##############ECHO OF PROBLEM################# ##############temp/sub_lin_sinpostode.ode################# diff ( y , x , 1 ) = ( 0.1 * x + 1.0 ) - sin ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.1); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(cos(c(x)) + (c(0.05) * c(x) * c(x)) + c(x)) ; } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 1.095504165278026 y[1] (numeric) = 1.095504165278026 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 1.104561097956697 y[1] (numeric) = 1.104561097956697 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] = 0.12 y[1] (closed_form) = 1.113528635853866 y[1] (numeric) = 1.113528635853866 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] = 0.13 y[1] (closed_form) = 1.122406893714788 y[1] (numeric) = 1.122406893714788 absolute error = 2.220446049250313e-16 relative error = 1.978289746511967e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 1.131195996212637 y[1] (numeric) = 1.131195996212637 absolute error = 2.220446049250313e-16 relative error = 1.962918943034274e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 1.139896077936042 y[1] (numeric) = 1.139896077936042 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] = 0.1600000000000001 y[1] (closed_form) = 1.148507283375627 y[1] (numeric) = 1.148507283375627 absolute error = 2.220446049250313e-16 relative error = 1.933332144593899e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 1.157029766909561 y[1] (numeric) = 1.157029766909561 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] = 0.1800000000000001 y[1] (closed_form) = 1.165463692788121 y[1] (numeric) = 1.165463692788121 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] = 0.1900000000000001 y[1] (closed_form) = 1.17380923511727 y[1] (numeric) = 1.17380923511727 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 1.182066577841242 y[1] (numeric) = 1.182066577841242 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] = 0.2100000000000001 y[1] (closed_form) = 1.190235914724148 y[1] (numeric) = 1.190235914724148 absolute error = 4.440892098500626e-16 relative error = 3.731102417229493e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (closed_form) = 1.198317449330606 y[1] (numeric) = 1.198317449330605 absolute error = 4.440892098500626e-16 relative error = 3.705939608057415e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (closed_form) = 1.206311395005375 y[1] (numeric) = 1.206311395005375 absolute error = 4.440892098500626e-16 relative error = 3.68138120628533e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = 1.21421797485203 y[1] (numeric) = 1.214217974852029 absolute error = 4.440892098500626e-16 relative error = 3.657409287687257e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = 1.222037421710645 y[1] (numeric) = 1.222037421710644 absolute error = 4.440892098500626e-16 relative error = 3.634006634824759e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 1.229769978134513 y[1] (numeric) = 1.229769978134513 absolute error = 6.661338147750939e-16 relative error = 5.416735053050966e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 1.237415896365891 y[1] (numeric) = 1.23741589636589 absolute error = 6.661338147750939e-16 relative error = 5.383265373682619e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 1.244975438310771 y[1] (numeric) = 1.244975438310771 absolute error = 2.220446049250313e-16 relative error = 1.783525988483031e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 1.252448875512697 y[1] (numeric) = 1.252448875512697 absolute error = 2.220446049250313e-16 relative error = 1.772883582446717e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 1.259836489125606 y[1] (numeric) = 1.259836489125606 absolute error = 4.440892098500626e-16 relative error = 3.524974976381929e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 1.267138569885714 y[1] (numeric) = 1.267138569885713 absolute error = 4.440892098500626e-16 relative error = 3.504661766314288e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 1.274355418082441 y[1] (numeric) = 1.274355418082441 absolute error = 4.440892098500626e-16 relative error = 3.484814389680207e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 1.281487343528387 y[1] (numeric) = 1.281487343528386 absolute error = 6.661338147750939e-16 relative error = 5.19813026745151e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 1.288534665528347 y[1] (numeric) = 1.288534665528345 absolute error = 1.110223024625157e-15 relative error = 8.616167297058511e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = 1.295497712847379 y[1] (numeric) = 1.295497712847378 absolute error = 8.881784197001252e-16 relative error = 6.855885663804027e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (closed_form) = 1.302376823677935 y[1] (numeric) = 1.302376823677934 absolute error = 1.110223024625157e-15 relative error = 8.524591381239934e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (closed_form) = 1.309172345606035 y[1] (numeric) = 1.309172345606034 absolute error = 1.110223024625157e-15 relative error = 8.480342778026054e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (closed_form) = 1.31588463557651 y[1] (numeric) = 1.315884635576509 absolute error = 8.881784197001252e-16 relative error = 6.749667833236763e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = 1.322514059857313 y[1] (numeric) = 1.322514059857312 absolute error = 8.881784197001252e-16 relative error = 6.715833477006295e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (closed_form) = 1.329060994002885 y[1] (numeric) = 1.329060994002884 absolute error = 8.881784197001252e-16 relative error = 6.68275138393082e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 1.335525822816605 y[1] (numeric) = 1.335525822816604 absolute error = 6.661338147750939e-16 relative error = 4.987801833514736e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 1.341908940312309 y[1] (numeric) = 1.341908940312308 absolute error = 8.881784197001252e-16 relative error = 6.618768181791944e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 1.348210749674885 y[1] (numeric) = 1.348210749674885 absolute error = 6.661338147750939e-16 relative error = 4.940873041812855e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 1.354431663219964 y[1] (numeric) = 1.354431663219963 absolute error = 6.661338147750939e-16 relative error = 4.918179579407188e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 1.360572102352677 y[1] (numeric) = 1.360572102352676 absolute error = 6.661338147750939e-16 relative error = 4.895983194299127e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (closed_form) = 1.366632497525525 y[1] (numeric) = 1.366632497525525 absolute error = 2.220446049250313e-16 relative error = 1.624757243275521e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = 1.372613288195329 y[1] (numeric) = 1.372613288195329 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] = 0.4800000000000003 y[1] (closed_form) = 1.378514922779284 y[1] (numeric) = 1.378514922779285 absolute error = 2.220446049250313e-16 relative error = 1.610752275915573e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = 1.384337858610122 y[1] (numeric) = 1.384337858610122 absolute error = 6.661338147750939e-16 relative error = 4.811930921573537e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (closed_form) = 1.390082561890373 y[1] (numeric) = 1.390082561890373 absolute error = 4.440892098500626e-16 relative error = 3.194696646263556e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (closed_form) = 1.395749507645752 y[1] (numeric) = 1.395749507645752 absolute error = 2.220446049250313e-16 relative error = 1.590862856900161e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (closed_form) = 1.40133917967765 y[1] (numeric) = 1.40133917967765 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] = 0.5300000000000004 y[1] (closed_form) = 1.406852070514761 y[1] (numeric) = 1.406852070514761 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] = 0.5400000000000004 y[1] (closed_form) = 1.412288681363824 y[1] (numeric) = 1.412288681363825 absolute error = 4.440892098500626e-16 relative error = 3.144464837183379e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (closed_form) = 1.417649522059506 y[1] (numeric) = 1.417649522059506 absolute error = 4.440892098500626e-16 relative error = 3.132574045557516e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (closed_form) = 1.422935111013416 y[1] (numeric) = 1.422935111013417 absolute error = 4.440892098500626e-16 relative error = 3.120937886856848e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = 1.428145975162269 y[1] (numeric) = 1.42814597516227 absolute error = 6.661338147750939e-16 relative error = 4.664325820750966e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = 1.433282649915187 y[1] (numeric) = 1.433282649915188 absolute error = 6.661338147750939e-16 relative error = 4.647609561271893e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = 1.438345679100164 y[1] (numeric) = 1.438345679100164 absolute error = 6.661338147750939e-16 relative error = 4.631249806317982e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = 1.443335614909679 y[1] (numeric) = 1.443335614909679 absolute error = 6.661338147750939e-16 relative error = 4.615238534225316e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 1.44825301784548 y[1] (numeric) = 1.448253017845481 absolute error = 1.332267629550188e-15 relative error = 9.199135877045576e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = 1.453098456662534 y[1] (numeric) = 1.453098456662535 absolute error = 1.110223024625157e-15 relative error = 7.640384032717979e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (closed_form) = 1.457872508312152 y[1] (numeric) = 1.457872508312153 absolute error = 1.332267629550188e-15 relative error = 9.138437153826414e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = 1.462575757884293 y[1] (numeric) = 1.462575757884294 absolute error = 1.110223024625157e-15 relative error = 7.590875335108545e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = 1.467208798549056 y[1] (numeric) = 1.467208798549057 absolute error = 1.110223024625157e-15 relative error = 7.566905444699296e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = 1.471772231497365 y[1] (numeric) = 1.471772231497366 absolute error = 1.110223024625157e-15 relative error = 7.543443209929484e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (closed_form) = 1.476266665880849 y[1] (numeric) = 1.476266665880851 absolute error = 1.110223024625157e-15 relative error = 7.520477501012432e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (closed_form) = 1.480692718750928 y[1] (numeric) = 1.480692718750929 absolute error = 1.110223024625157e-15 relative error = 7.497997461361938e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (closed_form) = 1.485051014997107 y[1] (numeric) = 1.485051014997107 absolute error = 4.440892098500626e-16 relative error = 2.990396998926853e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 1.489342187284489 y[1] (numeric) = 1.489342187284489 absolute error = 8.881784197001252e-16 relative error = 5.963561814625941e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = 1.493566875990509 y[1] (numeric) = 1.493566875990509 absolute error = 2.220446049250313e-16 relative error = 1.486673335452589e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (closed_form) = 1.497725729140895 y[1] (numeric) = 1.497725729140895 absolute error = 2.220446049250313e-16 relative error = 1.482545172355405e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (closed_form) = 1.501819402344871 y[1] (numeric) = 1.501819402344871 absolute error = 2.220446049250313e-16 relative error = 1.478504037025632e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (closed_form) = 1.505848558729588 y[1] (numeric) = 1.505848558729588 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] = 0.7500000000000006 y[1] (closed_form) = 1.509813868873821 y[1] (numeric) = 1.509813868873821 absolute error = 2.220446049250313e-16 relative error = 1.470675356099727e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 1.513716010740905 y[1] (numeric) = 1.513716010740905 absolute error = 2.220446049250313e-16 relative error = 1.466884166841501e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = 1.517555669610944 y[1] (numeric) = 1.517555669610943 absolute error = 6.661338147750939e-16 relative error = 4.389518144964467e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (closed_form) = 1.521333538012278 y[1] (numeric) = 1.521333538012277 absolute error = 8.881784197001252e-16 relative error = 5.838157100385684e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = 1.525050315652236 y[1] (numeric) = 1.525050315652236 absolute error = 2.220446049250313e-16 relative error = 1.455982157743214e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (closed_form) = 1.528706709347166 y[1] (numeric) = 1.528706709347166 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] = 0.8100000000000006 y[1] (closed_form) = 1.532303432951747 y[1] (numeric) = 1.532303432951747 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] = 0.8200000000000006 y[1] (closed_form) = 1.535841207287614 y[1] (numeric) = 1.535841207287614 absolute error = 4.440892098500626e-16 relative error = 2.891504718995985e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = 1.539320760071267 y[1] (numeric) = 1.539320760071268 absolute error = 6.661338147750939e-16 relative error = 4.327452939335746e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (closed_form) = 1.542742825841308 y[1] (numeric) = 1.542742825841309 absolute error = 8.881784197001252e-16 relative error = 5.757138551046396e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = 1.546108145884982 y[1] (numeric) = 1.546108145884983 absolute error = 8.881784197001252e-16 relative error = 5.744607335935985e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (closed_form) = 1.549417468164052 y[1] (numeric) = 1.549417468164053 absolute error = 1.110223024625157e-15 relative error = 7.165422150175516e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (closed_form) = 1.552671547240001 y[1] (numeric) = 1.552671547240003 absolute error = 1.332267629550188e-15 relative error = 8.580485885236969e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (closed_form) = 1.55587114419858 y[1] (numeric) = 1.555871144198582 absolute error = 1.332267629550188e-15 relative error = 8.562840403061981e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (closed_form) = 1.559017026573697 y[1] (numeric) = 1.559017026573698 absolute error = 1.110223024625157e-15 relative error = 7.121301472025165e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = 1.562109968270665 y[1] (numeric) = 1.562109968270666 absolute error = 1.332267629550188e-15 relative error = 8.528641751291531e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = 1.565150749488812 y[1] (numeric) = 1.565150749488813 absolute error = 1.554312234475219e-15 relative error = 9.930750983461929e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (closed_form) = 1.568140156643463 y[1] (numeric) = 1.568140156643465 absolute error = 1.77635683940025e-15 relative error = 1.132779383191402e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = 1.571078982287299 y[1] (numeric) = 1.5710789822873 absolute error = 1.554312234475219e-15 relative error = 9.893278772097956e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = 1.573968025031098 y[1] (numeric) = 1.5739680250311 absolute error = 1.554312234475219e-15 relative error = 9.875119505331179e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = 1.576808089463884 y[1] (numeric) = 1.576808089463885 absolute error = 1.554312234475219e-15 relative error = 9.85733295548786e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = 1.579599986072457 y[1] (numeric) = 1.579599986072459 absolute error = 1.554312234475219e-15 relative error = 9.839910408836393e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = 1.582344531160355 y[1] (numeric) = 1.582344531160356 absolute error = 1.77635683940025e-15 relative error = 1.122610660585798e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 1.585042546766217 y[1] (numeric) = 1.585042546766219 absolute error = 1.998401444325282e-15 relative error = 1.260787256722158e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = 1.587694860581588 y[1] (numeric) = 1.587694860581589 absolute error = 1.77635683940025e-15 relative error = 1.118827605670748e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (closed_form) = 1.59030230586814 y[1] (numeric) = 1.590302305868141 absolute error = 1.332267629550188e-15 relative error = 8.377448895308669e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 1.592865721374355 y[1] (numeric) = 1.592865721374357 absolute error = 1.998401444325282e-15 relative error = 1.254595046844892e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = 1.595385951251649 y[1] (numeric) = 1.595385951251652 absolute error = 2.442490654175344e-15 relative error = 1.530971644986033e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = 1.597863844969955 y[1] (numeric) = 1.597863844969957 absolute error = 2.664535259100376e-15 relative error = 1.667560892305238e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 1.600300257232778 y[1] (numeric) = 1.60030025723278 absolute error = 2.664535259100376e-15 relative error = 1.665022077611774e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = 1.602696047891726 y[1] (numeric) = 1.602696047891729 absolute error = 2.886579864025407e-15 relative error = 1.801077545441366e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = 1.605052081860526 y[1] (numeric) = 1.605052081860529 absolute error = 2.886579864025407e-15 relative error = 1.798433768379263e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = 1.607369229028532 y[1] (numeric) = 1.607369229028535 absolute error = 2.886579864025407e-15 relative error = 1.795841186887725e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = 1.609648364173738 y[1] (numeric) = 1.609648364173741 absolute error = 2.886579864025407e-15 relative error = 1.793298417388906e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = 1.611890366875299 y[1] (numeric) = 1.611890366875302 absolute error = 3.108624468950438e-15 relative error = 1.928558252368371e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y[1] (closed_form) = 1.614096121425575 y[1] (numeric) = 1.614096121425579 absolute error = 3.552713678800501e-15 relative error = 2.201054591261103e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = 1.616266516741705 y[1] (numeric) = 1.616266516741708 absolute error = 3.774758283725532e-15 relative error = 2.335480098502082e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 1.618402446276709 y[1] (numeric) = 1.618402446276713 absolute error = 3.996802888650564e-15 relative error = 2.469597656531966e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 1.620504807930155 y[1] (numeric) = 1.620504807930159 absolute error = 4.218847493575595e-15 relative error = 2.603415597985336e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 1.622574503958355 y[1] (numeric) = 1.62257450395836 absolute error = 4.662936703425657e-15 relative error = 2.873788964420543e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 1.624612440884154 y[1] (numeric) = 1.624612440884159 absolute error = 4.884981308350689e-15 relative error = 3.006859473322857e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 1.62661952940627 y[1] (numeric) = 1.626619529406275 absolute error = 5.10702591327572e-15 relative error = 3.139656091021991e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 1.628596684308227 y[1] (numeric) = 1.628596684308232 absolute error = 5.10702591327572e-15 relative error = 3.13584447425362e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = 1.630544824366878 y[1] (numeric) = 1.630544824366883 absolute error = 5.329070518200751e-15 relative error = 3.268276001102863e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = 1.632464872260529 y[1] (numeric) = 1.632464872260535 absolute error = 5.773159728050814e-15 relative error = 3.536467967029836e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = 1.63435775447667 y[1] (numeric) = 1.634357754476676 absolute error = 5.995204332975845e-15 relative error = 3.668232562028956e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = 1.636224401219326 y[1] (numeric) = 1.636224401219333 absolute error = 6.883382752675971e-15 relative error = 4.206869636919254e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 1.638065746316043 y[1] (numeric) = 1.63806574631605 absolute error = 7.105427357601002e-15 relative error = 4.337693632615711e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 1.639882727124498 y[1] (numeric) = 1.639882727124506 absolute error = 7.771561172376096e-15 relative error = 4.739095694972881e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 1.641676284438772 y[1] (numeric) = 1.641676284438779 absolute error = 7.549516567451064e-15 relative error = 4.598663353434484e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = 1.643447362395264 y[1] (numeric) = 1.643447362395271 absolute error = 7.327471962526033e-15 relative error = 4.458598510783159e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = 1.645196908378284 y[1] (numeric) = 1.645196908378292 absolute error = 7.549516567451064e-15 relative error = 4.588822486235298e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = 1.646925872925314 y[1] (numeric) = 1.646925872925321 absolute error = 7.327471962526033e-15 relative error = 4.449181400927767e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = 1.648635209631951 y[1] (numeric) = 1.648635209631958 absolute error = 7.549516567451064e-15 relative error = 4.579252295076517e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = 1.650325875056552 y[1] (numeric) = 1.65032587505656 absolute error = 7.993605777301127e-15 relative error = 4.843652940378946e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y[1] (closed_form) = 1.651998828624582 y[1] (numeric) = 1.651998828624591 absolute error = 8.43769498715119e-15 relative error = 5.107567173141539e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y[1] (closed_form) = 1.653655032532664 y[1] (numeric) = 1.653655032532673 absolute error = 8.659739592076221e-15 relative error = 5.236726778990507e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = 1.655295451652367 y[1] (numeric) = 1.655295451652377 absolute error = 9.325873406851315e-15 relative error = 5.633963047226366e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = 1.656921053433718 y[1] (numeric) = 1.656921053433727 absolute error = 9.103828801926284e-15 relative error = 5.4944252069584e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = 1.658532807808454 y[1] (numeric) = 1.658532807808463 absolute error = 9.103828801926284e-15 relative error = 5.489085750408441e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y[1] (closed_form) = 1.660131687093036 y[1] (numeric) = 1.660131687093045 absolute error = 9.325873406851315e-15 relative error = 5.617550390343633e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y[1] (closed_form) = 1.661718665891413 y[1] (numeric) = 1.661718665891423 absolute error = 9.547918011776346e-15 relative error = 5.745808967400903e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y[1] (closed_form) = 1.663294720997567 y[1] (numeric) = 1.663294720997576 absolute error = 9.547918011776346e-15 relative error = 5.740364525446188e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y[1] (closed_form) = 1.664860831297828 y[1] (numeric) = 1.664860831297837 absolute error = 9.547918011776346e-15 relative error = 5.734964648266335e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y[1] (closed_form) = 1.666417977672993 y[1] (numeric) = 1.666417977673003 absolute error = 9.992007221626409e-15 relative error = 5.996099031276279e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y[1] (closed_form) = 1.667967142900234 y[1] (numeric) = 1.667967142900245 absolute error = 1.021405182655144e-14 relative error = 6.123652896897844e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y[1] (closed_form) = 1.669509311554824 y[1] (numeric) = 1.669509311554835 absolute error = 1.043609643147647e-14 relative error = 6.250996241379014e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = 1.671045469911679 y[1] (numeric) = 1.671045469911689 absolute error = 1.021405182655144e-14 relative error = 6.11237217087294e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = 1.67257660584673 y[1] (numeric) = 1.67257660584674 absolute error = 1.06581410364015e-14 relative error = 6.372288718582129e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = 1.674103708738138 y[1] (numeric) = 1.674103708738149 absolute error = 1.043609643147647e-14 relative error = 6.233841055965833e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y[1] (closed_form) = 1.675627769367359 y[1] (numeric) = 1.675627769367369 absolute error = 1.021405182655144e-14 relative error = 6.095656811899102e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y[1] (closed_form) = 1.677149779820062 y[1] (numeric) = 1.677149779820073 absolute error = 1.06581410364015e-14 relative error = 6.354913058239196e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y[1] (closed_form) = 1.678670733386924 y[1] (numeric) = 1.678670733386934 absolute error = 1.043609643147647e-14 relative error = 6.216881145250187e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y[1] (closed_form) = 1.680191624464302 y[1] (numeric) = 1.680191624464313 absolute error = 1.088018564132653e-14 relative error = 6.475562360213217e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y[1] (closed_form) = 1.681713448454792 y[1] (numeric) = 1.681713448454804 absolute error = 1.13242748511766e-14 relative error = 6.733771952398711e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y[1] (closed_form) = 1.683237201667695 y[1] (numeric) = 1.683237201667706 absolute error = 1.154631945610163e-14 relative error = 6.859591413890998e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = 1.684763881219377 y[1] (numeric) = 1.684763881219389 absolute error = 1.154631945610163e-14 relative error = 6.853375469887671e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = 1.686294484933571 y[1] (numeric) = 1.686294484933583 absolute error = 1.199040866595169e-14 relative error = 7.110506956573505e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = 1.687830011241582 y[1] (numeric) = 1.687830011241594 absolute error = 1.221245327087672e-14 relative error = 7.235594336833208e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = 1.689371459082457 y[1] (numeric) = 1.689371459082469 absolute error = 1.199040866595169e-14 relative error = 7.097556077136525e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y[1] (closed_form) = 1.690919827803083 y[1] (numeric) = 1.690919827803095 absolute error = 1.176836406102666e-14 relative error = 6.959741004584842e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y[1] (closed_form) = 1.692476117058258 y[1] (numeric) = 1.69247611705827 absolute error = 1.221245327087672e-14 relative error = 7.215731523646871e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y[1] (closed_form) = 1.694041326710723 y[1] (numeric) = 1.694041326710736 absolute error = 1.287858708565182e-14 relative error = 7.602286250393806e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999937 y[1] (closed_form) = 1.695616456731182 y[1] (numeric) = 1.695616456731194 absolute error = 1.265654248072678e-14 relative error = 7.464272023595556e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999936 y[1] (closed_form) = 1.697202507098297 y[1] (numeric) = 1.69720250709831 absolute error = 1.265654248072678e-14 relative error = 7.457296597072345e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999935 y[1] (closed_form) = 1.698800477698701 y[1] (numeric) = 1.698800477698714 absolute error = 1.310063169057685e-14 relative error = 7.711695318289389e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y[1] (closed_form) = 1.700411368227002 y[1] (numeric) = 1.700411368227015 absolute error = 1.332267629550188e-14 relative error = 7.834972492211265e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y[1] (closed_form) = 1.702036178085819 y[1] (numeric) = 1.702036178085832 absolute error = 1.310063169057685e-14 relative error = 7.697034798232296e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y[1] (closed_form) = 1.70367590628584 y[1] (numeric) = 1.703675906285854 absolute error = 1.332267629550188e-14 relative error = 7.819959328148541e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y[1] (closed_form) = 1.705331551345926 y[1] (numeric) = 1.70533155134594 absolute error = 1.354472090042691e-14 relative error = 7.942573331113701e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999929 y[1] (closed_form) = 1.707004111193254 y[1] (numeric) = 1.707004111193268 absolute error = 1.376676550535194e-14 relative error = 8.064869565972224e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999928 y[1] (closed_form) = 1.708694583063529 y[1] (numeric) = 1.708694583063543 absolute error = 1.398881011027697e-14 relative error = 8.186840555903415e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999927 y[1] (closed_form) = 1.710403963401259 y[1] (numeric) = 1.710403963401274 absolute error = 1.443289932012704e-14 relative error = 8.438298570956415e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999926 y[1] (closed_form) = 1.712133247760116 y[1] (numeric) = 1.712133247760131 absolute error = 1.465494392505207e-14 relative error = 8.559464600213958e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999925 y[1] (closed_form) = 1.713883430703375 y[1] (numeric) = 1.713883430703389 absolute error = 1.48769885299771e-14 relative error = 8.680280270795085e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999924 y[1] (closed_form) = 1.715655505704462 y[1] (numeric) = 1.715655505704477 absolute error = 1.509903313490213e-14 relative error = 8.800737143732328e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y[1] (closed_form) = 1.717450465047608 y[1] (numeric) = 1.717450465047624 absolute error = 1.532107773982716e-14 relative error = 8.920826569168301e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y[1] (closed_form) = 1.719269299728622 y[1] (numeric) = 1.719269299728638 absolute error = 1.576516694967722e-14 relative error = 9.169690258626542e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y[1] (closed_form) = 1.721112999355787 y[1] (numeric) = 1.721112999355803 absolute error = 1.598721155460225e-14 relative error = 9.288879672971077e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y[1] (closed_form) = 1.722982552050908 y[1] (numeric) = 1.722982552050924 absolute error = 1.598721155460225e-14 relative error = 9.278800609775352e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999918 y[1] (closed_form) = 1.724878944350492 y[1] (numeric) = 1.724878944350508 absolute error = 1.598721155460225e-14 relative error = 9.268599171533327e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999917 y[1] (closed_form) = 1.726803161107104 y[1] (numeric) = 1.72680316110712 absolute error = 1.643130076445232e-14 relative error = 9.515445150052732e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999916 y[1] (closed_form) = 1.728756185390874 y[1] (numeric) = 1.728756185390891 absolute error = 1.643130076445232e-14 relative error = 9.504695285146398e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999915 y[1] (closed_form) = 1.730738998391199 y[1] (numeric) = 1.730738998391216 absolute error = 1.687538997430238e-14 relative error = 9.750395634459513e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999914 y[1] (closed_form) = 1.732752579318618 y[1] (numeric) = 1.732752579318635 absolute error = 1.731947918415244e-14 relative error = 9.995356169640273e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999913 y[1] (closed_form) = 1.734797905306895 y[1] (numeric) = 1.734797905306912 absolute error = 1.731947918415244e-14 relative error = 9.983571648991895e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y[1] (closed_form) = 1.736875951315307 y[1] (numeric) = 1.736875951315325 absolute error = 1.77635683940025e-14 relative error = 1.022730977451237e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y[1] (closed_form) = 1.738987690031147 y[1] (numeric) = 1.738987690031165 absolute error = 1.798561299892754e-14 relative error = 1.034257637476744e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y[1] (closed_form) = 1.741134091772458 y[1] (numeric) = 1.741134091772476 absolute error = 1.77635683940025e-14 relative error = 1.020229773108363e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999908 y[1] (closed_form) = 1.743316124391 y[1] (numeric) = 1.743316124391018 absolute error = 1.798561299892754e-14 relative error = 1.031689706031402e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999907 y[1] (closed_form) = 1.745534753175466 y[1] (numeric) = 1.745534753175485 absolute error = 1.84297022087776e-14 relative error = 1.05581983831891e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999906 y[1] (closed_form) = 1.747790940754958 y[1] (numeric) = 1.747790940754976 absolute error = 1.84297022087776e-14 relative error = 1.054456902083317e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999905 y[1] (closed_form) = 1.750085647002717 y[1] (numeric) = 1.750085647002736 absolute error = 1.865174681370263e-14 relative error = 1.065761944030941e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999904 y[1] (closed_form) = 1.752419828940144 y[1] (numeric) = 1.752419828940163 absolute error = 1.887379141862766e-14 relative error = 1.077013116773647e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999903 y[1] (closed_form) = 1.754794440641094 y[1] (numeric) = 1.754794440641114 absolute error = 1.953992523340276e-14 relative error = 1.113516476964907e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999902 y[1] (closed_form) = 1.757210433136473 y[1] (numeric) = 1.757210433136493 absolute error = 1.998401444325282e-14 relative error = 1.137257898451185e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y[1] (closed_form) = 1.75966875431913 y[1] (numeric) = 1.759668754319151 absolute error = 2.065014825802791e-14 relative error = 1.173524744776075e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y[1] (closed_form) = 1.762170348849076 y[1] (numeric) = 1.762170348849097 absolute error = 2.087219286295294e-14 relative error = 1.184459429622407e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y[1] (closed_form) = 1.764716158059014 y[1] (numeric) = 1.764716158059035 absolute error = 2.109423746787797e-14 relative error = 1.195333162874149e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999897 y[1] (closed_form) = 1.767307119860206 y[1] (numeric) = 1.767307119860227 absolute error = 2.109423746787797e-14 relative error = 1.193580743880358e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999896 y[1] (closed_form) = 1.769944168648685 y[1] (numeric) = 1.769944168648707 absolute error = 2.131628207280301e-14 relative error = 1.204347710531318e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999895 y[1] (closed_form) = 1.772628235211817 y[1] (numeric) = 1.772628235211839 absolute error = 2.176037128265307e-14 relative error = 1.22757670505304e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999894 y[1] (closed_form) = 1.775360246635219 y[1] (numeric) = 1.775360246635241 absolute error = 2.176037128265307e-14 relative error = 1.225687649810498e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999893 y[1] (closed_form) = 1.778141126210054 y[1] (numeric) = 1.778141126210076 absolute error = 2.19824158875781e-14 relative error = 1.236258222902229e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999892 y[1] (closed_form) = 1.780971793340703 y[1] (numeric) = 1.780971793340726 absolute error = 2.242650509742816e-14 relative error = 1.259228539232565e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999891 y[1] (closed_form) = 1.783853163452826 y[1] (numeric) = 1.783853163452849 absolute error = 2.287059430727822e-14 relative error = 1.28208951139285e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.00999999999989 y[1] (closed_form) = 1.786786147901815 y[1] (numeric) = 1.786786147901838 absolute error = 2.287059430727822e-14 relative error = 1.279984979407562e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999889 y[1] (closed_form) = 1.789771653881666 y[1] (numeric) = 1.789771653881689 absolute error = 2.309263891220326e-14 relative error = 1.290256154304367e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999887 y[1] (closed_form) = 1.792810584334256 y[1] (numeric) = 1.79281058433428 absolute error = 2.331468351712829e-14 relative error = 1.300454365946639e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999886 y[1] (closed_form) = 1.795903837859053 y[1] (numeric) = 1.795903837859076 absolute error = 2.309263891220326e-14 relative error = 1.285850524142353e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999885 y[1] (closed_form) = 1.799052308623251 y[1] (numeric) = 1.799052308623274 absolute error = 2.353672812205332e-14 relative error = 1.30828481246691e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999884 y[1] (closed_form) = 1.80225688627236 y[1] (numeric) = 1.802256886272384 absolute error = 2.398081733190338e-14 relative error = 1.330599289954904e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999883 y[1] (closed_form) = 1.805518455841242 y[1] (numeric) = 1.805518455841266 absolute error = 2.420286193682841e-14 relative error = 1.340493743419068e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999882 y[1] (closed_form) = 1.808837897665601 y[1] (numeric) = 1.808837897665626 absolute error = 2.509104035652854e-14 relative error = 1.38713592792974e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.089999999999881 y[1] (closed_form) = 1.81221608729396 y[1] (numeric) = 1.812216087293986 absolute error = 2.531308496145357e-14 relative error = 1.396802795148541e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09999999999988 y[1] (closed_form) = 1.815653895400101 y[1] (numeric) = 1.815653895400127 absolute error = 2.575717417130363e-14 relative error = 1.418616964199982e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999879 y[1] (closed_form) = 1.819152187695998 y[1] (numeric) = 1.819152187696024 absolute error = 2.597921877622866e-14 relative error = 1.428094853852332e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999878 y[1] (closed_form) = 1.822711824845249 y[1] (numeric) = 1.822711824845275 absolute error = 2.620126338115369e-14 relative error = 1.437487979394561e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y[1] (closed_form) = 1.82633366237701 y[1] (numeric) = 1.826333662377036 absolute error = 2.620126338115369e-14 relative error = 1.434637269240946e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999875 y[1] (closed_form) = 1.830018550600442 y[1] (numeric) = 1.830018550600469 absolute error = 2.664535259100376e-14 relative error = 1.4560154366884e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999874 y[1] (closed_form) = 1.833767334519681 y[1] (numeric) = 1.833767334519709 absolute error = 2.731148640577885e-14 relative error = 1.489364866068604e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999873 y[1] (closed_form) = 1.837580853749339 y[1] (numeric) = 1.837580853749366 absolute error = 2.753353101070388e-14 relative error = 1.498357525576378e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999872 y[1] (closed_form) = 1.84145994243054 y[1] (numeric) = 1.841459942430568 absolute error = 2.842170943040401e-14 relative error = 1.543433488587878e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.179999999999871 y[1] (closed_form) = 1.845405429147512 y[1] (numeric) = 1.845405429147541 absolute error = 2.864375403532904e-14 relative error = 1.552165913403705e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18999999999987 y[1] (closed_form) = 1.849418136844725 y[1] (numeric) = 1.849418136844755 absolute error = 2.930988785010413e-14 relative error = 1.58481671971215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999869 y[1] (closed_form) = 1.8534988827446 y[1] (numeric) = 1.85349888274463 absolute error = 2.997602166487923e-14 relative error = 1.617266778196905e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999868 y[1] (closed_form) = 1.857648478265785 y[1] (numeric) = 1.857648478265815 absolute error = 3.064215547965432e-14 relative error = 1.649513125769652e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999867 y[1] (closed_form) = 1.861867728942014 y[1] (numeric) = 1.861867728942044 absolute error = 3.086420008457935e-14 relative error = 1.657701006618639e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999865 y[1] (closed_form) = 1.866157434341557 y[1] (numeric) = 1.866157434341588 absolute error = 3.108624468950438e-14 relative error = 1.665788969218058e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999864 y[1] (closed_form) = 1.870518387987261 y[1] (numeric) = 1.870518387987292 absolute error = 3.175237850427948e-14 relative error = 1.697517581660669e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999863 y[1] (closed_form) = 1.8749513772772 y[1] (numeric) = 1.874951377277232 absolute error = 3.241851231905457e-14 relative error = 1.729032161150369e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999862 y[1] (closed_form) = 1.879457183405935 y[1] (numeric) = 1.879457183405967 absolute error = 3.26405569239796e-14 relative error = 1.736701278016278e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.269999999999861 y[1] (closed_form) = 1.884036581286395 y[1] (numeric) = 1.884036581286428 absolute error = 3.308464613382966e-14 relative error = 1.756051154337986e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27999999999986 y[1] (closed_form) = 1.888690339472389 y[1] (numeric) = 1.888690339472422 absolute error = 3.375077994860476e-14 relative error = 1.786993836058543e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999859 y[1] (closed_form) = 1.893419220081745 y[1] (numeric) = 1.89341922008178 absolute error = 3.463895836830488e-14 relative error = 1.829439460681582e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999858 y[1] (closed_form) = 1.898223978720107 y[1] (numeric) = 1.898223978720142 absolute error = 3.508304757815495e-14 relative error = 1.848203793200946e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999857 y[1] (closed_form) = 1.903105364405369 y[1] (numeric) = 1.903105364405404 absolute error = 3.552713678800501e-14 relative error = 1.866798205316687e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999856 y[1] (closed_form) = 1.908064119492775 y[1] (numeric) = 1.908064119492811 absolute error = 3.597122599785507e-14 relative error = 1.885221027447305e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999854 y[1] (closed_form) = 1.913100979600688 y[1] (numeric) = 1.913100979600725 absolute error = 3.68594044175552e-14 relative error = 1.92668368322349e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999853 y[1] (closed_form) = 1.918216673537022 y[1] (numeric) = 1.918216673537059 absolute error = 3.708144902248023e-14 relative error = 1.933120983361348e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999852 y[1] (closed_form) = 1.923411923226369 y[1] (numeric) = 1.923411923226406 absolute error = 3.752553823233029e-14 relative error = 1.950988125798046e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999851 y[1] (closed_form) = 1.9286874436378 y[1] (numeric) = 1.928687443637838 absolute error = 3.774758283725532e-14 relative error = 1.957164337942575e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36999999999985 y[1] (closed_form) = 1.934043942713376 y[1] (numeric) = 1.934043942713415 absolute error = 3.885780586188048e-14 relative error = 2.009148034525252e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999849 y[1] (closed_form) = 1.939482121297349 y[1] (numeric) = 1.939482121297388 absolute error = 3.930189507173054e-14 relative error = 2.026411826134335e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999848 y[1] (closed_form) = 1.945002673066078 y[1] (numeric) = 1.945002673066118 absolute error = 3.97459842815806e-14 relative error = 2.043492527386892e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999847 y[1] (closed_form) = 1.950606284458668 y[1] (numeric) = 1.950606284458708 absolute error = 4.04121180963557e-14 relative error = 2.071772167368509e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999846 y[1] (closed_form) = 1.956293634608319 y[1] (numeric) = 1.95629363460836 absolute error = 4.107825191113079e-14 relative error = 2.099799906538842e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y[1] (closed_form) = 1.962065395274419 y[1] (numeric) = 1.96206539527446 absolute error = 4.130029651605582e-14 relative error = 2.104939856516835e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y[1] (closed_form) = 1.967922230775364 y[1] (numeric) = 1.967922230775406 absolute error = 4.218847493575595e-14 relative error = 2.143808036516445e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y[1] (closed_form) = 1.973864797922132 y[1] (numeric) = 1.973864797922174 absolute error = 4.285460875053104e-14 relative error = 2.171101526084445e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y[1] (closed_form) = 1.979893745952596 y[1] (numeric) = 1.97989374595264 absolute error = 4.39648317751562e-14 relative error = 2.220565212907583e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y[1] (closed_form) = 1.986009716466608 y[1] (numeric) = 1.986009716466653 absolute error = 4.463096558993129e-14 relative error = 2.247268239419094e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y[1] (closed_form) = 1.992213343361834 y[1] (numeric) = 1.992213343361879 absolute error = 4.529709940470639e-14 relative error = 2.273707259096464e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999838 y[1] (closed_form) = 1.998505252770366 y[1] (numeric) = 1.998505252770412 absolute error = 4.574118861455645e-14 relative error = 2.28876999703399e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999837 y[1] (closed_form) = 2.004886062996111 y[1] (numeric) = 2.004886062996158 absolute error = 4.662936703425657e-14 relative error = 2.325786382323065e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999836 y[1] (closed_form) = 2.011356384452959 y[1] (numeric) = 2.011356384453006 absolute error = 4.707345624410664e-14 relative error = 2.340383663878119e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999835 y[1] (closed_form) = 2.017916819603744 y[1] (numeric) = 2.017916819603793 absolute error = 4.840572387365683e-14 relative error = 2.398796789015426e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y[1] (closed_form) = 2.024567962899999 y[1] (numeric) = 2.024567962900047 absolute error = 4.840572387365683e-14 relative error = 2.390916223149174e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999832 y[1] (closed_form) = 2.031310400722504 y[1] (numeric) = 2.031310400722553 absolute error = 4.884981308350689e-14 relative error = 2.404842365112284e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999831 y[1] (closed_form) = 2.038144711322662 y[1] (numeric) = 2.038144711322711 absolute error = 4.929390229335695e-14 relative error = 2.418567338202766e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54999999999983 y[1] (closed_form) = 2.045071464764659 y[1] (numeric) = 2.045071464764709 absolute error = 5.018208071305708e-14 relative error = 2.453805726482614e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999829 y[1] (closed_form) = 2.052091222868472 y[1] (numeric) = 2.052091222868522 absolute error = 5.062616992290714e-14 relative error = 2.467052602668435e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999828 y[1] (closed_form) = 2.059204539153675 y[1] (numeric) = 2.059204539153727 absolute error = 5.151434834260726e-14 relative error = 2.501662528569379e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999827 y[1] (closed_form) = 2.066411958784099 y[1] (numeric) = 2.066411958784151 absolute error = 5.195843755245733e-14 relative error = 2.514427838630506e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999826 y[1] (closed_form) = 2.073714018513306 y[1] (numeric) = 2.073714018513359 absolute error = 5.240252676230739e-14 relative error = 2.526989078266249e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999825 y[1] (closed_form) = 2.081111246630922 y[1] (numeric) = 2.081111246630976 absolute error = 5.329070518200751e-14 relative error = 2.560685079583275e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999824 y[1] (closed_form) = 2.088604162909804 y[1] (numeric) = 2.088604162909857 absolute error = 5.373479439185758e-14 relative error = 2.572761049992129e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y[1] (closed_form) = 2.096193278554062 y[1] (numeric) = 2.096193278554117 absolute error = 5.506706202140776e-14 relative error = 2.627003081480759e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999821 y[1] (closed_form) = 2.103879096147945 y[1] (numeric) = 2.103879096148001 absolute error = 5.595524044110789e-14 relative error = 2.659622434747225e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999982 y[1] (closed_form) = 2.111662109605578 y[1] (numeric) = 2.111662109605635 absolute error = 5.728750807065808e-14 relative error = 2.71291073557968e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999819 y[1] (closed_form) = 2.119542804121571 y[1] (numeric) = 2.119542804121629 absolute error = 5.861977570020827e-14 relative error = 2.765680201702877e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999818 y[1] (closed_form) = 2.127521656122502 y[1] (numeric) = 2.127521656122562 absolute error = 5.995204332975845e-14 relative error = 2.817928699208805e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999817 y[1] (closed_form) = 2.135599133219275 y[1] (numeric) = 2.135599133219336 absolute error = 6.084022174945858e-14 relative error = 2.848859638641357e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999816 y[1] (closed_form) = 2.143775694160357 y[1] (numeric) = 2.143775694160418 absolute error = 6.17284001691587e-14 relative error = 2.879424388349342e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999815 y[1] (closed_form) = 2.152051788785904 y[1] (numeric) = 2.152051788785967 absolute error = 6.261657858885883e-14 relative error = 2.909622292323385e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999814 y[1] (closed_form) = 2.160427857982782 y[1] (numeric) = 2.160427857982845 absolute error = 6.306066779870889e-14 relative error = 2.918897178894435e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999813 y[1] (closed_form) = 2.16890433364047 y[1] (numeric) = 2.168904333640533 absolute error = 6.261657858885883e-14 relative error = 2.88701431490793e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y[1] (closed_form) = 2.177481638607879 y[1] (numeric) = 2.177481638607943 absolute error = 6.394884621840902e-14 relative error = 2.936825968337128e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999981 y[1] (closed_form) = 2.186160186651065 y[1] (numeric) = 2.18616018665113 absolute error = 6.483702463810914e-14 relative error = 2.965794777254254e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999809 y[1] (closed_form) = 2.194940382411851 y[1] (numeric) = 2.194940382411917 absolute error = 6.572520305780927e-14 relative error = 2.994395819789369e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999808 y[1] (closed_form) = 2.203822621367365 y[1] (numeric) = 2.203822621367431 absolute error = 6.616929226765933e-14 relative error = 3.00247813168396e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999807 y[1] (closed_form) = 2.212807289790493 y[1] (numeric) = 2.21280728979056 absolute error = 6.750155989720952e-14 relative error = 3.050494284280875e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999806 y[1] (closed_form) = 2.221894764711251 y[1] (numeric) = 2.221894764711318 absolute error = 6.750155989720952e-14 relative error = 3.038017865170215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999805 y[1] (closed_form) = 2.231085413879081 y[1] (numeric) = 2.231085413879149 absolute error = 6.883382752675971e-14 relative error = 3.085217047207603e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999804 y[1] (closed_form) = 2.24037959572608 y[1] (numeric) = 2.24037959572615 absolute error = 6.972200594645983e-14 relative error = 3.112062173725688e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999803 y[1] (closed_form) = 2.249777659331155 y[1] (numeric) = 2.249777659331226 absolute error = 7.016609515630989e-14 relative error = 3.118801312000308e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999802 y[1] (closed_form) = 2.259279944385114 y[1] (numeric) = 2.259279944385186 absolute error = 7.149836278586008e-14 relative error = 3.164652656858735e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y[1] (closed_form) = 2.2688867811567 y[1] (numeric) = 2.268886781156773 absolute error = 7.283063041541027e-14 relative error = 3.2099720012596e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999799 y[1] (closed_form) = 2.278598490459562 y[1] (numeric) = 2.278598490459636 absolute error = 7.460698725481052e-14 relative error = 3.274248954661746e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999798 y[1] (closed_form) = 2.288415383620174 y[1] (numeric) = 2.28841538362025 absolute error = 7.549516567451064e-14 relative error = 3.299014952219057e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999797 y[1] (closed_form) = 2.298337762446708 y[1] (numeric) = 2.298337762446784 absolute error = 7.593925488436071e-14 relative error = 3.304094642883088e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999796 y[1] (closed_form) = 2.308365919198842 y[1] (numeric) = 2.308365919198919 absolute error = 7.72715225139109e-14 relative error = 3.347455525626947e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999795 y[1] (closed_form) = 2.318500136558548 y[1] (numeric) = 2.318500136558626 absolute error = 7.815970093361102e-14 relative error = 3.371132039251329e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999794 y[1] (closed_form) = 2.328740687601813 y[1] (numeric) = 2.328740687601892 absolute error = 7.904787935331115e-14 relative error = 3.394447470006476e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999793 y[1] (closed_form) = 2.339087835771338 y[1] (numeric) = 2.339087835771419 absolute error = 8.126832540256146e-14 relative error = 3.47435971235182e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999792 y[1] (closed_form) = 2.349541834850191 y[1] (numeric) = 2.349541834850272 absolute error = 8.126832540256146e-14 relative error = 3.458900973676139e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.909999999999791 y[1] (closed_form) = 2.360102928936429 y[1] (numeric) = 2.360102928936512 absolute error = 8.260059303211165e-14 relative error = 3.499872485194333e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y[1] (closed_form) = 2.370771352418692 y[1] (numeric) = 2.370771352418774 absolute error = 8.260059303211165e-14 relative error = 3.484123129286232e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999788 y[1] (closed_form) = 2.381547329952758 y[1] (numeric) = 2.381547329952842 absolute error = 8.393286066166183e-14 relative error = 3.524299500834476e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999787 y[1] (closed_form) = 2.392431076439083 y[1] (numeric) = 2.392431076439169 absolute error = 8.615330671091215e-14 relative error = 3.601077897681531e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999786 y[1] (closed_form) = 2.40342279700131 y[1] (numeric) = 2.403422797001397 absolute error = 8.704148513061227e-14 relative error = 3.621563598348644e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999785 y[1] (closed_form) = 2.414522686965754 y[1] (numeric) = 2.414522686965842 absolute error = 8.79296635503124e-14 relative error = 3.641699621419194e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999784 y[1] (closed_form) = 2.425730931841873 y[1] (numeric) = 2.425730931841962 absolute error = 8.926193117986259e-14 relative error = 3.67979523236262e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999783 y[1] (closed_form) = 2.437047707303716 y[1] (numeric) = 2.437047707303806 absolute error = 9.059419880941277e-14 relative error = 3.717374860488216e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999782 y[1] (closed_form) = 2.448473179172353 y[1] (numeric) = 2.448473179172445 absolute error = 9.192646643896296e-14 relative error = 3.754440408860695e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.999999999999781 y[1] (closed_form) = 2.4600075033993 y[1] (numeric) = 2.460007503399393 absolute error = 9.325873406851315e-14 relative error = 3.790993886792861e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.00999999999978 y[1] (closed_form) = 2.471650826050916 y[1] (numeric) = 2.471650826051011 absolute error = 9.50350909079134e-14 relative error = 3.845004719366281e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y[1] (closed_form) = 2.483403283293801 y[1] (numeric) = 2.483403283293897 absolute error = 9.547918011776346e-14 relative error = 3.844690903006579e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999777 y[1] (closed_form) = 2.495265001381179 y[1] (numeric) = 2.495265001381276 absolute error = 9.681144774731365e-14 relative error = 3.879806260807032e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999776 y[1] (closed_form) = 2.507236096640272 y[1] (numeric) = 2.50723609664037 absolute error = 9.814371537686384e-14 relative error = 3.914418570647482e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999775 y[1] (closed_form) = 2.519316675460666 y[1] (numeric) = 2.519316675460766 absolute error = 9.992007221626409e-14 relative error = 3.966157696232981e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999774 y[1] (closed_form) = 2.531506834283677 y[1] (numeric) = 2.531506834283778 absolute error = 1.016964290556643e-13 relative error = 4.017229093692757e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999773 y[1] (closed_form) = 2.543806659592701 y[1] (numeric) = 2.543806659592804 absolute error = 1.034727858950646e-13 relative error = 4.06763562414889e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999772 y[1] (closed_form) = 2.55621622790457 y[1] (numeric) = 2.556216227904675 absolute error = 1.048050535246148e-13 relative error = 4.100007361682684e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.089999999999771 y[1] (closed_form) = 2.568735605761898 y[1] (numeric) = 2.568735605762005 absolute error = 1.06581410364015e-13 relative error = 4.149177911691013e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09999999999977 y[1] (closed_form) = 2.581364849726429 y[1] (numeric) = 2.581364849726537 absolute error = 1.088018564132653e-13 relative error = 4.214896488762373e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999769 y[1] (closed_form) = 2.594104006373376 y[1] (numeric) = 2.594104006373486 absolute error = 1.105782132526656e-13 relative error = 4.26267462603617e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y[1] (closed_form) = 2.606953112286772 y[1] (numeric) = 2.606953112286884 absolute error = 1.119104808822158e-13 relative error = 4.292769223764441e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999766 y[1] (closed_form) = 2.619912194055802 y[1] (numeric) = 2.619912194055916 absolute error = 1.141309269314661e-13 relative error = 4.356288244713411e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999765 y[1] (closed_form) = 2.632981268272152 y[1] (numeric) = 2.632981268272268 absolute error = 1.154631945610163e-13 relative error = 4.385264565014812e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999764 y[1] (closed_form) = 2.646160341528346 y[1] (numeric) = 2.646160341528463 absolute error = 1.172395514004165e-13 relative error = 4.430553567011073e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999763 y[1] (closed_form) = 2.659449410417086 y[1] (numeric) = 2.659449410417205 absolute error = 1.190159082398168e-13 relative error = 4.475208581657183e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999762 y[1] (closed_form) = 2.672848461531594 y[1] (numeric) = 2.672848461531714 absolute error = 1.20348175869367e-13 relative error = 4.502618745561248e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.179999999999761 y[1] (closed_form) = 2.686357471466954 y[1] (numeric) = 2.686357471467077 absolute error = 1.225686219186173e-13 relative error = 4.562632606437353e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18999999999976 y[1] (closed_form) = 2.699976406822453 y[1] (numeric) = 2.699976406822577 absolute error = 1.243449787580175e-13 relative error = 4.605409826686472e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999759 y[1] (closed_form) = 2.713705224204914 y[1] (numeric) = 2.713705224205039 absolute error = 1.252331571777177e-13 relative error = 4.614840110882331e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y[1] (closed_form) = 2.727543870233045 y[1] (numeric) = 2.727543870233172 absolute error = 1.265654248072678e-13 relative error = 4.640270911442898e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y[1] (closed_form) = 2.741492281542772 y[1] (numeric) = 2.7414922815429 absolute error = 1.27453603226968e-13 relative error = 4.649059349357116e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999755 y[1] (closed_form) = 2.755550384793574 y[1] (numeric) = 2.755550384793703 absolute error = 1.292299600663682e-13 relative error = 4.689805738248158e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999754 y[1] (closed_form) = 2.76971809667582 y[1] (numeric) = 2.769718096675951 absolute error = 1.305622276959184e-13 relative error = 4.713917559069188e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999753 y[1] (closed_form) = 2.7839953239191 y[1] (numeric) = 2.783995323919232 absolute error = 1.323385845353187e-13 relative error = 4.753549095370689e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999752 y[1] (closed_form) = 2.798381963301549 y[1] (numeric) = 2.798381963301683 absolute error = 1.341149413747189e-13 relative error = 4.792588829313681e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.269999999999751 y[1] (closed_form) = 2.812877901660173 y[1] (numeric) = 2.812877901660309 absolute error = 1.363353874239692e-13 relative error = 4.846829197367703e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27999999999975 y[1] (closed_form) = 2.82748301590216 y[1] (numeric) = 2.827483015902298 absolute error = 1.381117442633695e-13 relative error = 4.884617997229681e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999749 y[1] (closed_form) = 2.842197173017196 y[1] (numeric) = 2.842197173017335 absolute error = 1.389999226830696e-13 relative error = 4.890579865559124e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999748 y[1] (closed_form) = 2.85702023009076 y[1] (numeric) = 2.8570202300909 absolute error = 1.398881011027697e-13 relative error = 4.896293684918215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y[1] (closed_form) = 2.871952034318417 y[1] (numeric) = 2.871952034318559 absolute error = 1.425526363618701e-13 relative error = 4.96361480478908e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999745 y[1] (closed_form) = 2.886992423021101 y[1] (numeric) = 2.886992423021245 absolute error = 1.443289932012704e-13 relative error = 4.999285486528464e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999744 y[1] (closed_form) = 2.902141223661379 y[1] (numeric) = 2.902141223661525 absolute error = 1.456612608308205e-13 relative error = 5.019096232920477e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y[1] (closed_form) = 2.917398253860708 y[1] (numeric) = 2.917398253860856 absolute error = 1.478817068800709e-13 relative error = 5.068958503844073e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y[1] (closed_form) = 2.932763321417668 y[1] (numeric) = 2.932763321417817 absolute error = 1.49213974509621e-13 relative error = 5.087828718394245e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y[1] (closed_form) = 2.948236224327188 y[1] (numeric) = 2.948236224327339 absolute error = 1.505462421391712e-13 relative error = 5.10631546064553e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y[1] (closed_form) = 2.963816750800741 y[1] (numeric) = 2.963816750800893 absolute error = 1.518785097687214e-13 relative error = 5.124423084783769e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y[1] (closed_form) = 2.979504679287527 y[1] (numeric) = 2.979504679287681 absolute error = 1.540989558179717e-13 relative error = 5.171965558208843e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y[1] (closed_form) = 2.995299778496623 y[1] (numeric) = 2.995299778496779 absolute error = 1.55875312657372e-13 relative error = 5.203997068220252e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999737 y[1] (closed_form) = 3.011201807420119 y[1] (numeric) = 3.011201807420276 absolute error = 1.576516694967722e-13 relative error = 5.235506604316305e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = 3.02721051535721 y[1] (numeric) = 3.027210515357369 absolute error = 1.594280263361725e-13 relative error = 5.266499489460185e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y[1] (closed_form) = 3.043325641939272 y[1] (numeric) = 3.043325641939433 absolute error = 1.612043831755727e-13 relative error = 5.296981070775254e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y[1] (closed_form) = 3.059546917155897 y[1] (numeric) = 3.059546917156061 absolute error = 1.63424829224823e-13 relative error = 5.341471585496718e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y[1] (closed_form) = 3.075874061381895 y[1] (numeric) = 3.075874061382059 absolute error = 1.643130076445232e-13 relative error = 5.341993994731449e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y[1] (closed_form) = 3.092306785405252 y[1] (numeric) = 3.092306785405418 absolute error = 1.665334536937735e-13 relative error = 5.385411773494169e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y[1] (closed_form) = 3.108844790456056 y[1] (numeric) = 3.108844790456224 absolute error = 1.683098105331737e-13 relative error = 5.413902007905751e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999729 y[1] (closed_form) = 3.125487768236371 y[1] (numeric) = 3.12548776823654 absolute error = 1.696420781627239e-13 relative error = 5.42769931422411e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999728 y[1] (closed_form) = 3.142235400951067 y[1] (numeric) = 3.142235400951238 absolute error = 1.714184350021242e-13 relative error = 5.455302137778748e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999727 y[1] (closed_form) = 3.1590873613396 y[1] (numeric) = 3.159087361339774 absolute error = 1.736388810513745e-13 relative error = 5.496488738372323e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999726 y[1] (closed_form) = 3.176043312708737 y[1] (numeric) = 3.176043312708912 absolute error = 1.745270594710746e-13 relative error = 5.495109552590658e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = 3.193102908966225 y[1] (numeric) = 3.193102908966402 absolute error = 1.77191594730175e-13 relative error = 5.549197748454064e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y[1] (closed_form) = 3.210265794655401 y[1] (numeric) = 3.210265794655579 absolute error = 1.785238623597252e-13 relative error = 5.561030574382345e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y[1] (closed_form) = 3.227531604990735 y[1] (numeric) = 3.227531604990916 absolute error = 1.807443084089755e-13 relative error = 5.60007865235124e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y[1] (closed_form) = 3.244899965894311 y[1] (numeric) = 3.244899965894493 absolute error = 1.825206652483757e-13 relative error = 5.624847211524812e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y[1] (closed_form) = 3.262370494033234 y[1] (numeric) = 3.262370494033418 absolute error = 1.84297022087776e-13 relative error = 5.649175114379224e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y[1] (closed_form) = 3.27994279685796 y[1] (numeric) = 3.279942796858145 absolute error = 1.851852005074761e-13 relative error = 5.645988725317872e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999718 y[1] (closed_form) = 3.297616472641555 y[1] (numeric) = 3.297616472641742 absolute error = 1.869615573468764e-13 relative error = 5.669596779916338e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999717 y[1] (closed_form) = 3.315391110519865 y[1] (numeric) = 3.315391110520054 absolute error = 1.891820033961267e-13 relative error = 5.706174538377834e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999716 y[1] (closed_form) = 3.333266290532602 y[1] (numeric) = 3.333266290532793 absolute error = 1.909583602355269e-13 relative error = 5.728866030832925e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999715 y[1] (closed_form) = 3.351241583665338 y[1] (numeric) = 3.351241583665531 absolute error = 1.931788062847772e-13 relative error = 5.76439511930061e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = 3.369316551892412 y[1] (numeric) = 3.369316551892608 absolute error = 1.958433415438776e-13 relative error = 5.812553926815815e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y[1] (closed_form) = 3.387490748220725 y[1] (numeric) = 3.387490748220923 absolute error = 1.976196983832779e-13 relative error = 5.833807767211683e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y[1] (closed_form) = 3.405763716734445 y[1] (numeric) = 3.405763716734644 absolute error = 1.993960552226781e-13 relative error = 5.854664968181217e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y[1] (closed_form) = 3.424134992640592 y[1] (numeric) = 3.424134992640794 absolute error = 2.016165012719284e-13 relative error = 5.888100256130607e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y[1] (closed_form) = 3.442604102315523 y[1] (numeric) = 3.442604102315727 absolute error = 2.038369473211787e-13 relative error = 5.92101041139399e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999708 y[1] (closed_form) = 3.461170563352292 y[1] (numeric) = 3.461170563352497 absolute error = 2.05613304160579e-13 relative error = 5.940571271975506e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999707 y[1] (closed_form) = 3.479833884608885 y[1] (numeric) = 3.479833884609092 absolute error = 2.069455717901292e-13 relative error = 5.946995708773286e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999706 y[1] (closed_form) = 3.498593566257345 y[1] (numeric) = 3.498593566257554 absolute error = 2.096101070492296e-13 relative error = 5.991267721716588e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999705 y[1] (closed_form) = 3.517449099833742 y[1] (numeric) = 3.517449099833954 absolute error = 2.113864638886298e-13 relative error = 6.00965238981344e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999704 y[1] (closed_form) = 3.536399968289029 y[1] (numeric) = 3.536399968289242 absolute error = 2.136069099378801e-13 relative error = 6.040236168230338e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y[1] (closed_form) = 3.555445646040738 y[1] (numeric) = 3.555445646040955 absolute error = 2.162714451969805e-13 relative error = 6.082822428682473e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y[1] (closed_form) = 3.574585599025547 y[1] (numeric) = 3.574585599025765 absolute error = 2.184918912462308e-13 relative error = 6.112369817239598e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y[1] (closed_form) = 3.593819284752676 y[1] (numeric) = 3.593819284752897 absolute error = 2.207123372954811e-13 relative error = 6.141442287648873e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y[1] (closed_form) = 3.613146152358145 y[1] (numeric) = 3.613146152358369 absolute error = 2.238209617644316e-13 relative error = 6.194627959302263e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y[1] (closed_form) = 3.632565642659852 y[1] (numeric) = 3.632565642660078 absolute error = 2.260414078136819e-13 relative error = 6.222637938296662e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999697 y[1] (closed_form) = 3.652077188213495 y[1] (numeric) = 3.652077188213723 absolute error = 2.278177646530821e-13 relative error = 6.238032574676355e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999696 y[1] (closed_form) = 3.671680213369317 y[1] (numeric) = 3.671680213369547 absolute error = 2.300382107023324e-13 relative error = 6.265202777320248e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999695 y[1] (closed_form) = 3.691374134329667 y[1] (numeric) = 3.691374134329898 absolute error = 2.318145675417327e-13 relative error = 6.279899005247512e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999694 y[1] (closed_form) = 3.711158359207381 y[1] (numeric) = 3.711158359207614 absolute error = 2.331468351712829e-13 relative error = 6.28231976662612e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999693 y[1] (closed_form) = 3.731032288084971 y[1] (numeric) = 3.731032288085207 absolute error = 2.362554596402333e-13 relative error = 6.332174084762378e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y[1] (closed_form) = 3.750995313074615 y[1] (numeric) = 3.750995313074853 absolute error = 2.384759056894836e-13 relative error = 6.35767005248561e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y[1] (closed_form) = 3.771046818378945 y[1] (numeric) = 3.771046818379185 absolute error = 2.402522625288839e-13 relative error = 6.3709700276848e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y[1] (closed_form) = 3.791186180352629 y[1] (numeric) = 3.791186180352871 absolute error = 2.424727085781342e-13 relative error = 6.395695094973709e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y[1] (closed_form) = 3.811412767564731 y[1] (numeric) = 3.811412767564975 absolute error = 2.446931546273845e-13 relative error = 6.420011936511644e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y[1] (closed_form) = 3.831725940861855 y[1] (numeric) = 3.831725940862102 absolute error = 2.473576898864849e-13 relative error = 6.455516226999463e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999686 y[1] (closed_form) = 3.852125053432063 y[1] (numeric) = 3.852125053432312 absolute error = 2.491340467258851e-13 relative error = 6.467444417566828e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999685 y[1] (closed_form) = 3.87260945086955 y[1] (numeric) = 3.872609450869802 absolute error = 2.513544927751354e-13 relative error = 6.490571692394559e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999684 y[1] (closed_form) = 3.893178471240089 y[1] (numeric) = 3.893178471240343 absolute error = 2.535749388243858e-13 relative error = 6.51331401058567e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999683 y[1] (closed_form) = 3.913831445147223 y[1] (numeric) = 3.913831445147478 absolute error = 2.557953848736361e-13 relative error = 6.535677084172798e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y[1] (closed_form) = 3.934567695799198 y[1] (numeric) = 3.934567695799456 absolute error = 2.580158309228864e-13 relative error = 6.557666581727923e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y[1] (closed_form) = 3.955386539076652 y[1] (numeric) = 3.955386539076913 absolute error = 2.606803661819868e-13 relative error = 6.590515581894056e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y[1] (closed_form) = 3.976287283601018 y[1] (numeric) = 3.976287283601282 absolute error = 2.633449014410871e-13 relative error = 6.622884179600722e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y[1] (closed_form) = 3.997269230803666 y[1] (numeric) = 3.997269230803932 absolute error = 2.660094367001875e-13 relative error = 6.654779083937394e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y[1] (closed_form) = 4.018331674995755 y[1] (numeric) = 4.018331674996023 absolute error = 2.682298827494378e-13 relative error = 6.675155374020268e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y[1] (closed_form) = 4.039473903438806 y[1] (numeric) = 4.039473903439076 absolute error = 2.700062395888381e-13 relative error = 6.684193190578151e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999675 y[1] (closed_form) = 4.060695196415972 y[1] (numeric) = 4.060695196416245 absolute error = 2.726707748479384e-13 relative error = 6.714879144058918e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999674 y[1] (closed_form) = 4.081994827304012 y[1] (numeric) = 4.081994827304287 absolute error = 2.753353101070388e-13 relative error = 6.745116585286963e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999673 y[1] (closed_form) = 4.103372062645947 y[1] (numeric) = 4.103372062646224 absolute error = 2.771116669464391e-13 relative error = 6.753266891614775e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999672 y[1] (closed_form) = 4.124826162224414 y[1] (numeric) = 4.124826162224694 absolute error = 2.797762022055394e-13 relative error = 6.782739228328188e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y[1] (closed_form) = 4.146356379135677 y[1] (numeric) = 4.14635637913596 absolute error = 2.824407374646398e-13 relative error = 6.81178151704161e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999674 y[1] (closed_form) = 4.167961959864336 y[1] (numeric) = 4.167961959864611 absolute error = 2.753353101070388e-13 relative error = 6.605993834838185e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999677 y[1] (closed_form) = 4.18964214435864 y[1] (numeric) = 4.189642144358909 absolute error = 2.691180611691379e-13 relative error = 6.423414026696907e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999681 y[1] (closed_form) = 4.211396166106528 y[1] (numeric) = 4.211396166106792 absolute error = 2.637889906509372e-13 relative error = 6.263694514753105e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999684 y[1] (closed_form) = 4.233223252212268 y[1] (numeric) = 4.233223252212523 absolute error = 2.557953848736361e-13 relative error = 6.042567793700895e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999687 y[1] (closed_form) = 4.255122623473739 y[1] (numeric) = 4.255122623473989 absolute error = 2.495781359357352e-13 relative error = 5.865357077112574e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999691 y[1] (closed_form) = 4.277093494460364 y[1] (numeric) = 4.277093494460606 absolute error = 2.424727085781342e-13 relative error = 5.669100030012944e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999694 y[1] (closed_form) = 4.299135073591639 y[1] (numeric) = 4.299135073591875 absolute error = 2.362554596402333e-13 relative error = 5.495418394539014e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999697 y[1] (closed_form) = 4.321246563216298 y[1] (numeric) = 4.321246563216527 absolute error = 2.291500322826323e-13 relative error = 5.302868719253924e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999701 y[1] (closed_form) = 4.343427159692076 y[1] (numeric) = 4.343427159692298 absolute error = 2.220446049250313e-13 relative error = 5.112198196522145e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999704 y[1] (closed_form) = 4.365676053466071 y[1] (numeric) = 4.365676053466286 absolute error = 2.149391775674303e-13 relative error = 4.923388151917093e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999707 y[1] (closed_form) = 4.387992429155702 y[1] (numeric) = 4.387992429155908 absolute error = 2.060573933704291e-13 relative error = 4.695937759630018e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.119999999999711 y[1] (closed_form) = 4.410375465630241 y[1] (numeric) = 4.410375465630439 absolute error = 1.980637875931279e-13 relative error = 4.49085999903241e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999714 y[1] (closed_form) = 4.432824336092931 y[1] (numeric) = 4.432824336093123 absolute error = 1.918465386552271e-13 relative error = 4.327862421553108e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999717 y[1] (closed_form) = 4.455338208163664 y[1] (numeric) = 4.455338208163848 absolute error = 1.838529328779259e-13 relative error = 4.12657635151123e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.149999999999721 y[1] (closed_form) = 4.477916243962214 y[1] (numeric) = 4.47791624396239 absolute error = 1.767475055203249e-13 relative error = 3.94709270765486e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999724 y[1] (closed_form) = 4.500557600192027 y[1] (numeric) = 4.500557600192197 absolute error = 1.696420781627239e-13 relative error = 3.769356893809908e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999727 y[1] (closed_form) = 4.523261428224555 y[1] (numeric) = 4.523261428224717 absolute error = 1.616484723854228e-13 relative error = 3.573715005211895e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.179999999999731 y[1] (closed_form) = 4.546026874184109 y[1] (numeric) = 4.546026874184264 absolute error = 1.554312234475219e-13 relative error = 3.419056414518396e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999734 y[1] (closed_form) = 4.568853079033251 y[1] (numeric) = 4.568853079033399 absolute error = 1.483257960899209e-13 relative error = 3.24645580683251e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999737 y[1] (closed_form) = 4.591739178658698 y[1] (numeric) = 4.591739178658839 absolute error = 1.412203687323199e-13 relative error = 3.075531149257743e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.209999999999741 y[1] (closed_form) = 4.614684303957731 y[1] (numeric) = 4.614684303957864 absolute error = 1.332267629550188e-13 relative error = 2.887017923214344e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999744 y[1] (closed_form) = 4.637687580925101 y[1] (numeric) = 4.637687580925226 absolute error = 1.252331571777177e-13 relative error = 2.700336212659173e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999747 y[1] (closed_form) = 4.660748130740436 y[1] (numeric) = 4.660748130740553 absolute error = 1.172395514004165e-13 relative error = 2.515466361015117e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999751 y[1] (closed_form) = 4.683865069856118 y[1] (numeric) = 4.683865069856227 absolute error = 1.092459456231154e-13 relative error = 2.332388828324452e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999754 y[1] (closed_form) = 4.707037510085637 y[1] (numeric) = 4.707037510085738 absolute error = 1.012523398458143e-13 relative error = 2.151084193165313e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999757 y[1] (closed_form) = 4.730264558692408 y[1] (numeric) = 4.730264558692502 absolute error = 9.414691248821327e-14 relative error = 1.990309660697676e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999761 y[1] (closed_form) = 4.753545318479048 y[1] (numeric) = 4.753545318479135 absolute error = 8.615330671091215e-14 relative error = 1.812401080431435e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y[1] (closed_form) = 4.776878887877093 y[1] (numeric) = 4.77687888787717 absolute error = 7.72715225139109e-14 relative error = 1.617615274065518e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y[1] (closed_form) = 4.80026436103715 y[1] (numeric) = 4.800264361037218 absolute error = 6.838973831690964e-14 relative error = 1.424707748848509e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y[1] (closed_form) = 4.823700827919486 y[1] (numeric) = 4.823700827919546 absolute error = 5.950795411990839e-14 relative error = 1.233657646748685e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999774 y[1] (closed_form) = 4.847187374385033 y[1] (numeric) = 4.847187374385086 absolute error = 5.240252676230739e-14 relative error = 1.081091418896422e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y[1] (closed_form) = 4.870723082286795 y[1] (numeric) = 4.870723082286838 absolute error = 4.263256414560601e-14 relative error = 8.752820356518833e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999781 y[1] (closed_form) = 4.894307029561665 y[1] (numeric) = 4.8943070295617 absolute error = 3.552713678800501e-14 relative error = 7.258869656811626e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999784 y[1] (closed_form) = 4.917938290322631 y[1] (numeric) = 4.91793829032266 absolute error = 2.842170943040401e-14 relative error = 5.779191960649725e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999787 y[1] (closed_form) = 4.941615934951365 y[1] (numeric) = 4.941615934951386 absolute error = 2.131628207280301e-14 relative error = 4.313625816615147e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999791 y[1] (closed_form) = 4.96533903019118 y[1] (numeric) = 4.965339030191194 absolute error = 1.4210854715202e-14 relative error = 2.862010958122802e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y[1] (closed_form) = 4.989106639240359 y[1] (numeric) = 4.989106639240365 absolute error = 6.217248937900877e-15 relative error = 1.246164772065789e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = 5.012917821845834 y[1] (numeric) = 5.012917821845832 absolute error = 1.77635683940025e-15 relative error = 3.543558666888675e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = 5.036771634397206 y[1] (numeric) = 5.036771634397198 absolute error = 7.993605777301127e-15 relative error = 1.587049474848345e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = 5.060667130021112 y[1] (numeric) = 5.060667130021095 absolute error = 1.687538997430238e-14 relative error = 3.334617658251706e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = 5.084603358675905 y[1] (numeric) = 5.084603358675881 absolute error = 2.486899575160351e-14 relative error = 4.89103947688846e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y[1] (closed_form) = 5.108579367246664 y[1] (numeric) = 5.10857936724663 absolute error = 3.375077994860476e-14 relative error = 6.606686031932041e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y[1] (closed_form) = 5.132594199640499 y[1] (numeric) = 5.132594199640456 absolute error = 4.263256414560601e-14 relative error = 8.306240954835688e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = 5.156646896882161 y[1] (numeric) = 5.15664689688211 absolute error = 5.062616992290714e-14 relative error = 9.817653008880053e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y[1] (closed_form) = 5.180736497209941 y[1] (numeric) = 5.180736497209882 absolute error = 5.950795411990839e-14 relative error = 1.148638888543281e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y[1] (closed_form) = 5.204862036171845 y[1] (numeric) = 5.204862036171776 absolute error = 6.838973831690964e-14 relative error = 1.3139587147868e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 5.229022546722033 y[1] (numeric) = 5.229022546721957 absolute error = 7.638334409421077e-14 relative error = 1.460757596887661e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y[1] (closed_form) = 5.253217059317532 y[1] (numeric) = 5.253217059317446 absolute error = 8.526512829121202e-14 relative error = 1.623103087658997e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y[1] (closed_form) = 5.277444602015179 y[1] (numeric) = 5.277444602015087 absolute error = 9.237055564881302e-14 relative error = 1.750289441475929e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 5.301704200568826 y[1] (numeric) = 5.301704200568724 absolute error = 1.012523398458143e-13 relative error = 1.909807413151243e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y[1] (closed_form) = 5.325994878526753 y[1] (numeric) = 5.325994878526642 absolute error = 1.110223024625157e-13 relative error = 2.084536410467334e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y[1] (closed_form) = 5.35031565732932 y[1] (numeric) = 5.350315657329202 absolute error = 1.181277298201167e-13 relative error = 2.207864682867733e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = 5.374665556406817 y[1] (numeric) = 5.37466555640669 absolute error = 1.270095140171179e-13 relative error = 2.363114740520319e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y[1] (closed_form) = 5.399043593277525 y[1] (numeric) = 5.399043593277391 absolute error = 1.341149413747189e-13 relative error = 2.48404998140242e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y[1] (closed_form) = 5.423448783645958 y[1] (numeric) = 5.423448783645816 absolute error = 1.412203687323199e-13 relative error = 2.603884988425822e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y[1] (closed_form) = 5.447880141501297 y[1] (numeric) = 5.447880141501146 absolute error = 1.501021529293212e-13 relative error = 2.755239635062104e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y[1] (closed_form) = 5.472336679215986 y[1] (numeric) = 5.472336679215827 absolute error = 1.589839371263224e-13 relative error = 2.905229455821783e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y[1] (closed_form) = 5.496817407644497 y[1] (numeric) = 5.496817407644331 absolute error = 1.660893644839234e-13 relative error = 3.021555059350175e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y[1] (closed_form) = 5.521321336222242 y[1] (numeric) = 5.52132133622207 absolute error = 1.714184350021242e-13 relative error = 3.104663260179145e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y[1] (closed_form) = 5.545847473064629 y[1] (numeric) = 5.54584747306445 absolute error = 1.785238623597252e-13 relative error = 3.219054675174344e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y[1] (closed_form) = 5.570394825066249 y[1] (numeric) = 5.570394825066062 absolute error = 1.865174681370263e-13 relative error = 3.34837069892632e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y[1] (closed_form) = 5.594962398000187 y[1] (numeric) = 5.594962397999992 absolute error = 1.953992523340276e-13 relative error = 3.492414040242152e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y[1] (closed_form) = 5.619549196617445 y[1] (numeric) = 5.619549196617242 absolute error = 2.033928581113287e-13 relative error = 3.619380327406978e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y[1] (closed_form) = 5.644154224746461 y[1] (numeric) = 5.64415422474625 absolute error = 2.113864638886298e-13 relative error = 3.7452283454945e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y[1] (closed_form) = 5.668776485392731 y[1] (numeric) = 5.668776485392511 absolute error = 2.193800696659309e-13 relative error = 3.86997212240116e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y[1] (closed_form) = 5.693414980838505 y[1] (numeric) = 5.693414980838277 absolute error = 2.282618538629322e-13 relative error = 4.009225651584501e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y[1] (closed_form) = 5.718068712742558 y[1] (numeric) = 5.718068712742322 absolute error = 2.362554596402333e-13 relative error = 4.131735232802372e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y[1] (closed_form) = 5.742736682240023 y[1] (numeric) = 5.742736682239778 absolute error = 2.451372438372346e-13 relative error = 4.268648510305993e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y[1] (closed_form) = 5.767417890042278 y[1] (numeric) = 5.767417890042025 absolute error = 2.531308496145357e-13 relative error = 4.388980553179234e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y[1] (closed_form) = 5.792111336536873 y[1] (numeric) = 5.792111336536611 absolute error = 2.620126338115369e-13 relative error = 4.523611833197173e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y[1] (closed_form) = 5.81681602188749 y[1] (numeric) = 5.816816021887221 absolute error = 2.691180611691379e-13 relative error = 4.626552742196103e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y[1] (closed_form) = 5.841530946133928 y[1] (numeric) = 5.84153094613365 absolute error = 2.779998453661392e-13 relative error = 4.759023754725231e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y[1] (closed_form) = 5.866255109292095 y[1] (numeric) = 5.866255109291809 absolute error = 2.859934511434403e-13 relative error = 4.875230378072533e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y[1] (closed_form) = 5.890987511454007 y[1] (numeric) = 5.890987511453713 absolute error = 2.939870569207415e-13 relative error = 4.990454594397534e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y[1] (closed_form) = 5.915727152887781 y[1] (numeric) = 5.915727152887478 absolute error = 3.028688411177427e-13 relative error = 5.119722956963901e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y[1] (closed_form) = 5.9404730341376 y[1] (numeric) = 5.94047303413729 absolute error = 3.099742684753437e-13 relative error = 5.21800649029196e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y[1] (closed_form) = 5.965224156123667 y[1] (numeric) = 5.96522415612335 absolute error = 3.170796958329447e-13 relative error = 5.315469922575215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y[1] (closed_form) = 5.989979520242104 y[1] (numeric) = 5.989979520241778 absolute error = 3.25961480029946e-13 relative error = 5.441779540788333e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y[1] (closed_form) = 6.014738128464816 y[1] (numeric) = 6.014738128464483 absolute error = 3.33066907387547e-13 relative error = 5.537513026731855e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y[1] (closed_form) = 6.039498983439293 y[1] (numeric) = 6.03949898343895 absolute error = 3.428368700042483e-13 relative error = 5.676577990067219e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y[1] (closed_form) = 6.06426108858834 y[1] (numeric) = 6.06426108858799 absolute error = 3.508304757815495e-13 relative error = 5.785213905808548e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y[1] (closed_form) = 6.089023448209742 y[1] (numeric) = 6.089023448209383 absolute error = 3.597122599785507e-13 relative error = 5.907552549897162e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y[1] (closed_form) = 6.113785067575826 y[1] (numeric) = 6.113785067575458 absolute error = 3.677058657558518e-13 relative error = 6.014373447734739e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y[1] (closed_form) = 6.138544953032935 y[1] (numeric) = 6.138544953032558 absolute error = 3.765876499528531e-13 relative error = 6.134803163195677e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y[1] (closed_form) = 6.163302112100794 y[1] (numeric) = 6.163302112100412 absolute error = 3.819167204710538e-13 relative error = 6.19662501569107e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y[1] (closed_form) = 6.188055553571758 y[1] (numeric) = 6.188055553571367 absolute error = 3.907985046680551e-13 relative error = 6.315368394559507e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y[1] (closed_form) = 6.212804287609927 y[1] (numeric) = 6.212804287609528 absolute error = 3.996802888650564e-13 relative error = 6.433170439025914e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y[1] (closed_form) = 6.237547325850134 y[1] (numeric) = 6.237547325849725 absolute error = 4.085620730620576e-13 relative error = 6.55004365848837e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y[1] (closed_form) = 6.262283681496777 y[1] (numeric) = 6.262283681496362 absolute error = 4.156675004196586e-13 relative error = 6.637634472673841e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y[1] (closed_form) = 6.287012369422504 y[1] (numeric) = 6.287012369422079 absolute error = 4.2543746303636e-13 relative error = 6.766925815280982e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y[1] (closed_form) = 6.311732406266714 y[1] (numeric) = 6.311732406266281 absolute error = 4.32542890393961e-13 relative error = 6.852997918043915e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y[1] (closed_form) = 6.336442810533903 y[1] (numeric) = 6.336442810533462 absolute error = 4.414246745909622e-13 relative error = 6.966442967923957e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y[1] (closed_form) = 6.361142602691808 y[1] (numeric) = 6.361142602691356 absolute error = 4.511946372076636e-13 relative error = 7.092981015969273e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 6.385830805269357 y[1] (numeric) = 6.385830805268898 absolute error = 4.591882429849647e-13 relative error = 7.190736131092906e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y[1] (closed_form) = 6.410506442954421 y[1] (numeric) = 6.410506442953954 absolute error = 4.671818487622659e-13 relative error = 7.28775258116666e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y[1] (closed_form) = 6.43516854269134 y[1] (numeric) = 6.435168542690867 absolute error = 4.725109192804666e-13 relative error = 7.3426347133847e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 6.459816133778229 y[1] (numeric) = 6.45981613377775 absolute error = 4.796163466380676e-13 relative error = 7.424612972034372e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y[1] (closed_form) = 6.48444824796405 y[1] (numeric) = 6.484448247963561 absolute error = 4.884981308350689e-13 relative error = 7.533380052627373e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y[1] (closed_form) = 6.50906391954543 y[1] (numeric) = 6.509063919544933 absolute error = 4.973799150320701e-13 relative error = 7.641343228148931e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = ( 0.1 * x + 1.0 ) - sin ( x ) ; Iterations = 4900 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %