##############ECHO OF PROBLEM################# ##############temp/diff2postode.ode################# diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb 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 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $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 def exact_soln_y (x) x = c(x) return(neg(cos(c(x)))) end def exact_soln_yp (x) x = c(x) return(sin(c(x))) end def exact_soln_ypp (x) x = c(x) return(cos(c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -1.0 y[1] (closed_form) -0.5403023058681398 y[1] (numeric) -0.5403023058681398 absolute error 0.0 relative error 0.0% 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 1.1102230246251565e-16 relative error 2.0234072185120535e-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 3.9862767892270536e-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 3.3306690738754696e-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] -0.94 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 3.3306690738754696e-16 relative error 5.5712274185759903e-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 3.3306690738754696e-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 3.3306690738754696e-16 relative error 5.2274395238901166e-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 3.3306690738754696e-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 1.1102230246251565e-16 relative error 1.6633481021594994e-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 1.1102230246251565e-16 relative error 1.6450776428952143e-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 1.1102230246251565e-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 1.1102230246251565e-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 0.0 relative error 0.0% 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 0.0 relative error 0.0% 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 0.0 relative error 0.0% 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 0.0 relative error 0.0% 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 0.0 relative error 0.0% 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 1.1102230246251565e-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) -0.738468558729588 y[1] (numeric) -0.738468558729588 absolute error 0.0 relative error 0.0% 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 2.9797669408170024e-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 3.3306690738754696e-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 3.3306690738754696e-16 relative error 4.3919257801893467e-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 5.4180477495375636e-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 5.3807106082373774e-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 3.3306690738754696e-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 3.3306690738754696e-16 relative error 3.9561292505137114e-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 3.3306690738754696e-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 5.1776228864085386e-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 3.3306690738754696e-16 relative error 3.8602709547666916e-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 3.3306690738754696e-16 relative error 3.8163162812218966e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.49999999999999956 y[1] (closed_form) -0.877582561890373 y[1] (numeric) -0.8775825618903728 absolute error 2.220446049250313e-16 relative error 2.5301847890725178e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.48999999999999955 y[1] (closed_form) -0.8823328586101217 y[1] (numeric) -0.8823328586101216 absolute error 1.1102230246251565e-16 relative error 1.2582814000308394e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.47999999999999954 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] -0.46999999999999953 y[1] (closed_form) -0.8915682881953292 y[1] (numeric) -0.891568288195329 absolute error 2.220446049250313e-16 relative error 2.4904946470727845e-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 1.1102230246251565e-16 relative error 1.2390156019776399e-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 2.4659372476725828e-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 1.1102230246251565e-16 relative error 1.2271024964728235e-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 0.0 relative error 0.0% 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 1.1102230246251565e-16 relative error 1.2158980090651643e-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] -0.39999999999999947 y[1] (closed_form) -0.9210609940028853 y[1] (numeric) -0.921060994002885 absolute error 3.3306690738754696e-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] -0.38999999999999946 y[1] (closed_form) -0.9249090598573132 y[1] (numeric) -0.924909059857313 absolute error 2.220446049250313e-16 relative error 2.4007182388210836e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.37999999999999945 y[1] (closed_form) -0.9286646355765105 y[1] (numeric) -0.9286646355765104 absolute error 1.1102230246251565e-16 relative error 1.1955047948347204e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.36999999999999944 y[1] (closed_form) -0.9323273456060346 y[1] (numeric) -0.9323273456060346 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.35999999999999943 y[1] (closed_form) -0.935896823677935 y[1] (numeric) -0.9358968236779349 absolute error 1.1102230246251565e-16 relative error 1.1862664735436813e-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 0.0 relative error 0.0% 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 1.1102230246251565e-16 relative error 1.1776372636702425e-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 1.1102230246251565e-16 relative error 1.1735447490483739e-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) -0.949235418082441 y[1] (numeric) -0.949235418082441 absolute error 0.0 relative error 0.0% 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 0.0 relative error 0.0% 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 1.1102230246251565e-16 relative error 1.1621277290908398e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.28999999999999937 y[1] (closed_form) -0.9582438755126973 y[1] (numeric) -0.9582438755126973 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.27999999999999936 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] -0.26999999999999935 y[1] (closed_form) -0.9637708963658906 y[1] (numeric) -0.9637708963658905 absolute error 1.1102230246251565e-16 relative error 1.1519574089770667e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.25999999999999934 y[1] (closed_form) -0.9663899781345134 y[1] (numeric) -0.9663899781345132 absolute error 2.220446049250313e-16 relative error 2.2976708156024002e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.24999999999999933 y[1] (closed_form) -0.968912421710645 y[1] (numeric) -0.9689124217106446 absolute error 3.3306690738754696e-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] -0.23999999999999932 y[1] (closed_form) -0.9713379748520298 y[1] (numeric) -0.9713379748520296 absolute error 2.220446049250313e-16 relative error 2.2859664779281055e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.22999999999999932 y[1] (closed_form) -0.973666395005375 y[1] (numeric) -0.9736663950053749 absolute error 1.1102230246251565e-16 relative error 1.1402499154949552e-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 1.1102230246251565e-16 relative error 1.1376431257061779e-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 3.3306690738754696e-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 3.3306690738754696e-16 relative error 3.3984110357194485e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.18999999999999928 y[1] (closed_form) -0.9820042351172704 y[1] (numeric) -0.9820042351172701 absolute error 3.3306690738754696e-16 relative error 3.3917054069300657e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.17999999999999927 y[1] (closed_form) -0.9838436927881216 y[1] (numeric) -0.9838436927881212 absolute error 3.3306690738754696e-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] -0.16999999999999926 y[1] (closed_form) -0.9855847669095609 y[1] (numeric) -0.9855847669095605 absolute error 3.3306690738754696e-16 relative error 3.3793836772855666e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.15999999999999925 y[1] (closed_form) -0.987227283375627 y[1] (numeric) -0.9872272833756269 absolute error 1.1102230246251565e-16 relative error 1.1245870564161984e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.14999999999999925 y[1] (closed_form) -0.9887710779360424 y[1] (numeric) -0.9887710779360424 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.13999999999999924 y[1] (closed_form) -0.9902159962126372 y[1] (numeric) -0.9902159962126375 absolute error 2.220446049250313e-16 relative error 2.2423855580429327e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.12999999999999923 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] -0.11999999999999922 y[1] (closed_form) -0.9928086358538664 y[1] (numeric) -0.9928086358538665 absolute error 1.1102230246251565e-16 relative error 1.1182648745498751e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.10999999999999921 y[1] (closed_form) -0.9939560979566969 y[1] (numeric) -0.9939560979566971 absolute error 2.220446049250313e-16 relative error 2.2339478109897868e-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 2.2315947276762124e-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 2.2294693067764013e-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 1.1102230246251565e-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 2.2258972711034713e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.059999999999999165 y[1] (closed_form) -0.9982005399352042 y[1] (numeric) -0.9982005399352044 absolute error 2.220446049250313e-16 relative error 2.2244488561331053e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] -0.049999999999999156 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 2.2222235910986504e-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 3.3306690738754696e-16 relative error 3.3321684372149054e-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 3.3306690738754696e-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] -0.00999999999999912 y[1] (closed_form) -0.9999500004166653 y[1] (numeric) -0.9999500004166656 absolute error 3.3306690738754696e-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) -1.0 y[1] (numeric) -1.0000000000000002 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] 0.010000000000000883 y[1] (closed_form) -0.9999500004166653 y[1] (numeric) -0.9999500004166656 absolute error 3.3306690738754696e-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] 0.020000000000000892 y[1] (closed_form) -0.9998000066665778 y[1] (numeric) -0.9998000066665781 absolute error 3.3306690738754696e-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 3.3306690738754696e-16 relative error 3.3321684372149054e-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 4.4444471821973014e-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 4.4517945422069425e-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 3.3306690738754696e-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] 0.10000000000000096 y[1] (closed_form) -0.9950041652780257 y[1] (numeric) -0.9950041652780262 absolute error 4.440892098500626e-16 relative error 4.4631894553524255e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.11000000000000097 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] 0.12000000000000098 y[1] (closed_form) -0.9928086358538661 y[1] (numeric) -0.9928086358538666 absolute error 4.440892098500626e-16 relative error 4.4730594981995016e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.13000000000000098 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] 0.14000000000000098 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 3.3306690738754696e-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 1.1102230246251565e-16 relative error 1.1264612257618559e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.18000000000000102 y[1] (closed_form) -0.9838436927881212 y[1] (numeric) -0.9838436927881216 absolute error 3.3306690738754696e-16 relative error 3.3853640555814963e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.19000000000000103 y[1] (closed_form) -0.9820042351172701 y[1] (numeric) -0.9820042351172704 absolute error 3.3306690738754696e-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] 0.20000000000000104 y[1] (closed_form) -0.9800665778412414 y[1] (numeric) -0.9800665778412417 absolute error 3.3306690738754696e-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] 0.21000000000000105 y[1] (closed_form) -0.978030914724148 y[1] (numeric) -0.9780309147241484 absolute error 3.3306690738754696e-16 relative error 3.4054844522116964e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.22000000000000106 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] 0.23000000000000106 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] 0.24000000000000107 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] 0.25000000000000105 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] 0.26000000000000106 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 1.0427415689226613e-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 1.2212453270876722e-15 relative error 1.2783405019999246e-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 1.1102230246251565e-15 relative error 1.1657921759057505e-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 1.2212453270876722e-15 relative error 1.2865568475676156e-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 1.3322676295501878e-15 relative error 1.4082536988580495e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.34000000000000113 y[1] (closed_form) -0.9427546655283459 y[1] (numeric) -0.9427546655283472 absolute error 1.3322676295501878e-15 relative error 1.4131647164042917e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.35000000000000114 y[1] (closed_form) -0.9393727128473786 y[1] (numeric) -0.9393727128473798 absolute error 1.2212453270876722e-15 relative error 1.3000647244541474e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.36000000000000115 y[1] (closed_form) -0.9358968236779345 y[1] (numeric) -0.9358968236779356 absolute error 1.1102230246251565e-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] 0.37000000000000116 y[1] (closed_form) -0.932327345606034 y[1] (numeric) -0.9323273456060353 absolute error 1.2212453270876722e-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] 0.38000000000000117 y[1] (closed_form) -0.9286646355765098 y[1] (numeric) -0.9286646355765111 absolute error 1.3322676295501878e-15 relative error 1.4346057538016654e-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 1.1102230246251565e-15 relative error 1.2003591194105426e-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 1.2212453270876722e-15 relative error 1.3259114597614232e-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 1.4432899320127035e-15 relative error 1.5737184197608345e-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 1.5543122344752192e-15 relative error 1.7022572126912312e-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 1.6653345369377348e-15 relative error 1.8321202284391742e-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 1.5543122344752192e-15 relative error 1.7179434950619542e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.45000000000000123 y[1] (closed_form) -0.9004471023526763 y[1] (numeric) -0.900447102352678 absolute error 1.6653345369377348e-15 relative error 1.8494529357544388e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.46000000000000124 y[1] (closed_form) -0.8960524975255247 y[1] (numeric) -0.8960524975255264 absolute error 1.6653345369377348e-15 relative error 1.8585234029664613e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.47000000000000125 y[1] (closed_form) -0.8915682881953284 y[1] (numeric) -0.8915682881953301 absolute error 1.6653345369377348e-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] 0.48000000000000126 y[1] (closed_form) -0.8869949227792836 y[1] (numeric) -0.8869949227792853 absolute error 1.6653345369377348e-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] 0.49000000000000127 y[1] (closed_form) -0.8823328586101209 y[1] (numeric) -0.8823328586101228 absolute error 1.887379141862766e-15 relative error 2.1390783800524288e-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 2.1506570707116422e-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 2.1625792260257436e-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 1.6653345369377348e-15 relative error 1.9189879365841187e-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 2.1874868743677943e-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 1.7763568394002505e-15 relative error 2.0710491545634177e-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 1.7763568394002505e-15 relative error 2.0836431016775644e-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 1.7763568394002505e-15 relative error 2.0966020934066971e-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 2.2418065752911055e-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 2.2563818504677266e-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 1.9984014443252818e-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 1.9984014443252818e-15 relative error 2.4213197737068225e-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 2.3026702935534673e-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 1.9984014443252818e-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 1.9984014443252818e-15 relative error 2.4731849148299964e-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 2.1094237467877974e-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 1.9984014443252818e-15 relative error 2.5102903085926065e-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 1.9984014443252818e-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 2.8328459723743477e-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 2.3314683517128287e-15 relative error 2.9983926846842567e-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 2.8790373059608555e-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 2.6645352591003757e-15 relative error 3.5135406241514824e-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) -0.751805729140894 y[1] (numeric) -0.7518057291408967 absolute error 2.6645352591003757e-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 2.7755575615628914e-15 relative error 3.7247086760212587e-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 2.9976021664879227e-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 2.9976021664879227e-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 3.1086244689504383e-15 relative error 4.2887279645128306e-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 3.1086244689504383e-15 relative error 4.4166301882250324e-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 3.1086244689504383e-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 3.3306690738754696e-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 3.3306690738754696e-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 3.6637359812630166e-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 3.6637359812630166e-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 3.6637359812630166e-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 3.6637359812630166e-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 3.9968028886505635e-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 3.9968028886505635e-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 3.9968028886505635e-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 3.9968028886505635e-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 3.9968028886505635e-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 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 2 Minutes 59.0 Seconds Percent Done 100.05000000000007%