##############ECHO OF PROBLEM################# ##############temp/add_c_sinpostode.ode################# diff ( y , x , 1 ) = 1.0 + sin ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(-0.5); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.001); glob_type_given_pole=3; // 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) - c(cos(c(x))) + c(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -0.5 y[1] (closed_form) = 0.6224174381096272 y[1] (numeric) = 0.6224174381096272 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] = -0.49 y[1] (closed_form) = 0.6276671413898784 y[1] (numeric) = 0.6276671413898784 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] = -0.48 y[1] (closed_form) = 0.6330050772207159 y[1] (numeric) = 0.6330050772207159 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] = -0.47 y[1] (closed_form) = 0.6384317118046712 y[1] (numeric) = 0.6384317118046711 absolute error = 1.110223024625157e-16 relative error = 1.738984771741461e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.46 y[1] (closed_form) = 0.6439475024744747 y[1] (numeric) = 0.6439475024744747 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] = -0.45 y[1] (closed_form) = 0.6495528976473233 y[1] (numeric) = 0.6495528976473232 absolute error = 1.110223024625157e-16 relative error = 1.709211102970024e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4399999999999999 y[1] (closed_form) = 0.6552483367800366 y[1] (numeric) = 0.6552483367800366 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] = -0.4299999999999999 y[1] (closed_form) = 0.661034250325115 y[1] (numeric) = 0.6610342503251148 absolute error = 2.220446049250313e-16 relative error = 3.359048412632532e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4199999999999999 y[1] (closed_form) = 0.6669110596876919 y[1] (numeric) = 0.6669110596876917 absolute error = 2.220446049250313e-16 relative error = 3.329448532897515e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4099999999999999 y[1] (closed_form) = 0.6728791771833948 y[1] (numeric) = 0.672879177183395 absolute error = 1.110223024625157e-16 relative error = 1.649958955889287e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3999999999999999 y[1] (closed_form) = 0.678939005997115 y[1] (numeric) = 0.6789390059971151 absolute error = 1.110223024625157e-16 relative error = 1.635232347557704e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3899999999999999 y[1] (closed_form) = 0.685090940142687 y[1] (numeric) = 0.6850909401426871 absolute error = 1.110223024625157e-16 relative error = 1.620548396675521e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3799999999999999 y[1] (closed_form) = 0.6913353644234899 y[1] (numeric) = 0.6913353644234898 absolute error = 1.110223024625157e-16 relative error = 1.605910939549549e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3699999999999999 y[1] (closed_form) = 0.6976726543939658 y[1] (numeric) = 0.6976726543939655 absolute error = 2.220446049250313e-16 relative error = 3.182647385225534e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3599999999999999 y[1] (closed_form) = 0.7041031763220653 y[1] (numeric) = 0.7041031763220652 absolute error = 1.110223024625157e-16 relative error = 1.576790251713517e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3499999999999999 y[1] (closed_form) = 0.7106272871526211 y[1] (numeric) = 0.710627287152621 absolute error = 1.110223024625157e-16 relative error = 1.562314091643816e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3399999999999999 y[1] (closed_form) = 0.7172453344716538 y[1] (numeric) = 0.7172453344716536 absolute error = 2.220446049250313e-16 relative error = 3.095797131794473e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3299999999999998 y[1] (closed_form) = 0.7239576564716133 y[1] (numeric) = 0.7239576564716129 absolute error = 3.33066907387547e-16 relative error = 4.600640719939768e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3199999999999998 y[1] (closed_form) = 0.7307645819175592 y[1] (numeric) = 0.7307645819175591 absolute error = 1.110223024625157e-16 relative error = 1.519262224931429e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3099999999999998 y[1] (closed_form) = 0.7376664301142866 y[1] (numeric) = 0.7376664301142867 absolute error = 1.110223024625157e-16 relative error = 1.50504751104527e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2999999999999998 y[1] (closed_form) = 0.744663510874394 y[1] (numeric) = 0.744663510874394 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] = -0.2899999999999998 y[1] (closed_form) = 0.751756124487303 y[1] (numeric) = 0.751756124487303 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] = -0.2799999999999998 y[1] (closed_form) = 0.7589445616892292 y[1] (numeric) = 0.7589445616892294 absolute error = 2.220446049250313e-16 relative error = 2.925702562922555e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2699999999999998 y[1] (closed_form) = 0.7662291036341096 y[1] (numeric) = 0.7662291036341098 absolute error = 2.220446049250313e-16 relative error = 2.897887901567653e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2599999999999998 y[1] (closed_form) = 0.7736100218654869 y[1] (numeric) = 0.7736100218654871 absolute error = 2.220446049250313e-16 relative error = 2.870239508914219e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2499999999999998 y[1] (closed_form) = 0.7810875782893554 y[1] (numeric) = 0.7810875782893557 absolute error = 3.33066907387547e-16 relative error = 4.264142928978467e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2399999999999998 y[1] (closed_form) = 0.7886620251479706 y[1] (numeric) = 0.7886620251479708 absolute error = 2.220446049250313e-16 relative error = 2.815459573869691e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2299999999999998 y[1] (closed_form) = 0.7963336049946255 y[1] (numeric) = 0.7963336049946255 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] = -0.2199999999999998 y[1] (closed_form) = 0.8041025506693948 y[1] (numeric) = 0.8041025506693948 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] = -0.2099999999999997 y[1] (closed_form) = 0.8119690852758519 y[1] (numeric) = 0.8119690852758523 absolute error = 4.440892098500626e-16 relative error = 5.469287167493468e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1999999999999997 y[1] (closed_form) = 0.8199334221587584 y[1] (numeric) = 0.819933422158759 absolute error = 5.551115123125783e-16 relative error = 6.770202278753989e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1899999999999997 y[1] (closed_form) = 0.8279957648827299 y[1] (numeric) = 0.8279957648827303 absolute error = 4.440892098500626e-16 relative error = 5.363423687474532e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1799999999999997 y[1] (closed_form) = 0.8361563072118789 y[1] (numeric) = 0.8361563072118792 absolute error = 2.220446049250313e-16 relative error = 2.655539436943648e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1699999999999997 y[1] (closed_form) = 0.8444152330904395 y[1] (numeric) = 0.8444152330904401 absolute error = 5.551115123125783e-16 relative error = 6.573916369094257e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1599999999999997 y[1] (closed_form) = 0.8527727166243733 y[1] (numeric) = 0.8527727166243737 absolute error = 4.440892098500626e-16 relative error = 5.207591673522943e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1499999999999997 y[1] (closed_form) = 0.861228922063958 y[1] (numeric) = 0.8612289220639583 absolute error = 3.33066907387547e-16 relative error = 3.867344661270122e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1399999999999997 y[1] (closed_form) = 0.869784003787363 y[1] (numeric) = 0.8697840037873632 absolute error = 2.220446049250313e-16 relative error = 2.55287064326507e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1299999999999997 y[1] (closed_form) = 0.8784381062852122 y[1] (numeric) = 0.8784381062852124 absolute error = 1.110223024625157e-16 relative error = 1.263860272774515e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1199999999999997 y[1] (closed_form) = 0.8871913641461342 y[1] (numeric) = 0.8871913641461342 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] = -0.1099999999999997 y[1] (closed_form) = 0.8960439020433035 y[1] (numeric) = 0.8960439020433035 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] = -0.09999999999999964 y[1] (closed_form) = 0.9049958347219746 y[1] (numeric) = 0.9049958347219746 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] = -0.08999999999999964 y[1] (closed_form) = 0.9140472669880062 y[1] (numeric) = 0.9140472669880062 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] = -0.07999999999999963 y[1] (closed_form) = 0.9231982936973808 y[1] (numeric) = 0.9231982936973812 absolute error = 3.33066907387547e-16 relative error = 3.607750465543261e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.06999999999999962 y[1] (closed_form) = 0.9324489997467207 y[1] (numeric) = 0.9324489997467209 absolute error = 2.220446049250313e-16 relative error = 2.381305626209528e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.05999999999999961 y[1] (closed_form) = 0.9417994600647961 y[1] (numeric) = 0.9417994600647963 absolute error = 2.220446049250313e-16 relative error = 2.357663327920729e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.0499999999999996 y[1] (closed_form) = 0.9512497396050341 y[1] (numeric) = 0.9512497396050342 absolute error = 1.110223024625157e-16 relative error = 1.167120450499287e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.03999999999999959 y[1] (closed_form) = 0.9607998933390225 y[1] (numeric) = 0.9607998933390225 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] = -0.02999999999999958 y[1] (closed_form) = 0.9704499662510129 y[1] (numeric) = 0.9704499662510129 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] = -0.01999999999999957 y[1] (closed_form) = 0.9801999933334227 y[1] (numeric) = 0.9801999933334227 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] = -0.009999999999999565 y[1] (closed_form) = 0.9900499995833352 y[1] (numeric) = 0.9900499995833352 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] = 4.371503159461554e-16 y[1] (closed_form) = 1 y[1] (numeric) = 1 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] = 0.01000000000000044 y[1] (closed_form) = 1.010049999583335 y[1] (numeric) = 1.010049999583336 absolute error = 4.440892098500626e-16 relative error = 4.396705212942507e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.02000000000000045 y[1] (closed_form) = 1.020199993333423 y[1] (numeric) = 1.020199993333423 absolute error = 4.440892098500626e-16 relative error = 4.352962289276598e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.03000000000000046 y[1] (closed_form) = 1.030449966251013 y[1] (numeric) = 1.030449966251014 absolute error = 6.661338147750939e-16 relative error = 6.464494508147975e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.04000000000000047 y[1] (closed_form) = 1.040799893339023 y[1] (numeric) = 1.040799893339023 absolute error = 8.881784197001252e-16 relative error = 8.53361366948965e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.05000000000000047 y[1] (closed_form) = 1.051249739605034 y[1] (numeric) = 1.051249739605035 absolute error = 8.881784197001252e-16 relative error = 8.448786108939474e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.06000000000000048 y[1] (closed_form) = 1.061799460064796 y[1] (numeric) = 1.061799460064797 absolute error = 6.661338147750939e-16 relative error = 6.273631131197252e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07000000000000049 y[1] (closed_form) = 1.072448999746721 y[1] (numeric) = 1.072448999746722 absolute error = 8.881784197001252e-16 relative error = 8.281777687422762e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.0800000000000005 y[1] (closed_form) = 1.083198293697381 y[1] (numeric) = 1.083198293697382 absolute error = 4.440892098500626e-16 relative error = 4.099796061663019e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000051 y[1] (closed_form) = 1.094047266988006 y[1] (numeric) = 1.094047266988007 absolute error = 2.220446049250313e-16 relative error = 2.029570491376818e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1000000000000005 y[1] (closed_form) = 1.104995834721975 y[1] (numeric) = 1.104995834721975 absolute error = 2.220446049250313e-16 relative error = 2.00946101286345e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1100000000000005 y[1] (closed_form) = 1.116043902043304 y[1] (numeric) = 1.116043902043304 absolute error = 4.440892098500626e-16 relative error = 3.979137460784508e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1200000000000005 y[1] (closed_form) = 1.127191364146134 y[1] (numeric) = 1.127191364146135 absolute error = 4.440892098500626e-16 relative error = 3.939785416884092e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1300000000000005 y[1] (closed_form) = 1.138438106285213 y[1] (numeric) = 1.138438106285213 absolute error = 6.661338147750939e-16 relative error = 5.851295833277453e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1400000000000005 y[1] (closed_form) = 1.149784003787363 y[1] (numeric) = 1.149784003787364 absolute error = 4.440892098500626e-16 relative error = 3.862370744307126e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1500000000000005 y[1] (closed_form) = 1.161228922063958 y[1] (numeric) = 1.161228922063959 absolute error = 4.440892098500626e-16 relative error = 3.824303730402635e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000006 y[1] (closed_form) = 1.172772716624374 y[1] (numeric) = 1.172772716624374 absolute error = 2.220446049250313e-16 relative error = 1.893330240186256e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000006 y[1] (closed_form) = 1.18441523309044 y[1] (numeric) = 1.18441523309044 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] = 0.1800000000000006 y[1] (closed_form) = 1.196156307211879 y[1] (numeric) = 1.196156307211879 absolute error = 2.220446049250313e-16 relative error = 1.856317636635592e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000006 y[1] (closed_form) = 1.20799576488273 y[1] (numeric) = 1.207995764882731 absolute error = 2.220446049250313e-16 relative error = 1.838124034702944e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000006 y[1] (closed_form) = 1.219933422158759 y[1] (numeric) = 1.219933422158759 absolute error = 4.440892098500626e-16 relative error = 3.64027414761877e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000006 y[1] (closed_form) = 1.231969085275852 y[1] (numeric) = 1.231969085275852 absolute error = 2.220446049250313e-16 relative error = 1.802355331630037e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000006 y[1] (closed_form) = 1.244102550669395 y[1] (numeric) = 1.244102550669395 absolute error = 4.440892098500626e-16 relative error = 3.569554693149036e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000006 y[1] (closed_form) = 1.256333604994626 y[1] (numeric) = 1.256333604994625 absolute error = 4.440892098500626e-16 relative error = 3.53480324083158e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000006 y[1] (closed_form) = 1.268662025147971 y[1] (numeric) = 1.268662025147971 absolute error = 6.661338147750939e-16 relative error = 5.250679862490555e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000006 y[1] (closed_form) = 1.281087578289356 y[1] (numeric) = 1.281087578289355 absolute error = 8.881784197001252e-16 relative error = 6.93300313539934e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000006 y[1] (closed_form) = 1.293610021865488 y[1] (numeric) = 1.293610021865487 absolute error = 8.881784197001252e-16 relative error = 6.865890064915406e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000006 y[1] (closed_form) = 1.30622910363411 y[1] (numeric) = 1.30622910363411 absolute error = 8.881784197001252e-16 relative error = 6.799560790898701e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000006 y[1] (closed_form) = 1.31894456168923 y[1] (numeric) = 1.318944561689229 absolute error = 8.881784197001252e-16 relative error = 6.73400873318433e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000006 y[1] (closed_form) = 1.331756124487304 y[1] (numeric) = 1.331756124487303 absolute error = 8.881784197001252e-16 relative error = 6.669227220877652e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000007 y[1] (closed_form) = 1.344663510874395 y[1] (numeric) = 1.344663510874394 absolute error = 6.661338147750939e-16 relative error = 4.953907125373892e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000007 y[1] (closed_form) = 1.357666430114288 y[1] (numeric) = 1.357666430114287 absolute error = 4.440892098500626e-16 relative error = 3.270974371905767e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000007 y[1] (closed_form) = 1.37076458191756 y[1] (numeric) = 1.37076458191756 absolute error = 4.440892098500626e-16 relative error = 3.239719027674519e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000007 y[1] (closed_form) = 1.383957656471614 y[1] (numeric) = 1.383957656471614 absolute error = 2.220446049250313e-16 relative error = 1.604417619908486e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000007 y[1] (closed_form) = 1.397245334471655 y[1] (numeric) = 1.397245334471654 absolute error = 4.440892098500626e-16 relative error = 3.178319504054652e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000007 y[1] (closed_form) = 1.410627287152622 y[1] (numeric) = 1.410627287152622 absolute error = 6.661338147750939e-16 relative error = 4.722252439336386e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000007 y[1] (closed_form) = 1.424103176322066 y[1] (numeric) = 1.424103176322065 absolute error = 8.881784197001252e-16 relative error = 6.236756117586669e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000007 y[1] (closed_form) = 1.437672654393967 y[1] (numeric) = 1.437672654393966 absolute error = 8.881784197001252e-16 relative error = 6.177890474480271e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000007 y[1] (closed_form) = 1.451335364423491 y[1] (numeric) = 1.45133536442349 absolute error = 1.110223024625157e-15 relative error = 7.649665624086593e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000007 y[1] (closed_form) = 1.465090940142688 y[1] (numeric) = 1.465090940142687 absolute error = 1.110223024625157e-15 relative error = 7.577843765227501e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000007 y[1] (closed_form) = 1.478939005997116 y[1] (numeric) = 1.478939005997115 absolute error = 1.332267629550188e-15 relative error = 9.008266224285288e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000008 y[1] (closed_form) = 1.492879177183396 y[1] (numeric) = 1.492879177183395 absolute error = 8.881784197001252e-16 relative error = 5.949432702088087e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000008 y[1] (closed_form) = 1.506911059687693 y[1] (numeric) = 1.506911059687692 absolute error = 8.881784197001252e-16 relative error = 5.894033453335993e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000008 y[1] (closed_form) = 1.521034250325116 y[1] (numeric) = 1.521034250325115 absolute error = 8.881784197001252e-16 relative error = 5.839305850675485e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000008 y[1] (closed_form) = 1.535248336780038 y[1] (numeric) = 1.535248336780037 absolute error = 8.881784197001252e-16 relative error = 5.785242676523275e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000008 y[1] (closed_form) = 1.549552897647324 y[1] (numeric) = 1.549552897647323 absolute error = 8.881784197001252e-16 relative error = 5.73183671915067e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000008 y[1] (closed_form) = 1.563947502474476 y[1] (numeric) = 1.563947502474475 absolute error = 1.110223024625157e-15 relative error = 7.098850970819435e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000008 y[1] (closed_form) = 1.578431711804672 y[1] (numeric) = 1.578431711804671 absolute error = 1.110223024625157e-15 relative error = 7.033709575916986e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000008 y[1] (closed_form) = 1.593005077220717 y[1] (numeric) = 1.593005077220716 absolute error = 1.110223024625157e-15 relative error = 6.969362750319286e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000008 y[1] (closed_form) = 1.60766714138988 y[1] (numeric) = 1.607667141389879 absolute error = 8.881784197001252e-16 relative error = 5.52464124465632e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000008 y[1] (closed_form) = 1.622417438109629 y[1] (numeric) = 1.622417438109628 absolute error = 8.881784197001252e-16 relative error = 5.474413667144707e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000008 y[1] (closed_form) = 1.63725549235425 y[1] (numeric) = 1.637255492354249 absolute error = 1.110223024625157e-15 relative error = 6.781000459670101e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000008 y[1] (closed_form) = 1.652180820322351 y[1] (numeric) = 1.65218082032235 absolute error = 8.881784197001252e-16 relative error = 5.37579427611825e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000008 y[1] (closed_form) = 1.66719292948524 y[1] (numeric) = 1.667192929485239 absolute error = 1.332267629550188e-15 relative error = 7.991082531531228e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000008 y[1] (closed_form) = 1.682291318636177 y[1] (numeric) = 1.682291318636176 absolute error = 1.332267629550188e-15 relative error = 7.919363399142122e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000008 y[1] (closed_form) = 1.697475477940495 y[1] (numeric) = 1.697475477940494 absolute error = 1.110223024625157e-15 relative error = 6.540436307051472e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000008 y[1] (closed_form) = 1.712744888986585 y[1] (numeric) = 1.712744888986584 absolute error = 1.110223024625157e-15 relative error = 6.48212720857725e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000008 y[1] (closed_form) = 1.728099024837733 y[1] (numeric) = 1.728099024837731 absolute error = 1.332267629550188e-15 relative error = 7.709440317954504e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000008 y[1] (closed_form) = 1.743537350084814 y[1] (numeric) = 1.743537350084813 absolute error = 1.332267629550188e-15 relative error = 7.641176310248701e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000009 y[1] (closed_form) = 1.759059320899838 y[1] (numeric) = 1.759059320899837 absolute error = 1.332267629550188e-15 relative error = 7.573750434230228e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000009 y[1] (closed_form) = 1.774664385090323 y[1] (numeric) = 1.774664385090322 absolute error = 1.332267629550188e-15 relative error = 7.507152567793154e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000009 y[1] (closed_form) = 1.790351982154522 y[1] (numeric) = 1.79035198215452 absolute error = 1.554312234475219e-15 relative error = 8.681601439091039e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000009 y[1] (closed_form) = 1.806121543337468 y[1] (numeric) = 1.806121543337466 absolute error = 1.332267629550188e-15 relative error = 7.37640074370819e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000009 y[1] (closed_form) = 1.82197249168785 y[1] (numeric) = 1.821972491687848 absolute error = 1.332267629550188e-15 relative error = 7.312226916861922e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000009 y[1] (closed_form) = 1.837904242115709 y[1] (numeric) = 1.837904242115708 absolute error = 1.110223024625157e-15 relative error = 6.040701137656225e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000009 y[1] (closed_form) = 1.853916201450946 y[1] (numeric) = 1.853916201450944 absolute error = 1.332267629550188e-15 relative error = 7.186234353567353e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000009 y[1] (closed_form) = 1.870007768502636 y[1] (numeric) = 1.870007768502635 absolute error = 1.110223024625157e-15 relative error = 5.936996858115413e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000009 y[1] (closed_form) = 1.886178334119152 y[1] (numeric) = 1.886178334119151 absolute error = 6.661338147750939e-16 relative error = 3.531658712887185e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000009 y[1] (closed_form) = 1.902427281249074 y[1] (numeric) = 1.902427281249073 absolute error = 8.881784197001252e-16 relative error = 4.668658972956776e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000009 y[1] (closed_form) = 1.918753985002895 y[1] (numeric) = 1.918753985002894 absolute error = 8.881784197001252e-16 relative error = 4.628933290261206e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.700000000000001 y[1] (closed_form) = 1.935157812715513 y[1] (numeric) = 1.935157812715512 absolute error = 1.110223024625157e-15 relative error = 5.737118788607913e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.710000000000001 y[1] (closed_form) = 1.951638124009493 y[1] (numeric) = 1.951638124009493 absolute error = 6.661338147750939e-16 relative error = 3.413203536968074e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.720000000000001 y[1] (closed_form) = 1.968194270859107 y[1] (numeric) = 1.968194270859106 absolute error = 8.881784197001252e-16 relative error = 4.512656259854064e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.730000000000001 y[1] (closed_form) = 1.984825597655131 y[1] (numeric) = 1.98482559765513 absolute error = 6.661338147750939e-16 relative error = 3.356132728044535e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.740000000000001 y[1] (closed_form) = 2.001531441270414 y[1] (numeric) = 2.001531441270413 absolute error = 1.332267629550188e-15 relative error = 6.656241326414386e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.750000000000001 y[1] (closed_form) = 2.018311131126181 y[1] (numeric) = 2.01831113112618 absolute error = 4.440892098500626e-16 relative error = 2.200301048740037e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.760000000000001 y[1] (closed_form) = 2.035163989259097 y[1] (numeric) = 2.035163989259096 absolute error = 8.881784197001252e-16 relative error = 4.364161435577815e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.770000000000001 y[1] (closed_form) = 2.052089330389058 y[1] (numeric) = 2.052089330389058 absolute error = 4.440892098500626e-16 relative error = 2.164083226171578e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.780000000000001 y[1] (closed_form) = 2.069086461987725 y[1] (numeric) = 2.069086461987724 absolute error = 8.881784197001252e-16 relative error = 4.292611430296984e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.790000000000001 y[1] (closed_form) = 2.086154684347766 y[1] (numeric) = 2.086154684347765 absolute error = 4.440892098500626e-16 relative error = 2.128745357101392e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.800000000000001 y[1] (closed_form) = 2.103293290652836 y[1] (numeric) = 2.103293290652836 absolute error = 4.440892098500626e-16 relative error = 2.111399355589742e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000011 y[1] (closed_form) = 2.120501567048255 y[1] (numeric) = 2.120501567048254 absolute error = 4.440892098500626e-16 relative error = 2.094264945383824e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000011 y[1] (closed_form) = 2.137778792712388 y[1] (numeric) = 2.137778792712387 absolute error = 1.332267629550188e-15 relative error = 6.232018177427154e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000011 y[1] (closed_form) = 2.155124239928735 y[1] (numeric) = 2.155124239928733 absolute error = 1.77635683940025e-15 relative error = 8.242479976277333e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000011 y[1] (closed_form) = 2.172537174158694 y[1] (numeric) = 2.172537174158693 absolute error = 1.332267629550188e-15 relative error = 6.132312235651862e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000011 y[1] (closed_form) = 2.19001685411502 y[1] (numeric) = 2.190016854115018 absolute error = 1.77635683940025e-15 relative error = 8.111156021756152e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000011 y[1] (closed_form) = 2.20756253183595 y[1] (numeric) = 2.207562531835948 absolute error = 2.220446049250313e-15 relative error = 1.005836082660657e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000011 y[1] (closed_form) = 2.225173452760001 y[1] (numeric) = 2.225173452759999 absolute error = 1.77635683940025e-15 relative error = 7.983003919073996e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000011 y[1] (closed_form) = 2.242848855801422 y[1] (numeric) = 2.242848855801419 absolute error = 2.220446049250313e-15 relative error = 9.900114506186358e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000011 y[1] (closed_form) = 2.260587973426305 y[1] (numeric) = 2.260587973426302 absolute error = 3.108624468950438e-15 relative error = 1.375139789069474e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000011 y[1] (closed_form) = 2.278390031729338 y[1] (numeric) = 2.278390031729334 absolute error = 3.996802888650564e-15 relative error = 1.754222425919288e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000011 y[1] (closed_form) = 2.29625425051119 y[1] (numeric) = 2.296254250511187 absolute error = 3.108624468950438e-15 relative error = 1.353780605200142e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000012 y[1] (closed_form) = 2.314179843356539 y[1] (numeric) = 2.314179843356535 absolute error = 4.440892098500626e-15 relative error = 1.91899178071634e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000012 y[1] (closed_form) = 2.332166017712704 y[1] (numeric) = 2.3321660177127 absolute error = 3.996802888650564e-15 relative error = 1.713772886790654e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000012 y[1] (closed_form) = 2.350211974968904 y[1] (numeric) = 2.3502119749689 absolute error = 4.440892098500626e-15 relative error = 1.8895708752226e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000012 y[1] (closed_form) = 2.368316910536119 y[1] (numeric) = 2.368316910536115 absolute error = 3.552713678800501e-15 relative error = 1.500100625467505e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000012 y[1] (closed_form) = 2.386480013927545 y[1] (numeric) = 2.386480013927542 absolute error = 3.108624468950438e-15 relative error = 1.302598157457194e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000012 y[1] (closed_form) = 2.404700468839648 y[1] (numeric) = 2.404700468839644 absolute error = 3.552713678800501e-15 relative error = 1.477403828392319e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000012 y[1] (closed_form) = 2.422977453233785 y[1] (numeric) = 2.422977453233781 absolute error = 4.440892098500626e-15 relative error = 1.832824359373904e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000012 y[1] (closed_form) = 2.441310139418415 y[1] (numeric) = 2.441310139418411 absolute error = 3.996802888650564e-15 relative error = 1.637154912895544e-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) = 2.459697694131862 y[1] (numeric) = 2.459697694131859 absolute error = 3.552713678800501e-15 relative error = 1.444370048919533e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 2.478139278625645 y[1] (numeric) = 2.478139278625643 absolute error = 1.77635683940025e-15 relative error = 7.16810735668337e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999999 y[1] (closed_form) = 2.496634048748349 y[1] (numeric) = 2.496634048748349 absolute error = 4.440892098500626e-16 relative error = 1.778751716026225e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999998 y[1] (closed_form) = 2.51518115503004 y[1] (numeric) = 2.515181155030044 absolute error = 3.108624468950438e-15 relative error = 1.235944561183431e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999997 y[1] (closed_form) = 2.533779742767216 y[1] (numeric) = 2.533779742767221 absolute error = 4.884981308350689e-15 relative error = 1.927942364483369e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999996 y[1] (closed_form) = 2.552428952108265 y[1] (numeric) = 2.552428952108272 absolute error = 6.661338147750939e-15 relative error = 2.609803552905471e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999995 y[1] (closed_form) = 2.571127918139462 y[1] (numeric) = 2.57112791813947 absolute error = 8.43769498715119e-15 relative error = 3.281709528189066e-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) = 2.589875770971453 y[1] (numeric) = 2.589875770971464 absolute error = 1.021405182655144e-14 relative error = 3.943838519605975e-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) = 2.608671635826245 y[1] (numeric) = 2.608671635826258 absolute error = 1.243449787580175e-14 relative error = 4.766601401660647e-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) = 2.627514633124683 y[1] (numeric) = 2.627514633124697 absolute error = 1.465494392505207e-14 relative error = 5.577492791210137e-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) = 2.646403878574404 y[1] (numeric) = 2.646403878574421 absolute error = 1.687538997430238e-14 relative error = 6.376725076216642e-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) = 2.665338483258272 y[1] (numeric) = 2.66533848325829 absolute error = 1.820765760385257e-14 relative error = 6.831274045761879e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999988 y[1] (closed_form) = 2.684317553723265 y[1] (numeric) = 2.684317553723286 absolute error = 2.087219286295294e-14 relative error = 7.775604951806953e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999987 y[1] (closed_form) = 2.703340192069818 y[1] (numeric) = 2.703340192069839 absolute error = 2.176037128265307e-14 relative error = 8.049438744885525e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999986 y[1] (closed_form) = 2.722405496041615 y[1] (numeric) = 2.722405496041638 absolute error = 2.353672812205332e-14 relative error = 8.6455629612399e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999985 y[1] (closed_form) = 2.741512559115813 y[1] (numeric) = 2.741512559115839 absolute error = 2.531308496145357e-14 relative error = 9.233255152264373e-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) = 2.760660470593695 y[1] (numeric) = 2.760660470593723 absolute error = 2.797762022055394e-14 relative error = 1.013439375054231e-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) = 2.779848315691736 y[1] (numeric) = 2.779848315691766 absolute error = 3.019806626980426e-14 relative error = 1.086320649200235e-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) = 2.799075175633083 y[1] (numeric) = 2.799075175633115 absolute error = 3.286260152890463e-14 relative error = 1.174052123179289e-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) = 2.818340127739429 y[1] (numeric) = 2.818340127739465 absolute error = 3.597122599785507e-14 relative error = 1.27632664502802e-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) = 2.837642245523286 y[1] (numeric) = 2.837642245523324 absolute error = 3.819167204710538e-14 relative error = 1.345894539995563e-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) = 2.856980598780627 y[1] (numeric) = 2.856980598780667 absolute error = 4.04121180963557e-14 relative error = 1.414504463684625e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999977 y[1] (closed_form) = 2.876354253683908 y[1] (numeric) = 2.876354253683951 absolute error = 4.263256414560601e-14 relative error = 1.482173626249413e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999976 y[1] (closed_form) = 2.895762272875451 y[1] (numeric) = 2.895762272875495 absolute error = 4.485301019485632e-14 relative error = 1.548918936301975e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999975 y[1] (closed_form) = 2.915203715561175 y[1] (numeric) = 2.915203715561222 absolute error = 4.707345624410664e-14 relative error = 1.614757006271345e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999974 y[1] (closed_form) = 2.93467763760468 y[1] (numeric) = 2.93467763760473 absolute error = 4.973799150320701e-14 relative error = 1.694836627569213e-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) = 2.954183091621657 y[1] (numeric) = 2.954183091621709 absolute error = 5.195843755245733e-14 relative error = 1.758808981739025e-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) = 2.973719127074625 y[1] (numeric) = 2.97371912707468 absolute error = 5.417888360170764e-14 relative error = 1.821923365540098e-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) = 2.993284790367986 y[1] (numeric) = 2.993284790368042 absolute error = 5.595524044110789e-14 relative error = 1.869359060693617e-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) = 3.012879124943382 y[1] (numeric) = 3.012879124943439 absolute error = 5.773159728050814e-14 relative error = 1.916160419532033e-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) = 3.03250117137535 y[1] (numeric) = 3.032501171375409 absolute error = 5.906386491005833e-14 relative error = 1.947694710477909e-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) = 3.052149967467265 y[1] (numeric) = 3.052149967467327 absolute error = 6.17284001691587e-14 relative error = 2.022456328395362e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999966 y[1] (closed_form) = 3.07182454834756 y[1] (numeric) = 3.071824548347624 absolute error = 6.394884621840902e-14 relative error = 2.081787068626993e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999965 y[1] (closed_form) = 3.091523946566207 y[1] (numeric) = 3.091523946566274 absolute error = 6.661338147750939e-14 relative error = 2.154710189177013e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999964 y[1] (closed_form) = 3.111247192191469 y[1] (numeric) = 3.111247192191538 absolute error = 6.927791673660977e-14 relative error = 2.226692784503969e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999963 y[1] (closed_form) = 3.130993312906885 y[1] (numeric) = 3.130993312906956 absolute error = 7.105427357601002e-14 relative error = 2.269384392585676e-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) = 3.150761334108505 y[1] (numeric) = 3.150761334108577 absolute error = 7.283063041541027e-14 relative error = 2.311524825031452e-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) = 3.170550279002349 y[1] (numeric) = 3.170550279002423 absolute error = 7.460698725481052e-14 relative error = 2.353124243097841e-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) = 3.190359168702085 y[1] (numeric) = 3.190359168702162 absolute error = 7.638334409421077e-14 relative error = 2.39419263020738e-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) = 3.210187022326918 y[1] (numeric) = 3.210187022326996 absolute error = 7.815970093361102e-14 relative error = 2.434739795220922e-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) = 3.230032857099673 y[1] (numeric) = 3.230032857099754 absolute error = 8.038014698286133e-14 relative error = 2.488524127740194e-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) = 3.249895688445081 y[1] (numeric) = 3.249895688445164 absolute error = 8.260059303211165e-14 relative error = 2.541638284754673e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999955 y[1] (closed_form) = 3.269774530088224 y[1] (numeric) = 3.26977453008831 absolute error = 8.526512829121202e-14 relative error = 2.607676080005168e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999954 y[1] (closed_form) = 3.289668394153171 y[1] (numeric) = 3.289668394153258 absolute error = 8.704148513061227e-14 relative error = 2.64590453205903e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999953 y[1] (closed_form) = 3.30957629126176 y[1] (numeric) = 3.30957629126185 absolute error = 8.926193117986259e-14 relative error = 2.69708033066166e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999952 y[1] (closed_form) = 3.329497230632537 y[1] (numeric) = 3.329497230632628 absolute error = 9.14823772291129e-14 relative error = 2.747633378020053e-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) = 3.349430220179832 y[1] (numeric) = 3.349430220179926 absolute error = 9.414691248821327e-14 relative error = 2.810833673171985e-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) = 3.369374266612967 y[1] (numeric) = 3.369374266613063 absolute error = 9.592326932761353e-14 relative error = 2.84691642237891e-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) = 3.389328375535587 y[1] (numeric) = 3.389328375535686 absolute error = 9.85878045867139e-14 relative error = 2.908771109294918e-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) = 3.409291551545094 y[1] (numeric) = 3.409291551545195 absolute error = 1.016964290556643e-13 relative error = 2.982919692203368e-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) = 3.429262798332189 y[1] (numeric) = 3.429262798332293 absolute error = 1.034727858950646e-13 relative error = 3.017347808554895e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999945 y[1] (closed_form) = 3.449241118780504 y[1] (numeric) = 3.44924111878061 absolute error = 1.056932319443149e-13 relative error = 3.064245969028783e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999944 y[1] (closed_form) = 3.469225515066308 y[1] (numeric) = 3.469225515066417 absolute error = 1.088018564132653e-13 relative error = 3.136200167465498e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999943 y[1] (closed_form) = 3.489214988758294 y[1] (numeric) = 3.489214988758405 absolute error = 1.110223024625157e-13 relative error = 3.181870501537227e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999942 y[1] (closed_form) = 3.509208540917417 y[1] (numeric) = 3.50920854091753 absolute error = 1.13242748511766e-13 relative error = 3.227016781458099e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.549999999999941 y[1] (closed_form) = 3.529205172196789 y[1] (numeric) = 3.529205172196904 absolute error = 1.150191053511662e-13 relative error = 3.259065419525367e-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) = 3.549203882941612 y[1] (numeric) = 3.549203882941728 absolute error = 1.163513729807164e-13 relative error = 3.2782386365554e-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) = 3.569203673289143 y[1] (numeric) = 3.569203673289262 absolute error = 1.185718190299667e-13 relative error = 3.322080494238053e-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) = 3.589203543268683 y[1] (numeric) = 3.589203543268804 absolute error = 1.20792265079217e-13 relative error = 3.365433685301996e-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) = 3.609202492901565 y[1] (numeric) = 3.609202492901688 absolute error = 1.234568003383174e-13 relative error = 3.420611633210586e-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) = 3.629199522301159 y[1] (numeric) = 3.629199522301285 absolute error = 1.261213355974178e-13 relative error = 3.475183296548223e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999934 y[1] (closed_form) = 3.649193631772856 y[1] (numeric) = 3.649193631772984 absolute error = 1.283417816466681e-13 relative error = 3.516990179123954e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999933 y[1] (closed_form) = 3.669183821914036 y[1] (numeric) = 3.669183821914166 absolute error = 1.301181384860683e-13 relative error = 3.54624202006298e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999932 y[1] (closed_form) = 3.689169093714012 y[1] (numeric) = 3.689169093714144 absolute error = 1.314504061156185e-13 relative error = 3.563143970266837e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.639999999999931 y[1] (closed_form) = 3.709148448653924 y[1] (numeric) = 3.709148448654058 absolute error = 1.341149413747189e-13 relative error = 3.615787915509021e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.64999999999993 y[1] (closed_form) = 3.729120888806594 y[1] (numeric) = 3.72912088880673 absolute error = 1.363353874239692e-13 relative error = 3.655965882822312e-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) = 3.749085416936317 y[1] (numeric) = 3.749085416936455 absolute error = 1.381117442633695e-13 relative error = 3.683878303744593e-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) = 3.769041036598583 y[1] (numeric) = 3.769041036598724 absolute error = 1.407762795224698e-13 relative error = 3.735068898308285e-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) = 3.788986752239724 y[1] (numeric) = 3.788986752239867 absolute error = 1.429967255717202e-13 relative error = 3.774009647491978e-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) = 3.808921569296463 y[1] (numeric) = 3.808921569296609 absolute error = 1.456612608308205e-13 relative error = 3.824212659168125e-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) = 3.828844494295374 y[1] (numeric) = 3.828844494295522 absolute error = 1.478817068800709e-13 relative error = 3.862306424311591e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999923 y[1] (closed_form) = 3.848754534952224 y[1] (numeric) = 3.848754534952375 absolute error = 1.505462421391712e-13 relative error = 3.911557382316667e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999922 y[1] (closed_form) = 3.868650700271208 y[1] (numeric) = 3.868650700271361 absolute error = 1.532107773982716e-13 relative error = 3.96031560532283e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.729999999999921 y[1] (closed_form) = 3.88853200064404 y[1] (numeric) = 3.888532000644195 absolute error = 1.554312234475219e-13 relative error = 3.997169713963484e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.73999999999992 y[1] (closed_form) = 3.908397447948917 y[1] (numeric) = 3.908397447949075 absolute error = 1.576516694967722e-13 relative error = 4.033665245061145e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999919 y[1] (closed_form) = 3.92824605564933 y[1] (numeric) = 3.92824605564949 absolute error = 1.603162047558726e-13 relative error = 4.081114127902375e-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) = 3.948076838892717 y[1] (numeric) = 3.948076838892879 absolute error = 1.625366508051229e-13 relative error = 4.11685631859962e-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) = 3.967888814608943 y[1] (numeric) = 3.967888814609108 absolute error = 1.652011860642233e-13 relative error = 4.163453004428622e-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) = 3.987681001608616 y[1] (numeric) = 3.987681001608783 absolute error = 1.669775429036235e-13 relative error = 4.187334514377289e-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) = 4.007452420681195 y[1] (numeric) = 4.007452420681364 absolute error = 1.696420781627239e-13 relative error = 4.233165122242121e-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) = 4.027202094692916 y[1] (numeric) = 4.027202094693087 absolute error = 1.714184350021242e-13 relative error = 4.256514348460957e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999912 y[1] (closed_form) = 4.046929048684501 y[1] (numeric) = 4.046929048684675 absolute error = 1.740829702612245e-13 relative error = 4.301606679213022e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.819999999999911 y[1] (closed_form) = 4.066632309968658 y[1] (numeric) = 4.066632309968834 absolute error = 1.758593271006248e-13 relative error = 4.324446217316858e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.82999999999991 y[1] (closed_form) = 4.086310908227345 y[1] (numeric) = 4.086310908227523 absolute error = 1.77635683940025e-13 relative error = 4.347091739455625e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999909 y[1] (closed_form) = 4.105963875608801 y[1] (numeric) = 4.105963875608981 absolute error = 1.803002191991254e-13 relative error = 4.391178896389874e-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) = 4.125590246824332 y[1] (numeric) = 4.125590246824514 absolute error = 1.820765760385257e-13 relative error = 4.413346094626797e-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) = 4.145189059244838 y[1] (numeric) = 4.145189059245023 absolute error = 1.856292897173262e-13 relative error = 4.47818632791489e-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) = 4.164759352997075 y[1] (numeric) = 4.164759352997264 absolute error = 1.891820033961267e-13 relative error = 4.542447410796643e-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) = 4.184300171059646 y[1] (numeric) = 4.184300171059838 absolute error = 1.918465386552271e-13 relative error = 4.584913386045228e-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) = 4.203810559358693 y[1] (numeric) = 4.203810559358886 absolute error = 1.927347170749272e-13 relative error = 4.584762190243168e-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) = 4.223289566863313 y[1] (numeric) = 4.223289566863507 absolute error = 1.936228954946273e-13 relative error = 4.584646456966324e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.909999999999901 y[1] (closed_form) = 4.242736245680653 y[1] (numeric) = 4.242736245680849 absolute error = 1.962874307537277e-13 relative error = 4.626434908687984e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9199999999999 y[1] (closed_form) = 4.262149651150704 y[1] (numeric) = 4.262149651150901 absolute error = 1.971756091734278e-13 relative error = 4.626200985697298e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999899 y[1] (closed_form) = 4.281528841940764 y[1] (numeric) = 4.281528841940964 absolute error = 1.998401444325282e-13 relative error = 4.667494995594684e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999898 y[1] (closed_form) = 4.300872880139569 y[1] (numeric) = 4.300872880139772 absolute error = 2.025046796916286e-13 relative error = 4.708455360927966e-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) = 4.320180831351087 y[1] (numeric) = 4.320180831351291 absolute error = 2.042810365310288e-13 relative error = 4.728529765434431e-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) = 4.339451764787953 y[1] (numeric) = 4.339451764788159 absolute error = 2.051692149507289e-13 relative error = 4.727998513903391e-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) = 4.358684753364549 y[1] (numeric) = 4.358684753364757 absolute error = 2.078337502098293e-13 relative error = 4.768267538720221e-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) = 4.377878873789711 y[1] (numeric) = 4.377878873789921 absolute error = 2.104982854689297e-13 relative error = 4.808225433763814e-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) = 4.397033206659059 y[1] (numeric) = 4.397033206659271 absolute error = 2.122746423083299e-13 relative error = 4.827678853706448e-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) = 4.416146836546934 y[1] (numeric) = 4.41614683654715 absolute error = 2.158273559871304e-13 relative error = 4.887232331157942e-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) = 4.435218852097943 y[1] (numeric) = 4.43521885209816 absolute error = 2.167155344068306e-13 relative error = 4.886242181810712e-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) = 4.45424834611809 y[1] (numeric) = 4.454248346118309 absolute error = 2.193800696659309e-13 relative error = 4.925187205987792e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999888 y[1] (closed_form) = 4.473234415665496 y[1] (numeric) = 4.473234415665718 absolute error = 2.220446049250313e-13 relative error = 4.963849069644544e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999887 y[1] (closed_form) = 4.492176162140698 y[1] (numeric) = 4.492176162140923 absolute error = 2.247091401841317e-13 relative error = 5.002233484918565e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999886 y[1] (closed_form) = 4.511072691376498 y[1] (numeric) = 4.511072691376724 absolute error = 2.264854970235319e-13 relative error = 5.020657225419764e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999885 y[1] (closed_form) = 4.529923113727385 y[1] (numeric) = 4.529923113727615 absolute error = 2.300382107023324e-13 relative error = 5.078192387089957e-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) = 4.548726544158502 y[1] (numeric) = 4.548726544158734 absolute error = 2.327027459614328e-13 relative error = 5.115777871067473e-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) = 4.567482102334139 y[1] (numeric) = 4.567482102334373 absolute error = 2.335909243811329e-13 relative error = 5.114216523404875e-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) = 4.586188912705778 y[1] (numeric) = 4.586188912706013 absolute error = 2.353672812205332e-13 relative error = 5.132088662297826e-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) = 4.604846104599634 y[1] (numeric) = 4.604846104599873 absolute error = 2.389199948993337e-13 relative error = 5.188446898598503e-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) = 4.623452812303735 y[1] (numeric) = 4.623452812303976 absolute error = 2.406963517387339e-13 relative error = 5.205986986569931e-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) = 4.642008175154482 y[1] (numeric) = 4.642008175154724 absolute error = 2.424727085781342e-13 relative error = 5.22344423855016e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999877 y[1] (closed_form) = 4.660511337622717 y[1] (numeric) = 4.660511337622962 absolute error = 2.451372438372346e-13 relative error = 5.259878714559179e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999876 y[1] (closed_form) = 4.678961449399283 y[1] (numeric) = 4.67896144939953 absolute error = 2.469136006766348e-13 relative error = 5.277102693554683e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999875 y[1] (closed_form) = 4.697357665480041 y[1] (numeric) = 4.697357665480291 absolute error = 2.495781359357352e-13 relative error = 5.313160157461202e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999874 y[1] (closed_form) = 4.715699146250381 y[1] (numeric) = 4.715699146250635 absolute error = 2.531308496145357e-13 relative error = 5.367832886790688e-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) = 4.733985057569177 y[1] (numeric) = 4.733985057569432 absolute error = 2.557953848736361e-13 relative error = 5.403383867142639e-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) = 4.752214570852203 y[1] (numeric) = 4.75221457085246 absolute error = 2.566835632933362e-13 relative error = 5.401346245342322e-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) = 4.770386863154986 y[1] (numeric) = 4.770386863155244 absolute error = 2.584599201327364e-13 relative error = 5.418007544188965e-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) = 4.788501117255109 y[1] (numeric) = 4.788501117255369 absolute error = 2.602362769721367e-13 relative error = 5.434608254227803e-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) = 4.806556521733922 y[1] (numeric) = 4.806556521734184 absolute error = 2.620126338115369e-13 relative error = 5.451150582059903e-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) = 4.824552271057691 y[1] (numeric) = 4.824552271057954 absolute error = 2.629008122312371e-13 relative error = 5.449227150224265e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999866 y[1] (closed_form) = 4.842487565658145 y[1] (numeric) = 4.84248756565841 absolute error = 2.655653474903374e-13 relative error = 5.484068753705604e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999865 y[1] (closed_form) = 4.860361612012438 y[1] (numeric) = 4.860361612012706 absolute error = 2.673417043297377e-13 relative error = 5.500448848682363e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999864 y[1] (closed_form) = 4.878173622722496 y[1] (numeric) = 4.878173622722765 absolute error = 2.691180611691379e-13 relative error = 5.516779064926842e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999863 y[1] (closed_form) = 4.895922816593758 y[1] (numeric) = 4.89592281659403 absolute error = 2.717825964282383e-13 relative error = 5.551202635529407e-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) = 4.913608418713296 y[1] (numeric) = 4.913608418713569 absolute error = 2.726707748479384e-13 relative error = 5.549298023210028e-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) = 4.9312296605273 y[1] (numeric) = 4.931229660527575 absolute error = 2.744471316873387e-13 relative error = 5.565490771686992e-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) = 4.948785779917941 y[1] (numeric) = 4.948785779918218 absolute error = 2.771116669464391e-13 relative error = 5.599589056187315e-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) = 4.966276021279576 y[1] (numeric) = 4.966276021279855 absolute error = 2.788880237858393e-13 relative error = 5.615636798898322e-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) = 4.983699635594313 y[1] (numeric) = 4.983699635594593 absolute error = 2.797762022055394e-13 relative error = 5.613825524462526e-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) = 5.001055880506903 y[1] (numeric) = 5.001055880507186 absolute error = 2.833289158843399e-13 relative error = 5.665381924419168e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999855 y[1] (closed_form) = 5.018344020398988 y[1] (numeric) = 5.018344020399273 absolute error = 2.851052727237402e-13 relative error = 5.681262017207673e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999854 y[1] (closed_form) = 5.03556332646265 y[1] (numeric) = 5.035563326462937 absolute error = 2.868816295631405e-13 relative error = 5.697110947955592e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999853 y[1] (closed_form) = 5.052713076773301 y[1] (numeric) = 5.052713076773588 absolute error = 2.868816295631405e-13 relative error = 5.677774003869326e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999852 y[1] (closed_form) = 5.069792556361868 y[1] (numeric) = 5.069792556362155 absolute error = 2.868816295631405e-13 relative error = 5.658646312917573e-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) = 5.086801057286289 y[1] (numeric) = 5.086801057286578 absolute error = 2.895461648222408e-13 relative error = 5.692107113320216e-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) = 5.103737878702314 y[1] (numeric) = 5.103737878702605 absolute error = 2.90434343241941e-13 relative error = 5.690620289374801e-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) = 5.120602326933582 y[1] (numeric) = 5.120602326933874 absolute error = 2.913225216616411e-13 relative error = 5.689223709666523e-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) = 5.137393715540989 y[1] (numeric) = 5.137393715541283 absolute error = 2.939870569207415e-13 relative error = 5.722494190612824e-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) = 5.154111365391335 y[1] (numeric) = 5.154111365391632 absolute error = 2.966515921798418e-13 relative error = 5.755630236703627e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999845 y[1] (closed_form) = 5.170754604725234 y[1] (numeric) = 5.170754604725532 absolute error = 2.97539770599542e-13 relative error = 5.754281402711293e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999844 y[1] (closed_form) = 5.187322769224286 y[1] (numeric) = 5.187322769224584 absolute error = 2.984279490192421e-13 relative error = 5.753024484803152e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999843 y[1] (closed_form) = 5.203815202077515 y[1] (numeric) = 5.203815202077815 absolute error = 3.002043058586423e-13 relative error = 5.768927108303e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999842 y[1] (closed_form) = 5.220231254047048 y[1] (numeric) = 5.220231254047349 absolute error = 3.010924842783425e-13 relative error = 5.767799731954726e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.459999999999841 y[1] (closed_form) = 5.236570283533033 y[1] (numeric) = 5.236570283533337 absolute error = 3.037570195374428e-13 relative error = 5.800686386137888e-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) = 5.252831656637804 y[1] (numeric) = 5.252831656638111 absolute error = 3.064215547965432e-13 relative error = 5.833454693133558e-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) = 5.269014747229271 y[1] (numeric) = 5.269014747229578 absolute error = 3.073097332162433e-13 relative error = 5.832394630852821e-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) = 5.285118937003523 y[1] (numeric) = 5.285118937003833 absolute error = 3.099742684753437e-13 relative error = 5.865038652301139e-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) = 5.301143615546671 y[1] (numeric) = 5.301143615546984 absolute error = 3.126388037344441e-13 relative error = 5.897572795756142e-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) = 5.317088180395883 y[1] (numeric) = 5.317088180396198 absolute error = 3.153033389935445e-13 relative error = 5.930000186118196e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999834 y[1] (closed_form) = 5.332952037099627 y[1] (numeric) = 5.332952037099943 absolute error = 3.161915174132446e-13 relative error = 5.929014834815731e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999833 y[1] (closed_form) = 5.348734599277119 y[1] (numeric) = 5.348734599277437 absolute error = 3.179678742526448e-13 relative error = 5.944730820923853e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999832 y[1] (closed_form) = 5.364435288676958 y[1] (numeric) = 5.364435288677277 absolute error = 3.18856052672345e-13 relative error = 5.943888508551383e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.549999999999831 y[1] (closed_form) = 5.380053535234959 y[1] (numeric) = 5.380053535235278 absolute error = 3.18856052672345e-13 relative error = 5.926633454185876e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.55999999999983 y[1] (closed_form) = 5.395588777131143 y[1] (numeric) = 5.395588777131462 absolute error = 3.18856052672345e-13 relative error = 5.90956920260113e-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) = 5.411040460845937 y[1] (numeric) = 5.411040460846258 absolute error = 3.206324095117452e-13 relative error = 5.925522306325889e-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) = 5.426408041215511 y[1] (numeric) = 5.426408041215835 absolute error = 3.232969447708456e-13 relative error = 5.957844347776459e-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) = 5.441690981486301 y[1] (numeric) = 5.441690981486625 absolute error = 3.232969447708456e-13 relative error = 5.941111795410013e-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) = 5.456888753368682 y[1] (numeric) = 5.45688875336901 absolute error = 3.277378368693462e-13 relative error = 6.00594682578099e-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) = 5.472000837089798 y[1] (numeric) = 5.472000837090127 absolute error = 3.295141937087465e-13 relative error = 6.021822794237614e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999823 y[1] (closed_form) = 5.487026721445536 y[1] (numeric) = 5.487026721445868 absolute error = 3.312905505481467e-13 relative error = 6.037706163400449e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999822 y[1] (closed_form) = 5.501965903851652 y[1] (numeric) = 5.501965903851984 absolute error = 3.321787289678468e-13 relative error = 6.0374552436849e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.639999999999821 y[1] (closed_form) = 5.516817890394016 y[1] (numeric) = 5.51681789039435 absolute error = 3.339550858072471e-13 relative error = 6.053400573340218e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.64999999999982 y[1] (closed_form) = 5.53158219587802 y[1] (numeric) = 5.531582195878354 absolute error = 3.339550858072471e-13 relative error = 6.037243486250662e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999819 y[1] (closed_form) = 5.546258343877087 y[1] (numeric) = 5.546258343877422 absolute error = 3.348432642269472e-13 relative error = 6.037282136282108e-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) = 5.56084586678031 y[1] (numeric) = 5.56084586678065 absolute error = 3.392841563254478e-13 relative error = 6.101304809620464e-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) = 5.575344305839227 y[1] (numeric) = 5.575344305839566 absolute error = 3.392841563254478e-13 relative error = 6.085438633271586e-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) = 5.589753211213676 y[1] (numeric) = 5.589753211214018 absolute error = 3.419486915845482e-13 relative error = 6.117420191262837e-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) = 5.604072142016795 y[1] (numeric) = 5.604072142017139 absolute error = 3.437250484239485e-13 relative error = 6.133487216319963e-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) = 5.618300666359104 y[1] (numeric) = 5.618300666359449 absolute error = 3.446132268436486e-13 relative error = 6.133762632304484e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999812 y[1] (closed_form) = 5.632438361391692 y[1] (numeric) = 5.632438361392039 absolute error = 3.463895836830488e-13 relative error = 6.14990456100546e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.729999999999811 y[1] (closed_form) = 5.646484813348504 y[1] (numeric) = 5.646484813348852 absolute error = 3.481659405224491e-13 relative error = 6.166065296047048e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.73999999999981 y[1] (closed_form) = 5.660439617587716 y[1] (numeric) = 5.660439617588067 absolute error = 3.508304757815495e-13 relative error = 6.197936900368549e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999809 y[1] (closed_form) = 5.674302378632198 y[1] (numeric) = 5.674302378632551 absolute error = 3.526068326209497e-13 relative error = 6.214100149980838e-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) = 5.688072710209068 y[1] (numeric) = 5.688072710209422 absolute error = 3.534950110406498e-13 relative error = 6.214671103029147e-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) = 5.701750235288308 y[1] (numeric) = 5.701750235288665 absolute error = 3.561595462997502e-13 relative error = 6.246495051562725e-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) = 5.715334586120475 y[1] (numeric) = 5.715334586120834 absolute error = 3.588240815588506e-13 relative error = 6.278269034856586e-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) = 5.728825404273473 y[1] (numeric) = 5.728825404273834 absolute error = 3.606004383982508e-13 relative error = 6.294491679380863e-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) = 5.742222340668395 y[1] (numeric) = 5.742222340668757 absolute error = 3.623767952376511e-13 relative error = 6.31074127295932e-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) = 5.755525055614434 y[1] (numeric) = 5.755525055614798 absolute error = 3.641531520770513e-13 relative error = 6.327018795997163e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.819999999999801 y[1] (closed_form) = 5.768733218842845 y[1] (numeric) = 5.768733218843211 absolute error = 3.659295089164516e-13 relative error = 6.343325216031635e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8299999999998 y[1] (closed_form) = 5.781846509539981 y[1] (numeric) = 5.781846509540348 absolute error = 3.677058657558518e-13 relative error = 6.359661487885252e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999799 y[1] (closed_form) = 5.794864616379366 y[1] (numeric) = 5.794864616379733 absolute error = 3.677058657558518e-13 relative error = 6.345374570382882e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999798 y[1] (closed_form) = 5.80778723755283 y[1] (numeric) = 5.807787237553199 absolute error = 3.68594044175552e-13 relative error = 6.346548678509491e-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) = 5.820614080800692 y[1] (numeric) = 5.820614080801063 absolute error = 3.703704010149522e-13 relative error = 6.363081212283422e-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) = 5.833344863440983 y[1] (numeric) = 5.833344863441355 absolute error = 3.721467578543525e-13 relative error = 6.379646096130684e-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) = 5.845979312397716 y[1] (numeric) = 5.84597931239809 absolute error = 3.739231146937527e-13 relative error = 6.396244234062965e-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) = 5.858517164228188 y[1] (numeric) = 5.858517164228564 absolute error = 3.75699471533153e-13 relative error = 6.412876518091559e-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) = 5.870958165149332 y[1] (numeric) = 5.87095816514971 absolute error = 3.774758283725532e-13 relative error = 6.429543828353133e-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) = 5.883302071063092 y[1] (numeric) = 5.88330207106347 absolute error = 3.783640067922533e-13 relative error = 6.431150435964004e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.91999999999979 y[1] (closed_form) = 5.895548647580826 y[1] (numeric) = 5.895548647581206 absolute error = 3.801403636316536e-13 relative error = 6.447921751737898e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999789 y[1] (closed_form) = 5.907697670046758 y[1] (numeric) = 5.907697670047138 absolute error = 3.801403636316536e-13 relative error = 6.434661772877163e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999788 y[1] (closed_form) = 5.91974892356043 y[1] (numeric) = 5.919748923560812 absolute error = 3.819167204710538e-13 relative error = 6.451569575037825e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999787 y[1] (closed_form) = 5.9317022029982 y[1] (numeric) = 5.931702202998584 absolute error = 3.836930773104541e-13 relative error = 6.468515515099781e-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) = 5.943557313033754 y[1] (numeric) = 5.943557313034139 absolute error = 3.854694341498544e-13 relative error = 6.485500414113114e-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) = 5.955314068157632 y[1] (numeric) = 5.955314068158018 absolute error = 3.863576125695545e-13 relative error = 6.487611033570227e-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) = 5.966972292695786 y[1] (numeric) = 5.966972292696173 absolute error = 3.872457909892546e-13 relative error = 6.489820498467623e-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) = 5.978531820827145 y[1] (numeric) = 5.978531820827534 absolute error = 3.890221478286549e-13 relative error = 6.506984649198248e-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) = 5.989992496600196 y[1] (numeric) = 5.989992496600585 absolute error = 3.890221478286549e-13 relative error = 6.494534810343358e-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) = 6.001354173948577 y[1] (numeric) = 6.001354173948968 absolute error = 3.907985046680551e-13 relative error = 6.511838717409509e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999779 y[1] (closed_form) = 6.01261671670569 y[1] (numeric) = 6.012616716706082 absolute error = 3.925748615074554e-13 relative error = 6.529184879134404e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999778 y[1] (closed_form) = 6.023779998618309 y[1] (numeric) = 6.023779998618703 absolute error = 3.934630399271555e-13 relative error = 6.531829515975105e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999777 y[1] (closed_form) = 6.034843903359214 y[1] (numeric) = 6.034843903359608 absolute error = 3.943512183468556e-13 relative error = 6.534571973391811e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999776 y[1] (closed_form) = 6.045808324538816 y[1] (numeric) = 6.045808324539212 absolute error = 3.961275751862559e-13 relative error = 6.552102778026346e-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) = 6.056673165715802 y[1] (numeric) = 6.0566731657162 absolute error = 3.979039320256561e-13 relative error = 6.569678124255038e-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) = 6.067438340406776 y[1] (numeric) = 6.067438340407174 absolute error = 3.979039320256561e-13 relative error = 6.558021848788654e-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) = 6.078103772094904 y[1] (numeric) = 6.078103772095304 absolute error = 3.996802888650564e-13 relative error = 6.575739800627012e-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) = 6.088669394237574 y[1] (numeric) = 6.088669394237973 absolute error = 3.996802888650564e-13 relative error = 6.564328968876533e-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) = 6.099135150273041 y[1] (numeric) = 6.099135150273443 absolute error = 4.023448241241567e-13 relative error = 6.596752067481976e-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) = 6.10950099362609 y[1] (numeric) = 6.109500993626493 absolute error = 4.032330025438569e-13 relative error = 6.600097175932063e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999768 y[1] (closed_form) = 6.119766887712691 y[1] (numeric) = 6.119766887713096 absolute error = 4.050093593832571e-13 relative error = 6.618052073134315e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999767 y[1] (closed_form) = 6.129932805943659 y[1] (numeric) = 6.129932805944063 absolute error = 4.04121180963557e-13 relative error = 6.592587451720777e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999766 y[1] (closed_form) = 6.139998731727305 y[1] (numeric) = 6.139998731727712 absolute error = 4.076738946423575e-13 relative error = 6.639641349366707e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999765 y[1] (closed_form) = 6.149964658471109 y[1] (numeric) = 6.149964658471518 absolute error = 4.094502514817577e-13 relative error = 6.65776592582156e-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) = 6.159830589582366 y[1] (numeric) = 6.159830589582778 absolute error = 4.11226608321158e-13 relative error = 6.675940228236682e-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) = 6.169596538467855 y[1] (numeric) = 6.169596538468267 absolute error = 4.11226608321158e-13 relative error = 6.665372780166937e-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) = 6.179262528532491 y[1] (numeric) = 6.179262528532904 absolute error = 4.130029651605582e-13 relative error = 6.683693454575429e-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) = 6.188828593176991 y[1] (numeric) = 6.188828593177404 absolute error = 4.130029651605582e-13 relative error = 6.673362477931322e-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) = 6.198294775794526 y[1] (numeric) = 6.19829477579494 absolute error = 4.138911435802584e-13 relative error = 6.677500160150158e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999758 y[1] (closed_form) = 6.207661129766392 y[1] (numeric) = 6.207661129766806 absolute error = 4.138911435802584e-13 relative error = 6.667424895273464e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999757 y[1] (closed_form) = 6.216927718456663 y[1] (numeric) = 6.216927718457078 absolute error = 4.147793219999585e-13 relative error = 6.67177327425847e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999756 y[1] (closed_form) = 6.226094615205858 y[1] (numeric) = 6.226094615206274 absolute error = 4.165556788393587e-13 relative error = 6.690481025168068e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999755 y[1] (closed_form) = 6.235161903323609 y[1] (numeric) = 6.235161903324027 absolute error = 4.174438572590589e-13 relative error = 6.694996276464663e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999754 y[1] (closed_form) = 6.244129676080327 y[1] (numeric) = 6.244129676080745 absolute error = 4.18332035678759e-13 relative error = 6.699605187273459e-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) = 6.252998036697875 y[1] (numeric) = 6.252998036698294 absolute error = 4.192202140984591e-13 relative error = 6.704307464005598e-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) = 6.261767098339249 y[1] (numeric) = 6.261767098339667 absolute error = 4.18332035678759e-13 relative error = 6.680734513260791e-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) = 6.270436984097257 y[1] (numeric) = 6.270436984097678 absolute error = 4.209965709378594e-13 relative error = 6.713990938838363e-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) = 6.27900782698222 y[1] (numeric) = 6.27900782698264 absolute error = 4.201083925181592e-13 relative error = 6.690681140941806e-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) = 6.287479769908653 y[1] (numeric) = 6.287479769909075 absolute error = 4.218847493575595e-13 relative error = 6.709918199286529e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999747 y[1] (closed_form) = 6.295852965680993 y[1] (numeric) = 6.295852965681414 absolute error = 4.209965709378594e-13 relative error = 6.686886959284668e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999746 y[1] (closed_form) = 6.304127576978305 y[1] (numeric) = 6.304127576978729 absolute error = 4.236611061969597e-13 relative error = 6.720376468016039e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999745 y[1] (closed_form) = 6.312303776338024 y[1] (numeric) = 6.31230377633845 absolute error = 4.2543746303636e-13 relative error = 6.739812881489209e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999744 y[1] (closed_form) = 6.320381746138693 y[1] (numeric) = 6.32038174613912 absolute error = 4.263256414560601e-13 relative error = 6.745251451251579e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999743 y[1] (closed_form) = 6.32836167858173 y[1] (numeric) = 6.328361678582158 absolute error = 4.272138198757602e-13 relative error = 6.750780716621501e-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) = 6.336243775672207 y[1] (numeric) = 6.336243775672636 absolute error = 4.289901767151605e-13 relative error = 6.770417804350485e-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) = 6.344028249198651 y[1] (numeric) = 6.344028249199081 absolute error = 4.298783551348606e-13 relative error = 6.776110355264589e-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) = 6.351715320711863 y[1] (numeric) = 6.351715320712292 absolute error = 4.289901767151605e-13 relative error = 6.753926381371289e-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) = 6.359305221502764 y[1] (numeric) = 6.359305221503194 absolute error = 4.298783551348606e-13 relative error = 6.759832091111304e-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) = 6.366798192579266 y[1] (numeric) = 6.366798192579695 absolute error = 4.298783551348606e-13 relative error = 6.751876565459534e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999736 y[1] (closed_form) = 6.374194484642171 y[1] (numeric) = 6.374194484642603 absolute error = 4.316547119742609e-13 relative error = 6.771909972535027e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999735 y[1] (closed_form) = 6.381494358060106 y[1] (numeric) = 6.381494358060539 absolute error = 4.32542890393961e-13 relative error = 6.778081529565883e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999734 y[1] (closed_form) = 6.388698082843478 y[1] (numeric) = 6.38869808284391 absolute error = 4.32542890393961e-13 relative error = 6.770438746440888e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999733 y[1] (closed_form) = 6.395805938617478 y[1] (numeric) = 6.395805938617911 absolute error = 4.32542890393961e-13 relative error = 6.76291454970974e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999732 y[1] (closed_form) = 6.402818214594118 y[1] (numeric) = 6.402818214594551 absolute error = 4.32542890393961e-13 relative error = 6.755507901318425e-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) = 6.409735209543311 y[1] (numeric) = 6.409735209543745 absolute error = 4.334310688136611e-13 relative error = 6.762074479587476e-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) = 6.416557231762994 y[1] (numeric) = 6.416557231763427 absolute error = 4.334310688136611e-13 relative error = 6.754885106737728e-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) = 6.423284599048294 y[1] (numeric) = 6.42328459904873 absolute error = 4.352074256530614e-13 relative error = 6.775465401572645e-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) = 6.429917638659758 y[1] (numeric) = 6.429917638660195 absolute error = 4.369837824924616e-13 relative error = 6.796102330535386e-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) = 6.436456687290619 y[1] (numeric) = 6.436456687291056 absolute error = 4.369837824924616e-13 relative error = 6.789197903798944e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999725 y[1] (closed_form) = 6.442902091033128 y[1] (numeric) = 6.442902091033567 absolute error = 4.387601393318619e-13 relative error = 6.809976826165088e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999724 y[1] (closed_form) = 6.44925420534395 y[1] (numeric) = 6.449254205344388 absolute error = 4.387601393318619e-13 relative error = 6.803269422506227e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999723 y[1] (closed_form) = 6.455513395008612 y[1] (numeric) = 6.455513395009052 absolute error = 4.39648317751562e-13 relative error = 6.810431500173124e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999722 y[1] (closed_form) = 6.461680034105033 y[1] (numeric) = 6.461680034105474 absolute error = 4.414246745909622e-13 relative error = 6.831422668115774e-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) = 6.467754505966107 y[1] (numeric) = 6.46775450596655 absolute error = 4.423128530106624e-13 relative error = 6.838739049273683e-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) = 6.473737203141378 y[1] (numeric) = 6.47373720314182 absolute error = 4.414246745909622e-13 relative error = 6.818699319100583e-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) = 6.47962852735778 y[1] (numeric) = 6.479628527358222 absolute error = 4.423128530106624e-13 relative error = 6.826206952191221e-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) = 6.485428889479467 y[1] (numeric) = 6.48542888947991 absolute error = 4.432010314303625e-13 relative error = 6.833796792519218e-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) = 6.491138709466728 y[1] (numeric) = 6.491138709467172 absolute error = 4.432010314303625e-13 relative error = 6.827785559165367e-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) = 6.496758416333988 y[1] (numeric) = 6.496758416334433 absolute error = 4.458655666894629e-13 relative error = 6.862892816954357e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999714 y[1] (closed_form) = 6.502288448106912 y[1] (numeric) = 6.502288448107358 absolute error = 4.46753745109163e-13 relative error = 6.870715574594845e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999713 y[1] (closed_form) = 6.507729251778596 y[1] (numeric) = 6.507729251779042 absolute error = 4.46753745109163e-13 relative error = 6.864971295280346e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999712 y[1] (closed_form) = 6.513081283264873 y[1] (numeric) = 6.51308128326532 absolute error = 4.476419235288631e-13 relative error = 6.872966942375845e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.639999999999711 y[1] (closed_form) = 6.518345007358723 y[1] (numeric) = 6.518345007359171 absolute error = 4.476419235288631e-13 relative error = 6.867416852337655e-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) = 6.523520897683788 y[1] (numeric) = 6.523520897684238 absolute error = 4.503064587879635e-13 relative error = 6.90281315643286e-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) = 6.528609436647018 y[1] (numeric) = 6.528609436647467 absolute error = 4.485301019485632e-13 relative error = 6.870224146520864e-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) = 6.533611115390421 y[1] (numeric) = 6.533611115390872 absolute error = 4.511946372076636e-13 relative error = 6.905746749218669e-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) = 6.538526433741959 y[1] (numeric) = 6.538526433742411 absolute error = 4.520828156273637e-13 relative error = 6.914139144477535e-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) = 6.543355900165558 y[1] (numeric) = 6.543355900166011 absolute error = 4.529709940470639e-13 relative error = 6.922609758023446e-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) = 6.548100031710269 y[1] (numeric) = 6.548100031710722 absolute error = 4.529709940470639e-13 relative error = 6.917594292290529e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999703 y[1] (closed_form) = 6.552759353958557 y[1] (numeric) = 6.55275935395901 absolute error = 4.529709940470639e-13 relative error = 6.912675555122007e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999702 y[1] (closed_form) = 6.557334400973745 y[1] (numeric) = 6.557334400974199 absolute error = 4.53859172466764e-13 relative error = 6.921397395859013e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.729999999999701 y[1] (closed_form) = 6.561825715246613 y[1] (numeric) = 6.561825715247067 absolute error = 4.53859172466764e-13 relative error = 6.91665996876765e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7399999999997 y[1] (closed_form) = 6.566233847641142 y[1] (numeric) = 6.566233847641596 absolute error = 4.547473508864641e-13 relative error = 6.925543034837662e-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) = 6.570559357339432 y[1] (numeric) = 6.570559357339887 absolute error = 4.547473508864641e-13 relative error = 6.920983833415997e-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) = 6.574802811785785 y[1] (numeric) = 6.574802811786241 absolute error = 4.556355293061642e-13 relative error = 6.930025771866591e-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) = 6.57896478662996 y[1] (numeric) = 6.578964786630415 absolute error = 4.547473508864641e-13 relative error = 6.912141433111485e-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) = 6.583045865669607 y[1] (numeric) = 6.583045865670064 absolute error = 4.565237077258644e-13 relative error = 6.934840149096062e-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) = 6.587046640791891 y[1] (numeric) = 6.587046640792348 absolute error = 4.574118861455645e-13 relative error = 6.944111846922868e-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) = 6.590967711914297 y[1] (numeric) = 6.590967711914756 absolute error = 4.583000645652646e-13 relative error = 6.95345637540917e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999692 y[1] (closed_form) = 6.59480968692465 y[1] (numeric) = 6.594809686925108 absolute error = 4.583000645652646e-13 relative error = 6.949405461599956e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.819999999999691 y[1] (closed_form) = 6.598573181620317 y[1] (numeric) = 6.598573181620775 absolute error = 4.583000645652646e-13 relative error = 6.945441869794137e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.82999999999969 y[1] (closed_form) = 6.602258819646631 y[1] (numeric) = 6.602258819647089 absolute error = 4.583000645652646e-13 relative error = 6.9415646536225e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999689 y[1] (closed_form) = 6.605867232434527 y[1] (numeric) = 6.605867232434983 absolute error = 4.565237077258644e-13 relative error = 6.91088227574954e-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) = 6.609399059137399 y[1] (numeric) = 6.609399059137858 absolute error = 4.591882429849647e-13 relative error = 6.947503681898941e-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) = 6.612854946567188 y[1] (numeric) = 6.612854946567648 absolute error = 4.600764214046649e-13 relative error = 6.957303995356742e-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) = 6.616235549129698 y[1] (numeric) = 6.616235549130159 absolute error = 4.60964599824365e-13 relative error = 6.967173348068003e-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) = 6.619541528759155 y[1] (numeric) = 6.619541528759616 absolute error = 4.60964599824365e-13 relative error = 6.963693751624119e-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) = 6.622773554852019 y[1] (numeric) = 6.622773554852479 absolute error = 4.600764214046649e-13 relative error = 6.946884376978293e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999682 y[1] (closed_form) = 6.625932304200041 y[1] (numeric) = 6.625932304200501 absolute error = 4.600764214046649e-13 relative error = 6.943572621667625e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.909999999999681 y[1] (closed_form) = 6.629018460922584 y[1] (numeric) = 6.629018460923042 absolute error = 4.583000645652646e-13 relative error = 6.913543343813247e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.91999999999968 y[1] (closed_form) = 6.632032716398214 y[1] (numeric) = 6.632032716398673 absolute error = 4.591882429849647e-13 relative error = 6.923793392176524e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999679 y[1] (closed_form) = 6.634975769195565 y[1] (numeric) = 6.634975769196022 absolute error = 4.574118861455645e-13 relative error = 6.89394960972136e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999678 y[1] (closed_form) = 6.637848325003472 y[1] (numeric) = 6.637848325003931 absolute error = 4.591882429849647e-13 relative error = 6.917727258926552e-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) = 6.640651096560418 y[1] (numeric) = 6.640651096560878 absolute error = 4.600764214046649e-13 relative error = 6.928182413362529e-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) = 6.643384803583249 y[1] (numeric) = 6.643384803583708 absolute error = 4.591882429849647e-13 relative error = 6.911962148230401e-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) = 6.646050172695206 y[1] (numeric) = 6.646050172695665 absolute error = 4.583000645652646e-13 relative error = 6.895826132161261e-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) = 6.648647937353267 y[1] (numeric) = 6.648647937353727 absolute error = 4.600764214046649e-13 relative error = 6.919849354932377e-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) = 6.651178837774799 y[1] (numeric) = 6.651178837775258 absolute error = 4.591882429849647e-13 relative error = 6.903862520987176e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.999999999999671 y[1] (closed_form) = 6.653643620863532 y[1] (numeric) = 6.653643620863993 absolute error = 4.60964599824365e-13 relative error = 6.928002551548432e-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) = 6.656043040134882 y[1] (numeric) = 6.656043040135343 absolute error = 4.60964599824365e-13 relative error = 6.925505094315372e-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) = 6.658377855640585 y[1] (numeric) = 6.658377855641047 absolute error = 4.618527782440651e-13 relative error = 6.936415869712331e-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) = 6.660648833892704 y[1] (numeric) = 6.660648833893164 absolute error = 4.591882429849647e-13 relative error = 6.894046727826062e-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) = 6.662856747786972 y[1] (numeric) = 6.662856747787432 absolute error = 4.591882429849647e-13 relative error = 6.891762203014215e-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) = 6.665002376525508 y[1] (numeric) = 6.665002376525967 absolute error = 4.591882429849647e-13 relative error = 6.889543574691738e-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) = 6.667086505538891 y[1] (numeric) = 6.667086505539349 absolute error = 4.583000645652646e-13 relative error = 6.874068068331159e-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) = 6.669109926407624 y[1] (numeric) = 6.669109926408082 absolute error = 4.583000645652646e-13 relative error = 6.871982462765194e-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) = 6.671073436782973 y[1] (numeric) = 6.671073436783431 absolute error = 4.574118861455645e-13 relative error = 6.856645942817632e-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) = 6.672977840307203 y[1] (numeric) = 6.672977840307661 absolute error = 4.583000645652646e-13 relative error = 6.867999198153578e-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) = 6.674823946533215 y[1] (numeric) = 6.674823946533673 absolute error = 4.574118861455645e-13 relative error = 6.852793269298677e-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) = 6.676612570843592 y[1] (numeric) = 6.676612570844051 absolute error = 4.583000645652646e-13 relative error = 6.864260277234542e-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) = 6.678344534369061 y[1] (numeric) = 6.67834453436952 absolute error = 4.591882429849647e-13 relative error = 6.875779478309691e-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) = 6.680020663906378 y[1] (numeric) = 6.680020663906837 absolute error = 4.591882429849647e-13 relative error = 6.874054229593329e-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) = 6.681641791835653 y[1] (numeric) = 6.681641791836111 absolute error = 4.583000645652646e-13 relative error = 6.859093600696536e-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) = 6.683208756037112 y[1] (numeric) = 6.68320875603757 absolute error = 4.583000645652646e-13 relative error = 6.857485398032353e-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) = 6.684722399807305 y[1] (numeric) = 6.684722399807763 absolute error = 4.574118861455645e-13 relative error = 6.842645943812863e-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) = 6.686183571774786 y[1] (numeric) = 6.686183571775241 absolute error = 4.556355293061642e-13 relative error = 6.814583004116053e-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) = 6.68759312581524 y[1] (numeric) = 6.687593125815694 absolute error = 4.53859172466764e-13 relative error = 6.786584708851244e-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) = 6.688951920966105 y[1] (numeric) = 6.688951920966558 absolute error = 4.53859172466764e-13 relative error = 6.785206080554572e-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) = 6.690260821340666 y[1] (numeric) = 6.690260821341119 absolute error = 4.529709940470639e-13 relative error = 6.77060291285165e-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) = 6.691520696041642 y[1] (numeric) = 6.691520696042094 absolute error = 4.520828156273637e-13 relative error = 6.756054956159556e-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) = 6.692732419074279 y[1] (numeric) = 6.692732419074732 absolute error = 4.529709940470639e-13 relative error = 6.768102557874526e-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) = 6.693896869258952 y[1] (numeric) = 6.693896869259404 absolute error = 4.520828156273637e-13 relative error = 6.753656718308713e-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) = 6.695014930143278 y[1] (numeric) = 6.695014930143729 absolute error = 4.511946372076636e-13 relative error = 6.739262599344312e-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) = 6.696087489913767 y[1] (numeric) = 6.696087489914217 absolute error = 4.503064587879635e-13 relative error = 6.724918983902981e-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) = 6.697115441307004 y[1] (numeric) = 6.697115441307453 absolute error = 4.494182803682634e-13 relative error = 6.710624660824949e-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) = 6.69809968152037 y[1] (numeric) = 6.698099681520821 absolute error = 4.511946372076636e-13 relative error = 6.736158890744502e-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) = 6.699041112122334 y[1] (numeric) = 6.699041112122783 absolute error = 4.494182803682634e-13 relative error = 6.708695660264166e-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) = 6.699940638962286 y[1] (numeric) = 6.699940638962734 absolute error = 4.485301019485632e-13 relative error = 6.694538446209778e-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) = 6.700799172079956 y[1] (numeric) = 6.700799172080403 absolute error = 4.476419235288631e-13 relative error = 6.680425901943771e-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) = 6.701617625614417 y[1] (numeric) = 6.701617625614864 absolute error = 4.46753745109163e-13 relative error = 6.666356841990127e-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) = 6.702396917712663 y[1] (numeric) = 6.702396917713109 absolute error = 4.458655666894629e-13 relative error = 6.652330086735956e-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) = 6.703137970437802 y[1] (numeric) = 6.703137970438246 absolute error = 4.440892098500626e-13 relative error = 6.62509427388465e-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) = 6.703841709676843 y[1] (numeric) = 6.703841709677286 absolute error = 4.432010314303625e-13 relative error = 6.611150003595876e-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) = 6.704509065048118 y[1] (numeric) = 6.704509065048561 absolute error = 4.432010314303625e-13 relative error = 6.610491941025985e-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) = 6.70514096980831 y[1] (numeric) = 6.705140969808753 absolute error = 4.432010314303625e-13 relative error = 6.609868956163541e-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) = 6.705738360759138 y[1] (numeric) = 6.705738360759581 absolute error = 4.423128530106624e-13 relative error = 6.596035055572752e-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) = 6.706302178153672 y[1] (numeric) = 6.706302178154113 absolute error = 4.405364961712621e-13 relative error = 6.568992635111877e-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) = 6.706833365602308 y[1] (numeric) = 6.706833365602748 absolute error = 4.39648317751562e-13 relative error = 6.555229476945254e-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) = 6.70733286997841 y[1] (numeric) = 6.70733286997885 absolute error = 4.39648317751562e-13 relative error = 6.554741299919668e-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) = 6.707801641323624 y[1] (numeric) = 6.707801641324064 absolute error = 4.39648317751562e-13 relative error = 6.554283225119458e-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) = 6.708240632752874 y[1] (numeric) = 6.708240632753313 absolute error = 4.387601393318619e-13 relative error = 6.540614199043826e-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) = 6.708650800359047 y[1] (numeric) = 6.708650800359487 absolute error = 4.39648317751562e-13 relative error = 6.553453605425878e-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) = 6.709033103117393 y[1] (numeric) = 6.709033103117832 absolute error = 4.39648317751562e-13 relative error = 6.55308016809869e-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) = 6.70938850278962 y[1] (numeric) = 6.709388502790059 absolute error = 4.387601393318619e-13 relative error = 6.539495203615572e-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) = 6.709717963827725 y[1] (numeric) = 6.709717963828164 absolute error = 4.39648317751562e-13 relative error = 6.552411295403446e-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) = 6.710022453277545 y[1] (numeric) = 6.710022453277984 absolute error = 4.387601393318619e-13 relative error = 6.538877364226214e-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) = 6.710302940682054 y[1] (numeric) = 6.710302940682494 absolute error = 4.39648317751562e-13 relative error = 6.551840082899072e-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) = 6.710560397984414 y[1] (numeric) = 6.710560397984855 absolute error = 4.405364961712621e-13 relative error = 6.564824247816647e-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) = 6.710795799430776 y[1] (numeric) = 6.710795799431216 absolute error = 4.405364961712621e-13 relative error = 6.564593966763664e-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) = 6.711010121472857 y[1] (numeric) = 6.711010121473298 absolute error = 4.414246745909622e-13 relative error = 6.577618966458708e-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) = 6.711204342670298 y[1] (numeric) = 6.711204342670739 absolute error = 4.414246745909622e-13 relative error = 6.577428611201031e-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) = 6.71137944359281 y[1] (numeric) = 6.711379443593252 absolute error = 4.423128530106624e-13 relative error = 6.590490922591594e-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) = 6.711536406722109 y[1] (numeric) = 6.711536406722552 absolute error = 4.432010314303625e-13 relative error = 6.603570398373512e-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) = 6.711676216353684 y[1] (numeric) = 6.711676216354127 absolute error = 4.432010314303625e-13 relative error = 6.603432840673362e-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) = 6.711799858498353 y[1] (numeric) = 6.711799858498796 absolute error = 4.423128530106624e-13 relative error = 6.590078106256614e-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) = 6.711908320783673 y[1] (numeric) = 6.711908320784114 absolute error = 4.414246745909622e-13 relative error = 6.576738737984165e-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) = 6.712002592355169 y[1] (numeric) = 6.712002592355611 absolute error = 4.414246745909622e-13 relative error = 6.576646366223632e-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) = 6.712083663777433 y[1] (numeric) = 6.712083663777873 absolute error = 4.405364961712621e-13 relative error = 6.563334401635521e-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) = 6.712152526935053 y[1] (numeric) = 6.712152526935495 absolute error = 4.414246745909622e-13 relative error = 6.576499458550422e-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) = 6.712210174933442 y[1] (numeric) = 6.712210174933882 absolute error = 4.405364961712621e-13 relative error = 6.563210696477193e-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) = 6.712257601999511 y[1] (numeric) = 6.71225760199995 absolute error = 4.39648317751562e-13 relative error = 6.549932136403635e-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) = 6.712295803382261 y[1] (numeric) = 6.712295803382701 absolute error = 4.39648317751562e-13 relative error = 6.549894859073813e-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) = 6.712325775253253 y[1] (numeric) = 6.712325775253693 absolute error = 4.39648317751562e-13 relative error = 6.5498656124892e-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) = 6.712348514606992 y[1] (numeric) = 6.712348514607431 absolute error = 4.387601393318619e-13 relative error = 6.536611416660794e-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) = 6.712365019161226 y[1] (numeric) = 6.712365019161666 absolute error = 4.405364961712621e-13 relative error = 6.563059293016687e-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) = 6.712376287257181 y[1] (numeric) = 6.712376287257622 absolute error = 4.405364961712621e-13 relative error = 6.563048275579834e-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) = 6.712383317759724 y[1] (numeric) = 6.712383317760163 absolute error = 4.387601393318619e-13 relative error = 6.536577524870841e-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) = 6.712387109957477 y[1] (numeric) = 6.712387109957917 absolute error = 4.39648317751562e-13 relative error = 6.549805762831624e-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) = 6.712388663462891 y[1] (numeric) = 6.712388663463331 absolute error = 4.405364961712621e-13 relative error = 6.563036174725785e-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) = 6.712388978112282 y[1] (numeric) = 6.712388978112721 absolute error = 4.39648317751562e-13 relative error = 6.549803939926078e-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) = 6.712389053865852 y[1] (numeric) = 6.712389053866291 absolute error = 4.387601393318619e-13 relative error = 6.536571939005348e-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) = 6.712389890707693 y[1] (numeric) = 6.712389890708132 absolute error = 4.387601393318619e-13 relative error = 6.536571124082946e-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) = 6.712392488545788 y[1] (numeric) = 6.712392488546228 absolute error = 4.39648317751562e-13 relative error = 6.549800514522802e-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) = 6.712397847112023 y[1] (numeric) = 6.712397847112465 absolute error = 4.414246745909622e-13 relative error = 6.57625910509585e-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) = 6.712406965862212 y[1] (numeric) = 6.712406965862653 absolute error = 4.405364961712621e-13 relative error = 6.563018279608661e-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) = 6.712420843876154 y[1] (numeric) = 6.712420843876593 absolute error = 4.39648317751562e-13 relative error = 6.54977284615073e-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) = 6.712440479757725 y[1] (numeric) = 6.712440479758166 absolute error = 4.405364961712621e-13 relative error = 6.562985511748815e-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) = 6.712466871535021 y[1] (numeric) = 6.712466871535462 absolute error = 4.405364961712621e-13 relative error = 6.562959707695649e-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) = 6.712501016560553 y[1] (numeric) = 6.712501016560993 absolute error = 4.39648317751562e-13 relative error = 6.549694617056985e-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) = 6.712543911411514 y[1] (numeric) = 6.712543911411953 absolute error = 4.39648317751562e-13 relative error = 6.549652762854147e-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) = 6.71259655179012 y[1] (numeric) = 6.712596551790559 absolute error = 4.39648317751562e-13 relative error = 6.549601400285502e-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) = 6.712659932424044 y[1] (numeric) = 6.712659932424484 absolute error = 4.39648317751562e-13 relative error = 6.549539559242923e-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) = 6.712735046966944 y[1] (numeric) = 6.712735046967382 absolute error = 4.387601393318619e-13 relative error = 6.536235025842553e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y[1] (closed_form) = 6.712822887899092 y[1] (numeric) = 6.712822887899532 absolute error = 4.39648317751562e-13 relative error = 6.549380567512015e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y[1] (closed_form) = 6.712924446428136 y[1] (numeric) = 6.712924446428576 absolute error = 4.39648317751562e-13 relative error = 6.549281483206524e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y[1] (closed_form) = 6.713040712389976 y[1] (numeric) = 6.713040712390415 absolute error = 4.387601393318619e-13 relative error = 6.535937410927075e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y[1] (closed_form) = 6.713172674149778 y[1] (numeric) = 6.713172674150218 absolute error = 4.39648317751562e-13 relative error = 6.549039315560929e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y[1] (closed_form) = 6.713321318503142 y[1] (numeric) = 6.713321318503582 absolute error = 4.405364961712621e-13 relative error = 6.562124398203061e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y[1] (closed_form) = 6.713487630577424 y[1] (numeric) = 6.713487630577864 absolute error = 4.405364961712621e-13 relative error = 6.561961835824099e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y[1] (closed_form) = 6.713672593733222 y[1] (numeric) = 6.713672593733663 absolute error = 4.414246745909622e-13 relative error = 6.575010449615961e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y[1] (closed_form) = 6.713877189466041 y[1] (numeric) = 6.713877189466483 absolute error = 4.414246745909622e-13 relative error = 6.574810085646935e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y[1] (closed_form) = 6.714102397308145 y[1] (numeric) = 6.714102397308586 absolute error = 4.414246745909622e-13 relative error = 6.57458955001849e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 6.714349194730604 y[1] (numeric) = 6.714349194731045 absolute error = 4.405364961712621e-13 relative error = 6.561119825537127e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y[1] (closed_form) = 6.714618557045549 y[1] (numeric) = 6.71461855704599 absolute error = 4.405364961712621e-13 relative error = 6.560856620947049e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y[1] (closed_form) = 6.714911457308638 y[1] (numeric) = 6.714911457309078 absolute error = 4.39648317751562e-13 relative error = 6.54734348392696e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 6.715228866221757 y[1] (numeric) = 6.715228866222196 absolute error = 4.387601393318619e-13 relative error = 6.533807679122707e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y[1] (closed_form) = 6.715571752035944 y[1] (numeric) = 6.715571752036384 absolute error = 4.39648317751562e-13 relative error = 6.546699729896785e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y[1] (closed_form) = 6.715941080454573 y[1] (numeric) = 6.715941080455011 absolute error = 4.387601393318619e-13 relative error = 6.533114779830142e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = 1.0 + sin ( x ) ; Iterations = 5500 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %