671,1.507432e6,3,1000000,27893,16.426870091,60875.86950285087,1.6980106280430194,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000422062,0.0,0.197552826,26,29,6532.0,4,1000000,5683,0.319258827,3.1322548209450133e6,17.800604147430512,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000422062,0.00034778,0.007437403,26,29,6948.0,4,1000000,5683,0.31865171,3.1382226067451513e6,17.834519074132693,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001454252,0.0,0.162749368,77,101,19175.0,4,1000000,23078,1.070005011,934575.0624713664,21.56812329171419,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001454252,0.043562969,0.014515897,61,79,16863.0,4,1000000,16308,0.735867718,1.3589398957707777e6,22.161591820229845,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011621733,0.0,0.082766494,356,493,85898.0,4,1000000,120271,4.84551426,206376.44351912403,24.821101238488566,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011621733,0.006195958,0.032464041,148,221,43962.0,4,1000000,43511,1.772960393,564028.3922574914,24.541439375515704,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059685482,0.0,0.489193295,2183,3015,504653.0,4,1000000,749880,32.687658868,30592.585539338295,22.940768044239004,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059685482,0.055994537,0.135945621,621,983,185533.0,4,1000000,189455,10.196835842,98069.6380225202,18.579783271556565,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.039591441,0.0,6.510710069,15866,21617,3.982352e6,4,1000000,5405897,237.966946723,4202.264279854072,22.71700786367029,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.039591441,0.640614183,0.546447189,2234,3977,1.145088e6,4,1000000,648737,36.456954636,27429.608698378062,17.79460205815969,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,43.65494964,18.511698708,6.337512756,15033,27047,6.074251e6,4,1000000,4340484,250.654946467,3989.548237906628,17.31657029386191,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000154694,0.0,0.016521915,34,37,8624.0,4,1000000,41,0.094403111,1.0592871245524948e7,0.4343077210665229,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000154694,0.000365451,0.007846395,34,37,9296.0,4,1000000,41,0.095364289,1.0486105548377758e7,0.4299303274834881,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000454003,0.0,0.059000415,280,385,69428.0,4,1000000,555,0.137236503,7.286691063528484e6,4.044113540258309,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000454003,0.003244713,0.040646297,200,285,57156.0,4,1000000,899,0.149994089,6.666929388130755e6,5.993569519929549,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.008454683,0.0,2.331775454,7854,11241,1.982968e6,4,1000000,15833,12.236253762,81724.35938730901,1.2939417821792636,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.008454683,0.270852591,1.30331116,4998,7671,1.507432e6,4,1000000,27893,12.659176209,78994.08172303134,2.203381921500513,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000413252,0.0,0.143073739,26,29,6532.0,5,1000000,5683,0.269337367,3.712815682199789e6,21.099931521941404,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000413252,0.000382241,0.007462694,26,29,6948.0,5,1000000,5683,0.268163175,3.729072793085777e6,21.192320683106473,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001425911,0.0,0.162960172,77,101,19175.0,5,1000000,23078,0.834405712,1.1984577593591544e6,27.658008170490564,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001425911,0.044672164,0.014594958,61,79,16863.0,5,1000000,16308,0.933567282,1.0711600752092337e6,17.468478506512184,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011554321,0.0,0.083364585,356,493,85898.0,5,1000000,120271,3.969103991,251946.03171585183,30.301801180497215,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011554321,0.006345572,0.032632617,148,221,43962.0,5,1000000,43511,1.436361166,696203.7290278565,30.292520453731065,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.060042395,0.0,0.490456751,2183,3015,504653.0,5,1000000,749880,26.294862678,38030.24234223004,28.518118127591464,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.060042395,0.040309208,0.136546763,621,983,185533.0,5,1000000,189455,8.806703481,113549.86598077787,21.51258985938827,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.042384898,0.0,6.543593732,15866,21617,3.982352e6,5,1000000,5405897,191.983645358,5208.777019184409,28.15811206167794,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.042384898,0.528700782,0.546099641,2234,3977,1.145088e6,5,1000000,648737,31.472241708,31774.031518886302,20.612989885467744,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.147109337,18.339093794,6.3069457,15033,27047,6.074251e6,5,1000000,4340484,213.464950286,4684.60980905859,20.333473922461863,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000164015,0.0,0.016842494,34,37,8624.0,5,1000000,41,0.090457259,1.1054944744677706e7,0.4532527345317859,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000164015,0.000381851,0.007886717,34,37,9296.0,5,1000000,41,0.09120457,1.0964362860325968e7,0.44953887727336467,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000423002,0.0,0.057193913,280,385,69428.0,5,1000000,555,0.126378072,7.91276511956916e6,4.3915846413608834,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000423002,0.003400608,0.040203966,200,285,57156.0,5,1000000,899,0.134988849,7.408019309802397e6,6.659809359512355,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.008469303,0.0,2.299039913,7854,11241,1.982968e6,5,1000000,15833,11.802467581,84728.04463448244,1.3414991306977606,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.008469303,0.3065725,1.301002324,4998,7671,1.507432e6,5,1000000,27893,12.07699346,82802.06520870302,2.309598004866353,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000417043,0.0,0.143020139,26,29,6532.0,6,1000000,5683,0.230687349,4.334871436751393e6,24.635074375058164,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000417043,0.00034728,0.007539307,26,29,6948.0,6,1000000,5683,0.23281343,4.29528485534533e6,24.410103832927515,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001459612,0.0,0.164676412,77,101,19175.0,6,1000000,23078,0.704806482,1.418829175864475e6,32.74373972060036,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001459612,0.043699365,0.014504647,61,79,16863.0,6,1000000,16308,0.917638498,1.0897537561681506e6,17.771704255590198,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011739657,0.0,0.083612243,356,493,85898.0,6,1000000,120271,3.324746697,300774.7931300524,36.17448514454453,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011739657,0.005715194,0.032312268,148,221,43962.0,6,1000000,43511,1.20584806,829291.8761257533,36.08331882210765,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059683435,0.0,0.493719767,2183,3015,504653.0,6,1000000,749880,22.811595267,43837.355007198144,32.872755772797746,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059683435,0.040256967,0.137925133,621,983,185533.0,6,1000000,189455,7.853848082,127326.1195733936,24.122569983777286,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.054503402,0.0,6.554282919,15866,21617,3.982352e6,6,1000000,5405897,160.707695505,6222.477379553287,33.63807179869497,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.054503402,0.501320626,0.554327439,2234,3977,1.145088e6,6,1000000,648737,27.60822707,36221.08719493374,23.497959443579727,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,43.669608476,17.802861267,6.213337504,15033,27047,6.074251e6,6,1000000,4340484,182.721755884,5472.802049006386,23.754609728879437,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000166535,0.0,0.01668645,34,37,8624.0,6,1000000,41,0.085374503,1.1713098933062017e7,0.4802370562555427,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000166535,0.000375531,0.007825246,34,37,9296.0,6,1000000,41,0.086987749,1.1495871677286418e7,0.47133073876874315,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000452273,0.0,0.057925504,280,385,69428.0,6,1000000,555,0.113074279,8.843744208176645e6,4.9082780355380375,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000452273,0.00314191,0.039873736,200,285,57156.0,6,1000000,899,0.120100791,8.326339832349647e6,7.485379509282333,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.009214085,0.0,2.321825459,7854,11241,1.982968e6,6,1000000,15833,10.267792035,97391.92190407468,1.5420062995072146,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.009214085,0.297605192,1.291820411,4998,7671,1.507432e6,6,1000000,27893,10.720895566,93275.78968042342,2.6017416015560504,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000407492,0.0,0.142142425,26,29,6532.0,7,1000000,5683,0.205797674,4.85914141089855e6,27.614500638136462,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000407492,0.000369221,0.007512386,26,29,6948.0,7,1000000,5683,0.20531643,4.870530819184807e6,27.679226645427256,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001469573,0.0,0.165391603,77,101,19175.0,7,1000000,23078,0.610286318,1.6385751580948927e6,37.81503749851393,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001469573,0.047330541,0.014504177,61,79,16863.0,7,1000000,16308,0.43291809,2.3099057837938815e6,37.66994352211062,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011569733,0.0,0.082708966,356,493,85898.0,7,1000000,120271,2.860309674,349612.4944406981,42.0482443188772,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011569733,0.006750314,0.032273987,148,221,43962.0,7,1000000,43511,1.044942608,956990.3575029644,41.63960744531148,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059614693,0.0,0.492936576,2183,3015,504653.0,7,1000000,749880,19.095801878,52367.531166737004,39.269364271312746,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059614693,0.056236605,0.138333034,621,983,185533.0,7,1000000,189455,6.34676174,157560.66494470296,29.8506557770987,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.050310742,0.0,6.551371601,15866,21617,3.982352e6,7,1000000,5405897,138.132281353,7239.437372676693,39.13565277464082,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.050310742,0.495498539,0.733534099,2234,3977,1.145088e6,7,1000000,648737,23.74606662,42112.23761824012,27.31976669574424,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,43.349001903,18.422956294,6.20023174,15033,27047,6.074251e6,7,1000000,4340484,161.251631842,6201.487628849766,26.91745782922035,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000164355,0.0,0.01704772,34,37,8624.0,7,1000000,41,0.086480955,1.156323955950764e7,0.4740928219398133,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000164355,0.000412952,0.00836477,34,37,9296.0,7,1000000,41,0.089418719,1.1183340705205139e7,0.45851696891341065,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000420162,0.0,0.057607305,280,385,69428.0,7,1000000,555,0.110367501,9.060638239874616e6,5.028654223130412,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000420162,0.003228623,0.039971169,200,285,57156.0,7,1000000,899,0.115717315,8.641749076186221e6,7.7689324194914136,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.006768464,0.0,2.307065796,7854,11241,1.982968e6,7,1000000,15833,9.046608035,110538.6677670953,1.7501587267564198,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.006768464,0.289403906,1.307146192,4998,7671,1.507432e6,7,1000000,27893,9.386326727,106537.94919832434,2.9716630169888605,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000407091,0.0,0.273066077,26,29,6532.0,8,1000000,5683,0.187113846,5.3443399373021275e6,30.37188386368799,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000407091,0.000411822,0.007487655,26,29,6948.0,8,1000000,5683,0.187552789,5.33183220218602e6,30.300802405023152,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001461052,0.0,0.16462108,77,101,19175.0,8,1000000,23078,0.564297766,1.7721140508644152e6,40.89684806584898,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001461052,0.056890616,0.01465998,61,79,16863.0,8,1000000,16308,0.385435328,2.5944689740531514e6,42.310600028858794,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.01160686,0.0,0.083179479,356,493,85898.0,8,1000000,120271,2.508861262,398587.20573605,47.938481821080465,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.01160686,0.007306783,0.032529438,148,221,43962.0,8,1000000,43511,0.918300754,1.0889678524645967e6,47.382080228587064,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.060035062,0.0,0.490512261,2183,3015,504653.0,8,1000000,749880,16.796615652,59535.80296879201,44.64470793023776,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.060035062,0.040415015,0.138334341,621,983,185533.0,8,1000000,189455,5.866855301,170449.0649069785,32.292427591951615,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.085570766,0.0,6.62849813,15866,21617,3.982352e6,8,1000000,5405897,123.327489076,8108.492336074032,43.83367439410561,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.085570766,0.488386218,0.552508179,2234,3977,1.145088e6,8,1000000,648737,21.553492489,46396.19312324247,30.098927138192952,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.412101158,18.197264492,6.353428834,15033,27047,6.074251e6,8,1000000,4340484,148.047148125,6754.604952982102,29.318254724739568,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000146674,0.0,0.017128359,34,37,8624.0,8,1000000,41,0.088785018,1.1263161539258799e7,0.46178962310961075,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000146674,0.000415051,0.008459913,34,37,9296.0,8,1000000,41,0.088094555,1.1351439371025825e7,0.4654090142120588,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000453451,0.0,0.062898243,280,385,69428.0,8,1000000,555,0.105873779,9.445209280760631e6,5.242091150822151,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000453451,0.003255032,0.043431236,200,285,57156.0,8,1000000,899,0.10929342,9.149681655126173e6,8.22556380795843,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007021448,0.0,2.438662754,7854,11241,1.982968e6,8,1000000,15833,8.719411378,114686.64072016445,1.8158335825223637,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007021448,0.279258146,1.385337411,4998,7671,1.507432e6,8,1000000,27893,8.849104422,113005.78593172353,3.152070386993564,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000415981,0.0,0.142074969,26,29,6532.0,9,1000000,5683,0.90093379,1.1099594788203028e6,6.30789971813578,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000415981,0.000436702,0.007530575,26,29,6948.0,9,1000000,5683,0.874710346,1.1432355917280987e6,6.497007867790785,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001457917,0.0,0.165713831,77,101,19175.0,9,1000000,23078,0.512481676,1.9512892788775533e6,45.03185397793617,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001457917,0.043212987,0.014603927,61,79,16863.0,9,1000000,16308,0.358141002,2.7921963539935593e6,45.53513814092696,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011681223,0.0,0.08335605,356,493,85898.0,9,1000000,120271,2.287616782,437136.15316536,52.57480227735101,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011681223,0.006810646,0.032095143,148,221,43962.0,9,1000000,43511,0.84204133,1.1875901625873875e6,51.67323556433981,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.060532594,0.0,0.49242029,2183,3015,504653.0,9,1000000,749880,15.65187103,63890.12521782835,47.90992709834512,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.060532594,0.04373095,0.136935272,621,983,185533.0,9,1000000,189455,5.660829724,176652.54896474606,33.46770866411597,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.06867787,0.0,6.528005973,15866,21617,3.982352e6,9,1000000,5405897,112.246015855,8909.002180458729,48.161148160335294,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.06867787,0.599657175,0.545603133,2234,3977,1.138176e6,9,1000000,648737,19.835588588,50414.43542567591,32.705709594746715,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,45.069601648,18.052478781,6.444323717,15033,27047,6.074251e6,9,1000000,4340484,135.847359555,7361.203068471374,31.951184139450902,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000162754,0.0,0.016933906,34,37,8624.0,9,1000000,41,0.086219465,1.1598309036132386e7,0.47553067048142783,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000162754,0.000432842,0.00814777,34,37,9296.0,9,1000000,41,0.085579369,1.1685059281051721e7,0.4790874305231206,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000410271,0.0,0.061241763,280,385,69428.0,9,1000000,555,0.108576561,9.210090932977699e6,5.111600467802623,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000410271,0.003269348,0.043063382,200,285,57156.0,9,1000000,899,0.106781435,9.364923780992456e6,8.419066479112217,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007349228,0.0,2.422015697,7854,11241,1.982968e6,9,1000000,15833,8.26459201,120998.10841116161,1.9157630504739218,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007349228,0.331438575,1.379430053,4998,7671,1.507432e6,9,1000000,27893,8.701080396,114928.25654842966,3.205693859905349,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000404781,0.0,0.141596923,26,29,6532.0,10,1000000,5683,0.16322332,6.126575540798949e6,34.81732879836043,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000404781,0.000389751,0.007607107,26,29,6948.0,10,1000000,5683,0.166281055,6.013914212896953e6,34.177074471893384,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.094137777,0.0,0.162168485,77,101,19175.0,10,1000000,23078,0.448930803,2.2275147824953324e6,51.40658615042729,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.094137777,0.044206691,0.0143803,61,79,16863.0,10,1000000,16308,0.321777464,3.1077378371034707e6,50.680988647483396,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011551814,0.0,0.082958195,356,493,85898.0,10,1000000,120271,2.048706218,488112.93254931684,58.70583051063888,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011551814,0.006589459,0.03239809,148,221,43962.0,10,1000000,43511,0.751390472,1.3308659575337283e6,57.907308678250054,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.060020652,0.0,0.492926956,2183,3015,504653.0,10,1000000,749880,14.500608235,68962.62444952538,51.71369282221009,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.060020652,0.039742322,0.136650449,621,983,185533.0,10,1000000,189455,3.777879044,264698.7868995416,50.14850867205266,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.088321527,0.0,6.430067533,15866,21617,3.982352e6,10,1000000,5405897,99.408929763,10059.458464989932,54.38039633751368,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.088321527,0.68403137,0.551130398,2234,3977,1.145088e6,10,1000000,648737,19.80851602,50483.33751959679,32.75040893245066,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.122659554,16.118877974,6.126612105,15033,27047,6.074251e6,10,1000000,4340484,129.639490484,7713.698937465503,33.481186818886016,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000161575,0.0,0.01714635,34,37,8624.0,10,1000000,41,0.085320822,1.1720468422116233e7,0.4805392053067656,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000161575,0.000402971,0.008176434,34,37,9296.0,10,1000000,41,0.091957683,1.0874567163681148e7,0.44585725371092705,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.00035024,0.0,0.060008547,280,385,69428.0,10,1000000,555,0.102871544,9.720861193645544e6,5.395077962473277,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.00035024,0.003186318,0.042141327,200,285,57156.0,10,1000000,899,0.102263958,9.77861623544827e6,8.790975995667994,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007332621,0.0,2.39644201,7854,11241,1.982968e6,10,1000000,15833,7.093082377,140982.43145217033,2.232174837182213,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007332621,0.273692037,1.348103426,4998,7671,1.507432e6,10,1000000,27893,8.406378912,118957.28356623476,3.318075510512986,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000406502,0.0,0.141790228,26,29,6532.0,11,1000000,5683,0.152140033,6.572891961972954e6,37.353745019892294,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000406502,0.000421482,0.007437875,26,29,6948.0,11,1000000,5683,0.153610833,6.509957536653681e6,36.99608868080286,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001448078,0.0,0.16399523,77,101,19175.0,11,1000000,23078,0.413552565,2.4180722951144073e6,55.80427242665029,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001448078,0.001287738,0.014476007,61,79,16863.0,11,1000000,16308,0.302012973,3.311116042687345e6,53.997680424145216,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011549805,0.0,0.082902214,356,493,85898.0,11,1000000,120271,1.842802374,542651.7862734206,65.26527298689057,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011549805,0.006389496,0.032343334,148,221,43962.0,11,1000000,43511,0.692055287,1.4449712599334568e6,62.87214449096464,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059032921,0.0,0.489917204,2183,3015,504653.0,11,1000000,749880,13.442805766,74389.23223373754,55.7829974674351,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059032921,0.056634255,0.138971179,621,983,185533.0,11,1000000,189455,5.206396863,192071.4125937349,36.38888947294605,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.075847276,0.0,6.517554046,15866,21617,3.982352e6,11,1000000,5405897,92.762839214,10780.178878451981,58.27653665848693,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.075847276,0.477987998,0.547846858,2234,3977,1.145088e6,11,1000000,648737,18.732986297,53381.77181927183,34.63073050471895,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,43.3795548,18.064181564,6.438537503,15033,27047,6.074251e6,11,1000000,4340484,118.034265281,8472.116106448711,36.77308440618293,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000158504,0.0,0.016891054,34,37,8624.0,11,1000000,41,0.084551612,1.1827095620601533e7,0.4849109204446629,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000158504,0.00040669,0.008044817,34,37,9296.0,11,1000000,41,0.086822992,1.1517686467197537e7,0.47222514515509906,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.00037811,0.0,0.059958124,280,385,69428.0,11,1000000,555,0.116438315,8.588238330312492e6,4.766472273323433,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.00037811,0.003211239,0.041741948,200,285,57156.0,11,1000000,899,0.100392355,9.960917840805706e6,8.95486513888433,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007829143,0.0,2.377448136,7854,11241,1.982968e6,11,1000000,15833,6.894505859,145043.027078527,2.2964662477343176,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007829143,0.262388836,1.33119686,4998,7671,1.507432e6,11,1000000,27893,7.386928053,135374.27098587717,3.7759945406090716,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.00040974,0.0,0.141702878,26,29,6532.0,12,1000000,5683,0.143172598,6.984576755392816e6,39.69334970089737,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.00040974,0.000403,0.007448387,26,29,6948.0,12,1000000,5683,0.143856539,6.951369794875991e6,39.50463454428026,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001466116,0.0,0.165770224,77,101,19175.0,12,1000000,23078,0.379379799,2.6358809895410375e6,60.83086147662806,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001466116,0.056434153,0.014473034,61,79,16863.0,12,1000000,16308,0.279254485,3.580963077459615e6,58.398345867211404,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011630684,0.0,0.082986855,356,493,85898.0,12,1000000,120271,1.707706374,585580.7621410213,70.42838384346277,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011630684,0.006989227,0.032451591,148,221,43962.0,12,1000000,43511,2.082187754,480264.08669388416,20.896770676137592,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.058567663,0.0,0.489796923,2183,3015,504653.0,12,1000000,749880,12.15359975,82280.14913852993,61.70023823600082,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.058567663,0.038658372,0.137284537,621,983,185533.0,12,1000000,189455,4.557444916,219421.19289017865,41.570442099008794,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.039638784,0.0,6.623001613,15866,21617,3.982352e6,12,1000000,5405897,85.315424704,11721.20989222615,63.363653392755666,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.039638784,0.574728966,0.549160788,2234,3977,1.138176e6,12,1000000,648737,16.951035133,58993.447429839616,38.271232105291865,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.556395718,18.009618638,6.208598348,15033,27047,6.074251e6,12,1000000,4340484,112.038671956,8925.489588030117,38.74094474901131,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000165094,0.0,0.017016445,34,37,8624.0,12,1000000,41,0.083614769,1.195960967134885e7,0.4903439965253028,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000165094,0.000432322,0.007975779,34,37,9296.0,12,1000000,41,0.083883417,1.1921307402153157e7,0.4887736034882794,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.00041339,0.0,0.059370275,280,385,69428.0,12,1000000,555,0.100982046,9.902750435458595e6,5.496026491679521,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.00041339,0.00342609,0.04155883,200,285,57156.0,12,1000000,899,0.10106195,9.894920887633773e6,8.89553387798276,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007424875,0.0,2.379512773,7854,11241,1.982968e6,12,1000000,15833,7.089738308,141048.92967228545,2.2332277035012957,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007424875,0.271811669,1.346133294,4998,7671,1.507432e6,12,1000000,27893,7.350202463,136050.67411868926,3.7948614531926,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000420601,0.0,0.199208162,26,29,6532.0,13,1000000,5683,0.13693181,7.302905000671503e6,41.50240911881615,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000420601,0.000441932,0.007450497,26,29,6948.0,13,1000000,5683,0.138500682,7.220181052971276e6,41.03228892403577,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001455728,0.0,0.164987673,77,101,19175.0,13,1000000,23078,0.37253838,2.6842871867322773e6,61.9479796954075,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001455728,0.054855247,0.014512752,61,79,16863.0,13,1000000,16308,0.268950039,3.7181626882009865e6,60.63579711918169,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011599836,0.0,0.08336237,356,493,85898.0,13,1000000,120271,1.615288411,619084.488683303,74.45791053842953,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011599836,0.006554602,0.032276442,148,221,43962.0,13,1000000,43511,0.590283163,1.6941021914257105e6,73.71208045112408,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059994894,0.0,0.494121795,2183,3015,504653.0,13,1000000,749880,11.856984434,84338.47624295532,63.24373656506734,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059994894,0.041637961,0.138584724,621,983,185533.0,13,1000000,189455,5.992954,166862.6190022483,31.612957483070954,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.182937115,0.0,6.506259066,15866,21617,3.982352e6,13,1000000,5405897,79.059668403,12648.674351915874,68.37743073299896,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.182937115,0.525640731,0.550328317,2234,3977,1.145088e6,13,1000000,648737,15.602344521,64092.93158820128,41.57945615973493,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.179409787,17.440270822,6.406795075,15033,27047,6.074251e6,13,1000000,4340484,104.625069586,9557.938684838984,41.48607993452465,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000165235,0.0,0.016713706,34,37,8624.0,13,1000000,41,0.084085553,1.1892649382944535e7,0.48759862470072596,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000165235,0.000453142,0.007955822,34,37,9296.0,13,1000000,41,0.086006094,1.1627083076229459e7,0.4767104061254078,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000393691,0.0,0.05921868,280,385,69428.0,13,1000000,555,0.101050817,9.896011033735631e6,5.492286123723275,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000393691,0.003135373,0.04122057,200,285,57156.0,13,1000000,899,0.100139352,9.986084191956824e6,8.977489688569186,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007931792,0.0,2.381974379,7854,11241,1.982968e6,13,1000000,15833,7.287740552,137216.73992984925,2.172552643309303,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007931792,0.276362209,1.337076687,4998,7671,1.507432e6,13,1000000,27893,7.488008263,133546.86117818992,3.7250225988432515,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000433602,0.0,0.19790805,26,29,6532.0,14,1000000,5683,0.163627644,6.111436769205087e6,34.73129515939251,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000433602,0.000460842,0.007439379,26,29,6948.0,14,1000000,5683,0.166542072,6.004488763656069e6,34.12350964385744,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001474269,0.0,0.164875928,77,101,19175.0,14,1000000,23078,0.476240234,2.099780590986355e6,48.4587364787831,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001474269,0.054595011,0.014531929,61,79,16863.0,14,1000000,16308,0.349355032,2.862417622197009e6,46.68030658278882,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011707363,0.0,0.083493312,356,493,85898.0,14,1000000,120271,2.199906287,454564.81756034,54.670965172799654,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011707363,0.020122448,0.032385537,148,221,43962.0,14,1000000,43511,0.815282938,1.2265680457549328e6,53.36920223884288,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.058648849,0.0,0.489621657,2183,3015,504653.0,14,1000000,749880,16.294662534,61369.78890562644,46.019977304551155,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.058648849,0.041027757,0.138319561,621,983,185533.0,14,1000000,189455,6.108266651,163712.5648135036,31.016163966742322,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.058122779,0.0,6.745873339,15866,21617,3.982352e6,14,1000000,5405897,110.224918617,9072.358705699873,49.044236710066826,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.058122779,0.554504009,0.554020905,2234,3977,1.138176e6,14,1000000,648737,21.039018147,47530.73518036735,30.834946548705975,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.019966769,17.074345772,6.281667473,15033,27047,6.074251e6,14,1000000,4340484,125.032802475,7997.901192368679,34.71476215905717,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000149754,0.0,0.016892621,34,37,8624.0,14,1000000,41,0.084228586,1.1872453848388243e7,0.48677060778391795,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000149754,0.00047204,0.0083509,34,37,9296.0,14,1000000,41,0.085440358,1.1704070809253866e7,0.4798669031794085,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000387639,0.0,0.061399285,280,385,69428.0,14,1000000,555,0.103503535,9.661505764030186e6,5.362135699036753,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000387639,0.003215103,0.04300004,200,285,57156.0,14,1000000,899,0.104006715,9.61476381597092e6,8.643672670557857,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007503002,0.0,2.430352466,7854,11241,1.982968e6,14,1000000,15833,9.085069077,110070.70959225025,1.7427495449740982,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007503002,0.287303313,1.373863604,4998,7671,1.507432e6,14,1000000,27893,10.2203346,97844.15473051147,2.7291670078981562,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.00041835,0.0,0.01530602,26,29,6532.0,15,1000000,5683,0.125605168,7.961455853472526e6,45.244953615284366,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.00041835,0.00043469,0.007037656,26,29,6948.0,15,1000000,5683,0.126756881,7.889118066892164e6,44.833857974148174,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001466615,0.0,0.016836368,77,101,19175.0,15,1000000,23078,0.316180837,3.162747019990968e6,72.98987572735156,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001466615,0.004920647,0.014455553,61,79,16863.0,15,1000000,16308,0.23628643,4.232151630544336e6,69.01792879091703,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011839341,0.0,0.082894507,356,493,85898.0,15,1000000,120271,1.391799054,718494.5248568907,86.4140549990631,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011839341,0.006005022,0.032279897,148,221,43962.0,15,1000000,43511,0.523911268,1.908720161369005e6,83.05032294132678,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059756873,0.0,0.495767672,2183,3015,504653.0,15,1000000,749880,11.089154664,90178.19935782978,67.6228281344494,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059756873,0.056267986,0.13583358,621,983,185533.0,15,1000000,189455,2.576653341,388100.32536697376,73.52754714240001,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.062927729,0.0,6.441152895,15866,21617,3.982352e6,15,1000000,5405897,71.577072238,13970.954227841465,75.5255395474255,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.062927729,0.537386579,0.53776467,2234,3977,1.145088e6,15,1000000,648737,15.725552892,63590.76891399641,41.253684652959286,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.930203723,17.990357214,6.306877837,15033,27047,6.074251e6,15,1000000,4340484,96.169861291,10398.268091227708,45.13351627768441,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000155975,0.0,0.016687037,34,37,8624.0,15,1000000,41,0.08481308,1.1790634180482538e7,0.4834160013997841,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000155975,0.000465442,0.007947819,34,37,9296.0,15,1000000,41,0.084251407,1.1869237981984086e7,0.48663875726134753,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000437462,0.0,0.057456228,280,385,69428.0,15,1000000,555,0.099751788,1.0024882962498879e7,5.563810044186878,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000437462,0.003150218,0.039776466,200,285,57156.0,15,1000000,899,0.100170341,9.98299486671409e6,8.974712385175966,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007333603,0.0,2.291339497,7854,11241,1.982968e6,15,1000000,15833,7.122189548,140406.2603586298,2.2230523202581858,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007333603,1.221216593,1.284172659,4998,7671,1.507432e6,15,1000000,27893,5.732480059,174444.56669849184,4.865782298921033,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.00041067,0.0,0.142104349,26,29,6532.0,17,1000000,5683,0.114945742,8.699756794818899e6,49.4407178649558,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.00041067,0.000481492,0.00747717,26,29,6948.0,17,1000000,5683,0.115779695,8.637093058502184e6,49.084599851467914,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001462887,0.0,0.164664435,77,101,19175.0,17,1000000,23078,0.299937297,3.3340301789810425e6,76.9427484705245,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001462887,0.043099733,0.014542889,61,79,16863.0,17,1000000,16308,0.218010362,4.586937936463772e6,74.8037838678512,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011627975,0.0,0.083358846,356,493,85898.0,17,1000000,120271,1.234705223,809909.9132101104,97.40867517169319,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011627975,0.020343508,0.032486925,148,221,43962.0,17,1000000,43511,0.469799577,2.1285672634822316e6,92.61609020137539,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059366449,0.0,0.492151119,2183,3015,504653.0,17,1000000,749880,9.698243677,103111.45330072117,77.3212166011448,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059366449,0.044129573,0.137817937,621,983,185533.0,17,1000000,189455,4.376145145,228511.61624347814,43.29266825540815,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.133548318,0.0,6.591354593,15866,21617,3.982352e6,17,1000000,5405897,64.298133716,15552.550940544006,84.07548847183402,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.133548318,0.631323,0.543495513,2234,3977,1.145088e6,17,1000000,648737,14.424643621,69325.8028603326,44.974213370203586,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,43.600370462,16.889184011,6.413356503,15033,27047,6.074251e6,17,1000000,4340484,92.101226674,10857.618688832274,47.127320196977465,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000156424,0.0,0.01669466,34,37,8624.0,17,1000000,41,0.09352269,1.0692592353791364e7,0.4383962865054459,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000156424,0.000482022,0.007777769,34,37,9296.0,17,1000000,41,0.083675977,1.1950861356539644e7,0.4899853156181254,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.00037662,0.0,0.057922253,280,385,69428.0,17,1000000,555,0.097341419,1.0273119195026323e7,5.7015811532396095,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.00037662,0.003276365,0.040298299,200,285,57156.0,17,1000000,899,0.100945103,9.906374556871768e6,8.90583072662772,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.008089669,0.0,2.330026015,7854,11241,1.982968e6,17,1000000,15833,6.688160696,149517.93855642132,2.3673175211638187,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.008089669,0.279663459,1.307680333,4998,7671,1.507432e6,17,1000000,27893,7.127043604,140310.6330707388,3.913684488242118,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000417741,0.0,0.141964132,26,29,6532.0,18,1000000,5683,1.665133875,600552.3129484109,3.412938794485819,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000417741,0.000595565,0.006998161,26,29,6948.0,18,1000000,5683,0.116941405,8.551291135932565e6,48.596987525504765,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001459098,0.0,0.165762719,77,101,19175.0,18,1000000,23078,0.278548247,3.590042338338607e6,82.85099708417837,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001459098,0.105453888,0.014604248,61,79,16863.0,18,1000000,16308,0.208209969,4.802843998310187e6,78.32477992444254,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011777765,0.0,0.082411482,356,493,85898.0,18,1000000,120271,1.174831368,851185.9891027356,102.37299009537512,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011777765,0.006045106,0.032114551,148,221,43962.0,18,1000000,43511,0.453976722,2.20275611400181e6,95.84412127633276,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.058751581,0.0,0.487105201,2183,3015,504653.0,18,1000000,749880,7.472277073,133828.01390132552,100.35495106432599,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.058751581,0.040675993,0.136792303,621,983,185533.0,18,1000000,189455,5.296651946,188798.51086971915,35.76882187682264,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.073234334,0.0,6.681835042,15866,21617,3.982352e6,18,1000000,5405897,63.247644301,15810.865543717793,85.4719106101874,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.073234334,1.331188827,0.543555643,2234,3977,1.145088e6,18,1000000,648737,12.187577675,82050.75911444396,53.22936331562704,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,43.586633098,16.755729566,6.179858194,15033,27047,6.074251e6,18,1000000,4340484,89.333988184,11193.947794430867,48.58715129856247,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000154654,0.0,0.016545081,34,37,8624.0,18,1000000,41,0.083440861,1.1984535969733102e7,0.4913659747590572,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000154654,0.000483663,0.007793422,34,37,9296.0,18,1000000,41,0.085689999,1.166997329525001e7,0.4784689051052504,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.00037723,0.0,0.05688874,280,385,97076.0,18,1000000,555,0.100137825,9.986236469585793e6,5.5423612406201155,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.00037723,0.003351257,0.040167046,200,285,84804.0,18,1000000,899,0.100677819,9.932674445400927e6,8.929474326415434,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007476644,0.0,3.347976748,7854,11241,1.982968e6,18,1000000,15833,7.723920471,129467.93066481847,2.0498657462160708,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007476644,0.808089997,1.289335465,4998,7671,1.507432e6,18,1000000,27893,7.245894911,138009.17792526897,3.8494899998695273,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000410484,0.0,0.015828233,26,29,6532.0,19,1000000,5683,0.13693236,7.302875667957523e6,41.5022424210026,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000410484,0.000594739,0.007065233,26,29,6948.0,19,1000000,5683,0.13650559,7.325707320850376e6,41.63199470439268,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001441257,0.0,0.016986027,77,101,19175.0,19,1000000,23078,0.370139455,2.701684423239884e6,62.349473119530046,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001441257,0.097376896,0.014550616,61,79,16863.0,19,1000000,16308,0.272982118,3.6632436121694976e6,59.74017682726017,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011583987,0.0,0.081275111,356,493,85898.0,19,1000000,120271,1.68103571,594871.3605851955,71.54577340894205,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011583987,0.020756044,0.03172744,148,221,43962.0,19,1000000,43511,0.628366552,1.5914278008865118e6,69.24461504437302,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059385562,0.0,0.485523517,2183,3015,504653.0,19,1000000,749880,10.887383733,91849.43091231081,68.87605125252364,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059385562,0.040927375,0.133672425,621,983,185533.0,19,1000000,189455,3.023195652,330775.8131163123,62.66713167395095,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.081441245,0.0,6.497476939,15866,21617,3.982352e6,19,1000000,5405897,87.003003319,11493.856095213861,62.134602183548324,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.081441245,0.534920906,0.532804256,2234,3977,1.138176e6,19,1000000,648737,17.755552873,56320.409009659794,36.537133179699666,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,45.898825009,17.323749893,6.408782669,15033,27047,6.074251e6,19,1000000,4340484,103.48667799,9663.079532774555,41.94244210273543,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000151255,0.0,0.01660337,34,37,8624.0,19,1000000,41,0.086201613,1.1600710998296518e7,0.47562915093015723,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000151255,0.000534036,0.008090178,34,37,9296.0,19,1000000,41,0.086314013,1.15856042981109e7,0.4750097762225469,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000434153,0.0,0.058026217,280,385,69428.0,19,1000000,555,0.101539966,9.848338928929718e6,5.465828105555994,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000434153,0.003201204,0.040336135,200,285,57156.0,19,1000000,899,0.104367604,9.581517268519454e6,8.613784024398988,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.006960925,0.0,2.320436756,7854,11241,1.982968e6,19,1000000,15833,7.309057177,136816.55181830848,2.166216464939278,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.006960925,1.266961147,1.308558954,4998,7671,1.507432e6,19,1000000,27893,6.550468692,152660.83192204044,4.258168584801474,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000404812,0.0,0.200703456,26,29,6532.0,20,1000000,5683,0.111115467,8.999647186831335e6,51.144994962762475,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000404812,0.00070275,0.006980661,26,29,6948.0,20,1000000,5683,0.110483365,9.051136340751389e6,51.437607824490144,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001442371,0.0,0.163397018,77,101,19175.0,20,1000000,23078,0.260815052,3.834134542204259e6,88.48415696498988,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001442371,0.048953799,0.014519028,61,79,16863.0,20,1000000,16308,0.19673382,5.083010130134209e6,82.89372920222868,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011641204,0.0,0.083430389,356,493,85898.0,20,1000000,120271,1.100749528,908471.8862582152,109.26282223216181,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011641204,0.006226049,0.032522974,148,221,43962.0,20,1000000,43511,0.423896024,2.359069072089244e6,102.64545439567509,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059874538,0.0,0.494569063,2183,3015,504653.0,20,1000000,749880,9.498751261,105276.99615693725,78.94511387816411,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059874538,0.038633965,0.137945957,621,983,185533.0,20,1000000,189455,4.891235922,204447.30451503256,38.73356407689549,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.057037696,0.0,6.542092434,15866,21617,3.982352e6,20,1000000,5405897,58.972751977,16956.983801434442,91.66770786122305,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.057037696,0.516124806,0.551520206,2234,3977,1.145088e6,20,1000000,648737,14.571131735,68628.8490274225,44.52207363150299,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,43.663565538,17.362861333,6.456050818,15033,27047,6.074251e6,20,1000000,4340484,87.116633356,11478.864155752259,49.82382620621619,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000160695,0.0,0.016807439,34,37,8624.0,20,1000000,41,0.083890988,1.1920231527133761e7,0.4887294926124842,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000160695,0.000552586,0.00790665,34,37,9296.0,20,1000000,41,0.086044687,1.162186806490446e7,0.47649659066108285,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000388931,0.0,0.057527763,280,385,69428.0,20,1000000,555,0.09798986,1.0205137551987521e7,5.663851341353074,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000388931,0.003330873,0.040734664,200,285,57156.0,20,1000000,899,0.097699489,1.0235468068824802e7,9.201685793873496,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007872829,0.0,2.315555075,7854,11241,1.982968e6,20,1000000,15833,5.938879054,168381.9439505966,2.6659913185697954,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007872829,0.304652076,1.30535135,4998,7671,1.507432e6,20,1000000,27893,6.802860618,146996.98496747887,4.100186901697889,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000427081,0.0,0.200705864,26,29,6532.0,21,1000000,5683,0.132355911,7.555386022767053e6,42.93725876738516,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000427081,0.000640117,0.007067806,26,29,6948.0,21,1000000,5683,0.132775012,7.5315376360124145e6,42.80172838545855,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.00145627,0.0,0.164241291,77,101,19175.0,21,1000000,23078,0.351809805,2.8424449398162737e6,65.59794432107996,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.00145627,0.044098518,0.014517161,61,79,16863.0,21,1000000,16308,0.261509195,3.8239573182120803e6,62.3610959454026,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011700384,0.0,0.082728055,356,493,85898.0,21,1000000,120271,1.567690265,637881.1059338944,76.71859849177542,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011700384,0.005964225,0.032067425,148,221,43962.0,21,1000000,43511,0.590455359,1.693608136089421e6,73.69058360938679,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.058883945,0.0,0.48991812,2183,3015,504653.0,21,1000000,749880,10.178572031,98245.6082203266,73.67241669225851,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.058883945,0.039810298,0.13777968,621,983,185533.0,21,1000000,189455,2.803938235,356641.23678530316,67.56746551515961,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.049784158,0.0,6.503108277,15866,21617,3.982352e6,21,1000000,5405897,81.999182639,12195.243511175995,65.92623031133577,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.049784158,0.772138765,0.544950769,2234,3977,1.145088e6,21,1000000,648737,15.666363232,63831.023524171025,41.409546708000136,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.049110282,18.174132251,6.377158396,15033,27047,6.074251e6,21,1000000,4340484,104.343923343,9583.691775828609,41.597860813915666,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000150664,0.0,0.01648405,34,37,8624.0,21,1000000,41,0.085276418,1.1726571348247765e7,0.4807894252781584,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000150664,0.000555676,0.007938267,34,37,9296.0,21,1000000,41,0.086782259,1.1523092525166923e7,0.4724467935318438,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000383201,0.0,0.058518877,280,385,69428.0,21,1000000,555,0.10080708,9.919938163073467e6,5.505565680505774,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000383201,0.003249359,0.041138322,200,285,57156.0,21,1000000,899,0.102582918,9.748211685692154e6,8.763642305437246,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.00735883,0.0,2.33206607,7854,11241,1.982968e6,21,1000000,15833,6.868782102,145586.21676306016,2.3050665700095316,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.00735883,0.272714525,1.311328212,4998,7671,1.507432e6,21,1000000,27893,5.933915473,168522.79149410123,4.700606223144965,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000415891,0.0,0.143533258,26,29,6532.0,22,1000000,5683,0.127025589,7.872429546459336e6,44.7390171125284,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000415891,0.000768171,0.007040532,26,29,6948.0,22,1000000,5683,0.126339788,7.915162878063401e6,44.98187063603431,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001423479,0.0,0.162726149,77,101,19175.0,22,1000000,23078,0.335932705,2.976786675176506e6,68.6982828897234,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001423479,0.054166224,0.014242587,61,79,16863.0,22,1000000,16308,0.24833839,4.026763642947029e6,65.66846148918015,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011607646,0.0,0.081636612,356,493,85898.0,22,1000000,120271,1.495740563,668565.1407315615,80.40899804092562,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011607646,0.020442707,0.031650571,148,221,43962.0,22,1000000,43511,0.562850204,1.7766716488566825e6,77.3047601134031,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.058712968,0.0,0.482523458,2183,3015,504653.0,22,1000000,749880,9.63506425,103787.57982854138,77.82823036182661,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.058712968,0.039481743,0.135408874,621,983,185533.0,22,1000000,189455,2.688105149,372009.2572911477,70.4790138400944,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.05063437,0.0,6.743597196,15866,21617,3.982352e6,22,1000000,5405897,77.792137687,12854.76951441472,69.49155995366598,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.05063437,0.482857975,0.537015756,2234,3977,1.145088e6,22,1000000,648737,13.786531413,72534.56072765704,47.05585332277805,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,43.940430668,17.427320589,6.301196467,15033,27047,6.074251e6,22,1000000,4340484,97.461221746,10260.49111723804,44.535497526513836,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000145284,0.0,0.016729384,34,37,8624.0,22,1000000,41,0.083770387,1.1937392625391595e7,0.4894330976410554,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000145284,0.000638957,0.007924591,34,37,9296.0,22,1000000,41,0.091911785,1.0879997597696532e7,0.44607990150555776,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.00036924,0.0,0.056999387,280,385,69428.0,22,1000000,555,0.099511458,1.0049094045029469e7,5.577247194991355,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.00036924,1.640451357,0.040055926,200,285,57156.0,22,1000000,899,0.100271188,9.972954544031134e6,8.96568613508399,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.008588179,0.0,3.936726533,7854,11241,1.982968e6,22,1000000,15833,7.049285322,141858.35220474284,2.2460432904576937,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.008588179,0.277769226,1.297184584,4998,7671,1.507432e6,22,1000000,27893,5.486379394,182269.5676302695,5.084045049911107,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000423241,0.0,0.015855803,26,29,6532.0,23,1000000,5683,0.106534032,9.386671857120737e6,53.34445616401715,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000423241,0.000660028,0.007064059,26,29,6948.0,23,1000000,5683,0.106979864,9.347553479783822e6,53.122146425611454,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001428108,0.0,0.016960283,77,101,19175.0,23,1000000,23078,0.244038792,4.097709187152508e6,94.5669326211056,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001428108,0.001368106,0.014461536,61,79,16863.0,23,1000000,16308,0.18357695,5.447306973996463e6,88.83468213193433,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011528528,0.0,0.082864302,356,493,85898.0,23,1000000,120271,1.001508846,998493.4271863636,120.08980298113113,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011528528,0.0059906,0.032287092,148,221,43962.0,23,1000000,43511,0.391252657,2.5558931859215465e6,111.20946841263242,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.058927324,0.0,0.494615797,2183,3015,504653.0,23,1000000,749880,6.069646219,164754.24825744692,123.5459156832943,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.058927324,0.055735339,0.137030441,621,983,185533.0,23,1000000,189455,1.864789664,536253.5085351053,101.59590845951837,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.060817011,0.0,6.497156437,15866,21617,3.982352e6,23,1000000,5405897,51.81410486,19299.764083582395,104.33253676014581,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.060817011,0.69420666,0.542125672,2234,3977,1.145088e6,23,1000000,648737,11.569424596,86434.7221162355,56.07340232152027,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.554818844,17.671846662,6.391343969,15033,27047,6.074251e6,23,1000000,4340484,83.525674418,11972.36666411756,51.96586594773565,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000160744,0.0,0.016323608,34,37,8624.0,23,1000000,41,0.082486012,1.2123267639609005e7,0.4970539732239692,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000160744,0.000497013,0.007752658,34,37,9296.0,23,1000000,41,0.092014128,1.0867896286535475e7,0.4455837477479545,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000424901,0.0,0.057579774,280,385,69428.0,23,1000000,555,0.098676215,1.0134154416036326e7,5.624455700900161,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000424901,0.003399111,0.040439684,200,285,57156.0,23,1000000,899,0.110401911,9.057814225697596e6,8.14297498890214,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.008506678,0.0,2.310066104,7854,11241,1.982968e6,23,1000000,15833,6.638997558,150625.14954460238,2.3848479927396893,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.008506678,0.270773674,1.294349501,4998,7671,1.507432e6,23,1000000,27893,5.383888908,185739.3451254325,5.180827553583689,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000408091,0.0,0.14232551,26,29,6532.0,24,1000000,5683,0.105721407,9.458822279956982e6,53.754487016995526,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000408091,0.000611327,0.007482191,26,29,6948.0,24,1000000,5683,0.104711341,9.550063922875365e6,54.2730132737007,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001457919,0.0,0.258417857,77,101,19175.0,24,1000000,23078,0.242744157,4.119563627642745e6,95.07128939873927,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001457919,0.047001061,0.014479228,61,79,16863.0,24,1000000,16308,0.182641123,5.475218196068582e6,89.28985834148644,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011604201,0.0,0.082862174,356,493,85898.0,24,1000000,120271,0.981573423,1.0187724897274445e6,122.52878611200947,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011604201,0.006026652,0.032303288,148,221,43962.0,24,1000000,43511,0.380717463,2.626619730337928e6,114.28685108673358,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059288681,0.0,0.489246707,2183,3015,504653.0,24,1000000,749880,6.071818112,164695.31556349757,123.50172323475556,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059288681,0.039297125,0.137484132,621,983,185533.0,24,1000000,189455,1.840260229,543401.4082581144,102.95011380154106,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.061162219,0.0,6.617809772,15866,21617,3.982352e6,24,1000000,5405897,51.02899748,19596.70088349147,105.93774651596388,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.061162219,0.66031384,0.546571635,2234,3977,1.138176e6,24,1000000,648737,11.413522581,87615.36965499958,56.83933206387547,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,43.413276858,17.050615309,6.306375212,15033,27047,6.074251e6,24,1000000,4340484,84.297324495,11862.772703531224,51.49017511531402,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000165665,0.0,0.016812522,34,37,8624.0,24,1000000,41,0.084695197,1.1807044973282252e7,0.4840888439045723,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000165665,0.000786182,0.007959505,34,37,9296.0,24,1000000,41,0.086371813,1.1577851214029742e7,0.4746918997752194,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000427902,0.0,0.057325801,280,385,69428.0,24,1000000,555,0.099209088,1.0079721728719046e7,5.594245559439071,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000427902,0.003379831,0.040259662,200,285,57156.0,24,1000000,899,0.098414007,1.0161155210355371e7,9.134878534109477,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.006958857,0.0,2.286882489,7854,11241,1.982968e6,24,1000000,15833,2.392241475,418018.00129729795,6.618479014540118,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.006958857,0.274585684,1.29250863,4998,7671,1.507432e6,24,1000000,27893,2.416107871,413888.80521551846,11.544600443876456,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000409941,0.0,0.142497803,26,29,6532.0,25,1000000,5683,0.120858791,8.274118843369863e6,47.021817386870936,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000409941,0.000735279,0.006927667,26,29,6948.0,25,1000000,5683,0.122440564,8.1672279784663515e6,46.41435660162428,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.00147537,0.0,0.163736294,77,101,19175.0,25,1000000,23078,0.312122407,3.2038712299178187e6,73.93894024404342,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.00147537,0.005064427,0.014409798,61,79,16863.0,25,1000000,16308,0.232201876,4.306597419566068e6,70.23199071828343,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011659123,0.0,0.082959462,356,493,85898.0,25,1000000,120271,1.357502049,736647.138570912,88.59728800306215,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011659123,0.020293186,0.032191946,148,221,43962.0,25,1000000,43511,0.51519719,1.9410043754314731e6,84.45504137939884,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059742587,0.0,0.489405917,2183,3015,504653.0,25,1000000,749880,8.578687849,116567.94344330502,87.41196942926557,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059742587,0.038469905,0.136097041,621,983,185533.0,25,1000000,189455,2.427661266,411919.08195976465,78.04012967268721,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.040528935,0.0,6.377305922,15866,21617,3.982352e6,25,1000000,5405897,70.679364159,14148.40119034467,76.48479954968067,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.040528935,0.495834203,0.525194863,2234,3977,1.145088e6,25,1000000,648737,15.161621245,65956.00720007301,42.78810224295377,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.191322169,17.736855882,6.243765961,15033,27047,6.074251e6,25,1000000,4340484,95.480681833,10473.322779041784,45.4592899492664,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000192655,0.0,0.016413412,34,37,8624.0,25,1000000,41,0.088184074,1.1339916094146432e7,0.4649365598600037,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000192655,0.000613926,0.007854442,34,37,9296.0,25,1000000,41,0.086237971,1.1595820128931373e7,0.47542862528618635,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000400061,0.0,0.057935399,280,385,69428.0,25,1000000,555,0.099864538,1.0013564574844375e7,5.557528339038629,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000400061,0.003247007,0.040525221,200,285,57156.0,25,1000000,899,0.101078821,9.893269332850648e6,8.894049130232732,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007606845,0.0,2.309299453,7854,11241,1.982968e6,25,1000000,15833,2.90948746,343703.1483201512,5.441851947352954,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007606845,0.275659801,1.297847276,4998,7671,1.507432e6,25,1000000,27893,2.816935511,354995.70227825496,9.901895123647366,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000419261,0.0,0.141908,26,29,6532.0,26,1000000,5683,0.116330012,8.596233962393127e6,48.85239760828014,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000419261,0.000888713,0.0070368,26,29,6948.0,26,1000000,5683,0.120551425,8.295215091816625e6,47.141707366793874,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001452069,0.0,0.163530013,77,101,19175.0,26,1000000,23078,0.305885095,3.269201462725734e6,75.44663135678448,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001452069,0.054664352,0.014713346,61,79,16863.0,26,1000000,16308,0.23101698,4.328686142464506e6,70.59221361131117,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011465369,0.0,0.083496698,356,493,85898.0,26,1000000,120271,1.306085592,765646.605494443,92.08508288942215,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011465369,0.00594023,0.032555846,148,221,43962.0,26,1000000,43511,0.499128308,2.0034928573916908e6,87.17397771796986,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.058807894,0.0,0.490884266,2183,3015,504653.0,26,1000000,749880,8.316959592,120236.24606303126,90.16275619774588,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.058807894,0.041670632,0.138550201,621,983,185533.0,26,1000000,189455,2.339688221,427407.37463412655,80.97446416130845,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.065216369,0.0,6.55502101,15866,21617,3.982352e6,26,1000000,5405897,68.431043183,14613.250850579248,78.99772893339382,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.065216369,0.723082829,0.551094247,2234,3977,1.145088e6,26,1000000,648737,14.348122957,69695.52763082026,45.214067508635445,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.459085831,17.273919436,6.408854381,15033,27047,6.074251e6,26,1000000,4340484,96.406020509,10372.796166880935,45.02295579760803,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000147214,0.0,0.016454423,34,37,8624.0,26,1000000,41,0.08207173,1.2184463517462105e7,0.4995630042159463,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000147214,0.000504183,0.007825341,34,37,9296.0,26,1000000,41,0.098996356,1.0101381913491847e7,0.4141566584531657,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000400021,0.0,0.058831034,280,385,69428.0,26,1000000,555,0.098630806,1.0138820116708769e7,5.627045164773367,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000400021,0.003438432,0.041036915,200,285,57156.0,26,1000000,899,0.099072997,1.0093567675155723e7,9.074117339964996,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.008298083,0.0,2.324292667,7854,11241,1.982968e6,26,1000000,15833,7.089997675,141043.7698063138,2.233146007343366,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.008298083,0.29820357,1.305469483,4998,7671,1.507432e6,26,1000000,27893,5.975700262,167344.4041962893,4.667737466247098,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000408641,0.0,0.142183729,26,29,6532.0,27,1000000,5683,0.115308445,8.672391688223703e6,49.2852019641753,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000408641,0.000893654,0.007026039,26,29,6948.0,27,1000000,5683,0.11626875,8.600763317744449e6,48.8781379347417,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001452919,0.0,0.164519121,77,101,19175.0,27,1000000,23078,0.292747623,3.4159115956340316e6,78.83240780404218,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001452919,0.043963633,0.014514861,61,79,16863.0,27,1000000,16308,0.218225677,4.5824121787465e6,74.72997781099792,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011602242,0.0,0.083522509,356,493,85898.0,27,1000000,120271,1.269833194,787505.0083152889,94.71401485508812,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011602242,0.020493892,0.032217528,148,221,43962.0,27,1000000,43511,0.485644327,2.0591201099318103e6,89.594375103243,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.058532646,0.0,0.489563453,2183,3015,504653.0,27,1000000,749880,8.057249379,124111.83431982985,93.06898231975401,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.058532646,0.041256231,0.137830172,621,983,185533.0,27,1000000,189455,2.274933951,439573.2014814878,83.27934088667526,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.059505591,0.0,6.517906429,15866,21617,3.982352e6,27,1000000,5405897,63.564091665,15732.152758042563,85.04639739824403,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.059505591,0.65469958,0.545434278,2234,3977,1.145088e6,27,1000000,648737,12.446658979,80342.84555294715,52.121376595482275,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.079556123,17.393668293,6.13490961,15033,27047,6.074251e6,27,1000000,4340484,94.992763414,10527.117688341936,45.69278589236516,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000163794,0.0,0.016924446,34,37,8624.0,27,1000000,41,0.08506503,1.175571207110607e7,0.4819841949153489,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000163794,0.000934005,0.007869352,34,37,9296.0,27,1000000,41,0.08467079,1.181044844390846e7,0.4842283862002469,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000485343,0.0,0.058476875,280,385,97076.0,27,1000000,555,0.098062981,1.0197528055974558e7,5.65962807106588,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000485343,0.003547926,0.040617604,200,285,84804.0,27,1000000,899,0.100165667,9.983460700161863e6,8.975131169445515,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.006948797,0.0,2.325682101,7854,11241,1.982968e6,27,1000000,15833,2.616692478,382161.83537330444,6.050768339465529,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.006948797,0.305781465,1.312325041,4998,7671,1.507432e6,27,1000000,27893,2.661758172,375691.52995165484,10.479163844941509,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000405331,0.0,0.015740284,26,29,6532.0,28,1000000,5683,0.116657192,8.572124725923456e6,48.715384817423,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000405331,0.000812422,0.006984048,26,29,6948.0,28,1000000,5683,0.118101911,8.467263497539848e6,48.119458456518956,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001473579,0.0,0.016987577,77,101,19175.0,28,1000000,23078,0.291200503,3.434060002293334e6,79.25123673292555,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001473579,0.054734394,0.01446226,61,79,16863.0,28,1000000,16308,0.218457373,4.57755207007822e6,74.65071915883561,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011734456,0.0,0.083898629,356,493,85898.0,28,1000000,120271,1.237756094,807913.6146834433,97.1685783515924,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011734456,0.006211148,0.032353861,148,221,43962.0,28,1000000,43511,0.471445277,2.121136956474378e6,92.29279011315664,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.058816225,0.0,0.49721511,2183,3015,504653.0,28,1000000,749880,7.794910191,128288.84175658619,96.20123665642885,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.058816225,0.055109294,0.138443968,621,983,185533.0,28,1000000,189455,2.222597536,449924.0117937394,85.2403536543829,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.079222924,0.0,6.606410694,15866,21617,3.982352e6,28,1000000,5405897,63.879552949,15654.461464349595,84.62640626674309,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.079222924,1.28329987,0.545708727,2234,3977,1.138176e6,28,1000000,648737,14.110413924,70869.6431859542,45.97575971152637,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.965066645,17.36147327,6.35183787,15033,27047,6.074251e6,28,1000000,4340484,94.600814659,10570.73349320109,45.88209959550344,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000155415,0.0,0.016396131,34,37,8624.0,28,1000000,41,0.110215698,9.073117696900127e6,0.3719978255729052,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000155415,0.00070995,0.007901293,34,37,9296.0,28,1000000,41,0.087826165,1.1386128495989777e7,0.46683126833558086,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.00037914,0.0,0.057832477,280,385,69428.0,28,1000000,555,0.100612589,9.939114080445739e6,5.516208314647384,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.00037914,0.003666268,0.040869592,200,285,57156.0,28,1000000,899,0.099545271,1.0045680623040345e7,9.03106688011327,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007724138,0.0,2.323637288,7854,11241,1.982968e6,28,1000000,15833,5.269062601,189787.07897875668,3.0048988214706545,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007724138,2.408674928,1.304009658,4998,7671,1.507432e6,28,1000000,27893,5.102390263,195986.57657598308,5.4666535804338965,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000413841,0.0,0.142478877,26,29,6532.0,29,1000000,5683,0.117250108,8.52877679225677e6,48.46903851039522,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000413841,0.000717229,0.007494732,26,29,6948.0,29,1000000,5683,0.115910813,8.627322802058166e6,49.02907548409656,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001466809,0.0,0.165851436,77,101,19175.0,29,1000000,23078,0.283288009,3.529976448809028e6,81.46479648561474,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001466809,0.047285403,0.014684436,61,79,16863.0,29,1000000,16308,0.214885727,4.653636209165256e6,75.891499299067,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011692435,0.0,0.083338635,356,493,85898.0,29,1000000,120271,1.205114085,829796.9565263193,99.80050975837693,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011692435,0.006197437,0.032254829,148,221,43962.0,29,1000000,43511,0.464593422,2.152419626810816e6,93.65393038216543,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059114922,0.0,0.488709441,2183,3015,504653.0,29,1000000,749880,7.608926198,131424.5892229641,98.55267096651633,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059114922,0.041005754,0.136972879,621,983,185533.0,29,1000000,189455,2.172059656,460392.51142925327,87.22366325282918,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.069863893,0.0,6.535049187,15866,21617,3.982352e6,29,1000000,5405897,61.699851543,16207.494426515397,87.6160454978163,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.069863893,0.76155773,0.548914073,2234,3977,1.145088e6,29,1000000,648737,12.76469636,78341.07226660267,50.82275219901902,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.25040979,18.276184581,6.408821608,15033,27047,6.074251e6,29,1000000,4340484,92.655675141,10792.647061048734,46.84531188612905,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000146754,0.0,0.016515495,34,37,8624.0,29,1000000,41,0.084834815,1.1787613375475625e7,0.48329214839450063,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000146754,0.000651647,0.00779705,34,37,9296.0,29,1000000,41,0.084444815,1.1842053298358222e7,0.4855241852326871,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000405191,0.0,0.058123168,280,385,97076.0,29,1000000,555,0.099254407,1.0075119384875273e7,5.591691258605777,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000405191,0.00341406,0.040336018,200,285,84804.0,29,1000000,899,0.100144421,9.98557872734618e6,8.977035275884216,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.00755218,0.0,2.310492932,7854,11241,1.982968e6,29,1000000,15833,7.922187587,126227.76083224297,1.998564137256903,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.00755218,0.508861284,1.282758132,4998,7671,1.507432e6,29,1000000,27893,6.192440206,161487.22744727947,4.504363235186966,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000411711,0.0,0.274984062,26,29,6532.0,30,1000000,5683,0.109756585,9.111070647834023e6,51.77821449164075,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000411711,0.000972775,0.007121299,26,29,6948.0,30,1000000,5683,0.110194877,9.074832035975683e6,51.57227046044981,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001479169,0.0,0.16636271,77,101,19175.0,30,1000000,23078,0.280284877,3.567798629392338e6,82.33765676911638,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001479169,0.044134713,0.014609189,61,79,16863.0,30,1000000,16308,0.205694166,4.861586594536668e6,79.28275418370399,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.01169115,0.0,0.083739496,356,493,85898.0,30,1000000,120271,1.182140452,845923.1712341403,101.74002572750128,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.01169115,0.020658839,0.032307059,148,221,43962.0,30,1000000,43511,0.450374954,2.2203721390776983e6,96.61061214340972,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059127042,0.0,0.488309493,2183,3015,504653.0,30,1000000,749880,7.322706133,136561.53638249516,102.40476490250548,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059127042,0.040020385,0.137561709,621,983,185533.0,30,1000000,189455,2.105343829,474981.7992793043,89.98767678246058,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.078320652,0.0,6.689802283,15866,21617,3.982352e6,30,1000000,5405897,62.173269261,16084.082627246999,86.94889402238667,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.078320652,0.50995426,0.54556123,2234,3977,1.145088e6,30,1000000,648737,13.637599451,73326.68799908721,47.569735592463836,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,45.073327993,17.839024815,6.429905842,15033,27047,6.074251e6,30,1000000,4340484,87.271565278,11458.485897606408,49.73537470278625,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000151094,0.0,0.016554493,34,37,8624.0,30,1000000,41,0.081790186,1.2226405745060904e7,0.5012826355474971,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000151094,0.000802442,0.007813049,34,37,9296.0,30,1000000,41,0.081665023,1.2245144411457522e7,0.5020509208697583,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.00037645,0.0,0.058408251,280,385,69428.0,30,1000000,555,0.097089136,1.029981356513462e7,5.716396528649715,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.00037645,0.003598586,0.040477552,200,285,57156.0,30,1000000,899,0.098708439,1.0130846056637568e7,9.107630604917173,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007178483,0.0,2.336679771,7854,11241,1.982968e6,30,1000000,15833,6.452549555,154977.5002076679,2.453758760788006,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007178483,0.275604039,1.309060995,4998,7671,1.507432e6,30,1000000,27893,5.996552347,166762.48986641256,4.651506129843845,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000404691,0.0,0.143217533,26,29,6532.0,31,1000000,5683,0.111881284,8.938045437519291e6,50.79491222142214,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000404691,0.000791241,0.006978167,26,29,6948.0,31,1000000,5683,0.111635977,8.957685746773193e6,50.906528098912055,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.00148659,0.0,0.163976389,77,101,19175.0,31,1000000,23078,0.27386377,3.651450500371042e6,84.26817464756292,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.00148659,0.056830101,0.014485947,61,79,16863.0,31,1000000,16308,0.209463007,4.77411269093449e6,77.85622976375967,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011509178,0.0,0.083144205,356,493,85898.0,31,1000000,120271,1.154230517,866378.0633691216,104.20015605946762,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011509178,0.006169325,0.032209112,148,221,43962.0,31,1000000,43511,0.4471104,2.2365840740899784e6,97.31600964772905,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.058965489,0.0,0.492342271,2183,3015,504653.0,31,1000000,749880,7.254778168,137840.18985044726,103.36360156505339,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.058965489,0.038548093,0.138808216,621,983,185533.0,31,1000000,189455,2.064680135,484336.52411733015,91.75997617664879,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.053294635,0.0,6.701804628,15866,21617,3.982352e6,31,1000000,5405897,60.586121209,16505.43028741459,89.22665607444368,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.053294635,0.501315142,0.551778024,2234,3977,1.145088e6,31,1000000,648737,13.491158885,74122.61678363592,48.08608404436561,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,43.580015892,17.239105461,6.159284061,15033,27047,6.074251e6,31,1000000,4340484,89.925538592,11120.311489454481,48.267534094993344,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000172175,0.0,0.017105608,34,37,8624.0,31,1000000,41,0.084727992,1.1802474912895374e7,0.4839014714287103,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000172175,0.000569505,0.007803169,34,37,9296.0,31,1000000,41,0.084725272,1.1802853816745492e7,0.48391700648656516,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000437242,0.0,0.058075297,280,385,69428.0,31,1000000,555,0.099416636,1.0058678710472561e7,5.582566684312271,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000437242,0.003540115,0.040624909,200,285,57156.0,31,1000000,899,1.659228333,602689.8047189988,0.5418181344423799,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.008013255,0.0,2.522018696,7854,11241,1.982968e6,31,1000000,15833,5.636040249,177429.5348897534,2.809241825909466,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.008013255,0.286873825,1.300153125,4998,7671,1.507432e6,31,1000000,27893,5.670523125,176350.57259377636,4.918946521358204,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000412731,0.0,0.142470243,26,29,6532.0,32,1000000,5683,0.110025002,9.088843279457519e6,51.651896357157085,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000412731,0.000668098,0.007424499,26,29,6948.0,32,1000000,5683,0.113386203,8.819415180522447e6,50.120736470909065,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.001461169,0.0,0.166073446,77,101,19175.0,32,1000000,23078,0.272306687,3.6723299417175166e6,84.75003039495685,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.001461169,0.043691222,0.014658764,61,79,16863.0,32,1000000,16308,0.203634964,4.9107480383378565e6,80.08447900921377,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.01194448,0.0,0.082184375,356,493,85898.0,32,1000000,120271,1.120815496,892207.5074522345,107.3066891287877,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.01194448,0.020337885,0.031659009,148,221,43962.0,32,1000000,43511,0.434748566,2.300180099961503e6,100.08313632942496,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.058911311,0.0,0.480375851,2183,3015,504653.0,32,1000000,749880,7.000379449,142849.39941974852,107.11990763688101,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.058911311,0.040457235,0.133862493,621,983,185533.0,32,1000000,189455,2.021705335,494631.92419186054,93.71049119776893,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.105426537,0.0,6.499117119,15866,21617,3.982352e6,32,1000000,5405897,59.782552585,16727.288427140687,90.42599832641457,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.105426537,0.723664774,0.535145095,2234,3977,1.145088e6,32,1000000,648737,12.797201332,78142.08544953131,50.69366208827259,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,45.254736182,17.576269218,6.287089464,15033,27047,6.074251e6,32,1000000,4340484,91.843900017,10888.039377845489,47.259360710908304,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000155274,0.0,0.016660837,34,37,8624.0,32,1000000,41,0.084980562,1.1767396878359077e7,0.4824632720127222,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000155274,0.000809242,0.00781239,34,37,9296.0,32,1000000,41,0.081593791,1.2255834515643476e7,0.5024892151413826,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000409221,0.0,0.057314679,280,385,69428.0,32,1000000,555,0.10277155,9.730319334485078e6,5.400327230639219,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000409221,0.0037051,0.040008235,200,285,57156.0,32,1000000,899,0.10315745,9.693919343682885e6,8.714833489970912,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.008137958,0.0,2.31488204,7854,11241,1.982968e6,32,1000000,15833,6.657499011,150206.55629805246,2.3782204058670646,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.008137958,0.302658517,1.29706989,4998,7671,1.507432e6,32,1000000,27893,6.412540428,155944.43594204192,4.3497581517313755,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000411471,0.0,0.142903939,26,29,6532.0,16,1000000,5683,0.121450921,8.233778647096467e6,46.792564051449226,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000411471,0.000490633,0.007063541,26,29,6948.0,16,1000000,5683,0.124183905,8.052573318579408e6,45.762774169486775,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.0014748,0.0,0.165657992,77,101,19175.0,16,1000000,23078,0.314326726,3.181403034751808e6,73.42041923600223,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.0014748,0.054176899,0.014648245,61,79,16863.0,16,1000000,16308,0.22867412,4.373035304563542e6,71.31545974682224,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.011792768,0.0,0.083745345,356,493,85898.0,16,1000000,120271,1.308872574,764016.3143948648,91.8890061485848,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.011792768,0.005878518,0.032334261,148,221,43962.0,16,1000000,43511,0.499459283,2.0021652095312043e6,87.11621043191224,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.059422891,0.0,0.491688913,2183,3015,504653.0,16,1000000,749880,10.786761156,92706.23364491227,69.5185504856468,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.059422891,0.322175708,0.137101523,621,983,185533.0,16,1000000,189455,2.460037469,406497.8735492585,77.01305463327476,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,1.084890041,0.0,6.535008218,15866,21617,3.982352e6,16,1000000,5405897,68.669290878,14562.550263940124,78.72364678418312,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,1.084890041,0.499852753,0.546009167,2234,3977,1.138176e6,16,1000000,648737,15.400034363,64934.92004164562,42.125685223057054,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,44.395917114,17.849095588,6.21393922,15033,27047,6.074251e6,16,1000000,4340484,95.530794222,10467.828810008028,45.43544346457889,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.000155704,0.0,0.016556525,34,37,8624.0,16,1000000,41,0.086056758,1.1620237889974894e7,0.47642975348897065,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.000155704,0.000444912,0.007915573,34,37,9296.0,16,1000000,41,0.086358596,1.1579623179607969e7,0.47476455036392673,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000404401,0.0,0.058490865,280,385,69428.0,16,1000000,555,0.100309332,9.969162191210683e6,5.532885016121929,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000404401,0.003280859,0.040743287,200,285,57156.0,16,1000000,899,0.09951871,1.0048361760316227e7,9.033477222524288,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.007139763,0.0,2.333970735,7854,11241,1.982968e6,16,1000000,15833,7.878134284,126933.60686056568,2.0097397974233364,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.007139763,0.469152506,1.297009285,4998,7671,1.507432e6,16,1000000,27893,6.215374959,160891.3390739167,4.4877421207887584,none,0.0,0.0,0.0

data/qed_gen_results.csv

@@ -0,0 +1,9 @@
+process_name,cpu_threads,graph_gen_samples,graph_gen_mean,graph_gen_std,graph_gen_median,graph_nodes,graph_data_nodes,graph_u_nodes,graph_v_nodes,graph_s1_nodes,graph_s2_nodes,graph_edges,graph_nodes_reduced,graph_data_nodes_reduced,graph_u_nodes_reduced,graph_v_nodes_reduced,graph_s1_nodes_reduced,graph_s2_nodes_reduced,graph_edges_reduced,graph_mem,graph_mem_reduced
+ke->ke,4,621,108190.55233494364,15933.10900718239,108119.0,26,15,4,4,0,2,29,26,15,4,4,0,2,29,23980.0,25292.0
+ke->kke,4,622,153201.41318327974,23413.42529125677,151041.5,77,41,5,18,6,6,101,59,32,5,12,3,6,77,35423.0,47607.0
+ke->kkke,4,598,404339.652173913,35709.9373272436,398624.0,356,181,6,96,48,24,493,148,77,6,32,8,24,221,95474.0,156874.0
+ke->kkkke,4,613,1.9826555334420882e6,120582.30781418575,1.972286e6,2183,1095,7,600,360,120,3015,543,275,7,110,30,120,885,470405.0,788269.0
+ke->kkkkke,4,565,1.3094592946902655e7,626078.9227119224,1.3065283e7,15866,7937,8,4320,2880,720,21617,2234,1121,8,312,72,720,3977,3.619736e6,5.464312e6
+ke->kkkkkke,4,386,1.46437015619171e8,3.4493988193742386e6,1.46310623e8,131069,65539,9,35280,25200,5040,176419,13441,6725,9,1358,308,5040,24869,2.7220139e7,4.1642163e7
+ke->kkkkkkke,4,95,1.4519048337473683e9,3.4428550325367525e7,1.44881422e9,1209632,604821,10,322560,241920,40320,1612821,90592,45301,10,4160,800,40320,175381,2.47916222e8,3.6695295e8
+ke->kkkkkkkke,4,10,2.09393503407e10,1.2609409886873345e9,2.1513879476e10,12337955,6168983,11,3265920,2540160,362880,16329623,778859,389435,11,22338,4194,362880,1526945,2.636058833e9,3.753461609e9

data/qed_gen_results_hemera_6a02f3bee6f84c044413deb3dfedddb62d60289b.csv

@@ -0,0 +1,8 @@
+process_name,cpu_threads,graph_gen_samples,graph_gen_mean,graph_gen_std,graph_gen_median,graph_nodes,graph_data_nodes,graph_u_nodes,graph_v_nodes,graph_s1_nodes,graph_s2_nodes,graph_edges,graph_nodes_reduced,graph_data_nodes_reduced,graph_u_nodes_reduced,graph_v_nodes_reduced,graph_s1_nodes_reduced,graph_s2_nodes_reduced,graph_edges_reduced,graph_mem,graph_mem_reduced,graph_elapsed_reduce
+ke->ke,1,6,177788.33333333334,6157.674128002121,175347.5,26,15,4,4,0,2,29,26,15,4,4,0,2,29,23980.0,25292.0,0.000193079
+ke->kke,1,6,346796.1666666667,56632.60001595077,326470.5,77,41,5,18,6,6,101,59,32,5,12,3,6,77,35423.0,47607.0,0.001499723
+ke->kkke,1,6,972626.6666666666,29393.45134322723,958283.5,356,181,6,96,48,24,493,188,97,6,44,16,24,273,95474.0,156410.0,0.012116826
+ke->kkkke,1,6,5.031542666666667e6,148489.76737494968,4.9797725e6,2183,1095,7,600,360,120,3015,853,430,7,210,85,120,1295,470405.0,817069.0,0.08102289
+ke->kkkkke,1,6,3.6893237333333336e7,863015.9091128429,3.66682815e7,15866,7937,8,4320,2880,720,21617,4982,2495,8,1242,516,720,7655,3.619736e6,6.021232e6,1.097368983
+ke->kkkkkke,1,4,3.90280476e8,8.363211430288846e6,3.888844705e8,131069,65539,9,35280,25200,5040,176419,34679,17344,9,8666,3619,5040,53415,2.7220139e7,4.5248803e7,46.545818049
+ke->kkkkkkke,1,1,4.374390864e9,NaN,4.374390864e9,1209632,604821,10,322560,241920,40320,1612821,277168,138589,10,69288,28960,40320,427085,2.47916222e8,3.92899086e8,3448.827815646

data/qed_gen_results_hemera_a198f37f8e02a3dfdc31679d0c7126633832ea84.csv

@@ -0,0 +1,49 @@
+process_name,cpu_threads,graph_gen_samples,graph_gen_mean,graph_gen_std,graph_gen_median,graph_nodes,graph_data_nodes,graph_u_nodes,graph_v_nodes,graph_s1_nodes,graph_s2_nodes,graph_edges,graph_nodes_reduced,graph_data_nodes_reduced,graph_u_nodes_reduced,graph_v_nodes_reduced,graph_s1_nodes_reduced,graph_s2_nodes_reduced,graph_edges_reduced,graph_mem,graph_mem_reduced,graph_elapsed_reduce
+ke->ke,1,367,163591.83378746593,8244.06944429464,161415.0,26,15,4,4,0,2,29,26,15,4,4,0,2,29,23980.0,25292.0,0.00018103
+ke->kke,1,365,276647.57808219176,12219.038493744352,273586.0,77,41,5,18,6,6,101,59,32,5,12,3,6,77,35423.0,47607.0,0.001373516
+ke->kkke,1,365,812335.7726027397,15951.11600371844,810553.0,356,181,6,96,48,24,493,148,77,6,32,8,24,221,95474.0,156874.0,0.012610364
+ke->kkkke,1,363,4.373731104683195e6,50585.69128404933,4.362524e6,2183,1095,7,600,360,120,3015,543,275,7,110,30,120,885,470405.0,788269.0,0.051800489
+ke->kkkkke,1,346,3.110679258381503e7,230966.46375778675,3.10600265e7,15866,7937,8,4320,2880,720,21617,2234,1121,8,312,72,720,3977,3.619736e6,5.522784e6,0.593557378
+ke->kkkkkke,1,231,3.2812668651082253e8,2.8467563184950906e6,3.27443771e8,131069,65539,9,35280,25200,5040,176419,13441,6725,9,1358,308,5040,24869,2.7220139e7,4.1450691e7,16.947993752
+ke->kkkkkkke,1,54,3.2961057175925927e9,6.6541001965338744e7,3.276489101e9,1209632,604821,10,322560,241920,40320,1612821,90592,45301,10,4160,800,40320,175381,2.47916222e8,3.67755278e8,891.940045588
+ke->kkkkkkkke,1,6,3.9249114226166664e10,8.105963054167406e9,3.6105827785e10,12337955,6168983,11,3265920,2540160,362880,16329623,0,0,0,0,0,0,0,2.636058833e9,-1.0,-1.0
+ke->ke,2,324,198319.9537037037,16737.410208574984,196973.0,26,15,4,4,0,2,29,26,15,4,4,0,2,29,23980.0,25292.0,0.000167656
+ke->kke,2,320,333413.134375,18305.68357885323,332569.0,77,41,5,18,6,6,101,59,32,5,12,3,6,77,35423.0,47319.0,0.001350622
+ke->kkke,2,319,875648.4231974921,43850.159366328604,875459.0,356,181,6,96,48,24,493,148,77,6,32,8,24,221,95474.0,154426.0,0.027575666
+ke->kkkke,2,319,4.192190119122257e6,195656.34037978342,4.175425e6,2183,1095,7,600,360,120,3015,543,275,7,110,30,120,885,470405.0,788269.0,0.052157649
+ke->kkkkke,2,315,2.93219354031746e7,1.3066366525419788e6,2.9198563e7,15866,7937,8,4320,2880,720,21617,2234,1121,8,312,72,720,3977,3.619736e6,5.489832e6,0.553458761
+ke->kkkkkke,2,199,3.190660898341709e8,1.2884918309451135e7,3.19042521e8,131069,65539,9,35280,25200,5040,176419,13441,6725,9,1358,308,5040,24869,2.7220139e7,4.1583723e7,18.630557854
+ke->kkkkkkke,2,47,3.344206026787234e9,9.279381184171565e7,3.336634389e9,1209632,604821,10,322560,241920,40320,1612821,90592,45301,10,4160,800,40320,175381,2.47916222e8,3.47729046e8,1009.782477087
+ke->kkkkkkkke,2,6,3.6058775391166664e10,8.153891159038606e8,3.6067091006e10,12337955,6168983,11,3265920,2540160,362880,16329623,0,0,0,0,0,0,0,2.636058833e9,-1.0,-1.0
+ke->ke,3,309,235713.21035598704,19813.534912077153,232082.0,26,15,4,4,0,2,29,26,15,4,4,0,2,29,23980.0,25292.0,0.00019762
+ke->kke,3,307,362589.3029315961,18556.58163253827,360702.0,77,41,5,18,6,6,101,59,32,5,12,3,6,77,35423.0,47319.0,0.001468295
+ke->kkke,3,307,910030.1628664496,36238.53981785484,905656.0,356,181,6,96,48,24,493,148,77,6,32,8,24,221,95474.0,154858.0,0.014372412
+ke->kkkke,3,305,4.1099876524590165e6,195198.13565678694,4.065734e6,2183,1095,7,600,360,120,3015,543,275,7,110,30,120,885,470405.0,788413.0,0.079820723
+ke->kkkkke,3,292,2.926505180821918e7,1.3171365432771866e6,2.90031685e7,15866,7937,8,4320,2880,720,21617,2234,1121,8,312,72,720,3977,3.619736e6,5.527392e6,0.609388774
+ke->kkkkkke,3,200,3.09932223355e8,1.1990379192933526e7,3.091332075e8,131069,65539,9,35280,25200,5040,176419,13441,6725,9,1358,308,5040,24869,2.7220139e7,4.1111723e7,17.892442653
+ke->kkkkkkke,3,46,3.448601302804348e9,8.803199424165167e7,3.456859858e9,1209632,604821,10,322560,241920,40320,1612821,90592,45301,10,4160,800,40320,175381,2.47916222e8,3.67081654e8,1030.174149301
+ke->kkkkkkkke,3,5,3.8856149529e10,1.2944467519101532e9,3.8413979685e10,12337955,6168983,11,3265920,2540160,362880,16329623,0,0,0,0,0,0,0,2.636058833e9,-1.0,-1.0
+ke->ke,4,360,218479.25,15099.08526269704,213265.0,26,15,4,4,0,2,29,26,15,4,4,0,2,29,23980.0,25292.0,0.00018319
+ke->kke,4,359,355889.86072423396,19186.908833615867,357721.0,77,41,5,18,6,6,101,59,32,5,12,3,6,77,35423.0,47607.0,0.001431696
+ke->kkke,4,358,930918.5754189944,31808.004708813798,926156.0,356,181,6,96,48,24,493,148,77,6,32,8,24,221,95474.0,156730.0,0.012686494
+ke->kkkke,4,357,4.18535349859944e6,83409.76365370877,4.163246e6,2183,1095,7,600,360,120,3015,543,275,7,110,30,120,885,470405.0,792733.0,0.069768067
+ke->kkkkke,4,301,2.8807327441860463e7,394631.4977459108,2.8986579e7,15866,7937,8,4320,2880,720,21617,2234,1121,8,312,72,720,3977,3.619736e6,5.536608e6,0.578988643
+ke->kkkkkke,4,200,3.1101288635e8,1.2242934298760163e7,3.05370731e8,131069,65539,9,35280,25200,5040,176419,13441,6725,9,1358,308,5040,24869,2.7220139e7,4.1569819e7,16.910096874
+ke->kkkkkkke,4,54,2.751006164148148e9,9.159053921609345e7,2.7311236935e9,1209632,604821,10,322560,241920,40320,1612821,90592,45301,10,4160,800,40320,175381,2.47916222e8,3.69321686e8,879.942655414
+ke->kkkkkkkke,4,6,3.3901058634e10,1.2573456781427138e9,3.36394407355e10,12337955,6168983,11,3265920,2540160,362880,16329623,0,0,0,0,0,0,0,2.636058833e9,-1.0,-1.0
+ke->ke,5,308,276433.788961039,20974.753647754293,273738.5,26,15,4,4,0,2,29,26,15,4,4,0,2,29,23980.0,25292.0,0.000247319
+ke->kke,5,307,376616.01954397396,19704.176972319336,373621.0,77,41,5,18,6,6,101,59,32,5,12,3,6,77,35423.0,47607.0,0.001515396
+ke->kkke,5,306,952992.4509803922,34085.869866316905,948944.0,356,181,6,96,48,24,493,148,77,6,32,8,24,221,95474.0,154426.0,0.013131685
+ke->kkkke,5,307,4.25323387296417e6,312175.1065181335,4.225936e6,2183,1095,7,600,360,120,3015,543,275,7,110,30,120,885,470405.0,788269.0,0.057499781
+ke->kkkkke,5,293,2.9532872167235494e7,1.2718150700116598e6,2.9466345e7,15866,7937,8,4320,2880,720,21617,2234,1121,8,312,72,720,3977,3.619736e6,5.486496e6,0.667497736
+ke->kkkkkke,5,198,3.247416337626263e8,1.3008937043360736e7,3.23659444e8,131069,65539,9,35280,25200,5040,176419,13441,6725,9,1358,308,5040,24869,2.7220139e7,4.1624555e7,17.47025299
+ke->kkkkkkke,5,49,3.0149285022040815e9,9.474792234833725e7,2.992396182e9,1209632,604821,10,322560,241920,40320,1612821,90592,45301,10,4160,800,40320,175381,2.47916222e8,3.64448638e8,991.043118381
+ke->kkkkkkkke,5,6,3.5096400832333336e10,2.2986165538874135e9,3.38597258525e10,12337955,6168983,11,3265920,2540160,362880,16329623,0,0,0,0,0,0,0,2.636058833e9,-1.0,-1.0
+ke->ke,6,318,251745.46226415093,21897.783128584524,250364.0,26,15,4,4,0,2,29,26,15,4,4,0,2,29,23980.0,25292.0,0.000206335
+ke->kke,6,318,394313.1698113208,21249.33364513439,389394.0,77,41,5,18,6,6,101,59,32,5,12,3,6,77,35423.0,47607.0,0.001527776
+ke->kkke,6,317,957311.1640378549,37757.77996624451,954502.0,356,181,6,96,48,24,493,148,77,6,32,8,24,221,95474.0,156730.0,0.013595493
+ke->kkkke,6,315,4.0828651174603174e6,170982.13799683942,4.04163e6,2183,1095,7,600,360,120,3015,543,275,7,110,30,120,885,470405.0,788269.0,0.073712887
+ke->kkkkke,6,301,2.8771192594684385e7,1.2257176793540926e6,2.8225655e7,15866,7937,8,4320,2880,720,21617,2234,1121,8,312,72,720,3977,3.619736e6,5.527392e6,0.602918502
+ke->kkkkkke,6,201,3.074898551243781e8,1.1587677476111867e7,3.06073884e8,131069,65539,9,35280,25200,5040,176419,13441,6725,9,1358,308,5040,24869,2.7220139e7,4.0967755e7,18.044061008
+ke->kkkkkkke,6,51,2.819152255392157e9,1.0769465159606656e8,2.797451893e9,1209632,604821,10,322560,241920,40320,1612821,90592,45301,10,4160,800,40320,175381,2.47916222e8,3.67052486e8,948.254854257
+ke->kkkkkkkke,6,6,3.30252982335e10,2.951298864612307e9,3.1297002603e10,12337955,6168983,11,3265920,2540160,362880,16329623,0,0,0,0,0,0,0,2.636058833e9,-1.0,-1.0

data/qed_gen_results_onesided.csv

@@ -0,0 +1,9 @@
+process_name,cpu_threads,graph_gen_samples,graph_gen_mean,graph_gen_std,graph_gen_median,graph_nodes,graph_data_nodes,graph_u_nodes,graph_v_nodes,graph_s1_nodes,graph_s2_nodes,graph_edges,graph_nodes_reduced,graph_data_nodes_reduced,graph_u_nodes_reduced,graph_v_nodes_reduced,graph_s1_nodes_reduced,graph_s2_nodes_reduced,graph_edges_reduced,graph_mem,graph_mem_reduced,graph_elapsed_reduce
+ke->ke,12,10,108808.9,8914.379537827883,105358.0,26,15,4,4,0,2,29,26,15,4,4,0,2,29,23980.0,25292.0,0.000106035
+ke->kke,12,10,165478.4,9600.214525380843,163445.5,77,41,5,18,6,6,101,59,32,5,12,3,6,77,35423.0,47319.0,0.000519342
+ke->kkke,12,10,374438.5,20482.285974036742,368261.0,356,181,6,96,48,24,493,188,97,6,44,16,24,273,95474.0,156554.0,0.012867533
+ke->kkkke,12,11,1.6873362727272727e6,51816.76295387605,1.67913e6,2183,1095,7,600,360,120,3015,853,430,7,210,85,120,1295,470405.0,821533.0,0.021791955
+ke->kkkkke,12,11,1.1873603272727273e7,141285.96370063865,1.1860729e7,15866,7937,8,4320,2880,720,21617,4982,2495,8,1242,516,720,7655,3.619736e6,6.016976e6,0.415923098
+ke->kkkkkke,12,8,1.3225809575e8,1.1404915362397024e7,1.30853327e8,131069,65539,9,35280,25200,5040,176419,34679,17344,9,8666,3619,5040,53415,2.7220139e7,4.5851723e7,17.679961505
+ke->kkkkkkke,12,2,1.4026342725e9,7.484155987190072e7,1.4026342725e9,1209632,604821,10,322560,241920,40320,1612821,277168,138589,10,69288,28960,40320,427085,2.47916222e8,4.00541614e8,1429.500021529
+ke->kkkkkkkke,12,1,1,1,1,12337955,6168983,11,3265920,2540160,362880,16329623,

data/results_home.csv

@@ -0,0 +1,721 @@
+process_name,graph_gen_time,optimization_time,function_generation_time,graph_nodes,graph_edges,graph_mem,cpu_threads,n_inputs,nflops_likwid,cpu_time,cpu_rate,cpu_gflops,gpu_name,gpu_time,gpu_rate,gpu_gflops
+QED Process: 'ke->ke' not optimized,0.00019665,0.0,0.072381258,26,29,6532.0,1,100000,5683,0.0824823,1.2123813230232426e6,6.889963058741088,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.00019665,0.000110042,0.003403799,26,29,6948.0,1,100000,5683,0.082738295,1.2086301754223965e6,6.868645286925479,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000622632,0.0,0.078001544,77,101,19175.0,1,100000,23078,0.257568263,388246.59076883236,8.959954821763112,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000622632,0.049578764,0.00620289,61,79,16863.0,1,100000,16308,0.168163394,594659.7390868551,9.697711025028433,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005311179,0.0,0.033756191,356,493,85898.0,1,100000,120271,1.150337569,86931.00416335269,10.455278801730591,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005311179,0.002622341,0.013491686,148,221,43962.0,1,100000,43511,0.421484201,237256.81713037685,10.323281370159826,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.026338818,0.0,0.203131043,2183,3015,504653.0,1,100000,749880,7.125628257,14033.850264608323,10.52370363642449,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.026338818,0.038573127,0.055940031,625,988,186117.0,1,100000,190720,2.038312244,49060.19688316213,9.356760749556681,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.467320314,0.0,3.413432692,15866,21617,3.982352e6,1,100000,5405897,52.403777069,1908.2593964234698,10.315853746347447,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.467320314,0.25668962,0.225824948,2234,3977,1.145088e6,1,100000,648737,6.812051568,14679.86538295683,9.523371828943265,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,16.035909195,7.665939615,3.05702573,15143,27212,6.101363e6,1,100000,4383934,50.231122779,1990.7976264031818,8.727525401508206,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,0.008560239,0.0,0.007682685,34,37,8624.0,1,100000,41,0.03024704,3.3061086307949475e6,0.13555045386259285,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,0.008560239,0.000130372,0.003397626,34,37,9296.0,1,100000,41,0.02990487,3.343936957425329e6,0.1371014152544385,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000189085,0.0,0.023001858,280,385,69428.0,1,100000,555,0.05285058,1.8921268224492522e6,1.050130386459335,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000189085,0.001475527,0.016071504,200,285,57156.0,1,100000,899,0.041354174,2.41813559134321e6,2.173903896617546,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.012556411,0.0,1.040277287,7854,11241,1.982968e6,1,100000,15833,1.983044822,50427.503650242754,0.7984186652942935,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.012556411,0.158031895,0.559544102,4998,7671,1.507432e6,1,100000,27893,2.043067013,48946.020548372486,1.3652513511557538,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000204986,0.0,0.071620201,26,29,6532.0,2,100000,5683,0.055272834,1.809207032879841e6,10.281723567856137,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000204986,0.000106436,0.003035027,26,29,6948.0,2,100000,5683,0.054903251,1.8213857682125235e6,10.350935320751772,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000650255,0.0,0.078910689,77,101,19175.0,2,100000,23078,0.146648869,681900.9289461346,15.736909638218895,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000650255,0.046799102,0.006051157,61,79,16863.0,2,100000,16308,0.102055815,979855.9739099629,15.979491222523675,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005481979,0.0,0.033766492,356,493,85898.0,2,100000,120271,0.608586885,164315.0755705161,19.762338453941542,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005481979,0.002701463,0.012951494,148,221,43962.0,2,100000,43511,0.223412826,447601.8758206836,19.475605218833763,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.027135956,0.0,0.215225126,2183,3015,504653.0,2,100000,749880,3.635591963,27505.837018487215,20.626077063423192,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.027135956,0.018974798,0.054606789,625,988,186117.0,2,100000,190720,1.13190931,88346.30046465472,16.849406424618948,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.468394997,0.0,3.316599541,15866,21617,3.982352e6,2,100000,5405897,27.082867868,3692.371150920685,19.960578127648677,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.468394997,0.245220662,0.227063823,2234,3977,1.138176e6,2,100000,648737,3.695895951,27057.0387602343,17.55290215419812,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,13.862538591,6.973572072,3.192370886,15143,27212,6.101363e6,2,100000,4383934,26.433906364,3783.0201341784555,16.58451058890949,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,7.773e-5,0.0,0.008041519,34,37,8624.0,2,100000,41,0.028219999,3.543586234712482e6,0.14528703562321177,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,7.773e-5,0.000133137,0.003707494,34,37,9296.0,2,100000,41,0.027671641,3.6138080860473723e6,0.14816613152794228,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000202732,0.0,0.025338438,280,385,69428.0,2,100000,555,0.057648018,1.7346650148492528e6,0.9627390832413353,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000202732,0.00136251,0.017705538,200,285,57156.0,2,100000,899,0.033795628,2.958962620845513e6,2.6601073961401163,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.003273657,0.0,1.087775863,7854,11241,1.982968e6,2,100000,15833,1.119657899,89312.9947007144,1.414092645096411,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.003273657,0.173125065,0.59992154,4998,7671,1.507432e6,2,100000,27893,1.124877472,88898.57116811385,2.4796478455921998,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000210286,0.0,0.084380396,26,29,6532.0,3,100000,5683,0.045421003,2.201624653687194e6,12.511832906904324,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000210286,0.000106675,0.003398638,26,29,6948.0,3,100000,5683,0.044431443,2.250658390725685e6,12.790491634494066,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000623874,0.0,0.079180302,77,101,19175.0,3,100000,23078,0.103375944,967343.0406594401,22.324342692338558,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000623874,0.022584183,0.006219111,61,79,16863.0,3,100000,16308,0.079537561,1.2572676197601783e6,20.50352034304899,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005507448,0.0,0.03403981,356,493,85898.0,3,100000,120271,0.415454139,240700.45430453637,28.949284339660892,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005507448,0.002588967,0.013112074,148,221,43962.0,3,100000,43511,0.157101963,636529.2838511508,27.696025669647423,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.02641195,0.0,0.202098557,2183,3015,504653.0,3,100000,749880,2.490307124,40155.689648181724,30.11194855337851,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.02641195,0.028889571,0.054649993,625,988,186117.0,3,100000,190720,0.794878547,125805.38294487396,23.99360263524636,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.4947072,0.0,3.290070629,15866,21617,3.982352e6,3,100000,5405897,18.467092823,5415.037491740667,29.273134931488396,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.4947072,0.255108626,0.226165271,2234,3977,1.138176e6,3,100000,648737,2.728612972,36648.656671415985,23.775339583044392,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,20.201904504,7.506362023,3.223142719,15143,27212,6.101363e6,3,100000,4383934,18.90718226,5288.9953999946265,23.186606759880043,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,8.0926e-5,0.0,0.008066998,34,37,8624.0,3,100000,41,0.026953154,3.710140935639666e6,0.15211577836122628,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,8.0926e-5,0.000127906,0.003653991,34,37,9296.0,3,100000,41,0.026891605,3.7186326364677753e6,0.15246393809517877,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000175288,0.0,0.025111039,280,385,69428.0,3,100000,555,0.030766684,3.25026902476718e6,1.803899308745785,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000175288,0.001399621,0.01748941,200,285,57156.0,3,100000,899,0.03129897,3.194993317671476e6,2.872298992586657,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.004333604,0.0,1.155472435,7854,11241,1.982968e6,3,100000,15833,0.836011492,119615.5805953921,1.893873487566843,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.004333604,0.198659763,0.60282031,4998,7671,1.507432e6,3,100000,27893,0.914295415,109373.83952647296,3.0507645059119106,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000199415,0.0,0.070793608,26,29,6532.0,4,100000,5683,0.040210377,2.4869202295715855e6,14.133167664655321,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000199415,0.000126905,0.003454968,26,29,6948.0,4,100000,5683,0.041220667,2.4259675371094793e6,13.786773513393172,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000663721,0.0,0.080346783,77,101,19175.0,4,100000,23078,0.110453804,905355.8716728308,20.893802806465587,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000663721,0.022581668,0.006154297,61,79,16863.0,4,100000,16308,0.065433734,1.5282636934642917e6,24.92292431301567,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005550922,0.0,0.034032145,356,493,85898.0,4,100000,120271,0.355187741,281541.24835068564,33.86124748038531,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005550922,0.002464536,0.012920443,148,221,43962.0,4,100000,43511,0.133729591,747777.6552834891,32.536553559039895,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.026860746,0.0,0.216342057,2183,3015,504653.0,4,100000,749880,1.990489966,50238.88676060777,37.673136404044556,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.026860746,0.018042117,0.054615127,625,988,186117.0,4,100000,190720,0.646573437,154661.47273847874,29.497036080682665,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.498043244,0.0,3.216718732,15866,21617,3.982352e6,4,100000,5405897,14.78739279,6762.517329466298,36.557472143809875,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.498043244,0.26833359,0.226585555,2234,3977,1.145088e6,4,100000,648737,2.228880527,44865.5721060997,29.105956651394802,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,20.52490455,7.36346994,3.230448983,15143,27212,6.101363e6,4,100000,4383934,15.145737093,6602.517882488375,28.94500263064879,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,8.1617e-5,0.0,0.007946445,34,37,8624.0,4,100000,41,0.027708462,3.6090057975790934e6,0.14796923770074283,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,8.1617e-5,0.000151953,0.003659953,34,37,9296.0,4,100000,41,0.027503787,3.6358629449828127e6,0.14907038074429532,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000201499,0.0,0.025004664,280,385,97076.0,4,100000,555,0.030051954,3.327570646487746e6,1.846801708800699,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000201499,0.00144058,0.017421279,200,285,84804.0,4,100000,899,0.031001547,3.225645481498068e6,2.899855287866763,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.004075705,0.0,1.106278353,7854,11241,1.982968e6,4,100000,15833,0.747688444,133745.54709581682,2.1175932471680676,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.004075705,0.2179023,0.603551358,4998,7671,1.507432e6,4,100000,27893,0.798295587,125266.88313009552,3.4940691711477543,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.00021249,0.0,0.071758772,26,29,6532.0,5,100000,5683,0.037722238,2.6509561813379154e6,15.065383978543373,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.00021249,0.000128207,0.003388731,26,29,6948.0,5,100000,5683,0.037747517,2.6491808719498026e6,15.055294895290727,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000669002,0.0,0.079791155,77,101,19175.0,5,100000,23078,0.074692884,1.3388156226502112e6,30.897186939521575,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000669002,0.055928147,0.006221709,61,79,16863.0,5,100000,16308,0.057755274,1.731443608076381e6,28.23638236050962,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005641639,0.0,0.034156435,356,493,85898.0,5,100000,120271,0.267365342,374020.0552994636,44.98376607092179,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005641639,0.002696054,0.013351179,148,221,43962.0,5,100000,43511,0.109401897,914060.9325997336,39.77170523834701,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.037868721,0.0,0.204703198,2183,3015,504653.0,5,100000,749880,1.590788561,62861.90537926555,47.13888560580365,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.037868721,0.031440864,0.055081783,625,988,186117.0,5,100000,190720,0.518984242,192684.07767956852,36.74870729504731,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.48451362,0.0,3.317284522,15866,21617,3.982352e6,5,100000,5405897,11.973981036,8351.4413209231,45.147031582454225,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.48451362,0.284478973,0.227699963,2234,3977,1.145088e6,5,100000,648737,1.870657698,53457.134411557105,34.679621006750324,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,20.631308049,7.881924357,3.22329305,15143,27212,6.101363e6,5,100000,4383934,12.868099468,7771.1553480509665,34.068232149602466,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,7.3412e-5,0.0,0.008071939,34,37,8624.0,5,100000,41,0.02668265,3.747753690131977e6,0.15365790129541104,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,7.3412e-5,0.000136603,0.003747363,34,37,9296.0,5,100000,41,0.026440112,3.782132239076748e6,0.15506742180214667,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000203843,0.0,0.025660107,280,385,97076.0,5,100000,555,0.102800045,972762.2200943589,0.5398830321523691,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000203843,0.001414931,0.017827188,200,285,84804.0,5,100000,899,0.029653875,3.372240558780261e6,3.0316442623434545,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.004244973,0.0,1.123334519,7854,11241,1.982968e6,5,100000,15833,0.697350597,143399.89157562878,2.2704504833169303,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.004244973,0.210167515,0.609427917,4998,7671,1.507432e6,5,100000,27893,0.694494505,143989.62019145134,4.016302476000152,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000217019,0.0,0.072640674,26,29,6532.0,6,100000,5683,0.035535357,2.8140986454702006e6,15.99252260220715,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000217019,0.000127887,0.003475969,26,29,6948.0,6,100000,5683,0.035467827,2.8194566303709554e6,16.02297203039814,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000641007,0.0,0.080568555,77,101,19175.0,6,100000,23078,0.066319202,1.5078589154314615e6,34.79836805032727,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000641007,0.028034489,0.00614493,61,79,16863.0,6,100000,16308,0.051946182,1.9250692957569046e6,31.394030075203602,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005625187,0.0,0.034643776,356,493,85898.0,6,100000,120271,0.229036924,436610.82350197824,52.51162035340643,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005625187,0.002540333,0.013054136,148,221,43962.0,6,100000,43511,0.095970493,1.0419869365472572e6,45.33789359610771,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.027808544,0.0,0.206085697,2183,3015,504653.0,6,100000,749880,1.404462265,71201.62819041635,53.392676947429415,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.027808544,0.032291546,0.057021257,625,988,186117.0,6,100000,190720,0.447460514,223483.40662747284,42.622755311991625,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.49093305,0.0,3.299901483,15866,21617,3.982352e6,6,100000,5405897,9.942076724,10058.260741299828,54.37392156661051,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.49093305,0.254814458,0.244901846,2234,3977,1.138176e6,6,100000,648737,1.564164415,63931.89810548145,41.47498778125572,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,21.303684969,7.785481408,3.214586387,15143,27212,6.101363e6,6,100000,4383934,10.669533723,9372.480803395647,41.08833725835349,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,7.263e-5,0.0,0.008140542,34,37,8624.0,6,100000,41,0.02653737,3.768270932650824e6,0.1544991082386838,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,7.263e-5,0.000168405,0.003804063,34,37,9296.0,6,100000,41,0.026435814,3.7827471474871174e6,0.15509263304697182,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000190368,0.0,0.025956198,280,385,69428.0,6,100000,555,0.028665437,3.4885217343799784e6,1.936129562580888,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000190368,0.001377188,0.018422768,200,285,57156.0,6,100000,899,0.029482815,3.3918063794111926e6,3.049233935090662,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.00363711,0.0,1.130765482,7854,11241,1.982968e6,6,100000,15833,0.579223861,172644.82134309036,2.7334854563251496,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.00363711,0.243135065,0.620473447,4998,7671,1.507432e6,6,100000,27893,0.545745614,183235.55413859908,5.110989311587944,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000199324,0.0,0.071191136,26,29,6532.0,7,100000,5683,0.052309593,1.911695241062189e6,10.86416405495642,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000199324,0.000153867,0.01405148,26,29,6948.0,7,100000,5683,0.038133752,2.6223488315547863e6,14.902808409725852,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000635486,0.0,0.079286551,77,101,19175.0,7,100000,23078,0.07829659,1.2771948305794671e6,29.47510230011294,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000635486,0.00055968,0.006198143,61,79,16863.0,7,100000,16308,0.062181697,1.6081902685930235e6,26.226366900215027,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005559912,0.0,0.033962591,356,493,85898.0,7,100000,120271,0.280872442,356033.5050599233,42.82050568706203,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005559912,0.002734428,0.013027765,148,221,43962.0,7,100000,43511,0.117309389,852446.6869399516,37.090807795444235,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.03640752,0.0,0.200605098,2183,3015,504653.0,7,100000,749880,1.698812892,58864.63451679527,44.14141213145444,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.03640752,0.019327164,0.055315214,625,988,186117.0,7,100000,190720,0.546626255,182940.35291078364,34.890384107144655,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.493328995,0.0,3.277609499,15866,21617,3.982352e6,7,100000,5405897,12.349060054,8097.782305918001,43.7757770742152,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.493328995,0.254465955,0.225476553,2234,3977,1.138176e6,7,100000,648737,1.84596466,54172.218009850745,35.14352219505654,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,20.354166676,8.136814031,3.122265441,15143,27212,6.101363e6,7,100000,4383934,12.551496712,7967.177325106883,34.92757955956512,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,7.0436e-5,0.0,0.00772483,34,37,8624.0,7,100000,41,0.028256097,3.539059198444852e6,0.14510142713623894,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,7.0436e-5,0.000154167,0.003407226,34,37,9296.0,7,100000,41,0.02822149,3.5433990196832274e6,0.14527935980701231,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000191089,0.0,0.02310209,280,385,69428.0,7,100000,555,0.032475391,3.0792546885732645e6,1.7089863521581619,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000191089,0.00150813,0.016067441,200,285,57156.0,7,100000,899,0.031485621,3.176052967162376e6,2.8552716174789756,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.003718157,0.0,1.027864283,7854,11241,1.982968e6,7,100000,15833,0.61048082,163805.31005052704,2.5935294740299946,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.003718157,0.140383585,0.562648549,4998,7671,1.507432e6,7,100000,27893,0.595371127,167962.46150512435,4.684976938762433,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000213622,0.0,0.071437091,26,29,6532.0,8,100000,5683,0.033169841,3.014786836029754e6,17.133033589157094,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000213622,0.000132196,0.003413108,26,29,6948.0,8,100000,5683,0.032476483,3.07915115069572e6,17.498815989403777,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000650616,0.0,0.101786238,77,101,19175.0,8,100000,23078,0.056394016,1.773237784661408e6,40.92278159441598,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000650616,0.028072042,0.006219805,61,79,16863.0,8,100000,16308,0.045276849,2.2086342625123933e6,36.01840755305211,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005519964,0.0,0.034373845,356,493,85898.0,8,100000,120271,0.177277243,564088.1948959461,67.84345128833033,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005519964,0.002580501,0.013205408,148,221,43962.0,8,100000,43511,0.078145799,1.2796593198823137e6,55.67925666739935,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.045895753,0.0,0.203006313,2183,3015,504653.0,8,100000,749880,1.033056164,96800.15809866461,72.58850255502662,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.045895753,0.018104013,0.054920251,625,988,186117.0,8,100000,190720,0.427299262,234028.01945396292,44.6338238702598,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.469422093,0.0,3.248820867,15866,21617,3.982352e6,8,100000,5405897,7.598237788,13160.94636547587,71.14672047428691,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.469422093,0.255219861,0.227804236,2234,3977,1.138176e6,8,100000,648737,1.247508409,80159.7803097454,52.0026153988033,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,20.509141628,7.630200059,3.177848915,15143,27212,6.101363e6,8,100000,4383934,8.441482409,11846.260544638895,51.933224374500966,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,7.3141e-5,0.0,0.008056289,34,37,8624.0,8,100000,41,0.026607966,3.758272992381304e6,0.15408919268763346,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,7.3141e-5,0.000149459,0.003720501,34,37,9296.0,8,100000,41,0.026463467,3.7787943658327158e6,0.15493056899914134,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000187081,0.0,0.025608607,280,385,69428.0,8,100000,555,0.028112731,3.5571072764150877e6,1.9741945384103736,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000187081,0.001400232,0.017930107,200,285,57156.0,8,100000,899,0.028727437,3.4809927526775184e6,3.1294124846570894,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.004377189,0.0,1.110232322,7854,11241,1.982968e6,8,100000,15833,0.49678182,201295.61101893787,3.1871134092628433,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.004377189,0.141260407,0.612406608,4998,7671,1.507432e6,8,100000,27893,0.462906186,216026.49310890824,6.025626972286777,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.00021779,0.0,0.071241092,26,29,6532.0,9,100000,5683,0.031910881,3.1337273326925696e6,17.80897243169187,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.00021779,0.000170198,0.00344002,26,29,6948.0,9,100000,5683,0.032748578,3.053567699947155e6,17.353425238799684,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.00066338,0.0,0.07943127,77,101,19175.0,9,100000,23078,0.055122883,1.8141286260372123e6,41.86646043168678,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.00066338,0.022855714,0.006175409,61,79,16863.0,9,100000,16308,0.113941609,877642.5124907618,14.312594093699344,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005746952,0.0,0.034117431,356,493,85898.0,9,100000,120271,0.160966122,621248.7370479113,74.71820685348933,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005746952,0.002613084,0.012920879,148,221,43962.0,9,100000,43511,0.072581179,1.3777676441436699e6,59.94804796433522,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.040246771,0.0,0.201198504,2183,3015,504653.0,9,100000,749880,0.941510261,106212.33155099941,79.64650318346344,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.040246771,0.025969914,0.05489325,625,988,186117.0,9,100000,190720,0.353194101,283130.43654146424,53.99863685718806,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.49543456,0.0,3.252799749,15866,21617,3.982352e6,9,100000,5405897,6.81045975,14683.296527815175,79.37638864982648,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.49543456,0.246068988,0.223835456,2234,3977,1.145088e6,9,100000,648737,1.209820879,82656.86411583248,53.62256605591281,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,20.475062483,7.867178657,3.192467452,15143,27212,6.101363e6,9,100000,4383934,7.835347411,12762.675954816064,55.950729049300605,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,7.769e-5,0.0,0.008166532,34,37,8624.0,9,100000,41,0.026227082,3.812852684107214e6,0.15632696004839577,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,7.769e-5,0.000168074,0.003757433,34,37,9296.0,9,100000,41,0.026345901,3.7956568651799e6,0.1556219314723759,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000192,0.0,0.025151234,280,385,69428.0,9,100000,555,0.02871873,3.482048126779979e6,1.9325367103628883,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000192,0.001457603,0.017443567,200,285,57156.0,9,100000,899,0.028334518,3.5292641999415695e6,3.172808515747471,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.003802149,0.0,1.17054367,7854,11241,1.982968e6,9,100000,15833,0.443107243,225679.0011441993,3.5731756251161078,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.003802149,0.267479623,0.598344848,4998,7671,1.507432e6,9,100000,27893,0.447276029,223575.58535738118,6.236193802373433,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000198903,0.0,0.071003343,26,29,6532.0,10,100000,5683,0.031059097,3.2196686207586783e6,18.297376771771567,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000198903,0.000143998,0.003447835,26,29,6948.0,10,100000,5683,0.075479753,1.3248586014848247e6,7.529171432238258,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000660305,0.0,0.082246555,77,101,19175.0,10,100000,23078,0.050729283,1.9712480462221396e6,45.49246241071454,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000660305,0.052896847,0.006264592,61,79,16863.0,10,100000,16308,0.041722419,2.3967929568033917e6,39.08689953954971,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005640577,0.0,0.034903588,356,493,85898.0,10,100000,120271,0.149114887,670623.8526003108,80.65660137609198,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005640577,0.002615909,0.013320851,148,221,43962.0,10,100000,43511,0.067952125,1.4716243237426348e6,64.03184595036578,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.026612515,0.0,0.204402158,2183,3015,504653.0,10,100000,749880,0.858505625,116481.47325767376,87.3471271664644,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.026612515,0.02883768,0.055567181,625,988,186117.0,10,100000,190720,0.302256706,330844.60332866857,63.098682746843664,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.470333352,0.0,3.255176829,15866,21617,3.982352e6,10,100000,5405897,6.1241531,16328.788383817511,88.27174813771393,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.470333352,0.323388193,0.230010253,2234,3977,1.138176e6,10,100000,648737,1.024181497,97638.94416460054,63.34199572051046,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,20.551357162,7.805497892,3.247159084,15143,27212,6.101363e6,10,100000,4383934,7.125449968,14034.201411713568,61.52501273165911,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,7.9093e-5,0.0,0.008300571,34,37,8624.0,10,100000,41,0.026168127,3.8214427803717097e6,0.1566791539952401,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,7.9093e-5,0.000162774,0.003805094,34,37,9296.0,10,100000,41,0.02631421,3.800228089689943e6,0.15580935167728766,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.00020712,0.0,0.026033607,280,385,69428.0,10,100000,555,0.029921091,3.342124122412515e6,1.8548788879389457,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.00020712,0.001408268,0.018204386,200,285,57156.0,10,100000,899,0.027956448,3.5769923274945375e6,3.215716102417589,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.003507099,0.0,1.124185585,7854,11241,1.982968e6,10,100000,15833,0.415316294,240780.34366742184,3.81227518128629,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.003507099,0.221534785,0.619633607,4998,7671,1.507432e6,10,100000,27893,0.412460441,242447.4932857864,6.76258793022044,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.015352061,0.0,0.071164515,26,29,6532.0,11,100000,5683,0.030695967,3.257756955498421e6,18.513832778097527,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.015352061,0.000158245,0.003442925,26,29,6948.0,11,100000,5683,0.030374116,3.2922768847001176e6,18.710009535750768,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000659914,0.0,0.108328064,77,101,19175.0,11,100000,23078,0.048463048,2.0634277893540661e6,47.619786522713135,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000659914,0.050305585,0.006195878,61,79,16863.0,11,100000,16308,0.04044843,2.472283843897031e6,40.318004926272785,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005454738,0.0,0.034115126,356,493,85898.0,11,100000,120271,0.138428491,722394.64056572,86.88312581547972,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005454738,0.002816887,0.013604578,148,221,43962.0,11,100000,43511,0.064107834,1.559871762318471e6,67.87158025023899,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.026552149,0.0,0.204497642,2183,3015,504653.0,11,100000,749880,0.741265329,134904.4614495925,101.16215755182041,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.026552149,0.031970206,0.055528075,625,988,186117.0,11,100000,190720,0.320150164,312353.42425125226,59.57204507319883,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.479830353,0.0,3.300714313,15866,21617,3.982352e6,11,100000,5405897,5.751710851,17386.131290416637,93.98763498446942,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.479830353,0.281598845,0.229794337,2234,3977,1.145088e6,11,100000,648737,1.080207262,92574.8266261887,60.05671530099378,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,20.674437441,7.534210292,3.127661153,15143,27212,6.101363e6,11,100000,4383934,6.892937209,14507.603503109178,63.60037625579943,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,8.0615e-5,0.0,0.007790346,34,37,8624.0,11,100000,41,0.025992388,3.8472802114218976e6,0.1577384886682978,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,8.0615e-5,0.000188544,0.003460519,34,37,9296.0,11,100000,41,0.026332184,3.7976341043340727e6,0.15570299827769696,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000210616,0.0,0.023266226,280,385,97076.0,11,100000,555,0.030232882,3.3076568750541215e6,1.8357495656550373,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000210616,0.001478013,0.016521128,200,285,84804.0,11,100000,899,0.109023117,917236.6627529095,0.8245957598148655,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.004629265,0.0,1.052010711,7854,11241,1.982968e6,11,100000,15833,0.412454911,242450.74390688975,3.838722628277785,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.004629265,0.241362926,0.56448209,4998,7671,1.507432e6,11,100000,27893,0.442037188,226225.31025602305,6.31010257897125,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000203393,0.0,0.070659462,26,29,6532.0,12,100000,5683,0.033455655,2.9890313012852385e6,16.98666488520401,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000203393,0.000216528,0.003151821,26,29,6948.0,12,100000,5683,0.033940821,2.9463046872083615e6,16.74384953740512,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000669121,0.0,0.092727523,77,101,19175.0,12,100000,23078,0.056770402,1.761481273287443e6,40.651464824927615,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000669121,0.022366007,0.006118807,61,79,16863.0,12,100000,16308,0.04734225,2.1122781447861055e6,34.447031985171805,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005531834,0.0,0.034217524,356,493,85898.0,12,100000,120271,0.175310192,570417.4917565546,68.60468215105257,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005531834,0.010367324,0.013272941,148,221,43962.0,12,100000,43511,0.080128162,1.2480006717238815e6,54.301757227377806,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.036289724,0.0,0.203914306,2183,3015,504653.0,12,100000,749880,1.058099558,94509.0650912076,70.87045773059475,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.036289724,0.01857383,0.055614081,625,988,186117.0,12,100000,190720,0.371447652,269216.9393495049,51.345054672737575,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.47392103,0.0,3.418015152,15866,21617,3.982352e6,12,100000,5405897,7.362401452,13582.524757983001,73.42572984160603,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.47392103,0.24433505,0.245399444,2234,3977,1.138176e6,12,100000,648737,1.206022378,82917.20106042677,53.79145626433808,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,21.85574372,7.202209362,3.282453299,15143,27212,6.101363e6,12,100000,4383934,8.051222592,12420.47389167501,54.45053778982639,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,7.9674e-5,0.0,0.008081925,34,37,8624.0,12,100000,41,0.027444507,3.6437163910432057e6,0.14939237203277145,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,7.9674e-5,0.000182983,0.003809851,34,37,9296.0,12,100000,41,0.027505654,3.635616153682439e6,0.14906026230098,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000211618,0.0,0.025668991,280,385,97076.0,12,100000,555,0.029793919,3.3563896042007767e6,1.8627962303314312,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000211618,0.001483823,0.01806652,200,285,84804.0,12,100000,899,0.030056296,3.3270899381613755e6,2.991053854407076,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.004193271,0.0,1.122633972,7854,11241,1.982968e6,12,100000,15833,0.328658591,304267.1110337718,4.817461168997709,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.004193271,0.157784085,0.608300419,4998,7671,1.507432e6,12,100000,27893,0.497965281,200817.21319844385,5.601394527744194,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000219093,0.0,0.007540139,26,29,6532.0,13,100000,5683,0.03379996,2.958583382938915e6,16.813629365241855,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000219093,0.000280772,0.003128958,26,29,6948.0,13,100000,5683,0.03363445,2.9731421206530803e6,16.896366671671455,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000648491,0.0,0.007044634,77,101,19175.0,13,100000,23078,0.055231975,1.810545431337554e6,41.78376746440807,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000648491,0.055606727,0.006170847,61,79,16863.0,13,100000,16308,0.047026351,2.126467350188408e6,34.67842954687256,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005305628,0.0,0.033617788,356,493,85898.0,13,100000,120271,0.166277204,601405.3495871869,72.33162280020056,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005305628,0.002689449,0.012844264,148,221,43962.0,13,100000,43511,0.079018953,1.2655191723433742e6,55.06400470783256,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.026408798,0.0,0.205014722,2183,3015,504653.0,13,100000,749880,0.987545224,101261.18538142006,75.93373769381928,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.026408798,0.026387296,0.054257294,625,988,186117.0,13,100000,190720,0.358948439,278591.54445299035,53.132979358074316,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.480205834,0.0,3.272532423,15866,21617,3.982352e6,13,100000,5405897,6.887609534,14518.825364062805,78.48727447911102,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.480205834,0.265121603,0.225761334,2234,3977,1.138176e6,13,100000,648737,1.201180954,83251.40326858696,54.008265602253296,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,20.624208865,7.56375444,3.239264871,15143,27212,6.101363e6,13,100000,4383934,7.506884592,13321.105283351346,58.398846369263595,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,9.2027e-5,0.0,0.008342066,34,37,8624.0,13,100000,41,0.100122395,998777.5462223012,0.040949879395114346,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,9.2027e-5,0.000199104,0.003719808,34,37,9296.0,13,100000,41,0.027749195,3.603708143605607e6,0.1477520338878299,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000203392,0.0,0.025589026,280,385,97076.0,13,100000,555,0.031802997,3.1443577471645204e6,1.7451185496763089,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000203392,0.001604106,0.01784822,200,285,84804.0,13,100000,899,0.030398246,3.28966348913684e6,2.9574074767340193,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.003740327,0.0,1.108119441,7854,11241,1.982968e6,13,100000,15833,0.42196106,236988.69274809386,3.75224197228057,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.003740327,0.282806429,0.606750337,4998,7671,1.507432e6,13,100000,27893,0.401760011,248904.81198239516,6.942701920624948,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000201328,0.0,0.071371538,26,29,6532.0,14,100000,5683,0.034235791,2.92091980582543e6,16.59958725650592,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000201328,0.000192852,0.003462742,26,29,6948.0,14,100000,5683,0.034379308,2.9087263769241665e6,16.530292000060037,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000660174,0.0,0.078403477,77,101,19175.0,14,100000,23078,0.05803808,1.7230066880227602e6,39.76354834618926,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000660174,0.002547325,0.006218809,61,79,16863.0,14,100000,16308,0.048919375,2.0441798367211355e6,33.33648477724828,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005635505,0.0,0.034088797,356,493,85898.0,14,100000,120271,0.178264327,560964.7296399352,67.46778899852464,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005635505,0.002703907,0.013217324,148,221,43962.0,14,100000,43511,0.085195904,1.173765349094717e6,51.07170410446024,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.027118047,0.0,0.207087755,2183,3015,504653.0,14,100000,749880,1.026742523,97395.40124218659,73.03486348349088,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.027118047,0.026508019,0.055348931,625,988,186117.0,14,100000,190720,0.385814333,259192.02955064917,49.43310387589981,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.478298932,0.0,3.444202994,15866,21617,3.982352e6,14,100000,5405897,6.937833032,14413.72248925001,77.91909916346916,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.478298932,0.264855503,0.234932995,2234,3977,1.145088e6,14,100000,648737,1.272042405,78613.73143452713,50.999636289640826,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,20.065628495,8.255575251,3.216813505,15143,27212,6.101363e6,14,100000,4383934,7.705401166,12977.909630617149,56.894299278589955,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,9.1727e-5,0.0,0.008192038,34,37,8624.0,14,100000,41,0.027977726,3.574271904728783e6,0.14654514809388008,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,9.1727e-5,0.000215356,0.003847033,34,37,9296.0,14,100000,41,0.028887321,3.4617263400784032e6,0.14193077994321454,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000229163,0.0,0.02634237,280,385,69428.0,14,100000,555,0.030221726,3.308877858266599e6,1.8364272113379625,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000229163,0.001629043,0.018505728,200,285,57156.0,14,100000,899,0.030659561,3.261625305072046e6,2.9322011492597695,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.003980301,0.0,1.123271404,7854,11241,1.982968e6,14,100000,15833,0.417802482,239347.54892145423,3.789589742073385,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.003980301,0.264419313,0.615279444,4998,7671,1.507432e6,14,100000,27893,0.514228576,194466.0500547523,5.424241534177206,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000192431,0.0,0.070409633,26,29,6532.0,15,100000,5683,0.037940971,2.635673188227049e6,14.97853072869432,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000192431,0.000338092,0.003070615,26,29,6948.0,15,100000,5683,0.032602189,3.0672787032797094e6,17.43134487073859,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000624465,0.0,0.077373059,77,101,19175.0,15,100000,23078,0.055895256,1.7890605957686284e6,41.28794042914841,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000624465,0.029367508,0.005917498,61,79,16863.0,15,100000,16308,0.04922265,2.0315850528161323e6,33.13108904132549,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005515392,0.0,0.033536773,356,493,85898.0,15,100000,120271,0.155466629,643224.85566983,77.36129661626613,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005515392,0.002700832,0.012928527,148,221,43962.0,15,100000,43511,0.072620399,1.3770235550482173e6,59.91567190370298,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.037685839,0.0,0.196800436,2183,3015,504653.0,15,100000,749880,0.942158874,106139.21150627511,79.59167192432558,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.037685839,0.054947908,0.054073591,625,988,186117.0,15,100000,190720,0.252204214,396504.0806177807,75.62125825542313,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.449096158,0.0,3.295232568,15866,21617,3.982352e6,15,100000,5405897,6.220426136,16076.069036695333,86.90557337726419,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.449096158,0.253339946,0.223118551,2234,3977,1.145088e6,15,100000,648737,1.160937313,86137.29516677184,55.88045045460606,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,19.978574089,7.687533494,3.174034592,15143,27212,6.101363e6,15,100000,4383934,7.126567847,14031.999995916127,61.51536187009657,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,7.6137e-5,0.0,0.007995388,34,37,8624.0,15,100000,41,0.032055094,3.1196289737911858e6,0.1279047879254386,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,7.6137e-5,0.000223701,0.003664872,34,37,9296.0,15,100000,41,0.027909655,3.5829894708479918e6,0.14690256830476767,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000222019,0.0,0.02485495,280,385,69428.0,15,100000,555,0.029982985,3.335224961757477e6,1.8510498537753997,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000222019,0.001506758,0.017433791,200,285,57156.0,15,100000,899,0.030101003,3.3221484347215937e6,2.986611442814713,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.00399057,0.0,1.186148628,7854,11241,1.982968e6,15,100000,15833,0.284421574,351590.7692712508,5.566736649871714,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.00399057,0.148404243,0.590075328,4998,7671,1.507432e6,15,100000,27893,0.258166221,387347.343942413,10.804279464585726,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000209253,0.0,0.070626692,26,29,6532.0,16,100000,5683,0.032619503,3.0656506323839454e6,17.422092543837962,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000209253,0.000232608,0.003362619,26,29,6948.0,16,100000,5683,0.033023052,3.028187703547207e6,17.20919071925878,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000676666,0.0,0.123326844,77,101,19175.0,16,100000,23078,0.054284759,1.8421376799333307e6,42.5128533775014,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000676666,0.053513561,0.006111523,61,79,16863.0,16,100000,16308,0.045688822,2.1887191576092727e6,35.69363202229202,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.00561791,0.0,0.033558886,356,493,85898.0,16,100000,120271,0.163807135,610474.018729404,73.42232070660414,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.00561791,0.002815864,0.013194219,148,221,43962.0,16,100000,43511,0.07743008,1.291487752563345e6,56.19392360178371,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.027177763,0.0,0.200980796,2183,3015,504653.0,16,100000,749880,0.845138916,118323.74312295897,88.72860849304448,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.027177763,0.027390363,0.055386164,625,988,186117.0,16,100000,190720,0.269311569,371317.1341703483,70.81760382896883,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.493311984,0.0,3.327198042,15866,21617,3.982352e6,16,100000,5405897,6.30875024,15850.999991402417,85.68887330052236,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.493311984,0.264244421,0.223179712,2234,3977,1.145088e6,16,100000,648737,1.151761833,86823.50563703738,56.32562057645472,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,21.071311543,7.669157907,3.298744517,15143,27212,6.101363e6,16,100000,4383934,7.086616408,14111.106661157946,61.862160269476796,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,8.1327e-5,0.0,0.008000147,34,37,8624.0,16,100000,41,0.027687176,3.611780414152747e6,0.14808299698026264,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,8.1327e-5,0.000266905,0.003754835,34,37,9296.0,16,100000,41,0.028117356,3.5565221708613e6,0.14581740900531331,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000190067,0.0,0.025770928,280,385,97076.0,16,100000,555,0.030116313,3.3204595794976633e6,1.8428550666212031,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000190067,0.00156009,0.018142348,200,285,84804.0,16,100000,899,0.030151361,3.316599870898033e6,2.981623283937332,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.003748684,0.0,1.174588317,7854,11241,1.982968e6,16,100000,15833,0.384297211,260215.2634409829,4.119988266061083,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.003748684,0.303695629,0.609461614,4998,7671,1.507432e6,16,100000,27893,0.298997564,334450.8853590526,9.328838545320055,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000204535,0.0,0.071344438,26,29,6532.0,17,100000,5683,0.07940887,1.2593051632645067e6,7.156631242832192,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000204535,0.000233841,0.003087638,26,29,6948.0,17,100000,5683,0.033259859,3.006627298089267e6,17.086662935041307,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.0006581,0.0,0.090267873,77,101,19175.0,17,100000,23078,0.051660757,1.9357052781863029e6,44.672206409983495,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.0006581,0.022646138,0.006025668,61,79,16863.0,17,100000,16308,0.120931433,826914.8683618096,13.485327673244392,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005652467,0.0,0.033585859,356,493,85898.0,17,100000,120271,0.156899568,637350.3845466293,76.65476809980765,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005652467,0.002929192,0.012864444,148,221,43962.0,17,100000,43511,0.073959574,1.3520899944610281e6,58.8307877489938,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.022417958,0.0,0.203452889,2183,3015,504653.0,17,100000,749880,0.814905226,122713.6565203473,92.02051675147803,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.022417958,0.020606734,0.054928422,625,988,186117.0,17,100000,190720,0.255536772,391333.1111500461,74.6350509585368,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.491198923,0.0,3.239538816,15866,21617,3.982352e6,17,100000,5405897,5.947755765,16813.064280220995,90.88969375325382,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.491198923,0.263739731,0.224207879,2234,3977,1.138176e6,17,100000,648737,1.084560716,92203.2289430627,59.81564613483566,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,20.80966719,7.841797599,3.19420691,15143,27212,6.101363e6,17,100000,4383934,6.931204652,14427.506475536686,63.24923617332545,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,8.6667e-5,0.0,0.008044473,34,37,8624.0,17,100000,41,0.027894066,3.5849918760499097e6,0.1469846669180463,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,8.6667e-5,0.000389672,0.00371556,34,37,9296.0,17,100000,41,0.028312663,3.5319884957483513e6,0.1448115283256824,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000175058,0.0,0.025415803,280,385,69428.0,17,100000,555,0.030180528,3.3133946496893624e6,1.838934030577596,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000175058,0.001551825,0.017563782,200,285,57156.0,17,100000,899,0.030315177,3.2986777547101243e6,2.9655113014844017,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.004749295,0.0,1.096758609,7854,11241,1.982968e6,17,100000,15833,0.234580035,426293.7380838911,6.749508755082248,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.004749295,0.379091961,0.598157088,4998,7671,1.507432e6,17,100000,27893,0.248119732,403031.22687557957,11.24175001124054,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000191951,0.0,0.07200298,26,29,6532.0,18,100000,5683,0.036220242,2.7608871304614698e6,15.690121562412532,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000191951,0.000327271,0.003037972,26,29,6948.0,18,100000,5683,0.034878493,2.867096350751163e6,16.29370856131886,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000640516,0.0,0.077888377,77,101,19175.0,18,100000,23078,0.055488503,1.8021751280621141e6,41.59059760541747,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000640516,0.02261514,0.006057849,61,79,16863.0,18,100000,16308,0.04201281,2.3802264118967527e6,38.81673232521224,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005638229,0.0,0.034131361,356,493,85898.0,18,100000,120271,0.153714234,650557.839685816,78.24324193685277,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005638229,0.002807187,0.01299213,148,221,43962.0,18,100000,43511,0.074310313,1.3457082329877953e6,58.55311092553196,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.036543396,0.0,0.202376615,2183,3015,504653.0,18,100000,749880,0.791880277,126281.71568920134,94.69613296101831,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.036543396,0.030470557,0.054285071,625,988,186117.0,18,100000,190720,0.254711372,392601.2380789971,74.87690812642633,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.486813647,0.0,3.300479061,15866,21617,3.982352e6,18,100000,5405897,5.518618679,18120.476484546758,97.95742946638187,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.486813647,0.354780872,0.25089597,2234,3977,1.145088e6,18,100000,648737,0.984940957,101528.92850002582,65.86557248832125,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,20.418652872,6.929368719,3.185691047,15143,27212,6.101363e6,18,100000,4383934,6.401607689,15621.075963750767,68.48176603406975,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,7.6307e-5,0.0,0.008123005,34,37,8624.0,18,100000,41,0.031621308,3.162424527157447e6,0.12965940561345532,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,7.6307e-5,0.000263508,0.003783621,34,37,9296.0,18,100000,41,0.026947981,3.71085314332083e6,0.15214497887615402,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000215115,0.0,0.025871273,280,385,97076.0,18,100000,555,0.034854116,2.8691016005111136e6,1.592351388283668,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000215115,0.001485727,0.018028439,200,285,84804.0,18,100000,899,0.034885107,2.86655276705902e6,2.577030937586059,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.095263826,0.0,1.119845161,7854,11241,1.982968e6,18,100000,15833,0.261790675,381984.5760357966,6.0479617923747675,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.095263826,0.394726816,0.609843355,4998,7671,1.507432e6,18,100000,27893,0.244098175,409671.2316673404,11.426959664897126,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000198032,0.0,0.007585898,26,29,6532.0,19,100000,5683,0.031645716,3.159985383171612e6,17.95819693256427,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000198032,0.000379462,0.00308339,26,29,6948.0,19,100000,5683,0.032193543,3.1062129446268156e6,17.652608164314195,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000653882,0.0,0.007017101,77,101,19175.0,19,100000,23078,0.04982756,2.006921470768386e6,46.31573370239281,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000653882,0.022923143,0.006095572,61,79,16863.0,19,100000,16308,0.042384307,2.3593638088738834e6,38.476504995115285,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005640124,0.0,0.034326708,356,493,85898.0,19,100000,120271,0.143717735,695808.3496097402,83.68556601591305,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005640124,0.00280319,0.01296108,148,221,43962.0,19,100000,43511,0.069578112,1.4372335943809457e6,62.53547092510933,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.027640086,0.0,0.205273989,2183,3015,504653.0,19,100000,749880,0.726001985,137740.67022695538,103.28897378978931,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.027640086,0.033037501,0.05573045,625,988,186117.0,19,100000,190720,0.245884783,406694.54522527324,77.5647836653641,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.462550233,0.0,3.276486253,15866,21617,3.982352e6,19,100000,5405897,5.250009982,19047.58283181489,102.9692708877596,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.462550233,0.258602504,0.222852389,2234,3977,1.145088e6,19,100000,648737,1.030208981,97067.6841731008,62.97139822740489,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,20.565537773,7.495132115,3.202080031,15143,27212,6.101363e6,19,100000,4383934,6.393994566,15639.675474819602,68.5633050630278,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,8.5454e-5,0.0,0.007956643,34,37,8624.0,19,100000,41,0.028324957,3.530455491953615e6,0.1447486751700982,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,8.5454e-5,0.000427605,0.003731691,34,37,9296.0,19,100000,41,0.027873867,3.587589766428892e6,0.14709118042358457,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.00020721,0.0,0.025494816,280,385,69428.0,19,100000,555,0.029700512,3.366945324040205e6,1.868654654842314,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.00020721,0.001567344,0.017660128,200,285,57156.0,19,100000,899,0.030051419,3.3276298866286483e6,2.991539268079155,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.003972646,0.0,1.184366509,7854,11241,1.982968e6,19,100000,15833,0.448761029,222835.74895715824,3.5281584132386867,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.003972646,0.137865794,0.59921788,4998,7671,1.507432e6,19,100000,27893,0.34066514,293543.38985198195,8.187805773141333,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized,0.000214784,0.0,0.070692874,26,29,6532.0,20,100000,5683,0.031641497,3.1604067279117675e6,17.960591434722577,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000214784,0.000394952,0.003131132,26,29,6948.0,20,100000,5683,0.031958329,3.129074739796314e6,17.78253174626245,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized,0.000655194,0.0,0.077342315,77,101,19175.0,20,100000,23078,0.048152859,2.0767198890516553e6,47.926541599534104,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000655194,0.028522579,0.006073399,61,79,16863.0,20,100000,16308,0.04192926,2.3849693507588734e6,38.894080172175705,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized,0.005568786,0.0,0.033698908,356,493,85898.0,20,100000,120271,0.13970245,715807.0599334514,86.09083090525614,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005568786,0.010602299,0.013480763,148,221,43962.0,20,100000,43511,0.066047249,1.514067603330458e6,65.87859548851156,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized,0.027657981,0.0,0.215276301,2183,3015,504653.0,20,100000,749880,0.704801573,141883.90581245197,106.39590329064148,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced,0.027657981,0.019562589,0.055222912,625,988,186117.0,20,100000,190720,0.32541373,307301.1086532827,58.60846744235407,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized,0.483390353,0.0,3.311541537,15866,21617,3.982352e6,20,100000,5405897,4.983021895,20068.14381055414,108.48631842104318,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced,0.483390353,0.274925435,0.223765363,2234,3977,1.145088e6,20,100000,648737,1.019978472,98041.28493410005,63.60300906429327,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced,20.542625682,7.425827696,3.214107217,15143,27212,6.101363e6,20,100000,4383934,6.210099291,16102.802115406628,70.59362168900303,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized,8.2609e-5,0.0,0.007986983,34,37,8624.0,20,100000,41,0.029346239,3.407591684917444e6,0.13971125908161522,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced,8.2609e-5,0.000432775,0.003719557,34,37,9296.0,20,100000,41,0.027930466,3.5803197841382236e6,0.14679311114966717,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized,0.000199826,0.0,0.025378973,280,385,69428.0,20,100000,555,0.030437014,3.2854734041913575e6,1.8234377393262033,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced,0.000199826,0.001550351,0.017680147,200,285,57156.0,20,100000,899,0.030056019,3.327120601035021e6,2.991081420330484,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized,0.004990961,0.0,1.096316706,7854,11241,1.982968e6,20,100000,15833,0.376119369,265873.0398965441,4.209567840681983,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced,0.004990961,0.274653582,0.593927868,4998,7671,1.507432e6,20,100000,27893,0.406462983,246024.86372049284,6.862371523755707,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000195467,0.0,0.015341014,26,29,6532.0,1,100000,9004,2.621861154,38140.84504339089,0.3434201687706916,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000195467,0.000110994,0.000172893,26,29,6948.0,1,100000,5683,2.634625606,37956.05712335888,0.21570427263204853,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000623012,0.0,0.000385905,77,101,19175.0,1,100000,23078,3.342933167,29913.849605836287,0.6903518212034898,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000623012,0.000535013,0.00030562,61,79,16863.0,1,100000,16308,3.199522377,31254.664983391674,0.5097010765491514,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006202609,0.0,0.006745647,356,493,85898.0,1,100000,126762,7.168748504,13949.436215289497,1.7682584335225273,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006202609,0.002730569,0.000572214,148,221,43962.0,1,100000,43511,4.574875808,21858.516864027624,0.951085927270706,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.02619531,0.0,0.015685488,2183,3015,504653.0,1,100000,763724,29.913689979,3342.9510057168463,2.5530919138900927,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.02619531,0.018832521,0.002253709,625,988,186117.0,1,100000,190720,9.767410299,10238.12832048615,1.9526158332831185,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.478365701,0.0,0.057283911,15866,21617,3.982352e6,1,100000,5409487,214.637570347,465.90165849497885,2.520288964907028,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.478365701,0.264683009,0.00842117,2234,3977,1.145088e6,1,100000,648737,30.223621295,3308.670361633447,2.1464568843949974,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 16.461170919,0.0,0.623217925,131069,176419,3.0347603e7,1,100000,44215420,2121.319671102,47.14046702261107,2.084335548400898,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,16.461170919,7.057532997,0.064176663,15143,27212,6.101363e6,1,100000,4383934,216.337755422,462.2401661001551,2.0264303803321173,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,984.119653346,305.81976463,0.553236498,90592,175381,4.1886806e7,1,100000,24116153,1525.758117258,65.54118825840752,1.5806013238415593,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,0.002405731,0.0,0.00445273,34,37,8624.0,1,100000,2996,2.595163207,38533.222007104385,0.11544553313328473,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,0.002405731,0.000125882,0.000241175,34,37,9296.0,1,100000,81,2.562597736,39022.901876160875,0.003160855051969031,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.008769387,0.0,0.001379441,280,385,69428.0,1,100000,1559,4.599120224,21743.288961693383,0.03389778749127998,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.008769387,0.00142548,0.000893845,200,285,57156.0,1,100000,1107,4.496498569,22239.526704050422,0.024619156061383818,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.012050487,0.0,0.045386557,7854,11241,1.982968e6,1,100000,59501,57.13627857,1750.2014919905205,0.10413873897492797,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.012050487,0.161514085,0.021869129,4998,7671,1.507432e6,1,100000,32693,43.060341001,2322.32252869706,0.07592369043069298,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000187492,0.0,0.004398054,26,29,6532.0,2,100000,9004,1.430887645,69886.68911177859,0.6292597487624544,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000187492,0.000114451,0.000182402,26,29,6948.0,2,100000,5683,1.426904081,70081.79549806754,0.39827484381551786,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000653,0.0,0.000395924,77,101,19175.0,2,100000,23078,2.023122959,49428.53302867391,1.1407116852357366,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000653,0.000529612,0.000301251,61,79,16863.0,2,100000,16308,1.928809293,51845.457382914006,0.8454957190005616,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.015934701,0.0,0.007450113,356,493,85898.0,2,100000,126762,4.159202156,24043.072745512396,3.0477479873666424,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.015934701,0.002714336,0.011936518,148,221,43962.0,2,100000,43511,2.478782891,40342.37946497106,1.7553372729003558,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.033997938,0.0,0.016333771,2183,3015,504653.0,2,100000,763990,17.87819532,5593.405721892516,4.2733060374686636,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.033997938,0.026387917,0.002328573,625,988,186117.0,2,100000,190720,6.382929957,15666.786362011148,2.987969494962766,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.495324229,0.0,0.056559994,15866,21617,3.982352e6,2,100000,5409487,123.066509327,812.5687528382723,4.395580105084847,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.495324229,0.281677103,0.008282128,2234,3977,1.138176e6,2,100000,648737,17.01024193,5878.811154568923,3.813802311981579,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 16.782531066,0.0,0.623308264,131069,176419,3.0347603e7,2,100000,44215420,1243.588944119,80.4124228290268,3.555469048603008,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,16.782531066,7.395488075,0.069214414,15143,27212,6.101363e6,2,100000,4383934,118.43254641,844.3624918256116,3.701629436239021,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1040.043677037,320.518015345,0.51873347,90592,175381,4.1886806e7,2,100000,24116153,884.232176994,113.09246892592843,2.727355283765436,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,6.4825e-5,0.0,0.004537465,34,37,8624.0,2,100000,2996,1.380237814,72451.28265990254,0.21706404284906802,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,6.4825e-5,0.000123519,0.000254601,34,37,9296.0,2,100000,81,1.377614032,72589.27223238388,0.005879731050823094,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.000173385,0.0,0.001270822,280,385,69428.0,2,100000,1559,2.704558487,36974.61174556585,0.057643419711337164,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.000173385,0.001369753,0.000888955,200,285,57156.0,2,100000,1107,2.51847975,39706.493570178594,0.0439550883821877,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.003131272,0.0,0.035593297,7854,11241,1.982968e6,2,100000,59876,32.301088791,3095.8708744165565,0.18536836447656574,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.003131272,0.162091596,0.02290205,4998,7671,1.507432e6,2,100000,32693,25.84827697,3868.7298235028156,0.12648038411977755,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000197722,0.0,0.004396904,26,29,6532.0,3,100000,9004,1.202166931,83183.12325960994,0.748980841829528,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000197722,0.000122787,0.000180829,26,29,6948.0,3,100000,5683,1.169424304,85512.1615464561,0.4859656140685101,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000824761,0.0,0.000385544,77,101,19175.0,3,100000,23078,1.767179879,56587.3351028574,1.3059225195037432,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000824761,0.000624855,0.000342731,61,79,16863.0,3,100000,16308,1.653439456,60479.9889328394,0.9863076595167448,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006507667,0.0,0.00699636,356,493,85898.0,3,100000,126762,3.630774754,27542.33098316845,3.491320960088399,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006507667,0.002754845,0.00059571,148,221,43962.0,3,100000,43511,2.150285617,46505.44988507914,2.0234986299496787,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.0393518,0.0,0.016350118,2183,3015,504653.0,3,100000,763930,17.071515789,5857.710658852849,4.474880903617456,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.0393518,0.034457366,0.002240603,625,988,186117.0,3,100000,190720,5.76745105,17338.68205088624,3.3068334407450237,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.481070432,0.0,0.058617713,15866,21617,3.982352e6,3,100000,5409487,105.937393041,943.9537554156906,5.106305568522358,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.481070432,0.254673519,0.009305947,2234,3977,1.138176e6,3,100000,648737,14.750586949,6779.3912435992515,4.3980419371988475,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 20.965560165,0.0,0.566615824,131069,176419,3.0347603e7,3,100000,44215420,889.944350977,112.36657650584316,4.968335374167988,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,20.965560165,7.125540881,0.063275726,15143,27212,6.101363e6,3,100000,4383934,96.18889764,1039.6210212769417,4.557629942290709,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1072.979030258,329.046139293,0.539195131,90592,175381,4.1886806e7,3,100000,24116153,645.933297177,154.81474702889918,3.733536126005228,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,6.2351e-5,0.0,0.004652638,34,37,8624.0,3,100000,2996,1.145378587,87307.37691012902,0.26157290122274657,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,6.2351e-5,0.000128929,0.00025915,34,37,9296.0,3,100000,81,1.155877416,86514.36442633982,0.007007663518533525,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.000391084,0.0,0.001308455,280,385,69428.0,3,100000,1559,2.209845643,45252.02939705957,0.07054791383001587,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.000391084,0.001483713,0.000902021,200,285,57156.0,3,100000,1107,2.101154899,47592.87382743313,0.05268531132696848,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.003437843,0.0,0.035960929,7854,11241,1.982968e6,3,100000,59876,24.729839461,4043.6979042142275,0.24212045571273108,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.003437843,0.172187706,0.022303105,4998,7671,1.507432e6,3,100000,32693,21.631139716,4622.964915992501,0.15113859199854285,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000181441,0.0,0.004308673,26,29,6532.0,4,100000,9004,0.922249065,108430.57889139741,0.9763089323381423,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000181441,0.000127656,0.000171261,26,29,6948.0,4,100000,5683,0.902528684,110799.8025689342,0.629675277999253,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000770848,0.0,0.000397197,77,101,19175.0,4,100000,23078,1.31523758,76031.89075543295,1.7546639748538817,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000770848,0.000552366,0.000307052,61,79,16863.0,4,100000,16308,1.229117507,81359.18610750046,1.3268056070411174,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.00630751,0.0,0.006912007,356,493,85898.0,4,100000,126762,3.020837562,33103.40193657854,4.196253436284569,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.00630751,0.002969199,0.015130515,148,221,43962.0,4,100000,43511,1.76856187,56543.1165831931,2.4602475456513146,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.026731519,0.0,0.016506119,2183,3015,504653.0,4,100000,763658,13.432736172,7444.499670025976,5.685051729012697,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.026731519,0.017970706,0.002300329,625,988,186117.0,4,100000,190720,4.796349993,20849.187433349176,3.976357027288355,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.474512314,0.0,0.05887403,15866,21617,3.982352e6,4,100000,5409487,84.780025536,1179.5231172410672,6.380614968915029,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.474512314,0.276075152,0.008927085,2234,3977,1.145088e6,4,100000,648737,11.427711129,8750.658716445054,5.6768760837304155,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 20.034059322,0.0,0.607240697,131069,176419,3.0347603e7,4,100000,44215420,777.00148127,128.69988334713486,5.690519396144573,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,20.034059322,7.261357316,0.083732148,15143,27212,6.101363e6,4,100000,4383934,79.76974225,1253.6081624358014,5.495735445979832,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,996.105510653,303.701743802,0.517350032,90592,175381,4.1886806e7,4,100000,24116153,487.836824736,204.98657528389018,4.943487612492314,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,7.3772e-5,0.0,0.00433355,34,37,8624.0,4,100000,2996,0.887801463,112637.79591226018,0.3374628365531315,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,7.3772e-5,0.000138397,0.000260933,34,37,9296.0,4,100000,81,0.877240258,113993.85640142384,0.00923350236851533,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.000387588,0.0,0.00130087,280,385,69428.0,4,100000,1559,1.772766073,56409.02176719398,0.08794166493505542,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.000387588,0.001435229,0.000902531,200,285,57156.0,4,100000,1107,1.664771248,60068.31276076916,0.06649562222617146,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.003275429,0.0,0.05913799,7854,11241,1.982968e6,4,100000,59501,19.869452007,5032.851432680179,0.2994596930959033,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.003275429,0.16158831,0.02148023,4998,7671,1.507432e6,4,100000,32693,17.310382898,5776.879725263256,0.18886352885803162,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000185548,0.0,0.004342287,26,29,6532.0,5,100000,9004,0.796853073,125493.64919121044,1.129944817317659,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000185548,0.000115473,0.000179105,26,29,6948.0,5,100000,5683,0.755232888,132409.48797240408,0.7524831201471723,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000727253,0.0,0.000372999,77,101,19175.0,5,100000,23078,1.121831803,89139.92252009636,2.0571711319187838,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000727253,0.009358875,0.000311982,61,79,16863.0,5,100000,16308,1.080798881,92524.15204896941,1.508883871614593,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.013275271,0.0,0.006991248,356,493,85898.0,5,100000,126762,2.556249367,39119.81408815348,4.958905873442512,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.013275271,0.01066261,0.000614395,148,221,43962.0,5,100000,43511,1.568718121,63746.315326716365,2.7736659261807555,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.026578105,0.0,0.015896007,2183,3015,504653.0,5,100000,763658,11.436205218,8744.159281315198,6.6775471884506015,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.026578105,0.018865917,0.002396844,625,988,186117.0,5,100000,190720,4.021630429,24865.53694215645,4.742355205608078,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.462830418,0.0,0.063246146,15866,21617,3.982352e6,5,100000,5409487,76.612721595,1305.2662523677573,7.060820823722102,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.462830418,0.270765344,0.009198265,2234,3977,1.138176e6,5,100000,648737,10.182445661,9820.823339427396,6.371131470750111,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 20.460232334,0.0,0.634077978,131069,176419,3.0347603e7,5,100000,44215420,628.274257022,159.16615854037505,7.03759854964927,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,20.460232334,6.930488685,0.067813145,15143,27212,6.101363e6,5,100000,4383934,69.266527038,1443.6987716323563,6.329080130717323,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,996.196988947,300.786223055,0.538602431,90592,175381,4.1886806e7,5,100000,24116153,447.573058293,223.42721070251693,5.388204797665136,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,8.3942e-5,0.0,0.004405,34,37,8624.0,5,100000,2996,0.783716111,127597.22378605025,0.3822812824630066,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,8.3942e-5,0.000134049,0.000262086,34,37,9296.0,5,100000,81,0.766053119,130539.25050333227,0.010573679290769914,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.00020201,0.0,0.001324225,280,385,97076.0,5,100000,1559,1.549350102,64543.19128447058,0.10062283521248963,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.00020201,0.001535041,0.00090682,200,285,84804.0,5,100000,1107,1.422593577,70294.14557802408,0.07781561915487266,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.003459706,0.0,0.037216462,7854,11241,1.982968e6,5,100000,59501,16.824688305,5943.646514407151,0.3536529112537399,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.003459706,0.174508516,0.022171792,4998,7671,1.507432e6,5,100000,32693,15.014079758,6660.414864701694,0.21774894317169247,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000196419,0.0,0.004471007,26,29,6532.0,6,100000,9004,0.665819145,150190.93510746077,1.3523191797075766,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000196419,0.000128257,0.0001867,26,29,6948.0,6,100000,5683,0.643209117,155470.4331095481,0.8835384713615618,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.00080887,0.0,0.00039912,77,101,19175.0,6,100000,23078,0.962923589,103850.40011726206,2.3966595339061736,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.00080887,0.000541475,0.000311862,61,79,16863.0,6,100000,16308,0.904934014,110505.2948092633,1.8021203477494658,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006566991,0.0,0.007147371,356,493,85898.0,6,100000,126762,2.307346718,43339.823711747864,5.493842733348583,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006566991,0.002805484,0.017265375,148,221,43962.0,6,100000,43511,1.303795345,76699.15403786013,3.3372568913413323,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.028135309,0.0,0.016663072,2183,3015,504653.0,6,100000,763658,9.972498107,10027.577736997207,7.6576399594798135,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.028135309,0.026806645,0.002302292,625,988,186117.0,6,100000,190720,3.676338359,27200.978319961003,5.187770585182962,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.484629127,0.0,0.056936072,15866,21617,3.982352e6,6,100000,5409487,69.113911913,1446.8867009854564,7.826914799453713,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.484629127,0.275935088,0.008667164,2234,3977,1.145088e6,6,100000,648737,9.30941058,10741.818629724676,6.968615192391697,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 20.732339707,0.0,0.628233918,131069,176419,3.0347603e7,6,100000,44215420,582.688575813,171.61826085310554,7.588173483289619,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,20.732339707,7.397597977,0.068873962,15143,27212,6.101363e6,6,100000,4383934,57.469960363,1740.0394809456222,7.628218241859865,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1075.435192418,313.241587036,0.544431835,90592,175381,4.1886806e7,6,100000,24116153,381.557577984,262.0836428629216,6.320449230079575,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,7.1909e-5,0.0,0.004495034,34,37,8624.0,6,100000,2996,0.67597446,147934.5832089573,0.4432120112940361,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,7.1909e-5,0.000141152,0.000269951,34,37,9296.0,6,100000,81,0.603840177,165606.7347105325,0.013414145511553134,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.000422796,0.0,0.001341338,280,385,69428.0,6,100000,1559,1.388725307,72008.48108401326,0.11226122200997667,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.000422796,0.001433466,0.000905117,200,285,57156.0,6,100000,1107,1.282397683,77978.93065906296,0.08632267623958269,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.003268336,0.0,0.036040866,7854,11241,1.982968e6,6,100000,59501,14.648639395,6826.572578073897,0.4061878949679749,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.003268336,0.169649995,0.021970796,4998,7671,1.507432e6,6,100000,32693,13.612503713,7346.18716059556,0.24016889684135065,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000193123,0.0,0.004418486,26,29,6532.0,7,100000,9004,0.606207547,164960.0050261334,1.4852998852553052,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000193123,0.000122947,0.00019181,26,29,6948.0,7,100000,5683,0.556301767,179758.55180053742,1.021567849882454,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000714799,0.0,0.000399752,77,101,19175.0,7,100000,23078,0.872702479,114586.58867863718,2.644429293525589,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000714799,0.000535905,0.000307143,61,79,16863.0,7,100000,16308,0.79957029,125067.17827146879,2.039595543251113,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006319495,0.0,0.006971923,356,493,85898.0,7,100000,126762,2.089060383,47868.41051305313,6.067895453455641,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006319495,0.002734156,0.000641959,148,221,43962.0,7,100000,43511,1.190928755,83968.07918203302,3.6535350932894386,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.028021922,0.0,0.017550787,2183,3015,504653.0,7,100000,763658,9.398939859,10639.497805089637,8.124937614839142,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.028021922,0.028555462,0.002317553,625,988,186117.0,7,100000,190720,3.267926454,30600.443861763848,5.836116653315601,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.512417516,0.0,0.060332671,15866,21617,3.982352e6,7,100000,5409487,63.45447959,1575.9328678783984,8.524988361660913,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.512417516,0.275001638,0.008548596,2234,3977,1.138176e6,7,100000,648737,8.402601257,11901.076457328314,7.720668637697798,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 21.498140202,0.0,0.590171518,131069,176419,3.0347603e7,7,100000,44215420,504.292730708,198.29752425660658,8.767808319966047,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,21.498140202,7.304728361,0.069172542,15143,27212,6.101363e6,7,100000,4383934,54.316946116,1841.0460666628544,8.071024447209554,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1109.530287056,308.816305574,0.516079381,90592,175381,4.1886806e7,7,100000,24116153,331.115050018,302.0098301015427,7.28331527023281,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,7.6027e-5,0.0,0.004460999,34,37,8624.0,7,100000,2996,0.487438525,205154.07558317226,0.6146416104471841,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,7.6027e-5,0.000147545,0.000260613,34,37,9296.0,7,100000,81,0.561137008,178209.59689759047,0.014434977348704829,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.00020775,0.0,0.001314627,280,385,97076.0,7,100000,1559,1.31459795,76068.8847871701,0.11859139138319819,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.00020775,0.001473052,0.000904496,200,285,84804.0,7,100000,1107,1.122185164,89111.85355859864,0.0986468218893687,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.003220766,0.0,0.036372342,7854,11241,1.982968e6,7,100000,59501,13.51947188,7396.738636509521,0.440113345610953,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.003220766,0.152428025,0.021451316,4998,7671,1.507432e6,7,100000,32693,12.509668604,7993.816876014184,0.2613418551275317,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000195387,0.0,0.004436682,26,29,6532.0,8,100000,9004,0.580562495,172246.7449434535,1.5509096914708553,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000195387,0.000130031,0.000188845,26,29,6948.0,8,100000,5683,0.500970179,199612.67993957782,1.1343988600966208,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000632661,0.0,0.000385644,77,101,19175.0,8,100000,23078,0.810776251,123338.59048863532,2.846407991296726,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000632661,0.000547797,0.00031069,61,79,16863.0,8,100000,16308,0.765485478,130636.05107346008,2.130412720905987,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006564217,0.0,0.007039925,356,493,85898.0,8,100000,126762,1.942894595,51469.59606421675,6.524388936292243,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006564217,0.003082479,0.000633532,148,221,43962.0,8,100000,43511,1.239888609,80652.40641306674,3.5092668554389466,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.042983459,0.0,0.016640412,2183,3015,504653.0,8,100000,763658,8.376172323,11938.627351948284,9.117028286334122,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.042983459,0.03871419,0.002443526,625,988,186117.0,8,100000,190720,3.025044793,33057.36173937045,6.3047000309327315,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.497971652,0.0,0.061682846,15866,21617,3.982352e6,8,100000,5409487,58.214662294,1717.7802989730078,9.292310196150599,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.497971652,0.285039568,0.008657918,2234,3977,1.145088e6,8,100000,648737,7.825655445,12778.482352413357,8.289874305857584,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 21.440469292,0.0,0.619933285,131069,176419,3.0347603e7,8,100000,44215420,420.804925975,237.63980368884987,10.507343728820045,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,21.440469292,6.814793959,0.083507684,15143,27212,6.101363e6,8,100000,4383934,49.980652717,2000.774190889805,8.771262001764304,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1026.954309236,318.915913008,0.532459221,90592,175381,4.1886806e7,8,100000,24116153,313.975960695,318.49572106936296,7.68089153915408,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,0.00879256,0.0,0.004721763,34,37,8624.0,8,100000,2996,0.510352009,195943.1886942959,0.5870457933281106,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,0.00879256,0.000145351,0.000268718,34,37,9296.0,8,100000,81,0.496736,201314.17896025252,0.016306448495780456,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.008993688,0.0,0.001454618,280,385,69428.0,8,100000,1559,1.093255124,91469.957747941,0.14260166412904005,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.008993688,0.001412807,0.000895779,200,285,57156.0,8,100000,1107,1.068619627,93578.66678973136,0.10359158413623261,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.012560102,0.0,0.035720391,7854,11241,1.982968e6,8,100000,59501,11.539769394,8665.68443317369,0.5156168894582678,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.012560102,0.182841117,0.023654133,4998,7671,1.507432e6,8,100000,32693,11.319989901,8833.930142567184,0.28880767815094893,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000192151,0.0,0.004419239,26,29,6532.0,9,100000,9004,0.499617151,200153.256948539,1.8021799255646451,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000192151,0.000144419,0.000189836,26,29,6948.0,9,100000,5683,0.473167241,211341.765310418,1.2010552522591054,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000720049,0.0,0.000390263,77,101,19175.0,9,100000,23078,0.713142859,140224.35860919137,3.2360977479829187,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000720049,0.000586912,0.000302844,61,79,16863.0,9,100000,16308,0.669478566,149369.97997931423,2.4359256335026567,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006486729,0.0,0.007169737,356,493,85898.0,9,100000,126762,1.859962653,53764.5203997545,6.81529813491368,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006486729,0.011565693,0.000634915,148,221,43962.0,9,100000,43511,1.059319005,94400.26991680377,4.107450144350048,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.027804232,0.0,0.016383501,2183,3015,504653.0,9,100000,763658,8.189393269,12210.916818287189,9.324964315619559,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.027804232,0.018959994,0.002288757,625,988,186117.0,9,100000,190720,2.808391467,35607.571513818446,6.791076039115453,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.501027171,0.0,0.060402748,15866,21617,3.982352e6,9,100000,5409487,55.95715777,1787.0814742061907,9.667194002659224,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.501027171,0.275197987,0.010019027,2234,3977,1.145088e6,9,100000,648737,7.535833401,13269.932425354582,8.608696151827255,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 20.061923933,0.0,0.631593435,131069,176419,3.0347603e7,9,100000,44215420,456.092378702,219.25382810515595,9.694400096277276,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,20.061923933,7.147906349,0.071919256,15143,27212,6.101363e6,9,100000,4383934,48.923940753,2043.9890667202242,8.960713165223058,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1070.574012771,303.932890405,0.551100765,90592,175381,4.1886806e7,9,100000,24116153,310.445583911,322.11764374354397,7.768238380518799,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,7.1638e-5,0.0,0.004635444,34,37,8624.0,9,100000,2996,0.469519075,212983.89208148784,0.6380997406761376,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,7.1638e-5,0.000154478,0.000267958,34,37,9296.0,9,100000,81,0.457044333,218797.15550482494,0.01772256959589082,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.000195107,0.0,0.001288145,280,385,69428.0,9,100000,1559,1.080429932,92555.74752070087,0.14429441038477267,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.000195107,0.001432054,0.000910126,200,285,57156.0,9,100000,1107,1.064446018,93945.58137188692,0.10399775857867882,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.003507468,0.0,0.036663988,7854,11241,1.982968e6,9,100000,59501,11.601946655,8619.24321612906,0.5128535906028951,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.003507468,0.177030041,0.022671498,4998,7671,1.507432e6,9,100000,32693,11.417097776,8758.793343279502,0.2863512307718368,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000192201,0.0,0.004471929,26,29,6532.0,10,100000,9004,0.45313443,220685.06248796853,1.9870483026416688,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000192201,0.000178705,0.000184305,26,29,6948.0,10,100000,5683,0.434670391,230059.37848662896,1.3074274479395125,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000650626,0.0,0.000389822,77,101,19175.0,10,100000,23078,0.719073683,139067.80676883706,3.209406844611222,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000650626,0.000616089,0.000327572,61,79,16863.0,10,100000,16308,0.69419122,144052.52777469586,2.3492086229497398,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006433624,0.0,0.00691854,356,493,85898.0,10,100000,126762,1.684039798,59381.01945023036,7.5272567875501,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006433624,0.002841964,0.000581732,148,221,43962.0,10,100000,43511,1.00668735,99335.70735740347,4.3221959628279825,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.027172803,0.0,0.016521661,2183,3015,504653.0,10,100000,763658,7.451972784,13419.265327257803,10.247729321283039,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.027172803,0.041021627,0.002394881,625,988,186117.0,10,100000,190720,2.746619741,36408.389012594664,6.943807952482055,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.474783115,0.0,0.064700007,15866,21617,3.982352e6,10,100000,5409487,51.220265118,1952.352252953444,10.561224131772365,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.474783115,0.30433297,0.008515192,2234,3977,1.145088e6,10,100000,648737,7.112795448,14059.169946763806,9.120703733753711,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 20.502990213,0.0,0.615116117,131069,176419,3.0347603e7,10,100000,44215420,392.698996733,254.647964043542,11.259366682330109,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,20.502990213,7.655999141,0.069640348,15143,27212,6.101363e6,10,100000,4383934,43.903968997,2277.698401409519,9.98527946368484,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1027.754171961,327.732417425,0.521515848,90592,175381,4.1886806e7,10,100000,24116153,277.563406443,360.27803982343704,8.6885203309221,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,7.2379e-5,0.0,0.004619645,34,37,8624.0,10,100000,2996,0.443378437,225540.9637794361,0.6757207274831906,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,7.2379e-5,0.000166412,0.000264781,34,37,9296.0,10,100000,81,0.420363951,237889.09529970612,0.019269016719276198,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.000437034,0.0,0.00127453,280,385,69428.0,10,100000,1559,0.967781506,103329.10825431706,0.1610900797684803,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.000437034,0.001457062,0.00090646,200,285,57156.0,10,100000,1107,0.949767711,105288.90258304433,0.11655481515943007,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.003220665,0.0,0.072880564,7854,11241,1.982968e6,10,100000,59501,11.007636322,9084.602459125466,0.5405429309204244,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.003220665,0.168780534,0.022267224,4998,7671,1.507432e6,10,100000,32693,10.635029698,9402.888646263562,0.30740863851229466,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000203011,0.0,0.004438546,26,29,6532.0,11,100000,9004,0.43307902,230904.74343458153,2.079066309884972,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000203011,0.000175709,0.000177883,26,29,6948.0,11,100000,5683,0.416968958,239826.00642420005,1.362931194508729,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000857655,0.0,0.000394191,77,101,19175.0,11,100000,23078,0.641316372,155929.27978454914,3.598535918867825,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000857655,0.000600769,0.000334005,61,79,16863.0,11,100000,16308,0.596780391,167565.82741003632,2.7326635134028723,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006490225,0.0,0.006883675,356,493,85898.0,11,100000,126762,1.660801892,60211.87745612226,7.63257801009297,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006490225,0.002768473,0.000615147,148,221,43962.0,11,100000,43511,1.038536978,96289.30131364086,4.189643789457827,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.038627779,0.0,0.016443034,2183,3015,504653.0,11,100000,763658,7.365776052,13576.301980135195,10.367651617546084,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.038627779,0.047676602,0.002288046,625,988,186117.0,11,100000,190720,2.647619556,37769.77692032125,7.20345185424367,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.482752786,0.0,0.058686491,15866,21617,3.982352e6,11,100000,5409487,49.704248059,2011.900469378349,10.883349434396077,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.482752786,0.254153975,0.009649984,2234,3977,1.145088e6,11,100000,648737,6.75425175,14805.489001798016,9.604868518559439,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 21.121444865,0.0,0.62464809,131069,176419,3.0347603e7,11,100000,44215420,438.79481545,227.89694973366167,10.07655934919274,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,21.121444865,7.186122492,0.068743552,15143,27212,6.101363e6,11,100000,4383934,44.808839824,2231.702503184185,9.783636481594257,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1077.593096899,297.354005967,0.506558376,90592,175381,4.1886806e7,11,100000,24116153,266.27345329,375.55377287682296,9.056912246424712,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,6.8913e-5,0.0,0.004442985,34,37,8624.0,11,100000,2996,0.32442652,308236.20707702934,0.9234756764027799,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,6.8913e-5,0.000162694,0.00025898,34,37,9296.0,11,100000,81,0.415785133,240508.83993488053,0.019481216034725322,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.000206098,0.0,0.001313495,280,385,69428.0,11,100000,1559,0.987170609,101299.61233479147,0.15792609562993992,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.000206098,0.001450329,0.000935615,200,285,57156.0,11,100000,1107,0.952019511,105039.8640411898,0.1162791294935971,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.003369012,0.0,0.035907999,7854,11241,1.982968e6,11,100000,59501,10.379516522,9634.360115718693,0.573254061245378,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.003369012,0.16550609,0.021617199,4998,7671,1.507432e6,11,100000,32693,10.473261621,9548.12393872501,0.31215681592873673,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000189566,0.0,0.004392718,26,29,6532.0,12,100000,9004,0.483418508,206860.09812433575,1.8625683235115191,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000189566,0.00015017,0.000190698,26,29,6948.0,12,100000,5683,0.474794125,210617.60189218854,1.1969398315533075,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.00063235,0.0,0.000405222,77,101,19175.0,12,100000,23078,0.761176533,131375.56882616086,3.03188537737014,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.00063235,0.000549831,0.000305079,61,79,16863.0,12,100000,16308,0.732970629,136431.1147588971,2.224918619488094,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006426914,0.0,0.006823249,356,493,85898.0,12,100000,126762,1.770026671,56496.32383420735,7.161587001871792,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006426914,0.003004358,0.000636378,148,221,43962.0,12,100000,43511,1.060312526,94311.81613712259,4.103601431942341,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.028221685,0.0,0.028572612,2183,3015,504653.0,12,100000,763724,7.925861447,12616.925071009256,9.635848482931472,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.028221685,0.019081115,0.002303726,625,988,186117.0,12,100000,190720,2.850211859,35085.11119418509,6.691432406954981,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.501636999,0.0,0.059006557,15866,21617,3.982352e6,12,100000,5409487,53.447711606,1870.9874940421973,10.121082526183844,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.501636999,0.274365688,0.008454246,2234,3977,1.145088e6,12,100000,648737,7.431523955,13456.190224983267,8.729528477984971,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 21.426177611,0.0,0.602913882,131069,176419,3.0347603e7,12,100000,44215420,466.11689765,214.53845699258142,9.485907982078924,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,21.426177611,6.998987577,0.066746343,15143,27212,6.101363e6,12,100000,4383934,47.535508651,2103.6905428779146,9.222440496400948,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1277.601276217,320.211942438,0.537374028,90592,175381,4.1886806e7,12,100000,24116153,279.210766456,358.15237810952647,8.63725754780319,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,7.4344e-5,0.0,0.004510293,34,37,8624.0,12,100000,2996,0.413678932,241733.36436674034,0.724233159642754,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,7.4344e-5,0.000168255,0.000274109,34,37,9296.0,12,100000,81,0.402990007,248145.11095308626,0.02009975398719999,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.000189135,0.0,0.00129061,280,385,69428.0,12,100000,1559,1.173806842,85192.8924094651,0.1328157192663561,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.000189135,0.001409239,0.000916038,200,285,57156.0,12,100000,1107,1.067306001,93693.84216551407,0.10371908327722408,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.003632179,0.0,0.036494649,7854,11241,1.982968e6,12,100000,59501,11.781685979,8487.749561331268,0.5050295866487717,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.003632179,0.160353604,0.022260904,4998,7671,1.507432e6,12,100000,32693,10.987711019,9101.07663252879,0.2975414983472637,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000190067,0.0,0.00443606,26,29,6532.0,13,100000,9004,0.547994075,182483.72484684255,1.6430834585209704,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000190067,0.000239683,0.00019697,26,29,6948.0,13,100000,5683,0.535694281,186673.63745852644,1.0608662816768057,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000692326,0.0,0.000390523,77,101,19175.0,13,100000,23078,0.773510555,129280.71808923151,2.983540412063285,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000692326,0.000669993,0.000346038,61,79,16863.0,13,100000,16308,0.732189653,136576.6363813939,2.227291786107772,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006391773,0.0,0.006974107,356,493,85898.0,13,100000,126762,1.759510745,56833.980857559356,7.20438908146594,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006391773,0.002807798,0.000618633,148,221,43962.0,13,100000,43511,1.092329881,91547.43611742322,3.9833204929052015,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.027766638,0.0,0.027217819,2183,3015,504653.0,13,100000,763724,7.929688029,12610.836597137963,9.631198569312593,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.027766638,0.028320476,0.002329986,625,988,186117.0,13,100000,190720,2.780140397,35969.40647598525,6.860085203099907,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.482710195,0.0,0.06206015,15866,21617,3.982352e6,13,100000,5409487,51.839821213,1929.0189985246855,10.435003195272305,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.482710195,0.28921717,0.008750996,2234,3977,1.145088e6,13,100000,648737,7.412424255,13490.862983530074,8.752021979346349,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 21.293659591,0.0,0.590692775,131069,176419,3.0347603e7,13,100000,44215420,432.433232805,231.24957198905588,10.22479695031634,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,21.293659591,7.131638858,0.069339076,15143,27212,6.101363e6,13,100000,4383934,47.786343106,2092.648097766747,9.174031145834967,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1273.316510634,335.674993987,0.526574681,90592,175381,4.1886806e7,13,100000,24116153,276.276950121,361.9556389203057,8.728977567414848,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,6.6799e-5,0.0,0.004478593,34,37,8624.0,13,100000,2996,0.423255672,236263.81550298515,0.7078463912469435,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,6.6799e-5,0.000204415,0.000288797,34,37,9296.0,13,100000,81,0.408583807,244747.82966619133,0.019824574202961496,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.000203362,0.0,0.00130099,280,385,69428.0,13,100000,1559,1.122865416,89057.86800009522,0.13884121621214843,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.000203362,0.001497029,0.000891972,200,285,57156.0,13,100000,1107,1.020172954,98022.59470603452,0.1085110123395802,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.003168585,0.0,0.035867809,7854,11241,1.982968e6,13,100000,59501,12.393978637,8068.43411053396,0.48007989801088113,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.003168585,0.163690849,0.021576369,4998,7671,1.507432e6,13,100000,32693,11.010561284,9082.189129205886,0.29692400920112805,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.00018669,0.0,0.004397457,26,29,6532.0,14,100000,9004,0.527073004,189727.03826811817,1.708302252566136,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.00018669,0.000324185,0.000194946,26,29,6948.0,14,100000,5683,0.458397399,218151.3250689278,1.2397539803667166,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.00069971,0.0,0.000378761,77,101,19175.0,14,100000,23078,0.714559165,139946.42417048838,3.2296835770065306,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.00069971,0.000598515,0.000293827,61,79,16863.0,14,100000,16308,0.66240769,150964.43098358353,2.4619279404802805,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006402956,0.0,0.00695377,356,493,85898.0,14,100000,126762,1.710281995,58469.88993180624,7.411760187535623,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006402956,0.002759405,0.000600759,148,221,43962.0,14,100000,43511,1.014717235,98549.62205308359,4.28799260515172,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.032679416,0.0,0.016512948,2183,3015,504653.0,14,100000,763658,7.828665801,12773.568643998884,9.7546378835389,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.032679416,0.020024394,0.002360496,625,988,186117.0,14,100000,190720,2.754124738,36309.17605882236,6.9248860579386005,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.460803463,0.0,0.063617462,15866,21617,3.982352e6,14,100000,5409487,53.318832953,1875.5099176335868,10.14554651780996,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.460803463,0.277162604,0.008708737,2234,3977,1.138176e6,14,100000,648737,7.348664671,13607.914427587031,8.827957582009526,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 21.631277771,0.0,0.603453127,131069,176419,3.0347603e7,14,100000,44215420,492.807533409,202.91897590982268,8.97214774582269,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,21.631277771,8.014043848,0.077142734,15143,27212,6.101363e6,14,100000,4383934,48.363597019,2067.670855017551,9.064532562120512,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1004.863551823,371.561277878,0.559492832,90592,175381,4.1886806e7,14,100000,24116153,287.505533129,347.81939294062664,8.388065696523272,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,0.000165329,0.0,0.004508541,34,37,8624.0,14,100000,2996,0.48208598,207431.87760822248,0.6214659053142345,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,0.000165329,0.000199836,0.000276263,34,37,9296.0,14,100000,81,0.380482809,262823.96374969993,0.021288741063725695,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.009012974,0.0,0.001376105,280,385,69428.0,14,100000,1559,1.131267759,88396.40235870985,0.13780999127722865,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.009012974,0.010351988,0.000909896,200,285,57156.0,14,100000,1107,1.023356495,97717.6580092942,0.10817344741628869,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.012403858,0.0,0.037485522,7854,11241,1.982968e6,14,100000,59501,12.151121801,8229.692833115236,0.48967495326318966,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.012403858,0.172663397,0.023039674,4998,7671,1.507432e6,14,100000,32693,10.867387443,9201.843637627266,0.3008358740449482,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000202691,0.0,0.004543188,26,29,6532.0,15,100000,9004,0.473289592,211287.13094540226,1.9024293270324018,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000202691,0.000320078,0.000190136,26,29,6948.0,15,100000,5683,0.347731884,287577.8857253136,1.6343051245769573,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000921408,0.0,0.000428156,77,101,19175.0,15,100000,23078,0.596355302,167685.27028204405,3.8698406675690125,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000921408,0.000675864,0.000329456,61,79,16863.0,15,100000,16308,0.567362661,176254.10848106552,2.8743520011092163,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006585229,0.0,0.007174396,356,493,85898.0,15,100000,126762,1.61234507,62021.46293659086,7.8619646847681315,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006585229,0.003182472,0.00066316,148,221,43962.0,15,100000,43511,0.897758569,111388.52187330111,4.846625975229205,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.028997821,0.0,0.017354753,2183,3015,504653.0,15,100000,763658,6.913065187,14465.363380060371,11.046590468090143,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.028997821,0.027657896,0.002407135,625,988,186117.0,15,100000,190720,2.435452561,41060.130507711416,7.830988090430721,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.492174748,0.0,0.059349767,15866,21617,3.982352e6,15,100000,5409487,46.812768582,2136.16931937777,11.555580162972895,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.492174748,0.269955216,0.032080581,2234,3977,1.138176e6,15,100000,648737,6.667653226,14997.780569939916,9.729615173601111,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 22.643020237,0.0,0.636924565,131069,176419,3.0347603e7,15,100000,44215420,424.818800537,235.3944784778667,10.408065731579836,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,22.643020237,7.985771306,0.072474025,15143,27212,6.101363e6,15,100000,4383934,44.334372178,2255.5862435246777,9.888341222920115,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1485.530249489,397.658153187,0.638985585,90592,175381,4.1886806e7,15,100000,24116153,269.663356096,370.8327354807528,8.943058986262361,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,0.000209875,0.0,0.00492289,34,37,8624.0,15,100000,2996,0.338031835,295830.1249939965,0.8863070544820136,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,0.000209875,0.000229513,0.00028484,34,37,9296.0,15,100000,81,0.336089426,297539.85774012416,0.024100728476950058,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.009123376,0.0,0.001690262,280,385,69428.0,15,100000,1559,1.057567801,94556.58531343656,0.1474137165036476,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.009123376,0.001499313,0.000924644,200,285,57156.0,15,100000,1107,0.904579185,110548.64146581042,0.12237734610265213,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.012292082,0.0,0.038656782,7854,11241,1.982968e6,15,100000,59501,11.503757351,8692.8120047062,0.5172310070920236,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.012292082,0.151905146,0.023436589,4998,7671,1.507432e6,15,100000,32693,10.327723176,9682.676258440411,0.3165557349171924,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.00021785,0.0,0.004706243,26,29,6532.0,16,100000,9004,0.445157112,224639.7896480198,2.0226566659907705,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.00021785,0.000230936,0.000219173,26,29,6948.0,16,100000,5683,0.430360336,232363.42114948065,1.3205213223924985,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000654273,0.0,0.000412897,77,101,19175.0,16,100000,23078,0.70587896,141667.3476143842,3.269399048244759,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000654273,0.000666236,0.000331079,61,79,16863.0,16,100000,16308,0.65326842,153076.43372688978,2.496370481218119,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006661125,0.0,0.00739416,356,493,85898.0,16,100000,126762,1.667412207,59973.172548568255,7.602319298601609,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006661125,0.003100975,0.000661416,148,221,43962.0,16,100000,43511,0.962123267,103936.7858879563,4.522393490770867,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.028562832,0.0,0.016842333,2183,3015,504653.0,16,100000,763868,7.366911173,13574.210093166817,10.368904715447151,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.028562832,0.029729073,0.002601641,625,988,186117.0,16,100000,190720,2.634451943,37958.55918560591,7.23945640787876,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.516360245,0.0,0.076747543,15866,21617,3.982352e6,16,100000,5409487,49.351015764,2026.3007448156077,10.961247537170347,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.516360245,0.301078852,0.009558346,2234,3977,1.138176e6,16,100000,648737,6.847931323,14602.950187910346,9.473474096054394,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 25.939934347,0.0,0.733047632,131069,176419,3.0347603e7,16,100000,44215420,491.777573424,203.34396158765492,8.990938666062029,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,25.939934347,8.631827729,0.087097207,15143,27212,6.101363e6,16,100000,4383934,47.6305863,2099.491267442156,9.204031150042761,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1018.788654921,349.205570635,0.589884785,90592,175381,4.1886806e7,16,100000,24116153,279.01475952,358.40397895808064,8.643325192361853,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,7.4714e-5,0.0,0.004896817,34,37,8624.0,16,100000,2996,0.341596256,292743.2553593328,0.877058793056561,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,7.4714e-5,0.000208412,0.000282656,34,37,9296.0,16,100000,81,0.425742198,234883.92851300118,0.019025598209553095,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.000189145,0.0,0.001344022,280,385,69428.0,16,100000,1559,1.04091459,96069.36146413318,0.14977213452258364,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.000189145,0.001545932,0.000962788,200,285,57156.0,16,100000,1107,0.966884694,103424.94882848978,0.1144914183531382,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.003313152,0.0,0.039354251,7854,11241,1.982968e6,16,100000,59876,11.327704054,8827.914246637503,0.5285801934316672,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.003313152,0.181675267,0.023872797,4998,7671,1.507432e6,16,100000,32693,10.187305474,9816.138355251995,0.32091901124825345,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000204324,0.0,0.004517888,26,29,6532.0,17,100000,9004,0.445654406,224389.1200303762,2.020399636753507,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000204324,0.000252147,0.000211478,26,29,6948.0,17,100000,5683,0.410519847,243593.58196876655,1.3843423263285002,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000668741,0.0,0.000443246,77,101,19175.0,17,100000,23078,0.734380018,136169.28231835415,3.142514697342977,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000668741,0.010516274,0.00033681,61,79,16863.0,17,100000,16308,0.688909173,145157.01622106286,2.367220620533093,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.0067054,0.0,0.007253146,356,493,85898.0,17,100000,126762,1.614123061,61953.1449715159,7.853304562879299,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.0067054,0.002838497,0.000685182,148,221,43962.0,17,100000,43511,0.987985459,101216.06455748454,4.40401218496071,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.035435199,0.0,0.017731226,2183,3015,504653.0,17,100000,763724,6.980259274,14326.11541701309,10.941198170742904,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.035435199,0.021006666,0.002401755,625,988,186117.0,17,100000,190720,2.472852313,40439.13155439623,7.712551170054448,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.541442108,0.0,0.061882985,15866,21617,3.982352e6,17,100000,5409487,46.233916066,2162.9143388426724,11.70025699808303,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.541442108,0.293481088,0.009062498,2234,3977,1.145088e6,17,100000,648737,6.636799281,15067.504043143594,9.774847370436845,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 25.279624872,0.0,0.698198729,131069,176419,3.0347603e7,17,100000,44215420,426.554493162,234.43663495069845,10.365714277731811,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,25.279624872,7.203989148,0.076809539,15143,27212,6.101363e6,17,100000,4383934,43.245261875,2312.392055551635,10.137374153662703,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1303.028701647,315.773847431,0.549036859,90592,175381,4.1886806e7,17,100000,24116153,250.493910178,399.21130189927726,9.62744083593216,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,7.3732e-5,0.0,0.004866481,34,37,8624.0,17,100000,2996,0.32696764,305840.6636204121,0.9162986282067547,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,7.3732e-5,0.000468063,0.000258529,34,37,9296.0,17,100000,81,0.31206863,320442.3334700447,0.025955829011073624,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.000208843,0.0,0.001385504,280,385,69428.0,17,100000,1559,0.908598646,110059.59610465897,0.17158291032716333,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.000208843,0.00204185,0.000921047,200,285,57156.0,17,100000,1107,0.813174128,122974.89130150978,0.13613320467077134,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.00405205,0.0,0.040316398,7854,11241,1.982968e6,17,100000,59501,11.695236098,8550.490059546637,0.5087627090330844,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.00405205,0.179589539,0.024358764,4998,7671,1.507432e6,17,100000,32693,9.799341759,10204.767060823968,0.333624449519518,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000200797,0.0,0.004519631,26,29,6532.0,18,100000,9004,0.339515342,294537.49986944627,2.652015648824494,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000200797,0.000499213,0.000200947,26,29,6948.0,18,100000,5683,0.402154105,248660.89580261777,1.4131398708462768,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000905517,0.0,0.000413669,77,101,19175.0,18,100000,23078,0.68732477,145491.62836078205,3.357655799310128,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000905517,0.000730469,0.000315138,61,79,16863.0,18,100000,16308,0.545751821,183233.47014539785,2.9881714311311485,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006653348,0.0,0.007026629,356,493,85898.0,18,100000,126762,1.566665018,63829.8544047787,8.091200004058557,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006653348,0.00330121,0.000656176,148,221,43962.0,18,100000,43511,0.878339556,113851.18581634275,4.953778946054889,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.029153787,0.0,0.016601616,2183,3015,504653.0,18,100000,763658,6.950765677,14386.90421271124,10.986674497270641,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.029153787,0.05377634,0.002536926,625,988,186117.0,18,100000,190720,2.33175583,42886.13701032325,8.17924405060885,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.582735557,0.0,0.071983304,15866,21617,3.982352e6,18,100000,5409487,47.202414306,2118.5357035283846,11.46019134727265,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.582735557,0.294595232,0.009367837,2234,3977,1.145088e6,18,100000,648737,6.469811286,15456.401366202075,10.027139453105836,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 26.210031525,0.0,0.691078455,131069,176419,3.0347603e7,18,100000,44215420,382.223052854,261.627338417491,11.5679626516115,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,26.210031525,7.637359227,0.075329431,15143,27212,6.101363e6,18,100000,4383934,40.687638293,2457.7489428086133,10.774609153842736,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1440.310788852,366.525255894,0.588198648,90592,175381,4.1886806e7,18,100000,24116153,252.867478334,395.4640614872388,9.537071812827657,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,0.008546751,0.0,0.005411528,34,37,8624.0,18,100000,2996,0.309817259,322770.9144505729,0.9670216596939164,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,0.008546751,0.000270081,0.000281553,34,37,9296.0,18,100000,81,0.428070756,233606.24055337245,0.018922105484823166,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.000194335,0.0,0.001407287,280,385,69428.0,18,100000,1559,0.967821986,103324.78642410175,0.16108334203517463,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.000194335,0.002010812,0.000964292,200,285,57156.0,18,100000,1107,0.927882287,107772.29116348032,0.11930392631797271,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.012187129,0.0,0.040607299,7854,11241,1.982968e6,18,100000,59501,11.250098869,8888.810770859369,0.5288931296769033,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.012187129,0.170900529,0.023162198,4998,7671,1.507432e6,18,100000,32693,9.690556975,10319.324292502806,0.3373696690947942,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.00020186,0.0,0.004519896,26,29,6532.0,19,100000,9004,0.41413132,241469.3001244146,2.174189578320229,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.00020186,0.000516958,0.000187271,26,29,6948.0,19,100000,5683,0.299569181,333812.7095256838,1.897057628234461,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000878145,0.0,0.000417847,77,101,19175.0,19,100000,23078,0.651422135,153510.28868553875,3.542710442284863,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000878145,0.000736833,0.000331259,61,79,16863.0,19,100000,16308,0.544147214,183773.7976546913,2.9969830921527056,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.006877918,0.0,0.007123874,356,493,85898.0,19,100000,126762,1.458224311,68576.55522930039,8.692901293976576,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.006877918,0.011849797,0.000624075,148,221,43962.0,19,100000,43511,0.852092557,117358.14281968902,5.1063701522274885,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.085399356,0.0,0.018310871,2183,3015,504653.0,19,100000,763658,6.637971971,15064.842159153492,11.504387233574837,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.085399356,0.021113683,0.00254313,625,988,186117.0,19,100000,190720,2.411972756,41459.83811435721,7.907220325170207,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.607280651,0.0,0.063307163,15866,21617,3.982352e6,19,100000,5409487,44.735065778,2235.38287606986,12.092274608122517,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.607280651,0.307961491,0.010492587,2234,3977,1.145088e6,19,100000,648737,6.334775639,15785.878726998748,10.240883607716988,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 23.320951934,0.0,0.693430599,131069,176419,3.0347603e7,19,100000,44215420,401.881428291,248.82961231935948,11.002105817137654,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,23.320951934,8.541698254,0.074750241,15143,27212,6.101363e6,19,100000,4383934,41.849364229,2389.522561269971,10.475509200118509,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1510.327292637,352.109391098,0.559711443,90592,175381,4.1886806e7,19,100000,24116153,252.7304947,395.67840880738794,9.542241045595514,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,6.7811e-5,0.0,0.004609839,34,37,8624.0,19,100000,2996,0.291110435,343512.2481954314,1.0291626955935125,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,6.7811e-5,0.000267526,0.000275612,34,37,9296.0,19,100000,81,0.402995661,248141.6294951126,0.020099471989104122,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.000188534,0.0,0.001300941,280,385,69428.0,19,100000,1559,0.912485361,109590.79923255887,0.1708520560035593,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.000188534,0.001636229,0.000925687,200,285,57156.0,19,100000,1107,0.883178546,113227.38811184844,0.12534271863981622,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.003363252,0.0,0.044650314,7854,11241,1.982968e6,19,100000,59501,11.140588158,8976.186766960818,0.5340920888209356,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.003363252,0.184699007,0.022146943,4998,7671,1.507432e6,19,100000,32693,9.337544845,10709.453251359459,0.35012415514669476,none,0.0,0.0,0.0
+QED Process: 'ke->ke' not optimized tape, 0.000207631,0.0,0.004728839,26,29,6532.0,20,100000,9004,0.392654728,254676.67359910154,2.2931087690863103,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced tape,0.000207631,0.000541655,0.000193453,26,29,6948.0,20,100000,5683,0.401698527,248942.90936745206,1.41474255393523,none,0.0,0.0,0.0
+QED Process: 'ke->kke' not optimized tape, 0.000755719,0.0,0.000411374,77,101,19175.0,20,100000,23078,0.608986178,164207.33936591906,3.78957697788668,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced tape,0.000755719,0.000786648,0.000320689,61,79,16863.0,20,100000,16308,0.561425046,178118.16681936916,2.904751064490272,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' not optimized tape, 0.00680686,0.0,0.007280525,356,493,85898.0,20,100000,126762,1.516938227,65922.26250225547,8.356437839310908,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced tape,0.00680686,0.00329476,0.000682818,148,221,43962.0,20,100000,43511,0.855509301,116889.43636627978,5.0859762657332,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' not optimized tape, 0.035807443,0.0,0.018407324,2183,3015,504653.0,20,100000,763658,6.483258145,15424.343403188675,11.77892323459226,none,0.0,0.0,0.0
+QED Process: 'ke->kkkke' reduced tape,0.035807443,0.029869831,0.002495287,625,988,186117.0,20,100000,190720,2.344648014,42650.325082014635,8.134269999641832,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' not optimized tape, 0.500300279,0.0,0.071999229,15866,21617,3.982352e6,20,100000,5409487,44.308437428,2256.9064901577103,12.208706318723763,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkke' reduced tape,0.500300279,0.28806712,0.009827571,2234,3977,1.138176e6,20,100000,648737,5.958160655,16783.703191366865,10.888209257257767,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' not optimized tape, 25.051627576,0.0,0.693667467,131069,176419,3.0347603e7,20,100000,44215420,422.526537587,236.6715249912784,10.464530879529871,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkke' reduced tape,25.051627576,7.237220203,0.078058525,15143,27212,6.101363e6,20,100000,4383934,42.190217391,2370.2176993601356,10.390877959626676,none,0.0,0.0,0.0
+QED Process: 'ke->kkkkkkke' reduced tape,1196.394580677,340.587143784,0.578833843,90592,175381,4.1886806e7,20,100000,24116154,279.106526191,358.28614029457464,8.640483735409568,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' not optimized tape,9.1416e-5,0.0,0.004836266,34,37,8624.0,20,100000,2996,0.38678703,258540.21009959927,0.7745864694583994,none,0.0,0.0,0.0
+ABC Process: 'AB->AB' reduced tape,9.1416e-5,0.000329175,0.000266465,34,37,9296.0,20,100000,81,0.359330419,278295.3925200527,0.022541926794124267,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' not optimized tape,0.000265963,0.0,0.001384653,280,385,69428.0,20,100000,1559,0.892257011,112075.33117383372,0.17472544130000678,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBB' reduced tape,0.000265963,0.001669343,0.000980082,200,285,57156.0,20,100000,1107,0.841548395,118828.57907417195,0.13154323703510837,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' not optimized tape,0.004729409,0.0,0.041125808,7854,11241,1.982968e6,20,100000,59504,9.909170632,10091.661927494397,0.6004942513336267,none,0.0,0.0,0.0
+ABC Process: 'AB->ABBBBB' reduced tape,0.004729409,0.196479377,0.023861131,4998,7671,1.507432e6,20,100000,32693,9.075344922,11018.86494226627,0.36023975155751115,none,0.0,0.0,0.0

data/singularity_homepc_results.csv

@@ -0,0 +1,97 @@
+process_name,graph_gen_time,optimization_time,function_generation_time,graph_nodes,graph_edges,graph_mem,cpu_threads,n_inputs,nflops_likwid,cpu_time,cpu_rate,cpu_gflops,gpu_name,gpu_time,gpu_rate,gpu_gflops
+QED Process: 'ke->ke' no optimization,0.000221518,0.0,0.076346293,26,29,6532.0,1,100000,5683,0.086186253,1.1602778461664878e6,6.59385899976415,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000221518,0.000117106,0.003614977,26,29,6948.0,1,100000,5683,0.086626002,1.1543878014825156e6,6.560385875825136,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.00066327,0.0,0.084021406,77,101,19175.0,1,100000,23078,0.270498122,369688.333732683,8.531667365882857,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.00066327,0.029167501,0.006483402,61,79,16863.0,1,100000,16308,0.181935913,549644.0936320252,8.963595878951066,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.006063462,0.0,0.035553646,356,493,85898.0,1,100000,120271,1.199812544,83346.35314497928,10.024149239099803,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.006063462,0.002954241,0.013902962,148,221,43962.0,1,100000,43511,0.435115663,229823.9491323483,9.999869850697607,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.000235685,0.0,0.075679887,26,29,6532.0,2,100000,5683,0.055355402,1.8065084235139329e6,10.26638737082968,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000235685,9.8981e-5,0.003594457,26,29,6948.0,2,100000,5683,0.055994886,1.7858773745873864e6,10.149141119780117,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.00065845,0.0,0.082042796,77,101,19175.0,2,100000,23078,0.160231685,624096.2890704169,14.402894159167081,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.00065845,0.028895496,0.006503071,61,79,16863.0,2,100000,16308,0.106436305,939529.0450941528,15.321839667395443,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.005661736,0.0,0.034808678,356,493,85898.0,2,100000,120271,0.620175294,161244.73349304366,19.393065341941853,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005661736,0.002755388,0.013644252,148,221,43962.0,2,100000,43511,0.228774759,437111.15875331336,19.01914362851542,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.000218101,0.0,0.076264355,26,29,6532.0,3,100000,5683,0.050665491,1.9737300088535608e6,11.216707640314786,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000218101,0.000128448,0.003242828,26,29,6948.0,3,100000,5683,0.072984976,1.3701450008012608e6,7.786534039553565,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.000695342,0.0,0.097129092,77,101,19175.0,3,100000,23078,0.119935587,833780.8860684527,19.24199528868775,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000695342,0.029709036,0.006407135,61,79,16863.0,3,100000,16308,0.087404054,1.1441116907460608e6,18.65817345268676,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.022064122,0.0,0.03663888,356,493,85898.0,3,100000,120271,0.476353198,209928.2641952579,25.248282263027868,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.022064122,0.010551003,0.013701032,148,221,43962.0,3,100000,43511,0.170405831,586834.3789245099,25.53375066138435,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.00021267,0.0,0.086773717,26,29,6532.0,4,100000,5683,0.041951463,2.3837070950302733e6,13.546607421057043,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.00021267,0.000121484,0.003464937,26,29,6948.0,4,100000,5683,0.043205825,2.314502731981162e6,13.153319025848944,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.000684641,0.0,0.085586085,77,101,19175.0,4,100000,23078,0.091246099,1.0959372630275406e6,25.292040156149582,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000684641,0.05730277,0.006948781,61,79,16863.0,4,100000,16308,0.068751105,1.4545220764088081e6,23.720346022074846,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.005607071,0.0,0.036123215,356,493,85898.0,4,100000,120271,0.335336275,298208.1195957699,35.86578875190284,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005607071,0.002691243,0.013817787,148,221,43962.0,4,100000,43511,0.134833158,741657.3303133639,32.27025209926478,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.00023815,0.0,0.080547541,26,29,6532.0,5,100000,5683,0.041168092,2.429065694859018e6,13.8043803438838,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.00023815,0.000153696,0.003356137,26,29,6948.0,5,100000,5683,0.045756827,2.185466225619185e6,12.420004560193826,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.000897943,0.0,0.098053657,77,101,19175.0,5,100000,23078,0.080404746,1.2437076786487205e6,28.702285807855173,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000897943,0.000581051,0.006567074,61,79,16863.0,5,100000,16308,0.08312713,1.202976693649835e6,19.618143920041508,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.00574661,0.0,0.037455126,356,493,85898.0,5,100000,120271,0.283356036,352912.89859800274,42.445187227280385,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.00574661,0.003115262,0.014315688,148,221,43962.0,5,100000,43511,0.115244153,867722.9811390084,37.75549463233939,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.000224744,0.0,0.076885463,26,29,6532.0,6,100000,5683,0.03953493,2.529408803809694e6,14.37463023205049,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000224744,0.000138508,0.003362109,26,29,6948.0,6,100000,5683,0.084441256,1.184255241300532e6,6.7301225363109225,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.000718106,0.0,0.094876895,77,101,19175.0,6,100000,23078,0.076512764,1.306971474720218e6,30.16228769359319,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000718106,0.029791235,0.006595418,61,79,16863.0,6,100000,16308,0.056293132,1.7764156380568768e6,28.969786225431548,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.005668259,0.0,0.036226264,356,493,85898.0,6,100000,120271,0.24165661,413810.32366546895,49.76938143756962,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005668259,0.002705742,0.01385029,148,221,43962.0,6,100000,43511,0.102296354,977551.9467683081,42.534262755835854,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.000224073,0.0,0.076151638,26,29,6532.0,7,100000,5683,0.039683036,2.5199684822501987e6,14.32098088462788,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000224073,0.000137366,0.003257647,26,29,6948.0,7,100000,5683,0.044023983,2.2714891562628485e6,12.90887287504177,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.000693579,0.0,0.117181072,77,101,19175.0,7,100000,23078,0.08102353,1.2342093710308599e6,28.483083864650183,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000693579,0.052699947,0.00657028,61,79,16863.0,7,100000,16308,0.062383365,1.6029914385028766e6,26.141584379104913,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.005981163,0.0,0.03714658,356,493,85898.0,7,100000,120271,0.284440029,351567.9574058826,42.2834298051629,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005981163,0.002827226,0.013832877,148,221,43962.0,7,100000,43511,0.12095232,826772.0701843504,35.97367954579127,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.000227358,0.0,0.087982831,26,29,6532.0,8,100000,5683,0.038577702,2.592170990381957e6,14.731307738340663,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000227358,0.000131283,0.00358018,26,29,6948.0,8,100000,5683,0.037625264,2.6577886603001645e6,15.104212956485835,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.000686625,0.0,0.086321324,77,101,19175.0,8,100000,23078,0.071813645,1.3924930283095923e6,32.13595410732877,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000686625,0.032879545,0.006435109,61,79,16863.0,8,100000,16308,0.058067196,1.722142739594314e6,28.084703797304073,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.006248709,0.0,0.036577372,356,493,85898.0,8,100000,120271,0.256489446,389879.5898214073,46.891208147410474,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.006248709,0.002962728,0.014268867,148,221,43962.0,8,100000,43511,0.108013889,925806.8654485721,40.28278252253282,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.000211057,0.0,0.07707584,26,29,6532.0,9,100000,5683,0.036530301,2.7374534910073695e6,15.55694818939488,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000211057,0.000162875,0.003619465,26,29,6948.0,9,100000,5683,0.036196266,2.762715911083204e6,15.70051452268585,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.000669602,0.0,0.110030151,77,101,19175.0,9,100000,23078,0.059213688,1.6887987115411558e6,38.97409666494679,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000669602,0.000557426,0.006374502,61,79,16863.0,9,100000,16308,0.047210683,2.118164653538268e6,34.54302916990208,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.005898744,0.0,0.036433113,356,493,85898.0,9,100000,120271,0.171036178,584671.6242688724,70.31904092244156,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005898744,0.002558788,0.01376731,148,221,43962.0,9,100000,43511,0.082465833,1.2126234145964426e6,52.762457392505816,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.000224924,0.0,0.077441757,26,29,6532.0,10,100000,5683,0.036579646,2.73376073677695e6,15.535962267103406,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000224924,0.000139469,0.003645977,26,29,6948.0,10,100000,5683,0.106126326,942273.2678035042,5.354938980927315,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.000679782,0.0,0.102684554,77,101,19175.0,10,100000,23078,0.063933026,1.5641368203031716e6,36.09714953895659,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000679782,0.02384501,0.006682196,61,79,16863.0,10,100000,16308,0.051995087,1.923258634032096e6,31.36450180379542,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.018473242,0.0,0.035702944,356,493,85898.0,10,100000,120271,0.209342666,477685.70980174677,57.451738003565886,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.018473242,0.002601901,0.013714899,148,221,43962.0,10,100000,43511,0.091342875,1.0947761388066665e6,47.63480457561687,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.000226858,0.0,0.093169541,26,29,6532.0,11,100000,5683,0.033549598,2.9806616460799323e6,16.939100134672255,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000226858,0.000146002,0.003515996,26,29,6948.0,11,100000,5683,0.03517745,2.8427302149530454e6,16.15523581157816,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.000706774,0.0,0.084382302,77,101,19175.0,11,100000,23078,0.060738871,1.6463921431796122e6,37.995437880299086,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000706774,0.023541413,0.006270281,61,79,16863.0,11,100000,16308,0.050268545,1.9893155849249267e6,32.441758558955705,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.005735379,0.0,0.039783449,356,493,85898.0,11,100000,120271,0.195017069,512775.62786055414,61.67203753841671,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.005735379,0.00275681,0.013533609,148,221,43962.0,11,100000,43511,0.085348426,1.171667770416762e6,50.98043635860373,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.000227249,0.0,0.077273713,26,29,6532.0,12,100000,5683,0.034006851,2.9405839429237363e6,16.711338547635595,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000227249,0.000162082,0.003808429,26,29,6948.0,12,100000,5683,0.034761157,2.876774210938951e6,16.348707840766057,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.000671376,0.0,0.086502994,77,101,19175.0,12,100000,23078,0.060896495,1.6421306349404838e6,37.89709079315649,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000671376,0.0005545,0.00638866,61,79,16863.0,12,100000,16308,0.053085842,1.8837414314724442e6,30.720055264452622,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.00589155,0.0,0.036595917,356,493,85898.0,12,100000,120271,0.183184673,545897.1995981345,65.65560209286723,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.00589155,0.002941467,0.0140628,148,221,43962.0,12,100000,43511,0.082717269,1.2089373985497516e6,52.60207514829824,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.00020243,0.0,0.07351055,26,29,6532.0,13,100000,5683,0.03426045,2.9188174702900867e6,16.587639683658562,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.00020243,0.00018666,0.003180458,26,29,6948.0,13,100000,5683,0.036528437,2.73759317980126e6,15.557742040810561,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.000649463,0.0,0.085458859,77,101,19175.0,13,100000,23078,0.056745574,1.7622519775727354e6,40.66925113842358,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000649463,0.023744455,0.006343052,61,79,16863.0,13,100000,16308,0.048610134,2.0571842077209663e6,33.54856005951352,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.016563426,0.0,0.035803778,356,493,85898.0,13,100000,120271,0.171455937,583240.2292374396,70.1468856106161,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.016563426,0.002889105,0.013906849,148,221,43962.0,13,100000,43511,0.079703702,1.2546468669673586e6,54.59093982861675,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.000215617,0.0,0.075539676,26,29,6532.0,14,100000,5683,0.034475014,2.9006514689160096e6,16.484402297849684,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000215617,0.000175659,0.003260683,26,29,6948.0,14,100000,5683,0.035111653,2.8480573102041082e6,16.185509693889948,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.000659363,0.0,0.084012087,77,101,19175.0,14,100000,23078,0.053867069,1.8564217778398155e6,42.842501788987256,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000659363,0.024033773,0.006425781,61,79,16863.0,14,100000,16308,0.046639671,2.1440974572912403e6,34.96594133350555,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.006857645,0.0,0.036011529,356,493,85898.0,14,100000,120271,0.158956374,629103.4293472245,75.66289855102004,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.006857645,0.010993406,0.013796697,148,221,43962.0,14,100000,43511,0.076985656,1.2989432732767777e6,56.51832076354587,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.000236356,0.0,0.075072915,26,29,6532.0,15,100000,5683,0.036551101,2.735895698463365e6,15.548095254367304,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000236356,0.000311852,0.003495446,26,29,6948.0,15,100000,5683,0.036288895,2.755663957251936e6,15.660438269062753,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.000688499,0.0,0.083327476,77,101,19175.0,15,100000,23078,0.05833869,1.714128308331915e6,39.55865309968393,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000688499,0.031409148,0.00639916,61,79,16863.0,15,100000,16308,0.048503318,2.0617146233171101e6,33.62244207705543,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.044098897,0.0,0.035616548,356,493,85898.0,15,100000,120271,0.174533677,572955.3271257788,68.90991014874454,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.044098897,0.002820964,0.013448835,148,221,43962.0,15,100000,43511,0.082111068,1.217862615061833e6,52.99042024395542,none,0.0,0.0,0.0
+QED Process: 'ke->ke' no optimization,0.000206569,0.0,0.081030603,26,29,6532.0,16,100000,5683,0.035064231,2.8519091150180935e6,16.207399500647824,none,0.0,0.0,0.0
+QED Process: 'ke->ke' reduced,0.000206569,0.000323635,0.0034872,26,29,6948.0,16,100000,5683,0.03428592,2.916649166771666e6,16.575317214763377,none,0.0,0.0,0.0
+QED Process: 'ke->kke' no optimization,0.000683149,0.0,0.083208997,77,101,19175.0,16,100000,23078,0.054342847,1.8401685874131697e6,42.46741066032113,none,0.0,0.0,0.0
+QED Process: 'ke->kke' reduced,0.000683149,0.028225894,0.00650278,61,79,16863.0,16,100000,16308,0.046233237,2.1629461073642755e6,35.27332511889661,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' no optimization,0.020724006,0.0,0.036160978,356,493,85898.0,16,100000,120271,0.237323357,421366.0267750215,50.67811340625861,none,0.0,0.0,0.0
+QED Process: 'ke->kkke' reduced,0.020724006,0.00273602,0.013774424,148,221,43962.0,16,100000,43511,0.077327366,1.293203236742863e6,56.26856603391871,none,0.0,0.0,0.0

docs/Project.toml

@@ -2,3 +2,4 @@
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 DocumenterTools = "35a29f4d-8980-5a13-9543-d66fff28ecb8"
 MetagraphOptimization = "3e869610-d48d-4942-ba70-c1b702a33ca4"
+QEDprocesses = "46de9c38-1bb3-4547-a1ec-da24d767fdad"

examples/Project.toml

@@ -5,5 +5,6 @@ CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
 DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
 MetagraphOptimization = "3e869610-d48d-4942-ba70-c1b702a33ca4"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+QEDbase = "10e22c08-3ccb-4172-bfcf-7d7aa3d04d93"
 QEDprocesses = "46de9c38-1bb3-4547-a1ec-da24d767fdad"
 StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"

examples/full_node_bench.jl

@@ -0,0 +1,245 @@
+using MetagraphOptimization
+using CUDA
+using UUIDs
+using DataFrames
+using CSV
+using Random
+using BenchmarkTools
+using Dates
+
+using Base.Threads
+
+
+function log(x...)
+    println(now(), " ", join(x, " ")...)
+    #flush(stdout)
+    return nothing
+end
+
+results_filename = "full_node_bench.csv"
+
+df = DataFrame(
+    process_name = String[],
+    cpu_threads = Int[],
+    gpu_devices = Int[],
+    n_inputs = Int[],
+    chunk_size = Int[],
+    time = Float64[],
+    std = Float64[],
+    rate = Float64[],
+    cpu_chunks = Float64[],
+    gpu_chunks = Float64[],
+)
+
+# if they exist, read existing results and append new ones
+if isfile(results_filename)
+    df = CSV.read(results_filename, DataFrame)
+end
+
+nInputs = 16_777_216 # 2^30
+
+lck = ReentrantLock()
+
+progress = 1
+cpu_chunks = 0
+gpu_chunks = 0
+
+chunkSizes = [1024, 4096, 16384, 65536, 262144, 1048576]    # 2^10 to 2^20
+
+function cpu_worker(compute_func, inputs, chunk_size)
+    global progress
+    global cpu_chunks
+    global lck
+    quit = false
+    work_start = 0
+    work_end = 0
+    while true
+        lock(lck) do
+            if progress >= nInputs
+                quit = true
+            else
+                work_start = progress
+                progress = progress + chunk_size
+                work_end = min(progress - 1, nInputs)
+                cpu_chunks = cpu_chunks + 1
+                #log("CPU Worker $(Threads.threadid()) computing $(cpu_chunks)th cpu chunk ($work_start, $work_end)")
+            end
+        end
+        if quit
+            break
+        end
+
+        for i in work_start:work_end
+            compute_func(inputs[i])
+        end
+    end
+
+    #log("CPU Worker on $(Threads.threadid()) finished!")
+
+    return nothing
+end
+
+# called with a specific device selected
+function gpu_worker(kernel!, inputs, chunk_size)
+    global progress
+    global gpu_chunks
+    global lck
+    cuOutputs = CuVector{ComplexF64}()
+    resize!(cuOutputs, chunk_size)
+
+    quit = false
+    work_start = 0
+    work_end = 0
+    while true
+        lock(lck) do
+            if progress >= nInputs
+                quit = true
+            else
+                work_start = progress
+                progress = progress + chunk_size
+                work_end = min(progress - 1, nInputs)
+                gpu_chunks = gpu_chunks + 1
+                #log("GPU Worker $(CUDA.device()) computing $(gpu_chunks)th gpu chunk ($work_start, $work_end)")
+            end
+        end
+        if quit
+            break
+        end
+
+        cuInputs = CuVector(inputs[work_start:work_end])
+        ts = 32
+        bs = Int(chunk_size / 32)
+        CUDA.@sync threads = ts blocks = bs always_inline = true kernel!(cuInputs, cuOutputs, chunk_size)
+    end
+
+    #log("GPU Worker on Device $(CUDA.device()) finished!")
+
+    return nothing
+end
+
+cpu_gpu_ratio = Vector{Tuple{Int, Int}}()
+
+function full_compute(compute_func, kernel!, inputs, chunk_size)
+    global progress
+    progress = 1
+    global cpu_chunks
+    cpu_chunks = 0
+    global gpu_chunks
+    gpu_chunks = 0
+
+    tasks = Vector()
+
+    for dev in CUDA.devices()
+        t = Threads.@spawn device!(dev) do
+            gpu_worker(kernel!, inputs, chunk_size)
+            return nothing
+        end
+        push!(tasks, t)
+    end
+
+    for i in 1:(Threads.nthreads() - length(CUDA.devices()))
+        t = Threads.@spawn cpu_worker(compute_func, inputs, chunk_size)
+        push!(tasks, t)
+    end
+
+    for t in tasks
+        wait(t)
+    end
+
+    push!(cpu_gpu_ratio, (cpu_chunks, gpu_chunks))
+    return nothing
+end
+
+function bench(compute_function, kernel!, inputs, chunk_size)
+    global cpu_gpu_ratio
+    empty!(cpu_gpu_ratio)
+
+    bench = @benchmark begin
+        full_compute($compute_function, $kernel!, $inputs, $chunk_size)
+    end gcsample = true seconds = 30
+
+    time = median(bench.times) / 1e9
+    s = std(bench.times) / 1e9
+    rate = length(inputs) / time
+
+    med_cpu_chunks = median(getindex.(cpu_gpu_ratio, 1))
+    med_gpu_chunks = median(getindex.(cpu_gpu_ratio, 2))
+
+    log("CPU/GPU ratios: $(cpu_gpu_ratio)")
+
+    return (time, rate, s, med_cpu_chunks, med_gpu_chunks)
+end
+
+function full_node_bench(process::MetagraphOptimization.AbstractProcessDescription, func, kernel!, chunk_size, inputs)
+    process_name = string(process)
+    log("\n--- Benchmarking $(process_name) on $(nInputs) with chunk size $(chunk_size) ---")
+
+    log("Available Cuda Devices:")
+    display.(CUDA.devices())
+
+    log("Benchmarking full node...")
+    (time, rate, s, med_cpu_chunks, med_gpu_chunks) = bench(func, kernel!, inputs, chunk_size)
+    log(
+        "Benchmarking complete with median time $(time), $(med_cpu_chunks) cpu chunks, and $(med_gpu_chunks) gpu chunks.",
+    )
+
+    push!(
+        df,
+        Dict(
+            :process_name => process_name,
+            :cpu_threads => Threads.nthreads() - length(CUDA.devices()),
+            :gpu_devices => length(CUDA.devices()),
+            :n_inputs => nInputs,
+            :chunk_size => chunk_size,
+            :time => time,
+            :std => s,
+            :rate => rate,
+            :cpu_chunks => med_cpu_chunks,
+            :gpu_chunks => med_gpu_chunks,
+        ),
+    )
+
+    return nothing
+end
+
+# use "mock" machine that only uses cpu for compilation
+machine = Machine(
+    [
+        MetagraphOptimization.NumaNode(
+            0,
+            1,
+            MetagraphOptimization.default_strategy(MetagraphOptimization.NumaNode),
+            -1.0,
+            UUIDs.uuid1(),
+        ),
+    ],
+    [-1.0;;],
+)
+
+optimizer = ReductionOptimizer()
+processes = ["ke->ke", "ke->kke", "ke->kkke", "ke->kkkke", "ke->kkkkke"]
+
+for proc in processes
+    process = parse_process(proc, QEDModel())
+    graph = gen_graph(process)
+    optimize_to_fixpoint!(optimizer, graph)
+    compute_func = get_compute_function(graph, process, machine)
+    kernel! = get_cuda_kernel(graph, process, machine)
+
+    log("Generating $nInputs inputs with $(Threads.nthreads()) threads...")
+    inputs = Vector{typeof(gen_process_input(process))}()
+    resize!(inputs, nInputs)
+    procs = Vector{typeof(process)}()
+    for i in 1:Threads.nthreads()
+        push!(procs, copy(process))
+    end
+
+    @inbounds Threads.@threads for i in eachindex(inputs)
+        inputs[i] = gen_process_input(procs[Threads.nthreads()])
+    end
+
+    for chunk_size in chunkSizes
+        full_node_bench(process, compute_func, kernel!, chunk_size, inputs)
+        CSV.write(results_filename, df)
+    end
+end;

examples/import_bench.jl

@@ -34,9 +34,10 @@ function import_bench()
     bench_txt("AB->ABBB.txt")
     bench_txt("AB->ABBBBB.txt")
     bench_txt("AB->ABBBBBBB.txt")
-    #bench_txt("AB->ABBBBBBBBB.txt")
+    bench_txt("AB->ABBBBBBBBB.txt")
     bench_txt("ABAB->ABAB.txt")
-    return bench_txt("ABAB->ABC.txt")
+    bench_txt("ABAB->ABC.txt")
+    return nothing
 end
 
 import_bench()

examples/qed_bench.jl

@@ -2,44 +2,117 @@ using MetagraphOptimization
 using LIKWID
 using CUDA
 using UUIDs
+using DataFrames
+using CSV
+using Random
+using BenchmarkTools
+using Dates
 
-function cpu_bench(compute_function, inputs)
-    compute_function.(inputs[begin:10]) # make sure it's compiled
+DISABLE_GPU = false
 
-    time = @elapsed Threads.@threads for i in eachindex(inputs)
-        @invokelatest compute_function(inputs[i])
-    end
-    rate = length(inputs) / time
-    return (time, rate)
+function log(x...)
+    println(now(), " ", join(x, " ")...)
+    return flush(stdout)
 end
 
-function gpu_bench(compute_function, inputs)
-    CUDA.@sync compute_function.(inputs[begin:10])  # make sure it's compiled
+results_filename = "bench_results_$(Threads.nthreads()).csv"
 
-    time = @elapsed CUDA.@sync compute_function.(inputs)
+df = DataFrame(
+    process_name = String[],
+    graph_gen_time = Float64[],
+    optimization_time = Float64[],
+    function_generation_time = Float64[],
+    graph_nodes = Int[],
+    graph_edges = Int[],
+    graph_mem = Float64[],
+    cpu_threads = Int[],
+    n_inputs = Int[],
+    nflops_likwid = Int[],
+    cpu_time = Float64[],
+    cpu_std = Float64[],
+    cpu_rate = Float64[],
+    cpu_gflops = Float64[],
+    gpu_name = String[],
+    gpu_time = Float64[],
+    gpu_std = Float64[],
+    gpu_rate = Float64[],
+    gpu_gflops = Float64[],
+)
+
+# if they exist, read existing results and append new ones
+if isfile(results_filename)
+    df = CSV.read(results_filename, DataFrame)
+end
+
+nInputs = 2^20
+
+function cpu_bench(compute_function, inputs)
+    bench = @benchmark begin
+        @inbounds Threads.@threads for i in eachindex($inputs)
+            @invokelatest $compute_function($inputs[i])
+        end
+    end gcsample = true samples = 20 evals = 1
+
+    time = median(bench.times) / 1e9
+    s = std(bench.times) / 1e9
     rate = length(inputs) / time
 
-    return (time, rate)
+    return (time, rate, s)
+end
+
+function gpu_bench(kernel!, inputs)
+    n = length(inputs)
+    outputs = CuVector{ComplexF64}()
+    resize!(outputs, n)
+    ts = 32
+    bs = Int(n / ts)
+    bench = @benchmark begin
+        @cuda threads = $ts blocks = $bs always_inline = true $kernel!($inputs, $outputs, $n)
+        CUDA.device_synchronize()
+    end gcsample = true samples = 20 evals = 1
+
+    time = median(bench.times) / 1e9
+    s = std(bench.times) / 1e9
+    rate = length(inputs) / time
+
+    return (time, rate, s)
 end
 
 function bench_process(
     process::MetagraphOptimization.AbstractProcessDescription,
+    process_name::String,
+    graph::DAG,
     func,
-    io::IO = stdout;
-    use_likwid = true,
+    kernel!,
+    gen_time::Float64,
+    opt_time::Float64,
+    func_time::Float64;
+    use_likwid = false,
+    use_gpu = true,
 )
-    println(io, "\n--- Benchmarking $(process) ---")
+    log("\n--- Benchmarking $(process_name) ---")
+    if DISABLE_GPU
+        use_gpu = false
+    end
 
-    NFLOPs = GraphProperties(graph).computeEffort
+    graph_props = GraphProperties(graph)
+    NFLOPs = graph_props.computeEffort
+    nflops_likwid = 0
     if use_likwid
         input = gen_process_input(process)
         func(input) # compile first
+
+        # get rid of annoying output to console
+        oldstd = stdout
+        redirect_stdout(devnull)
         _, events = @perfmon "FLOPS_DP" func(input)
+        redirect_stdout(oldstd) # recover original stdout
+
         NFLOPs = first(events["FLOPS_DP"])["RETIRED_SSE_AVX_FLOPS_ALL"]
+        nflops_likwid = NFLOPs
     end
 
-    nInputs = 10000000  # ten million
-    println(io, "Generating $nInputs inputs with $(Threads.nthreads()) threads...")
+    log("Generating $nInputs inputs with $(Threads.nthreads()) threads...")
 
     inputs = Vector{typeof(gen_process_input(process))}()
     resize!(inputs, nInputs)
@@ -48,35 +121,76 @@ function bench_process(
         push!(processes, copy(process))
     end
 
-    Threads.@threads for i in eachindex(inputs)
+    @inbounds Threads.@threads for i in eachindex(inputs)
         inputs[i] = gen_process_input(processes[Threads.nthreads()])
     end
 
-    println(io, "Benchmarking CPU with $(Threads.nthreads()) threads...")
-    (time_cpu, rate_cpu) = cpu_bench(func, inputs)
-    flops_cpu = (rate_cpu * NFLOPs) / 1024^3
+    log("Benchmarking CPU with $(Threads.nthreads()) threads...")
+    (time_cpu, rate_cpu, std_cpu) = cpu_bench(func, inputs)
+    flops_cpu = (rate_cpu * NFLOPs) / 10^9
 
-    println(io, "Benchmarking GPU...")
-    cuInputs = CuArray(inputs)
-    (time_gpu, rate_gpu) = gpu_bench(func, cuInputs)
-    flops_gpu = (rate_gpu * NFLOPs) / 1024^3
+    time_gpu = 0.0
+    std_gpu = 0.0
+    rate_gpu = 0.0
+    flops_gpu = 0.0
+    gpu_name = "none"
+    if use_gpu
+        log("Benchmarking GPU...")
+        gpu_name = "$(name(first(CUDA.devices())))"
+        cuInputs = CuArray(inputs)
+        (time_gpu, rate_gpu, std_gpu) = gpu_bench(kernel!, cuInputs)
+        flops_gpu = (rate_gpu * NFLOPs) / 10^9
+    else
+        log("Skipping GPU...")
+    end
 
-    println(io, "\nBenchmark Summary for $(process):")
+    log("\nBenchmark Summary for $(process):")
 
     if use_likwid
-        println(io, "Measured FLOPS by LIKWID: $NFLOPs")
+        log("Measured FLOPS by LIKWID: $NFLOPs")
     else
-        println(io, "Total graph compute effort: $NFLOPs")
+        log("Total graph compute effort: $NFLOPs")
     end
-    println(io, "Total input size: $(bytes_to_human_readable(Base.summarysize(inputs)))")
-    println(io, "CPU, $(Threads.nthreads()) threads")
-    println(io, "  Time:  $time_cpu")
-    println(io, "  Rate:  $rate_cpu")
-    println(io, "  GFLOPS: $flops_cpu")
-    println(io, "GPU, $(name(first(CUDA.devices())))")
-    println(io, "  Time:  $time_gpu")
-    println(io, "  Rate:  $rate_gpu")
-    return println(io, "  GFLOPS: $flops_gpu")
+    log("Total input size: $(bytes_to_human_readable(Base.summarysize(inputs)))")
+    log("CPU, $(Threads.nthreads()) threads")
+    log("  Time:  $time_cpu")
+    log("  Rate:  $rate_cpu")
+    log("  GFLOPS: $flops_cpu")
+    if use_gpu
+        log("GPU, $gpu_name")
+        log("  Time:  $time_gpu")
+        log("  Rate:  $rate_gpu")
+        log("  GFLOPS: $flops_gpu")
+    end
+
+    if (process_name != "warmup")
+        push!(
+            df,
+            Dict(
+                :process_name => process_name,
+                :graph_gen_time => gen_time,
+                :optimization_time => opt_time,
+                :function_generation_time => func_time,
+                :graph_nodes => graph_props.noNodes,
+                :graph_edges => graph_props.noEdges,
+                :graph_mem => MetagraphOptimization.mem(graph),
+                :cpu_threads => Threads.nthreads(),
+                :n_inputs => nInputs,
+                :nflops_likwid => nflops_likwid,
+                :cpu_time => time_cpu,
+                :cpu_std => std_cpu,
+                :cpu_rate => rate_cpu,
+                :cpu_gflops => flops_cpu,
+                :gpu_name => gpu_name,
+                :gpu_time => time_gpu,
+                :gpu_std => std_gpu,
+                :gpu_rate => rate_gpu,
+                :gpu_gflops => flops_gpu,
+            ),
+        )
+    end
+
+    return nothing
 end
 
 # use "mock" machine that only uses cpu
@@ -92,57 +206,67 @@ machine = Machine(
     ],
     [-1.0;;],
 )
-optimizer = ReductionOptimizer()
 
 # sadly cannot put these in functions because the world age must increase after the function is created which happens only in the global scope
 
-# compton
-process = parse_process("ke->ke", QEDModel())
-graph = gen_graph(process)
-optimize_to_fixpoint!(optimizer, graph)
-compute_func = get_compute_function(graph, process, machine)
-bench_process(process, compute_func)
+## -- WARMUP TO COMPILE FUNCTIONS first
+#=
+optimizer = RandomWalkOptimizer(MersenneTwister(0))
 
 # 2-photon compton
 process = parse_process("ke->kke", QEDModel())
-graph = gen_graph(process)
-optimize_to_fixpoint!(optimizer, graph)
-compute_func = get_compute_function(graph, process, machine)
-bench_process(process, compute_func)
+gen_time = @elapsed graph = gen_graph(process)
+opt_time = @elapsed optimize!(optimizer, graph, 200)
+func_gen_time = @elapsed compute_func = get_compute_function(graph, process, machine)
+kernel! = get_cuda_kernel(graph, process, machine)
+bench_process(process, "warmup", graph, compute_func, kernel!, gen_time, opt_time, func_gen_time)
 
-# 3-photon compton
-process = parse_process("ke->kkke", QEDModel())
-graph = gen_graph(process)
-optimize_to_fixpoint!(optimizer, graph)
-compute_func = get_compute_function(graph, process, machine)
-bench_process(process, compute_func)
-
-# AB->AB
-process = parse_process("AB->AB", ABCModel())
-graph = parse_dag("input/AB->AB.txt", ABCModel())
-optimize_to_fixpoint!(optimizer, graph)
-compute_func = get_compute_function(graph, process, machine)
-bench_process(process, compute_func)
+optimizer = ReductionOptimizer()
 
 # AB->AB^3
 process = parse_process("AB->ABBB", ABCModel())
-graph = parse_dag("input/AB->ABBB.txt", ABCModel())
-optimize_to_fixpoint!(optimizer, graph)
-compute_func = get_compute_function(graph, process, machine)
-bench_process(process, compute_func)
+gen_time = @elapsed graph = parse_dag("input/AB->ABBB.txt", ABCModel())
+opt_time = @elapsed optimize_to_fixpoint!(optimizer, graph)
+func_gen_time = @elapsed compute_func = get_compute_function(graph, process, machine)
+kernel! = get_cuda_kernel(graph, process, machine)
+bench_process(process, "warmup", graph, compute_func, kernel!, gen_time, opt_time, func_gen_time)
+=#
+## -- WARMUP END
 
-exit(0)
+optimizer = ReductionOptimizer()
 
-# 4-photon compton
-process = parse_process("ke->kkkke", QEDModel())
-graph = gen_graph(process)
-optimize_to_fixpoint!(optimizer, graph)
-compute_func = get_compute_function(graph, process, machine)
-bench_process(process, compute_func)
+processes = ["ke->ke", "ke->kke", "ke->kkke", "ke->kkkke", "ke->kkkkke", "ke->kkkkkke"]
 
-# AB->AB^5
-process = parse_process("AB->ABBBBB", ABCModel())
-graph = parse_dag("input/AB->ABBBBB.txt", ABCModel())
-optimize_to_fixpoint!(optimizer, graph)
-compute_func = get_compute_function(graph, process, machine)
-bench_process(process, compute_func)
+for process_str in processes
+    # compton
+    process = parse_process(process_str, QEDModel())
+    gen_time = @elapsed graph = gen_graph(process)
+    func_gen_time = @elapsed compute_func = get_compute_function(graph, process, machine)
+    kernel! = get_cuda_kernel(graph, process, machine)
+    bench_process(process, "$process not optimized", graph, compute_func, kernel!, gen_time, 0.0, func_gen_time)
+
+    opt_time = @elapsed optimize_to_fixpoint!(optimizer, graph)
+    func_gen_time = @elapsed compute_func = get_compute_function(graph, process, machine)
+    kernel! = get_cuda_kernel(graph, process, machine)
+    bench_process(process, "$process reduced", graph, compute_func, kernel!, gen_time, opt_time, func_gen_time)
+
+    CSV.write(results_filename, df)
+end
+
+processes = ["AB->AB", "AB->ABBB", "AB->ABBBBB"]
+
+for process_str in processes
+    # AB->AB
+    process = parse_process(process_str, ABCModel())
+    gen_time = @elapsed graph = parse_dag("input/$(process_str).txt", ABCModel())
+    func_gen_time = @elapsed compute_func = get_compute_function(graph, process, machine)
+    kernel! = get_cuda_kernel(graph, process, machine)
+    bench_process(process, "$process not optimized", graph, compute_func, kernel!, gen_time, 0.0, func_gen_time)
+
+    opt_time = @elapsed optimize_to_fixpoint!(optimizer, graph)
+    func_gen_time = @elapsed compute_func = get_compute_function(graph, process, machine)
+    kernel! = get_cuda_kernel(graph, process, machine)
+    bench_process(process, "$process reduced", graph, compute_func, kernel!, gen_time, opt_time, func_gen_time)
+
+    CSV.write(results_filename, df)
+end

examples/qed_bench_reduction_steps.jl

@@ -0,0 +1,163 @@
+using MetagraphOptimization
+using CUDA
+using UUIDs
+using BenchmarkTools
+using DataFrames
+using CSV
+
+results_filename = "bench_results_reduction_steps.csv"
+
+df = DataFrame(
+    threads = Int[],
+    process = String[],
+    operations = Int[],
+    cumulative_optimization_time = Float64[],
+    graph_nodes = Int[],
+    graph_edges = Int[],
+    graph_ce = Float64[],
+    graph_dt = Float64[],
+    graph_ci = Float64[],
+    gen_func_t = Float64[],
+    cpu_compile_t = Float64[],
+    cpu_st_t = Float64[],
+    cpu_mt_t = Float64[],
+    gpu_compile_t = Float64[],
+    gpu_t = Float64[],
+)
+
+# if they exist, read existing results and append new ones
+if isfile(results_filename)
+    df = CSV.read(results_filename, DataFrame)
+end
+
+function bench(func, inputs)
+    compile_time = @elapsed func(inputs[1])
+
+    single_thread = @benchmark $func.($inputs)
+    multi_threaded = @benchmark Threads.@threads for i in eachindex($inputs)
+        $func($inputs[i])
+    end
+
+    return (
+        cpu_compile_time = compile_time,
+        gpu_compile_time = 0.0,
+        cpu_single_thread_time = mean(single_thread.times) / 1e9,
+        cpu_multi_thread_time = mean(multi_threaded.times) / 1e9,
+        gpu_time = 0.0,
+    )
+end
+
+# preparation of machine
+machine = Machine(
+    [
+        MetagraphOptimization.NumaNode(
+            0,
+            1,
+            MetagraphOptimization.default_strategy(MetagraphOptimization.NumaNode),
+            -1.0,
+            UUIDs.uuid1(),
+        ),
+    ],
+    [-1.0;;],
+)
+
+# bench and produce data
+n_inputs = 50_000
+optimizer = ReductionOptimizer()
+processes = [("ke->kke", 5), ("ke->ke", 1), ("ke->kke", 1), ("ke->kkke", 1), ("ke->kkkke", 1), ("ke->kkkkke", 1)]
+
+for (process_str, STEPSIZE) in processes
+    n = 0
+    opt_time_cum = 0
+
+    process = parse_process(process_str, QEDModel())
+    graph = gen_graph(process)
+    inputs = [gen_process_input(process) for _ in 1:n_inputs]
+
+    get_compute_function(graph, process, machine)
+
+    while true
+        func_gen_time = @elapsed func = get_compute_function(graph, process, machine)
+        res = bench(func, inputs)
+
+        graph_properties = get_properties(graph)
+        push!(
+            df,
+            (
+                Threads.nthreads(),
+                process_str,
+                n,
+                opt_time_cum,
+                graph_properties.noNodes,
+                graph_properties.noEdges,
+                graph_properties.computeEffort,
+                graph_properties.data,
+                graph_properties.computeIntensity,
+                func_gen_time,
+                res.cpu_compile_time,
+                res.cpu_single_thread_time,
+                res.cpu_multi_thread_time,
+                res.gpu_compile_time,
+                res.gpu_time,
+            ),
+        )
+        CSV.write(results_filename, df)
+
+        if fixpoint_reached(optimizer, graph)
+            break
+        end
+
+        opt_time_cum += @elapsed optimize!(optimizer, graph, STEPSIZE)
+        n += STEPSIZE
+    end
+end
+
+CSV.write(results_filename, df)
+
+for (process_str, STEPSIZE) in [("AB->AB", 1), ("AB->ABBB", 1), ("AB->ABBBBB", 1)]
+    n = 0
+    opt_time_cum = 0
+
+    process = parse_process(process_str, ABCModel())
+    graph = parse_dag("input/$process_str.txt", ABCModel())
+    inputs = [gen_process_input(process) for _ in 1:n_inputs]
+
+    get_compute_function(graph, process, machine)
+
+    while true
+        func_gen_time = @elapsed func = get_compute_function(graph, process, machine)
+        res = bench(func, inputs)
+
+        graph_properties = get_properties(graph)
+        push!(
+            df,
+            (
+                Threads.nthreads(),
+                process_str,
+                n,
+                opt_time_cum,
+                graph_properties.noNodes,
+                graph_properties.noEdges,
+                graph_properties.computeEffort,
+                graph_properties.data,
+                graph_properties.computeIntensity,
+                func_gen_time,
+                res.cpu_compile_time,
+                res.cpu_single_thread_time,
+                res.cpu_multi_thread_time,
+                res.gpu_compile_time,
+                res.gpu_time,
+            ),
+        )
+        CSV.write(results_filename, df)
+
+        if fixpoint_reached(optimizer, graph)
+            break
+        end
+
+        opt_time_cum += @elapsed optimize!(optimizer, graph, STEPSIZE)
+        n += STEPSIZE
+    end
+end
+
+CSV.write(results_filename, df)

examples/qed_bench_reduction_steps_gpu.jl

@@ -0,0 +1,173 @@
+using MetagraphOptimization
+using CUDA
+using UUIDs
+using BenchmarkTools
+using DataFrames
+using CSV
+using Dates
+
+results_filename = "bench_results_reduction_steps_gpu.csv"
+
+df = DataFrame(
+    threads = Int[],
+    process = String[],
+    operations = Int[],
+    cumulative_optimization_time = Float64[],
+    graph_nodes = Int[],
+    graph_edges = Int[],
+    graph_ce = Float64[],
+    graph_dt = Float64[],
+    graph_ci = Float64[],
+    gen_func_t = Float64[],
+    cpu_compile_t = Float64[],
+    cpu_st_t = Float64[],
+    cpu_mt_t = Float64[],
+    gpu_compile_t = Float64[],
+    gpu_t = Float64[],
+)
+
+# if they exist, read existing results and append new ones
+if isfile(results_filename)
+    df = CSV.read(results_filename, DataFrame)
+end
+
+function log(x...)
+    println(now(), " ", join(x, " ")...)
+    return flush(stdout)
+end
+
+function bench(func, inputs)
+    # todo: use gpu kernel instead of broadcasting
+    gpu_compile_time = @elapsed func.(inputs[1:2])
+
+    gpu_time = @benchmark $func.($inputs)
+
+    return (
+        cpu_compile_time = 0.0,
+        gpu_compile_time = gpu_compile_time,
+        cpu_single_thread_time = 0.0,
+        cpu_multi_thread_time = 0.0,
+        gpu_time = mean(gpu_time.times) / 1e9,
+    )
+end
+
+for dev in CUDA.devices()
+    log("CUDA device: $(dev)")
+end
+
+
+# preparation of machine
+machine = Machine(
+    [
+        MetagraphOptimization.NumaNode(
+            0,
+            1,
+            MetagraphOptimization.default_strategy(MetagraphOptimization.NumaNode),
+            -1.0,
+            UUIDs.uuid1(),
+        ),
+    ],
+    [-1.0;;],
+)
+
+
+# bench and produce data
+n_inputs = 50_000
+optimizer = ReductionOptimizer()
+processes = [("ke->kke", 50), ("ke->ke", 1), ("ke->kke", 1), ("ke->kkke", 1)]
+
+for (process_str, STEPSIZE) in processes
+    n = 0
+    opt_time_cum = 0
+
+    process = parse_process(process_str, QEDModel())
+    graph = gen_graph(process)
+    inputs = CuVector([gen_process_input(process) for _ in 1:n_inputs])
+
+    get_compute_function(graph, process, machine)
+
+    while true
+        func_gen_time = @elapsed func = get_compute_function(graph, process, machine)
+        res = bench(func, inputs)
+
+        graph_properties = get_properties(graph)
+        push!(
+            df,
+            (
+                Threads.nthreads(),
+                process_str,
+                n,
+                opt_time_cum,
+                graph_properties.noNodes,
+                graph_properties.noEdges,
+                graph_properties.computeEffort,
+                graph_properties.data,
+                graph_properties.computeIntensity,
+                func_gen_time,
+                res.cpu_compile_time,
+                res.cpu_single_thread_time,
+                res.cpu_multi_thread_time,
+                res.gpu_compile_time,
+                res.gpu_time,
+            ),
+        )
+        CSV.write(results_filename, df)
+
+        if fixpoint_reached(optimizer, graph)
+            break
+        end
+
+        opt_time_cum += @elapsed optimize!(optimizer, graph, STEPSIZE)
+        n += STEPSIZE
+    end
+end
+
+CSV.write(results_filename, df)
+
+for (process_str, STEPSIZE) in [("AB->AB", 1), ("AB->ABBB", 1), ("AB->ABBBBB", 1)]
+    n = 0
+    opt_time_cum = 0
+
+    process = parse_process(process_str, ABCModel())
+    graph = parse_dag("input/$process_str.txt", ABCModel())
+    inputs = CuVector([gen_process_input(process) for _ in 1:n_inputs])
+
+    get_compute_function(graph, process, machine)
+
+    while true
+        func_gen_time = @elapsed func = get_compute_function(graph, process, machine)
+        res = bench(func, inputs)
+
+        graph_properties = get_properties(graph)
+        push!(
+            df,
+            (
+                Threads.nthreads(),
+                process_str,
+                n,
+                opt_time_cum,
+                graph_properties.noNodes,
+                graph_properties.noEdges,
+                graph_properties.computeEffort,
+                graph_properties.data,
+                graph_properties.computeIntensity,
+                func_gen_time,
+                res.cpu_compile_time,
+                res.cpu_single_thread_time,
+                res.cpu_multi_thread_time,
+                res.gpu_compile_time,
+                res.gpu_time,
+            ),
+        )
+        CSV.write(results_filename, df)
+
+        if fixpoint_reached(optimizer, graph)
+            break
+        end
+
+        opt_time_cum += @elapsed optimize!(optimizer, graph, STEPSIZE)
+        n += STEPSIZE
+    end
+end
+
+CSV.write(results_filename, df)

examples/qed_bench_tape.jl

@@ -0,0 +1,232 @@
+using MetagraphOptimization
+using LIKWID
+using UUIDs
+using DataFrames
+using CSV
+using Random
+using BenchmarkTools
+using Dates
+
+function log(x...)
+    println(now(), " ", join(x, " ")...)
+    return flush(stdout)
+end
+
+results_filename = "bench_results_tape_$(Threads.nthreads()).csv"
+
+df = DataFrame(
+    process_name = String[],
+    graph_gen_time = Float64[],
+    optimization_time = Float64[],
+    function_generation_time = Float64[],
+    graph_nodes = Int[],
+    graph_edges = Int[],
+    graph_mem = Float64[],
+    cpu_threads = Int[],
+    n_inputs = Int[],
+    nflops_likwid = Int[],
+    cpu_time = Float64[],
+    cpu_rate = Float64[],
+    cpu_gflops = Float64[],
+    cpu_std = Float64[],
+    gpu_name = String[],
+    gpu_time = Float64[],
+    gpu_std = Float64[],
+    gpu_rate = Float64[],
+    gpu_gflops = Float64[],
+)
+
+# if they exist, read existing results and append new ones
+if isfile(results_filename)
+    df = CSV.read(results_filename, DataFrame)
+end
+
+nInputs = 1_000_000
+
+# use "mock" machine that only uses cpu
+machine = Machine(
+    [
+        MetagraphOptimization.NumaNode(
+            0,
+            1,
+            MetagraphOptimization.default_strategy(MetagraphOptimization.NumaNode),
+            -1.0,
+            UUIDs.uuid1(),
+        ),
+    ],
+    [-1.0;;],
+)
+
+
+function cpu_bench(tape, inputs)
+    bench = @benchmark begin
+        @inbounds Threads.@threads for i in eachindex($inputs)
+            execute_tape($tape, $inputs[i])
+        end
+    end gcsample = true seconds = 300
+
+    time = mean(bench.times) / 1e9
+    s = std(bench.times) / 1e9
+    rate = length(inputs) / time
+
+    return (time, rate, s)
+end
+
+function bench_process(
+    process::MetagraphOptimization.AbstractProcessDescription,
+    process_name::String,
+    graph::DAG,
+    gen_time::Float64,
+    opt_time::Float64,
+    io::IO = stdout;
+    use_likwid = false,
+)
+    log("\n--- Benchmarking $(process_name) ---")
+
+    func_time = @elapsed tape = gen_tape(graph, process, machine)
+
+    graph_props = GraphProperties(graph)
+    NFLOPs = graph_props.computeEffort
+    nflops_likwid = 0
+    if use_likwid
+        input = gen_process_input(process)
+
+        # get rid of annoying output to console
+        oldstd = stdout
+        redirect_stdout(devnull)
+        _, events = @perfmon "FLOPS_DP" execute_tape(tape, input)
+        redirect_stdout(oldstd) # recover original stdout
+
+        NFLOPs = first(events["FLOPS_DP"])["RETIRED_SSE_AVX_FLOPS_ALL"]
+        nflops_likwid = NFLOPs
+    end
+
+    log("Generating $nInputs inputs with $(Threads.nthreads()) threads...")
+
+    inputs = Vector{typeof(gen_process_input(process))}()
+    resize!(inputs, nInputs)
+    processes = Vector{typeof(process)}()
+    for i in 1:Threads.nthreads()
+        push!(processes, copy(process))
+    end
+
+    @inbounds Threads.@threads for i in eachindex(inputs)
+        inputs[i] = gen_process_input(processes[Threads.nthreads()])
+    end
+
+    log("Benchmarking CPU with $(Threads.nthreads()) threads...")
+    (time_cpu, rate_cpu, std_cpu) = cpu_bench(tape, inputs)
+    flops_cpu = (rate_cpu * NFLOPs) / 10^9
+
+    log("\nBenchmark Summary for $(process):")
+
+    if use_likwid
+        log("Measured FLOPS by LIKWID: $NFLOPs")
+    else
+        log("Total graph compute effort: $NFLOPs")
+    end
+    log("Total input size: $(bytes_to_human_readable(Base.summarysize(inputs)))")
+    log("CPU, $(Threads.nthreads()) threads")
+    log("  Time:  $time_cpu")
+    log("  Rate:  $rate_cpu")
+    log("  GFLOPS: $flops_cpu")
+
+    if (process_name != "warmup")
+        push!(
+            df,
+            Dict(
+                :process_name => process_name,
+                :graph_gen_time => gen_time,
+                :optimization_time => opt_time,
+                :function_generation_time => func_time,
+                :graph_nodes => graph_props.noNodes,
+                :graph_edges => graph_props.noEdges,
+                :graph_mem => MetagraphOptimization.mem(graph),
+                :cpu_threads => Threads.nthreads(),
+                :n_inputs => nInputs,
+                :nflops_likwid => nflops_likwid,
+                :cpu_time => time_cpu,
+                :cpu_std => std_cpu,
+                :cpu_rate => rate_cpu,
+                :cpu_gflops => flops_cpu,
+                :gpu_name => "none",
+                :gpu_time => 0.0,
+                :gpu_std => 0.0,
+                :gpu_rate => 0.0,
+                :gpu_gflops => 0.0,
+            ),
+        )
+    end
+
+    return nothing
+end
+
+function bench_qed(process_string::String, skip_unoptimized = false)
+    optimizer = ReductionOptimizer()
+
+    process = parse_process(process_string, QEDModel())
+    gen_time = @elapsed graph = gen_graph(process)
+    opt_time = 0.0
+    if !skip_unoptimized
+        bench_process(process, "$process not optimized tape", graph, gen_time, opt_time)
+    end
+
+    opt_time = @elapsed optimize_to_fixpoint!(optimizer, graph)
+    bench_process(process, "$process reduced tape", graph, gen_time, opt_time)
+
+    return nothing
+end
+
+function bench_abc(process_string::String)
+    optimizer = ReductionOptimizer()
+
+    process = parse_process(process_string, ABCModel())
+    gen_time = @elapsed graph = parse_dag("input/$process_string.txt", ABCModel())
+    bench_process(process, "$process not optimized tape", graph, gen_time, 0.0)
+
+    opt_time = @elapsed optimize_to_fixpoint!(optimizer, graph)
+    bench_process(process, "$process reduced tape", graph, gen_time, opt_time)
+
+    return nothing
+end
+
+# sadly cannot put these in functions because the world age must increase after the function is created which happens only in the global scope
+
+## -- WARMUP TO COMPILE FUNCTIONS first
+optimizer = ReductionOptimizer()
+
+process = parse_process("ke->kke", QEDModel())
+gen_time = @elapsed graph = gen_graph(process)
+opt_time = @elapsed optimize_to_fixpoint!(optimizer, graph)
+bench_process(process, "warmup", graph, gen_time, opt_time)
+
+# AB->AB^3
+process = parse_process("AB->ABBB", ABCModel())
+gen_time = @elapsed graph = parse_dag("input/AB->ABBB.txt", ABCModel())
+opt_time = @elapsed optimize_to_fixpoint!(optimizer, graph)
+bench_process(process, "warmup", graph, gen_time, opt_time)
+
+## -- WARMUP END
+
+# compton
+bench_qed("ke->ke")
+CSV.write(results_filename, df)
+bench_qed("ke->kke")
+CSV.write(results_filename, df)
+bench_qed("ke->kkke")
+CSV.write(results_filename, df)
+bench_qed("ke->kkkke")
+CSV.write(results_filename, df)
+bench_qed("ke->kkkkke")
+CSV.write(results_filename, df)
+bench_qed("ke->kkkkkke")
+CSV.write(results_filename, df)
+bench_qed("ke->kkkkkkke")
+CSV.write(results_filename, df)
+
+bench_abc("AB->AB")
+CSV.write(results_filename, df)
+bench_abc("AB->ABBB")
+CSV.write(results_filename, df)
+bench_abc("AB->ABBBBB")
+CSV.write(results_filename, df)

examples/qed_gen_bench.jl

@@ -0,0 +1,144 @@
+using MetagraphOptimization
+using DataFrames
+using CSV
+using BenchmarkTools
+using StatsBase
+
+results_filename = "qed_gen_results_$(Threads.nthreads()).csv"
+
+df = DataFrame(
+    process_name = String[],
+    cpu_threads = Int[],
+    graph_gen_samples = Int[],
+    graph_gen_mean = Float64[],
+    graph_gen_std = Float64[],
+    graph_gen_median = Float64[],
+    graph_nodes = Int[],
+    graph_data_nodes = Int[],
+    graph_u_nodes = Int[],
+    graph_v_nodes = Int[],
+    graph_s1_nodes = Int[],
+    graph_s2_nodes = Int[],
+    graph_edges = Int[],
+    graph_nodes_reduced = Int[],
+    graph_data_nodes_reduced = Int[],
+    graph_u_nodes_reduced = Int[],
+    graph_v_nodes_reduced = Int[],
+    graph_s1_nodes_reduced = Int[],
+    graph_s2_nodes_reduced = Int[],
+    graph_edges_reduced = Int[],
+    graph_mem = Float64[],
+    graph_mem_reduced = Float64[],
+    graph_elapsed_reduce = Float64[],
+)
+
+function bench_process(process::AbstractString; warmup = false, optimize = true)
+    println("Benchmarking $process...")
+    model = QEDModel()
+
+    proc = parse_process(process, model)
+
+    gen_bench = @benchmark gen_graph($proc) gcsample = true seconds = 5
+
+    graph = gen_graph(proc)
+
+    props = GraphProperties(graph)
+    node_dict = countmap(typeof.(graph.nodes))
+    graph_size = Base.summarysize(graph)
+
+    reduce_elapsed = -1.0
+    node_dict_reduced = Dict()
+    graph_size_reduced = -1.0
+    props_reduced = GraphProperties()
+    if optimize
+        reduce_elapsed = @elapsed optimize_to_fixpoint!(ReductionOptimizer(), graph)
+
+        props_reduced = GraphProperties(graph)
+        node_dict_reduced = countmap(typeof.(graph.nodes))
+        graph_size_reduced = Base.summarysize(graph)
+    end
+
+    if warmup
+        return nothing
+    end
+
+    push!(
+        df,
+        Dict(
+            :process_name => process,
+            :cpu_threads => Threads.nthreads(),
+            :graph_gen_samples => length(gen_bench.times),
+            :graph_gen_mean => mean(gen_bench.times),
+            :graph_gen_std => std(gen_bench.times),
+            :graph_gen_median => median(gen_bench.times),
+            :graph_nodes => props.noNodes,
+            :graph_data_nodes => get(node_dict, DataTaskNode{DataTask}, 0),
+            :graph_u_nodes => get(node_dict, ComputeTaskNode{ComputeTaskQED_U}, 0),
+            :graph_v_nodes => get(node_dict, ComputeTaskNode{ComputeTaskQED_V}, 0),
+            :graph_s1_nodes => get(node_dict, ComputeTaskNode{ComputeTaskQED_S1}, 0),
+            :graph_s2_nodes => get(node_dict, ComputeTaskNode{ComputeTaskQED_S2}, 0),
+            :graph_edges => props.noEdges,
+            :graph_nodes_reduced => props_reduced.noNodes,
+            :graph_data_nodes_reduced => get(node_dict_reduced, DataTaskNode{DataTask}, 0),
+            :graph_u_nodes_reduced => get(node_dict_reduced, ComputeTaskNode{ComputeTaskQED_U}, 0),
+            :graph_v_nodes_reduced => get(node_dict_reduced, ComputeTaskNode{ComputeTaskQED_V}, 0),
+            :graph_s1_nodes_reduced => get(node_dict_reduced, ComputeTaskNode{ComputeTaskQED_S1}, 0),
+            :graph_s2_nodes_reduced => get(node_dict_reduced, ComputeTaskNode{ComputeTaskQED_S2}, 0),
+            :graph_edges_reduced => props_reduced.noEdges,
+            :graph_mem => graph_size,
+            :graph_mem_reduced => graph_size_reduced,
+            :graph_elapsed_reduce => reduce_elapsed,
+        ),
+    )
+    return nothing
+end
+
+processes = [
+    ("ke->ke", true),
+    ("ke->kke", true),
+    ("ke->kkke", true),
+    ("ke->kkkke", true),
+    ("ke->kkkkke", true),
+    ("ke->kkkkkke", true),
+    ("ke->kkkkkkke", true),
+    #("ke->kkkkkkkke", false),
+    #("ke->kkkkkkkkke", false),
+]
+
+df = DataFrame(
+    process_name = String[],
+    cpu_threads = Int[],
+    graph_gen_samples = Int[],
+    graph_gen_mean = Float64[],
+    graph_gen_std = Float64[],
+    graph_gen_median = Float64[],
+    graph_nodes = Int[],
+    graph_data_nodes = Int[],
+    graph_u_nodes = Int[],
+    graph_v_nodes = Int[],
+    graph_s1_nodes = Int[],
+    graph_s2_nodes = Int[],
+    graph_edges = Int[],
+    graph_nodes_reduced = Int[],
+    graph_data_nodes_reduced = Int[],
+    graph_u_nodes_reduced = Int[],
+    graph_v_nodes_reduced = Int[],
+    graph_s1_nodes_reduced = Int[],
+    graph_s2_nodes_reduced = Int[],
+    graph_edges_reduced = Int[],
+    graph_mem = Float64[],
+    graph_mem_reduced = Float64[],
+    graph_elapsed_reduce = Float64[],
+)
+
+# if they exist, read existing results and append new ones
+if isfile(results_filename)
+    df = CSV.read(results_filename, DataFrame)
+end
+
+bench_process("ke->kke", warmup = true)
+
+for (process, opt) in processes
+    bench_process(process, optimize = opt)
+    CSV.write(results_filename, df)
+end

experiments/CUDA_container.def

@@ -0,0 +1,63 @@
+Bootstrap: docker
+From: nvidia/cuda:12.3.1-devel-ubuntu20.04
+
+%labels
+    Requires CUDA driver 470.57+.
+
+%environment
+    export LANG=C
+
+%runscript
+    nvidia-smi
+    ./run.sh
+
+%post
+    . /.singularity.d/env/10-docker*.sh
+
+    apt-get update
+    apt-get install -y pciutils
+    DEBIAN_FRONTEND='noninteractive' apt-get -y -o Dpkg::Options::='--force-confdef' -o Dpkg::Options::='--force-confold' install build-essential cuda-compat-12-3 libibverbs-dev ibverbs-utils gcc wget git libcap2-bin
+    apt-get -y autoremove; apt-get -y clean
+
+    cd /tmp
+
+    # install slurm
+    : ${SLURM_VERSION:=17-02-11-1}
+    wget https://github.com/SchedMD/slurm/archive/slurm-${SLURM_VERSION}.tar.gz
+    tar -xf slurm-${SLURM_VERSION}.tar.gz
+        cd slurm-slurm-${SLURM_VERSION}
+        ./configure --prefix=/usr/ --sysconfdir=/etc/slurm --localstatedir=/var --disable-debug
+        make -C contribs/pmi2 -j$(nproc) install
+    cd ..
+    rm -rf slurm-*
+
+    # install julia
+    cd ~
+    wget https://julialang-s3.julialang.org/bin/linux/x64/1.9/julia-1.9.4-linux-x86_64.tar.gz
+    tar zxvf julia-1.9.4-linux-x86_64.tar.gz
+    mv julia-1.9.4/ /opt/julia-1.9.4
+    #mkdir /usr/local/bin
+    ln -s /opt/julia-1.9.4/bin/julia /usr/local/bin/julia
+
+    #Add nvidia driver paths to the environment variables
+    echo "\n #Nvidia driver paths \n" >> /environment
+    echo 'export PATH="/nvbin:$PATH"' >> /environment
+    echo 'export LD_LIBRARY_PATH="/nvlib:$LD_LIBRARY_PATH"' >> /environment
+
+    #Add CUDA paths
+    echo "\n #Cuda paths \n" >> /environment
+    echo 'export CPATH="/usr/local/cuda/include:$CPATH"' >> /environment
+    echo 'export PATH="/usr/local/cuda/bin:$PATH"' >> /environment
+    echo 'export LD_LIBRARY_PATH="/usr/local/cuda/lib64:$LD_LIBRARY_PATH"' >> /environment
+    echo 'export CUDA_HOME="/usr/local/cuda"' >> /environment
+
+    # install likwid
+    VERSION=5.3.0
+    wget http://ftp.fau.de/pub/likwid/likwid-$VERSION.tar.gz
+    tar -xaf likwid-$VERSION.tar.gz
+    cd likwid-$VERSION
+    # accessdaemon doesn't work because of permissions
+    sed -i 's/ACCESSMODE = accessdaemon/ACCESSMODE = perf_event/g' config.mk
+    make -j4
+    make -j4 install 
+    echo 'export LD_LIBRARY_PATH="/usr/local/lib:$LD_LIBRARY_PATH"' >> /environment

experiments/diagram_bench_hemera.sh

@@ -0,0 +1,22 @@
+#!/bin/bash
+#SBATCH --array=1-32
+#SBATCH --job-name=qed_bench
+#SBATCH --partition=intel
+#SBATCH --time=16:00:00
+#SBATCH --nodes=1
+#SBATCH --ntasks=1
+#SBATCH --cpus-per-task=32
+#SBATCH --mem=16GB
+#SBATCH --output=simulation-%A-%a.out
+#SBATCH --error=simulation-%A-%a.err
+
+cd $HOME/repos/metagraph_optimization
+
+module load singularity
+module load git 
+
+printf "Current git commit hash: " > results/git.txt
+git rev-parse HEAD >> results/git.txt
+git status >> results/git.txt
+
+singularity exec experiments/CUDA_container.sif ./experiments/run_qed_exec.sh $SLURM_ARRAY_TASK_ID

experiments/diagram_bench_hemera_a100.sh

@@ -0,0 +1,24 @@
+#!/bin/bash
+#SBATCH --job-name=qed_bench
+#SBATCH --partition=casus_a100
+#SBATCH --account=casus
+#SBATCH --time=8:00:00
+#SBATCH --nodes=1
+#SBATCH --ntasks=1
+#SBATCH --cpus-per-task=32
+#SBATCH --gres=gpu:1
+#SBATCH --mem=256GB
+#SBATCH --output=simulation-%A-%a.out
+#SBATCH --error=simulation-%A-%a.err
+
+cd $HOME/repos/metagraph_optimization
+
+module load singularity
+module load git
+module load cuda/12.1
+
+printf "Current git commit hash: " > results/git.txt
+git rev-parse HEAD >> results/git.txt
+git status >> results/git.txt
+
+singularity exec --nv experiments/CUDA_container.sif ./experiments/run_qed_exec.sh 32

experiments/full_node.sh

@@ -0,0 +1,25 @@
+#!/bin/bash
+
+SCRIPT_DIR=$( cd -- "$( dirname -- "${BASH_SOURCE[0]}" )" &> /dev/null && pwd )
+LOG_FILE="$SCRIPT_DIR/../julia_full_node.log"
+
+cd $SCRIPT_DIR/..
+
+echo "Writing system info..."
+
+# collect some information of the used node and system
+uname -a > results/system_full_node.txt
+julia --version > results/julia_full_node.txt
+lscpu > results/cpu_full_node.txt
+nvidia-smi > results/cuda_gpu_full_node.txt
+lsblk > results/storage_full_node.txt
+lspci > results/pci_full_node.txt
+
+echo "Initiating julia..."
+julia --threads=8 --project=./ -e 'using Pkg; Pkg.instantiate(); Pkg.add(url="https://github.com/QEDjl-project/QEDprocesses.jl/")' >> $LOG_FILE 2>&1 || exit 1    # need current dev version of QEDprocesses
+julia --threads=8 --project=./ -e 'using Pkg; Pkg.instantiate(); Pkg.add(url="https://github.com/AntonReinhard/QEDbase.jl/tree/fix_bs_multiplication")' >> $LOG_FILE 2>&1 || exit 1 # need a specific fix for abs*bs multiplication for gpu
+julia --threads=8 -e 'using Pkg; Pkg.add("CSV"); Pkg.add("DataFrames"); Pkg.add("CUDA"); Pkg.add("Random"); Pkg.add("BenchmarkTools"); Pkg.add("Dates")' >> $LOG_FILE 2>&1 || exit 1        # add requirements for the bench script
+julia --project -e 'using CUDA; CUDA.set_runtime_version!(VersionNumber("12.1"))' >> $LOG_FILE 2>&1 || echo "Failed to set CUDA version number"
+
+echo "Benchmarking Full Node 128 Threads + *GPUs*"
+julia --project -O3 --threads=128 examples/full_node_bench.jl >> $LOG_FILE 2>&1 || echo "-- Something went wrong, check logs --"

experiments/full_node_hemera.sh

@@ -0,0 +1,24 @@
+#!/bin/bash
+#SBATCH --job-name=qed_bench
+#SBATCH --partition=casus_a100
+#SBATCH --account=casus
+#SBATCH --time=8:00:00
+#SBATCH --nodes=1
+#SBATCH --ntasks=1
+#SBATCH --cpus-per-task=128
+#SBATCH --gres=gpu:4
+#SBATCH --mem=2048GB
+#SBATCH --output=simulation-%A-%a.out
+#SBATCH --error=simulation-%A-%a.err
+
+cd $HOME/repos/metagraph_optimization
+
+module load singularity
+module load git
+module load cuda/12.1
+
+printf "Current git commit hash: " > results/git_reduce_bench_gpu.txt
+git rev-parse HEAD >> results/git_reduce_bench_gpu.txt
+git status >> results/git_reduce_bench_gpu.txt
+
+singularity exec --nv experiments/CUDA_container.sif ./experiments/full_node.sh

experiments/gen_diagram_hemera.sh

@@ -0,0 +1,22 @@
+#!/bin/bash
+#SBATCH --array=1-8
+#SBATCH --job-name=qed_diag_gen
+#SBATCH --partition=intel
+#SBATCH --time=4:00:00
+#SBATCH --nodes=1
+#SBATCH --ntasks=1
+#SBATCH --cpus-per-task=8
+#SBATCH --mem=64GB
+#SBATCH --output=simulation-%A-%a.out
+#SBATCH --error=simulation-%A-%a.err
+
+cd $HOME/repos/metagraph_optimization
+
+module load singularity
+module load git 
+
+printf "Current git commit hash: " > results/git.txt
+git rev-parse HEAD >> results/git.txt
+git status >> results/git.txt
+
+singularity exec experiments/CUDA_container.sif ./experiments/run_gen_diagram.sh $SLURM_ARRAY_TASK_ID

experiments/reduce_bench_hemera.sh

@@ -0,0 +1,21 @@
+#!/bin/bash
+#SBATCH --job-name=qed_bench
+#SBATCH --partition=intel
+#SBATCH --time=48:00:00
+#SBATCH --nodes=1
+#SBATCH --ntasks=1
+#SBATCH --cpus-per-task=32
+#SBATCH --mem=24GB
+#SBATCH --output=simulation-%A-%a.out
+#SBATCH --error=simulation-%A-%a.err
+
+cd $HOME/repos/metagraph_optimization
+
+module load singularity
+module load git 
+
+printf "Current git commit hash: " > results/git_reduce_bench.txt
+git rev-parse HEAD >> results/git_reduce_bench.txt
+git status >> results/git_reduce_bench.txt
+
+singularity exec experiments/CUDA_container.sif ./experiments/run_reduce_bench.sh

experiments/reduce_bench_hemera_gpu.sh

@@ -0,0 +1,24 @@
+#!/bin/bash
+#SBATCH --job-name=qed_bench
+#SBATCH --partition=casus_a100
+#SBATCH --account=casus
+#SBATCH --time=48:00:00
+#SBATCH --nodes=1
+#SBATCH --ntasks=1
+#SBATCH --cpus-per-task=32
+#SBATCH --gres=gpu:1
+#SBATCH --mem=24GB
+#SBATCH --output=simulation-%A-%a.out
+#SBATCH --error=simulation-%A-%a.err
+
+cd $HOME/repos/metagraph_optimization
+
+module load singularity
+module load git 
+module load cuda/12.1
+
+printf "Current git commit hash: " > results/git_reduce_bench_gpu.txt
+git rev-parse HEAD >> results/git_reduce_bench_gpu.txt
+git status >> results/git_reduce_bench_gpu.txt
+
+singularity exec --nv experiments/CUDA_container.sif ./experiments/run_reduce_bench_gpu.sh

experiments/run_gen_diagram.sh

@@ -0,0 +1,27 @@
+#!/bin/bash
+
+# first arg = number of threads
+i=$1
+
+SCRIPT_DIR=$( cd -- "$( dirname -- "${BASH_SOURCE[0]}" )" &> /dev/null && pwd )
+LOG_FILE="$SCRIPT_DIR/../julia.log"
+
+cd $SCRIPT_DIR/..
+
+echo "Writing system info..."
+
+# collect some information of the used node and system
+uname -a > results/system.txt
+julia --version > results/julia.txt
+lscpu > results/cpu.txt
+lsblk > results/storage.txt
+lspci > results/pci.txt
+
+echo "Initiating julia..."
+julia --threads=8 --project=./ -e 'using Pkg; Pkg.instantiate(); Pkg.add(url="https://github.com/QEDjl-project/QEDprocesses.jl/")' >> $LOG_FILE 2>&1 || exit 1    # need current dev version of QEDprocesses
+julia --threads=8 --project=./ -e 'using Pkg; Pkg.instantiate(); Pkg.add(url="https://github.com/AntonReinhard/QEDbase.jl/tree/fix_bs_multiplication")' >> $LOG_FILE 2>&1 || exit 1 # need a specific fix for abs*bs multiplication for gpu
+julia --threads=8 -e 'using Pkg; Pkg.add("CSV"); Pkg.add("DataFrames"); Pkg.add("BenchmarkTools"); Pkg.add("StatsBase")' >> $LOG_FILE 2>&1 || exit 1        # add requirements for the bench script
+
+echo "Benchmarking with $i threads..."
+
+julia --project -O3 --threads=$i examples/qed_gen_bench.jl >> $LOG_FILE 2>&1 || echo "-- Something went wrong, check logs --"

experiments/run_qed_exec.sh

@@ -0,0 +1,31 @@
+#!/bin/bash
+
+# first arg = number of threads
+i=$1
+
+SCRIPT_DIR=$( cd -- "$( dirname -- "${BASH_SOURCE[0]}" )" &> /dev/null && pwd )
+LOG_FILE="$SCRIPT_DIR/../julia_$i.log"
+
+cd $SCRIPT_DIR/..
+
+echo "Writing system info..."
+
+# collect some information of the used node and system
+uname -a > results/system_$i.txt
+julia --version > results/julia_$i.txt
+lscpu > results/cpu_$i.txt
+nvidia-smi > results/cuda_gpu_$i.txt
+lsblk > results/storage_$i.txt
+lspci > results/pci_$i.txt
+
+echo "Initiating julia..."
+#julia --threads=8 --project=./ -e 'using Pkg; Pkg.instantiate(); Pkg.add(url="https://github.com/QEDjl-project/QEDprocesses.jl/")' >> $LOG_FILE 2>&1 || exit 1    # need current dev version of QEDprocesses
+#julia --threads=8 --project=./ -e 'using Pkg; Pkg.instantiate(); Pkg.add(url="https://github.com/AntonReinhard/QEDbase.jl/tree/fix_bs_multiplication")' >> $LOG_FILE 2>&1 || exit 1 # need a specific fix for abs*bs multiplication for gpu
+#julia --threads=8 -e 'using Pkg; Pkg.add("CSV"); Pkg.add("DataFrames"); Pkg.add("LIKWID"); Pkg.add("CUDA"); Pkg.add("Random"); Pkg.add("BenchmarkTools"); Pkg.add("Dates")' >> $LOG_FILE 2>&1 || exit 1        # add requirements for the bench script
+#julia --project -e 'using CUDA; CUDA.set_runtime_version!(VersionNumber("12.1"))' >> $LOG_FILE 2>&1 || echo "Failed to set CUDA version number"
+
+echo "Benchmarking $i Threads"
+julia --project -O3 --threads=$i examples/qed_bench.jl >> $LOG_FILE 2>&1 || echo "-- Something went wrong, check logs --"
+
+echo "Benchmarking Tape variant $i Threads"
+julia --project -O3 --threads=$i examples/qed_bench_tape.jl >> $LOG_FILE 2>&1 || echo "-- Something went wrong, check logs --"

experiments/run_reduce_bench.sh

@@ -0,0 +1,24 @@
+#!/bin/bash
+
+SCRIPT_DIR=$( cd -- "$( dirname -- "${BASH_SOURCE[0]}" )" &> /dev/null && pwd )
+LOG_FILE="$SCRIPT_DIR/../julia_bench_reduce.log"
+
+cd $SCRIPT_DIR/..
+
+echo "Writing system info..."
+
+# collect some information of the used node and system
+uname -a > results/system_bench_reduce.txt
+julia --version > results/julia_bench_reduce.txt
+lscpu > results/cpu_bench_reduce.txt
+nvidia-smi > results/cuda_gpu_bench_reduce.txt
+lsblk > results/storage_bench_reduce.txt
+lspci > results/pci_bench_reduce.txt
+
+echo "Initiating julia..."
+julia --threads=8 --project=./ -e 'using Pkg; Pkg.instantiate(); Pkg.add(url="https://github.com/QEDjl-project/QEDprocesses.jl/")' >> $LOG_FILE 2>&1 || exit 1    # need current dev version of QEDprocesses
+julia --threads=8 --project=./ -e 'using Pkg; Pkg.instantiate(); Pkg.add(url="https://github.com/AntonReinhard/QEDbase.jl/tree/fix_bs_multiplication")' >> $LOG_FILE 2>&1 || exit 1 # need a specific fix for abs*bs multiplication for gpu
+julia --threads=8 -e 'using Pkg; Pkg.add("CSV"); Pkg.add("DataFrames"); Pkg.add("LIKWID"); Pkg.add("CUDA"); Pkg.add("Random"); Pkg.add("BenchmarkTools"); Pkg.add("Dates")' >> $LOG_FILE 2>&1 || exit 1        # add requirements for the bench script
+
+echo "Benchmarking Reduction 32 Threads"
+julia --project -O3 --threads=32 examples/qed_bench_reduction_steps.jl >> $LOG_FILE 2>&1 || echo "-- Something went wrong, check logs --"

experiments/run_reduce_bench_gpu.sh

@@ -0,0 +1,25 @@
+#!/bin/bash
+
+SCRIPT_DIR=$( cd -- "$( dirname -- "${BASH_SOURCE[0]}" )" &> /dev/null && pwd )
+LOG_FILE="$SCRIPT_DIR/../julia_bench_reduce_gpu.log"
+
+cd $SCRIPT_DIR/..
+
+echo "Writing system info..."
+
+# collect some information of the used node and system
+uname -a > results/system_bench_reduce_gpu.txt
+julia --version > results/julia_bench_reduce_gpu.txt
+lscpu > results/cpu_bench_reduce_gpu.txt
+nvidia-smi > results/cuda_gpu_bench_reduce_gpu.txt
+lsblk > results/storage_bench_reduce_gpu.txt
+lspci > results/pci_bench_reduce_gpu.txt
+
+echo "Initiating julia..."
+julia --threads=8 --project=./ -e 'using Pkg; Pkg.instantiate(); Pkg.add(url="https://github.com/QEDjl-project/QEDprocesses.jl/")' >> $LOG_FILE 2>&1 || exit 1    # need current dev version of QEDprocesses
+julia --threads=8 --project=./ -e 'using Pkg; Pkg.instantiate(); Pkg.add(url="https://github.com/AntonReinhard/QEDbase.jl/tree/fix_bs_multiplication")' >> $LOG_FILE 2>&1 || exit 1 # need a specific fix for abs*bs multiplication for gpu
+julia --threads=8 -e 'using Pkg; Pkg.add("CSV"); Pkg.add("DataFrames"); Pkg.add("LIKWID"); Pkg.add("CUDA"); Pkg.add("Random"); Pkg.add("BenchmarkTools"); Pkg.add("Dates")' >> $LOG_FILE 2>&1 || exit 1        # add requirements for the bench script
+julia --project -e 'using CUDA; CUDA.set_runtime_version!(VersionNumber("12.1"))' >> $LOG_FILE 2>&1 || echo "Failed to set CUDA version number"
+
+echo "Benchmarking Reduction 32 Threads, *GPU*"
+julia --project --threads=32 examples/qed_bench_reduction_steps_gpu.jl >> $LOG_FILE 2>&1 || echo "-- Something went wrong, check logs --"