#-------------------------------------------------------------------- # NJet -- multi-leg one-loop matrix elements in the Standard Model # version : 2.1.0-git 7a30b93fd94e82c4492861be01ef3e2b04db7762 # Authors : Simon Badger, Valery Yundin # Homepage: https://bitbucket.org/njet/njet #-------------------------------------------------------------------- ==================================================== This is QCDLoop - version 1.95 Authors: Keith Ellis and Giulia Zanderighi (ellis@fnal.gov, g.zanderighi1@physics.ox.ac.uk) 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) ==================== 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: 2293ms Other evaluation time: 88ms Total evaluation time: 2381ms DblLoop: (-1.7901392509833181e+08,0.0000000000000000e+00)/e^4 + (-3.9023849419776869e+09,0.0000000000000000e+00)/e^3 + (-4.1585010428068954e+10,0.0000000000000000e+00)/e^2 + (-2.8798547236992969e+11,0.0000000000000000e+00)/e^1 + (-1.4533437561516753e+12,0.0000000000000000e+00) Absolute error: (-2.3841857910156250e-07,0.0000000000000000e+00)/e^4 + (-6.1988830566406250e-06,0.0000000000000000e+00)/e^3 + (-6.8664550781250000e-05,0.0000000000000000e+00)/e^2 + (1.2476196289062500e+00,0.0000000000000000e+00)/e^1 + (2.8826904296875000e+01,0.0000000000000000e+00) Fractional error[e^0]: -1.9834883643224280e-11 Fractional error[e^1]: -4.3322311317969163e-12 Fractional error[e^2]: 1.6511851283534357e-15 Fractional error[e^3]: 1.5884857974823718e-15 Fractional error[e^4]: 1.3318437600348681e-15 ==================== 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: 2096ms Other evaluation time: 64ms Total evaluation time: 2160ms DblLoop: (-6.8240608822655334e+09,0.0000000000000000e+00)/e^4 + (-1.5883504998224304e+11,0.0000000000000000e+00)/e^3 + (-1.8323567124203962e+12,0.0000000000000000e+00)/e^2 + (-1.3932975187000627e+13,0.0000000000000000e+00)/e^1 + (-7.8236303192101438e+13,0.0000000000000000e+00) Absolute error: (-6.6757202148437500e-06,0.0000000000000000e+00)/e^4 + (-2.4414062500000000e-04,0.0000000000000000e+00)/e^3 + (-3.9062500000000000e-03,0.0000000000000000e+00)/e^2 + (3.1718750000000000e+01,0.0000000000000000e+00)/e^1 + (7.4131250000000000e+02,0.0000000000000000e+00) Fractional error[e^0]: -9.4753007204312955e-12 Fractional error[e^1]: -2.2765238274157974e-12 Fractional error[e^2]: 2.1318174422709196e-15 Fractional error[e^3]: 1.5370702186154358e-15 Fractional error[e^4]: 9.7826211254836650e-16 ==================== 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: 8676ms Other evaluation time: 63ms Total evaluation time: 8739ms DblLoop: (-1.2442681272578602e+10,0.0000000000000000e+00)/e^4 + (-2.9450205052378027e+11,0.0000000000000000e+00)/e^3 + (-3.4829705320913574e+12,0.0000000000000000e+00)/e^2 + (-2.7401227999010000e+13,0.0000000000000000e+00)/e^1 + (-1.6027121325776962e+14,0.0000000000000000e+00) Absolute error: (-1.1444091796875000e-05,0.0000000000000000e+00)/e^4 + (-3.0517578125000000e-04,0.0000000000000000e+00)/e^3 + (-4.3945312500000000e-03,0.0000000000000000e+00)/e^2 + (3.3713608476562500e+06,0.0000000000000000e+00)/e^1 + (9.2629004137931250e+11,0.0000000000000000e+00) Fractional error[e^0]: -5.7795160001037045e-03 Fractional error[e^1]: -1.2303685250084617e-07 Fractional error[e^2]: 1.2617193311024925e-15 Fractional error[e^3]: 1.0362433154785720e-15 Fractional error[e^4]: 9.1974483201588469e-16 ==================== 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: 2153ms Other evaluation time: 101ms Total evaluation time: 2254ms DblLoop: (-4.1275503918608487e+08,0.0000000000000000e+00)/e^4 + (-9.1496423234050884e+09,0.0000000000000000e+00)/e^3 + (-9.9910591324485703e+10,0.0000000000000000e+00)/e^2 + (-7.1425045756477539e+11,0.0000000000000000e+00)/e^1 + (-3.7411634391932412e+12,0.0000000000000000e+00) Absolute error: (-6.5565109252929688e-07,0.0000000000000000e+00)/e^4 + (-1.5258789062500000e-05,0.0000000000000000e+00)/e^3 + (-1.0070800781250000e-03,0.0000000000000000e+00)/e^2 + (-1.2265612792968750e+02,0.0000000000000000e+00)/e^1 + (-2.6653706054687500e+03,0.0000000000000000e+00) Fractional error[e^0]: 7.1244431011640607e-10 Fractional error[e^1]: 1.7172705544758270e-10 Fractional error[e^2]: 1.0079813008555268e-14 Fractional error[e^3]: 1.6676924106057689e-15 Fractional error[e^4]: 1.5884750766996831e-15 ==================== 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: 2306ms Other evaluation time: 87ms Total evaluation time: 2393ms DblLoop: (-1.9856987281463394e+10,0.0000000000000000e+00)/e^4 + (-4.7351851028611182e+11,0.0000000000000000e+00)/e^3 + (-5.4982027050021016e+12,0.0000000000000000e+00)/e^2 + (-4.1181673859379016e+13,0.0000000000000000e+00)/e^1 + (-2.2202278814166594e+14,0.0000000000000000e+00) Absolute error: (-7.6293945312500000e-06,0.0000000000000000e+00)/e^4 + (-4.2724609375000000e-04,0.0000000000000000e+00)/e^3 + (-2.9296875000000000e-03,0.0000000000000000e+00)/e^2 + (1.7968750000000000e-01,0.0000000000000000e+00)/e^1 + (1.0625000000000000e+00,0.0000000000000000e+00) Fractional error[e^0]: -4.7855448032751091e-15 Fractional error[e^1]: -4.3632879181543190e-15 Fractional error[e^2]: 5.3284457798084766e-16 Fractional error[e^3]: 9.0227960358265007e-16 Fractional error[e^4]: 3.8421712332827455e-16 ==================== 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: 2111ms Other evaluation time: 87ms Total evaluation time: 2198ms DblLoop: (-1.1344636172545881e+09,0.0000000000000000e+00)/e^4 + (-2.5729051084810799e+10,0.0000000000000000e+00)/e^3 + (-2.8472459777491644e+11,0.0000000000000000e+00)/e^2 + (-2.0395760426214292e+12,0.0000000000000000e+00)/e^1 + (-1.0572741711499336e+13,0.0000000000000000e+00) Absolute error: (-9.5367431640625000e-07,0.0000000000000000e+00)/e^4 + (-2.2888183593750000e-05,0.0000000000000000e+00)/e^3 + (2.1972656250000000e-03,0.0000000000000000e+00)/e^2 + (-7.6159912109375000e+01,0.0000000000000000e+00)/e^1 + (-1.7144492187500000e+03,0.0000000000000000e+00) Fractional error[e^0]: 1.6215748625404293e-10 Fractional error[e^1]: 3.7341050550627220e-11 Fractional error[e^2]: -7.7171612223577750e-15 Fractional error[e^3]: 8.8958522093580400e-16 Fractional error[e^4]: 8.4063896091630531e-16 ==================== 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: 2127ms Other evaluation time: 86ms Total evaluation time: 2213ms DblLoop: (-1.0778066928171151e+09,0.0000000000000000e+00)/e^4 + (-2.4297287833242004e+10,0.0000000000000000e+00)/e^3 + (-2.7039268595276324e+11,0.0000000000000000e+00)/e^2 + (-1.9757475143433652e+12,0.0000000000000000e+00)/e^1 + (-1.0625174324367598e+13,0.0000000000000000e+00) Absolute error: (2.3841857910156250e-06,0.0000000000000000e+00)/e^4 + (5.3405761718750000e-05,0.0000000000000000e+00)/e^3 + (4.5776367187500000e-04,0.0000000000000000e+00)/e^2 + (-8.0432128906250000e+00,0.0000000000000000e+00)/e^1 + (-2.1093750000000000e+02,0.0000000000000000e+00) Fractional error[e^0]: 1.9852615454622654e-11 Fractional error[e^1]: 4.0709720408268569e-12 Fractional error[e^2]: -1.6929587805306608e-15 Fractional error[e^3]: -2.1980132961870595e-15 Fractional error[e^4]: -2.2120717999848047e-15 ==================== 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: 2125ms Other evaluation time: 88ms Total evaluation time: 2213ms DblLoop: (-3.4840740627387106e+08,0.0000000000000000e+00)/e^4 + (-7.6787669749089899e+09,0.0000000000000000e+00)/e^3 + (-8.2791024757351700e+10,0.0000000000000000e+00)/e^2 + (-5.8042667544046729e+11,0.0000000000000000e+00)/e^1 + (-2.9659312428135649e+12,0.0000000000000000e+00) Absolute error: (-7.7486038208007812e-07,0.0000000000000000e+00)/e^4 + (-1.9073486328125000e-05,0.0000000000000000e+00)/e^3 + (-1.5258789062500000e-04,0.0000000000000000e+00)/e^2 + (-2.3801269531250000e+00,0.0000000000000000e+00)/e^1 + (-5.5802734375000000e+01,0.0000000000000000e+00) Fractional error[e^0]: 1.8814574515241955e-11 Fractional error[e^1]: 4.1006505280254347e-12 Fractional error[e^2]: 1.8430487008973814e-15 Fractional error[e^3]: 2.4839256602588936e-15 Fractional error[e^4]: 2.2240066316816099e-15 ==================== 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: 2104ms Other evaluation time: 87ms Total evaluation time: 2191ms DblLoop: (-2.1259192994617388e+08,0.0000000000000000e+00)/e^4 + (-4.6524768178206444e+09,0.0000000000000000e+00)/e^3 + (-4.9729702023000168e+10,0.0000000000000000e+00)/e^2 + (-3.4497004954691663e+11,0.0000000000000000e+00)/e^1 + (-1.7401490637461099e+12,0.0000000000000000e+00) Absolute error: (-3.5762786865234375e-07,0.0000000000000000e+00)/e^4 + (-8.5830688476562500e-06,0.0000000000000000e+00)/e^3 + (-9.9182128906250000e-05,0.0000000000000000e+00)/e^2 + (-5.9814453125000000e-03,0.0000000000000000e+00)/e^1 + (-1.6113281250000000e-01,0.0000000000000000e+00) Fractional error[e^0]: 9.2597131968178048e-14 Fractional error[e^1]: 1.7339027896352235e-14 Fractional error[e^2]: 1.9944243554963972e-15 Fractional error[e^3]: 1.8448386061334121e-15 Fractional error[e^4]: 1.6822269252783562e-15 ==================== 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: 2122ms Other evaluation time: 86ms Total evaluation time: 2208ms DblLoop: (-4.4585865480666292e+08,0.0000000000000000e+00)/e^4 + (-9.8800582159604626e+09,0.0000000000000000e+00)/e^3 + (-1.0793548536861368e+11,0.0000000000000000e+00)/e^2 + (-7.7283327494778052e+11,0.0000000000000000e+00)/e^1 + (-4.0626837529152441e+12,0.0000000000000000e+00) Absolute error: (-5.3644180297851562e-07,0.0000000000000000e+00)/e^4 + (-1.1444091796875000e-05,0.0000000000000000e+00)/e^3 + (-1.2207031250000000e-04,0.0000000000000000e+00)/e^2 + (-5.2636718750000000e-01,0.0000000000000000e+00)/e^1 + (-1.2669921875000000e+01,0.0000000000000000e+00) Fractional error[e^0]: 3.1186089406807740e-12 Fractional error[e^1]: 6.8108763502136483e-13 Fractional error[e^2]: 1.1309562567223751e-15 Fractional error[e^3]: 1.1583020612558702e-15 Fractional error[e^4]: 1.2031656158186100e-15 ######################################################################## # 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