##############ECHO OF PROBLEM################# ##############temp/divpostode.ode################# diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.0); x_end=c(1.5); 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(1.570796327); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.0); 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(2.0) - ln(float_abs(cos(c(x))))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 2 y[1] (numeric) = 2 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] = 0.01 y[1] (closed_form) = 2.000050000833355 y[1] (numeric) = 2.000050000833355 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] = 0.02000000000000001 y[1] (closed_form) = 2.000200013334756 y[1] (numeric) = 2.000200013334755 absolute error = 4.440892098500626e-16 relative error = 2.220224012046036e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.03000000000000002 y[1] (closed_form) = 2.000450067516204 y[1] (numeric) = 2.000450067516204 absolute error = 4.440892098500626e-16 relative error = 2.219946486349704e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.04000000000000003 y[1] (closed_form) = 2.0008002134244 y[1] (numeric) = 2.0008002134244 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] = 0.05000000000000004 y[1] (closed_form) = 2.001250521180819 y[1] (numeric) = 2.00125052118082 absolute error = 4.440892098500626e-16 relative error = 2.219058559385318e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.06000000000000005 y[1] (closed_form) = 2.001801081037935 y[1] (numeric) = 2.001801081037935 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] = 0.07000000000000005 y[1] (closed_form) = 2.002452003451651 y[1] (numeric) = 2.00245200345165 absolute error = 8.881784197001252e-16 relative error = 4.435454223967223e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.08000000000000006 y[1] (closed_form) = 2.003203419170097 y[1] (numeric) = 2.003203419170096 absolute error = 4.440892098500626e-16 relative error = 2.216895226916313e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000007 y[1] (closed_form) = 2.004055479338916 y[1] (numeric) = 2.004055479338915 absolute error = 8.881784197001252e-16 relative error = 4.431905348214768e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1000000000000001 y[1] (closed_form) = 2.005008355623235 y[1] (numeric) = 2.005008355623235 absolute error = 8.881784197001252e-16 relative error = 4.429799093899758e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1100000000000001 y[1] (closed_form) = 2.006062240346532 y[1] (numeric) = 2.006062240346531 absolute error = 1.332267629550188e-15 relative error = 6.641207848665994e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1200000000000001 y[1] (closed_form) = 2.007217346646628 y[1] (numeric) = 2.007217346646626 absolute error = 1.332267629550188e-15 relative error = 6.637385989992317e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1300000000000001 y[1] (closed_form) = 2.008473908649082 y[1] (numeric) = 2.008473908649081 absolute error = 1.332267629550188e-15 relative error = 6.633233440638933e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1400000000000001 y[1] (closed_form) = 2.009832181658296 y[1] (numeric) = 2.009832181658294 absolute error = 1.77635683940025e-15 relative error = 8.838334143573088e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1500000000000001 y[1] (closed_form) = 2.011292442366642 y[1] (numeric) = 2.01129244236664 absolute error = 1.332267629550188e-15 relative error = 6.62393792909866e-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) = 2.01285498908201 y[1] (numeric) = 2.012854989082008 absolute error = 1.332267629550188e-15 relative error = 6.618795873406594e-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) = 2.014520141974147 y[1] (numeric) = 2.014520141974146 absolute error = 8.881784197001252e-16 relative error = 4.408883292821022e-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) = 2.016288243340249 y[1] (numeric) = 2.016288243340248 absolute error = 8.881784197001252e-16 relative error = 4.405017103252756e-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) = 2.01815965789026 y[1] (numeric) = 2.01815965789026 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] = 0.2000000000000001 y[1] (closed_form) = 2.020134773052408 y[1] (numeric) = 2.020134773052408 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] = 0.2100000000000002 y[1] (closed_form) = 2.022213999299519 y[1] (numeric) = 2.022213999299519 absolute error = 4.440892098500626e-16 relative error = 2.196054472987983e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000002 y[1] (closed_form) = 2.024397770496703 y[1] (numeric) = 2.024397770496702 absolute error = 8.881784197001252e-16 relative error = 4.38737106236885e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000002 y[1] (closed_form) = 2.026686544271061 y[1] (numeric) = 2.02668654427106 absolute error = 8.881784197001252e-16 relative error = 4.382416324866738e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000002 y[1] (closed_form) = 2.029080802404081 y[1] (numeric) = 2.029080802404081 absolute error = 4.440892098500626e-16 relative error = 2.188622598587006e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000002 y[1] (closed_form) = 2.031581051247469 y[1] (numeric) = 2.031581051247469 absolute error = 4.440892098500626e-16 relative error = 2.185929080099338e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000002 y[1] (closed_form) = 2.034187822163188 y[1] (numeric) = 2.034187822163188 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] = 0.2700000000000002 y[1] (closed_form) = 2.036901671988538 y[1] (numeric) = 2.036901671988538 absolute error = 4.440892098500626e-16 relative error = 2.180219182679141e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000002 y[1] (closed_form) = 2.039723183527177 y[1] (numeric) = 2.039723183527177 absolute error = 4.440892098500626e-16 relative error = 2.177203325610706e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000002 y[1] (closed_form) = 2.042652966067024 y[1] (numeric) = 2.042652966067024 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] = 0.3000000000000002 y[1] (closed_form) = 2.045691655926058 y[1] (numeric) = 2.045691655926058 absolute error = 4.440892098500626e-16 relative error = 2.170851157180036e-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) = 2.048839917027086 y[1] (numeric) = 2.048839917027085 absolute error = 8.881784197001252e-16 relative error = 4.335030825584913e-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) = 2.05209844150263 y[1] (numeric) = 2.05209844150263 absolute error = 4.440892098500626e-16 relative error = 2.164073617856667e-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) = 2.055467950331153 y[1] (numeric) = 2.055467950331152 absolute error = 4.440892098500626e-16 relative error = 2.160526072802625e-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) = 2.058949194005907 y[1] (numeric) = 2.058949194005907 absolute error = 4.440892098500626e-16 relative error = 2.156873084303937e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000003 y[1] (closed_form) = 2.062542953237805 y[1] (numeric) = 2.062542953237805 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] = 0.3600000000000003 y[1] (closed_form) = 2.066250039693758 y[1] (numeric) = 2.066250039693758 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] = 0.3700000000000003 y[1] (closed_form) = 2.070071296772055 y[1] (numeric) = 2.070071296772055 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] = 0.3800000000000003 y[1] (closed_form) = 2.07400760041643 y[1] (numeric) = 2.074007600416431 absolute error = 8.881784197001252e-16 relative error = 4.282426060163869e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000003 y[1] (closed_form) = 2.078059859970587 y[1] (numeric) = 2.078059859970588 absolute error = 8.881784197001252e-16 relative error = 4.274075241089045e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000003 y[1] (closed_form) = 2.082229019075056 y[1] (numeric) = 2.082229019075056 absolute error = 4.440892098500626e-16 relative error = 2.132758720495265e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 2.086516056608366 y[1] (numeric) = 2.086516056608366 absolute error = 4.440892098500626e-16 relative error = 2.128376670975301e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 2.090921987674673 y[1] (numeric) = 2.090921987674673 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] = 0.4300000000000003 y[1] (closed_form) = 2.095447864640073 y[1] (numeric) = 2.095447864640073 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] = 0.4400000000000003 y[1] (closed_form) = 2.100094778220038 y[1] (numeric) = 2.100094778220038 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] = 0.4500000000000003 y[1] (closed_form) = 2.10486385862049 y[1] (numeric) = 2.10486385862049 absolute error = 4.440892098500626e-16 relative error = 2.109823911087128e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000004 y[1] (closed_form) = 2.109756276735282 y[1] (numeric) = 2.109756276735282 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] = 0.4700000000000004 y[1] (closed_form) = 2.114773245402945 y[1] (numeric) = 2.114773245402945 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] = 0.4800000000000004 y[1] (closed_form) = 2.119916020725824 y[1] (numeric) = 2.119916020725823 absolute error = 8.881784197001252e-16 relative error = 4.189686813140965e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000004 y[1] (closed_form) = 2.125185903454887 y[1] (numeric) = 2.125185903454885 absolute error = 1.332267629550188e-15 relative error = 6.268946294930425e-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) = 2.130584240443723 y[1] (numeric) = 2.130584240443721 absolute error = 1.77635683940025e-15 relative error = 8.337416590626335e-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) = 2.136112426175486 y[1] (numeric) = 2.136112426175484 absolute error = 1.77635683940025e-15 relative error = 8.315839642301294e-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) = 2.141771904366788 y[1] (numeric) = 2.141771904366786 absolute error = 2.220446049250313e-15 relative error = 1.036733204279652e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (closed_form) = 2.147564169652822 y[1] (numeric) = 2.147564169652819 absolute error = 2.220446049250313e-15 relative error = 1.033936997379349e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (closed_form) = 2.153490769358282 y[1] (numeric) = 2.153490769358279 absolute error = 2.664535259100376e-15 relative error = 1.237309812056627e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (closed_form) = 2.159553305358981 y[1] (numeric) = 2.159553305358978 absolute error = 2.664535259100376e-15 relative error = 1.233836299612642e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (closed_form) = 2.165753436039385 y[1] (numeric) = 2.165753436039382 absolute error = 2.220446049250313e-15 relative error = 1.025253388636403e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = 2.172092878351663 y[1] (numeric) = 2.172092878351662 absolute error = 1.332267629550188e-15 relative error = 6.133566583769688e-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) = 2.17857340998226 y[1] (numeric) = 2.178573409982259 absolute error = 8.881784197001252e-16 relative error = 4.076880841519853e-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) = 2.185196871632402 y[1] (numeric) = 2.185196871632401 absolute error = 8.881784197001252e-16 relative error = 4.064523573277092e-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) = 2.191965169419438 y[1] (numeric) = 2.191965169419437 absolute error = 4.440892098500626e-16 relative error = 2.025986617149048e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 2.198880277406405 y[1] (numeric) = 2.198880277406404 absolute error = 8.881784197001252e-16 relative error = 4.039230461186082e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = 2.205944240267755 y[1] (numeric) = 2.205944240267754 absolute error = 8.881784197001252e-16 relative error = 4.026295875875445e-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) = 2.213159176099776 y[1] (numeric) = 2.213159176099776 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] = 0.6400000000000005 y[1] (closed_form) = 2.220527279384879 y[1] (numeric) = 2.220527279384878 absolute error = 4.440892098500626e-16 relative error = 1.999926837075752e-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) = 2.228050824119617 y[1] (numeric) = 2.228050824119616 absolute error = 8.881784197001252e-16 relative error = 3.986347214727818e-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) = 2.235732167117059 y[1] (numeric) = 2.235732167117058 absolute error = 8.881784197001252e-16 relative error = 3.972651253863817e-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) = 2.243573751494981 y[1] (numeric) = 2.243573751494981 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] = 0.6800000000000005 y[1] (closed_form) = 2.251578110362207 y[1] (numeric) = 2.251578110362207 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] = 0.6900000000000005 y[1] (closed_form) = 2.259747870716431 y[1] (numeric) = 2.259747870716432 absolute error = 8.881784197001252e-16 relative error = 3.930431492866224e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 2.268085757567932 y[1] (numeric) = 2.268085757567932 absolute error = 4.440892098500626e-16 relative error = 1.957991263638371e-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) = 2.276594598304711 y[1] (numeric) = 2.276594598304712 absolute error = 8.881784197001252e-16 relative error = 3.901346424881778e-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) = 2.285277327315926 y[1] (numeric) = 2.285277327315927 absolute error = 8.881784197001252e-16 relative error = 3.886523570175603e-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) = 2.294136990891822 y[1] (numeric) = 2.294136990891822 absolute error = 4.440892098500626e-16 relative error = 1.935757156670176e-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) = 2.303176752419951 y[1] (numeric) = 2.303176752419951 absolute error = 4.440892098500626e-16 relative error = 1.928159483997298e-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) = 2.312399897899106 y[1] (numeric) = 2.312399897899106 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] = 0.7600000000000006 y[1] (closed_form) = 2.32180984179426 y[1] (numeric) = 2.32180984179426 absolute error = 4.440892098500626e-16 relative error = 1.912685534603803e-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) = 2.331410133257819 y[1] (numeric) = 2.331410133257818 absolute error = 8.881784197001252e-16 relative error = 3.809618938470601e-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) = 2.341204462744726 y[1] (numeric) = 2.341204462744725 absolute error = 8.881784197001252e-16 relative error = 3.793681559357971e-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) = 2.351196669051421 y[1] (numeric) = 2.35119666905142 absolute error = 1.332267629550188e-15 relative error = 5.666338537676156e-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) = 2.361390746811344 y[1] (numeric) = 2.361390746811343 absolute error = 1.77635683940025e-15 relative error = 7.522502753087e-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) = 2.371790854482695 y[1] (numeric) = 2.371790854482693 absolute error = 1.77635683940025e-15 relative error = 7.48951719770286e-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) = 2.382401322867441 y[1] (numeric) = 2.382401322867439 absolute error = 2.220446049250313e-15 relative error = 9.320201545967075e-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) = 2.393226664204251 y[1] (numeric) = 2.393226664204248 absolute error = 2.664535259100376e-15 relative error = 1.11336518974743e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (closed_form) = 2.404271581882078 y[1] (numeric) = 2.404271581882075 absolute error = 2.664535259100376e-15 relative error = 1.10825053175339e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = 2.415540980825635 y[1] (numeric) = 2.415540980825632 absolute error = 3.108624468950438e-15 relative error = 1.286926818309622e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (closed_form) = 2.427039978609021 y[1] (numeric) = 2.427039978609018 absolute error = 2.664535259100376e-15 relative error = 1.097853880687811e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (closed_form) = 2.438773917359315 y[1] (numeric) = 2.438773917359313 absolute error = 2.220446049250313e-15 relative error = 9.104763805472358e-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) = 2.450748376518226 y[1] (numeric) = 2.450748376518225 absolute error = 1.332267629550188e-15 relative error = 5.436166529029545e-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) = 2.462969186536775 y[1] (numeric) = 2.462969186536772 absolute error = 2.664535259100376e-15 relative error = 1.081838649734399e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = 2.475442443585815 y[1] (numeric) = 2.475442443585812 absolute error = 3.552713678800501e-15 relative error = 1.435183309555846e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = 2.488174525373867 y[1] (numeric) = 2.488174525373864 absolute error = 3.108624468950438e-15 relative error = 1.249359495183861e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (closed_form) = 2.501172108173523 y[1] (numeric) = 2.50117210817352 absolute error = 3.108624468950438e-15 relative error = 1.242867077716018e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = 2.514442185168662 y[1] (numeric) = 2.514442185168658 absolute error = 3.552713678800501e-15 relative error = 1.412923192172023e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = 2.527992086247063 y[1] (numeric) = 2.527992086247059 absolute error = 3.996802888650564e-15 relative error = 1.581018750174977e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = 2.541829499376963 y[1] (numeric) = 2.541829499376959 absolute error = 3.996802888650564e-15 relative error = 1.572411874844569e-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) = 2.555962493721842 y[1] (numeric) = 2.555962493721838 absolute error = 3.996802888650564e-15 relative error = 1.563717346583852e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = 2.570399544665549 y[1] (numeric) = 2.570399544665546 absolute error = 3.108624468950438e-15 relative error = 1.209393487250606e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 2.585149560940141 y[1] (numeric) = 2.585149560940138 absolute error = 3.108624468950438e-15 relative error = 1.202493084314984e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = 2.600221914071749 y[1] (numeric) = 2.600221914071747 absolute error = 2.664535259100376e-15 relative error = 1.024733790866302e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (closed_form) = 2.615626470386015 y[1] (numeric) = 2.615626470386013 absolute error = 1.77635683940025e-15 relative error = 6.791324600481256e-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) = 2.631373625844502 y[1] (numeric) = 2.631373625844502 absolute error = 4.440892098500626e-16 relative error = 1.687670673173744e-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) = 2.6474743440177 y[1] (numeric) = 2.647474344017701 absolute error = 4.440892098500626e-16 relative error = 1.677407038347842e-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) = 2.663940197539414 y[1] (numeric) = 2.663940197539416 absolute error = 1.77635683940025e-15 relative error = 6.668155843141702e-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) = 2.680783413432427 y[1] (numeric) = 2.68078341343243 absolute error = 3.552713678800501e-15 relative error = 1.32525203677371e-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) = 2.698016922747217 y[1] (numeric) = 2.698016922747223 absolute error = 5.329070518200751e-15 relative error = 1.975180538443214e-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) = 2.715654415015488 y[1] (numeric) = 2.715654415015496 absolute error = 7.549516567451064e-15 relative error = 2.779999003447575e-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) = 2.733710398089729 y[1] (numeric) = 2.733710398089738 absolute error = 9.769962616701378e-15 relative error = 3.573883547989745e-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) = 2.752200264020703 y[1] (numeric) = 2.752200264020715 absolute error = 1.154631945610163e-14 relative error = 4.195304973640818e-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) = 2.771140361718708 y[1] (numeric) = 2.771140361718721 absolute error = 1.332267629550188e-14 relative error = 4.807651203650663e-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) = 2.790548077254211 y[1] (numeric) = 2.790548077254226 absolute error = 1.509903313490213e-14 relative error = 5.410776921556922e-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) = 2.810441922782111 y[1] (numeric) = 2.810441922782128 absolute error = 1.687538997430238e-14 relative error = 6.004532538995542e-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) = 2.830841635225032 y[1] (numeric) = 2.830841635225051 absolute error = 1.865174681370263e-14 relative error = 6.588763773152555e-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) = 2.851768286029456 y[1] (numeric) = 2.851768286029477 absolute error = 2.176037128265307e-14 relative error = 7.630483650882534e-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) = 2.87324440351954 y[1] (numeric) = 2.873244403519565 absolute error = 2.442490654175344e-14 relative error = 8.500810620855817e-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) = 2.895294109624292 y[1] (numeric) = 2.895294109624319 absolute error = 2.708944180085382e-14 relative error = 9.356369603628655e-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) = 2.917943273052765 y[1] (numeric) = 2.917943273052795 absolute error = 2.930988785010413e-14 relative error = 1.004470790120604e-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) = 2.941219681350006 y[1] (numeric) = 2.941219681350037 absolute error = 3.108624468950438e-14 relative error = 1.056916791582054e-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) = 2.965153234696853 y[1] (numeric) = 2.965153234696887 absolute error = 3.419486915845482e-14 relative error = 1.15322435138671e-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) = 2.989776164836439 y[1] (numeric) = 2.989776164836476 absolute error = 3.730349362740526e-14 relative error = 1.247701887055682e-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) = 3.015123283140605 y[1] (numeric) = 3.015123283140644 absolute error = 3.952393967665557e-14 relative error = 1.310856504530281e-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) = 3.041232262597803 y[1] (numeric) = 3.041232262597846 absolute error = 4.307665335545607e-14 relative error = 1.416421030554906e-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) = 3.068143959445243 y[1] (numeric) = 3.068143959445289 absolute error = 4.574118861455645e-14 relative error = 1.490842320932913e-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) = 3.095902781327071 y[1] (numeric) = 3.09590278132712 absolute error = 4.840572387365683e-14 relative error = 1.563541470540219e-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) = 3.124557110295759 y[1] (numeric) = 3.124557110295809 absolute error = 5.062616992290714e-14 relative error = 1.62026706940604e-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) = 3.154159790761873 y[1] (numeric) = 3.154159790761926 absolute error = 5.329070518200751e-14 relative error = 1.689537268786734e-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) = 3.184768694738706 y[1] (numeric) = 3.184768694738764 absolute error = 5.773159728050814e-14 relative error = 1.812740667034367e-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) = 3.216447379556299 y[1] (numeric) = 3.21644737955636 absolute error = 6.128431095930864e-14 relative error = 1.905341630919597e-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) = 3.249265856812876 y[1] (numeric) = 3.24926585681294 absolute error = 6.439293542825908e-14 relative error = 1.981768752262719e-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) = 3.283301495931948 y[1] (numeric) = 3.283301495932016 absolute error = 6.838973831690964e-14 relative error = 2.082956390134911e-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) = 3.318640091629052 y[1] (numeric) = 3.318640091629125 absolute error = 7.238654120556021e-14 relative error = 2.181210954093764e-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) = 3.355377132316079 y[1] (numeric) = 3.355377132316155 absolute error = 7.638334409421077e-14 relative error = 2.276445868291607e-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) = 3.393619316613149 y[1] (numeric) = 3.39361931661323 absolute error = 8.08242361927114e-14 relative error = 2.381652997937742e-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) = 3.433486378584554 y[1] (numeric) = 3.433486378584639 absolute error = 8.570921750106208e-14 relative error = 2.496273701146748e-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) = 3.475113300329181 y[1] (numeric) = 3.475113300329272 absolute error = 9.015010959956271e-14 relative error = 2.594163177097656e-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) = 3.518653014960218 y[1] (numeric) = 3.518653014960313 absolute error = 9.50350909079134e-14 relative error = 2.700894078042187e-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) = 3.564279736472824 y[1] (numeric) = 3.564279736472925 absolute error = 1.012523398458143e-13 relative error = 2.840751774046012e-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) = 3.6121930994905 y[1] (numeric) = 3.612193099490606 absolute error = 1.06137321154165e-13 relative error = 2.938306957320073e-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) = 3.662623357400166 y[1] (numeric) = 3.662623357400278 absolute error = 1.114663916723657e-13 relative error = 3.043348463531006e-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) = 3.715837981167588 y[1] (numeric) = 3.715837981167706 absolute error = 1.181277298201167e-13 relative error = 3.179033381401593e-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) = 3.772150137669447 y[1] (numeric) = 3.772150137669572 absolute error = 1.243449787580175e-13 relative error = 3.296395271128889e-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) = 3.831929728955607 y[1] (numeric) = 3.831929728955738 absolute error = 1.310063169057685e-13 relative error = 3.418807915913277e-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) = 3.895617980714245 y[1] (numeric) = 3.895617980714382 absolute error = 1.376676550535194e-13 relative error = 3.533910556298404e-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) = 3.963747043924039 y[1] (numeric) = 3.963747043924184 absolute error = 1.452171716209705e-13 relative error = 3.663633678228065e-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) = 4.036966830539075 y[1] (numeric) = 4.036966830539229 absolute error = 1.536548666081217e-13 relative error = 3.806195915352701e-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) = 4.116082544013317 y[1] (numeric) = 4.116082544013478 absolute error = 1.616484723854228e-13 relative error = 3.927240784335928e-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) = 4.202108465746448 y[1] (numeric) = 4.202108465746621 absolute error = 1.723066134218243e-13 relative error = 4.100479909702101e-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) = 4.29634725495213 y[1] (numeric) = 4.296347254952313 absolute error = 1.829647544582258e-13 relative error = 4.258611876573379e-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) = 4.40051082125701 y[1] (numeric) = 4.400510821257202 absolute error = 1.927347170749272e-13 relative error = 4.379825999834091e-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) = 4.51691201953459 y[1] (numeric) = 4.516912019534796 absolute error = 2.060573933704291e-13 relative error = 4.56190850030461e-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) = 4.648783653977668 y[1] (numeric) = 4.64878365397789 absolute error = 2.211564265053312e-13 relative error = 4.757296595553585e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; Iterations = 1501 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %