##############ECHO OF PROBLEM################# ##############temp/div_lin_linpostode.ode################# diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-1.5); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(1.0); array_given_ord_poles[1][2]=c(0.0); /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.3407877024514202 y[1] (numeric) = 0.3407877024514202 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 0.3473453398890792 y[1] (numeric) = 0.3473453398890792 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 0.3538933324510595 y[1] (numeric) = 0.3538933324510595 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 0.3604317988446541 y[1] (numeric) = 0.3604317988446541 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 0.3669608555990131 y[1] (numeric) = 0.3669608555990131 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 0.3734806171181086 y[1] (numeric) = 0.3734806171181087 absolute error = 5.551115123125783e-17 relative error = 1.486319468453248e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 0.3799911957320993 y[1] (numeric) = 0.3799911957320994 absolute error = 5.551115123125783e-17 relative error = 1.460853615945202e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 0.3864927017471523 y[1] (numeric) = 0.3864927017471524 absolute error = 1.110223024625157e-16 relative error = 2.872558833857299e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 0.3929852434937783 y[1] (numeric) = 0.3929852434937784 absolute error = 1.110223024625157e-16 relative error = 2.825101051517558e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 0.3994689273737319 y[1] (numeric) = 0.3994689273737321 absolute error = 1.665334536937735e-16 relative error = 4.168871275886984e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 0.405943857905529 y[1] (numeric) = 0.4059438579055292 absolute error = 1.665334536937735e-16 relative error = 4.102376485088464e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (closed_form) = 0.4124101377686285 y[1] (numeric) = 0.4124101377686287 absolute error = 2.220446049250313e-16 relative error = 5.384072421847287e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (closed_form) = 0.4188678678463268 y[1] (numeric) = 0.418867867846327 absolute error = 2.220446049250313e-16 relative error = 5.301065609704263e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (closed_form) = 0.4253171472674083 y[1] (numeric) = 0.4253171472674085 absolute error = 2.220446049250313e-16 relative error = 5.220683114979747e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = 0.4317580734465958 y[1] (numeric) = 0.4317580734465961 absolute error = 2.775557561562891e-16 relative error = 6.428501821416896e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = 0.4381907421238421 y[1] (numeric) = 0.4381907421238424 absolute error = 3.33066907387547e-16 relative error = 7.600957194422313e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 0.4446152474025015 y[1] (numeric) = 0.4446152474025017 absolute error = 2.220446049250313e-16 relative error = 4.994084350958361e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 0.4510316817864208 y[1] (numeric) = 0.4510316817864211 absolute error = 2.220446049250313e-16 relative error = 4.923037868328219e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 0.4574401362159849 y[1] (numeric) = 0.4574401362159851 absolute error = 1.665334536937735e-16 relative error = 3.640551856060638e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 0.4638407001031523 y[1] (numeric) = 0.4638407001031526 absolute error = 2.775557561562891e-16 relative error = 5.983859460684762e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 0.4702334613655162 y[1] (numeric) = 0.4702334613655164 absolute error = 1.665334536937735e-16 relative error = 3.541505813094949e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 0.47661850645942 y[1] (numeric) = 0.4766185064594201 absolute error = 5.551115123125783e-17 relative error = 1.164687280895253e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 0.4829959204121624 y[1] (numeric) = 0.4829959204121625 absolute error = 5.551115123125783e-17 relative error = 1.149308904801673e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 0.4893657868533188 y[1] (numeric) = 0.4893657868533188 absolute error = 5.551115123125783e-17 relative error = 1.134348839304873e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 0.49572818804521 y[1] (numeric) = 0.4957281880452098 absolute error = 1.665334536937735e-16 relative error = 3.359370270035678e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = 0.5020832049125448 y[1] (numeric) = 0.5020832049125447 absolute error = 1.110223024625157e-16 relative error = 2.211233145746312e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (closed_form) = 0.508430917071264 y[1] (numeric) = 0.5084309170712636 absolute error = 3.33066907387547e-16 relative error = 6.55087832396437e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (closed_form) = 0.5147714028566103 y[1] (numeric) = 0.5147714028566099 absolute error = 3.33066907387547e-16 relative error = 6.470190564962733e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (closed_form) = 0.5211047393504509 y[1] (numeric) = 0.5211047393504504 absolute error = 4.440892098500626e-16 relative error = 8.522071981222298e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = 0.5274310024078742 y[1] (numeric) = 0.5274310024078738 absolute error = 4.440892098500626e-16 relative error = 8.419854119736376e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (closed_form) = 0.5337502666830851 y[1] (numeric) = 0.5337502666830846 absolute error = 5.551115123125783e-16 relative error = 1.040021049098935e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 0.5400626056546212 y[1] (numeric) = 0.5400626056546205 absolute error = 6.661338147750939e-16 relative error = 1.233438138098192e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 0.5463680916499091 y[1] (numeric) = 0.5463680916499083 absolute error = 7.771561172376096e-16 relative error = 1.422403923499215e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 0.5526667958691851 y[1] (numeric) = 0.5526667958691842 absolute error = 8.881784197001252e-16 relative error = 1.607077585153777e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 0.5589587884087956 y[1] (numeric) = 0.558958788408795 absolute error = 6.661338147750939e-16 relative error = 1.191740479958096e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 0.5652441382839004 y[1] (numeric) = 0.5652441382838997 absolute error = 6.661338147750939e-16 relative error = 1.178488673580053e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (closed_form) = 0.571522913450593 y[1] (numeric) = 0.5715229134505925 absolute error = 5.551115123125783e-16 relative error = 9.712847888478692e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = 0.5777951808274608 y[1] (numeric) = 0.5777951808274604 absolute error = 4.440892098500626e-16 relative error = 7.685927896007754e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (closed_form) = 0.5840610063165975 y[1] (numeric) = 0.584061006316597 absolute error = 5.551115123125783e-16 relative error = 9.504341264167071e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = 0.5903204548240868 y[1] (numeric) = 0.5903204548240863 absolute error = 4.440892098500626e-16 relative error = 7.522849771187405e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (closed_form) = 0.5965735902799729 y[1] (numeric) = 0.5965735902799724 absolute error = 5.551115123125783e-16 relative error = 9.304996422185963e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (closed_form) = 0.6028204756577327 y[1] (numeric) = 0.6028204756577321 absolute error = 5.551115123125783e-16 relative error = 9.208570954841912e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (closed_form) = 0.6090611729932649 y[1] (numeric) = 0.6090611729932645 absolute error = 4.440892098500626e-16 relative error = 7.291372846303132e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (closed_form) = 0.6152957434034105 y[1] (numeric) = 0.6152957434034101 absolute error = 4.440892098500626e-16 relative error = 7.217491988383567e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (closed_form) = 0.6215242471040179 y[1] (numeric) = 0.6215242471040173 absolute error = 5.551115123125783e-16 relative error = 8.931453839477885e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (closed_form) = 0.6277467434275658 y[1] (numeric) = 0.6277467434275652 absolute error = 5.551115123125783e-16 relative error = 8.842921418940524e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (closed_form) = 0.633963290840359 y[1] (numeric) = 0.6339632908403584 absolute error = 5.551115123125783e-16 relative error = 8.756209079184102e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = 0.640173946959306 y[1] (numeric) = 0.6401739469593054 absolute error = 5.551115123125783e-16 relative error = 8.671260599548659e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = 0.6463787685682932 y[1] (numeric) = 0.6463787685682927 absolute error = 5.551115123125783e-16 relative error = 8.588022059297077e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = 0.6525778116341665 y[1] (numeric) = 0.6525778116341659 absolute error = 5.551115123125783e-16 relative error = 8.506441721064405e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = 0.658771131322331 y[1] (numeric) = 0.6587711313223303 absolute error = 6.661338147750939e-16 relative error = 1.011176390559167e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 0.6649587820119804 y[1] (numeric) = 0.6649587820119798 absolute error = 6.661338147750939e-16 relative error = 1.001767076087871e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = 0.6711408173109669 y[1] (numeric) = 0.6711408173109662 absolute error = 6.661338147750939e-16 relative error = 9.925395648622083e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (closed_form) = 0.67731729007032 y[1] (numeric) = 0.6773172900703195 absolute error = 5.551115123125783e-16 relative error = 8.195738104588262e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = 0.6834882523984267 y[1] (numeric) = 0.6834882523984261 absolute error = 5.551115123125783e-16 relative error = 8.121741820208878e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = 0.6896537556748794 y[1] (numeric) = 0.689653755674879 absolute error = 4.440892098500626e-16 relative error = 6.439306770909803e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = 0.695813850564005 y[1] (numeric) = 0.6958138505640045 absolute error = 5.551115123125783e-16 relative error = 7.977873850349805e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (closed_form) = 0.7019685870280787 y[1] (numeric) = 0.7019685870280781 absolute error = 6.661338147750939e-16 relative error = 9.489510315487217e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (closed_form) = 0.7081180143402361 y[1] (numeric) = 0.7081180143402354 absolute error = 7.771561172376096e-16 relative error = 1.097495193596645e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (closed_form) = 0.7142621810970891 y[1] (numeric) = 0.7142621810970883 absolute error = 7.771561172376096e-16 relative error = 1.08805441167824e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 0.7204011352310542 y[1] (numeric) = 0.7204011352310535 absolute error = 6.661338147750939e-16 relative error = 9.246706899780841e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = 0.7265349240224019 y[1] (numeric) = 0.7265349240224015 absolute error = 4.440892098500626e-16 relative error = 6.112427567712761e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (closed_form) = 0.7326635941110337 y[1] (numeric) = 0.7326635941110331 absolute error = 5.551115123125783e-16 relative error = 7.576622023728564e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (closed_form) = 0.7387871915079935 y[1] (numeric) = 0.7387871915079932 absolute error = 3.33066907387547e-16 relative error = 4.508292932200128e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (closed_form) = 0.7449057616067238 y[1] (numeric) = 0.7449057616067235 absolute error = 3.33066907387547e-16 relative error = 4.471262333494892e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (closed_form) = 0.7510193491940689 y[1] (numeric) = 0.7510193491940685 absolute error = 3.33066907387547e-16 relative error = 4.434864531053248e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 0.7571279984610353 y[1] (numeric) = 0.7571279984610351 absolute error = 2.220446049250313e-16 relative error = 2.932722147065845e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = 0.7632317530133145 y[1] (numeric) = 0.7632317530133141 absolute error = 3.33066907387547e-16 relative error = 4.363902655681788e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (closed_form) = 0.769330655881574 y[1] (numeric) = 0.7693306558815737 absolute error = 3.33066907387547e-16 relative error = 4.329307623987588e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = 0.7754247495315237 y[1] (numeric) = 0.7754247495315234 absolute error = 3.33066907387547e-16 relative error = 4.295283424842588e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (closed_form) = 0.7815140758737626 y[1] (numeric) = 0.7815140758737624 absolute error = 2.220446049250313e-16 relative error = 2.841210565232327e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (closed_form) = 0.7875986762734122 y[1] (numeric) = 0.787598676273412 absolute error = 2.220446049250313e-16 relative error = 2.819260768385919e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (closed_form) = 0.7936785915595413 y[1] (numeric) = 0.7936785915595411 absolute error = 2.220446049250313e-16 relative error = 2.797664032851435e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = 0.7997538620343889 y[1] (numeric) = 0.7997538620343887 absolute error = 2.220446049250313e-16 relative error = 2.77641178699908e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (closed_form) = 0.8058245274823892 y[1] (numeric) = 0.8058245274823891 absolute error = 1.110223024625157e-16 relative error = 1.3777478678811e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = 0.8118906271790036 y[1] (numeric) = 0.8118906271790035 absolute error = 1.110223024625157e-16 relative error = 1.367453924776468e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (closed_form) = 0.8179521998993664 y[1] (numeric) = 0.8179521998993664 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (closed_form) = 0.8240092839267467 y[1] (numeric) = 0.8240092839267464 absolute error = 2.220446049250313e-16 relative error = 2.694685718429002e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (closed_form) = 0.8300619170608325 y[1] (numeric) = 0.8300619170608323 absolute error = 2.220446049250313e-16 relative error = 2.675036649208885e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (closed_form) = 0.8361101366258415 y[1] (numeric) = 0.8361101366258411 absolute error = 4.440892098500626e-16 relative error = 5.311372155374216e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = 0.8421539794784617 y[1] (numeric) = 0.8421539794784613 absolute error = 4.440892098500626e-16 relative error = 5.273254305882198e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = 0.8481934820156276 y[1] (numeric) = 0.8481934820156273 absolute error = 3.33066907387547e-16 relative error = 3.926779849758505e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (closed_form) = 0.8542286801821355 y[1] (numeric) = 0.8542286801821349 absolute error = 5.551115123125783e-16 relative error = 6.498394694430296e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = 0.860259609478101 y[1] (numeric) = 0.8602596094781004 absolute error = 5.551115123125783e-16 relative error = 6.452837099365286e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = 0.8662863049662644 y[1] (numeric) = 0.8662863049662637 absolute error = 6.661338147750939e-16 relative error = 7.689534175436781e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = 0.8723088012791457 y[1] (numeric) = 0.8723088012791448 absolute error = 8.881784197001252e-16 relative error = 1.018192661128385e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = 0.8783271326260547 y[1] (numeric) = 0.8783271326260539 absolute error = 7.771561172376096e-16 relative error = 8.848139700683499e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = 0.8843413327999583 y[1] (numeric) = 0.8843413327999575 absolute error = 7.771561172376096e-16 relative error = 8.787965555980697e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 0.8903514351842094 y[1] (numeric) = 0.8903514351842088 absolute error = 6.661338147750939e-16 relative error = 7.481695299758505e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = 0.8963574727591408 y[1] (numeric) = 0.8963574727591399 absolute error = 8.881784197001252e-16 relative error = 9.908752330319297e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (closed_form) = 0.9023594781085256 y[1] (numeric) = 0.9023594781085247 absolute error = 8.881784197001252e-16 relative error = 9.842844689367858e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 0.9083574834259092 y[1] (numeric) = 0.9083574834259089 absolute error = 2.220446049250313e-16 relative error = 2.444462769080523e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = 0.9143515205208184 y[1] (numeric) = 0.9143515205208188 absolute error = 4.440892098500626e-16 relative error = 4.856876156307014e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = 0.9203416208248421 y[1] (numeric) = 0.9203416208248429 absolute error = 8.881784197001252e-16 relative error = 9.650529755506536e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 0.9263278153975953 y[1] (numeric) = 0.9263278153975972 absolute error = 1.887379141862766e-15 relative error = 2.037485121887084e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = 0.9323101349325671 y[1] (numeric) = 0.9323101349325698 absolute error = 2.664535259100376e-15 relative error = 2.857992377496892e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = 0.9382886097628506 y[1] (numeric) = 0.9382886097628538 absolute error = 3.219646771412954e-15 relative error = 3.431403448696569e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = 0.9442632698667642 y[1] (numeric) = 0.9442632698667683 absolute error = 4.107825191113079e-15 relative error = 4.350296492727811e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = 0.950234144873363 y[1] (numeric) = 0.9502341448733678 absolute error = 4.773959005888173e-15 relative error = 5.023981754017475e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = 0.9562012640678424 y[1] (numeric) = 0.9562012640678479 absolute error = 5.440092820663267e-15 relative error = 5.689275914068748e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y[1] (closed_form) = 0.9621646563968393 y[1] (numeric) = 0.9621646563968453 absolute error = 5.995204332975845e-15 relative error = 6.230954642864326e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = 0.9681243504736301 y[1] (numeric) = 0.9681243504736369 absolute error = 6.772360450213455e-15 relative error = 6.995341504322509e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 0.9740803745832303 y[1] (numeric) = 0.9740803745832377 absolute error = 7.438494264988549e-15 relative error = 7.636427608113119e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 0.9800327566873965 y[1] (numeric) = 0.9800327566874046 absolute error = 8.104628079763643e-15 relative error = 8.269752234770246e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 0.9859815244295338 y[1] (numeric) = 0.9859815244295427 absolute error = 8.881784197001252e-15 relative error = 9.008063515328087e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 0.9919267051395096 y[1] (numeric) = 0.9919267051395193 absolute error = 9.658940314238862e-15 relative error = 9.737554462635804e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 0.9978683258383783 y[1] (numeric) = 0.9978683258383886 absolute error = 1.032507412901396e-14 relative error = 1.034713084047351e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 1.003806413243015 y[1] (numeric) = 1.003806413243026 absolute error = 1.110223024625157e-14 relative error = 1.106013081783707e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = 1.009740993770666 y[1] (numeric) = 1.009740993770678 absolute error = 1.154631945610163e-14 relative error = 1.143493185612314e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = 1.015672093543411 y[1] (numeric) = 1.015672093543423 absolute error = 1.221245327087672e-14 relative error = 1.202401183266807e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = 1.021599738392545 y[1] (numeric) = 1.021599738392557 absolute error = 1.243449787580175e-14 relative error = 1.217159461627021e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = 1.027523953862875 y[1] (numeric) = 1.027523953862888 absolute error = 1.310063169057685e-14 relative error = 1.274970928057327e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 1.033444765216949 y[1] (numeric) = 1.033444765216963 absolute error = 1.398881011027697e-14 relative error = 1.353609847483269e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 1.039362197439189 y[1] (numeric) = 1.039362197439203 absolute error = 1.443289932012704e-14 relative error = 1.388630388490868e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 1.045276275239966 y[1] (numeric) = 1.045276275239981 absolute error = 1.509903313490213e-14 relative error = 1.444501658801719e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = 1.05118702305959 y[1] (numeric) = 1.051187023059606 absolute error = 1.554312234475219e-14 relative error = 1.478625782452327e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = 1.057094465072234 y[1] (numeric) = 1.05709446507225 absolute error = 1.576516694967722e-14 relative error = 1.491367845597407e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = 1.062998625189781 y[1] (numeric) = 1.062998625189797 absolute error = 1.598721155460225e-14 relative error = 1.503972928633657e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = 1.068899527065605 y[1] (numeric) = 1.068899527065622 absolute error = 1.665334536937735e-14 relative error = 1.557989778056589e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = 1.074797194098287 y[1] (numeric) = 1.074797194098304 absolute error = 1.709743457922741e-14 relative error = 1.590759137920108e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y[1] (closed_form) = 1.080691649435257 y[1] (numeric) = 1.080691649435275 absolute error = 1.77635683940025e-14 relative error = 1.643722185073357e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y[1] (closed_form) = 1.08658291597638 y[1] (numeric) = 1.086582915976399 absolute error = 1.865174681370263e-14 relative error = 1.716550715040699e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = 1.092471016377472 y[1] (numeric) = 1.092471016377491 absolute error = 1.953992523340276e-14 relative error = 1.788598959649773e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = 1.098355973053752 y[1] (numeric) = 1.098355973053772 absolute error = 1.976196983832779e-14 relative error = 1.799231790344228e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = 1.104237808183243 y[1] (numeric) = 1.104237808183264 absolute error = 2.042810365310288e-14 relative error = 1.84997321244709e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y[1] (closed_form) = 1.110116543710104 y[1] (numeric) = 1.110116543710125 absolute error = 2.109423746787797e-14 relative error = 1.900182245494625e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y[1] (closed_form) = 1.115992201347904 y[1] (numeric) = 1.115992201347925 absolute error = 2.153832667772804e-14 relative error = 1.929971074324165e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y[1] (closed_form) = 1.121864802582845 y[1] (numeric) = 1.121864802582867 absolute error = 2.19824158875781e-14 relative error = 1.959453210134452e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y[1] (closed_form) = 1.127734368676926 y[1] (numeric) = 1.127734368676948 absolute error = 2.242650509742816e-14 relative error = 1.988633646391327e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y[1] (closed_form) = 1.133600920671047 y[1] (numeric) = 1.13360092067107 absolute error = 2.309263891220326e-14 relative error = 2.037104812735449e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y[1] (closed_form) = 1.139464479388068 y[1] (numeric) = 1.139464479388092 absolute error = 2.375877272697835e-14 relative error = 2.085082348485109e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y[1] (closed_form) = 1.145325065435811 y[1] (numeric) = 1.145325065435835 absolute error = 2.398081733190338e-14 relative error = 2.093800097073609e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = 1.151182699210007 y[1] (numeric) = 1.151182699210032 absolute error = 2.486899575160351e-14 relative error = 2.160299643894034e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = 1.157037400897203 y[1] (numeric) = 1.157037400897229 absolute error = 2.55351295663786e-14 relative error = 2.20694072175868e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = 1.162889190477606 y[1] (numeric) = 1.162889190477632 absolute error = 2.620126338115369e-14 relative error = 2.253117803115245e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y[1] (closed_form) = 1.16873808772789 y[1] (numeric) = 1.168738087727917 absolute error = 2.686739719592879e-14 relative error = 2.298838163831977e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y[1] (closed_form) = 1.174584112223949 y[1] (numeric) = 1.174584112223977 absolute error = 2.731148640577885e-14 relative error = 2.325204821140265e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y[1] (closed_form) = 1.180427283343608 y[1] (numeric) = 1.180427283343636 absolute error = 2.797762022055394e-14 relative error = 2.370126530903809e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y[1] (closed_form) = 1.186267620269284 y[1] (numeric) = 1.186267620269313 absolute error = 2.886579864025407e-14 relative error = 2.433329389341463e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y[1] (closed_form) = 1.192105141990604 y[1] (numeric) = 1.192105141990634 absolute error = 2.997602166487923e-14 relative error = 2.51454511930253e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y[1] (closed_form) = 1.197939867306982 y[1] (numeric) = 1.197939867307013 absolute error = 3.042011087472929e-14 relative error = 2.539368770079832e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = 1.20377181483015 y[1] (numeric) = 1.203771814830181 absolute error = 3.086420008457935e-14 relative error = 2.563957695664625e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = 1.209601002986648 y[1] (numeric) = 1.209601002986679 absolute error = 3.108624468950438e-14 relative error = 2.569958574170224e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = 1.215427450020272 y[1] (numeric) = 1.215427450020304 absolute error = 3.153033389935445e-14 relative error = 2.594176550712965e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = 1.221251173994485 y[1] (numeric) = 1.221251173994517 absolute error = 3.219646771412954e-14 relative error = 2.636351014412613e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y[1] (closed_form) = 1.227072192794782 y[1] (numeric) = 1.227072192794814 absolute error = 3.26405569239796e-14 relative error = 2.660035580273188e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y[1] (closed_form) = 1.232890524131023 y[1] (numeric) = 1.232890524131057 absolute error = 3.33066907387547e-14 relative error = 2.701512428464012e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y[1] (closed_form) = 1.238706185539727 y[1] (numeric) = 1.238706185539761 absolute error = 3.375077994860476e-14 relative error = 2.724680020379404e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999937 y[1] (closed_form) = 1.24451919438632 y[1] (numeric) = 1.244519194386354 absolute error = 3.419486915845482e-14 relative error = 2.747636943865419e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999936 y[1] (closed_form) = 1.250329567867362 y[1] (numeric) = 1.250329567867397 absolute error = 3.486100297322992e-14 relative error = 2.788145131422505e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999935 y[1] (closed_form) = 1.256137323012724 y[1] (numeric) = 1.256137323012759 absolute error = 3.530509218307998e-14 relative error = 2.810607688847597e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y[1] (closed_form) = 1.261942476687733 y[1] (numeric) = 1.261942476687769 absolute error = 3.597122599785507e-14 relative error = 2.850464792362808e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y[1] (closed_form) = 1.267745045595295 y[1] (numeric) = 1.267745045595331 absolute error = 3.641531520770513e-14 relative error = 2.872447842271441e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y[1] (closed_form) = 1.273545046277962 y[1] (numeric) = 1.273545046277999 absolute error = 3.730349362740526e-14 relative error = 2.929106727432039e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y[1] (closed_form) = 1.279342495119986 y[1] (numeric) = 1.279342495120025 absolute error = 3.819167204710538e-14 relative error = 2.985257833049897e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999929 y[1] (closed_form) = 1.285137408349331 y[1] (numeric) = 1.285137408349369 absolute error = 3.885780586188048e-14 relative error = 3.023630439004232e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999928 y[1] (closed_form) = 1.29092980203965 y[1] (numeric) = 1.290929802039689 absolute error = 3.952393967665557e-14 relative error = 3.061664516088198e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999927 y[1] (closed_form) = 1.296719692112241 y[1] (numeric) = 1.296719692112281 absolute error = 3.996802888650564e-14 relative error = 3.082241222187446e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999926 y[1] (closed_form) = 1.302507094337965 y[1] (numeric) = 1.302507094338005 absolute error = 4.019007349143067e-14 relative error = 3.085593442533868e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999925 y[1] (closed_form) = 1.308292024339131 y[1] (numeric) = 1.308292024339172 absolute error = 4.085620730620576e-14 relative error = 3.122866038019594e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999924 y[1] (closed_form) = 1.314074497591362 y[1] (numeric) = 1.314074497591404 absolute error = 4.174438572590589e-14 relative error = 3.176713786198683e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y[1] (closed_form) = 1.319854529425423 y[1] (numeric) = 1.319854529425465 absolute error = 4.263256414560601e-14 relative error = 3.230095680632729e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y[1] (closed_form) = 1.32563213502902 y[1] (numeric) = 1.325632135029064 absolute error = 4.352074256530614e-14 relative error = 3.283018072306568e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y[1] (closed_form) = 1.331407329448582 y[1] (numeric) = 1.331407329448625 absolute error = 4.374278717023117e-14 relative error = 3.285454886923882e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y[1] (closed_form) = 1.337180127590999 y[1] (numeric) = 1.337180127591044 absolute error = 4.463096558993129e-14 relative error = 3.337692855960725e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999918 y[1] (closed_form) = 1.342950544225351 y[1] (numeric) = 1.342950544225396 absolute error = 4.485301019485632e-14 relative error = 3.339885477370928e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999917 y[1] (closed_form) = 1.348718593984592 y[1] (numeric) = 1.348718593984638 absolute error = 4.551914400963142e-14 relative error = 3.374991952557853e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999916 y[1] (closed_form) = 1.354484291367228 y[1] (numeric) = 1.354484291367274 absolute error = 4.574118861455645e-14 relative error = 3.37701875954463e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999915 y[1] (closed_form) = 1.36024765073895 y[1] (numeric) = 1.360247650738997 absolute error = 4.640732242933154e-14 relative error = 3.411681865733855e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999914 y[1] (closed_form) = 1.366008686334257 y[1] (numeric) = 1.366008686334304 absolute error = 4.685141163918161e-14 relative error = 3.429803346632398e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999913 y[1] (closed_form) = 1.371767412258045 y[1] (numeric) = 1.371767412258092 absolute error = 4.729550084903167e-14 relative error = 3.447778422668555e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y[1] (closed_form) = 1.377523842487178 y[1] (numeric) = 1.377523842487226 absolute error = 4.818367926873179e-14 relative error = 3.497847208345527e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y[1] (closed_form) = 1.383277990872034 y[1] (numeric) = 1.383277990872083 absolute error = 4.907185768843192e-14 relative error = 3.547505130006187e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y[1] (closed_form) = 1.389029871138022 y[1] (numeric) = 1.389029871138072 absolute error = 4.996003610813204e-14 relative error = 3.596757502932615e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999908 y[1] (closed_form) = 1.394779496887086 y[1] (numeric) = 1.394779496887136 absolute error = 5.040412531798211e-14 relative error = 3.613770164422095e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999907 y[1] (closed_form) = 1.400526881599177 y[1] (numeric) = 1.400526881599228 absolute error = 5.084821452783217e-14 relative error = 3.630648950470103e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999906 y[1] (closed_form) = 1.40627203863371 y[1] (numeric) = 1.406272038633762 absolute error = 5.173639294753229e-14 relative error = 3.678974730792326e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999905 y[1] (closed_form) = 1.412014981230999 y[1] (numeric) = 1.412014981231051 absolute error = 5.195843755245733e-14 relative error = 3.679736988849778e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999904 y[1] (closed_form) = 1.417755722513663 y[1] (numeric) = 1.417755722513715 absolute error = 5.240252676230739e-14 relative error = 3.696160483090724e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999903 y[1] (closed_form) = 1.42349427548802 y[1] (numeric) = 1.423494275488073 absolute error = 5.284661597215745e-14 relative error = 3.712457217577494e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999902 y[1] (closed_form) = 1.429230653045459 y[1] (numeric) = 1.429230653045512 absolute error = 5.329070518200751e-14 relative error = 3.728628760407123e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y[1] (closed_form) = 1.434964867963786 y[1] (numeric) = 1.43496486796384 absolute error = 5.395683899678261e-14 relative error = 3.760150523639462e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y[1] (closed_form) = 1.440696932908557 y[1] (numeric) = 1.440696932908611 absolute error = 5.440092820663267e-14 relative error = 3.776014716488993e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y[1] (closed_form) = 1.44642686043439 y[1] (numeric) = 1.446426860434445 absolute error = 5.506706202140776e-14 relative error = 3.807110025934533e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999897 y[1] (closed_form) = 1.452154662986254 y[1] (numeric) = 1.45215466298631 absolute error = 5.551115123125783e-14 relative error = 3.822674860066423e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999896 y[1] (closed_form) = 1.457880352900744 y[1] (numeric) = 1.4578803529008 absolute error = 5.595524044110789e-14 relative error = 3.838122952255565e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999895 y[1] (closed_form) = 1.463603942407334 y[1] (numeric) = 1.463603942407391 absolute error = 5.706546346573305e-14 relative error = 3.898968963685068e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999894 y[1] (closed_form) = 1.469325443629617 y[1] (numeric) = 1.469325443629675 absolute error = 5.728750807065808e-14 relative error = 3.898898526465517e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999893 y[1] (closed_form) = 1.475044868586521 y[1] (numeric) = 1.475044868586578 absolute error = 5.750955267558311e-14 relative error = 3.898834123648884e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999892 y[1] (closed_form) = 1.480762229193508 y[1] (numeric) = 1.480762229193566 absolute error = 5.81756864903582e-14 relative error = 3.928766235619299e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999891 y[1] (closed_form) = 1.486477537263766 y[1] (numeric) = 1.486477537263825 absolute error = 5.88418203051333e-14 relative error = 3.958473561157635e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.00999999999989 y[1] (closed_form) = 1.492190804509367 y[1] (numeric) = 1.492190804509426 absolute error = 5.906386491005833e-14 relative error = 3.958197888069586e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999889 y[1] (closed_form) = 1.497902042542424 y[1] (numeric) = 1.497902042542484 absolute error = 6.017408793468348e-14 relative error = 4.017224506386853e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999887 y[1] (closed_form) = 1.503611262876223 y[1] (numeric) = 1.503611262876284 absolute error = 6.061817714453355e-14 relative error = 4.031505924515252e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999886 y[1] (closed_form) = 1.509318476926342 y[1] (numeric) = 1.509318476926403 absolute error = 6.106226635438361e-14 relative error = 4.045684677413749e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999885 y[1] (closed_form) = 1.515023696011752 y[1] (numeric) = 1.515023696011814 absolute error = 6.195044477408373e-14 relative error = 4.089074311983777e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999884 y[1] (closed_form) = 1.520726931355905 y[1] (numeric) = 1.520726931355967 absolute error = 6.23945339839338e-14 relative error = 4.102941343210237e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999883 y[1] (closed_form) = 1.526428194087807 y[1] (numeric) = 1.52642819408787 absolute error = 6.306066779870889e-14 relative error = 4.131256749774197e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999882 y[1] (closed_form) = 1.532127495243071 y[1] (numeric) = 1.532127495243135 absolute error = 6.372680161348399e-14 relative error = 4.159366750570177e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.089999999999881 y[1] (closed_form) = 1.537824845764965 y[1] (numeric) = 1.537824845765029 absolute error = 6.417089082333405e-14 relative error = 4.172834832266825e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09999999999988 y[1] (closed_form) = 1.543520256505434 y[1] (numeric) = 1.543520256505499 absolute error = 6.461498003318411e-14 relative error = 4.186208749827096e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999879 y[1] (closed_form) = 1.549213738226115 y[1] (numeric) = 1.54921373822618 absolute error = 6.52811138479592e-14 relative error = 4.21382229173281e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999878 y[1] (closed_form) = 1.554905301599337 y[1] (numeric) = 1.554905301599403 absolute error = 6.59472476627343e-14 relative error = 4.241238845536292e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y[1] (closed_form) = 1.560594957209106 y[1] (numeric) = 1.560594957209172 absolute error = 6.661338147750939e-14 relative error = 4.268460638668064e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999875 y[1] (closed_form) = 1.566282715552078 y[1] (numeric) = 1.566282715552145 absolute error = 6.705747068735946e-14 relative error = 4.281313330060166e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999874 y[1] (closed_form) = 1.571968587038515 y[1] (numeric) = 1.571968587038583 absolute error = 6.772360450213455e-14 relative error = 4.308203424708463e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999873 y[1] (closed_form) = 1.577652581993233 y[1] (numeric) = 1.577652581993301 absolute error = 6.838973831690964e-14 relative error = 4.334904851517112e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999872 y[1] (closed_form) = 1.583334710656533 y[1] (numeric) = 1.583334710656602 absolute error = 6.905587213168474e-14 relative error = 4.361419709105635e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.179999999999871 y[1] (closed_form) = 1.589014983185123 y[1] (numeric) = 1.589014983185192 absolute error = 6.94999613415348e-14 relative error = 4.373776337981701e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18999999999987 y[1] (closed_form) = 1.594693409653021 y[1] (numeric) = 1.594693409653091 absolute error = 6.994405055138486e-14 relative error = 4.38605001613467e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999869 y[1] (closed_form) = 1.600370000052457 y[1] (numeric) = 1.600370000052527 absolute error = 7.061018436615996e-14 relative error = 4.412116220864269e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999868 y[1] (closed_form) = 1.606044764294747 y[1] (numeric) = 1.606044764294818 absolute error = 7.105427357601002e-14 relative error = 4.424177654052604e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999867 y[1] (closed_form) = 1.611717712211175 y[1] (numeric) = 1.611717712211246 absolute error = 7.194245199571014e-14 relative error = 4.463712935003343e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999865 y[1] (closed_form) = 1.617388853553841 y[1] (numeric) = 1.617388853553913 absolute error = 7.238654120556021e-14 relative error = 4.475518737903219e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999864 y[1] (closed_form) = 1.62305819799652 y[1] (numeric) = 1.623058197996593 absolute error = 7.327471962526033e-14 relative error = 4.514608269482242e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999863 y[1] (closed_form) = 1.628725755135489 y[1] (numeric) = 1.628725755135562 absolute error = 7.371880883511039e-14 relative error = 4.526164616889598e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999862 y[1] (closed_form) = 1.634391534490359 y[1] (numeric) = 1.634391534490433 absolute error = 7.394085344003543e-14 relative error = 4.524059986831239e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.269999999999861 y[1] (closed_form) = 1.640055545504888 y[1] (numeric) = 1.640055545504962 absolute error = 7.438494264988549e-14 relative error = 4.535513620484497e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27999999999986 y[1] (closed_form) = 1.645717797547781 y[1] (numeric) = 1.645717797547856 absolute error = 7.505107646466058e-14 relative error = 4.560385539762116e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999859 y[1] (closed_form) = 1.65137829991349 y[1] (numeric) = 1.651378299913566 absolute error = 7.549516567451064e-14 relative error = 4.57164573850011e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999858 y[1] (closed_form) = 1.657037061822991 y[1] (numeric) = 1.657037061823067 absolute error = 7.616129948928574e-14 relative error = 4.596233919203763e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999857 y[1] (closed_form) = 1.662694092424558 y[1] (numeric) = 1.662694092424635 absolute error = 7.682743330406083e-14 relative error = 4.620659546100286e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999856 y[1] (closed_form) = 1.668349400794526 y[1] (numeric) = 1.668349400794603 absolute error = 7.771561172376096e-14 relative error = 4.658233562271194e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999854 y[1] (closed_form) = 1.674002995938043 y[1] (numeric) = 1.674002995938121 absolute error = 7.793765632868599e-14 relative error = 4.655765641865708e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999853 y[1] (closed_form) = 1.679654886789812 y[1] (numeric) = 1.679654886789891 absolute error = 7.860379014346108e-14 relative error = 4.679758369511853e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999852 y[1] (closed_form) = 1.685305082214826 y[1] (numeric) = 1.685305082214906 absolute error = 7.949196856316121e-14 relative error = 4.716770239527965e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999851 y[1] (closed_form) = 1.690953591009087 y[1] (numeric) = 1.690953591009167 absolute error = 8.01581023779363e-14 relative error = 4.74040818175864e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36999999999985 y[1] (closed_form) = 1.696600421900324 y[1] (numeric) = 1.696600421900405 absolute error = 8.08242361927114e-14 relative error = 4.763893439457122e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999849 y[1] (closed_form) = 1.702245583548696 y[1] (numeric) = 1.702245583548778 absolute error = 8.126832540256146e-14 relative error = 4.774183360378599e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999848 y[1] (closed_form) = 1.707889084547489 y[1] (numeric) = 1.707889084547571 absolute error = 8.193445921733655e-14 relative error = 4.797411023857288e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999847 y[1] (closed_form) = 1.7135309334238 y[1] (numeric) = 1.713530933423883 absolute error = 8.282263763703668e-14 relative error = 4.833448642304289e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999846 y[1] (closed_form) = 1.719171138639218 y[1] (numeric) = 1.719171138639301 absolute error = 8.348877145181177e-14 relative error = 4.856338591043121e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y[1] (closed_form) = 1.724809708590491 y[1] (numeric) = 1.724809708590575 absolute error = 8.393286066166183e-14 relative error = 4.866209892235096e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y[1] (closed_form) = 1.73044665161019 y[1] (numeric) = 1.730446651610275 absolute error = 8.459899447643693e-14 relative error = 4.888853082972369e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y[1] (closed_form) = 1.736081975967358 y[1] (numeric) = 1.736081975967443 absolute error = 8.482103908136196e-14 relative error = 4.885773843375053e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y[1] (closed_form) = 1.741715689868155 y[1] (numeric) = 1.74171568986824 absolute error = 8.570921750106208e-14 relative error = 4.920964885351074e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y[1] (closed_form) = 1.747347801456494 y[1] (numeric) = 1.74734780145658 absolute error = 8.637535131583718e-14 relative error = 4.943226027688329e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y[1] (closed_form) = 1.75297831881467 y[1] (numeric) = 1.752978318814757 absolute error = 8.704148513061227e-14 relative error = 4.965348641018448e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999838 y[1] (closed_form) = 1.758607249963982 y[1] (numeric) = 1.758607249964069 absolute error = 8.748557434046234e-14 relative error = 4.974707931077513e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999837 y[1] (closed_form) = 1.764234602865338 y[1] (numeric) = 1.764234602865426 absolute error = 8.815170815523743e-14 relative error = 4.996597845437791e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999836 y[1] (closed_form) = 1.769860385419867 y[1] (numeric) = 1.769860385419955 absolute error = 8.859579736508749e-14 relative error = 5.005807130039231e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999835 y[1] (closed_form) = 1.775484605469513 y[1] (numeric) = 1.775484605469602 absolute error = 8.948397578478762e-14 relative error = 5.039974748816495e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y[1] (closed_form) = 1.781107270797625 y[1] (numeric) = 1.781107270797715 absolute error = 8.992806499463768e-14 relative error = 5.048997692001201e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999832 y[1] (closed_form) = 1.78672838912954 y[1] (numeric) = 1.786728389129631 absolute error = 9.059419880941277e-14 relative error = 5.070395666212509e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999831 y[1] (closed_form) = 1.792347968133156 y[1] (numeric) = 1.792347968133247 absolute error = 9.126033262418787e-14 relative error = 5.091663797808262e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54999999999983 y[1] (closed_form) = 1.797966015419503 y[1] (numeric) = 1.797966015419595 absolute error = 9.192646643896296e-14 relative error = 5.112803337248542e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999829 y[1] (closed_form) = 1.803582538543301 y[1] (numeric) = 1.803582538543393 absolute error = 9.237055564881302e-14 relative error = 5.121504210360007e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999828 y[1] (closed_form) = 1.809197545003516 y[1] (numeric) = 1.809197545003608 absolute error = 9.259260025373806e-14 relative error = 5.117882262744178e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999827 y[1] (closed_form) = 1.814811042243907 y[1] (numeric) = 1.814811042244 absolute error = 9.348077867343818e-14 relative error = 5.150992389701063e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999826 y[1] (closed_form) = 1.820423037653566 y[1] (numeric) = 1.820423037653661 absolute error = 9.436895709313831e-14 relative error = 5.183902595232763e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999825 y[1] (closed_form) = 1.826033538567454 y[1] (numeric) = 1.826033538567549 absolute error = 9.570122472268849e-14 relative error = 5.240934665294665e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999824 y[1] (closed_form) = 1.831642552266923 y[1] (numeric) = 1.83164255226702 absolute error = 9.636735853746359e-14 relative error = 5.261253535423437e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y[1] (closed_form) = 1.837250085980246 y[1] (numeric) = 1.837250085980343 absolute error = 9.703349235223868e-14 relative error = 5.281452595522262e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999821 y[1] (closed_form) = 1.842856146883121 y[1] (numeric) = 1.842856146883219 absolute error = 9.769962616701378e-14 relative error = 5.301532967304915e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999982 y[1] (closed_form) = 1.848460742099191 y[1] (numeric) = 1.84846074209929 absolute error = 9.836575998178887e-14 relative error = 5.321495758145261e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999819 y[1] (closed_form) = 1.854063878700537 y[1] (numeric) = 1.854063878700636 absolute error = 9.880984919163893e-14 relative error = 5.32936595803226e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999818 y[1] (closed_form) = 1.859665563708177 y[1] (numeric) = 1.859665563708277 absolute error = 9.925393840148899e-14 relative error = 5.337192898468067e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999817 y[1] (closed_form) = 1.865265804092561 y[1] (numeric) = 1.865265804092661 absolute error = 9.992007221626409e-14 relative error = 5.356881147825176e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999816 y[1] (closed_form) = 1.87086460677405 y[1] (numeric) = 1.87086460677415 absolute error = 1.003641614261142e-13 relative error = 5.364587103883112e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999815 y[1] (closed_form) = 1.876461978623394 y[1] (numeric) = 1.876461978623495 absolute error = 1.010302952408892e-13 relative error = 5.384084324213532e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999814 y[1] (closed_form) = 1.882057926462213 y[1] (numeric) = 1.882057926462315 absolute error = 1.019184736605894e-13 relative error = 5.415267629523498e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999813 y[1] (closed_form) = 1.887652457063454 y[1] (numeric) = 1.887652457063557 absolute error = 1.028066520802895e-13 relative error = 5.446270138106976e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y[1] (closed_form) = 1.893245577151861 y[1] (numeric) = 1.893245577151964 absolute error = 1.030286966852145e-13 relative error = 5.441908748056216e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999981 y[1] (closed_form) = 1.898837293404427 y[1] (numeric) = 1.898837293404531 absolute error = 1.036948304999896e-13 relative error = 5.460964499705768e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999809 y[1] (closed_form) = 1.904427612450846 y[1] (numeric) = 1.904427612450951 absolute error = 1.045830089196897e-13 relative error = 5.491571758146258e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999808 y[1] (closed_form) = 1.91001654087396 y[1] (numeric) = 1.910016540874066 absolute error = 1.052491427344648e-13 relative error = 5.51037860050711e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999807 y[1] (closed_form) = 1.915604085210198 y[1] (numeric) = 1.915604085210304 absolute error = 1.056932319443149e-13 relative error = 5.517488334898661e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999806 y[1] (closed_form) = 1.921190251950011 y[1] (numeric) = 1.921190251950118 absolute error = 1.06581410364015e-13 relative error = 5.54767599178867e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999805 y[1] (closed_form) = 1.926775047538304 y[1] (numeric) = 1.926775047538411 absolute error = 1.072475441787901e-13 relative error = 5.566168417834364e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999804 y[1] (closed_form) = 1.932358478374858 y[1] (numeric) = 1.932358478374966 absolute error = 1.074695887837152e-13 relative error = 5.56157617680228e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999803 y[1] (closed_form) = 1.937940550814755 y[1] (numeric) = 1.937940550814863 absolute error = 1.079136779935652e-13 relative error = 5.568472053912891e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999802 y[1] (closed_form) = 1.94352127116879 y[1] (numeric) = 1.943521271168898 absolute error = 1.083577672034153e-13 relative error = 5.575332197843729e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y[1] (closed_form) = 1.94910064570388 y[1] (numeric) = 1.949100645703989 absolute error = 1.090239010181904e-13 relative error = 5.593549068822893e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999799 y[1] (closed_form) = 1.954678680643474 y[1] (numeric) = 1.954678680643583 absolute error = 1.094679902280404e-13 relative error = 5.600306143002691e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999798 y[1] (closed_form) = 1.960255382167952 y[1] (numeric) = 1.960255382168062 absolute error = 1.096900348329655e-13 relative error = 5.595701245398614e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999797 y[1] (closed_form) = 1.965830756415021 y[1] (numeric) = 1.965830756415132 absolute error = 1.105782132526656e-13 relative error = 5.625011862889003e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999796 y[1] (closed_form) = 1.971404809480108 y[1] (numeric) = 1.97140480948022 absolute error = 1.112443470674407e-13 relative error = 5.642897213828835e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999795 y[1] (closed_form) = 1.976977547416747 y[1] (numeric) = 1.976977547416858 absolute error = 1.116884362772907e-13 relative error = 5.649453956785217e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999794 y[1] (closed_form) = 1.98254897623696 y[1] (numeric) = 1.982548976237073 absolute error = 1.125766146969909e-13 relative error = 5.678377485063218e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999793 y[1] (closed_form) = 1.988119101911641 y[1] (numeric) = 1.988119101911754 absolute error = 1.13242748511766e-13 relative error = 5.695974069303967e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999792 y[1] (closed_form) = 1.993687930370924 y[1] (numeric) = 1.993687930371038 absolute error = 1.13464793116691e-13 relative error = 5.69120128522727e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.909999999999791 y[1] (closed_form) = 1.999255467504558 y[1] (numeric) = 1.999255467504673 absolute error = 1.143529715363911e-13 relative error = 5.719777857060201e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y[1] (closed_form) = 2.004821719162271 y[1] (numeric) = 2.004821719162385 absolute error = 1.145750161413162e-13 relative error = 5.714972810110624e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999788 y[1] (closed_form) = 2.010386691154129 y[1] (numeric) = 2.010386691154245 absolute error = 1.150191053511662e-13 relative error = 5.721242876172029e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999787 y[1] (closed_form) = 2.015950389250901 y[1] (numeric) = 2.015950389251017 absolute error = 1.154631945610163e-13 relative error = 5.727481944827063e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999786 y[1] (closed_form) = 2.021512819184405 y[1] (numeric) = 2.021512819184521 absolute error = 1.159072837708663e-13 relative error = 5.733690267550717e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999785 y[1] (closed_form) = 2.02707398664786 y[1] (numeric) = 2.027073986647977 absolute error = 1.167954621905665e-13 relative error = 5.761775986465559e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999784 y[1] (closed_form) = 2.032633897296236 y[1] (numeric) = 2.032633897296352 absolute error = 1.167954621905665e-13 relative error = 5.746015666959268e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999783 y[1] (closed_form) = 2.038192556746589 y[1] (numeric) = 2.038192556746706 absolute error = 1.167954621905665e-13 relative error = 5.730344849114656e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999782 y[1] (closed_form) = 2.043749970578406 y[1] (numeric) = 2.043749970578523 absolute error = 1.172395514004165e-13 relative error = 5.736491894223065e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.999999999999781 y[1] (closed_form) = 2.049306144333933 y[1] (numeric) = 2.04930614433405 absolute error = 1.172395514004165e-13 relative error = 5.720938851648338e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.00999999999978 y[1] (closed_form) = 2.054861083518511 y[1] (numeric) = 2.054861083518628 absolute error = 1.172395514004165e-13 relative error = 5.705473345169827e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y[1] (closed_form) = 2.060414793600898 y[1] (numeric) = 2.060414793601016 absolute error = 1.176836406102666e-13 relative error = 5.711648012611867e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999777 y[1] (closed_form) = 2.065967280013598 y[1] (numeric) = 2.065967280013716 absolute error = 1.181277298201167e-13 relative error = 5.717792869369119e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999776 y[1] (closed_form) = 2.071518548153176 y[1] (numeric) = 2.071518548153295 absolute error = 1.190159082398168e-13 relative error = 5.745346009376705e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999775 y[1] (closed_form) = 2.077068603380576 y[1] (numeric) = 2.077068603380696 absolute error = 1.194599974496668e-13 relative error = 5.751374665970938e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999774 y[1] (closed_form) = 2.082617451021434 y[1] (numeric) = 2.082617451021555 absolute error = 1.20348175869367e-13 relative error = 5.778698138265448e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999773 y[1] (closed_form) = 2.088165096366389 y[1] (numeric) = 2.088165096366509 absolute error = 1.199040866595169e-13 relative error = 5.742078864748852e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999772 y[1] (closed_form) = 2.093711544671383 y[1] (numeric) = 2.093711544671504 absolute error = 1.20348175869367e-13 relative error = 5.748078152201053e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.089999999999771 y[1] (closed_form) = 2.099256801157972 y[1] (numeric) = 2.099256801158094 absolute error = 1.212363542890671e-13 relative error = 5.775203596920197e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09999999999977 y[1] (closed_form) = 2.104800871013621 y[1] (numeric) = 2.104800871013743 absolute error = 1.221245327087672e-13 relative error = 5.802189384782752e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999769 y[1] (closed_form) = 2.110343759391998 y[1] (numeric) = 2.11034375939212 absolute error = 1.225686219186173e-13 relative error = 5.807993194148143e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y[1] (closed_form) = 2.115885471413269 y[1] (numeric) = 2.115885471413392 absolute error = 1.225686219186173e-13 relative error = 5.792781489101567e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999766 y[1] (closed_form) = 2.121426012164393 y[1] (numeric) = 2.121426012164515 absolute error = 1.225686219186173e-13 relative error = 5.777652447730958e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999765 y[1] (closed_form) = 2.126965386699397 y[1] (numeric) = 2.126965386699521 absolute error = 1.234568003383174e-13 relative error = 5.804363395395747e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999764 y[1] (closed_form) = 2.132503600039672 y[1] (numeric) = 2.132503600039796 absolute error = 1.243449787580175e-13 relative error = 5.830938749913683e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999763 y[1] (closed_form) = 2.138040657174244 y[1] (numeric) = 2.138040657174369 absolute error = 1.252331571777177e-13 relative error = 5.857379594606631e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999762 y[1] (closed_form) = 2.143576563060056 y[1] (numeric) = 2.143576563060182 absolute error = 1.261213355974178e-13 relative error = 5.883687001007964e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.179999999999761 y[1] (closed_form) = 2.149111322622243 y[1] (numeric) = 2.14911132262237 absolute error = 1.270095140171179e-13 relative error = 5.909862029024489e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18999999999976 y[1] (closed_form) = 2.1546449407544 y[1] (numeric) = 2.154644940754528 absolute error = 1.27453603226968e-13 relative error = 5.915294943321054e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999759 y[1] (closed_form) = 2.160177422318856 y[1] (numeric) = 2.160177422318984 absolute error = 1.27897692436818e-13 relative error = 5.92070313833414e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y[1] (closed_form) = 2.165708772146934 y[1] (numeric) = 2.165708772147062 absolute error = 1.283417816466681e-13 relative error = 5.926086798800696e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y[1] (closed_form) = 2.171238995039217 y[1] (numeric) = 2.171238995039347 absolute error = 1.296740492762183e-13 relative error = 5.972352632413738e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999755 y[1] (closed_form) = 2.176768095765811 y[1] (numeric) = 2.176768095765941 absolute error = 1.296740492762183e-13 relative error = 5.957182555572026e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999754 y[1] (closed_form) = 2.182296079066597 y[1] (numeric) = 2.182296079066727 absolute error = 1.301181384860683e-13 relative error = 5.962442023069664e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999753 y[1] (closed_form) = 2.187822949651487 y[1] (numeric) = 2.187822949651619 absolute error = 1.314504061156185e-13 relative error = 6.008274396086673e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999752 y[1] (closed_form) = 2.193348712200681 y[1] (numeric) = 2.193348712200814 absolute error = 1.327826737451687e-13 relative error = 6.053878847743373e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.269999999999751 y[1] (closed_form) = 2.198873371364911 y[1] (numeric) = 2.198873371365045 absolute error = 1.341149413747189e-13 relative error = 6.099257152378423e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27999999999975 y[1] (closed_form) = 2.20439693176569 y[1] (numeric) = 2.204396931765824 absolute error = 1.34559030584569e-13 relative error = 6.10411984545765e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999749 y[1] (closed_form) = 2.209919397995554 y[1] (numeric) = 2.209919397995689 absolute error = 1.35003119794419e-13 relative error = 6.108961255187402e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999748 y[1] (closed_form) = 2.215440774618308 y[1] (numeric) = 2.215440774618444 absolute error = 1.358912982141192e-13 relative error = 6.133826720668327e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y[1] (closed_form) = 2.220961066169264 y[1] (numeric) = 2.2209610661694 absolute error = 1.363353874239692e-13 relative error = 6.138576200217768e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999745 y[1] (closed_form) = 2.226480277155473 y[1] (numeric) = 2.226480277155609 absolute error = 1.358912982141192e-13 relative error = 6.103413518117142e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999744 y[1] (closed_form) = 2.231998412055966 y[1] (numeric) = 2.231998412056102 absolute error = 1.363353874239692e-13 relative error = 6.108220628095622e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y[1] (closed_form) = 2.23751547532198 y[1] (numeric) = 2.237515475322116 absolute error = 1.367794766338193e-13 relative error = 6.113006955365823e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y[1] (closed_form) = 2.243031471377192 y[1] (numeric) = 2.24303147137733 absolute error = 1.381117442633695e-13 relative error = 6.157369882044974e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y[1] (closed_form) = 2.248546404617944 y[1] (numeric) = 2.248546404618083 absolute error = 1.385558334732195e-13 relative error = 6.162017968082001e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y[1] (closed_form) = 2.254060279413467 y[1] (numeric) = 2.254060279413607 absolute error = 1.394440118929197e-13 relative error = 6.186347950251118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y[1] (closed_form) = 2.259573100106106 y[1] (numeric) = 2.259573100106246 absolute error = 1.398881011027697e-13 relative error = 6.190908410805598e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y[1] (closed_form) = 2.265084871011537 y[1] (numeric) = 2.265084871011677 absolute error = 1.398881011027697e-13 relative error = 6.175843691026853e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999737 y[1] (closed_form) = 2.270595596418986 y[1] (numeric) = 2.270595596419126 absolute error = 1.398881011027697e-13 relative error = 6.160854945873708e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = 2.276105280591448 y[1] (numeric) = 2.276105280591588 absolute error = 1.403321903126198e-13 relative error = 6.165452517036222e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y[1] (closed_form) = 2.281613927765894 y[1] (numeric) = 2.281613927766035 absolute error = 1.403321903126198e-13 relative error = 6.150566868691494e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y[1] (closed_form) = 2.287121542153489 y[1] (numeric) = 2.287121542153631 absolute error = 1.4166445794217e-13 relative error = 6.194006541899068e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y[1] (closed_form) = 2.292628127939797 y[1] (numeric) = 2.292628127939939 absolute error = 1.425526363618701e-13 relative error = 6.217869990540981e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y[1] (closed_form) = 2.298133689284988 y[1] (numeric) = 2.298133689285131 absolute error = 1.429967255717202e-13 relative error = 6.222297955877856e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y[1] (closed_form) = 2.303638230324047 y[1] (numeric) = 2.303638230324191 absolute error = 1.443289932012704e-13 relative error = 6.265262978422092e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999729 y[1] (closed_form) = 2.309141755166972 y[1] (numeric) = 2.309141755167117 absolute error = 1.452171716209705e-13 relative error = 6.288794150295463e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999728 y[1] (closed_form) = 2.314644267898977 y[1] (numeric) = 2.314644267899122 absolute error = 1.452171716209705e-13 relative error = 6.273844047439107e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999727 y[1] (closed_form) = 2.320145772580693 y[1] (numeric) = 2.320145772580839 absolute error = 1.456612608308205e-13 relative error = 6.278108149592767e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999726 y[1] (closed_form) = 2.325646273248361 y[1] (numeric) = 2.325646273248506 absolute error = 1.456612608308205e-13 relative error = 6.263259486463833e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = 2.331145773914028 y[1] (numeric) = 2.331145773914175 absolute error = 1.465494392505207e-13 relative error = 6.286584086265098e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y[1] (closed_form) = 2.336644278565744 y[1] (numeric) = 2.336644278565891 absolute error = 1.474376176702208e-13 relative error = 6.309801582666213e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y[1] (closed_form) = 2.342141791167745 y[1] (numeric) = 2.342141791167894 absolute error = 1.483257960899209e-13 relative error = 6.332912748889068e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y[1] (closed_form) = 2.347638315660652 y[1] (numeric) = 2.347638315660801 absolute error = 1.48769885299771e-13 relative error = 6.337001926887764e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y[1] (closed_form) = 2.35313385596165 y[1] (numeric) = 2.353133855961798 absolute error = 1.48769885299771e-13 relative error = 6.322202407774782e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y[1] (closed_form) = 2.358628415964676 y[1] (numeric) = 2.358628415964824 absolute error = 1.48769885299771e-13 relative error = 6.307474475114568e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999718 y[1] (closed_form) = 2.364121999540604 y[1] (numeric) = 2.364121999540754 absolute error = 1.49213974509621e-13 relative error = 6.311602131303556e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999717 y[1] (closed_form) = 2.369614610537429 y[1] (numeric) = 2.369614610537579 absolute error = 1.501021529293212e-13 relative error = 6.334454229891755e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999716 y[1] (closed_form) = 2.375106252780438 y[1] (numeric) = 2.375106252780589 absolute error = 1.505462421391712e-13 relative error = 6.338505570558497e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999715 y[1] (closed_form) = 2.3805969300724 y[1] (numeric) = 2.380596930072551 absolute error = 1.514344205588714e-13 relative error = 6.361195322312118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = 2.386086646193732 y[1] (numeric) = 2.386086646193885 absolute error = 1.523225989785715e-13 relative error = 6.383783221852205e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y[1] (closed_form) = 2.391575404902683 y[1] (numeric) = 2.391575404902837 absolute error = 1.540989558179717e-13 relative error = 6.443407784762793e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y[1] (closed_form) = 2.397063209935498 y[1] (numeric) = 2.397063209935652 absolute error = 1.545430450278218e-13 relative error = 6.447182718722731e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y[1] (closed_form) = 2.402550065006596 y[1] (numeric) = 2.40255006500675 absolute error = 1.545430450278218e-13 relative error = 6.432458881034703e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y[1] (closed_form) = 2.408035973808738 y[1] (numeric) = 2.408035973808893 absolute error = 1.549871342376719e-13 relative error = 6.436246631005769e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999708 y[1] (closed_form) = 2.413520940013194 y[1] (numeric) = 2.413520940013349 absolute error = 1.554312234475219e-13 relative error = 6.440019677089365e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999707 y[1] (closed_form) = 2.41900496726991 y[1] (numeric) = 2.419004967270066 absolute error = 1.56319401867222e-13 relative error = 6.462136456199351e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999706 y[1] (closed_form) = 2.424488059207673 y[1] (numeric) = 2.42448805920783 absolute error = 1.572075802869222e-13 relative error = 6.484155683501197e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999705 y[1] (closed_form) = 2.429970219434274 y[1] (numeric) = 2.429970219434431 absolute error = 1.572075802869222e-13 relative error = 6.469527034924814e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999704 y[1] (closed_form) = 2.435451451536669 y[1] (numeric) = 2.435451451536827 absolute error = 1.576516694967722e-13 relative error = 6.473201073143976e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y[1] (closed_form) = 2.440931759081142 y[1] (numeric) = 2.440931759081301 absolute error = 1.589839371263224e-13 relative error = 6.513247924070189e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y[1] (closed_form) = 2.446411145613459 y[1] (numeric) = 2.44641114561362 absolute error = 1.603162047558726e-13 relative error = 6.553117820907895e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y[1] (closed_form) = 2.45188961465903 y[1] (numeric) = 2.451889614659191 absolute error = 1.607602939657227e-13 relative error = 6.556587743778942e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y[1] (closed_form) = 2.457367169723059 y[1] (numeric) = 2.457367169723221 absolute error = 1.616484723854228e-13 relative error = 6.578116383138637e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y[1] (closed_form) = 2.462843814290704 y[1] (numeric) = 2.462843814290865 absolute error = 1.612043831755727e-13 relative error = 6.545457013562161e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999697 y[1] (closed_form) = 2.468319551827225 y[1] (numeric) = 2.468319551827387 absolute error = 1.625366508051229e-13 relative error = 6.584911207497497e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999696 y[1] (closed_form) = 2.473794385778138 y[1] (numeric) = 2.4737943857783 absolute error = 1.625366508051229e-13 relative error = 6.570337928630905e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999695 y[1] (closed_form) = 2.479268319569362 y[1] (numeric) = 2.479268319569525 absolute error = 1.63424829224823e-13 relative error = 6.591655608022662e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999694 y[1] (closed_form) = 2.484741356607371 y[1] (numeric) = 2.484741356607535 absolute error = 1.643130076445232e-13 relative error = 6.612881747534227e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999693 y[1] (closed_form) = 2.490213500279337 y[1] (numeric) = 2.490213500279503 absolute error = 1.656452752740734e-13 relative error = 6.651850343574649e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y[1] (closed_form) = 2.495684753953279 y[1] (numeric) = 2.495684753953445 absolute error = 1.660893644839234e-13 relative error = 6.655061871128966e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y[1] (closed_form) = 2.501155120978205 y[1] (numeric) = 2.501155120978371 absolute error = 1.660893644839234e-13 relative error = 6.640506344083355e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y[1] (closed_form) = 2.506624604684255 y[1] (numeric) = 2.506624604684421 absolute error = 1.665334536937735e-13 relative error = 6.643733305041532e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y[1] (closed_form) = 2.512093208382842 y[1] (numeric) = 2.512093208383009 absolute error = 1.674216321134736e-13 relative error = 6.664626597245218e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y[1] (closed_form) = 2.517560935366794 y[1] (numeric) = 2.517560935366962 absolute error = 1.678657213233237e-13 relative error = 6.667791788676868e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999686 y[1] (closed_form) = 2.523027788910492 y[1] (numeric) = 2.523027788910662 absolute error = 1.691979889528739e-13 relative error = 6.706148449753613e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999685 y[1] (closed_form) = 2.528493772270007 y[1] (numeric) = 2.528493772270178 absolute error = 1.70530256582424e-13 relative error = 6.744341570172309e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999684 y[1] (closed_form) = 2.533958888683236 y[1] (numeric) = 2.533958888683408 absolute error = 1.714184350021242e-13 relative error = 6.764846729269598e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999683 y[1] (closed_form) = 2.539423141370039 y[1] (numeric) = 2.539423141370211 absolute error = 1.718625242119742e-13 relative error = 6.767778138748984e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y[1] (closed_form) = 2.544886533532369 y[1] (numeric) = 2.544886533532543 absolute error = 1.731947918415244e-13 relative error = 6.805599760910578e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y[1] (closed_form) = 2.550349068354409 y[1] (numeric) = 2.550349068354584 absolute error = 1.740829702612245e-13 relative error = 6.825848760128748e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y[1] (closed_form) = 2.5558107490027 y[1] (numeric) = 2.555810749002875 absolute error = 1.749711486809247e-13 relative error = 6.846013490991066e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y[1] (closed_form) = 2.561271578626272 y[1] (numeric) = 2.561271578626448 absolute error = 1.758593271006248e-13 relative error = 6.866094504314387e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y[1] (closed_form) = 2.566731560356773 y[1] (numeric) = 2.56673156035695 absolute error = 1.767475055203249e-13 relative error = 6.886092346008993e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y[1] (closed_form) = 2.572190697308598 y[1] (numeric) = 2.572190697308774 absolute error = 1.767475055203249e-13 relative error = 6.871477519348159e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999675 y[1] (closed_form) = 2.577648992579012 y[1] (numeric) = 2.577648992579189 absolute error = 1.77191594730175e-13 relative error = 6.874155295787177e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999674 y[1] (closed_form) = 2.583106449248281 y[1] (numeric) = 2.583106449248458 absolute error = 1.77635683940025e-13 relative error = 6.876823988098495e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999673 y[1] (closed_form) = 2.588563070379789 y[1] (numeric) = 2.588563070379968 absolute error = 1.789679515695752e-13 relative error = 6.913795287333579e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999672 y[1] (closed_form) = 2.594018859020167 y[1] (numeric) = 2.594018859020347 absolute error = 1.794120407794253e-13 relative error = 6.916373801815543e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y[1] (closed_form) = 2.599473818199413 y[1] (numeric) = 2.599473818199593 absolute error = 1.798561299892754e-13 relative error = 6.918943700454616e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999674 y[1] (closed_form) = 2.604927950931014 y[1] (numeric) = 2.604927950931192 absolute error = 1.77635683940025e-13 relative error = 6.819216780123886e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999677 y[1] (closed_form) = 2.610381260212061 y[1] (numeric) = 2.610381260212237 absolute error = 1.758593271006248e-13 relative error = 6.736921145623701e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999681 y[1] (closed_form) = 2.615833749023373 y[1] (numeric) = 2.615833749023546 absolute error = 1.731947918415244e-13 relative error = 6.62101679459511e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999684 y[1] (closed_form) = 2.621285420329612 y[1] (numeric) = 2.621285420329783 absolute error = 1.70530256582424e-13 relative error = 6.505596653453358e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999687 y[1] (closed_form) = 2.626736277079401 y[1] (numeric) = 2.626736277079571 absolute error = 1.70086167372574e-13 relative error = 6.475190100229182e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999691 y[1] (closed_form) = 2.63218632220544 y[1] (numeric) = 2.632186322205608 absolute error = 1.674216321134736e-13 relative error = 6.36055398894389e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999694 y[1] (closed_form) = 2.637635558624618 y[1] (numeric) = 2.637635558624784 absolute error = 1.660893644839234e-13 relative error = 6.296903449790081e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999697 y[1] (closed_form) = 2.643083989238126 y[1] (numeric) = 2.64308398923829 absolute error = 1.63424829224823e-13 relative error = 6.183111467143749e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999701 y[1] (closed_form) = 2.648531616931575 y[1] (numeric) = 2.648531616931737 absolute error = 1.620925615952729e-13 relative error = 6.120091622053705e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999704 y[1] (closed_form) = 2.653978444575101 y[1] (numeric) = 2.653978444575262 absolute error = 1.612043831755727e-13 relative error = 6.074065277549057e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999707 y[1] (closed_form) = 2.659424475023478 y[1] (numeric) = 2.659424475023637 absolute error = 1.594280263361725e-13 relative error = 5.99483188311881e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.119999999999711 y[1] (closed_form) = 2.664869711116229 y[1] (numeric) = 2.664869711116386 absolute error = 1.572075802869222e-13 relative error = 5.899259525940311e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999714 y[1] (closed_form) = 2.670314155677731 y[1] (numeric) = 2.670314155677886 absolute error = 1.549871342376719e-13 relative error = 5.804078666479444e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999717 y[1] (closed_form) = 2.675757811517324 y[1] (numeric) = 2.675757811517478 absolute error = 1.536548666081217e-13 relative error = 5.742480352546915e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.149999999999721 y[1] (closed_form) = 2.681200681429422 y[1] (numeric) = 2.681200681429574 absolute error = 1.523225989785715e-13 relative error = 5.681133830585337e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999724 y[1] (closed_form) = 2.686642768193609 y[1] (numeric) = 2.68664276819376 absolute error = 1.509903313490213e-13 relative error = 5.620037510626734e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999727 y[1] (closed_form) = 2.692084074574753 y[1] (numeric) = 2.692084074574903 absolute error = 1.496580637194711e-13 relative error = 5.559189816280586e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.179999999999731 y[1] (closed_form) = 2.697524603323105 y[1] (numeric) = 2.697524603323252 absolute error = 1.474376176702208e-13 relative error = 5.465663500847816e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999734 y[1] (closed_form) = 2.702964357174402 y[1] (numeric) = 2.702964357174547 absolute error = 1.452171716209705e-13 relative error = 5.372515225201718e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999737 y[1] (closed_form) = 2.70840333884997 y[1] (numeric) = 2.708403338850113 absolute error = 1.438849039914203e-13 relative error = 5.312536058699295e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.209999999999741 y[1] (closed_form) = 2.713841551056825 y[1] (numeric) = 2.713841551056967 absolute error = 1.4210854715202e-13 relative error = 5.236434938387618e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999744 y[1] (closed_form) = 2.719278996487774 y[1] (numeric) = 2.719278996487914 absolute error = 1.403321903126198e-13 relative error = 5.16063965830182e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999747 y[1] (closed_form) = 2.724715677821511 y[1] (numeric) = 2.724715677821649 absolute error = 1.381117442633695e-13 relative error = 5.068849766144914e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999751 y[1] (closed_form) = 2.73015159772272 y[1] (numeric) = 2.730151597722856 absolute error = 1.363353874239692e-13 relative error = 4.993692934036689e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999754 y[1] (closed_form) = 2.735586758842167 y[1] (numeric) = 2.735586758842302 absolute error = 1.35003119794419e-13 relative error = 4.935069939129216e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999757 y[1] (closed_form) = 2.741021163816804 y[1] (numeric) = 2.741021163816938 absolute error = 1.332267629550188e-13 relative error = 4.860479178843837e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999761 y[1] (closed_form) = 2.746454815269858 y[1] (numeric) = 2.74645481526999 absolute error = 1.318944953254686e-13 relative error = 4.802354460454105e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y[1] (closed_form) = 2.75188771581093 y[1] (numeric) = 2.75188771581106 absolute error = 1.301181384860683e-13 relative error = 4.728322952222089e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y[1] (closed_form) = 2.757319868036086 y[1] (numeric) = 2.757319868036213 absolute error = 1.27453603226968e-13 relative error = 4.622372786866668e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y[1] (closed_form) = 2.762751274527955 y[1] (numeric) = 2.76275127452808 absolute error = 1.252331571777177e-13 relative error = 4.532914646799504e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999774 y[1] (closed_form) = 2.768181937855819 y[1] (numeric) = 2.768181937855942 absolute error = 1.239008895481675e-13 relative error = 4.475894010208692e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y[1] (closed_form) = 2.773611860575702 y[1] (numeric) = 2.773611860575824 absolute error = 1.221245327087672e-13 relative error = 4.403086619460105e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999781 y[1] (closed_form) = 2.779041045230468 y[1] (numeric) = 2.779041045230588 absolute error = 1.20348175869367e-13 relative error = 4.330564893091977e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999784 y[1] (closed_form) = 2.784469494349903 y[1] (numeric) = 2.784469494350022 absolute error = 1.190159082398168e-13 relative error = 4.27427588922477e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999787 y[1] (closed_form) = 2.789897210450812 y[1] (numeric) = 2.789897210450929 absolute error = 1.172395514004165e-13 relative error = 4.202289280094018e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999791 y[1] (closed_form) = 2.795324196037103 y[1] (numeric) = 2.795324196037218 absolute error = 1.150191053511662e-13 relative error = 4.114696446094782e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y[1] (closed_form) = 2.800750453599876 y[1] (numeric) = 2.800750453599988 absolute error = 1.123545700920658e-13 relative error = 4.011588035187271e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = 2.80617598561751 y[1] (numeric) = 2.80617598561762 absolute error = 1.101341240428155e-13 relative error = 3.924704815638284e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = 2.811600794555752 y[1] (numeric) = 2.811600794555861 absolute error = 1.088018564132653e-13 relative error = 3.869747676268409e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = 2.817024882867798 y[1] (numeric) = 2.817024882867905 absolute error = 1.070254995738651e-13 relative error = 3.799238701253876e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = 2.822448252994384 y[1] (numeric) = 2.822448252994489 absolute error = 1.048050535246148e-13 relative error = 3.71326749439694e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y[1] (closed_form) = 2.827870907363862 y[1] (numeric) = 2.827870907363966 absolute error = 1.034727858950646e-13 relative error = 3.659034987262619e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y[1] (closed_form) = 2.833292848392294 y[1] (numeric) = 2.833292848392396 absolute error = 1.016964290556643e-13 relative error = 3.589337018704944e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = 2.838714078483526 y[1] (numeric) = 2.838714078483626 absolute error = 9.992007221626409e-14 relative error = 3.519906177717009e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y[1] (closed_form) = 2.844134600029274 y[1] (numeric) = 2.844134600029371 absolute error = 9.769962616701378e-14 relative error = 3.435126669673376e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y[1] (closed_form) = 2.849554415409206 y[1] (numeric) = 2.849554415409302 absolute error = 9.592326932761353e-14 relative error = 3.366255047066319e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 2.85497352699102 y[1] (numeric) = 2.854973526991115 absolute error = 9.414691248821327e-14 relative error = 3.297645725893604e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y[1] (closed_form) = 2.86039193713053 y[1] (numeric) = 2.860391937130622 absolute error = 9.281464485866309e-14 relative error = 3.244822629159426e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y[1] (closed_form) = 2.865809648171736 y[1] (numeric) = 2.865809648171827 absolute error = 9.14823772291129e-14 relative error = 3.192200057232508e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 2.871226662446912 y[1] (numeric) = 2.871226662447002 absolute error = 8.970602038971265e-14 relative error = 3.124309953059001e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y[1] (closed_form) = 2.876642982276679 y[1] (numeric) = 2.876642982276767 absolute error = 8.79296635503124e-14 relative error = 3.056676274812584e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y[1] (closed_form) = 2.882058609970084 y[1] (numeric) = 2.88205860997017 absolute error = 8.570921750106208e-14 relative error = 2.973888775355326e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = 2.887473547824677 y[1] (numeric) = 2.887473547824762 absolute error = 8.43769498715119e-14 relative error = 2.922172219900632e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y[1] (closed_form) = 2.892887798126587 y[1] (numeric) = 2.892887798126669 absolute error = 8.260059303211165e-14 relative error = 2.855298884581808e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y[1] (closed_form) = 2.898301363150595 y[1] (numeric) = 2.898301363150676 absolute error = 8.08242361927114e-14 relative error = 2.788676057649557e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y[1] (closed_form) = 2.903714245160215 y[1] (numeric) = 2.903714245160295 absolute error = 7.993605777301127e-14 relative error = 2.752889954865402e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y[1] (closed_form) = 2.909126446407763 y[1] (numeric) = 2.90912644640784 absolute error = 7.72715225139109e-14 relative error = 2.656176138693697e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y[1] (closed_form) = 2.914537969134432 y[1] (numeric) = 2.914537969134507 absolute error = 7.593925488436071e-14 relative error = 2.605533216193213e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y[1] (closed_form) = 2.919948815570366 y[1] (numeric) = 2.919948815570439 absolute error = 7.283063041541027e-14 relative error = 2.494243393139203e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y[1] (closed_form) = 2.925358987934733 y[1] (numeric) = 2.925358987934804 absolute error = 7.149836278586008e-14 relative error = 2.444088506085779e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y[1] (closed_form) = 2.930768488435795 y[1] (numeric) = 2.930768488435864 absolute error = 6.927791673660977e-14 relative error = 2.363814030687381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y[1] (closed_form) = 2.936177319270979 y[1] (numeric) = 2.936177319271047 absolute error = 6.794564910705958e-14 relative error = 2.314085346995656e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y[1] (closed_form) = 2.941585482626952 y[1] (numeric) = 2.941585482627017 absolute error = 6.52811138479592e-14 relative error = 2.219249252945748e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y[1] (closed_form) = 2.946992980679687 y[1] (numeric) = 2.946992980679751 absolute error = 6.394884621840902e-14 relative error = 2.169969410774098e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y[1] (closed_form) = 2.952399815594532 y[1] (numeric) = 2.952399815594595 absolute error = 6.306066779870889e-14 relative error = 2.135912198125179e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y[1] (closed_form) = 2.957805989526284 y[1] (numeric) = 2.957805989526346 absolute error = 6.17284001691587e-14 relative error = 2.086965824930423e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y[1] (closed_form) = 2.963211504619253 y[1] (numeric) = 2.963211504619313 absolute error = 5.995204332975845e-14 relative error = 2.023211749694586e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y[1] (closed_form) = 2.968616363007331 y[1] (numeric) = 2.968616363007389 absolute error = 5.773159728050814e-14 relative error = 1.944730818030783e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y[1] (closed_form) = 2.974020566814059 y[1] (numeric) = 2.974020566814116 absolute error = 5.639932965095795e-14 relative error = 1.896400121784502e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y[1] (closed_form) = 2.979424118152696 y[1] (numeric) = 2.979424118152751 absolute error = 5.506706202140776e-14 relative error = 1.848245158717131e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y[1] (closed_form) = 2.984827019126283 y[1] (numeric) = 2.984827019126337 absolute error = 5.373479439185758e-14 relative error = 1.80026494157061e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y[1] (closed_form) = 2.99022927182771 y[1] (numeric) = 2.990229271827762 absolute error = 5.195843755245733e-14 relative error = 1.737607147451235e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y[1] (closed_form) = 2.995630878339781 y[1] (numeric) = 2.99563087833983 absolute error = 4.929390229335695e-14 relative error = 1.645526578383926e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y[1] (closed_form) = 3.001031840735276 y[1] (numeric) = 3.001031840735323 absolute error = 4.75175454539567e-14 relative error = 1.583373585343717e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y[1] (closed_form) = 3.006432161077021 y[1] (numeric) = 3.006432161077067 absolute error = 4.529709940470639e-14 relative error = 1.506672925840415e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y[1] (closed_form) = 3.011831841417947 y[1] (numeric) = 3.011831841417991 absolute error = 4.39648317751562e-14 relative error = 1.459737265891242e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y[1] (closed_form) = 3.017230883801155 y[1] (numeric) = 3.017230883801197 absolute error = 4.218847493575595e-14 relative error = 1.398251461704722e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y[1] (closed_form) = 3.022629290259976 y[1] (numeric) = 3.022629290260017 absolute error = 4.085620730620576e-14 relative error = 1.351677740894641e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y[1] (closed_form) = 3.028027062818038 y[1] (numeric) = 3.028027062818077 absolute error = 3.863576125695545e-14 relative error = 1.27593843963201e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y[1] (closed_form) = 3.033424203489324 y[1] (numeric) = 3.033424203489361 absolute error = 3.730349362740526e-14 relative error = 1.229748664380516e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y[1] (closed_form) = 3.038820714278235 y[1] (numeric) = 3.03882071427827 absolute error = 3.508304757815495e-14 relative error = 1.154495472974545e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y[1] (closed_form) = 3.044216597179648 y[1] (numeric) = 3.044216597179681 absolute error = 3.375077994860476e-14 relative error = 1.108685235468251e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y[1] (closed_form) = 3.049611854178979 y[1] (numeric) = 3.04961185417901 absolute error = 3.108624468950438e-14 relative error = 1.01935086089418e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y[1] (closed_form) = 3.055006487252244 y[1] (numeric) = 3.055006487252272 absolute error = 2.886579864025407e-14 relative error = 9.448686528393189e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y[1] (closed_form) = 3.060400498366111 y[1] (numeric) = 3.060400498366139 absolute error = 2.797762022055394e-14 relative error = 9.141816646380321e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y[1] (closed_form) = 3.065793889477971 y[1] (numeric) = 3.065793889477997 absolute error = 2.575717417130363e-14 relative error = 8.401469602931932e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y[1] (closed_form) = 3.071186662535983 y[1] (numeric) = 3.071186662536007 absolute error = 2.353672812205332e-14 relative error = 7.663724386787432e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y[1] (closed_form) = 3.076578819479142 y[1] (numeric) = 3.076578819479163 absolute error = 2.131628207280301e-14 relative error = 6.928566867144917e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y[1] (closed_form) = 3.08197036223733 y[1] (numeric) = 3.08197036223735 absolute error = 1.953992523340276e-14 relative error = 6.340075645379638e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y[1] (closed_form) = 3.087361292731377 y[1] (numeric) = 3.087361292731395 absolute error = 1.77635683940025e-14 relative error = 5.753640960591023e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y[1] (closed_form) = 3.092751612873117 y[1] (numeric) = 3.092751612873132 absolute error = 1.509903313490213e-14 relative error = 4.882071056742693e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y[1] (closed_form) = 3.098141324565442 y[1] (numeric) = 3.098141324565455 absolute error = 1.376676550535194e-14 relative error = 4.44355633366174e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y[1] (closed_form) = 3.103530429702358 y[1] (numeric) = 3.10353042970237 absolute error = 1.154631945610163e-14 relative error = 3.720382228444581e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 3.108918930169044 y[1] (numeric) = 3.108918930169053 absolute error = 9.769962616701378e-15 relative error = 3.142559467181136e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y[1] (closed_form) = 3.1143068278419 y[1] (numeric) = 3.114306827841908 absolute error = 8.43769498715119e-15 relative error = 2.709333233231294e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y[1] (closed_form) = 3.119694124588609 y[1] (numeric) = 3.119694124588615 absolute error = 6.217248937900877e-15 relative error = 1.992903371166472e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 3.125080822268186 y[1] (numeric) = 3.12508082226819 absolute error = 3.996802888650564e-15 relative error = 1.278943846882553e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y[1] (closed_form) = 3.130466922731031 y[1] (numeric) = 3.130466922731034 absolute error = 2.664535259100376e-15 relative error = 8.511622466771906e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y[1] (closed_form) = 3.135852427818986 y[1] (numeric) = 3.135852427818988 absolute error = 1.332267629550188e-15 relative error = 4.248502313856625e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 Finished! diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; Iterations = 4900 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %