#-------------------------------------------------------------------- # NJet -- multi-leg one-loop matrix elements in the Standard Model # version : 2.1.0-git b1299d2f884075dfc762c1b11b6435d8f19fb9b2 # Authors : Simon Badger, Valery Yundin # Homepage: https://bitbucket.org/njet/njet #-------------------------------------------------------------------- ## init: Switch floating point unit ==================================================== This is QCDLoop - version 1.97 Authors: Keith Ellis and Giulia Zanderighi (keith.ellis@durham.ac.uk, zanderi@mpp.mpg.de) For details see FERMILAB-PUB-07-633-T,OUTP-07/16P arXiv:0712.1851 [hep-ph], published in JHEP 0802:002,2008. ==================================================== ==================================================== FF 2.0, a package to evaluate one-loop integrals written by G. J. van Oldenborgh, NIKHEF-H, Amsterdam ==================================================== for the algorithms used see preprint NIKHEF-H 89/17, 'New Algorithms for One-loop Integrals', by G.J. van Oldenborgh and J.A.M. Vermaseren, published in Zeitschrift fuer Physik C46(1990)425. ==================================================== ffini: precx = 4.4408920985006262E-016 ffini: precc = 4.4408920985006262E-016 ffini: xalogm = 4.9406564584124654E-324 ffini: xclogm = 4.9406564584124654E-324 ## init: OneLOop is used to calculate the scalar one-loop integrals NJet: simple example of PentagonFunctions-cpp based 2-loop evaluation Notation: DblLoop = 2*Re(A2.cA0) LoopSqe2 = A1.cA1 ==================== Test point 1 ==================== # rnd seed 1, seq 1 # p0 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,5.0000000000000000e-01) # p1 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,-5.0000000000000000e-01) # p2 = (4.1073910982315065e-01,2.0393336282060184e-01,-3.5476001585959549e-01,-3.5540554501787405e-02) # p3 = (2.3727316959679573e-01,6.2348782873773469e-02,1.6215556401520548e-01,1.6160680475641931e-01) # p4 = (3.5198772058005368e-01,-2.6628214569437531e-01,1.9260445184439001e-01,-1.2606625025463189e-01) Pentagon functions evaluation time: 1654ms 2L evaluation time: 1036ms L^2 evaluation time: 114ms VV evaluation time: 2804ms Born: 5.8458405658021821e+06 Loop: (-7.8918847638329411e+08,0.0000000000000000e+00)/e^2 + (-5.0462088426728976e+08,0.0000000000000000e+00)/e^1 + (7.4476842329627037e+08,0.0000000000000000e+00) LoopSq: (1.3153141273054893e+09,0.0000000000000000e+00)/e^4 + (1.7647859641923294e+09,0.0000000000000000e+00)/e^3 + (-3.3913907745347524e+08,0.0000000000000000e+00)/e^2 + (3.7726335447368759e+08,0.0000000000000000e+00)/e^1 + (2.8010969891311846e+09,0.0000000000000000e+00) LoopSqe2: (1.3153141273054900e+09,0.0000000000000000e+00)/e^4 + (1.7647859641923308e+09,-5.4291059647937345e-08)/e^3 + (-2.5027440940650201e+09,-5.5039237167875399e-08)/e^2 + (-8.5996629200764866e+09,6.7833578754061818e-08)/e^1 + (-5.1807226400667248e+09,9.1444611882707250e-08) Absolute error: (7.1525573730468750e-07,0.0000000000000000e+00)/e^4 + (1.1920928955078125e-06,5.9376743521966091e-08)/e^3 + (1.9073486328125000e-05,-6.5350413080977887e-08)/e^2 + (3.4042358398437500e-02,-3.2608904376729697e-07)/e^1 + (-3.4002161026000977e+00,-9.5274444333881547e-08) Fractional error[e^4]: 5.4379081198643948e-16 Fractional error[e^3]: 6.7548865397588529e-16 Fractional error[e^2]: -7.6210294026287614e-15 Fractional error[e^1]: -3.9585689247148678e-12 Fractional error[e^0]: 6.5632081445616719e-10 LoopSqe2[/e4]/B/5^3: 9.9999999999999922e-01 DblLoop: (-4.3843804243516338e+08,0.0000000000000000e+00)/e^4 + (-4.2750137250455052e+08,0.0000000000000000e+00)/e^3 + (2.1487831375908298e+09,0.0000000000000000e+00)/e^2 + (3.4257126771665411e+09,0.0000000000000000e+00)/e^1 + (-4.7879848375011749e+09,0.0000000000000000e+00) Absolute error: (1.7881393432617188e-07,0.0000000000000000e+00)/e^4 + (-1.1920928955078125e-07,0.0000000000000000e+00)/e^3 + (-6.1988830566406250e-06,0.0000000000000000e+00)/e^2 + (-1.1998605728149414e-01,0.0000000000000000e+00)/e^1 + (1.2229750633239746e+01,0.0000000000000000e+00) Fractional error[e^4]: -4.0784310898982961e-16 Fractional error[e^3]: 2.7885124403784771e-16 Fractional error[e^2]: -2.8848341874046358e-15 Fractional error[e^1]: -3.5025137420671378e-11 Fractional error[e^0]: -2.5542584298621947e-09 DblLoop[/e4]/B/Nc/5^2: -9.9999999999999944e-01 ==================== Test point 2 ==================== # rnd seed 2, seq 1 # p0 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,5.0000000000000000e-01) # p1 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,-5.0000000000000000e-01) # p2 = (4.5262742135982199e-02,-3.7938713674424224e-02,-3.1787775991454215e-03,-2.4479893859525703e-02) # p3 = (4.9174017367771933e-01,1.4265227585006041e-01,3.2654221902632635e-01,3.3886414061796888e-01) # p4 = (4.6299708418629848e-01,-1.0471356217563620e-01,-3.2336344142718093e-01,-3.1438424675844312e-01) Pentagon functions evaluation time: 1665ms 2L evaluation time: 742ms L^2 evaluation time: 81ms VV evaluation time: 2488ms Born: 4.5974636458664918e+08 Loop: (-6.2065759219197594e+10,0.0000000000000000e+00)/e^2 + (-8.6129009271294830e+10,0.0000000000000000e+00)/e^1 + (-9.1020229566772995e+10,0.0000000000000000e+00) LoopSq: (1.0344293203199590e+11,0.0000000000000000e+00)/e^4 + (2.9151482693865753e+11,0.0000000000000000e+00)/e^3 + (6.4938956028294446e+11,0.0000000000000000e+00)/e^2 + (1.0555563720839404e+12,0.0000000000000000e+00)/e^1 + (1.1844111669951279e+12,0.0000000000000000e+00) LoopSqe2: (1.0344293203199591e+11,0.0000000000000000e+00)/e^4 + (2.9151482693865796e+11,5.4563993048817316e-07)/e^3 + (4.7923275740843103e+11,8.4760810370454465e-06)/e^2 + (5.5916794062480225e+11,-3.8797892898401187e-06)/e^1 + (3.9468778879733020e+11,3.1642007797927363e-05) Absolute error: (-7.6293945312500000e-05,0.0000000000000000e+00)/e^4 + (2.4414062500000000e-04,-1.7416609039977438e-06)/e^3 + (1.2854003906250000e-01,8.6013116948890911e-06)/e^2 + (5.1061298828125000e+04,-4.6183849576664215e-05)/e^1 + (8.5019341247558594e+04,-3.9008730709610973e-05) Fractional error[e^4]: -7.3754623746455235e-16 Fractional error[e^3]: 8.3748956292838343e-16 Fractional error[e^2]: 2.6822047757672467e-13 Fractional error[e^1]: 9.1316570780274348e-08 Fractional error[e^0]: 2.1540909970035965e-07 LoopSqe2[/e4]/B/5^3: 9.9999999999999845e-01 DblLoop: (-3.4480977343998657e+10,0.0000000000000000e+00)/e^4 + (-8.4528583953419891e+10,0.0000000000000000e+00)/e^3 + (-1.9732814870678371e+10,0.0000000000000000e+00)/e^2 + (3.1479878014932117e+11,0.0000000000000000e+00)/e^1 + (1.1454047862457717e+12,0.0000000000000000e+00) Absolute error: (6.1035156250000000e-05,0.0000000000000000e+00)/e^4 + (-4.5776367187500000e-05,0.0000000000000000e+00)/e^3 + (-2.0647430419921875e-01,0.0000000000000000e+00)/e^2 + (-1.5508559216308594e+05,0.0000000000000000e+00)/e^1 + (-2.1913297031738281e+07,0.0000000000000000e+00) Fractional error[e^4]: -1.7701109699149244e-15 Fractional error[e^3]: 5.4154896540944552e-16 Fractional error[e^2]: 1.0463499787150266e-11 Fractional error[e^1]: -4.9264991462013565e-07 Fractional error[e^0]: -1.9131487221702864e-05 DblLoop[/e4]/B/Nc/5^2: -9.9999999999999900e-01 ==================== Test point 3 ==================== # rnd seed 3, seq 1 # p0 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,5.0000000000000000e-01) # p1 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,-5.0000000000000000e-01) # p2 = (7.6196219725659056e-02,-1.9783128890417792e-02,4.6667929075996928e-03,-7.3435092127290255e-02) # p3 = (4.7539311855278965e-01,-3.5220386979451790e-01,7.9684674949917447e-02,3.0919476684969788e-01) # p4 = (4.4841066172155131e-01,3.7198699868493568e-01,-8.4351467857517126e-02,-2.3575967472240761e-01) Pentagon functions evaluation time: 6751ms 2L evaluation time: 743ms L^2 evaluation time: 81ms VV evaluation time: 7575ms Born: 7.0263859421881747e+08 Loop: (-9.4856210219540070e+10,0.0000000000000000e+00)/e^2 + (-1.5229548642970859e+11,0.0000000000000000e+00)/e^1 + (-2.4885764725424878e+11,0.0000000000000000e+00) LoopSq: (1.5809368369923291e+11,0.0000000000000000e+00)/e^4 + (5.0765170534730884e+11,0.0000000000000000e+00)/e^3 + (1.3660523256203921e+12,0.0000000000000000e+00)/e^2 + (1.9879085081456614e+12,0.0000000000000000e+00)/e^1 + (2.7128691197950381e+12,0.0000000000000000e+00) LoopSqe2: (1.5809368369923566e+11,0.0000000000000000e+00)/e^4 + (5.0765170534732153e+11,4.6386397092735144e-07)/e^3 + (1.1059986395447495e+12,1.4770845421036016e-05)/e^2 + (1.0275879996027628e+12,-4.5306066758232788e-06)/e^1 + (8.4912165931479946e+23,2.3525591721806904e-04) Absolute error: (-2.4414062500000000e-04,0.0000000000000000e+00)/e^4 + (-5.4931640625000000e-04,-1.1100732621185342e-05)/e^3 + (-1.3647460937500000e-01,4.0951505591579895e-06)/e^2 + (4.7080039687799316e+10,4.5174595764141401e-05)/e^1 + (6.6625680179200000e+11,-8.1348435256245466e-04) Fractional error[e^4]: -1.5442781728362013e-15 Fractional error[e^3]: -1.0820733988752634e-15 Fractional error[e^2]: -1.2339491613766866e-13 Fractional error[e^1]: 4.5816066075118782e-02 Fractional error[e^0]: 7.8464233538647146e-13 LoopSqe2[/e4]/B/5^3: 1.0000000000000109e+00 DblLoop: (-5.2697894566411606e+10,0.0000000000000000e+00)/e^4 + (-1.4989467377475537e+11,0.0000000000000000e+00)/e^3 + (-1.9602767757923120e+11,0.0000000000000000e+00)/e^2 + (3.4162837821023694e+11,0.0000000000000000e+00)/e^1 + (1.6683397849332510e+12,0.0000000000000000e+00) Absolute error: (9.9182128906250000e-05,0.0000000000000000e+00)/e^4 + (2.1362304687500000e-04,0.0000000000000000e+00)/e^3 + (-1.2544921875000000e+01,0.0000000000000000e+00)/e^2 + (1.3417374289019775e+08,0.0000000000000000e+00)/e^1 + (8.6524391396668701e+10,0.0000000000000000e+00) Fractional error[e^4]: -1.8820890231441305e-15 Fractional error[e^3]: -1.4251543533561997e-15 Fractional error[e^2]: 6.3995666478931504e-11 Fractional error[e^1]: 3.9274765051171393e-04 Fractional error[e^0]: 5.1862571508555423e-02 DblLoop[/e4]/B/Nc/5^2: -1.0000000000000058e+00 ==================== Test point 4 ==================== # rnd seed 4, seq 1 # p0 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,5.0000000000000000e-01) # p1 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,-5.0000000000000000e-01) # p2 = (2.9256410320928150e-01,2.1992770064354056e-01,-1.8996854216210698e-01,-3.3727050939863029e-02) # p3 = (2.1668577448382834e-01,6.5036456548073190e-02,-2.0173235143046242e-01,-4.5022689498335301e-02) # p4 = (4.9075012230689019e-01,-2.8496415719161372e-01,3.9170089359256938e-01,7.8749740438198337e-02) Pentagon functions evaluation time: 1663ms 2L evaluation time: 740ms L^2 evaluation time: 81ms VV evaluation time: 2484ms Born: 1.4177811795089565e+07 Loop: (-1.9140045923370967e+09,0.0000000000000000e+00)/e^2 + (-1.5903843490933704e+09,0.0000000000000000e+00)/e^1 + (-3.6924138552599633e+08,0.0000000000000000e+00) LoopSq: (3.1900076538951697e+09,0.0000000000000000e+00)/e^4 + (5.4537337409589233e+09,0.0000000000000000e+00)/e^3 + (8.1582394945044231e+09,0.0000000000000000e+00)/e^2 + (1.5058844919079062e+10,0.0000000000000000e+00)/e^1 + (1.6409766978302298e+10,0.0000000000000000e+00) LoopSqe2: (3.1900076538951654e+09,0.0000000000000000e+00)/e^4 + (5.4537337409589100e+09,-1.1330471092613204e-08)/e^3 + (2.9108872310890589e+09,-3.3816314548573700e-07)/e^2 + (-3.8986822582174692e+09,-1.3062048083156697e-06)/e^1 + (-1.6357098017339976e+09,-3.2142122563527664e-07) Absolute error: (1.4305114746093750e-06,0.0000000000000000e+00)/e^4 + (3.8146972656250000e-06,-3.3959919813753014e-08)/e^3 + (1.2049674987792969e-03,5.3048541559519435e-08)/e^2 + (3.2696723937988281e-03,-1.0617769703458180e-06)/e^1 + (-5.1576137542724609e-02,-6.5181779973499943e-07) Fractional error[e^4]: 4.4843512298870065e-16 Fractional error[e^3]: 6.9946525569733368e-16 Fractional error[e^2]: 4.1395196828991511e-13 Fractional error[e^1]: -8.3866090572196746e-13 Fractional error[e^0]: 3.1531349563381797e-11 LoopSqe2[/e4]/B/5^3: 1.0000000000000042e+00 DblLoop: (-1.0633358846317196e+09,0.0000000000000000e+00)/e^4 + (-1.4280214226213365e+09,0.0000000000000000e+00)/e^3 + (3.0161178666979623e+09,0.0000000000000000e+00)/e^2 + (1.0173489802397755e+10,0.0000000000000000e+00)/e^1 + (1.5559441323206953e+10,0.0000000000000000e+00) Absolute error: (1.1920928955078125e-07,0.0000000000000000e+00)/e^4 + (-2.3841857910156250e-07,0.0000000000000000e+00)/e^3 + (-2.0599365234375000e-04,0.0000000000000000e+00)/e^2 + (-4.8847198486328125e-03,0.0000000000000000e+00)/e^1 + (6.1860103607177734e+01,0.0000000000000000e+00) Fractional error[e^4]: -1.1210878074717541e-16 Fractional error[e^3]: 1.6695728462106071e-16 Fractional error[e^2]: -6.8297613504498514e-14 Fractional error[e^1]: -4.8014201060894068e-13 Fractional error[e^0]: 3.9757278119564106e-09 DblLoop[/e4]/B/Nc/5^2: -1.0000000000000020e+00 ==================== Test point 5 ==================== # rnd seed 5, seq 1 # p0 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,5.0000000000000000e-01) # p1 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,-5.0000000000000000e-01) # p2 = (2.6248344598488410e-01,-1.7078449739898194e-02,-1.6064712176262391e-01,2.0687771325100734e-01) # p3 = (2.9191254936802302e-01,-6.0232203877931878e-02,1.6671869070546871e-01,2.3192648892267564e-01) # p4 = (4.4560400464709282e-01,7.7310653617830072e-02,-6.0715689428448181e-03,-4.3880420217368304e-01) Pentagon functions evaluation time: 1672ms 2L evaluation time: 740ms L^2 evaluation time: 80ms VV evaluation time: 2492ms Born: 9.6198677029928899e+08 Loop: (-1.2986821399040387e+11,0.0000000000000000e+00)/e^2 + (-2.1999312532133734e+11,0.0000000000000000e+00)/e^1 + (1.0869862930423636e+11,0.0000000000000000e+00) LoopSq: (2.1644702331733957e+11,0.0000000000000000e+00)/e^4 + (7.3350161431498547e+11,0.0000000000000000e+00)/e^3 + (4.3865288904908838e+11,0.0000000000000000e+00)/e^2 + (2.8486808225701245e+11,0.0000000000000000e+00)/e^1 + (1.4614456899659114e+12,0.0000000000000000e+00) LoopSqe2: (2.1644702331733960e+11,0.0000000000000000e+00)/e^4 + (7.3350161431498560e+11,7.2295756761153740e-06)/e^3 + (8.2611806726501038e+10,1.2420322859196808e-05)/e^2 + (-4.4578559995979824e+12,3.0487281946989242e-05)/e^1 + (-8.9379980664919355e+12,-1.1953214379900601e-04) Absolute error: (3.0517578125000000e-05,0.0000000000000000e+00)/e^4 + (1.2207031250000000e-04,-3.9480482987852561e-06)/e^3 + (1.6784667968750000e-04,-9.8609979651831381e-06)/e^2 + (-1.5224609375000000e+00,1.5302441170206293e-05)/e^1 + (6.1269531250000000e+01,4.6061144530540332e-05) Fractional error[e^4]: 1.4099329090914429e-16 Fractional error[e^3]: 1.6642132766674413e-16 Fractional error[e^2]: 2.0317517112678817e-15 Fractional error[e^1]: 3.4152313076898365e-13 Fractional error[e^0]: -6.8549501570934676e-12 LoopSqe2[/e4]/B/5^3: 9.9999999999999811e-01 DblLoop: (-7.2149007772446594e+10,0.0000000000000000e+00)/e^4 + (-2.1804590192176498e+11,0.0000000000000000e+00)/e^3 + (2.1626070309184747e+11,0.0000000000000000e+00)/e^2 + (2.0638783855577271e+12,0.0000000000000000e+00)/e^1 + (2.2540438614911929e+12,0.0000000000000000e+00) Absolute error: (-4.5776367187500000e-05,0.0000000000000000e+00)/e^4 + (-1.2207031250000000e-04,0.0000000000000000e+00)/e^3 + (2.1362304687500000e-04,0.0000000000000000e+00)/e^2 + (5.0732421875000000e-01,0.0000000000000000e+00)/e^1 + (-2.0347656250000000e+01,0.0000000000000000e+00) Fractional error[e^4]: 6.3446980909114878e-16 Fractional error[e^3]: 5.5983768291044932e-16 Fractional error[e^2]: 9.8780334947987638e-16 Fractional error[e^1]: 2.4581110122576552e-13 Fractional error[e^0]: -9.0271784846896170e-12 DblLoop[/e4]/B/Nc/5^2: -9.9999999999999889e-01 ==================== Test point 6 ==================== # rnd seed 6, seq 1 # p0 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,5.0000000000000000e-01) # p1 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,-5.0000000000000000e-01) # p2 = (3.9003003321363972e-01,1.5572792751971823e-01,1.0676230598507759e-01,-3.4128294627741790e-01) # p3 = (3.2815579567625391e-01,1.1636097253886823e-01,-1.3715055965489417e-01,2.7447417782384087e-01) # p4 = (2.8181417111010632e-01,-2.7208890005858649e-01,3.0388253669816578e-02,6.6808768453577042e-02) Pentagon functions evaluation time: 1648ms 2L evaluation time: 741ms L^2 evaluation time: 80ms VV evaluation time: 2469ms Born: 4.4997161959518351e+07 Loop: (-6.0746168645349817e+09,0.0000000000000000e+00)/e^2 + (-6.7192412259947281e+09,0.0000000000000000e+00)/e^1 + (6.2660513899830179e+09,0.0000000000000000e+00) LoopSq: (1.0124361440891647e+10,0.0000000000000000e+00)/e^4 + (2.2495016394192059e+10,0.0000000000000000e+00)/e^3 + (9.8412318819273341e+08,0.0000000000000000e+00)/e^2 + (3.1934010681169968e+09,0.0000000000000000e+00)/e^1 + (3.5140769767349182e+10,0.0000000000000000e+00) LoopSqe2: (1.0124361440891649e+10,0.0000000000000000e+00)/e^4 + (2.2495016394192062e+10,6.7975249329332854e-07)/e^3 + (-1.5669783851021061e+10,-1.1588246162652638e-07)/e^2 + (-1.2423928337609927e+11,-1.2451300790417008e-07)/e^1 + (-1.5735278568938934e+11,4.0963072933664080e-07) Absolute error: (-1.1444091796875000e-05,0.0000000000000000e+00)/e^4 + (-6.4849853515625000e-05,-4.6402467868134067e-08)/e^3 + (-1.7726898193359375e-02,-8.3105461312626971e-07)/e^2 + (-9.8336279571058655e+08,-7.9022356658242643e-08)/e^1 + (-8.4599840637940063e+09,-1.9013864402950276e-06) Fractional error[e^4]: -1.1303519598434174e-15 Fractional error[e^3]: -2.8828542455460684e-15 Fractional error[e^2]: 1.1312790502980850e-12 Fractional error[e^1]: 7.9150713766895607e-03 Fractional error[e^0]: 5.3764437831395076e-02 LoopSqe2[/e4]/B/5^3: 1.0000000000000020e+00 DblLoop: (-3.3747871469638786e+09,0.0000000000000000e+00)/e^4 + (-6.2609168441772594e+09,0.0000000000000000e+00)/e^3 + (1.5628856143537975e+10,0.0000000000000000e+00)/e^2 + (5.4530044551249359e+10,0.0000000000000000e+00)/e^1 + (1.1344834601048307e+10,0.0000000000000000e+00) Absolute error: (4.2915344238281250e-06,0.0000000000000000e+00)/e^4 + (1.7166137695312500e-05,0.0000000000000000e+00)/e^3 + (-1.3797760009765625e-02,0.0000000000000000e+00)/e^2 + (4.4657499069841003e+08,0.0000000000000000e+00)/e^1 + (-8.5459663987097778e+09,0.0000000000000000e+00) Fractional error[e^4]: -1.2716459548238462e-15 Fractional error[e^3]: -2.7417929550170033e-15 Fractional error[e^2]: -8.8283876203381334e-13 Fractional error[e^1]: 8.1895218383455076e-03 Fractional error[e^0]: -7.5329140522860483e-01 DblLoop[/e4]/B/Nc/5^2: -1.0000000000000007e+00 ==================== Test point 7 ==================== # rnd seed 7, seq 1 # p0 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,5.0000000000000000e-01) # p1 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,-5.0000000000000000e-01) # p2 = (4.5548858867817760e-01,1.3787616956357607e-01,-3.9696828458843969e-01,1.7571624089259821e-01) # p3 = (8.3576886336348619e-02,3.9676937354651810e-02,4.2780086841083406e-02,5.9838956723052311e-02) # p4 = (4.6093452498547371e-01,-1.7755310691822793e-01,3.5418819774735633e-01,-2.3555519761565058e-01) Pentagon functions evaluation time: 1660ms 2L evaluation time: 742ms L^2 evaluation time: 81ms VV evaluation time: 2483ms Born: 5.4160932944175556e+07 Loop: (-7.3117259474636993e+09,0.0000000000000000e+00)/e^2 + (-7.4515115819522772e+09,0.0000000000000000e+00)/e^1 + (-3.0740965863653064e+09,0.0000000000000000e+00) LoopSq: (1.2186209912439495e+10,0.0000000000000000e+00)/e^4 + (2.5416232268760311e+10,0.0000000000000000e+00)/e^3 + (3.6900446322593094e+10,0.0000000000000000e+00)/e^2 + (4.8955273185771744e+10,0.0000000000000000e+00)/e^1 + (5.7465810073506927e+10,0.0000000000000000e+00) LoopSqe2: (1.2186209912439484e+10,0.0000000000000000e+00)/e^4 + (2.5416232268760292e+10,1.7912264671515743e-08)/e^3 + (1.6854934491857685e+10,6.0368028975688048e-07)/e^2 + (-2.8881717668937531e+10,-1.2737192420786414e-06)/e^1 + (-9.4993525213194580e+10,8.4404419453676383e-07) Absolute error: (-1.7166137695312500e-05,0.0000000000000000e+00)/e^4 + (-4.1961669921875000e-05,3.3694791157223847e-07)/e^3 + (0.0000000000000000e+00,2.3198131415824719e-07)/e^2 + (-5.9658050537109375e-02,-2.0867006043090441e-06)/e^1 + (-1.0649108886718750e-01,-5.8799321891456202e-06) Fractional error[e^4]: -1.4086527163617613e-15 Fractional error[e^3]: -1.6509791647383985e-15 Fractional error[e^2]: 0.0000000000000000e+00 Fractional error[e^1]: 2.0655991177862660e-12 Fractional error[e^0]: 1.1210352350666939e-12 LoopSqe2[/e4]/B/5^3: 9.9999999999999856e-01 DblLoop: (-4.0620699708131638e+09,0.0000000000000000e+00)/e^4 + (-6.9826517669552755e+09,0.0000000000000000e+00)/e^3 + (7.4789577199181490e+09,0.0000000000000000e+00)/e^2 + (3.7088089879748444e+10,0.0000000000000000e+00)/e^1 + (6.3441213153412628e+10,0.0000000000000000e+00) Absolute error: (1.4305114746093750e-06,0.0000000000000000e+00)/e^4 + (3.8146972656250000e-06,0.0000000000000000e+00)/e^3 + (-5.5313110351562500e-05,0.0000000000000000e+00)/e^2 + (-1.8244171142578125e-01,0.0000000000000000e+00)/e^1 + (3.6202751159667969e+01,0.0000000000000000e+00) Fractional error[e^4]: -3.5216317909044013e-16 Fractional error[e^3]: -5.4631068438464685e-16 Fractional error[e^2]: -7.3958314009786717e-15 Fractional error[e^1]: -4.9191455266991683e-12 Fractional error[e^0]: 5.7065036054911179e-10 DblLoop[/e4]/B/Nc/5^2: -9.9999999999999922e-01 ==================== Test point 8 ==================== # rnd seed 8, seq 1 # p0 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,5.0000000000000000e-01) # p1 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,-5.0000000000000000e-01) # p2 = (4.6819047457023277e-01,-3.4126835953167171e-02,-3.9409610175976073e-01,2.5045147658555689e-01) # p3 = (1.9305403530947712e-01,-1.0545445936812445e-01,1.2015766052904626e-01,-1.0821901018229617e-01) # p4 = (3.3875549012029005e-01,1.3958129532129163e-01,2.7393844123071448e-01,-1.4223246640326073e-01) Pentagon functions evaluation time: 1658ms 2L evaluation time: 740ms L^2 evaluation time: 81ms VV evaluation time: 2479ms Born: 1.3798112691222198e+07 Loop: (-1.8627452133149979e+09,0.0000000000000000e+00)/e^2 + (-1.4078933743158987e+09,0.0000000000000000e+00)/e^1 + (1.2444755120980000e+09,0.0000000000000000e+00) LoopSq: (3.1045753555249996e+09,0.0000000000000000e+00)/e^4 + (4.9114540311380939e+09,0.0000000000000000e+00)/e^3 + (2.1745183814812489e+09,0.0000000000000000e+00)/e^2 + (5.6543229886689529e+09,0.0000000000000000e+00)/e^1 + (8.0191229753144646e+09,0.0000000000000000e+00) LoopSqe2: (3.1045753555249977e+09,0.0000000000000000e+00)/e^4 + (4.9114540311380901e+09,-1.2720648534525480e-08)/e^3 + (-2.9323033839192591e+09,3.3510352892562878e-07)/e^2 + (-1.7292129524834862e+10,3.2985019515763270e-07)/e^1 + (-1.5783143159849716e+10,-5.6760791267151944e-07) Absolute error: (2.8610229492187500e-06,0.0000000000000000e+00)/e^4 + (1.9073486328125000e-06,3.2600626198586724e-08)/e^3 + (-4.1627883911132812e-04,2.2552673328846140e-07)/e^2 + (-6.7029953002929688e-01,-1.0882763490371872e-07)/e^1 + (2.8171920776367188e+00,2.0336838133516721e-06) Fractional error[e^4]: 9.2155049292882702e-16 Fractional error[e^3]: 3.8834703953658423e-16 Fractional error[e^2]: 1.4196308655993773e-13 Fractional error[e^1]: 3.8763272566667761e-11 Fractional error[e^0]: -1.7849372898063123e-10 LoopSqe2[/e4]/B/5^3: 1.0000000000000011e+00 DblLoop: (-1.0348584518416653e+09,0.0000000000000000e+00)/e^4 + (-1.2577032447040861e+09,0.0000000000000000e+00)/e^3 + (4.6706913287432957e+09,0.0000000000000000e+00)/e^2 + (1.0428642739033564e+10,0.0000000000000000e+00)/e^1 + (-4.1929733899017572e+09,0.0000000000000000e+00) Absolute error: (-5.9604644775390625e-07,0.0000000000000000e+00)/e^4 + (-4.7683715820312500e-07,0.0000000000000000e+00)/e^3 + (5.9127807617187500e-05,0.0000000000000000e+00)/e^2 + (8.4158172607421875e+00,0.0000000000000000e+00)/e^1 + (2.7854090642929077e+02,0.0000000000000000e+00) Fractional error[e^4]: 5.7596905808051726e-16 Fractional error[e^3]: 3.7913328140877607e-16 Fractional error[e^2]: 1.2659326736775930e-14 Fractional error[e^1]: 8.0699065749394845e-10 Fractional error[e^0]: -6.6430401657239484e-08 DblLoop[/e4]/B/Nc/5^2: -1.0000000000000004e+00 ==================== Test point 9 ==================== # rnd seed 9, seq 2 # p0 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,5.0000000000000000e-01) # p1 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,-5.0000000000000000e-01) # p2 = (2.5323840242931950e-01,-5.1955817076492800e-02,1.6517053238460871e-01,-1.8479441757978754e-01) # p3 = (3.8990530024048586e-01,3.3719891805378410e-01,4.9214349012809536e-02,1.8947554108703896e-01) # p4 = (3.5685629733019475e-01,-2.8524310097729122e-01,-2.1438488139741821e-01,-4.6811235072514177e-03) Pentagon functions evaluation time: 1642ms 2L evaluation time: 740ms L^2 evaluation time: 80ms VV evaluation time: 2462ms Born: 7.0976976386649664e+06 Loop: (-9.5818918121977139e+08,0.0000000000000000e+00)/e^2 + (-6.5555501482726169e+08,0.0000000000000000e+00)/e^1 + (9.7557651924078071e+08,0.0000000000000000e+00) LoopSq: (1.5969819686996200e+09,0.0000000000000000e+00)/e^4 + (2.2787747039541159e+09,0.0000000000000000e+00)/e^3 + (-5.7738662967046618e+08,0.0000000000000000e+00)/e^2 + (1.9623803582509762e+08,0.0000000000000000e+00)/e^1 + (3.3861959632116232e+09,0.0000000000000000e+00) LoopSqe2: (1.5969819686996198e+09,0.0000000000000000e+00)/e^4 + (2.2787747039541168e+09,2.4317837743481618e-08)/e^3 + (-3.2043166741268477e+09,-1.3227147377392612e-07)/e^2 + (-1.1953023546311596e+10,-3.4692530448410253e-07)/e^1 + (-7.3793186300983782e+09,-5.3545136324828491e-08) Absolute error: (4.0531158447265625e-06,0.0000000000000000e+00)/e^4 + (5.2452087402343750e-06,7.1866900430705982e-08)/e^3 + (-2.5749206542968750e-05,-5.0134200790807881e-08)/e^2 + (4.2219907802772522e+05,3.3358276141370879e-08)/e^1 + (8.5677039034080505e+05,3.0754381441511214e-07) Fractional error[e^4]: 2.5379847262940031e-15 Fractional error[e^3]: 2.3017671431637882e-15 Fractional error[e^2]: 8.0357870839920078e-15 Fractional error[e^1]: -3.5321529853256691e-05 Fractional error[e^0]: -1.1610426833261473e-04 LoopSqe2[/e4]/B/5^3: 1.0000000000000013e+00 DblLoop: (-5.3232732289987302e+08,0.0000000000000000e+00)/e^4 + (-5.6440488292141855e+08,0.0000000000000000e+00)/e^3 + (2.6794372936300192e+09,0.0000000000000000e+00)/e^2 + (4.7050179453323803e+09,0.0000000000000000e+00)/e^1 + (-6.0785780990370617e+09,0.0000000000000000e+00) Absolute error: (-5.3644180297851562e-07,0.0000000000000000e+00)/e^4 + (-4.7683715820312500e-07,0.0000000000000000e+00)/e^3 + (-3.5285949707031250e-05,0.0000000000000000e+00)/e^2 + (6.8022043352127075e+03,0.0000000000000000e+00)/e^1 + (-1.5494934036350250e+05,0.0000000000000000e+00) Fractional error[e^4]: 1.0077292295579133e-15 Fractional error[e^3]: 8.4484945582852889e-16 Fractional error[e^2]: -1.3169164208813012e-14 Fractional error[e^1]: 1.4457339832169704e-06 Fractional error[e^0]: 2.5491050347456886e-05 DblLoop[/e4]/B/Nc/5^2: -1.0000000000000009e+00 ==================== Test point 10 ==================== # rnd seed 10, seq 1 # p0 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,5.0000000000000000e-01) # p1 = (-5.0000000000000000e-01,0.0000000000000000e+00,0.0000000000000000e+00,-5.0000000000000000e-01) # p2 = (1.2148263360051487e-01,-9.8361108945026879e-02,5.9821876691037508e-02,3.8787441044541758e-02) # p3 = (3.9209836775641066e-01,-3.8766721207229399e-01,-4.0675018861748000e-02,-4.2435898976372906e-02) # p4 = (4.8641899864307447e-01,4.8602832101732091e-01,-1.9146857829289512e-02,3.6484579318311508e-03) Pentagon functions evaluation time: 1659ms 2L evaluation time: 741ms L^2 evaluation time: 80ms VV evaluation time: 2480ms Born: 1.7762093537555322e+07 Loop: (-2.3978826275699711e+09,0.0000000000000000e+00)/e^2 + (-1.9706873048985803e+09,0.0000000000000000e+00)/e^1 + (-5.6638101574625611e+08,0.0000000000000000e+00) LoopSq: (3.9964710459499569e+09,0.0000000000000000e+00)/e^4 + (6.8020112007036886e+09,0.0000000000000000e+00)/e^3 + (1.0287814962620544e+10,0.0000000000000000e+00)/e^2 + (1.7433784514197586e+10,0.0000000000000000e+00)/e^1 + (1.9706537294902790e+10,0.0000000000000000e+00) LoopSqe2: (3.9964710459499502e+09,0.0000000000000000e+00)/e^4 + (6.8020112007036610e+09,1.8754972175294427e-07)/e^3 + (3.7138835919648304e+09,3.5548333876533889e-07)/e^2 + (-5.7827894471834927e+09,3.6322554564094389e-07)/e^1 + (-9.2252594349244347e+09,2.6100357075620195e-07) Absolute error: (-4.7683715820312500e-07,0.0000000000000000e+00)/e^4 + (4.7683715820312500e-06,2.9163770998152927e-07)/e^3 + (9.0599060058593750e-06,3.7438967126490752e-07)/e^2 + (-1.3446807861328125e-04,-4.6606047021668928e-07)/e^1 + (-1.5142440795898438e-02,2.0425505766752394e-06) Fractional error[e^4]: -1.1931455344493359e-16 Fractional error[e^3]: 7.0102377684088010e-16 Fractional error[e^2]: 2.4394695691219097e-15 Fractional error[e^1]: 2.3253151414456898e-14 Fractional error[e^0]: 1.6414108354040530e-12 LoopSqe2[/e4]/B/5^3: 1.0000000000000007e+00 DblLoop: (-1.3321570153166490e+09,0.0000000000000000e+00)/e^4 + (-1.7788794946184480e+09,0.0000000000000000e+00)/e^3 + (3.5167244540345678e+09,0.0000000000000000e+00)/e^2 + (1.1971825938396790e+10,0.0000000000000000e+00)/e^1 + (1.6518567311712646e+10,0.0000000000000000e+00) Absolute error: (1.1920928955078125e-06,0.0000000000000000e+00)/e^4 + (4.7683715820312500e-07,0.0000000000000000e+00)/e^3 + (-5.7220458984375000e-06,0.0000000000000000e+00)/e^2 + (1.0681152343750000e-04,0.0000000000000000e+00)/e^1 + (3.4655189514160156e-01,0.0000000000000000e+00) Fractional error[e^4]: -8.9485915083700278e-16 Fractional error[e^3]: -2.6805478372519093e-16 Fractional error[e^2]: -1.6270953193028454e-15 Fractional error[e^1]: 8.9219074840478097e-15 Fractional error[e^0]: 2.0979537062870802e-11 DblLoop[/e4]/B/Nc/5^2: -9.9999999999999978e-01 ## init: Restore floating point unit ######################################################################## # This is OneLOop-3.5, date 14-05-2014 # # Author: Andreas van Hameren # # Please cite: vanHameren:2010cp, arXiv:1007.4716 # # vanHameren:2009dr, arXiv:0903.4665 # ######################################################################## total number of errors and warnings =================================== fferr: no errors the warning system has been disabled