##############ECHO OF PROBLEM################# ##############temp/mtest5postode.ode################# diff ( y1 , x , 1 ) = neg ( y2 ) ; diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.5); x_end=c(5.0); array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(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_y1 (double x) { return(neg(cos(c(x)))); } double exact_soln_y2 (double x) { return(neg(sin(c(x)))); } double exact_soln_y2p (double x) { return(neg(cos(c(x)))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.5 y1[1] (closed_form) = -0.8775825618903728 y1[1] (numeric) = -0.8775825618903728 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.479425538604203 y2[1] (numeric) = -0.479425538604203 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.51 y1[1] (closed_form) = -0.8727445076457513 y1[1] (numeric) = -0.8727445076457513 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.4881772468829075 y2[1] (numeric) = -0.4881772468829075 absolute error = 5.551115123125783e-17 relative error = 1.137110579931894e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.52 y1[1] (closed_form) = -0.8678191796776499 y1[1] (numeric) = -0.8678191796776498 absolute error = 1.110223024625157e-16 relative error = 1.279325291056078e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.4968801378437367 y2[1] (numeric) = -0.4968801378437367 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.53 y1[1] (closed_form) = -0.862807070514761 y1[1] (numeric) = -0.862807070514761 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.5055333412048469 y2[1] (numeric) = -0.5055333412048472 absolute error = 2.220446049250313e-16 relative error = 4.392284085473538e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.54 y1[1] (closed_form) = -0.8577086813638242 y1[1] (numeric) = -0.8577086813638241 absolute error = 1.110223024625157e-16 relative error = 1.294405721602135e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.5141359916531132 y2[1] (numeric) = -0.5141359916531133 absolute error = 1.110223024625157e-16 relative error = 2.159395651441229e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.55 y1[1] (closed_form) = -0.8525245220595057 y1[1] (numeric) = -0.8525245220595057 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.5226872289306592 y2[1] (numeric) = -0.5226872289306593 absolute error = 1.110223024625157e-16 relative error = 2.124067631988079e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000001 y1[1] (closed_form) = -0.8472551110134161 y1[1] (numeric) = -0.847255111013416 absolute error = 1.110223024625157e-16 relative error = 1.310376308379185e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.5311861979208834 y2[1] (numeric) = -0.5311861979208835 absolute error = 1.110223024625157e-16 relative error = 2.090082590569337e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000001 y1[1] (closed_form) = -0.8419009751622687 y1[1] (numeric) = -0.8419009751622687 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.5396320487339693 y2[1] (numeric) = -0.5396320487339694 absolute error = 1.110223024625157e-16 relative error = 2.057370438301155e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000001 y1[1] (closed_form) = -0.8364626499151869 y1[1] (numeric) = -0.8364626499151869 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.5480239367918737 y2[1] (numeric) = -0.5480239367918738 absolute error = 1.110223024625157e-16 relative error = 2.025865934113007e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000001 y1[1] (closed_form) = -0.8309406791001634 y1[1] (numeric) = -0.8309406791001636 absolute error = 1.110223024625157e-16 relative error = 1.336103830934636e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.5563610229127839 y2[1] (numeric) = -0.5563610229127841 absolute error = 2.220446049250313e-16 relative error = 3.99101654825736e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000001 y1[1] (closed_form) = -0.8253356149096782 y1[1] (numeric) = -0.8253356149096783 absolute error = 1.110223024625157e-16 relative error = 1.345177652059345e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.5646424733950355 y2[1] (numeric) = -0.5646424733950356 absolute error = 1.110223024625157e-16 relative error = 1.966240722115181e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000001 y1[1] (closed_form) = -0.8196480178454795 y1[1] (numeric) = -0.8196480178454795 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.5728674601004814 y2[1] (numeric) = -0.5728674601004816 absolute error = 2.220446049250313e-16 relative error = 3.876020552573967e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000001 y1[1] (closed_form) = -0.8138784566625339 y1[1] (numeric) = -0.8138784566625339 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.5810351605373052 y2[1] (numeric) = -0.5810351605373055 absolute error = 3.33066907387547e-16 relative error = 5.732302105083407e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000001 y1[1] (closed_form) = -0.8080275083121518 y1[1] (numeric) = -0.8080275083121518 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.5891447579422696 y2[1] (numeric) = -0.5891447579422699 absolute error = 3.33066907387547e-16 relative error = 5.653396773839822e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000001 y1[1] (closed_form) = -0.8020957578842925 y1[1] (numeric) = -0.8020957578842923 absolute error = 2.220446049250313e-16 relative error = 2.768305439125171e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.5971954413623921 y2[1] (numeric) = -0.5971954413623922 absolute error = 1.110223024625157e-16 relative error = 1.859061452465856e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000001 y1[1] (closed_form) = -0.7960837985490558 y1[1] (numeric) = -0.7960837985490554 absolute error = 3.33066907387547e-16 relative error = 4.183817180987674e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.6051864057360397 y2[1] (numeric) = -0.6051864057360397 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] = 0.6600000000000001 y1[1] (closed_form) = -0.789992231497365 y1[1] (numeric) = -0.7899922314973647 absolute error = 2.220446049250313e-16 relative error = 2.810718840920298e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.6131168519734339 y2[1] (numeric) = -0.6131168519734337 absolute error = 2.220446049250313e-16 relative error = 3.621570736644055e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000002 y1[1] (closed_form) = -0.7838216658808492 y1[1] (numeric) = -0.783821665880849 absolute error = 2.220446049250313e-16 relative error = 2.832845972374345e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.6209859870365598 y2[1] (numeric) = -0.6209859870365595 absolute error = 3.33066907387547e-16 relative error = 5.363517282845515e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000002 y1[1] (closed_form) = -0.7775727187509278 y1[1] (numeric) = -0.7775727187509277 absolute error = 1.110223024625157e-16 relative error = 1.427806040325835e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.6287930240184686 y2[1] (numeric) = -0.6287930240184683 absolute error = 3.33066907387547e-16 relative error = 5.296924340206489e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000002 y1[1] (closed_form) = -0.7712460149971065 y1[1] (numeric) = -0.7712460149971063 absolute error = 2.220446049250313e-16 relative error = 2.879037305960852e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.6365371822219681 y2[1] (numeric) = -0.6365371822219675 absolute error = 5.551115123125783e-16 relative error = 8.720802614779607e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000002 y1[1] (closed_form) = -0.7648421872844883 y1[1] (numeric) = -0.7648421872844884 absolute error = 1.110223024625157e-16 relative error = 1.451571373915599e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.6442176872376912 y2[1] (numeric) = -0.6442176872376907 absolute error = 5.551115123125783e-16 relative error = 8.61683128715098e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000002 y1[1] (closed_form) = -0.7583618759905081 y1[1] (numeric) = -0.7583618759905082 absolute error = 1.110223024625157e-16 relative error = 1.463975260063116e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.6518337710215368 y2[1] (numeric) = -0.6518337710215364 absolute error = 4.440892098500626e-16 relative error = 6.812921170900636e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000002 y1[1] (closed_form) = -0.7518057291408948 y1[1] (numeric) = -0.7518057291408951 absolute error = 2.220446049250313e-16 relative error = 2.953483809956684e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.6593846719714733 y2[1] (numeric) = -0.6593846719714728 absolute error = 5.551115123125783e-16 relative error = 8.418629305604997e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000002 y1[1] (closed_form) = -0.7451744023448702 y1[1] (numeric) = -0.7451744023448705 absolute error = 3.33066907387547e-16 relative error = 4.469650411225506e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.666869635003698 y2[1] (numeric) = -0.6668696350036974 absolute error = 5.551115123125783e-16 relative error = 8.324138379902392e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000002 y1[1] (closed_form) = -0.7384685587295877 y1[1] (numeric) = -0.7384685587295883 absolute error = 5.551115123125783e-16 relative error = 7.51706360075174e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.6742879116281453 y2[1] (numeric) = -0.6742879116281446 absolute error = 6.661338147750939e-16 relative error = 9.879070991598198e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000002 y1[1] (closed_form) = -0.7316888688738208 y1[1] (numeric) = -0.7316888688738212 absolute error = 4.440892098500626e-16 relative error = 6.069372225568809e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.6816387600233343 y2[1] (numeric) = -0.6816387600233336 absolute error = 7.771561172376096e-16 relative error = 1.140128999135855e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000002 y1[1] (closed_form) = -0.724836010740905 y1[1] (numeric) = -0.7248360107409056 absolute error = 6.661338147750939e-16 relative error = 9.190131352527485e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.6889214451105515 y2[1] (numeric) = -0.6889214451105508 absolute error = 7.771561172376096e-16 relative error = 1.128076535798503e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000002 y1[1] (closed_form) = -0.7179106696109432 y1[1] (numeric) = -0.7179106696109439 absolute error = 6.661338147750939e-16 relative error = 9.278784157590127e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.6961352386273569 y2[1] (numeric) = -0.696135238627356 absolute error = 8.881784197001252e-16 relative error = 1.275870506787503e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000002 y1[1] (closed_form) = -0.7109135380122772 y1[1] (numeric) = -0.7109135380122779 absolute error = 6.661338147750939e-16 relative error = 9.370110135159503e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.7032794192004104 y2[1] (numeric) = -0.7032794192004097 absolute error = 6.661338147750939e-16 relative error = 9.471822956691255e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000003 y1[1] (closed_form) = -0.703845315652236 y1[1] (numeric) = -0.7038453156522365 absolute error = 5.551115123125783e-16 relative error = 7.886839621830405e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.710353272417608 y2[1] (numeric) = -0.7103532724176074 absolute error = 6.661338147750939e-16 relative error = 9.377500472518158e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000003 y1[1] (closed_form) = -0.6967067093471653 y1[1] (numeric) = -0.6967067093471658 absolute error = 5.551115123125783e-16 relative error = 7.967649871388983e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.7173560908995229 y2[1] (numeric) = -0.7173560908995222 absolute error = 6.661338147750939e-16 relative error = 9.285957465556622e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000003 y1[1] (closed_form) = -0.6894984329517468 y1[1] (numeric) = -0.6894984329517475 absolute error = 6.661338147750939e-16 relative error = 9.661136022070002e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.7242871743701427 y2[1] (numeric) = -0.724287174370142 absolute error = 6.661338147750939e-16 relative error = 9.197095273078385e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000003 y1[1] (closed_form) = -0.6822212072876134 y1[1] (numeric) = -0.6822212072876142 absolute error = 7.771561172376096e-16 relative error = 1.139155612484461e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.7311458297268961 y2[1] (numeric) = -0.7311458297268951 absolute error = 9.992007221626409e-16 relative error = 1.366623020384143e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000003 y1[1] (closed_form) = -0.6748757600712669 y1[1] (numeric) = -0.6748757600712677 absolute error = 7.771561172376096e-16 relative error = 1.151554350026651e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.7379313711099629 y2[1] (numeric) = -0.7379313711099619 absolute error = 9.992007221626409e-16 relative error = 1.354056435708497e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000003 y1[1] (closed_form) = -0.6674628258413079 y1[1] (numeric) = -0.6674628258413087 absolute error = 7.771561172376096e-16 relative error = 1.16434367151165e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.7446431199708595 y2[1] (numeric) = -0.7446431199708584 absolute error = 1.110223024625157e-15 relative error = 1.490946461264026e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000003 y1[1] (closed_form) = -0.659983145884982 y1[1] (numeric) = -0.6599831458849826 absolute error = 6.661338147750939e-16 relative error = 1.00931943327411e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.7512804051402929 y2[1] (numeric) = -0.7512804051402919 absolute error = 9.992007221626409e-16 relative error = 1.329997049471897e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000003 y1[1] (closed_form) = -0.6524374681640516 y1[1] (numeric) = -0.6524374681640522 absolute error = 6.661338147750939e-16 relative error = 1.020992581326734e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.7578425628952772 y2[1] (numeric) = -0.7578425628952762 absolute error = 9.992007221626409e-16 relative error = 1.318480606770454e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000003 y1[1] (closed_form) = -0.644826547240001 y1[1] (numeric) = -0.6448265472400015 absolute error = 5.551115123125783e-16 relative error = 8.608695077592218e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.7643289370255053 y2[1] (numeric) = -0.7643289370255043 absolute error = 9.992007221626409e-16 relative error = 1.307291499457253e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000003 y1[1] (closed_form) = -0.63715114419858 y1[1] (numeric) = -0.6371511441985805 absolute error = 5.551115123125783e-16 relative error = 8.712399206483532e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.7707388788989695 y2[1] (numeric) = -0.7707388788989685 absolute error = 9.992007221626409e-16 relative error = 1.296419253677767e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000003 y1[1] (closed_form) = -0.6294120265736967 y1[1] (numeric) = -0.6294120265736971 absolute error = 4.440892098500626e-16 relative error = 7.055620024732162e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.7770717475268241 y2[1] (numeric) = -0.777071747526823 absolute error = 1.110223024625157e-15 relative error = 1.428726534143917e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000004 y1[1] (closed_form) = -0.6216099682706642 y1[1] (numeric) = -0.6216099682706648 absolute error = 6.661338147750939e-16 relative error = 1.071626661052905e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.7833269096274836 y2[1] (numeric) = -0.7833269096274824 absolute error = 1.221245327087672e-15 relative error = 1.559049372717763e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000004 y1[1] (closed_form) = -0.6137457494888112 y1[1] (numeric) = -0.6137457494888121 absolute error = 8.881784197001252e-16 relative error = 1.447143903546198e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.7895037396899507 y2[1] (numeric) = -0.7895037396899495 absolute error = 1.221245327087672e-15 relative error = 1.546851858570388e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000004 y1[1] (closed_form) = -0.6058201566434626 y1[1] (numeric) = -0.6058201566434633 absolute error = 7.771561172376096e-16 relative error = 1.282816540049495e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.7956016200363663 y2[1] (numeric) = -0.795601620036365 absolute error = 1.221245327087672e-15 relative error = 1.534996028580045e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000004 y1[1] (closed_form) = -0.5978339822872979 y1[1] (numeric) = -0.5978339822872987 absolute error = 7.771561172376096e-16 relative error = 1.299953064334399e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.8016199408837774 y2[1] (numeric) = -0.8016199408837763 absolute error = 1.110223024625157e-15 relative error = 1.384974310146461e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000004 y1[1] (closed_form) = -0.589788025031098 y1[1] (numeric) = -0.5897880250310985 absolute error = 5.551115123125783e-16 relative error = 9.412051258302654e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.8075581004051146 y2[1] (numeric) = -0.8075581004051136 absolute error = 9.992007221626409e-16 relative error = 1.237311249384271e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000004 y1[1] (closed_form) = -0.5816830894638831 y1[1] (numeric) = -0.5816830894638838 absolute error = 6.661338147750939e-16 relative error = 1.145183394258626e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.813415504789374 y2[1] (numeric) = -0.8134155047893731 absolute error = 8.881784197001252e-16 relative error = 1.091912330746769e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000004 y1[1] (closed_form) = -0.5735199860724564 y1[1] (numeric) = -0.573519986072457 absolute error = 6.661338147750939e-16 relative error = 1.161483175742261e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.8191915683009985 y2[1] (numeric) = -0.8191915683009975 absolute error = 9.992007221626409e-16 relative error = 1.21973999834371e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000004 y1[1] (closed_form) = -0.5652995311603539 y1[1] (numeric) = -0.5652995311603546 absolute error = 6.661338147750939e-16 relative error = 1.178373195193996e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.8248857133384503 y2[1] (numeric) = -0.8248857133384495 absolute error = 7.771561172376096e-16 relative error = 9.421379285287036e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000004 y1[1] (closed_form) = -0.557022546766217 y1[1] (numeric) = -0.5570225467662178 absolute error = 7.771561172376096e-16 relative error = 1.39519687622947e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.8304973704919707 y2[1] (numeric) = -0.8304973704919698 absolute error = 8.881784197001252e-16 relative error = 1.069453620514157e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000004 y1[1] (closed_form) = -0.5486898605815872 y1[1] (numeric) = -0.5486898605815881 absolute error = 8.881784197001252e-16 relative error = 1.618725774809644e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.8360259786005207 y2[1] (numeric) = -0.8360259786005199 absolute error = 8.881784197001252e-16 relative error = 1.062381364257252e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1 y1[1] (closed_form) = -0.5403023058681393 y1[1] (numeric) = -0.5403023058681404 absolute error = 1.110223024625157e-15 relative error = 2.054818224107499e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.8414709848078967 y2[1] (numeric) = -0.8414709848078957 absolute error = 9.992007221626409e-16 relative error = 1.187445247908046e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.009999999999999 y1[1] (closed_form) = -0.531860721374356 y1[1] (numeric) = -0.5318607213743562 absolute error = 2.220446049250313e-16 relative error = 4.174863756647725e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = -0.8468318446180149 y2[1] (numeric) = -0.8468318446180144 absolute error = 4.440892098500626e-16 relative error = 5.244125060629722e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y1[1] (closed_form) = -0.5233659512516511 y1[1] (numeric) = -0.5233659512516503 absolute error = 7.771561172376096e-16 relative error = 1.484919138088767e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.852108021949362 y2[1] (numeric) = -0.8521080219493622 absolute error = 2.220446049250313e-16 relative error = 2.605826951576648e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y1[1] (closed_form) = -0.5148188449699578 y1[1] (numeric) = -0.5148188449699561 absolute error = 1.665334536937735e-15 relative error = 3.234797158668337e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.8572989891886019 y2[1] (numeric) = -0.8572989891886026 absolute error = 6.661338147750939e-16 relative error = 7.770145808821751e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y1[1] (closed_form) = -0.5062202572327819 y1[1] (numeric) = -0.5062202572327791 absolute error = 2.775557561562891e-15 relative error = 5.482904964600361e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.8624042272433364 y2[1] (numeric) = -0.8624042272433377 absolute error = 1.221245327087672e-15 relative error = 1.416093855420174e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y1[1] (closed_form) = -0.4975710478917314 y1[1] (numeric) = -0.4975710478917277 absolute error = 3.663735981263017e-15 relative error = 7.363241886333034e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.8674232255940144 y2[1] (numeric) = -0.8674232255940163 absolute error = 1.887379141862766e-15 relative error = 2.175845753461676e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y1[1] (closed_form) = -0.4888720818605329 y1[1] (numeric) = -0.4888720818605283 absolute error = 4.6074255521944e-15 relative error = 9.424603537718117e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.8723554823449833 y2[1] (numeric) = -0.8723554823449857 absolute error = 2.442490654175344e-15 relative error = 2.799879984257877e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y1[1] (closed_form) = -0.4801242290285405 y1[1] (numeric) = -0.4801242290285348 absolute error = 5.717648576819556e-15 relative error = 1.190868577573842e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.8772005042746781 y2[1] (numeric) = -0.8772005042746809 absolute error = 2.775557561562891e-15 relative error = 3.164108488352829e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y1[1] (closed_form) = -0.4713283641737474 y1[1] (numeric) = -0.4713283641737406 absolute error = 6.772360450213455e-15 relative error = 1.436866729225092e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.8819578068849435 y2[1] (numeric) = -0.8819578068849467 absolute error = 3.219646771412954e-15 relative error = 3.65056780072584e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y1[1] (closed_form) = -0.4624853668753093 y1[1] (numeric) = -0.4624853668753016 absolute error = 7.716050021144838e-15 relative error = 1.668387926147113e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.8866269144494828 y2[1] (numeric) = -0.8866269144494865 absolute error = 3.663735981263017e-15 relative error = 4.132218322672816e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.099999999999989 y1[1] (closed_form) = -0.4535961214255868 y1[1] (numeric) = -0.4535961214255781 absolute error = 8.715250743307479e-15 relative error = 1.921368003746749e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.8912073600614305 y2[1] (numeric) = -0.8912073600614348 absolute error = 4.218847493575595e-15 relative error = 4.733856207476554e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999988 y1[1] (closed_form) = -0.4446615167417173 y1[1] (numeric) = -0.4446615167417075 absolute error = 9.769962616701378e-15 relative error = 2.19716846384444e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.8956986856800424 y2[1] (numeric) = -0.8956986856800472 absolute error = 4.773959005888173e-15 relative error = 5.329871621128521e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y1[1] (closed_form) = -0.4356824462767236 y1[1] (numeric) = -0.4356824462767129 absolute error = 1.076916333886402e-14 relative error = 2.471791882114063e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.9001004421764994 y2[1] (numeric) = -0.9001004421765043 absolute error = 4.884981308350689e-15 relative error = 5.427151326065897e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y1[1] (closed_form) = -0.4266598079301698 y1[1] (numeric) = -0.426659807930158 absolute error = 1.187938636348917e-14 relative error = 2.784275936634144e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.90441218937882 y2[1] (numeric) = -0.9044121893788253 absolute error = 5.329070518200751e-15 relative error = 5.892302846847887e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y1[1] (closed_form) = -0.4175945039583717 y1[1] (numeric) = -0.4175945039583588 absolute error = 1.293409823688307e-14 relative error = 3.097286509827347e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.908633496115877 y2[1] (numeric) = -0.9086334961158825 absolute error = 5.551115123125783e-15 relative error = 6.109300556115373e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y1[1] (closed_form) = -0.408487440884172 y1[1] (numeric) = -0.4084874408841579 absolute error = 1.404432126150823e-14 relative error = 3.438128044061591e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.9127639402605146 y2[1] (numeric) = -0.9127639402605202 absolute error = 5.662137425588298e-15 relative error = 6.203287811712031e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y1[1] (closed_form) = -0.3993395294062889 y1[1] (numeric) = -0.3993395294062738 absolute error = 1.509903313490213e-14 relative error = 3.781001384298307e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.9168031087717601 y2[1] (numeric) = -0.9168031087717661 absolute error = 5.995204332975845e-15 relative error = 6.53924956799897e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y1[1] (closed_form) = -0.390151684308247 y1[1] (numeric) = -0.3901516843082309 absolute error = 1.615374500829603e-14 relative error = 4.140375566220404e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.9207505977361286 y2[1] (numeric) = -0.9207505977361349 absolute error = 6.328271240363392e-15 relative error = 6.872948283631706e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y1[1] (closed_form) = -0.3809248243668997 y1[1] (numeric) = -0.3809248243668824 absolute error = 1.726396803292118e-14 relative error = 4.532119444201109e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.924606012408013 y2[1] (numeric) = -0.9246060124080195 absolute error = 6.550315845288424e-15 relative error = 7.084440028925402e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y1[1] (closed_form) = -0.371659872260552 y1[1] (numeric) = -0.3716598722605336 absolute error = 1.837419105754634e-14 relative error = 4.94381891318768e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.9283689672491591 y2[1] (numeric) = -0.9283689672491661 absolute error = 6.994405055138486e-15 relative error = 7.53407890815603e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999978 y1[1] (closed_form) = -0.3623577544766937 y1[1] (numeric) = -0.3623577544766742 absolute error = 1.94844140821715e-14 relative error = 5.377120771241755e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.9320390859672185 y2[1] (numeric) = -0.9320390859672257 absolute error = 7.216449660063518e-15 relative error = 7.742647029201233e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999977 y1[1] (closed_form) = -0.3530194012193515 y1[1] (numeric) = -0.3530194012193311 absolute error = 2.048361480433414e-14 relative error = 5.802404834856788e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.9356160015533779 y2[1] (numeric) = -0.9356160015533852 absolute error = 7.327471962526033e-15 relative error = 7.831708682152112e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y1[1] (closed_form) = -0.3436457463160694 y1[1] (numeric) = -0.3436457463160478 absolute error = 2.159383782895929e-14 relative error = 6.283749489248235e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.9390993563190594 y2[1] (numeric) = -0.9390993563190669 absolute error = 7.549516567451064e-15 relative error = 8.039103122211185e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y1[1] (closed_form) = -0.334237727124526 y1[1] (numeric) = -0.3342377271245034 absolute error = 2.264854970235319e-14 relative error = 6.776179905602064e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.9424888019316892 y2[1] (numeric) = -0.9424888019316968 absolute error = 7.66053886991358e-15 relative error = 8.127989270761447e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y1[1] (closed_form) = -0.3247962844388008 y1[1] (numeric) = -0.324796284438777 absolute error = 2.381428387820961e-14 relative error = 7.332067828102502e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.9457839994495305 y2[1] (numeric) = -0.9457839994495384 absolute error = 7.882583474838611e-15 relative error = 8.334443677865631e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y1[1] (closed_form) = -0.3153223623952944 y1[1] (numeric) = -0.3153223623952693 absolute error = 2.503552920529728e-14 relative error = 7.939661816281917e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.9489846193555777 y2[1] (numeric) = -0.9489846193555855 absolute error = 7.882583474838611e-15 relative error = 8.306334279886853e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y1[1] (closed_form) = -0.3058169083783162 y1[1] (numeric) = -0.30581690837829 absolute error = 2.620126338115369e-14 relative error = 8.567630717377132e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.9520903415905071 y2[1] (numeric) = -0.9520903415905149 absolute error = 7.771561172376096e-15 relative error = 8.162629986765095e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y1[1] (closed_form) = -0.2962808729253467 y1[1] (numeric) = -0.2962808729253194 absolute error = 2.731148640577885e-14 relative error = 9.218106500131876e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.9551008555846836 y2[1] (numeric) = -0.9551008555846914 absolute error = 7.771561172376096e-15 relative error = 8.136901068545879e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y1[1] (closed_form) = -0.2867152096319847 y1[1] (numeric) = -0.2867152096319562 absolute error = 2.847722058163527e-14 relative error = 9.932232272639949e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.9580158602892163 y2[1] (numeric) = -0.9580158602892241 absolute error = 7.882583474838611e-15 relative error = 8.228030246241363e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y1[1] (closed_form) = -0.2771208750565879 y1[1] (numeric) = -0.2771208750565584 absolute error = 2.953193245502916e-14 relative error = 1.065669717194663e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9608350642060639 y2[1] (numeric) = -0.9608350642060719 absolute error = 7.993605777301127e-15 relative error = 8.319435952211244e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999967 y1[1] (closed_form) = -0.2674988286246188 y1[1] (numeric) = -0.2674988286245882 absolute error = 3.064215547965432e-14 relative error = 1.1455061555673e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9635581854171843 y2[1] (numeric) = -0.9635581854171922 absolute error = 7.882583474838611e-15 relative error = 8.180703141892516e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999966 y1[1] (closed_form) = -0.2578500325327022 y1[1] (numeric) = -0.2578500325326705 absolute error = 3.169686735304822e-14 relative error = 1.229275290047839e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9661849516127253 y2[1] (numeric) = -0.9661849516127333 absolute error = 7.993605777301127e-15 relative error = 8.273370190622875e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y1[1] (closed_form) = -0.2481754516524067 y1[1] (numeric) = -0.2481754516523738 absolute error = 3.286260152890463e-14 relative error = 1.324168096002172e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9687151001182567 y2[1] (numeric) = -0.9687151001182644 absolute error = 7.771561172376096e-15 relative error = 8.022545711765385e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y1[1] (closed_form) = -0.2384760534337581 y1[1] (numeric) = -0.2384760534337241 absolute error = 3.397282455352979e-14 relative error = 1.424580123008723e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.971148377921036 y2[1] (numeric) = -0.9711483779210439 absolute error = 7.882583474838611e-15 relative error = 8.116765320365436e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y1[1] (closed_form) = -0.2287528078084955 y1[1] (numeric) = -0.2287528078084604 absolute error = 3.511080315377058e-14 relative error = 1.5348796585336e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.973484541695311 y2[1] (numeric) = -0.9734845416953186 absolute error = 7.66053886991358e-15 relative error = 7.86919415954243e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y1[1] (closed_form) = -0.2190066870930788 y1[1] (numeric) = -0.2190066870930426 absolute error = 3.622102617839573e-14 relative error = 1.653877635389354e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9757233578266508 y2[1] (numeric) = -0.9757233578266584 absolute error = 7.66053886991358e-15 relative error = 7.85113814122155e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y1[1] (closed_form) = -0.2092386658914577 y1[1] (numeric) = -0.2092386658914203 absolute error = 3.738676035425215e-14 relative error = 1.786799786500574e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9778646024353079 y2[1] (numeric) = -0.9778646024353156 absolute error = 7.66053886991358e-15 relative error = 7.833946387705935e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y1[1] (closed_form) = -0.1994497209976125 y1[1] (numeric) = -0.199449720997574 absolute error = 3.84969833788773e-14 relative error = 1.930159800992559e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9799080613986062 y2[1] (numeric) = -0.9799080613986136 absolute error = 7.438494264988549e-15 relative error = 7.591012420462907e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y1[1] (closed_form) = -0.189640831297875 y1[1] (numeric) = -0.1896408312978354 absolute error = 3.963496197911809e-14 relative error = 2.090001489018057e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9818535303723519 y2[1] (numeric) = -0.9818535303723591 absolute error = 7.216449660063518e-15 relative error = 7.349822999899789e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999957 y1[1] (closed_form) = -0.1798129776730413 y1[1] (numeric) = -0.1798129776730005 absolute error = 4.08006961549745e-14 relative error = 2.269062927658286e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9837008148112689 y2[1] (numeric) = -0.9837008148112761 absolute error = 7.216449660063518e-15 relative error = 7.336020821989512e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999956 y1[1] (closed_form) = -0.1699671429002839 y1[1] (numeric) = -0.169967142900242 absolute error = 4.193867475521529e-14 relative error = 2.467457770930456e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9854497299884528 y2[1] (numeric) = -0.9854497299884598 absolute error = 6.994405055138486e-15 relative error = 7.097678189247101e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999955 y1[1] (closed_form) = -0.1601043115548753 y1[1] (numeric) = -0.1601043115548322 absolute error = 4.307665335545607e-14 relative error = 2.690536746769101e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9871001010138432 y2[1] (numeric) = -0.98710010101385 absolute error = 6.883382752675971e-15 relative error = 6.973338109889868e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y1[1] (closed_form) = -0.1502254699117311 y1[1] (numeric) = -0.1502254699116868 absolute error = 4.421463195569686e-14 relative error = 2.943218082904073e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9886517628517129 y2[1] (numeric) = -0.9886517628517195 absolute error = 6.661338147750939e-15 relative error = 6.737800303452317e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y1[1] (closed_form) = -0.1403316058467831 y1[1] (numeric) = -0.1403316058467377 absolute error = 4.538036613155327e-14 relative error = 3.233795113917564e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9901045603371712 y2[1] (numeric) = -0.9901045603371773 absolute error = 6.106226635438361e-15 relative error = 6.167254328531666e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y1[1] (closed_form) = -0.1304237087381931 y1[1] (numeric) = -0.1304237087381465 absolute error = 4.654610030740969e-14 relative error = 3.568837350028461e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9914583481916802 y2[1] (numeric) = -0.9914583481916861 absolute error = 5.88418203051333e-15 relative error = 5.934875672029473e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y1[1] (closed_form) = -0.1205027693674153 y1[1] (numeric) = -0.1205027693673676 absolute error = 4.768407890765047e-14 relative error = 3.957094028458448e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9927129910375826 y2[1] (numeric) = -0.9927129910375881 absolute error = 5.551115123125783e-15 relative error = 5.59186307950273e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y1[1] (closed_form) = -0.1105697798201195 y1[1] (numeric) = -0.1105697798200706 absolute error = 4.883593529569907e-14 relative error = 4.416752513674881e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9938683634116393 y2[1] (numeric) = -0.9938683634116444 absolute error = 5.10702591327572e-15 relative error = 5.138533533500248e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y1[1] (closed_form) = -0.1006257333869828 y1[1] (numeric) = -0.1006257333869328 absolute error = 4.996003610813204e-14 relative error = 4.964936346451019e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9949243497775757 y2[1] (numeric) = -0.9949243497775805 absolute error = 4.773959005888173e-15 relative error = 4.798313567212858e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y1[1] (closed_form) = -0.09067162446436186 y1[1] (numeric) = -0.09067162446431076 absolute error = 5.109801470837283e-14 relative error = 5.635502287538337e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9958808445376353 y2[1] (numeric) = -0.9958808445376396 absolute error = 4.329869796038111e-15 relative error = 4.347778973546147e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999946 y1[1] (closed_form) = -0.08070844845485396 y1[1] (numeric) = -0.0807084484548017 absolute error = 5.226374888422924e-14 relative error = 6.475623046261894e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9967377520431391 y2[1] (numeric) = -0.9967377520431427 absolute error = 3.663735981263017e-15 relative error = 3.675727114532378e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999945 y1[1] (closed_form) = -0.07073720166775739 y1[1] (numeric) = -0.07073720166770402 absolute error = 5.33739719088544e-14 relative error = 7.545389222427031e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9974949866040506 y2[1] (numeric) = -0.9974949866040539 absolute error = 3.33066907387547e-15 relative error = 3.339033397265141e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y1[1] (closed_form) = -0.06075888121944153 y1[1] (numeric) = -0.06075888121938701 absolute error = 5.451888940299909e-14 relative error = 8.972990994698275e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9981524724975447 y2[1] (numeric) = -0.9981524724975477 absolute error = 2.997602166487923e-15 relative error = 3.003150569759568e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y1[1] (closed_form) = -0.05077448493363595 y1[1] (numeric) = -0.05077448493358031 absolute error = 5.564299021543206e-14 relative error = 1.095884877771964e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = -0.9987101439755801 y2[1] (numeric) = -0.9987101439755824 absolute error = 2.331468351712829e-15 relative error = 2.334479494152246e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y1[1] (closed_form) = -0.04078501124164894 y1[1] (numeric) = -0.04078501124159217 absolute error = 5.677402992176894e-14 relative error = 1.392031734045283e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = -0.9991679452714737 y2[1] (numeric) = -0.9991679452714756 absolute error = 1.887379141862766e-15 relative error = 1.888950852351419e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y1[1] (closed_form) = -0.03079145908252516 y1[1] (numeric) = -0.03079145908246727 absolute error = 5.78842529463941e-14 relative error = 1.87988015739224e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = -0.9995258306054773 y2[1] (numeric) = -0.9995258306054785 absolute error = 1.221245327087672e-15 relative error = 1.221824678955906e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y1[1] (closed_form) = -0.02079482780315259 y1[1] (numeric) = -0.02079482780309359 absolute error = 5.899794541797121e-14 relative error = 2.837145177467007e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = -0.9997837641893557 y2[1] (numeric) = -0.9997837641893563 absolute error = 6.661338147750939e-16 relative error = 6.662778879143015e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y1[1] (closed_form) = -0.01079611705832867 y1[1] (numeric) = -0.01079611705826857 absolute error = 6.010643371912039e-14 relative error = 5.567412190362575e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = -0.9999417202299656 y2[1] (numeric) = -0.9999417202299657 absolute error = 1.110223024625157e-16 relative error = 1.110287731938846e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y1[1] (closed_form) = -0.0007963267107956579 y1[1] (numeric) = -0.00079632671073445 absolute error = 6.120787470614841e-14 relative error = 7.686276734958688e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 y2[1] (closed_form) = -0.9999996829318346 y2[1] (numeric) = -0.9999996829318342 absolute error = 4.440892098500626e-16 relative error = 4.440893506566583e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999937 y1[1] (closed_form) = 0.009203543268744833 y1[1] (numeric) = 0.009203543268807134 absolute error = 6.230085891623105e-14 relative error = 6.76922540558964e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = -0.9999576464987406 y2[1] (numeric) = -0.9999576464987394 absolute error = 1.221245327087672e-15 relative error = 1.221297053293957e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999935 y1[1] (closed_form) = 0.01920249290162804 y1[1] (numeric) = 0.01920249290169143 absolute error = 6.339026525914448e-14 relative error = 3.301147699097447e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = -0.9998156151342921 y2[1] (numeric) = -0.9998156151342902 absolute error = 1.887379141862766e-15 relative error = 1.88772721019091e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999934 y1[1] (closed_form) = 0.02919952230122312 y1[1] (numeric) = 0.02919952230128759 absolute error = 6.446926326120206e-14 relative error = 2.207887601589344e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = -0.9995736030415071 y2[1] (numeric) = -0.9995736030415043 absolute error = 2.775557561562891e-15 relative error = 2.77674155571677e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y1[1] (closed_form) = 0.03919363177292092 y1[1] (numeric) = 0.03919363177298646 absolute error = 6.553785292240377e-14 relative error = 1.672155652788579e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = -0.9992316344213932 y2[1] (numeric) = -0.9992316344213897 absolute error = 3.441691376337985e-15 relative error = 3.444337887011456e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y1[1] (closed_form) = 0.04918382191410269 y1[1] (numeric) = 0.04918382191416928 absolute error = 6.659256479579767e-14 relative error = 1.353952625155861e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = -0.9987897434705274 y2[1] (numeric) = -0.9987897434705233 absolute error = 4.107825191113079e-15 relative error = 4.112802737480548e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y1[1] (closed_form) = 0.05916909371407943 y1[1] (numeric) = 0.05916909371414707 absolute error = 6.764033777528766e-14 relative error = 1.143170083052877e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = -0.9982479743776366 y2[1] (numeric) = -0.9982479743776319 absolute error = 4.662936703425657e-15 relative error = 4.671120626448346e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y1[1] (closed_form) = 0.06914844865399217 y1[1] (numeric) = 0.06914844865406085 absolute error = 6.868117186087375e-14 relative error = 9.932424110415463e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9976063813191786 y2[1] (numeric) = -0.9976063813191731 absolute error = 5.440092820663267e-15 relative error = 5.453145571773102e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999929 y1[1] (closed_form) = 0.07912088880666303 y1[1] (numeric) = 0.07912088880673275 absolute error = 6.972200594645983e-14 relative error = 8.812085783923639e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9968650284539244 y2[1] (numeric) = -0.9968650284539181 absolute error = 6.328271240363392e-15 relative error = 6.348172580773694e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999928 y1[1] (closed_form) = 0.08908541693638708 y1[1] (numeric) = 0.08908541693645784 absolute error = 7.076284003204591e-14 relative error = 7.943257433770029e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9960239899165432 y2[1] (numeric) = -0.9960239899165361 absolute error = 7.105427357601002e-15 relative error = 7.133791384077371e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999927 y1[1] (closed_form) = 0.0990410365986551 y1[1] (numeric) = 0.0990410365987269 absolute error = 7.1803674117632e-14 relative error = 7.249891215153844e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9950833498101874 y2[1] (numeric) = -0.9950833498101795 absolute error = 7.882583474838611e-15 relative error = 7.92153087109961e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999926 y1[1] (closed_form) = 0.1089867522397972 y1[1] (numeric) = 0.10898675223987 absolute error = 7.283063041541027e-14 relative error = 6.682521399955593e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9940432021980841 y2[1] (numeric) = -0.9940432021980755 absolute error = 8.548717289613705e-15 relative error = 8.599945425621646e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999924 y1[1] (closed_form) = 0.1189215692965373 y1[1] (numeric) = 0.1189215692966111 absolute error = 7.38159533497651e-14 relative error = 6.207112283029253e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9929036510941275 y2[1] (numeric) = -0.992903651094118 absolute error = 9.436895709313831e-15 relative error = 9.504341835096355e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999923 y1[1] (closed_form) = 0.1288444942954487 y1[1] (numeric) = 0.1288444942955235 absolute error = 7.482903185973555e-14 relative error = 5.807701157035689e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9916648104524785 y2[1] (numeric) = -0.9916648104524681 absolute error = 1.032507412901396e-14 relative error = 1.041185894687824e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y1[1] (closed_form) = 0.1387545349523006 y1[1] (numeric) = 0.1387545349523764 absolute error = 7.580047700628256e-14 relative error = 5.4629188899909e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9903268041561688 y2[1] (numeric) = -0.9903268041561576 absolute error = 1.121325254871408e-14 relative error = 1.132278001731822e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y1[1] (closed_form) = 0.1486507002712857 y1[1] (numeric) = 0.1486507002713625 absolute error = 7.67996777284452e-14 relative error = 5.166452467986141e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9888897660047132 y2[1] (numeric) = -0.9888897660047011 absolute error = 1.210143096841421e-14 relative error = 1.22373912486789e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y1[1] (closed_form) = 0.1585320006441188 y1[1] (numeric) = 0.1585320006441966 absolute error = 7.777112287499222e-14 relative error = 4.905705003343585e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9873538397007291 y2[1] (numeric) = -0.9873538397007162 absolute error = 1.287858708565182e-14 relative error = 1.304353775497077e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y1[1] (closed_form) = 0.1683974479489971 y1[1] (numeric) = 0.1683974479490759 absolute error = 7.877032359715486e-14 relative error = 4.677643548435021e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9857191788355671 y2[1] (numeric) = -0.9857191788355534 absolute error = 1.376676550535194e-14 relative error = 1.396621451721642e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999918 y1[1] (closed_form) = 0.1782460556494113 y1[1] (numeric) = 0.1782460556494909 absolute error = 7.968625759247061e-14 relative error = 4.470576210067951e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9839859468739516 y2[1] (numeric) = -0.9839859468739367 absolute error = 1.48769885299771e-14 relative error = 1.511910670801769e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999917 y1[1] (closed_form) = 0.1880768388927983 y1[1] (numeric) = 0.1880768388928789 absolute error = 8.060219158778636e-14 relative error = 4.285599016991598e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9821543171376341 y2[1] (numeric) = -0.9821543171376182 absolute error = 1.587618925213974e-14 relative error = 1.616465862351337e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999916 y1[1] (closed_form) = 0.1978888146090263 y1[1] (numeric) = 0.1978888146091078 absolute error = 8.154588115871775e-14 relative error = 4.120792846216696e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9802244727880621 y2[1] (numeric) = -0.9802244727880451 absolute error = 1.69864122767649e-14 relative error = 1.732910445344246e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999915 y1[1] (closed_form) = 0.2076810016087002 y1[1] (numeric) = 0.2076810016087826 absolute error = 8.240630400280224e-14 relative error = 3.967926934311842e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9781966068080624 y2[1] (numeric) = -0.9781966068080442 absolute error = 1.820765760385257e-14 relative error = 1.861349495298873e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999913 y1[1] (closed_form) = 0.2174524206812801 y1[1] (numeric) = 0.2174524206813634 absolute error = 8.329448242250237e-14 relative error = 3.830469311932243e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.976070921982543 y2[1] (numeric) = -0.9760709219825237 absolute error = 1.931788062847772e-14 relative error = 1.979147231354898e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999912 y1[1] (closed_form) = 0.2272020946930017 y1[1] (numeric) = 0.2272020946930859 absolute error = 8.421041641781812e-14 relative error = 3.706410212969396e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9738476308782151 y2[1] (numeric) = -0.9738476308781947 absolute error = 2.042810365310288e-14 relative error = 2.097669389479423e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y1[1] (closed_form) = 0.2369290486845884 y1[1] (numeric) = 0.2369290486846735 absolute error = 8.507083926190262e-14 relative error = 3.590561804650349e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9715269558223364 y2[1] (numeric) = -0.9715269558223149 absolute error = 2.153832667772804e-14 relative error = 2.216956158411189e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y1[1] (closed_form) = 0.2466323099687469 y1[1] (numeric) = 0.2466323099688328 absolute error = 8.590350653037149e-14 relative error = 3.483059723247823e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9691091288804785 y2[1] (numeric) = -0.9691091288804559 absolute error = 2.264854970235319e-14 relative error = 2.337048432153039e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y1[1] (closed_form) = 0.2563109082274347 y1[1] (numeric) = 0.2563109082275214 absolute error = 8.665290707199347e-14 relative error = 3.380773283168383e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.966594391833321 y2[1] (numeric) = -0.966594391833297 absolute error = 2.398081733190338e-14 relative error = 2.48095970083371e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999908 y1[1] (closed_form) = 0.2659638756088916 y1[1] (numeric) = 0.2659638756089791 absolute error = 8.748557434046234e-14 relative error = 3.2893780834023e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9639829961524726 y2[1] (numeric) = -0.9639829961524476 absolute error = 2.498001805406602e-14 relative error = 2.591333888021708e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999907 y1[1] (closed_form) = 0.2755902468244233 y1[1] (numeric) = 0.2755902468245117 absolute error = 8.842926391139372e-14 relative error = 3.208722548433704e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9612752029753256 y2[1] (numeric) = -0.9612752029752994 absolute error = 2.620126338115369e-14 relative error = 2.725677651941495e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999906 y1[1] (closed_form) = 0.2851890592449304 y1[1] (numeric) = 0.2851890592450196 absolute error = 8.920642002863133e-14 relative error = 3.127974834126358e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.958471283078941 y2[1] (numeric) = -0.9584712830789136 absolute error = 2.742250870824137e-14 relative error = 2.861067325893249e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999905 y1[1] (closed_form) = 0.2947593529971698 y1[1] (numeric) = 0.2947593529972597 absolute error = 8.992806499463768e-14 relative error = 3.050897760502994e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.955571516852972 y2[1] (numeric) = -0.9555715168529434 absolute error = 2.864375403532904e-14 relative error = 2.997552096326902e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999904 y1[1] (closed_form) = 0.3043001710597414 y1[1] (numeric) = 0.3043001710598321 absolute error = 9.070522111187529e-14 relative error = 2.980781141068359e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9525761942716248 y2[1] (numeric) = -0.9525761942715947 absolute error = 3.008704396734174e-14 relative error = 3.158492113100456e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999902 y1[1] (closed_form) = 0.3138105593587897 y1[1] (numeric) = 0.3138105593588812 absolute error = 9.14823772291129e-14 relative error = 2.915210291713548e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9494856148646611 y2[1] (numeric) = -0.9494856148646297 absolute error = 3.141931159689193e-14 relative error = 3.309087689692951e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999901 y1[1] (closed_form) = 0.32328956686341 y1[1] (numeric) = 0.3232895668635023 absolute error = 9.225953334635051e-14 relative error = 2.85377391672309e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9463000876874464 y2[1] (numeric) = -0.9463000876874137 absolute error = 3.275157922644212e-14 relative error = 3.46101407498333e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y1[1] (closed_form) = 0.3327362456807512 y1[1] (numeric) = 0.3327362456808441 absolute error = 9.298117831235686e-14 relative error = 2.79444092789245e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9430199312900437 y2[1] (numeric) = -0.9430199312900098 absolute error = 3.386180225106727e-14 relative error = 3.590783304520892e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y1[1] (closed_form) = 0.3421496511508034 y1[1] (numeric) = 0.3421496511508971 absolute error = 9.370282327836321e-14 relative error = 2.738650264970267e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9396454736853594 y2[1] (numeric) = -0.9396454736853243 absolute error = 3.519406988061746e-14 relative error = 3.745462609699348e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y1[1] (closed_form) = 0.3515288419408644 y1[1] (numeric) = 0.3515288419409588 absolute error = 9.442446824436956e-14 relative error = 2.686108705135894e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9361770523163419 y2[1] (numeric) = -0.9361770523163054 absolute error = 3.641531520770513e-14 relative error = 3.889789342475797e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999897 y1[1] (closed_form) = 0.3608728801396711 y1[1] (numeric) = 0.3608728801397662 absolute error = 9.509060205914466e-14 relative error = 2.63501657487648e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9326150140222377 y2[1] (numeric) = -0.9326150140222 absolute error = 3.763656053479281e-14 relative error = 4.035594534605614e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999896 y1[1] (closed_form) = 0.3701808313511901 y1[1] (numeric) = 0.3701808313512859 absolute error = 9.581224702515101e-14 relative error = 2.58825522314131e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9289597150039078 y2[1] (numeric) = -0.9289597150038691 absolute error = 3.874678355941796e-14 relative error = 4.170986419928335e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999895 y1[1] (closed_form) = 0.3794517647880571 y1[1] (numeric) = 0.3794517647881535 absolute error = 9.636735853746359e-14 relative error = 2.539647129887236e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9252115207882082 y2[1] (numeric) = -0.925211520788168 absolute error = 4.019007349143067e-14 relative error = 4.343879490085883e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999894 y1[1] (closed_form) = 0.388684753364654 y1[1] (numeric) = 0.388684753364751 absolute error = 9.697798120100742e-14 relative error = 2.495029207127792e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9213708061914367 y2[1] (numeric) = -0.9213708061913952 absolute error = 4.152234112098085e-14 relative error = 4.506583108772126e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999893 y1[1] (closed_form) = 0.3978788737898173 y1[1] (numeric) = 0.3978788737899149 absolute error = 9.758860386455126e-14 relative error = 2.452721425870508e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9174379552818526 y2[1] (numeric) = -0.9174379552818096 absolute error = 4.296563105299356e-14 relative error = 4.683219263562492e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999891 y1[1] (closed_form) = 0.4070332066591664 y1[1] (numeric) = 0.4070332066592645 absolute error = 9.808820422563258e-14 relative error = 2.409832972368955e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9134133613412694 y2[1] (numeric) = -0.913413361341225 absolute error = 4.440892098500626e-14 relative error = 4.861864612949778e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.99999999999989 y1[1] (closed_form) = 0.4161468365470427 y1[1] (numeric) = 0.4161468365471414 absolute error = 9.869882688917642e-14 relative error = 2.371730798391379e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9092974268257273 y2[1] (numeric) = -0.9092974268256816 absolute error = 4.574118861455645e-14 relative error = 5.03038799683341e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.009999999999889 y1[1] (closed_form) = 0.4252188520980521 y1[1] (numeric) = 0.4252188520981513 absolute error = 9.919842725025774e-14 relative error = 2.332879334037226e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9050905633252481 y2[1] (numeric) = -0.9050905633252009 absolute error = 4.718447854656915e-14 relative error = 5.21323284746404e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999888 y1[1] (closed_form) = 0.4342483461181997 y1[1] (numeric) = 0.4342483461182994 absolute error = 9.975353876257032e-14 relative error = 2.297154143574286e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.9007931915226759 y2[1] (numeric) = -0.9007931915226274 absolute error = 4.851674617611934e-14 relative error = 5.386002762088818e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999887 y1[1] (closed_form) = 0.4432344156656078 y1[1] (numeric) = 0.443234415665708 absolute error = 1.002531391236516e-13 relative error = 2.261853673368321e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.89640574115161 y2[1] (numeric) = -0.8964057411515601 absolute error = 4.984901380566953e-14 relative error = 5.560987789037209e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999886 y1[1] (closed_form) = 0.4521761621408102 y1[1] (numeric) = 0.4521761621409109 absolute error = 1.006972283335017e-13 relative error = 2.226946857542305e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8919286509534312 y2[1] (numeric) = -0.8919286509533799 absolute error = 5.129230373768223e-14 relative error = 5.750718253399875e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999885 y1[1] (closed_form) = 0.4610726913766107 y1[1] (numeric) = 0.4610726913767119 absolute error = 1.01196828694583e-13 relative error = 2.194812891486649e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8873623686334285 y2[1] (numeric) = -0.8873623686333757 absolute error = 5.284661597215745e-14 relative error = 5.955471838809576e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999884 y1[1] (closed_form) = 0.4699231137274995 y1[1] (numeric) = 0.4699231137276011 absolute error = 1.015854067532018e-13 relative error = 2.161745268229336e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8827073508160287 y2[1] (numeric) = -0.8827073508159742 absolute error = 5.451195050909519e-14 relative error = 6.175540563778131e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999883 y1[1] (closed_form) = 0.4787265441586169 y1[1] (numeric) = 0.4787265441587189 absolute error = 1.020294959630519e-13 relative error = 2.131268825763009e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8779640629991343 y2[1] (numeric) = -0.8779640629990784 absolute error = 5.595524044110789e-14 relative error = 6.373295081118037e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999881 y1[1] (closed_form) = 0.4874821023342559 y1[1] (numeric) = 0.4874821023343583 absolute error = 1.024735851729019e-13 relative error = 2.102099434670897e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8731329795075743 y2[1] (numeric) = -0.8731329795075168 absolute error = 5.750955267558311e-14 relative error = 6.586574327775031e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.08999999999988 y1[1] (closed_form) = 0.4961889127058952 y1[1] (numeric) = 0.4961889127059979 absolute error = 1.027511409290582e-13 relative error = 2.070806870083405e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8682145834456719 y2[1] (numeric) = -0.8682145834456131 absolute error = 5.88418203051333e-14 relative error = 6.77733609030253e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.099999999999879 y1[1] (closed_form) = 0.5048461045997532 y1[1] (numeric) = 0.5048461045998563 absolute error = 1.03139718987677e-13 relative error = 2.04299326166827e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8632093666489347 y2[1] (numeric) = -0.8632093666488744 absolute error = 6.0285110237146e-14 relative error = 6.9838341156073e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999878 y1[1] (closed_form) = 0.5134528123038551 y1[1] (numeric) = 0.5134528123039585 absolute error = 1.033617635926021e-13 relative error = 2.013072304128969e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8581178296348714 y2[1] (numeric) = -0.8581178296348094 absolute error = 6.195044477408373e-14 relative error = 7.219340122608059e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999877 y1[1] (closed_form) = 0.5220081751546024 y1[1] (numeric) = 0.5220081751547063 absolute error = 1.039168751049147e-13 relative error = 1.990713556816189e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8529404815529404 y2[1] (numeric) = -0.8529404815528769 absolute error = 6.350475700855895e-14 relative error = 7.445391370443159e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y1[1] (closed_form) = 0.5305113376228398 y1[1] (numeric) = 0.530511337622944 absolute error = 1.042499420123022e-13 relative error = 1.965084148426199e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8476778401336356 y2[1] (numeric) = -0.8476778401335704 absolute error = 6.517009154549669e-14 relative error = 7.688073046149547e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999875 y1[1] (closed_form) = 0.538961449399406 y1[1] (numeric) = 0.5389614493995106 absolute error = 1.045830089196897e-13 relative error = 1.940454350422136e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8423304316367132 y2[1] (numeric) = -0.8423304316366464 absolute error = 6.672440377997191e-14 relative error = 7.921404863685291e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999874 y1[1] (closed_form) = 0.5473576654801655 y1[1] (numeric) = 0.5473576654802703 absolute error = 1.048050535246148e-13 relative error = 1.914745332609443e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8368987907985668 y2[1] (numeric) = -0.8368987907984985 absolute error = 6.827871601444713e-14 relative error = 8.158539212285841e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999873 y1[1] (closed_form) = 0.5556991462505068 y1[1] (numeric) = 0.5556991462506119 absolute error = 1.051381204320023e-13 relative error = 1.891997156040375e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8313834607787539 y2[1] (numeric) = -0.831383460778684 absolute error = 6.994405055138486e-14 relative error = 8.412971131981446e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999872 y1[1] (closed_form) = 0.5639850575693041 y1[1] (numeric) = 0.5639850575694095 absolute error = 1.054711873393899e-13 relative error = 1.870106059085249e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8257849931056804 y2[1] (numeric) = -0.8257849931056088 absolute error = 7.16093850883226e-14 relative error = 8.671674308224967e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.17999999999987 y1[1] (closed_form) = 0.5722145708523305 y1[1] (numeric) = 0.5722145708524361 absolute error = 1.055822096418524e-13 relative error = 1.845150665852227e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8201039476214483 y2[1] (numeric) = -0.8201039476213752 absolute error = 7.316369732279782e-14 relative error = 8.921271204094903e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.189999999999869 y1[1] (closed_form) = 0.5803868631551156 y1[1] (numeric) = 0.5803868631552213 absolute error = 1.056932319443149e-13 relative error = 1.821082430600554e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8143408924258717 y2[1] (numeric) = -0.814340892425797 absolute error = 7.471800955727304e-14 relative error = 9.175274169849515e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999868 y1[1] (closed_form) = 0.5885011172552392 y1[1] (numeric) = 0.588501117255345 absolute error = 1.058042542467774e-13 relative error = 1.797859870517272e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8084964038196677 y2[1] (numeric) = -0.8084964038195912 absolute error = 7.649436639667329e-14 relative error = 9.461311891467e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999867 y1[1] (closed_form) = 0.5965565217340534 y1[1] (numeric) = 0.5965565217341592 absolute error = 1.058042542467774e-13 relative error = 1.773583061990985e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.8025710662468265 y2[1] (numeric) = -0.8025710662467482 absolute error = 7.827072323607354e-14 relative error = 9.752497508052675e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999866 y1[1] (closed_form) = 0.6045522710578228 y1[1] (numeric) = 0.604552271057929 absolute error = 1.06137321154165e-13 relative error = 1.755635140836538e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.7965654722361676 y2[1] (numeric) = -0.7965654722360876 absolute error = 7.993605777301127e-14 relative error = 1.003508946334441e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999865 y1[1] (closed_form) = 0.6124875656582784 y1[1] (numeric) = 0.6124875656583847 absolute error = 1.062483434566275e-13 relative error = 1.734702048072368e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.7904802223420875 y2[1] (numeric) = -0.7904802223420059 absolute error = 8.160139230994901e-14 relative error = 1.032301504877313e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999864 y1[1] (closed_form) = 0.6203616120125729 y1[1] (numeric) = 0.6203616120126791 absolute error = 1.062483434566275e-13 relative error = 1.712684044261497e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.7843159250845044 y2[1] (numeric) = -0.7843159250844213 absolute error = 8.315570454442422e-14 relative error = 1.060232259538333e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999863 y1[1] (closed_form) = 0.6281736227226323 y1[1] (numeric) = 0.6281736227227386 absolute error = 1.062483434566275e-13 relative error = 1.691384986783201e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.7780731968880075 y2[1] (numeric) = -0.7780731968879225 absolute error = 8.493206138382448e-14 relative error = 1.091569041621276e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999862 y1[1] (closed_form) = 0.6359228165938958 y1[1] (numeric) = 0.635922816594002 absolute error = 1.06137321154165e-13 relative error = 1.669028353513928e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.7717526620202139 y2[1] (numeric) = -0.7717526620201272 absolute error = 8.670841822322473e-14 relative error = 1.123526001144569e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.269999999999861 y1[1] (closed_form) = 0.6436084187134338 y1[1] (numeric) = 0.6436084187135398 absolute error = 1.060262988517024e-13 relative error = 1.647372777746566e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.7653549525293433 y2[1] (numeric) = -0.7653549525292549 absolute error = 8.837375276016246e-14 relative error = 1.154676695670487e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.279999999999859 y1[1] (closed_form) = 0.651229660527439 y1[1] (numeric) = 0.6512296605275449 absolute error = 1.059152765492399e-13 relative error = 1.626389014030132e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.7588807081810135 y2[1] (numeric) = -0.7588807081809233 absolute error = 9.015010959956271e-14 relative error = 1.18793518701571e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999858 y1[1] (closed_form) = 0.6587857799180812 y1[1] (numeric) = 0.6587857799181872 absolute error = 1.060262988517024e-13 relative error = 1.609419967517918e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.752330576394264 y2[1] (numeric) = -0.7523305763941722 absolute error = 9.181544413650045e-14 relative error = 1.22041356575655e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999857 y1[1] (closed_form) = 0.6662760212797177 y1[1] (numeric) = 0.6662760212798237 absolute error = 1.059152765492399e-13 relative error = 1.589660638631542e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.7457052121768153 y2[1] (numeric) = -0.7457052121767217 absolute error = 9.35918009759007e-14 relative error = 1.255077736451559e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999856 y1[1] (closed_form) = 0.6736996355944546 y1[1] (numeric) = 0.6736996355945603 absolute error = 1.056932319443149e-13 relative error = 1.568847990411247e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.7390052780595678 y2[1] (numeric) = -0.7390052780594725 absolute error = 9.536815781530095e-14 relative error = 1.290493595197486e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999855 y1[1] (closed_form) = 0.6810558805070465 y1[1] (numeric) = 0.6810558805071519 absolute error = 1.054711873393899e-13 relative error = 1.548642194541607e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.73223144403035 y2[1] (numeric) = -0.732231444030253 absolute error = 9.703349235223868e-14 relative error = 1.325175163444863e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999854 y1[1] (closed_form) = 0.6883440203991323 y1[1] (numeric) = 0.6883440203992375 absolute error = 1.051381204320023e-13 relative error = 1.527406606525594e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.7253843874669201 y2[1] (numeric) = -0.7253843874668211 absolute error = 9.903189379656396e-14 relative error = 1.365233323292061e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999853 y1[1] (closed_form) = 0.6955633264627964 y1[1] (numeric) = 0.6955633264629015 absolute error = 1.051381204320023e-13 relative error = 1.511553534121323e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.7184647930692285 y2[1] (numeric) = -0.7184647930691276 absolute error = 1.009192729384267e-13 relative error = 1.404651611491038e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999852 y1[1] (closed_form) = 0.7027130767734484 y1[1] (numeric) = 0.7027130767735533 absolute error = 1.049160758270773e-13 relative error = 1.493014422170797e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.7114733527909486 y2[1] (numeric) = -0.7114733527908459 absolute error = 1.02695629777827e-13 relative error = 1.443422011168448e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999851 y1[1] (closed_form) = 0.7097925563620153 y1[1] (numeric) = 0.7097925563621199 absolute error = 1.045830089196897e-13 relative error = 1.473430623951899e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.7044107657702822 y2[1] (numeric) = -0.7044107657701776 absolute error = 1.045830089196897e-13 relative error = 1.484687827070997e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36999999999985 y1[1] (closed_form) = 0.7168010572864379 y1[1] (numeric) = 0.7168010572865423 absolute error = 1.043609643147647e-13 relative error = 1.455926484118751e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.6972777382600457 y2[1] (numeric) = -0.6972777382599391 absolute error = 1.06581410364015e-13 relative error = 1.528535969468541e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999848 y1[1] (closed_form) = 0.7237378787024641 y1[1] (numeric) = 0.7237378787025681 absolute error = 1.040278974073772e-13 relative error = 1.437369805679938e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.690074983557046 y2[1] (numeric) = -0.6900749835569375 absolute error = 1.084687895058778e-13 relative error = 1.571840627329611e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999847 y1[1] (closed_form) = 0.7306023269337329 y1[1] (numeric) = 0.7306023269338365 absolute error = 1.035838081975271e-13 relative error = 1.417786453435733e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.6828032219307513 y2[1] (numeric) = -0.6828032219306409 absolute error = 1.103561686477406e-13 relative error = 1.616222142825985e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999846 y1[1] (closed_form) = 0.7373937155411416 y1[1] (numeric) = 0.7373937155412449 absolute error = 1.032507412901396e-13 relative error = 1.400211842249947e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.6754631805512643 y2[1] (numeric) = -0.6754631805511521 absolute error = 1.122435477896033e-13 relative error = 1.661727108470934e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999845 y1[1] (closed_form) = 0.744111365391489 y1[1] (numeric) = 0.7441113653915918 absolute error = 1.028066520802895e-13 relative error = 1.381603035000026e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.6680555934166063 y2[1] (numeric) = -0.6680555934164923 absolute error = 1.139088823265411e-13 relative error = 1.705080886217598e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y1[1] (closed_form) = 0.7507546047253879 y1[1] (numeric) = 0.7507546047254904 absolute error = 1.024735851729019e-13 relative error = 1.364941147585567e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.6605812012793177 y2[1] (numeric) = -0.6605812012792021 absolute error = 1.156852391659413e-13 relative error = 1.751264476523082e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y1[1] (closed_form) = 0.7573227692244411 y1[1] (numeric) = 0.7573227692245431 absolute error = 1.020294959630519e-13 relative error = 1.347239250016716e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.6530407515723838 y2[1] (numeric) = -0.6530407515722663 absolute error = 1.175726183078041e-13 relative error = 1.800387158453957e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y1[1] (closed_form) = 0.7638152020776721 y1[1] (numeric) = 0.7638152020777736 absolute error = 1.015854067532018e-13 relative error = 1.329973617661404e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.6454349983344915 y2[1] (numeric) = -0.6454349983343719 absolute error = 1.195710197521294e-13 relative error = 1.852564860298491e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y1[1] (closed_form) = 0.7702312540472058 y1[1] (numeric) = 0.7702312540473069 absolute error = 1.010302952408892e-13 relative error = 1.311687817262961e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.6377647021346264 y2[1] (numeric) = -0.637764702134505 absolute error = 1.214583988939921e-13 relative error = 1.904439027237875e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y1[1] (closed_form) = 0.776570283533192 y1[1] (numeric) = 0.7765702835332924 absolute error = 1.003641614261142e-13 relative error = 1.292402806987198e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.6300306299960167 y2[1] (numeric) = -0.6300306299958933 absolute error = 1.233457780358549e-13 relative error = 1.957774307522711e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y1[1] (closed_form) = 0.7828316566379647 y1[1] (numeric) = 0.7828316566380644 absolute error = 9.969802761133906e-14 relative error = 1.273556412364738e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.6222335553194311 y2[1] (numeric) = -0.622233555319306 absolute error = 1.251221348752551e-13 relative error = 2.010854827831041e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999837 y1[1] (closed_form) = 0.7890147472294312 y1[1] (numeric) = 0.7890147472295304 absolute error = 9.914291609902648e-14 relative error = 1.256540723062018e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.61437425780584 y2[1] (numeric) = -0.6143742578057129 absolute error = 1.271205363195804e-13 relative error = 2.069105837434911e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999836 y1[1] (closed_form) = 0.7951189370036849 y1[1] (numeric) = 0.7951189370037833 absolute error = 9.847678228425139e-14 relative error = 1.238516374108129e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.606453523378445 y2[1] (numeric) = -0.606453523378316 absolute error = 1.290079154614432e-13 relative error = 2.127251479103674e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999835 y1[1] (closed_form) = 0.8011436155468351 y1[1] (numeric) = 0.8011436155469328 absolute error = 9.769962616701378e-14 relative error = 1.219502025243341e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.5984721441040884 y2[1] (numeric) = -0.5984721441039577 absolute error = 1.307842723008434e-13 relative error = 2.185302584076444e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999834 y1[1] (closed_form) = 0.8070881803960481 y1[1] (numeric) = 0.8070881803961449 absolute error = 9.681144774731365e-14 relative error = 1.199515122372466e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.5904309181140467 y2[1] (numeric) = -0.5904309181139139 absolute error = 1.327826737451687e-13 relative error = 2.248911255685981e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y1[1] (closed_form) = 0.8129520370997928 y1[1] (numeric) = 0.8129520370998887 absolute error = 9.592326932761353e-14 relative error = 1.179937621779261e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.5823306495242176 y2[1] (numeric) = -0.5823306495240831 absolute error = 1.34559030584569e-13 relative error = 2.310698066373596e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999832 y1[1] (closed_form) = 0.8187345992772852 y1[1] (numeric) = 0.8187345992773803 absolute error = 9.514611321037592e-14 relative error = 1.162111791713254e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.5741721483547101 y2[1] (numeric) = -0.5741721483545736 absolute error = 1.364464097264317e-13 relative error = 2.376402445110214e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999831 y1[1] (closed_form) = 0.8244352886771266 y1[1] (numeric) = 0.8244352886772208 absolute error = 9.425793479067579e-14 relative error = 1.143303010984893e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.5659562304488422 y2[1] (numeric) = -0.5659562304487039 absolute error = 1.383337888682945e-13 relative error = 2.444248891095099e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54999999999983 y1[1] (closed_form) = 0.8300535352351273 y1[1] (numeric) = 0.8300535352352209 absolute error = 9.35918009759007e-14 relative error = 1.127539333344194e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.5576837173915582 y2[1] (numeric) = -0.557683717391418 absolute error = 1.402211680101573e-13 relative error = 2.514349328074534e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999829 y1[1] (closed_form) = 0.8355887771313135 y1[1] (numeric) = 0.8355887771314062 absolute error = 9.270362255620057e-14 relative error = 1.109440733209275e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.5493554364272699 y2[1] (numeric) = -0.5493554364271277 absolute error = 1.422195694544826e-13 relative error = 2.588844307783805e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999828 y1[1] (closed_form) = 0.8410404608461082 y1[1] (numeric) = 0.8410404608462 absolute error = 9.181544413650045e-14 relative error = 1.091688788005892e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.5409722203771336 y2[1] (numeric) = -0.5409722203769896 absolute error = 1.439959262938828e-13 relative error = 2.661798903342901e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999826 y1[1] (closed_form) = 0.8464080412156831 y1[1] (numeric) = 0.8464080412157742 absolute error = 9.103828801926284e-14 relative error = 1.07558392153867e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.5325349075557682 y2[1] (numeric) = -0.5325349075556224 absolute error = 1.457722831332831e-13 relative error = 2.737328221399599e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999825 y1[1] (closed_form) = 0.8516909814864742 y1[1] (numeric) = 0.8516909814865643 absolute error = 9.015010959956271e-14 relative error = 1.058483787655258e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.5240443416874248 y2[1] (numeric) = -0.5240443416872772 absolute error = 1.475486399726833e-13 relative error = 2.815575481600968e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999824 y1[1] (closed_form) = 0.8568887533688566 y1[1] (numeric) = 0.8568887533689459 absolute error = 8.926193117986259e-14 relative error = 1.041698013060966e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.5155013718216148 y2[1] (numeric) = -0.5155013718214655 absolute error = 1.493249968120836e-13 relative error = 2.896694460470928e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999823 y1[1] (closed_form) = 0.8620008370899739 y1[1] (numeric) = 0.8620008370900624 absolute error = 8.848477506262498e-14 relative error = 1.026504514326697e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.5069068522482059 y2[1] (numeric) = -0.5069068522480545 absolute error = 1.513233982564088e-13 relative error = 2.985230868063185e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y1[1] (closed_form) = 0.8670267214457137 y1[1] (numeric) = 0.8670267214458013 absolute error = 8.759659664292485e-14 relative error = 1.010310230079909e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = -0.4982616424119929 y2[1] (numeric) = -0.4982616424118398 absolute error = 1.531552662470403e-13 relative error = 3.07379202431967e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999821 y1[1] (closed_form) = 0.8719659038518289 y1[1] (numeric) = 0.8719659038519153 absolute error = 8.637535131583718e-14 relative error = 9.905817525006659e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.4895666068267556 y2[1] (numeric) = -0.4895666068266006 absolute error = 1.549316230864406e-13 relative error = 3.164668932194281e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999982 y1[1] (closed_form) = 0.8768178903941948 y1[1] (numeric) = 0.8768178903942802 absolute error = 8.537615059367454e-14 relative error = 9.737044776229602e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.4808226149888064 y2[1] (numeric) = -0.4808226149886495 absolute error = 1.568745133795346e-13 relative error = 3.262627598811813e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999819 y1[1] (closed_form) = 0.8815821958782003 y1[1] (numeric) = 0.8815821958782847 absolute error = 8.43769498715119e-14 relative error = 9.571081433587555e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.4720305412900424 y2[1] (numeric) = -0.4720305412898837 absolute error = 1.587063813701661e-13 relative error = 3.362205778813111e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999818 y1[1] (closed_form) = 0.8862583438772675 y1[1] (numeric) = 0.8862583438773508 absolute error = 8.326672684688674e-14 relative error = 9.395310907043808e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.4631912649305069 y2[1] (numeric) = -0.4631912649303464 absolute error = 1.605382493607976e-13 relative error = 3.465917030729916e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999817 y1[1] (closed_form) = 0.8908458667804932 y1[1] (numeric) = 0.8908458667805752 absolute error = 8.204548151979907e-14 relative error = 9.209840285425638e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.4543056698304698 y2[1] (numeric) = -0.4543056698303076 absolute error = 1.622590950489666e-13 relative error = 3.571584195933891e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999815 y1[1] (closed_form) = 0.8953443058394098 y1[1] (numeric) = 0.8953443058394908 absolute error = 8.093525849517391e-14 relative error = 9.03956812673253e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.4453746445420365 y2[1] (numeric) = -0.4453746445418724 absolute error = 1.640909630395981e-13 relative error = 3.684335537518694e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999814 y1[1] (closed_form) = 0.8997532112138603 y1[1] (numeric) = 0.8997532112139401 absolute error = 7.982503547054876e-14 relative error = 8.871881142036326e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.4363990821602933 y2[1] (numeric) = -0.4363990821601276 absolute error = 1.657562975765359e-13 relative error = 3.798273285910626e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999813 y1[1] (closed_form) = 0.9040721420169813 y1[1] (numeric) = 0.90407214201706 absolute error = 7.87148124459236e-14 relative error = 8.706695935825561e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.4273798802339988 y2[1] (numeric) = -0.4273798802338313 absolute error = 1.675326544159361e-13 relative error = 3.91999394833956e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999812 y1[1] (closed_form) = 0.9083006663592916 y1[1] (numeric) = 0.9083006663593689 absolute error = 7.72715225139109e-14 relative error = 8.507262559173882e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.4183179406758296 y2[1] (numeric) = -0.4183179406756603 absolute error = 1.693090112553364e-13 relative error = 4.047376284693951e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y1[1] (closed_form) = 0.9124383613918806 y1[1] (numeric) = 0.9124383613919568 absolute error = 7.616129948928574e-14 relative error = 8.347007612997042e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.4092141696721899 y2[1] (numeric) = -0.4092141696720188 absolute error = 1.711408792459679e-13 relative error = 4.182183607744181e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999981 y1[1] (closed_form) = 0.9164848133486933 y1[1] (numeric) = 0.9164848133487682 absolute error = 7.494005416219807e-14 relative error = 8.176900813923882e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.4000694775925937 y2[1] (numeric) = -0.4000694775924208 absolute error = 1.729172360853681e-13 relative error = 4.322180165452574e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999809 y1[1] (closed_form) = 0.9204396175879058 y1[1] (numeric) = 0.9204396175879794 absolute error = 7.360778653264788e-14 relative error = 7.997025022189251e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.3908847788986284 y2[1] (numeric) = -0.3908847788984537 absolute error = 1.746380817735371e-13 relative error = 4.467763678739396e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999808 y1[1] (closed_form) = 0.9243023786323902 y1[1] (numeric) = 0.9243023786324625 absolute error = 7.227551890309769e-14 relative error = 7.819466937869129e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.3816609920525094 y2[1] (numeric) = -0.3816609920523331 absolute error = 1.763589274617061e-13 relative error = 4.620826627140413e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999807 y1[1] (closed_form) = 0.9280727102092606 y1[1] (numeric) = 0.9280727102093318 absolute error = 7.116529587847253e-14 relative error = 7.668073319646073e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.372399039425235 y2[1] (numeric) = -0.372399039425057 absolute error = 1.780242619986439e-13 relative error = 4.780470494054135e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999806 y1[1] (closed_form) = 0.9317502352885015 y1[1] (numeric) = 0.9317502352885714 absolute error = 6.983302824892235e-14 relative error = 7.494822711506981e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.3630998472043496 y2[1] (numeric) = -0.3630998472041698 absolute error = 1.798006188380441e-13 relative error = 4.951823037723666e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999804 y1[1] (closed_form) = 0.9353345861206696 y1[1] (numeric) = 0.9353345861207382 absolute error = 6.861178292183467e-14 relative error = 7.335533609037624e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.3537643453013259 y2[1] (numeric) = -0.3537643453011444 absolute error = 1.815214645262131e-13 relative error = 5.131140742055239e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999803 y1[1] (closed_form) = 0.9388254042736685 y1[1] (numeric) = 0.9388254042737356 absolute error = 6.716849298982197e-14 relative error = 7.154524439162097e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.3443934672585747 y2[1] (numeric) = -0.3443934672583915 absolute error = 1.831867990631508e-13 relative error = 5.31911364409279e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999802 y1[1] (closed_form) = 0.9422223406685919 y1[1] (numeric) = 0.9422223406686577 absolute error = 6.583622536027178e-14 relative error = 6.987334360333149e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.3349881501560913 y2[1] (numeric) = -0.3349881501559064 absolute error = 1.848521336000886e-13 relative error = 5.518169329689864e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999801 y1[1] (closed_form) = 0.9455250556146312 y1[1] (numeric) = 0.9455250556146954 absolute error = 6.417089082333405e-14 relative error = 6.786799613852672e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.3255493345177481 y2[1] (numeric) = -0.3255493345175616 absolute error = 1.865729792882576e-13 relative error = 5.731020140607477e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y1[1] (closed_form) = 0.9487332188430438 y1[1] (numeric) = 0.9487332188431067 absolute error = 6.283862319378386e-14 relative error = 6.623423945291382e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.3160779642172434 y2[1] (numeric) = -0.3160779642170551 absolute error = 1.883493361276578e-13 relative error = 5.95895182361411e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999799 y1[1] (closed_form) = 0.9518465095401807 y1[1] (numeric) = 0.9518465095402421 absolute error = 6.139533326177116e-14 relative error = 6.450129579340486e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.3065749863837144 y2[1] (numeric) = -0.3065749863835244 absolute error = 1.900146706645955e-13 relative error = 6.197983498457046e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999798 y1[1] (closed_form) = 0.9548646163795663 y1[1] (numeric) = 0.9548646163796263 absolute error = 5.995204332975845e-14 relative error = 6.278590943820987e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.2970413513070254 y2[1] (numeric) = -0.2970413513068335 absolute error = 1.918465386552271e-13 relative error = 6.458580187946029e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999797 y1[1] (closed_form) = 0.9577872375530319 y1[1] (numeric) = 0.9577872375530904 absolute error = 5.850875339774575e-14 relative error = 6.108742224131606e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.2874780123427392 y2[1] (numeric) = -0.2874780123425457 absolute error = 1.935118731921648e-13 relative error = 6.731362569790366e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999796 y1[1] (closed_form) = 0.9606140808008955 y1[1] (numeric) = 0.9606140808009527 absolute error = 5.717648576819556e-14 relative error = 5.95207658423304e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.277885925816783 y2[1] (numeric) = -0.2778859258165879 absolute error = 1.9506618542664e-13 relative error = 7.01964969450277e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999794 y1[1] (closed_form) = 0.9633448634411881 y1[1] (numeric) = 0.9633448634412436 absolute error = 5.551115123125783e-14 relative error = 5.762334272792515e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.268266050929816 y2[1] (numeric) = -0.2682660509296193 absolute error = 1.966760088123465e-13 relative error = 7.331378984804941e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999793 y1[1] (closed_form) = 0.9659793123979213 y1[1] (numeric) = 0.9659793123979753 absolute error = 5.395683899678261e-14 relative error = 5.58571372122262e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.2586193496613103 y2[1] (numeric) = -0.258619349661112 absolute error = 1.98285832198053e-13 relative error = 7.667091903901601e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999792 y1[1] (closed_form) = 0.9685171642283948 y1[1] (numeric) = 0.968517164228447 absolute error = 5.218048215738236e-14 relative error = 5.387667259253364e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.2489467866733539 y2[1] (numeric) = -0.248946786673154 absolute error = 1.998401444325282e-13 relative error = 8.027424137622667e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999791 y1[1] (closed_form) = 0.9709581651495406 y1[1] (numeric) = 0.970958165149591 absolute error = 5.040412531798211e-14 relative error = 5.191173742302192e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.2392493292141851 y2[1] (numeric) = -0.2392493292139837 absolute error = 2.013944566670034e-13 relative error = 8.417764736414682e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.90999999999979 y1[1] (closed_form) = 0.9733020710633004 y1[1] (numeric) = 0.973302071063349 absolute error = 4.862776847858186e-14 relative error = 4.996164081461126e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.2295279470214686 y2[1] (numeric) = -0.2295279470212657 absolute error = 2.029765244770942e-13 relative error = 8.843216136033712e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y1[1] (closed_form) = 0.9755486475810363 y1[1] (numeric) = 0.9755486475810832 absolute error = 4.685141163918161e-14 relative error = 4.80257050792434e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.2197836122253227 y2[1] (numeric) = -0.2197836122251182 absolute error = 2.044753255603382e-13 relative error = 9.303483707907648e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999788 y1[1] (closed_form) = 0.9776976700469686 y1[1] (numeric) = 0.9776976700470139 absolute error = 4.529709940470639e-14 relative error = 4.633037470829844e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.2100172992511067 y2[1] (numeric) = -0.2100172992509007 absolute error = 2.060018822191978e-13 relative error = 9.808805415257347e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999787 y1[1] (closed_form) = 0.9797489235606416 y1[1] (numeric) = 0.979748923560685 absolute error = 4.340972026284362e-14 relative error = 4.430698439053378e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.2002299847219794 y2[1] (numeric) = -0.2002299847217718 absolute error = 2.07556194453673e-13 relative error = 1.03658897413325e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999786 y1[1] (closed_form) = 0.9817022029984133 y1[1] (numeric) = 0.9817022029984548 absolute error = 4.152234112098085e-14 relative error = 4.229626967746345e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.1904226473612376 y2[1] (numeric) = -0.1904226473610285 absolute error = 2.091105066881482e-13 relative error = 1.098138848429405e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999785 y1[1] (closed_form) = 0.9835573130339675 y1[1] (numeric) = 0.9835573130340071 absolute error = 3.952393967665557e-14 relative error = 4.018468385409748e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.1805962678944448 y2[1] (numeric) = -0.1805962678942342 absolute error = 2.106093077713922e-13 relative error = 1.166188594187835e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999783 y1[1] (closed_form) = 0.9853140681578467 y1[1] (numeric) = 0.9853140681578844 absolute error = 3.763656053479281e-14 relative error = 3.819752681006423e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.1707518289513588 y2[1] (numeric) = -0.1707518289511468 absolute error = 2.120803532790205e-13 relative error = 1.242038545539883e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999782 y1[1] (closed_form) = 0.9869722926960026 y1[1] (numeric) = 0.9869722926960384 absolute error = 3.574918139293004e-14 relative error = 3.622105874449421e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.1608903149676705 y2[1] (numeric) = -0.160890314967457 absolute error = 2.135791543622645e-13 relative error = 1.327482977487994e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999781 y1[1] (closed_form) = 0.988531820827363 y1[1] (numeric) = 0.9885318208273968 absolute error = 3.375077994860476e-14 relative error = 3.414233030997086e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.1510127120865603 y2[1] (numeric) = -0.1510127120863452 absolute error = 2.150224442942772e-13 relative error = 1.423869827402521e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99999999999978 y1[1] (closed_form) = 0.9899924966004144 y1[1] (numeric) = 0.9899924966004461 absolute error = 3.164135620181696e-14 relative error = 3.196120810053795e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.1411200080600848 y2[1] (numeric) = -0.1411200080598684 absolute error = 2.164934898019055e-13 relative error = 1.534109108821258e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.009999999999779 y1[1] (closed_form) = 0.9913541739487969 y1[1] (numeric) = 0.9913541739488263 absolute error = 2.942091015256665e-14 relative error = 2.967749662603047e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.131213192150403 y2[1] (numeric) = -0.1312131921501851 absolute error = 2.179090241583026e-13 relative error = 1.660724966652168e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y1[1] (closed_form) = 0.9926167167059102 y1[1] (numeric) = 0.9926167167059377 absolute error = 2.742250870824137e-14 relative error = 2.762648285759833e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.1212932550308502 y2[1] (numeric) = -0.1212932550306309 absolute error = 2.192829251512762e-13 relative error = 1.807874024779886e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999777 y1[1] (closed_form) = 0.9937799986185307 y1[1] (numeric) = 0.9937799986185563 absolute error = 2.55351295663786e-14 relative error = 2.569495220458793e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.1113611886868716 y2[1] (numeric) = -0.1113611886866509 absolute error = 2.206151927808264e-13 relative error = 1.981077926540083e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999776 y1[1] (closed_form) = 0.9948439033594367 y1[1] (numeric) = 0.9948439033594603 absolute error = 2.353672812205332e-14 relative error = 2.36587147416528e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.101417986316825 y2[1] (numeric) = -0.101417986316603 absolute error = 2.219613381981844e-13 relative error = 2.188579622403345e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999775 y1[1] (closed_form) = 0.9958083245390407 y1[1] (numeric) = 0.995808324539062 absolute error = 2.131628207280301e-14 relative error = 2.140600911593133e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.0914646422326614 y2[1] (numeric) = -0.09146464223243814 absolute error = 2.23265850252119e-13 relative error = 2.441007200183332e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999774 y1[1] (closed_form) = 0.9966731657160282 y1[1] (numeric) = 0.9966731657160472 absolute error = 1.909583602355269e-14 relative error = 1.915957676038553e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.08150215176049486 y2[1] (numeric) = -0.08150215176027027 absolute error = 2.245842400938614e-13 relative error = 2.755562095511695e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999772 y1[1] (closed_form) = 0.9974383404070023 y1[1] (numeric) = 0.9974383404070193 absolute error = 1.69864122767649e-14 relative error = 1.703003743553073e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.07153151114107049 y2[1] (numeric) = -0.07153151114084463 absolute error = 2.258609965721803e-13 relative error = 3.157503496979809e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999771 y1[1] (closed_form) = 0.9981037720951316 y1[1] (numeric) = 0.9981037720951463 absolute error = 1.476596622751458e-14 relative error = 1.479401905927994e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.06155371743014142 y2[1] (numeric) = -0.06155371742991431 absolute error = 2.271099974748836e-13 relative error = 3.689622771080161e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.08999999999977 y1[1] (closed_form) = 0.9986693942378018 y1[1] (numeric) = 0.9986693942378143 absolute error = 1.254552017826427e-14 relative error = 1.256223556128821e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.05156976839876393 y2[1] (numeric) = -0.05156976839853557 absolute error = 2.283589983775869e-13 relative error = 4.428156368898108e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.099999999999769 y1[1] (closed_form) = 0.9991351502732698 y1[1] (numeric) = 0.9991351502732803 absolute error = 1.043609643147647e-14 relative error = 1.044512989921547e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = -0.04158066243352122 y2[1] (numeric) = -0.04158066243329166 absolute error = 2.295594270229628e-13 relative error = 5.5208217856072e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999768 y1[1] (closed_form) = 0.9995009936263205 y1[1] (numeric) = 0.9995009936263287 absolute error = 8.215650382226158e-15 relative error = 8.219752090909587e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.03158739843668559 y2[1] (numeric) = -0.03158739843645485 absolute error = 2.30745977880531e-13 relative error = 7.30500102257686e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y1[1] (closed_form) = 0.9997668877129233 y1[1] (numeric) = 0.9997668877129291 absolute error = 5.773159728050814e-15 relative error = 5.774505836313054e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.02159097572632905 y2[1] (numeric) = -0.02159097572609713 absolute error = 2.319186509502913e-13 relative error = 1.074146226135944e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999766 y1[1] (closed_form) = 0.9999328059438911 y1[1] (numeric) = 0.9999328059438947 absolute error = 3.552713678800501e-15 relative error = 3.552952416084499e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.01159239393639229 y2[1] (numeric) = -0.01159239393615922 absolute error = 2.330705073383399e-13 relative error = 2.010546817311442e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999765 y1[1] (closed_form) = 0.9999987317275392 y1[1] (numeric) = 0.9999987317275403 absolute error = 1.110223024625157e-15 relative error = 1.11022443269223e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = -0.001592652916722195 y2[1] (numeric) = -0.001592652916487995 absolute error = 2.341998123212008e-13 relative error = 1.470501261525345e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999764 y1[1] (closed_form) = 0.999964658471344 y1[1] (numeric) = 0.9999646584713426 absolute error = 1.332267629550188e-15 relative error = 1.332314715588888e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.00840724736691237 y2[1] (numeric) = 0.00840724736714768 absolute error = 2.35310035345826e-13 relative error = 2.798895108902279e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999763 y1[1] (closed_form) = 0.9998305895826027 y1[1] (numeric) = 0.999830589582599 absolute error = 3.774758283725532e-15 relative error = 3.775397875455454e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.01840630693281626 y2[1] (numeric) = 0.01840630693305266 absolute error = 2.363942375183115e-13 relative error = 1.284311070010729e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999761 y1[1] (closed_form) = 0.9995965384680926 y1[1] (numeric) = 0.9995965384680864 absolute error = 6.217248937900877e-15 relative error = 6.219758371141391e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.02840352588336541 y2[1] (numeric) = 0.02840352588360286 absolute error = 2.374558882856093e-13 relative error = 8.360084915537752e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.17999999999976 y1[1] (closed_form) = 0.9992625285327301 y1[1] (numeric) = 0.9992625285327214 absolute error = 8.770761894538737e-15 relative error = 8.777234854805683e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.03839790450499574 y2[1] (numeric) = 0.03839790450523423 absolute error = 2.384897834772914e-13 relative error = 6.211010380690509e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.189999999999759 y1[1] (closed_form) = 0.9988285931772303 y1[1] (numeric) = 0.9988285931772193 absolute error = 1.099120794378905e-14 relative error = 1.100409821952183e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.04838844336817373 y2[1] (numeric) = 0.04838844336841323 absolute error = 2.395028619872619e-13 relative error = 4.94958806930311e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999758 y1[1] (closed_form) = 0.9982947757947672 y1[1] (numeric) = 0.9982947757947539 absolute error = 1.332267629550188e-14 relative error = 1.334543325131133e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.05837414342733847 y2[1] (numeric) = 0.05837414342757896 absolute error = 2.404881849216167e-13 relative error = 4.119772399246691e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y1[1] (closed_form) = 0.9976611297666342 y1[1] (numeric) = 0.9976611297666184 absolute error = 1.587618925213974e-14 relative error = 1.591340864994247e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.06835400612080543 y2[1] (numeric) = 0.0683540061210469 absolute error = 2.414735078559715e-13 relative error = 3.532689911827603e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y1[1] (closed_form) = 0.996927718456906 y1[1] (numeric) = 0.9969277184568877 absolute error = 1.831867990631508e-14 relative error = 1.837513348978765e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.0783270334706218 y2[1] (numeric) = 0.0783270334708642 absolute error = 2.424033196390951e-13 relative error = 3.09475935572121e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999755 y1[1] (closed_form) = 0.9960946152061025 y1[1] (numeric) = 0.9960946152060817 absolute error = 2.087219286295294e-14 relative error = 2.095402639902261e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.08829222818236342 y2[1] (numeric) = 0.08829222818260672 absolute error = 2.433053758466031e-13 relative error = 2.755682814392987e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999754 y1[1] (closed_form) = 0.9951619033238546 y1[1] (numeric) = 0.995161903323831 absolute error = 2.353672812205332e-14 relative error = 2.365115469497005e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.0982485937448634 y2[1] (numeric) = 0.09824859374510758 absolute error = 2.441796764784954e-13 relative error = 2.485324900553719e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999753 y1[1] (closed_form) = 0.994129676080573 y1[1] (numeric) = 0.9941296760805469 absolute error = 2.609024107869118e-14 relative error = 2.624430364211016e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1081951345298625 y2[1] (numeric) = 0.1081951345301075 absolute error = 2.450123437469642e-13 relative error = 2.264541236642572e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999752 y1[1] (closed_form) = 0.992998036698122 y1[1] (numeric) = 0.9929980366980934 absolute error = 2.864375403532904e-14 relative error = 2.88457307836923e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1181308558915709 y2[1] (numeric) = 0.1181308558918167 absolute error = 2.458172554398175e-13 relative error = 2.08088948128376e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.26999999999975 y1[1] (closed_form) = 0.9917670983394969 y1[1] (numeric) = 0.9917670983394657 absolute error = 3.11972669919669e-14 relative error = 3.145624314841668e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1280547642661322 y2[1] (numeric) = 0.1280547642663788 absolute error = 2.466360449204785e-13 relative error = 1.926020061291142e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.279999999999749 y1[1] (closed_form) = 0.9904369840975077 y1[1] (numeric) = 0.990436984097474 absolute error = 3.363975764614224e-14 relative error = 3.396456128583991e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1379658672709788 y2[1] (numeric) = 0.1379658672712262 absolute error = 2.474132010377161e-13 relative error = 1.793292833449681e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999748 y1[1] (closed_form) = 0.9890078269824701 y1[1] (numeric) = 0.9890078269824338 absolute error = 3.630429290524262e-14 relative error = 3.670779129828474e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1478631738040695 y2[1] (numeric) = 0.1478631738043177 absolute error = 2.481903571549537e-13 relative error = 1.678513660770097e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999747 y1[1] (closed_form) = 0.9874797699089047 y1[1] (numeric) = 0.9874797699088657 absolute error = 3.907985046680551e-14 relative error = 3.957534286541448e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1577456941429987 y2[1] (numeric) = 0.1577456941432476 absolute error = 2.489397576965757e-13 relative error = 1.578108100186293e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y1[1] (closed_form) = 0.9858529656812456 y1[1] (numeric) = 0.9858529656812037 absolute error = 4.18554080283684e-14 relative error = 4.245603501273176e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1676124400439679 y2[1] (numeric) = 0.1676124400442175 absolute error = 2.496614026625821e-13 relative error = 1.489515948798855e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999745 y1[1] (closed_form) = 0.9841275769785598 y1[1] (numeric) = 0.9841275769785151 absolute error = 4.474198789239381e-14 relative error = 4.546360547050147e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1774624248406093 y2[1] (numeric) = 0.1774624248408596 absolute error = 2.502997809017415e-13 relative error = 1.410438187839213e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999744 y1[1] (closed_form) = 0.9823037763382797 y1[1] (numeric) = 0.9823037763382323 absolute error = 4.740652315149418e-14 relative error = 4.826055268586143e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1872946635426515 y2[1] (numeric) = 0.1872946635429024 absolute error = 2.50938159140901e-13 relative error = 1.33980410543708e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y1[1] (closed_form) = 0.9803817461389496 y1[1] (numeric) = 0.9803817461388995 absolute error = 5.007105841059456e-14 relative error = 5.107302192007356e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.1971081729344178 y2[1] (numeric) = 0.1971081729346693 absolute error = 2.515487818044448e-13 relative error = 1.276196608489394e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y1[1] (closed_form) = 0.9783616785819875 y1[1] (numeric) = 0.9783616785819349 absolute error = 5.262457136723242e-14 relative error = 5.378846342745673e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2069019716731469 y2[1] (numeric) = 0.206901971673399 absolute error = 2.521594044679887e-13 relative error = 1.218738528341997e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y1[1] (closed_form) = 0.9762437756724661 y1[1] (numeric) = 0.9762437756724106 absolute error = 5.551115123125783e-14 relative error = 5.686197711531638e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2166750803871264 y2[1] (numeric) = 0.2166750803873791 absolute error = 2.527145159803013e-13 relative error = 1.166329397588243e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.369999999999739 y1[1] (closed_form) = 0.9740282491989112 y1[1] (numeric) = 0.9740282491988529 absolute error = 5.828670879282072e-14 relative error = 5.984088124831962e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2264265217736292 y2[1] (numeric) = 0.2264265217738825 absolute error = 2.532696274926138e-13 relative error = 1.118551066848172e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999738 y1[1] (closed_form) = 0.9717153207121239 y1[1] (numeric) = 0.9717153207120628 absolute error = 6.106226635438361e-14 relative error = 6.283966615822625e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2361553206966428 y2[1] (numeric) = 0.2361553206968966 absolute error = 2.537692278536952e-13 relative error = 1.074586111822899e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999737 y1[1] (closed_form) = 0.9693052215030254 y1[1] (numeric) = 0.9693052215029616 absolute error = 6.38378239159465e-14 relative error = 6.585936245856408e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2458605042843822 y2[1] (numeric) = 0.2458605042846364 absolute error = 2.542133170635452e-13 relative error = 1.033973788524819e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999736 y1[1] (closed_form) = 0.9667981925795285 y1[1] (numeric) = 0.9667981925794616 absolute error = 6.683542608243442e-14 relative error = 6.913068993655216e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2555411020265762 y2[1] (numeric) = 0.2555411020268309 absolute error = 2.546851618490109e-13 relative error = 9.966504794305995e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y1[1] (closed_form) = 0.964194484642436 y1[1] (numeric) = 0.9641944846423662 absolute error = 6.972200594645983e-14 relative error = 7.231114371320605e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2651961458715177 y2[1] (numeric) = 0.2651961458717728 absolute error = 2.550182287563985e-13 relative error = 9.616211725789926e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y1[1] (closed_form) = 0.961494358060372 y1[1] (numeric) = 0.9614943580602994 absolute error = 7.260858581048524e-14 relative error = 7.551639299991208e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2748246703228682 y2[1] (numeric) = 0.2748246703231235 absolute error = 2.552957845125547e-13 relative error = 9.289405649522997e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y1[1] (closed_form) = 0.9586980828437446 y1[1] (numeric) = 0.9586980828436692 absolute error = 7.538414337204813e-14 relative error = 7.863178692132085e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2844257125362062 y2[1] (numeric) = 0.2844257125364618 absolute error = 2.555178291174798e-13 relative error = 8.983640291837306e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y1[1] (closed_form) = 0.9558059386177453 y1[1] (numeric) = 0.9558059386176672 absolute error = 7.815970093361102e-14 relative error = 8.17736088213084e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.2939983124153112 y2[1] (numeric) = 0.2939983124155671 absolute error = 2.559064071760986e-13 relative error = 8.704349527510117e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y1[1] (closed_form) = 0.9528182145943865 y1[1] (numeric) = 0.9528182145943055 absolute error = 8.104628079763643e-14 relative error = 8.505954184779908e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3035415127081725 y2[1] (numeric) = 0.3035415127084287 absolute error = 2.561839629322549e-13 relative error = 8.439832846802487e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y1[1] (closed_form) = 0.9497352095435808 y1[1] (numeric) = 0.9497352095434971 absolute error = 8.37108160567368e-14 relative error = 8.814121579947125e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3130543591027133 y2[1] (numeric) = 0.3130543591029697 absolute error = 2.564060075371799e-13 relative error = 8.190462776883196e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999728 y1[1] (closed_form) = 0.9465572317632642 y1[1] (numeric) = 0.9465572317631776 absolute error = 8.659739592076221e-14 relative error = 9.148669833671545e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3225359003222217 y2[1] (numeric) = 0.3225359003224783 absolute error = 2.565170298396424e-13 relative error = 7.953131095898945e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999727 y1[1] (closed_form) = 0.9432845990485663 y1[1] (numeric) = 0.9432845990484768 absolute error = 8.948397578478762e-14 relative error = 9.486423914377977e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3319851882204769 y2[1] (numeric) = 0.3319851882207336 absolute error = 2.566835632933362e-13 relative error = 7.731777573247285e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999726 y1[1] (closed_form) = 0.9399176386600315 y1[1] (numeric) = 0.9399176386599389 absolute error = 9.259260025373806e-14 relative error = 9.851139764303202e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.3414012778765634 y2[1] (numeric) = 0.3414012778768203 absolute error = 2.569056078982612e-13 relative error = 7.525033576211383e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999725 y1[1] (closed_form) = 0.9364566872908928 y1[1] (numeric) = 0.9364566872907973 absolute error = 9.547918011776346e-14 relative error = 1.019579243904792e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3507832276893624 y2[1] (numeric) = 0.3507832276896194 absolute error = 2.570166302007237e-13 relative error = 7.326936122166191e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y1[1] (closed_form) = 0.9329020910334029 y1[1] (numeric) = 0.9329020910333047 absolute error = 9.825473767932635e-14 relative error = 1.053215965787864e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3601300994717109 y2[1] (numeric) = 0.3601300994719679 absolute error = 2.57072141351955e-13 relative error = 7.138313118760812e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y1[1] (closed_form) = 0.9292542053442256 y1[1] (numeric) = 0.9292542053441243 absolute error = 1.013633621482768e-13 relative error = 1.090803372912674e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3694409585442196 y2[1] (numeric) = 0.3694409585444767 absolute error = 2.57072141351955e-13 relative error = 6.958409331898298e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y1[1] (closed_form) = 0.9255133950088898 y1[1] (numeric) = 0.9255133950087854 absolute error = 1.044719866172272e-13 relative error = 1.128800373723643e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3787148738287403 y2[1] (numeric) = 0.3787148738289974 absolute error = 2.57072141351955e-13 relative error = 6.788012806389175e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y1[1] (closed_form) = 0.9216800341053117 y1[1] (numeric) = 0.9216800341052043 absolute error = 1.074695887837152e-13 relative error = 1.166018409935911e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3879509179414729 y2[1] (numeric) = 0.3879509179417299 absolute error = 2.570166302007237e-13 relative error = 6.624978014345048e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y1[1] (closed_form) = 0.9177545059663873 y1[1] (numeric) = 0.9177545059662768 absolute error = 1.104671909502031e-13 relative error = 1.203668194839121e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.3971481672857026 y2[1] (numeric) = 0.3971481672859596 absolute error = 2.569611190494925e-13 relative error = 6.470157493252094e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y1[1] (closed_form) = 0.9137372031416591 y1[1] (numeric) = 0.9137372031415455 absolute error = 1.135758154191535e-13 relative error = 1.24298118790229e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4063057021441595 y2[1] (numeric) = 0.4063057021444164 absolute error = 2.569056078982612e-13 relative error = 6.322963387974056e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999717 y1[1] (closed_form) = 0.9096285273580619 y1[1] (numeric) = 0.9096285273579452 absolute error = 1.16684439888104e-13 relative error = 1.282770233987757e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.415422606770989 y2[1] (numeric) = 0.4154226067712458 absolute error = 2.567945855957987e-13 relative error = 6.181526508434878e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999716 y1[1] (closed_form) = 0.9054288894797501 y1[1] (numeric) = 0.9054288894796302 absolute error = 1.199040866595169e-13 relative error = 1.324279444279854e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4244979694833257 y2[1] (numeric) = 0.4244979694835823 absolute error = 2.566280521421049e-13 relative error = 6.045448284580907e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999715 y1[1] (closed_form) = 0.9011387094670119 y1[1] (numeric) = 0.901138709466889 absolute error = 1.229016888260048e-13 relative error = 1.363848734216471e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4335308827524612 y2[1] (numeric) = 0.4335308827527177 absolute error = 2.564615186884112e-13 relative error = 5.915645894939539e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999714 y1[1] (closed_form) = 0.8967584163342736 y1[1] (numeric) = 0.8967584163341475 absolute error = 1.260103132949553e-13 relative error = 1.405175697263642e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.442520443294596 y2[1] (numeric) = 0.4425204432948522 absolute error = 2.562394740834861e-13 relative error = 5.790455061821893e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y1[1] (closed_form) = 0.8922884481071979 y1[1] (numeric) = 0.8922884481070689 absolute error = 1.290079154614432e-13 relative error = 1.445809544381151e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4514657521611672 y2[1] (numeric) = 0.4514657521614231 absolute error = 2.559064071760986e-13 relative error = 5.668345958715014e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y1[1] (closed_form) = 0.8877292517788827 y1[1] (numeric) = 0.8877292517787508 absolute error = 1.318944953254686e-13 relative error = 1.485751371391343e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4603659148287425 y2[1] (numeric) = 0.460365914828998 absolute error = 2.55573340268711e-13 relative error = 5.551526123817944e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y1[1] (closed_form) = 0.8830812832651618 y1[1] (numeric) = 0.8830812832650268 absolute error = 1.35003119794419e-13 relative error = 1.528773424970007e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4692200412884718 y2[1] (numeric) = 0.4692200412887271 absolute error = 2.552402733613235e-13 relative error = 5.439671175605312e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y1[1] (closed_form) = 0.8783450073590128 y1[1] (numeric) = 0.8783450073588749 absolute error = 1.378896996584444e-13 relative error = 1.569880838430994e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4780272461350878 y2[1] (numeric) = 0.4780272461353425 absolute error = 2.547406730002422e-13 relative error = 5.328999027981219e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y1[1] (closed_form) = 0.8735208976840797 y1[1] (numeric) = 0.8735208976839387 absolute error = 1.409983241273949e-13 relative error = 1.61413796168147e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4867866486554449 y2[1] (numeric) = 0.4867866486556993 absolute error = 2.543520949416234e-13 relative error = 5.225124716221576e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999707 y1[1] (closed_form) = 0.8686094366473098 y1[1] (numeric) = 0.8686094366471657 absolute error = 1.441069485963453e-13 relative error = 1.659053453904145e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.4954973729165907 y2[1] (numeric) = 0.4954973729168446 absolute error = 2.539080057317733e-13 relative error = 5.124305790709303e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999706 y1[1] (closed_form) = 0.8636111153907141 y1[1] (numeric) = 0.8636111153905668 absolute error = 1.473265953677583e-13 relative error = 1.705936766470461e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.504158547853358 y2[1] (numeric) = 0.5041585478536112 absolute error = 2.532418719169982e-13 relative error = 5.02306016619711e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999705 y1[1] (closed_form) = 0.8585264337422528 y1[1] (numeric) = 0.8585264337421024 absolute error = 1.504352198367087e-13 relative error = 1.752249132050283e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5127693073554707 y2[1] (numeric) = 0.5127693073557233 absolute error = 2.526867604046856e-13 relative error = 4.927883880333614e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999704 y1[1] (closed_form) = 0.8533559001658537 y1[1] (numeric) = 0.8533559001657002 absolute error = 1.535438443056591e-13 relative error = 1.799294342206074e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5213287903541541 y2[1] (numeric) = 0.5213287903544064 absolute error = 2.522426711948356e-13 relative error = 4.8384565721659e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999703 y1[1] (closed_form) = 0.8481000317105655 y1[1] (numeric) = 0.8481000317104092 absolute error = 1.56319401867222e-13 relative error = 1.843171748878908e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5298361409082414 y2[1] (numeric) = 0.5298361409084931 absolute error = 2.51687559682523e-13 relative error = 4.750290519085428e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y1[1] (closed_form) = 0.8427593539588539 y1[1] (numeric) = 0.8427593539586945 absolute error = 1.594280263361725e-13 relative error = 1.891738437399251e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5382905082897665 y2[1] (numeric) = 0.5382905082900176 absolute error = 2.510214258677479e-13 relative error = 4.663307674981719e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y1[1] (closed_form) = 0.8373344009740437 y1[1] (numeric) = 0.8373344009738808 absolute error = 1.628697177125105e-13 relative error = 1.945097651822849e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5466910470690366 y2[1] (numeric) = 0.5466910470692871 absolute error = 2.504663143554353e-13 relative error = 4.581496545411804e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y1[1] (closed_form) = 0.8318257152469123 y1[1] (numeric) = 0.8318257152467464 absolute error = 1.658673198789984e-13 relative error = 1.994015294775585e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5550369171991741 y2[1] (numeric) = 0.5550369171994237 absolute error = 2.495781359357352e-13 relative error = 4.496604247428365e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y1[1] (closed_form) = 0.826233847641442 y1[1] (numeric) = 0.8262338476412731 absolute error = 1.689759443479488e-13 relative error = 2.045134616916333e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5633272841001209 y2[1] (numeric) = 0.5633272841003698 absolute error = 2.489120021209601e-13 relative error = 4.418603698888489e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y1[1] (closed_form) = 0.8205593573397336 y1[1] (numeric) = 0.8205593573395616 absolute error = 1.719735465144367e-13 relative error = 2.095808730668525e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5715613187420956 y2[1] (numeric) = 0.5715613187423437 absolute error = 2.481348460037225e-13 relative error = 4.341351275307136e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999696 y1[1] (closed_form) = 0.8148028117860884 y1[1] (numeric) = 0.8148028117859132 absolute error = 1.751931932858497e-13 relative error = 2.150129954777862e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5797381977284957 y2[1] (numeric) = 0.579738197728743 absolute error = 2.473576898864849e-13 relative error = 4.266713679651793e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999695 y1[1] (closed_form) = 0.8089647866302646 y1[1] (numeric) = 0.8089647866300864 absolute error = 1.781907954523376e-13 relative error = 2.202701506880043e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5878571033782364 y2[1] (numeric) = 0.587857103378483 absolute error = 2.465805337692473e-13 relative error = 4.1945658622176e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999694 y1[1] (closed_form) = 0.803045865669913 y1[1] (numeric) = 0.8030458656697314 absolute error = 1.816324868286756e-13 relative error = 2.261794681890991e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.5959172238075185 y2[1] (numeric) = 0.5959172238077642 absolute error = 2.456923553495471e-13 relative error = 4.122927573392405e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999693 y1[1] (closed_form) = 0.797046640792197 y1[1] (numeric) = 0.7970466407920123 absolute error = 1.84741111297626e-13 relative error = 2.31782058718683e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.603917753011016 y2[1] (numeric) = 0.6039177530112608 absolute error = 2.44804176929847e-13 relative error = 4.053601267876316e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999692 y1[1] (closed_form) = 0.7909677119146051 y1[1] (numeric) = 0.7909677119144173 absolute error = 1.878497357665765e-13 relative error = 2.37493557495375e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6118578909424756 y2[1] (numeric) = 0.6118578909427194 absolute error = 2.438049762076844e-13 relative error = 3.984666698212215e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y1[1] (closed_form) = 0.7848096869249593 y1[1] (numeric) = 0.7848096869247685 absolute error = 1.908473379330644e-13 relative error = 2.431765829507562e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6197368435947207 y2[1] (numeric) = 0.6197368435949635 absolute error = 2.428057754855217e-13 relative error = 3.917885115191013e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y1[1] (closed_form) = 0.7785731816206271 y1[1] (numeric) = 0.7785731816204331 absolute error = 1.939559624020148e-13 relative error = 2.491171889561991e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6275538230790521 y2[1] (numeric) = 0.6275538230792937 absolute error = 2.416955524608966e-13 relative error = 3.851391602954995e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y1[1] (closed_form) = 0.7722588196469414 y1[1] (numeric) = 0.7722588196467446 absolute error = 1.968425422660403e-13 relative error = 2.548919316402654e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6353080477040353 y2[1] (numeric) = 0.6353080477042758 absolute error = 2.405853294362714e-13 relative error = 3.786908261365997e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y1[1] (closed_form) = 0.7658672324348381 y1[1] (numeric) = 0.7658672324346381 absolute error = 2.000621890374532e-13 relative error = 2.612230691753417e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6429987420536697 y2[1] (numeric) = 0.6429987420539092 absolute error = 2.394751064116463e-13 relative error = 3.724347976899429e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y1[1] (closed_form) = 0.7593990591377119 y1[1] (numeric) = 0.7593990591375086 absolute error = 2.032818358088662e-13 relative error = 2.676877635846562e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6506251370649293 y2[1] (numeric) = 0.6506251370651674 absolute error = 2.381428387820961e-13 relative error = 3.660215771194997e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999685 y1[1] (closed_form) = 0.7528549465675023 y1[1] (numeric) = 0.7528549465672959 absolute error = 2.063904602778166e-13 relative error = 2.741437261172478e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6581864701046682 y2[1] (numeric) = 0.6581864701049053 absolute error = 2.370326157574709e-13 relative error = 3.601298819159512e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999684 y1[1] (closed_form) = 0.746235549130013 y1[1] (numeric) = 0.7462355491298037 absolute error = 2.09277040141842e-13 relative error = 2.804436754397782e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6656819850458836 y2[1] (numeric) = 0.6656819850461195 absolute error = 2.359223927328458e-13 relative error = 3.544070562711477e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999683 y1[1] (closed_form) = 0.7395415287594717 y1[1] (numeric) = 0.7395415287592593 absolute error = 2.123856646107924e-13 relative error = 2.871855823526967e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6731109323433275 y2[1] (numeric) = 0.6731109323435621 absolute error = 2.345901251032956e-13 relative error = 3.485162903038995e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999682 y1[1] (closed_form) = 0.7327735548523369 y1[1] (numeric) = 0.7327735548521213 absolute error = 2.156053113822054e-13 relative error = 2.942318400473016e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.680472569108461 y2[1] (numeric) = 0.6804725691086944 absolute error = 2.333688797762079e-13 relative error = 3.42951193582957e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y1[1] (closed_form) = 0.7259323042003595 y1[1] (numeric) = 0.725932304200141 absolute error = 2.184918912462308e-13 relative error = 3.009810831974304e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6877661591837423 y2[1] (numeric) = 0.6877661591839742 absolute error = 2.319255898441952e-13 relative error = 3.372157625775746e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y1[1] (closed_form) = 0.7190184609229037 y1[1] (numeric) = 0.719018460922682 absolute error = 2.217115380176438e-13 relative error = 3.083530535962367e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.6949909732162417 y2[1] (numeric) = 0.6949909732164723 absolute error = 2.30593322214645e-13 relative error = 3.317932622167993e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y1[1] (closed_form) = 0.7120327163985356 y1[1] (numeric) = 0.7120327163983108 absolute error = 2.248201624865942e-13 relative error = 3.157441467349078e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7021462887305768 y2[1] (numeric) = 0.7021462887308058 absolute error = 2.289279876777073e-13 relative error = 3.260403015041073e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y1[1] (closed_form) = 0.7049757691958863 y1[1] (numeric) = 0.7049757691956585 absolute error = 2.278177646530821e-13 relative error = 3.231568723460339e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7092313902011588 y2[1] (numeric) = 0.7092313902013863 absolute error = 2.274846977456946e-13 relative error = 3.207482083966606e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y1[1] (closed_form) = 0.6978483250037953 y1[1] (numeric) = 0.6978483250035644 absolute error = 2.309263891220326e-13 relative error = 3.309120060161735e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7162455691237449 y2[1] (numeric) = 0.7162455691239709 absolute error = 2.259303855112194e-13 relative error = 3.154370445706529e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y1[1] (closed_form) = 0.6906510965607423 y1[1] (numeric) = 0.6906510965605084 absolute error = 2.339239912885205e-13 relative error = 3.387006731088959e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.723188124086288 y2[1] (numeric) = 0.7231881240865122 absolute error = 2.242650509742816e-13 relative error = 3.101061031078591e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999674 y1[1] (closed_form) = 0.6833848035835739 y1[1] (numeric) = 0.683384803583337 absolute error = 2.369215934550084e-13 relative error = 3.466884136325901e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7300583608390772 y2[1] (numeric) = 0.7300583608392999 absolute error = 2.227107387398064e-13 relative error = 3.05058815412837e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999673 y1[1] (closed_form) = 0.6760501726955326 y1[1] (numeric) = 0.6760501726952926 absolute error = 2.400302179239588e-13 relative error = 3.5504793522486e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7368555923641623 y2[1] (numeric) = 0.7368555923643837 absolute error = 2.213784711102562e-13 relative error = 3.004367116221173e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999672 y1[1] (closed_form) = 0.668647937353595 y1[1] (numeric) = 0.6686479373533519 absolute error = 2.430278200904468e-13 relative error = 3.634615565439613e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7435791389440555 y2[1] (numeric) = 0.7435791389442753 absolute error = 2.19824158875781e-13 relative error = 2.956298090717683e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999671 y1[1] (closed_form) = 0.6611788377751268 y1[1] (numeric) = 0.6611788377748806 absolute error = 2.461364445593972e-13 relative error = 3.72269090444045e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7502283282297014 y2[1] (numeric) = 0.7502283282299197 absolute error = 2.182698466413058e-13 relative error = 2.909378897439833e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y1[1] (closed_form) = 0.6536436208638616 y1[1] (numeric) = 0.6536436208636124 absolute error = 2.492450690283476e-13 relative error = 3.813164560513005e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7568024953077126 y2[1] (numeric) = 0.7568024953079292 absolute error = 2.16604512104368e-13 relative error = 2.862100923918037e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999673 y1[1] (closed_form) = 0.6460430401352083 y1[1] (numeric) = 0.6460430401349589 absolute error = 2.493560913308102e-13 relative error = 3.859744256027016e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7633009827668622 y2[1] (numeric) = 0.7633009827670743 absolute error = 2.120525977034049e-13 relative error = 2.778099366972424e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999676 y1[1] (closed_form) = 0.6383778556409084 y1[1] (numeric) = 0.6383778556406595 absolute error = 2.489120021209601e-13 relative error = 3.899132777264985e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7697231407638174 y2[1] (numeric) = 0.7697231407640249 absolute error = 2.075006833024418e-13 relative error = 2.69578335785167e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.02999999999968 y1[1] (closed_form) = 0.6306488338930242 y1[1] (numeric) = 0.6306488338927758 absolute error = 2.483568906086475e-13 relative error = 3.93811701950718e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7760683270881301 y2[1] (numeric) = 0.776068327088333 absolute error = 2.028377465990161e-13 relative error = 2.61365835351224e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999683 y1[1] (closed_form) = 0.6228567477872895 y1[1] (numeric) = 0.6228567477870418 absolute error = 2.476907567938724e-13 relative error = 3.976688984646928e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7823359072264553 y2[1] (numeric) = 0.7823359072266536 absolute error = 1.98285832198053e-13 relative error = 2.534535745662215e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999686 y1[1] (closed_form) = 0.6150023765258217 y1[1] (numeric) = 0.6150023765255747 absolute error = 2.470246229790973e-13 relative error = 4.016645014846145e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7885252544260022 y2[1] (numeric) = 0.788525254426196 absolute error = 1.938449400995523e-13 relative error = 2.458322533254303e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.05999999999969 y1[1] (closed_form) = 0.6070865055392015 y1[1] (numeric) = 0.6070865055389553 absolute error = 2.462474668618597e-13 relative error = 4.056217106047315e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.7946357497572086 y2[1] (numeric) = 0.7946357497573979 absolute error = 1.892930256985892e-13 relative error = 2.382135786823402e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999693 y1[1] (closed_form) = 0.599109926407931 y1[1] (numeric) = 0.5991099264076857 absolute error = 2.453592884421596e-13 relative error = 4.095396814959391e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8006667821756336 y2[1] (numeric) = 0.8006667821758184 absolute error = 1.848521336000886e-13 relative error = 2.308727397155082e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999696 y1[1] (closed_form) = 0.5910734367832764 y1[1] (numeric) = 0.5910734367830317 absolute error = 2.446931546273845e-13 relative error = 4.139809698758362e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.806617748583061 y2[1] (numeric) = 0.8066177485832412 absolute error = 1.801891968966629e-13 relative error = 2.233885842621129e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.0899999999997 y1[1] (closed_form) = 0.582977840307503 y1[1] (numeric) = 0.5829778403072592 absolute error = 2.438049762076844e-13 relative error = 4.182062496219148e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8124880538878092 y2[1] (numeric) = 0.8124880538879852 absolute error = 1.759703494030873e-13 relative error = 2.165820759592188e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999703 y1[1] (closed_form) = 0.574823946533512 y1[1] (numeric) = 0.5748239465332692 absolute error = 2.428057754855217e-13 relative error = 4.224002443700669e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8182771110642397 y2[1] (numeric) = 0.8182771110644115 absolute error = 1.717515019095117e-13 relative error = 2.098940561665401e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999706 y1[1] (closed_form) = 0.5666125708438859 y1[1] (numeric) = 0.5666125708436442 absolute error = 2.416955524608966e-13 relative error = 4.265622841740462e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8239843412114591 y2[1] (numeric) = 0.8239843412116268 absolute error = 1.676436767183986e-13 relative error = 2.034549303108373e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.11999999999971 y1[1] (closed_form) = 0.5583445343693511 y1[1] (numeric) = 0.5583445343691105 absolute error = 2.405853294362714e-13 relative error = 4.308904531643926e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8296091736112087 y2[1] (numeric) = 0.8296091736113721 absolute error = 1.63424829224823e-13 relative error = 1.969901423744515e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999713 y1[1] (closed_form) = 0.5500206639066647 y1[1] (numeric) = 0.5500206639064253 absolute error = 2.393640841091838e-13 relative error = 4.351910752025899e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8351510457849357 y2[1] (numeric) = 0.8351510457850949 absolute error = 1.592059817312474e-13 relative error = 1.906313624760107e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999716 y1[1] (closed_form) = 0.5416417918359367 y1[1] (numeric) = 0.5416417918356986 absolute error = 2.381428387820961e-13 relative error = 4.396685085449047e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8406094035500411 y2[1] (numeric) = 0.8406094035501962 absolute error = 1.550981565401344e-13 relative error = 1.845068064729321e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.14999999999972 y1[1] (closed_form) = 0.5332087560373918 y1[1] (numeric) = 0.5332087560371549 absolute error = 2.369215934550084e-13 relative error = 4.443317758240152e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8459837010752969 y2[1] (numeric) = 0.8459837010754478 absolute error = 1.509903313490213e-13 relative error = 1.784790075235532e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999723 y1[1] (closed_form) = 0.5247223998075822 y1[1] (numeric) = 0.5247223998073468 absolute error = 2.353672812205332e-13 relative error = 4.485558102852924e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8512734009354291 y2[1] (numeric) = 0.851273400935576 absolute error = 1.468825061579082e-13 relative error = 1.72544456336243e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999726 y1[1] (closed_form) = 0.516183571775059 y1[1] (numeric) = 0.516183571774825 absolute error = 2.34035013590983e-13 relative error = 4.533949284479942e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8564779741648599 y2[1] (numeric) = 0.8564779741650028 absolute error = 1.428857032692576e-13 relative error = 1.668293961775066e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.17999999999973 y1[1] (closed_form) = 0.5075931258155099 y1[1] (numeric) = 0.5075931258152774 absolute error = 2.324807013565078e-13 relative error = 4.580060082236129e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8615969003106034 y2[1] (numeric) = 0.8615969003107423 absolute error = 1.388889003806071e-13 relative error = 1.611993965281653e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999733 y1[1] (closed_form) = 0.498951920966372 y1[1] (numeric) = 0.4989519209661411 absolute error = 2.309263891220326e-13 relative error = 4.628229282588459e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8666296674843109 y2[1] (numeric) = 0.8666296674844459 absolute error = 1.35003119794419e-13 relative error = 1.557794809705878e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999736 y1[1] (closed_form) = 0.4902608213409294 y1[1] (numeric) = 0.4902608213407 absolute error = 2.293165657363261e-13 relative error = 4.67744016560643e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8715757724134588 y2[1] (numeric) = 0.8715757724135899 absolute error = 1.310063169057685e-13 relative error = 1.503097275673487e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.20999999999974 y1[1] (closed_form) = 0.4815206960419018 y1[1] (numeric) = 0.4815206960416742 absolute error = 2.276512311993883e-13 relative error = 4.72775590064312e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.876434720491676 y2[1] (numeric) = 0.8764347204918032 absolute error = 1.271205363195804e-13 relative error = 1.450427890947387e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999743 y1[1] (closed_form) = 0.4727324190745361 y1[1] (numeric) = 0.4727324190743101 absolute error = 2.259858966624506e-13 relative error = 4.780418848888366e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.881206025828204 y2[1] (numeric) = 0.8812060258283271 absolute error = 1.231237334309299e-13 relative error = 1.397218469031821e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999746 y1[1] (closed_form) = 0.4638968692592051 y1[1] (numeric) = 0.4638968692589809 absolute error = 2.242650509742816e-13 relative error = 4.834373022012619e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8858892112964848 y2[1] (numeric) = 0.8858892112966041 absolute error = 1.193489751472043e-13 relative error = 1.34722235721258e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.23999999999975 y1[1] (closed_form) = 0.4550149301435277 y1[1] (numeric) = 0.4550149301433052 absolute error = 2.225442052861126e-13 relative error = 4.890920946614089e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8904838085818745 y2[1] (numeric) = 0.8904838085819901 absolute error = 1.155742168634788e-13 relative error = 1.297881171444708e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999753 y1[1] (closed_form) = 0.4460874899140138 y1[1] (numeric) = 0.4460874899137931 absolute error = 2.206568261442499e-13 relative error = 4.946492137378318e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8949893582284734 y2[1] (numeric) = 0.8949893582285852 absolute error = 1.117994585797533e-13 relative error = 1.249170814735129e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999756 y1[1] (closed_form) = 0.4371154413072467 y1[1] (numeric) = 0.437115441307028 absolute error = 2.187694470023871e-13 relative error = 5.004843716985393e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.8994054096850713 y2[1] (numeric) = 0.8994054096851793 absolute error = 1.080247002960277e-13 relative error = 1.201067940361319e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.26999999999976 y1[1] (closed_form) = 0.4280996815206106 y1[1] (numeric) = 0.4280996815203937 absolute error = 2.168265567092931e-13 relative error = 5.064861434587498e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9037315213502026 y2[1] (numeric) = 0.9037315213503069 absolute error = 1.042499420123022e-13 relative error = 1.153549915538517e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999763 y1[1] (closed_form) = 0.4190411121225709 y1[1] (numeric) = 0.419041112122356 absolute error = 2.14883666416199e-13 relative error = 5.127985302629325e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9079672606163061 y2[1] (numeric) = 0.9079672606164069 absolute error = 1.008082506359642e-13 relative error = 1.11026305692496e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999766 y1[1] (closed_form) = 0.4099406389625186 y1[1] (numeric) = 0.4099406389623058 absolute error = 2.128297538206425e-13 relative error = 5.191721278458118e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9121122039129845 y2[1] (numeric) = 0.9121122039130821 absolute error = 9.758860386455126e-14 relative error = 1.069918848206325e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.29999999999977 y1[1] (closed_form) = 0.4007991720801862 y1[1] (numeric) = 0.4007991720799754 absolute error = 2.108313523763172e-13 relative error = 5.260274148823268e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9161659367493628 y2[1] (numeric) = 0.9161659367494567 absolute error = 9.392486788328824e-14 relative error = 1.025194935936408e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999773 y1[1] (closed_form) = 0.3916176256146439 y1[1] (numeric) = 0.3916176256144352 absolute error = 2.086664174782982e-13 relative error = 5.3283203775825e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.920128053755535 y2[1] (numeric) = 0.9201280537556255 absolute error = 9.048317650695026e-14 relative error = 9.833759131420892e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999776 y1[1] (closed_form) = 0.3823969177128871 y1[1] (numeric) = 0.3823969177126806 absolute error = 2.064459714290479e-13 relative error = 5.398735237297402e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9239981587231023 y2[1] (numeric) = 0.9239981587231896 absolute error = 8.72635297355373e-14 relative error = 9.444123769264768e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.32999999999978 y1[1] (closed_form) = 0.3731379704380219 y1[1] (numeric) = 0.3731379704378177 absolute error = 2.042255253797975e-13 relative error = 5.473190657602061e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9277758646447933 y2[1] (numeric) = 0.9277758646448772 absolute error = 8.382183835919932e-14 relative error = 9.034707794569673e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999783 y1[1] (closed_form) = 0.3638417096770603 y1[1] (numeric) = 0.3638417096768582 absolute error = 2.020050793305472e-13 relative error = 5.552004455724538e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9314607937531637 y2[1] (numeric) = 0.9314607937532442 absolute error = 8.049116928532385e-14 relative error = 8.641391009169404e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999786 y1[1] (closed_form) = 0.3545090650483313 y1[1] (numeric) = 0.3545090650481316 absolute error = 1.997291221300657e-13 relative error = 5.633963749356761e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9350525775583735 y2[1] (numeric) = 0.9350525775584508 absolute error = 7.738254481637341e-14 relative error = 8.275742634541058e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.35999999999979 y1[1] (closed_form) = 0.3451409698085207 y1[1] (numeric) = 0.3451409698083234 absolute error = 1.972311203246591e-13 relative error = 5.714509072454658e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9385508568850353 y2[1] (numeric) = 0.9385508568851095 absolute error = 7.427392034742297e-14 relative error = 7.913680947874401e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999793 y1[1] (closed_form) = 0.3357383607593457 y1[1] (numeric) = 0.3357383607591508 absolute error = 1.948996519729462e-13 relative error = 5.805105247197194e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9419552819081315 y2[1] (numeric) = 0.9419552819082025 absolute error = 7.105427357601002e-14 relative error = 7.543274605570917e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y1[1] (closed_form) = 0.3263021781538758 y1[1] (numeric) = 0.3263021781536833 absolute error = 1.924571613187709e-13 relative error = 5.898126773398767e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.945265512187997 y2[1] (numeric) = 0.9452655121880649 absolute error = 6.783462680459706e-14 relative error = 7.176251109339735e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.3899999999998 y1[1] (closed_form) = 0.3168333656025081 y1[1] (numeric) = 0.316833365602318 absolute error = 1.900701818158268e-13 relative error = 5.999058257465362e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9484812167043623 y2[1] (numeric) = 0.9484812167044271 absolute error = 6.483702463810914e-14 relative error = 6.835878612693559e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999803 y1[1] (closed_form) = 0.307332869978607 y1[1] (numeric) = 0.3073328699784195 absolute error = 1.875166688591889e-13 relative error = 6.101419248524954e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9516020738894555 y2[1] (numeric) = 0.9516020738895172 absolute error = 6.17284001691587e-14 relative error = 6.486787057625674e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y1[1] (closed_form) = 0.2978016413238179 y1[1] (numeric) = 0.297801641323633 absolute error = 1.848521336000886e-13 relative error = 6.207223465202046e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9546277716601587 y2[1] (numeric) = 0.9546277716602177 absolute error = 5.906386491005833e-14 relative error = 6.18710943296176e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.41999999999981 y1[1] (closed_form) = 0.2882406327530636 y1[1] (numeric) = 0.2882406327528814 absolute error = 1.822431094922194e-13 relative error = 6.322603019274785e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9575580074492164 y2[1] (numeric) = 0.9575580074492727 absolute error = 5.628830734849544e-14 relative error = 5.878318275301004e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999813 y1[1] (closed_form) = 0.2786508003592337 y1[1] (numeric) = 0.2786508003590541 absolute error = 1.796340853843503e-13 relative error = 6.446566281265581e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9603924882354914 y2[1] (numeric) = 0.960392488235545 absolute error = 5.362377208939506e-14 relative error = 5.583526812867609e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y1[1] (closed_form) = 0.2690331031175761 y1[1] (numeric) = 0.2690331031173992 absolute error = 1.769140389740187e-13 relative error = 6.575920841113058e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9631309305732672 y2[1] (numeric) = 0.9631309305733182 absolute error = 5.10702591327572e-14 relative error = 5.302525078533151e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.44999999999982 y1[1] (closed_form) = 0.2593885027898002 y1[1] (numeric) = 0.2593885027896261 absolute error = 1.741939925636871e-13 relative error = 6.715563361142805e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9657730606205921 y2[1] (numeric) = 0.9657730606206406 absolute error = 4.851674617611934e-14 relative error = 5.023617675247969e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999823 y1[1] (closed_form) = 0.2497179638279018 y1[1] (numeric) = 0.2497179638277303 absolute error = 1.714461905777398e-13 relative error = 6.865593005391292e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.968318614166663 y2[1] (numeric) = 0.9683186141667092 absolute error = 4.618527782440651e-14 relative error = 4.769636475918999e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y1[1] (closed_form) = 0.2400224532777181 y1[1] (numeric) = 0.2400224532775494 absolute error = 1.686706330161769e-13 relative error = 7.027285602360563e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9707673366582467 y2[1] (numeric) = 0.9707673366582903 absolute error = 4.363176486776865e-14 relative error = 4.494564580012128e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.47999999999983 y1[1] (closed_form) = 0.2303029406822246 y1[1] (numeric) = 0.2303029406820588 absolute error = 1.658395643033828e-13 relative error = 7.200931252207093e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9731189832251346 y2[1] (numeric) = 0.9731189832251759 absolute error = 4.130029651605582e-14 relative error = 4.244115799609353e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999833 y1[1] (closed_form) = 0.2205603979845814 y1[1] (numeric) = 0.2205603979844184 absolute error = 1.62980740014973e-13 relative error = 7.389392724362348e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9753733187046296 y2[1] (numeric) = 0.9753733187046686 absolute error = 3.896882816434299e-14 relative error = 3.995273134608252e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y1[1] (closed_form) = 0.2107957994309395 y1[1] (numeric) = 0.2107957994307794 absolute error = 1.600664045753319e-13 relative error = 7.593434262326115e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9775301176650626 y2[1] (numeric) = 0.9775301176650995 absolute error = 3.68594044175552e-14 relative error = 3.770666882939414e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.50999999999984 y1[1] (closed_form) = 0.201010121473017 y1[1] (numeric) = 0.2010101214728598 absolute error = 1.571243135600753e-13 relative error = 7.81673641151285e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9795891644283347 y2[1] (numeric) = 0.9795891644283694 absolute error = 3.47499806707674e-14 relative error = 3.547403537384642e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999843 y1[1] (closed_form) = 0.1912043426704551 y1[1] (numeric) = 0.1912043426703008 absolute error = 1.542099781204342e-13 relative error = 8.065192242323626e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9815502530914855 y2[1] (numeric) = 0.9815502530915181 absolute error = 3.26405569239796e-14 relative error = 3.325408640176606e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y1[1] (closed_form) = 0.1813794435929625 y1[1] (numeric) = 0.1813794435928112 absolute error = 1.512678871051776e-13 relative error = 8.339858371417276e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9834131875472829 y2[1] (numeric) = 0.9834131875473134 absolute error = 3.05311331771918e-14 relative error = 3.10460888300055e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.53999999999985 y1[1] (closed_form) = 0.1715364067222597 y1[1] (numeric) = 0.1715364067221114 absolute error = 1.482980405143053e-13 relative error = 8.645280809363088e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9851777815038337 y2[1] (numeric) = 0.9851777815038623 absolute error = 2.853273173286652e-14 relative error = 2.896201301790675e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999853 y1[1] (closed_form) = 0.1616762163538311 y1[1] (numeric) = 0.1616762163536858 absolute error = 1.453004383478174e-13 relative error = 8.9871251087312e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9868438585032129 y2[1] (numeric) = 0.9868438585032394 absolute error = 2.653433028854124e-14 relative error = 2.688807358925754e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999857 y1[1] (closed_form) = 0.1517998584984969 y1[1] (numeric) = 0.1517998584983546 absolute error = 1.422750806057138e-13 relative error = 9.372543690949658e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9884112519391087 y2[1] (numeric) = 0.9884112519391334 absolute error = 2.464695114667848e-14 relative error = 2.493592732612564e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.56999999999986 y1[1] (closed_form) = 0.1419083207838123 y1[1] (numeric) = 0.1419083207836731 absolute error = 1.391664561367634e-13 relative error = 9.80678619605217e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9898798050734839 y2[1] (numeric) = 0.9898798050735068 absolute error = 2.287059430727822e-14 relative error = 2.310441549575852e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999863 y1[1] (closed_form) = 0.1320025923553058 y1[1] (numeric) = 0.1320025923551697 absolute error = 1.361410983946598e-13 relative error = 1.031351702762129e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9912493710522489 y2[1] (numeric) = 0.99124937105227 absolute error = 2.109423746787797e-14 relative error = 2.128045483195176e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999867 y1[1] (closed_form) = 0.1220836637775656 y1[1] (numeric) = 0.1220836637774326 absolute error = 1.330741072891328e-13 relative error = 1.090023867006413e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9925198129199468 y2[1] (numeric) = 0.9925198129199663 absolute error = 1.942890293094024e-14 relative error = 1.957533006195747e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.59999999999987 y1[1] (closed_form) = 0.1121525269351837 y1[1] (numeric) = 0.1121525269350538 absolute error = 1.299238494567589e-13 relative error = 1.15845672859289e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9936910036334499 y2[1] (numeric) = 0.9936910036334677 absolute error = 1.787459069646502e-14 relative error = 1.798807741149537e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999873 y1[1] (closed_form) = 0.1022101749335684 y1[1] (numeric) = 0.1022101749334416 absolute error = 1.267597138365772e-13 relative error = 1.240186839705194e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9947628260746626 y2[1] (numeric) = 0.9947628260746787 absolute error = 1.609823385706477e-14 relative error = 1.61829869744816e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999877 y1[1] (closed_form) = 0.09225760199963459 y1[1] (numeric) = 0.09225760199951098 absolute error = 1.236094560042034e-13 relative error = 1.339829491825432e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9957351730622339 y2[1] (numeric) = 0.9957351730622486 absolute error = 1.465494392505207e-14 relative error = 1.471771242144936e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.62999999999988 y1[1] (closed_form) = 0.08229580338238188 y1[1] (numeric) = 0.08229580338226145 absolute error = 1.204314425962139e-13 relative error = 1.46339713140216e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9966079473622756 y2[1] (numeric) = 0.9966079473622886 absolute error = 1.298960938811433e-14 relative error = 1.303382079431933e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999883 y1[1] (closed_form) = 0.07232577525337053 y1[1] (numeric) = 0.0723257752532533 absolute error = 1.172256736126087e-13 relative error = 1.620800789233791e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9973810616980848 y2[1] (numeric) = 0.9973810616980964 absolute error = 1.154631945610163e-14 relative error = 1.157663795665371e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999887 y1[1] (closed_form) = 0.06234851460710512 y1[1] (numeric) = 0.06234851460699112 absolute error = 1.139990879472919e-13 relative error = 1.828417062790791e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9980544387588723 y2[1] (numeric) = 0.9980544387588826 absolute error = 1.021405182655144e-14 relative error = 1.023396262758281e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.65999999999989 y1[1] (closed_form) = 0.05236501916133592 y1[1] (numeric) = 0.05236501916122516 absolute error = 1.107655633880711e-13 relative error = 2.115258719696137e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9986280112074931 y2[1] (numeric) = 0.9986280112075021 absolute error = 8.992806499463768e-15 relative error = 9.005161480089165e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999893 y1[1] (closed_form) = 0.04237628725728795 y1[1] (numeric) = 0.04237628725718044 absolute error = 1.075112221471386e-13 relative error = 2.537060915563069e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9991017216871803 y2[1] (numeric) = 0.9991017216871881 absolute error = 7.882583474838611e-15 relative error = 7.889670594829238e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999897 y1[1] (closed_form) = 0.0323833177598277 y1[1] (numeric) = 0.03238331775972347 absolute error = 1.042360642244944e-13 relative error = 3.218819794733996e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9994755228272807 y2[1] (numeric) = 0.9994755228272875 absolute error = 6.772360450213455e-15 relative error = 6.775914262568475e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.6899999999999 y1[1] (closed_form) = 0.02238710995757748 y1[1] (numeric) = 0.02238710995747652 absolute error = 1.009643757488021e-13 relative error = 4.509933436701962e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9997493772479917 y2[1] (numeric) = 0.9997493772479975 absolute error = 5.773159728050814e-15 relative error = 5.774606975942891e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999903 y1[1] (closed_form) = 0.01238866346298736 y1[1] (numeric) = 0.01238866346288968 absolute error = 9.768054420877803e-14 relative error = 7.884671700107967e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9999232575640997 y2[1] (numeric) = 0.9999232575641044 absolute error = 4.662936703425657e-15 relative error = 4.663294576010741e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999907 y1[1] (closed_form) = 0.002388978112374797 y1[1] (numeric) = 0.002388978112280414 absolute error = 9.438326856181511e-14 relative error = 3.950779962064705e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 y2[1] (closed_form) = 0.9999971463877178 y2[1] (numeric) = 0.9999971463877214 absolute error = 3.663735981263017e-15 relative error = 3.663746436174846e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.71999999999991 y1[1] (closed_form) = -0.007610946134058199 y1[1] (numeric) = -0.007610946134149275 absolute error = 9.107645193573433e-14 relative error = 1.196650854329091e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 y2[1] (closed_form) = 0.9999710363300252 y2[1] (numeric) = 0.9999710363300278 absolute error = 2.664535259100376e-15 relative error = 2.664612436055585e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999913 y1[1] (closed_form) = -0.01761010929222022 y1[1] (numeric) = -0.01761010929230798 absolute error = 8.775619120271472e-14 relative error = 4.983284870439933e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9998449300020059 y2[1] (numeric) = 0.9998449300020077 absolute error = 1.77635683940025e-15 relative error = 1.776632341773926e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999917 y1[1] (closed_form) = -0.02760751145412807 y1[1] (numeric) = -0.0276075114542125 absolute error = 8.443246102274315e-14 relative error = 3.058314805484513e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9996188400141877 y2[1] (numeric) = 0.9996188400141889 absolute error = 1.221245327087672e-15 relative error = 1.221710994432977e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.74999999999992 y1[1] (closed_form) = -0.03760215288789667 y1[1] (numeric) = -0.03760215288797779 absolute error = 8.11156697366755e-14 relative error = 2.15720812525032e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.999292788975381 y2[1] (numeric) = 0.9992927889753815 absolute error = 5.551115123125783e-16 relative error = 5.555043711280641e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999923 y1[1] (closed_form) = -0.04759303413771152 y1[1] (numeric) = -0.04759303413778929 absolute error = 7.777806176889612e-14 relative error = 1.63423205051066e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9988668094904178 y2[1] (numeric) = 0.9988668094904177 absolute error = 1.110223024625157e-16 relative error = 1.111482546097961e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999927 y1[1] (closed_form) = -0.05757915612377331 y1[1] (numeric) = -0.05757915612384776 absolute error = 7.444739269502065e-14 relative error = 1.292957342670793e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9983409441568918 y2[1] (numeric) = 0.9983409441568912 absolute error = 5.551115123125783e-16 relative error = 5.560340037755089e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.77999999999993 y1[1] (closed_form) = -0.0675595202422052 y1[1] (numeric) = -0.06755952024227631 absolute error = 7.110978472724128e-14 relative error = 1.052550173125981e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 y2[1] (closed_form) = 0.9977152455608981 y2[1] (numeric) = 0.9977152455608969 absolute error = 1.221245327087672e-15 relative error = 1.224041962394901e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999933 y1[1] (closed_form) = -0.07753312846491227 y1[1] (numeric) = -0.07753312846498003 absolute error = 6.776523786555799e-14 relative error = 8.740165553389897e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9969897762717748 y2[1] (numeric) = 0.9969897762717732 absolute error = 1.554312234475219e-15 relative error = 1.559005188887234e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999937 y1[1] (closed_form) = -0.08749898343938357 y1[1] (numeric) = -0.08749898343944799 absolute error = 6.442069100387471e-14 relative error = 7.362450221893521e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9961646088358462 y2[1] (numeric) = 0.9961646088358442 absolute error = 1.998401444325282e-15 relative error = 2.006095605685777e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.80999999999994 y1[1] (closed_form) = -0.09745608858842651 y1[1] (numeric) = -0.09745608858848759 absolute error = 6.107614414219142e-14 relative error = 6.267042421549081e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9952398257691685 y2[1] (numeric) = 0.9952398257691663 absolute error = 2.220446049250313e-15 relative error = 2.231066313623701e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999943 y1[1] (closed_form) = -0.1074034482098237 y1[1] (numeric) = -0.1074034482098815 absolute error = 5.775935285612377e-14 relative error = 5.377793154581491e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9942155195492774 y2[1] (numeric) = 0.9942155195492752 absolute error = 2.220446049250313e-15 relative error = 2.233364904881932e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999947 y1[1] (closed_form) = -0.1173400675759025 y1[1] (numeric) = -0.117340067575957 absolute error = 5.441480599444048e-14 relative error = 4.637359353763943e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9930917926059416 y2[1] (numeric) = 0.9930917926059392 absolute error = 2.442490654175344e-15 relative error = 2.459481260806798e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.83999999999995 y1[1] (closed_form) = -0.1272649530330068 y1[1] (numeric) = -0.1272649530330579 absolute error = 5.10702591327572e-14 relative error = 4.012908339306256e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9918687573109189 y2[1] (numeric) = 0.9918687573109163 absolute error = 2.664535259100376e-15 relative error = 2.686378857545898e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999953 y1[1] (closed_form) = -0.1371771121008616 y1[1] (numeric) = -0.1371771121009093 absolute error = 4.773959005888173e-14 relative error = 3.480142519969401e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9905465359667196 y2[1] (numeric) = 0.9905465359667169 absolute error = 2.664535259100376e-15 relative error = 2.689964744059131e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999957 y1[1] (closed_form) = -0.1470755535718201 y1[1] (numeric) = -0.1470755535718645 absolute error = 4.446443213623752e-14 relative error = 3.023237448807195e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9891252607943761 y2[1] (numeric) = 0.9891252607943737 absolute error = 2.442490654175344e-15 relative error = 2.469344127571625e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.86999999999996 y1[1] (closed_form) = -0.156959287609984 y1[1] (numeric) = -0.156959287610025 absolute error = 4.107825191113079e-14 relative error = 2.617127825732936e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9876050739202216 y2[1] (numeric) = 0.9876050739202193 absolute error = 2.220446049250313e-15 relative error = 2.248313731759624e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999963 y1[1] (closed_form) = -0.1668273258501858 y1[1] (numeric) = -0.1668273258502235 absolute error = 3.774758283725532e-14 relative error = 2.262673854231374e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9859861273616763 y2[1] (numeric) = 0.9859861273616742 absolute error = 2.109423746787797e-15 relative error = 2.139405097343753e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999967 y1[1] (closed_form) = -0.1766786814968249 y1[1] (numeric) = -0.1766786814968593 absolute error = 3.438915818776422e-14 relative error = 1.946423750529417e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9842685830120473 y2[1] (numeric) = 0.9842685830120455 absolute error = 1.887379141862766e-15 relative error = 1.917544839323257e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.89999999999997 y1[1] (closed_form) = -0.1865123694225461 y1[1] (numeric) = -0.1865123694225772 absolute error = 3.111400026512001e-14 relative error = 1.668200364482575e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.982452612624338 y2[1] (numeric) = 0.9824526126243367 absolute error = 1.332267629550188e-15 relative error = 1.356062992179765e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999973 y1[1] (closed_form) = -0.1963274062667514 y1[1] (numeric) = -0.1963274062667793 absolute error = 2.78388423424758e-14 relative error = 1.417980447653394e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9805383977940741 y2[1] (numeric) = 0.9805383977940729 absolute error = 1.221245327087672e-15 relative error = 1.245484450007382e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999977 y1[1] (closed_form) = -0.2061228105339357 y1[1] (numeric) = -0.2061228105339603 absolute error = 2.453592884421596e-14 relative error = 1.190354855954984e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 y2[1] (closed_form) = 0.9785261299411433 y2[1] (numeric) = 0.9785261299411426 absolute error = 6.661338147750939e-16 relative error = 6.807521990395501e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.92999999999998 y1[1] (closed_form) = -0.2158976026918351 y1[1] (numeric) = -0.2158976026918563 absolute error = 2.123301534595612e-14 relative error = 9.8347619803187e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.9764160102906539 y2[1] (numeric) = 0.9764160102906539 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y1[1] (closed_form) = -0.2256508052693793 y1[1] (numeric) = -0.2256508052693973 absolute error = 1.798561299892754e-14 relative error = 7.970551214056835e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.9742082498528128 y2[1] (numeric) = 0.9742082498528134 absolute error = 5.551115123125783e-16 relative error = 5.698078541178918e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999987 y1[1] (closed_form) = -0.2353814429544382 y1[1] (numeric) = -0.235381442954453 absolute error = 1.479372180313021e-14 relative error = 6.284999198511061e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.9719030694018239 y2[1] (numeric) = 0.971903069401825 absolute error = 1.110223024625157e-15 relative error = 1.142318673104371e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.95999999999999 y1[1] (closed_form) = -0.2450885426913523 y1[1] (numeric) = -0.2450885426913638 absolute error = 1.154631945610163e-14 relative error = 4.711080872777587e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.9695006994538112 y2[1] (numeric) = 0.9695006994538131 absolute error = 1.887379141862766e-15 relative error = 1.946753770189192e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y1[1] (closed_form) = -0.254771133778237 y1[1] (numeric) = -0.2547711337782452 absolute error = 8.271161533457416e-15 relative error = 3.246506545226182e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.9670013802437677 y2[1] (numeric) = 0.9670013802437704 absolute error = 2.664535259100376e-15 relative error = 2.755461691718251e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999997 y1[1] (closed_form) = -0.2644282479640523 y1[1] (numeric) = -0.2644282479640575 absolute error = 5.10702591327572e-15 relative error = 1.931346576092731e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 0.9644053617015315 y2[1] (numeric) = 0.964405361701535 absolute error = 3.552713678800501e-15 relative error = 3.683838580627895e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.99 y1[1] (closed_form) = -0.2740589195454274 y1[1] (numeric) = -0.2740589195454294 absolute error = 1.942890293094024e-15 relative error = 7.089316035824094e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 0.9617129034267934 y2[1] (numeric) = 0.961712903426798 absolute error = 4.662936703425657e-15 relative error = 4.848574545283311e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 Finished! diff ( y1 , x , 1 ) = neg ( y2 ) ; diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; Iterations = 4500 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %