##############ECHO OF PROBLEM################# ##############temp/diff2postode.ode################# diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-1.0); x_end=c(1.0); array_y_init[0 + 1] = exact_soln_y(x_start); array_y_init[1 + 1] = exact_soln_yp(x_start); array_y_init[2 + 1] = exact_soln_ypp(x_start); glob_look_poles=true; 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(neg(cos(c(x)))); } double exact_soln_yp (double x) { return(sin(c(x))); } double exact_soln_ypp (double x) { return(cos(c(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (closed_form) = -0.5403023058681398 y[1] (numeric) = -0.5403023058681398 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] = -0.99 y[1] (closed_form) = -0.5486898605815875 y[1] (numeric) = -0.5486898605815874 absolute error = 1.110223024625157e-16 relative error = 2.023407218512054e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (closed_form) = -0.5570225467662173 y[1] (numeric) = -0.5570225467662171 absolute error = 2.220446049250313e-16 relative error = 3.986276789227054e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (closed_form) = -0.5652995311603544 y[1] (numeric) = -0.5652995311603539 absolute error = 4.440892098500626e-16 relative error = 7.855821301293297e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (closed_form) = -0.5735199860724567 y[1] (numeric) = -0.5735199860724564 absolute error = 3.33066907387547e-16 relative error = 5.807415878711301e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (closed_form) = -0.5816830894638836 y[1] (numeric) = -0.5816830894638831 absolute error = 4.440892098500626e-16 relative error = 7.63455596172417e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9399999999999999 y[1] (closed_form) = -0.5897880250310983 y[1] (numeric) = -0.5897880250310978 absolute error = 4.440892098500626e-16 relative error = 7.529641006642119e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9299999999999999 y[1] (closed_form) = -0.5978339822872983 y[1] (numeric) = -0.597833982287298 absolute error = 3.33066907387547e-16 relative error = 5.57122741857599e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9199999999999999 y[1] (closed_form) = -0.6058201566434629 y[1] (numeric) = -0.6058201566434627 absolute error = 2.220446049250313e-16 relative error = 3.665190114427126e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9099999999999999 y[1] (closed_form) = -0.6137457494888117 y[1] (numeric) = -0.6137457494888114 absolute error = 2.220446049250313e-16 relative error = 3.617859758865492e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8999999999999999 y[1] (closed_form) = -0.6216099682706645 y[1] (numeric) = -0.6216099682706642 absolute error = 3.33066907387547e-16 relative error = 5.358133305264521e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8899999999999999 y[1] (closed_form) = -0.629412026573697 y[1] (numeric) = -0.6294120265736965 absolute error = 4.440892098500626e-16 relative error = 7.055620024732158e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8799999999999999 y[1] (closed_form) = -0.6371511441985803 y[1] (numeric) = -0.63715114419858 absolute error = 3.33066907387547e-16 relative error = 5.227439523890117e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8699999999999999 y[1] (closed_form) = -0.6448265472400013 y[1] (numeric) = -0.644826547240001 absolute error = 3.33066907387547e-16 relative error = 5.165217046555329e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8599999999999999 y[1] (closed_form) = -0.6524374681640519 y[1] (numeric) = -0.6524374681640517 absolute error = 2.220446049250313e-16 relative error = 3.403308604422445e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8499999999999999 y[1] (closed_form) = -0.6599831458849823 y[1] (numeric) = -0.6599831458849821 absolute error = 2.220446049250313e-16 relative error = 3.364398110913697e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8399999999999999 y[1] (closed_form) = -0.6674628258413082 y[1] (numeric) = -0.6674628258413081 absolute error = 1.110223024625157e-16 relative error = 1.663348102159499e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8299999999999998 y[1] (closed_form) = -0.6748757600712673 y[1] (numeric) = -0.6748757600712672 absolute error = 1.110223024625157e-16 relative error = 1.645077642895214e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8199999999999998 y[1] (closed_form) = -0.6822212072876137 y[1] (numeric) = -0.6822212072876136 absolute error = 1.110223024625157e-16 relative error = 1.627365160692086e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.8099999999999998 y[1] (closed_form) = -0.6894984329517472 y[1] (numeric) = -0.6894984329517471 absolute error = 1.110223024625157e-16 relative error = 1.610189337011666e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7999999999999998 y[1] (closed_form) = -0.6967067093471655 y[1] (numeric) = -0.6967067093471655 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] = -0.7899999999999998 y[1] (closed_form) = -0.7038453156522362 y[1] (numeric) = -0.7038453156522362 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] = -0.7799999999999998 y[1] (closed_form) = -0.7109135380122775 y[1] (numeric) = -0.7109135380122775 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] = -0.7699999999999998 y[1] (closed_form) = -0.7179106696109435 y[1] (numeric) = -0.7179106696109435 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] = -0.7599999999999998 y[1] (closed_form) = -0.7248360107409053 y[1] (numeric) = -0.7248360107409053 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] = -0.7499999999999998 y[1] (closed_form) = -0.731688868873821 y[1] (numeric) = -0.7316888688738209 absolute error = 1.110223024625157e-16 relative error = 1.517343056392202e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7399999999999998 y[1] (closed_form) = -0.7384685587295881 y[1] (numeric) = -0.7384685587295881 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] = -0.7299999999999998 y[1] (closed_form) = -0.7451744023448705 y[1] (numeric) = -0.7451744023448703 absolute error = 2.220446049250313e-16 relative error = 2.979766940817002e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7199999999999998 y[1] (closed_form) = -0.7518057291408952 y[1] (numeric) = -0.7518057291408948 absolute error = 3.33066907387547e-16 relative error = 4.430225714935025e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7099999999999997 y[1] (closed_form) = -0.7583618759905083 y[1] (numeric) = -0.758361875990508 absolute error = 3.33066907387547e-16 relative error = 4.391925780189347e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6999999999999997 y[1] (closed_form) = -0.7648421872844886 y[1] (numeric) = -0.7648421872844882 absolute error = 4.440892098500626e-16 relative error = 5.806285495662394e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6899999999999997 y[1] (closed_form) = -0.7712460149971068 y[1] (numeric) = -0.7712460149971061 absolute error = 6.661338147750939e-16 relative error = 8.637111917882556e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6799999999999997 y[1] (closed_form) = -0.7775727187509281 y[1] (numeric) = -0.7775727187509275 absolute error = 6.661338147750939e-16 relative error = 8.566836241955008e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6699999999999997 y[1] (closed_form) = -0.7838216658808494 y[1] (numeric) = -0.7838216658808488 absolute error = 6.661338147750939e-16 relative error = 8.498537917123032e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6599999999999997 y[1] (closed_form) = -0.7899922314973653 y[1] (numeric) = -0.7899922314973645 absolute error = 7.771561172376096e-16 relative error = 9.837515943221038e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6499999999999997 y[1] (closed_form) = -0.796083798549056 y[1] (numeric) = -0.7960837985490552 absolute error = 7.771561172376096e-16 relative error = 9.762240088971236e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6399999999999997 y[1] (closed_form) = -0.8020957578842928 y[1] (numeric) = -0.8020957578842921 absolute error = 6.661338147750939e-16 relative error = 8.30491631737551e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6299999999999997 y[1] (closed_form) = -0.8080275083121521 y[1] (numeric) = -0.8080275083121515 absolute error = 5.551115123125783e-16 relative error = 6.869958096749982e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6199999999999997 y[1] (closed_form) = -0.8138784566625341 y[1] (numeric) = -0.8138784566625337 absolute error = 4.440892098500626e-16 relative error = 5.456456135614355e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.6099999999999997 y[1] (closed_form) = -0.8196480178454797 y[1] (numeric) = -0.8196480178454792 absolute error = 4.440892098500626e-16 relative error = 5.418047749537564e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5999999999999996 y[1] (closed_form) = -0.8253356149096785 y[1] (numeric) = -0.8253356149096781 absolute error = 4.440892098500626e-16 relative error = 5.380710608237377e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5899999999999996 y[1] (closed_form) = -0.8309406791001637 y[1] (numeric) = -0.8309406791001633 absolute error = 3.33066907387547e-16 relative error = 4.008311492803907e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5799999999999996 y[1] (closed_form) = -0.8364626499151872 y[1] (numeric) = -0.8364626499151867 absolute error = 4.440892098500626e-16 relative error = 5.30913376580641e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5699999999999996 y[1] (closed_form) = -0.8419009751622689 y[1] (numeric) = -0.8419009751622686 absolute error = 3.33066907387547e-16 relative error = 3.956129250513711e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5599999999999996 y[1] (closed_form) = -0.8472551110134163 y[1] (numeric) = -0.8472551110134159 absolute error = 4.440892098500626e-16 relative error = 5.241505233516738e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5499999999999996 y[1] (closed_form) = -0.8525245220595059 y[1] (numeric) = -0.8525245220595056 absolute error = 3.33066907387547e-16 relative error = 3.90683081564543e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5399999999999996 y[1] (closed_form) = -0.8577086813638244 y[1] (numeric) = -0.8577086813638239 absolute error = 4.440892098500626e-16 relative error = 5.177622886408539e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5299999999999996 y[1] (closed_form) = -0.8628070705147612 y[1] (numeric) = -0.8628070705147609 absolute error = 3.33066907387547e-16 relative error = 3.860270954766692e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5199999999999996 y[1] (closed_form) = -0.8678191796776501 y[1] (numeric) = -0.8678191796776497 absolute error = 4.440892098500626e-16 relative error = 5.117301164224312e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.5099999999999996 y[1] (closed_form) = -0.8727445076457515 y[1] (numeric) = -0.8727445076457512 absolute error = 3.33066907387547e-16 relative error = 3.816316281221897e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4999999999999996 y[1] (closed_form) = -0.877582561890373 y[1] (numeric) = -0.8775825618903728 absolute error = 2.220446049250313e-16 relative error = 2.530184789072518e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4899999999999995 y[1] (closed_form) = -0.8823328586101217 y[1] (numeric) = -0.8823328586101216 absolute error = 1.110223024625157e-16 relative error = 1.258281400030839e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4799999999999995 y[1] (closed_form) = -0.8869949227792844 y[1] (numeric) = -0.8869949227792842 absolute error = 2.220446049250313e-16 relative error = 2.503335692489458e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4699999999999995 y[1] (closed_form) = -0.8915682881953292 y[1] (numeric) = -0.891568288195329 absolute error = 2.220446049250313e-16 relative error = 2.490494647072784e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4599999999999995 y[1] (closed_form) = -0.8960524975255254 y[1] (numeric) = -0.8960524975255253 absolute error = 1.110223024625157e-16 relative error = 1.23901560197764e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4499999999999995 y[1] (closed_form) = -0.9004471023526771 y[1] (numeric) = -0.9004471023526769 absolute error = 2.220446049250313e-16 relative error = 2.465937247672583e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4399999999999995 y[1] (closed_form) = -0.9047516632199636 y[1] (numeric) = -0.9047516632199635 absolute error = 1.110223024625157e-16 relative error = 1.227102496472823e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4299999999999995 y[1] (closed_form) = -0.9089657496748853 y[1] (numeric) = -0.9089657496748853 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] = -0.4199999999999995 y[1] (closed_form) = -0.9130889403123085 y[1] (numeric) = -0.9130889403123084 absolute error = 1.110223024625157e-16 relative error = 1.215898009065164e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.4099999999999995 y[1] (closed_form) = -0.9171208228166053 y[1] (numeric) = -0.9171208228166051 absolute error = 2.220446049250313e-16 relative error = 2.421105261170513e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3999999999999995 y[1] (closed_form) = -0.9210609940028853 y[1] (numeric) = -0.921060994002885 absolute error = 3.33066907387547e-16 relative error = 3.616122162985697e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3899999999999995 y[1] (closed_form) = -0.9249090598573132 y[1] (numeric) = -0.924909059857313 absolute error = 2.220446049250313e-16 relative error = 2.400718238821084e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3799999999999994 y[1] (closed_form) = -0.9286646355765105 y[1] (numeric) = -0.9286646355765104 absolute error = 1.110223024625157e-16 relative error = 1.19550479483472e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3699999999999994 y[1] (closed_form) = -0.9323273456060346 y[1] (numeric) = -0.9323273456060346 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] = -0.3599999999999994 y[1] (closed_form) = -0.935896823677935 y[1] (numeric) = -0.9358968236779349 absolute error = 1.110223024625157e-16 relative error = 1.186266473543681e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3499999999999994 y[1] (closed_form) = -0.9393727128473791 y[1] (numeric) = -0.9393727128473791 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] = -0.3399999999999994 y[1] (closed_form) = -0.9427546655283464 y[1] (numeric) = -0.9427546655283465 absolute error = 1.110223024625157e-16 relative error = 1.177637263670243e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3299999999999994 y[1] (closed_form) = -0.9460423435283871 y[1] (numeric) = -0.9460423435283872 absolute error = 1.110223024625157e-16 relative error = 1.173544749048374e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.3199999999999994 y[1] (closed_form) = -0.9492354180824411 y[1] (numeric) = -0.9492354180824411 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] = -0.3099999999999994 y[1] (closed_form) = -0.9523335698857136 y[1] (numeric) = -0.9523335698857136 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] = -0.2999999999999994 y[1] (closed_form) = -0.9553364891256062 y[1] (numeric) = -0.9553364891256063 absolute error = 1.110223024625157e-16 relative error = 1.16212772909084e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2899999999999994 y[1] (closed_form) = -0.9582438755126973 y[1] (numeric) = -0.9582438755126973 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] = -0.2799999999999994 y[1] (closed_form) = -0.9610554383107711 y[1] (numeric) = -0.9610554383107709 absolute error = 2.220446049250313e-16 relative error = 2.310424519477408e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2699999999999994 y[1] (closed_form) = -0.9637708963658906 y[1] (numeric) = -0.9637708963658905 absolute error = 1.110223024625157e-16 relative error = 1.151957408977067e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2599999999999993 y[1] (closed_form) = -0.9663899781345134 y[1] (numeric) = -0.9663899781345132 absolute error = 2.220446049250313e-16 relative error = 2.2976708156024e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2499999999999993 y[1] (closed_form) = -0.968912421710645 y[1] (numeric) = -0.9689124217106446 absolute error = 3.33066907387547e-16 relative error = 3.437533670994815e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2399999999999993 y[1] (closed_form) = -0.9713379748520298 y[1] (numeric) = -0.9713379748520296 absolute error = 2.220446049250313e-16 relative error = 2.285966477928105e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2299999999999993 y[1] (closed_form) = -0.973666395005375 y[1] (numeric) = -0.9736663950053749 absolute error = 1.110223024625157e-16 relative error = 1.140249915494955e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2199999999999993 y[1] (closed_form) = -0.9758974493306056 y[1] (numeric) = -0.9758974493306055 absolute error = 1.110223024625157e-16 relative error = 1.137643125706178e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.2099999999999993 y[1] (closed_form) = -0.9780309147241484 y[1] (numeric) = -0.978030914724148 absolute error = 3.33066907387547e-16 relative error = 3.405484452211695e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1999999999999993 y[1] (closed_form) = -0.9800665778412417 y[1] (numeric) = -0.9800665778412414 absolute error = 3.33066907387547e-16 relative error = 3.398411035719448e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1899999999999993 y[1] (closed_form) = -0.9820042351172704 y[1] (numeric) = -0.9820042351172701 absolute error = 3.33066907387547e-16 relative error = 3.391705406930066e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1799999999999993 y[1] (closed_form) = -0.9838436927881216 y[1] (numeric) = -0.9838436927881212 absolute error = 3.33066907387547e-16 relative error = 3.385364055581495e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1699999999999993 y[1] (closed_form) = -0.9855847669095609 y[1] (numeric) = -0.9855847669095605 absolute error = 3.33066907387547e-16 relative error = 3.379383677285567e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1599999999999993 y[1] (closed_form) = -0.987227283375627 y[1] (numeric) = -0.9872272833756269 absolute error = 1.110223024625157e-16 relative error = 1.124587056416198e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1499999999999992 y[1] (closed_form) = -0.9887710779360424 y[1] (numeric) = -0.9887710779360424 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] = -0.1399999999999992 y[1] (closed_form) = -0.9902159962126372 y[1] (numeric) = -0.9902159962126375 absolute error = 2.220446049250313e-16 relative error = 2.242385558042933e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1299999999999992 y[1] (closed_form) = -0.9915618937147881 y[1] (numeric) = -0.9915618937147883 absolute error = 2.220446049250313e-16 relative error = 2.239341853821785e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1199999999999992 y[1] (closed_form) = -0.9928086358538664 y[1] (numeric) = -0.9928086358538665 absolute error = 1.110223024625157e-16 relative error = 1.118264874549875e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.1099999999999992 y[1] (closed_form) = -0.9939560979566969 y[1] (numeric) = -0.9939560979566971 absolute error = 2.220446049250313e-16 relative error = 2.233947810989787e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.0999999999999992 y[1] (closed_form) = -0.9950041652780258 y[1] (numeric) = -0.995004165278026 absolute error = 2.220446049250313e-16 relative error = 2.231594727676212e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.08999999999999919 y[1] (closed_form) = -0.9959527330119943 y[1] (numeric) = -0.9959527330119945 absolute error = 2.220446049250313e-16 relative error = 2.229469306776401e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.07999999999999918 y[1] (closed_form) = -0.9968017063026194 y[1] (numeric) = -0.9968017063026196 absolute error = 1.110223024625157e-16 relative error = 1.113785236928661e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.06999999999999917 y[1] (closed_form) = -0.9975510002532796 y[1] (numeric) = -0.9975510002532798 absolute error = 2.220446049250313e-16 relative error = 2.225897271103471e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.05999999999999917 y[1] (closed_form) = -0.9982005399352042 y[1] (numeric) = -0.9982005399352044 absolute error = 2.220446049250313e-16 relative error = 2.224448856133105e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.04999999999999916 y[1] (closed_form) = -0.9987502603949663 y[1] (numeric) = -0.9987502603949665 absolute error = 2.220446049250313e-16 relative error = 2.223224500960044e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.03999999999999915 y[1] (closed_form) = -0.999200106660978 y[1] (numeric) = -0.9992001066609782 absolute error = 2.220446049250313e-16 relative error = 2.22222359109865e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.02999999999999914 y[1] (closed_form) = -0.9995500337489875 y[1] (numeric) = -0.9995500337489879 absolute error = 3.33066907387547e-16 relative error = 3.332168437214905e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.01999999999999913 y[1] (closed_form) = -0.9998000066665778 y[1] (numeric) = -0.9998000066665781 absolute error = 3.33066907387547e-16 relative error = 3.33133531873061e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.009999999999999121 y[1] (closed_form) = -0.9999500004166653 y[1] (numeric) = -0.9999500004166656 absolute error = 3.33066907387547e-16 relative error = 3.33083561426834e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.81239525796218e-16 y[1] (closed_form) = -1 y[1] (numeric) = -1 absolute error = 2.220446049250313e-16 relative error = 2.220446049250313e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.01000000000000088 y[1] (closed_form) = -0.9999500004166653 y[1] (numeric) = -0.9999500004166656 absolute error = 3.33066907387547e-16 relative error = 3.33083561426834e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.02000000000000089 y[1] (closed_form) = -0.9998000066665778 y[1] (numeric) = -0.9998000066665781 absolute error = 3.33066907387547e-16 relative error = 3.33133531873061e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.0300000000000009 y[1] (closed_form) = -0.9995500337489875 y[1] (numeric) = -0.9995500337489879 absolute error = 3.33066907387547e-16 relative error = 3.332168437214905e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.04000000000000091 y[1] (closed_form) = -0.9992001066609779 y[1] (numeric) = -0.9992001066609784 absolute error = 4.440892098500626e-16 relative error = 4.444447182197301e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.05000000000000092 y[1] (closed_form) = -0.9987502603949662 y[1] (numeric) = -0.9987502603949666 absolute error = 4.440892098500626e-16 relative error = 4.446449001920089e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.06000000000000093 y[1] (closed_form) = -0.9982005399352041 y[1] (numeric) = -0.9982005399352045 absolute error = 4.440892098500626e-16 relative error = 4.448897712266211e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07000000000000094 y[1] (closed_form) = -0.9975510002532795 y[1] (numeric) = -0.9975510002532799 absolute error = 4.440892098500626e-16 relative error = 4.451794542206943e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.08000000000000095 y[1] (closed_form) = -0.9968017063026193 y[1] (numeric) = -0.9968017063026197 absolute error = 3.33066907387547e-16 relative error = 3.341355710785983e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000095 y[1] (closed_form) = -0.9959527330119942 y[1] (numeric) = -0.9959527330119946 absolute error = 4.440892098500626e-16 relative error = 4.458938613552803e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.100000000000001 y[1] (closed_form) = -0.9950041652780257 y[1] (numeric) = -0.9950041652780262 absolute error = 4.440892098500626e-16 relative error = 4.463189455352425e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.110000000000001 y[1] (closed_form) = -0.9939560979566967 y[1] (numeric) = -0.9939560979566973 absolute error = 5.551115123125783e-16 relative error = 5.584869527474468e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.120000000000001 y[1] (closed_form) = -0.9928086358538661 y[1] (numeric) = -0.9928086358538666 absolute error = 4.440892098500626e-16 relative error = 4.473059498199502e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.130000000000001 y[1] (closed_form) = -0.9915618937147879 y[1] (numeric) = -0.9915618937147884 absolute error = 5.551115123125783e-16 relative error = 5.598354634554463e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.140000000000001 y[1] (closed_form) = -0.990215996212637 y[1] (numeric) = -0.9902159962126376 absolute error = 5.551115123125783e-16 relative error = 5.605963895107333e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.150000000000001 y[1] (closed_form) = -0.9887710779360421 y[1] (numeric) = -0.9887710779360425 absolute error = 3.33066907387547e-16 relative error = 3.368493626277883e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.160000000000001 y[1] (closed_form) = -0.9872272833756268 y[1] (numeric) = -0.987227283375627 absolute error = 2.220446049250313e-16 relative error = 2.249174112832397e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.170000000000001 y[1] (closed_form) = -0.9855847669095605 y[1] (numeric) = -0.9855847669095607 absolute error = 1.110223024625157e-16 relative error = 1.126461225761856e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.180000000000001 y[1] (closed_form) = -0.9838436927881212 y[1] (numeric) = -0.9838436927881216 absolute error = 3.33066907387547e-16 relative error = 3.385364055581496e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.190000000000001 y[1] (closed_form) = -0.9820042351172701 y[1] (numeric) = -0.9820042351172704 absolute error = 3.33066907387547e-16 relative error = 3.391705406930067e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.200000000000001 y[1] (closed_form) = -0.9800665778412414 y[1] (numeric) = -0.9800665778412417 absolute error = 3.33066907387547e-16 relative error = 3.39841103571945e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.210000000000001 y[1] (closed_form) = -0.978030914724148 y[1] (numeric) = -0.9780309147241484 absolute error = 3.33066907387547e-16 relative error = 3.405484452211696e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000011 y[1] (closed_form) = -0.9758974493306053 y[1] (numeric) = -0.9758974493306058 absolute error = 5.551115123125783e-16 relative error = 5.688215628530891e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000011 y[1] (closed_form) = -0.9736663950053746 y[1] (numeric) = -0.9736663950053752 absolute error = 6.661338147750939e-16 relative error = 6.841499492969735e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000011 y[1] (closed_form) = -0.9713379748520293 y[1] (numeric) = -0.97133797485203 absolute error = 6.661338147750939e-16 relative error = 6.857899433784319e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000011 y[1] (closed_form) = -0.9689124217106445 y[1] (numeric) = -0.9689124217106451 absolute error = 5.551115123125783e-16 relative error = 5.729222784991361e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000011 y[1] (closed_form) = -0.966389978134513 y[1] (numeric) = -0.9663899781345137 absolute error = 6.661338147750939e-16 relative error = 6.893012446807204e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000011 y[1] (closed_form) = -0.9637708963658902 y[1] (numeric) = -0.963770896365891 absolute error = 7.771561172376096e-16 relative error = 8.063701862839471e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000011 y[1] (closed_form) = -0.9610554383107707 y[1] (numeric) = -0.9610554383107714 absolute error = 7.771561172376096e-16 relative error = 8.086485818170932e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000011 y[1] (closed_form) = -0.9582438755126969 y[1] (numeric) = -0.9582438755126979 absolute error = 9.992007221626409e-16 relative error = 1.042741568922661e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000011 y[1] (closed_form) = -0.9553364891256056 y[1] (numeric) = -0.9553364891256069 absolute error = 1.221245327087672e-15 relative error = 1.278340501999925e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000011 y[1] (closed_form) = -0.952333569885713 y[1] (numeric) = -0.9523335698857142 absolute error = 1.110223024625157e-15 relative error = 1.165792175905751e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000011 y[1] (closed_form) = -0.9492354180824405 y[1] (numeric) = -0.9492354180824417 absolute error = 1.221245327087672e-15 relative error = 1.286556847567616e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000011 y[1] (closed_form) = -0.9460423435283866 y[1] (numeric) = -0.9460423435283879 absolute error = 1.332267629550188e-15 relative error = 1.40825369885805e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000011 y[1] (closed_form) = -0.9427546655283459 y[1] (numeric) = -0.9427546655283472 absolute error = 1.332267629550188e-15 relative error = 1.413164716404292e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000011 y[1] (closed_form) = -0.9393727128473786 y[1] (numeric) = -0.9393727128473798 absolute error = 1.221245327087672e-15 relative error = 1.300064724454147e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000012 y[1] (closed_form) = -0.9358968236779345 y[1] (numeric) = -0.9358968236779356 absolute error = 1.110223024625157e-15 relative error = 1.186266473543682e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000012 y[1] (closed_form) = -0.932327345606034 y[1] (numeric) = -0.9323273456060353 absolute error = 1.221245327087672e-15 relative error = 1.309888992147747e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000012 y[1] (closed_form) = -0.9286646355765098 y[1] (numeric) = -0.9286646355765111 absolute error = 1.332267629550188e-15 relative error = 1.434605753801665e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000012 y[1] (closed_form) = -0.9249090598573126 y[1] (numeric) = -0.9249090598573138 absolute error = 1.110223024625157e-15 relative error = 1.200359119410543e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000012 y[1] (closed_form) = -0.9210609940028847 y[1] (numeric) = -0.9210609940028859 absolute error = 1.221245327087672e-15 relative error = 1.325911459761423e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000012 y[1] (closed_form) = -0.9171208228166047 y[1] (numeric) = -0.9171208228166061 absolute error = 1.443289932012704e-15 relative error = 1.573718419760835e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000012 y[1] (closed_form) = -0.9130889403123078 y[1] (numeric) = -0.9130889403123094 absolute error = 1.554312234475219e-15 relative error = 1.702257212691231e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000012 y[1] (closed_form) = -0.9089657496748846 y[1] (numeric) = -0.9089657496748863 absolute error = 1.665334536937735e-15 relative error = 1.832120228439174e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000012 y[1] (closed_form) = -0.9047516632199629 y[1] (numeric) = -0.9047516632199645 absolute error = 1.554312234475219e-15 relative error = 1.717943495061954e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000012 y[1] (closed_form) = -0.9004471023526763 y[1] (numeric) = -0.900447102352678 absolute error = 1.665334536937735e-15 relative error = 1.849452935754439e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000012 y[1] (closed_form) = -0.8960524975255247 y[1] (numeric) = -0.8960524975255264 absolute error = 1.665334536937735e-15 relative error = 1.858523402966461e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000013 y[1] (closed_form) = -0.8915682881953284 y[1] (numeric) = -0.8915682881953301 absolute error = 1.665334536937735e-15 relative error = 1.86787098530459e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000013 y[1] (closed_form) = -0.8869949227792836 y[1] (numeric) = -0.8869949227792853 absolute error = 1.665334536937735e-15 relative error = 1.877501769367095e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000013 y[1] (closed_form) = -0.8823328586101209 y[1] (numeric) = -0.8823328586101228 absolute error = 1.887379141862766e-15 relative error = 2.139078380052429e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000012 y[1] (closed_form) = -0.8775825618903721 y[1] (numeric) = -0.877582561890374 absolute error = 1.887379141862766e-15 relative error = 2.150657070711642e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000012 y[1] (closed_form) = -0.8727445076457506 y[1] (numeric) = -0.8727445076457525 absolute error = 1.887379141862766e-15 relative error = 2.162579226025744e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000012 y[1] (closed_form) = -0.8678191796776493 y[1] (numeric) = -0.867819179677651 absolute error = 1.665334536937735e-15 relative error = 1.918987936584119e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000012 y[1] (closed_form) = -0.8628070705147604 y[1] (numeric) = -0.8628070705147622 absolute error = 1.887379141862766e-15 relative error = 2.187486874367794e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000013 y[1] (closed_form) = -0.8577086813638235 y[1] (numeric) = -0.8577086813638253 absolute error = 1.77635683940025e-15 relative error = 2.071049154563418e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000013 y[1] (closed_form) = -0.8525245220595051 y[1] (numeric) = -0.8525245220595069 absolute error = 1.77635683940025e-15 relative error = 2.083643101677564e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000013 y[1] (closed_form) = -0.8472551110134154 y[1] (numeric) = -0.8472551110134172 absolute error = 1.77635683940025e-15 relative error = 2.096602093406697e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000013 y[1] (closed_form) = -0.841900975162268 y[1] (numeric) = -0.8419009751622699 absolute error = 1.887379141862766e-15 relative error = 2.241806575291106e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000013 y[1] (closed_form) = -0.8364626499151863 y[1] (numeric) = -0.8364626499151882 absolute error = 1.887379141862766e-15 relative error = 2.256381850467727e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000013 y[1] (closed_form) = -0.8309406791001628 y[1] (numeric) = -0.8309406791001648 absolute error = 1.998401444325282e-15 relative error = 2.404986895682347e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000013 y[1] (closed_form) = -0.8253356149096776 y[1] (numeric) = -0.8253356149096795 absolute error = 1.998401444325282e-15 relative error = 2.421319773706822e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000013 y[1] (closed_form) = -0.8196480178454788 y[1] (numeric) = -0.8196480178454807 absolute error = 1.887379141862766e-15 relative error = 2.302670293553467e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000013 y[1] (closed_form) = -0.8138784566625331 y[1] (numeric) = -0.8138784566625351 absolute error = 1.998401444325282e-15 relative error = 2.455405261026463e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000013 y[1] (closed_form) = -0.8080275083121511 y[1] (numeric) = -0.8080275083121531 absolute error = 1.998401444325282e-15 relative error = 2.473184914829996e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000013 y[1] (closed_form) = -0.8020957578842918 y[1] (numeric) = -0.8020957578842939 absolute error = 2.109423746787797e-15 relative error = 2.629890167168915e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000014 y[1] (closed_form) = -0.796083798549055 y[1] (numeric) = -0.796083798549057 absolute error = 1.998401444325282e-15 relative error = 2.510290308592606e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000014 y[1] (closed_form) = -0.7899922314973643 y[1] (numeric) = -0.7899922314973663 absolute error = 1.998401444325282e-15 relative error = 2.52964695682827e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000014 y[1] (closed_form) = -0.7838216658808485 y[1] (numeric) = -0.7838216658808507 absolute error = 2.220446049250313e-15 relative error = 2.832845972374348e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000014 y[1] (closed_form) = -0.777572718750927 y[1] (numeric) = -0.7775727187509294 absolute error = 2.331468351712829e-15 relative error = 2.998392684684257e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000014 y[1] (closed_form) = -0.7712460149971058 y[1] (numeric) = -0.771246014997108 absolute error = 2.220446049250313e-15 relative error = 2.879037305960856e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000014 y[1] (closed_form) = -0.7648421872844875 y[1] (numeric) = -0.76484218728449 absolute error = 2.55351295663786e-15 relative error = 3.338614160005881e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000014 y[1] (closed_form) = -0.7583618759905072 y[1] (numeric) = -0.7583618759905099 absolute error = 2.664535259100376e-15 relative error = 3.513540624151482e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000014 y[1] (closed_form) = -0.7518057291408941 y[1] (numeric) = -0.7518057291408967 absolute error = 2.664535259100376e-15 relative error = 3.544180571948025e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000014 y[1] (closed_form) = -0.7451744023448694 y[1] (numeric) = -0.7451744023448722 absolute error = 2.775557561562891e-15 relative error = 3.724708676021259e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000014 y[1] (closed_form) = -0.7384685587295869 y[1] (numeric) = -0.7384685587295899 absolute error = 2.997602166487923e-15 relative error = 4.059214344405944e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000014 y[1] (closed_form) = -0.7316888688738199 y[1] (numeric) = -0.7316888688738229 absolute error = 2.997602166487923e-15 relative error = 4.096826252258951e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000015 y[1] (closed_form) = -0.7248360107409042 y[1] (numeric) = -0.7248360107409073 absolute error = 3.108624468950438e-15 relative error = 4.288727964512831e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000015 y[1] (closed_form) = -0.7179106696109423 y[1] (numeric) = -0.7179106696109455 absolute error = 3.219646771412954e-15 relative error = 4.484745676168567e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000015 y[1] (closed_form) = -0.7109135380122763 y[1] (numeric) = -0.7109135380122795 absolute error = 3.219646771412954e-15 relative error = 4.528886565327099e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000015 y[1] (closed_form) = -0.7038453156522351 y[1] (numeric) = -0.7038453156522382 absolute error = 3.108624468950438e-15 relative error = 4.416630188225032e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000015 y[1] (closed_form) = -0.6967067093471644 y[1] (numeric) = -0.6967067093471675 absolute error = 3.108624468950438e-15 relative error = 4.461883927977836e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000015 y[1] (closed_form) = -0.689498432951746 y[1] (numeric) = -0.6894984329517492 absolute error = 3.219646771412954e-15 relative error = 4.66954907733384e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000015 y[1] (closed_form) = -0.6822212072876125 y[1] (numeric) = -0.6822212072876158 absolute error = 3.33066907387547e-15 relative error = 4.882095482076268e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000015 y[1] (closed_form) = -0.674875760071266 y[1] (numeric) = -0.6748757600712694 absolute error = 3.33066907387547e-15 relative error = 4.935232928685652e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000015 y[1] (closed_form) = -0.667462825841307 y[1] (numeric) = -0.6674628258413107 absolute error = 3.663735981263017e-15 relative error = 5.489048737126359e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000015 y[1] (closed_form) = -0.659983145884981 y[1] (numeric) = -0.6599831458849846 absolute error = 3.663735981263017e-15 relative error = 5.55125688300761e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000015 y[1] (closed_form) = -0.6524374681640507 y[1] (numeric) = -0.6524374681640542 absolute error = 3.552713678800501e-15 relative error = 5.445293767075922e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000015 y[1] (closed_form) = -0.64482654724 y[1] (numeric) = -0.6448265472400035 absolute error = 3.552713678800501e-15 relative error = 5.509564849659028e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000016 y[1] (closed_form) = -0.637151144198579 y[1] (numeric) = -0.6371511441985827 absolute error = 3.663735981263017e-15 relative error = 5.750183476279141e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000016 y[1] (closed_form) = -0.6294120265736957 y[1] (numeric) = -0.6294120265736993 absolute error = 3.663735981263017e-15 relative error = 5.820886520404044e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000016 y[1] (closed_form) = -0.6216099682706632 y[1] (numeric) = -0.6216099682706671 absolute error = 3.885780586188048e-15 relative error = 6.251155522808621e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000016 y[1] (closed_form) = -0.6137457494888103 y[1] (numeric) = -0.6137457494888143 absolute error = 3.996802888650564e-15 relative error = 6.5121475659579e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000016 y[1] (closed_form) = -0.6058201566434616 y[1] (numeric) = -0.6058201566434656 absolute error = 3.996802888650564e-15 relative error = 6.597342205968841e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000016 y[1] (closed_form) = -0.597833982287297 y[1] (numeric) = -0.5978339822873009 absolute error = 3.885780586188048e-15 relative error = 6.499765321672004e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000016 y[1] (closed_form) = -0.589788025031097 y[1] (numeric) = -0.5897880250311008 absolute error = 3.885780586188048e-15 relative error = 6.588435880811869e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000016 y[1] (closed_form) = -0.5816830894638821 y[1] (numeric) = -0.5816830894638861 absolute error = 3.996802888650564e-15 relative error = 6.87110036555177e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000016 y[1] (closed_form) = -0.5735199860724554 y[1] (numeric) = -0.5735199860724594 absolute error = 3.996802888650564e-15 relative error = 6.968899054453579e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000016 y[1] (closed_form) = -0.5652995311603529 y[1] (numeric) = -0.5652995311603569 absolute error = 3.996802888650564e-15 relative error = 7.070239171163987e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000016 y[1] (closed_form) = -0.557022546766216 y[1] (numeric) = -0.5570225467662201 absolute error = 4.107825191113079e-15 relative error = 7.374612060070067e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000017 y[1] (closed_form) = -0.5486898605815862 y[1] (numeric) = -0.5486898605815904 absolute error = 4.218847493575595e-15 relative error = 7.688947430345823e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 Finished! diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ; Iterations = 2000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %