##############ECHO OF PROBLEM################# ##############temp/mult_lin_cpostode.ode################# diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) * 2.0 ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* 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(c(0.2) * c(x) * c(x) + c(0.6) * 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) = 0.062 y[1] (numeric) = 0.062 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) = 0.06842000000000001 y[1] (numeric) = 0.06841999999999999 absolute error = 1.387778780781446e-17 relative error = 2.028323269192408e-14 % 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) = 0.07488000000000002 y[1] (numeric) = 0.07488 absolute error = 1.387778780781446e-17 relative error = 1.853337046983768e-14 % 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) = 0.08138000000000002 y[1] (numeric) = 0.08137999999999999 absolute error = 2.775557561562891e-17 relative error = 3.410613862819969e-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) = 0.08792000000000003 y[1] (numeric) = 0.08792 absolute error = 2.775557561562891e-17 relative error = 3.156912604143415e-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) = 0.09450000000000003 y[1] (numeric) = 0.0945 absolute error = 2.775557561562891e-17 relative error = 2.937097948743799e-14 % 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) = 0.10112 y[1] (numeric) = 0.10112 absolute error = 2.775557561562891e-17 relative error = 2.74481562654558e-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) = 0.10778 y[1] (numeric) = 0.10778 absolute error = 4.163336342344337e-17 relative error = 3.862809744242285e-14 % 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) = 0.11448 y[1] (numeric) = 0.11448 absolute error = 4.163336342344337e-17 relative error = 3.636736846911544e-14 % 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) = 0.12122 y[1] (numeric) = 0.12122 absolute error = 4.163336342344337e-17 relative error = 3.434529238033605e-14 % 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) = 0.1280000000000001 y[1] (numeric) = 0.128 absolute error = 2.775557561562891e-17 relative error = 2.168404344971008e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (closed_form) = 0.1348200000000001 y[1] (numeric) = 0.13482 absolute error = 2.775557561562891e-17 relative error = 2.058713515474626e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (closed_form) = 0.1416800000000001 y[1] (numeric) = 0.14168 absolute error = 8.326672684688674e-17 relative error = 5.877098168187937e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (closed_form) = 0.1485800000000001 y[1] (numeric) = 0.14858 absolute error = 5.551115123125783e-17 relative error = 3.736111941799556e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = 0.1555200000000001 y[1] (numeric) = 0.15552 absolute error = 5.551115123125783e-17 relative error = 3.569389868265034e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = 0.1625000000000001 y[1] (numeric) = 0.1625 absolute error = 5.551115123125783e-17 relative error = 3.41607084500048e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 0.1695200000000001 y[1] (numeric) = 0.16952 absolute error = 5.551115123125783e-17 relative error = 3.274607788535737e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 0.1765800000000001 y[1] (numeric) = 0.17658 absolute error = 5.551115123125783e-17 relative error = 3.14368281975636e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 0.1836800000000001 y[1] (numeric) = 0.18368 absolute error = 8.326672684688674e-17 relative error = 4.533249501681549e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 0.1908200000000001 y[1] (numeric) = 0.19082 absolute error = 1.110223024625157e-16 relative error = 5.818169084085294e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 0.1980000000000001 y[1] (numeric) = 0.198 absolute error = 8.326672684688674e-17 relative error = 4.205390244792257e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 0.2052200000000001 y[1] (numeric) = 0.20522 absolute error = 8.326672684688674e-17 relative error = 4.057437230625022e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 0.2124800000000001 y[1] (numeric) = 0.21248 absolute error = 1.110223024625157e-16 relative error = 5.225070710773513e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 0.2197800000000001 y[1] (numeric) = 0.21978 absolute error = 1.110223024625157e-16 relative error = 5.051519813564274e-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) = 0.2271200000000001 y[1] (numeric) = 0.22712 absolute error = 1.110223024625157e-16 relative error = 4.888266223252712e-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) = 0.2345000000000001 y[1] (numeric) = 0.2345 absolute error = 1.110223024625157e-16 relative error = 4.734426544243735e-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) = 0.2419200000000001 y[1] (numeric) = 0.24192 absolute error = 1.387778780781446e-16 relative error = 5.736519431140232e-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) = 0.2493800000000002 y[1] (numeric) = 0.24938 absolute error = 1.387778780781446e-16 relative error = 5.564916115091205e-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) = 0.2568800000000002 y[1] (numeric) = 0.2568800000000001 absolute error = 1.110223024625157e-16 relative error = 4.321951980010728e-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) = 0.2644200000000002 y[1] (numeric) = 0.26442 absolute error = 1.110223024625157e-16 relative error = 4.198710478122517e-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) = 0.2720000000000002 y[1] (numeric) = 0.272 absolute error = 1.665334536937735e-16 relative error = 6.12255344462402e-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) = 0.2796200000000002 y[1] (numeric) = 0.27962 absolute error = 1.665334536937735e-16 relative error = 5.955706090185729e-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) = 0.2872800000000002 y[1] (numeric) = 0.28728 absolute error = 1.665334536937735e-16 relative error = 5.796903846204866e-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) = 0.2949800000000002 y[1] (numeric) = 0.29498 absolute error = 2.220446049250313e-16 relative error = 7.527446095499055e-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) = 0.3027200000000002 y[1] (numeric) = 0.30272 absolute error = 1.665334536937735e-16 relative error = 5.50123723882708e-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) = 0.3105000000000002 y[1] (numeric) = 0.3105000000000001 absolute error = 1.665334536937735e-16 relative error = 5.363396254227806e-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) = 0.3183200000000003 y[1] (numeric) = 0.31832 absolute error = 2.220446049250313e-16 relative error = 6.975515359544833e-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) = 0.3261800000000002 y[1] (numeric) = 0.3261800000000001 absolute error = 1.665334536937735e-16 relative error = 5.105569124218939e-14 % 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) = 0.3340800000000003 y[1] (numeric) = 0.33408 absolute error = 2.220446049250313e-16 relative error = 6.646450099527992e-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) = 0.3420200000000003 y[1] (numeric) = 0.34202 absolute error = 2.220446049250313e-16 relative error = 6.492152649699759e-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) = 0.3500000000000003 y[1] (numeric) = 0.3500000000000001 absolute error = 2.220446049250313e-16 relative error = 6.344131569286603e-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) = 0.3580200000000003 y[1] (numeric) = 0.3580200000000001 absolute error = 2.220446049250313e-16 relative error = 6.202016784677703e-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) = 0.3660800000000003 y[1] (numeric) = 0.3660800000000001 absolute error = 2.220446049250313e-16 relative error = 6.065466699219601e-14 % 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) = 0.3741800000000003 y[1] (numeric) = 0.3741800000000001 absolute error = 2.220446049250313e-16 relative error = 5.934165506575208e-14 % 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) = 0.3823200000000003 y[1] (numeric) = 0.38232 absolute error = 2.775557561562891e-16 relative error = 7.259776003250912e-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) = 0.3905000000000003 y[1] (numeric) = 0.3905000000000001 absolute error = 2.775557561562891e-16 relative error = 7.107701822184094e-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) = 0.3987200000000004 y[1] (numeric) = 0.3987200000000001 absolute error = 2.775557561562891e-16 relative error = 6.961169646776909e-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) = 0.4069800000000003 y[1] (numeric) = 0.4069800000000001 absolute error = 2.775557561562891e-16 relative error = 6.819886877888076e-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) = 0.4152800000000004 y[1] (numeric) = 0.4152800000000001 absolute error = 2.775557561562891e-16 relative error = 6.683581105670605e-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) = 0.4236200000000003 y[1] (numeric) = 0.4236200000000001 absolute error = 2.775557561562891e-16 relative error = 6.551998398477147e-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) = 0.4320000000000004 y[1] (numeric) = 0.4320000000000001 absolute error = 3.33066907387547e-16 relative error = 7.709882115452469e-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) = 0.4404200000000004 y[1] (numeric) = 0.4404200000000001 absolute error = 2.775557561562891e-16 relative error = 6.302069755149378e-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) = 0.4488800000000004 y[1] (numeric) = 0.4488800000000001 absolute error = 3.33066907387547e-16 relative error = 7.419954272579458e-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) = 0.4573800000000004 y[1] (numeric) = 0.4573800000000001 absolute error = 3.33066907387547e-16 relative error = 7.2820610299433e-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) = 0.4659200000000004 y[1] (numeric) = 0.4659200000000001 absolute error = 2.775557561562891e-16 relative error = 5.957154793876393e-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) = 0.4745000000000004 y[1] (numeric) = 0.4745000000000001 absolute error = 3.33066907387547e-16 relative error = 7.019323654110572e-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) = 0.4831200000000004 y[1] (numeric) = 0.4831200000000001 absolute error = 3.33066907387547e-16 relative error = 6.894082368511895e-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) = 0.4917800000000004 y[1] (numeric) = 0.4917800000000001 absolute error = 3.33066907387547e-16 relative error = 6.772681023781908e-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) = 0.5004800000000005 y[1] (numeric) = 0.5004800000000001 absolute error = 3.33066907387547e-16 relative error = 6.654949396330456e-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) = 0.5092200000000005 y[1] (numeric) = 0.5092200000000001 absolute error = 3.33066907387547e-16 relative error = 6.5407271393022e-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) = 0.5180000000000005 y[1] (numeric) = 0.5180000000000001 absolute error = 3.33066907387547e-16 relative error = 6.429863076979666e-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) = 0.5268200000000005 y[1] (numeric) = 0.5268200000000002 absolute error = 3.33066907387547e-16 relative error = 6.322214558816041e-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) = 0.5356800000000005 y[1] (numeric) = 0.5356800000000002 absolute error = 3.33066907387547e-16 relative error = 6.217646867300378e-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) = 0.5445800000000005 y[1] (numeric) = 0.5445800000000002 absolute error = 3.33066907387547e-16 relative error = 6.116032674493125e-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) = 0.5535200000000005 y[1] (numeric) = 0.5535200000000001 absolute error = 3.33066907387547e-16 relative error = 6.017251542628029e-14 % 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) = 0.5625000000000004 y[1] (numeric) = 0.5625000000000001 absolute error = 3.33066907387547e-16 relative error = 5.921189464667497e-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) = 0.5715200000000005 y[1] (numeric) = 0.5715200000000001 absolute error = 3.33066907387547e-16 relative error = 5.827738441131486e-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) = 0.5805800000000005 y[1] (numeric) = 0.5805800000000001 absolute error = 4.440892098500626e-16 relative error = 7.649061453203041e-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) = 0.5896800000000005 y[1] (numeric) = 0.5896800000000001 absolute error = 4.440892098500626e-16 relative error = 7.531020381394353e-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) = 0.5988200000000006 y[1] (numeric) = 0.5988200000000001 absolute error = 4.440892098500626e-16 relative error = 7.416071771985942e-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) = 0.6080000000000005 y[1] (numeric) = 0.6080000000000001 absolute error = 4.440892098500626e-16 relative error = 7.304098846218128e-14 % 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) = 0.6172200000000005 y[1] (numeric) = 0.6172200000000001 absolute error = 4.440892098500626e-16 relative error = 7.19499060059723e-14 % 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) = 0.6264800000000006 y[1] (numeric) = 0.6264800000000001 absolute error = 4.440892098500626e-16 relative error = 7.088641454636416e-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) = 0.6357800000000006 y[1] (numeric) = 0.6357800000000001 absolute error = 4.440892098500626e-16 relative error = 6.984950924062761e-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) = 0.6451200000000006 y[1] (numeric) = 0.6451200000000001 absolute error = 4.440892098500626e-16 relative error = 6.883823317368276e-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) = 0.6545000000000005 y[1] (numeric) = 0.6545000000000002 absolute error = 3.33066907387547e-16 relative error = 5.088875590336848e-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) = 0.6639200000000006 y[1] (numeric) = 0.6639200000000002 absolute error = 4.440892098500626e-16 relative error = 6.688896400922734e-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) = 0.6733800000000005 y[1] (numeric) = 0.6733800000000002 absolute error = 3.33066907387547e-16 relative error = 4.946195422904552e-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) = 0.6828800000000006 y[1] (numeric) = 0.6828800000000002 absolute error = 4.440892098500626e-16 relative error = 6.503180790915859e-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) = 0.6924200000000006 y[1] (numeric) = 0.6924200000000001 absolute error = 4.440892098500626e-16 relative error = 6.413581494613995e-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) = 0.7020000000000006 y[1] (numeric) = 0.7020000000000002 absolute error = 4.440892098500626e-16 relative error = 6.326057120371257e-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) = 0.7116200000000006 y[1] (numeric) = 0.7116200000000001 absolute error = 4.440892098500626e-16 relative error = 6.240538628060794e-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) = 0.7212800000000007 y[1] (numeric) = 0.7212800000000001 absolute error = 5.551115123125783e-16 relative error = 7.696199982150867e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = 0.7309800000000006 y[1] (numeric) = 0.7309800000000002 absolute error = 4.440892098500626e-16 relative error = 6.075258007743881e-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) = 0.7407200000000007 y[1] (numeric) = 0.7407200000000002 absolute error = 5.551115123125783e-16 relative error = 7.494215254246919e-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) = 0.7505000000000007 y[1] (numeric) = 0.7505000000000002 absolute error = 5.551115123125783e-16 relative error = 7.396555793638611e-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) = 0.7603200000000008 y[1] (numeric) = 0.7603200000000001 absolute error = 6.661338147750939e-16 relative error = 8.761229676650531e-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) = 0.7701800000000008 y[1] (numeric) = 0.7701800000000001 absolute error = 6.661338147750939e-16 relative error = 8.649066643837717e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 0.7800800000000008 y[1] (numeric) = 0.7800800000000001 absolute error = 6.661338147750939e-16 relative error = 8.539301286728197e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = 0.7900200000000007 y[1] (numeric) = 0.7900200000000001 absolute error = 6.661338147750939e-16 relative error = 8.431860139934347e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (closed_form) = 0.8000000000000007 y[1] (numeric) = 0.8 absolute error = 6.661338147750939e-16 relative error = 8.326672684688666e-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) = 0.8100199999999996 y[1] (numeric) = 0.8100200000000001 absolute error = 4.440892098500626e-16 relative error = 5.482447468581798e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = 0.8200799999999985 y[1] (numeric) = 0.82008 absolute error = 1.554312234475219e-15 relative error = 1.895317815914572e-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) = 0.8301799999999974 y[1] (numeric) = 0.83018 absolute error = 2.664535259100376e-15 relative error = 3.209587389602718e-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) = 0.8403199999999962 y[1] (numeric) = 0.8403200000000001 absolute error = 3.885780586188048e-15 relative error = 4.624167681583285e-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) = 0.8504999999999951 y[1] (numeric) = 0.8505 absolute error = 4.884981308350689e-15 relative error = 5.743658210876798e-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) = 0.8607199999999939 y[1] (numeric) = 0.86072 absolute error = 6.106226635438361e-15 relative error = 7.094324095453114e-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) = 0.8709799999999928 y[1] (numeric) = 0.87098 absolute error = 7.216449660063518e-15 relative error = 8.285436703556428e-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) = 0.8812799999999916 y[1] (numeric) = 0.88128 absolute error = 8.326672684688674e-15 relative error = 9.448384945407535e-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) = 0.8916199999999904 y[1] (numeric) = 0.89162 absolute error = 9.547918011776346e-15 relative error = 1.070850587893547e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y[1] (closed_form) = 0.9019999999999893 y[1] (numeric) = 0.9019999999999999 absolute error = 1.06581410364015e-14 relative error = 1.181612088292864e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = 0.9124199999999881 y[1] (numeric) = 0.9124199999999999 absolute error = 1.176836406102666e-14 relative error = 1.28979681079183e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 0.9228799999999868 y[1] (numeric) = 0.9228799999999999 absolute error = 1.310063169057685e-14 relative error = 1.419537934571887e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 0.9333799999999857 y[1] (numeric) = 0.9333799999999999 absolute error = 1.4210854715202e-14 relative error = 1.522515450856267e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 0.9439199999999844 y[1] (numeric) = 0.9439199999999998 absolute error = 1.532107773982716e-14 relative error = 1.62313307693739e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 0.9544999999999833 y[1] (numeric) = 0.9544999999999997 absolute error = 1.643130076445232e-14 relative error = 1.721456339911221e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 0.965119999999982 y[1] (numeric) = 0.9651199999999996 absolute error = 1.765254609153999e-14 relative error = 1.829051940850912e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 0.9757799999999808 y[1] (numeric) = 0.9757799999999995 absolute error = 1.876276911616515e-14 relative error = 1.922848297379073e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = 0.9864799999999795 y[1] (numeric) = 0.9864799999999995 absolute error = 1.998401444325282e-14 relative error = 2.025790126840203e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = 0.9972199999999782 y[1] (numeric) = 0.9972199999999993 absolute error = 2.109423746787797e-14 relative error = 2.11530429272161e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = 1.007999999999977 y[1] (numeric) = 1.008 absolute error = 2.264854970235319e-14 relative error = 2.246879930789059e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = 1.018819999999976 y[1] (numeric) = 1.018819999999999 absolute error = 2.353672812205332e-14 relative error = 2.310194943371143e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 1.029679999999974 y[1] (numeric) = 1.029679999999999 absolute error = 2.509104035652854e-14 relative error = 2.436780393571708e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 1.040579999999973 y[1] (numeric) = 1.040579999999999 absolute error = 2.575717417130363e-14 relative error = 2.475270923072161e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 1.051519999999972 y[1] (numeric) = 1.051519999999999 absolute error = 2.753353101070388e-14 relative error = 2.618450529776383e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = 1.06249999999997 y[1] (numeric) = 1.062499999999999 absolute error = 2.819966482547898e-14 relative error = 2.654086101221624e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = 1.073519999999969 y[1] (numeric) = 1.073519999999999 absolute error = 2.997602166487923e-14 relative error = 2.792311430143834e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = 1.084579999999968 y[1] (numeric) = 1.084579999999999 absolute error = 3.064215547965432e-14 relative error = 2.825255442628043e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = 1.095679999999966 y[1] (numeric) = 1.095679999999999 absolute error = 3.241851231905457e-14 relative error = 2.95875733052128e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = 1.106819999999965 y[1] (numeric) = 1.106819999999998 absolute error = 3.33066907387547e-14 relative error = 3.009223788760209e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y[1] (closed_form) = 1.117999999999964 y[1] (numeric) = 1.117999999999999 absolute error = 3.486100297322992e-14 relative error = 3.118157689913332e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y[1] (closed_form) = 1.129219999999962 y[1] (numeric) = 1.129219999999998 absolute error = 3.574918139293004e-14 relative error = 3.165829633989057e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = 1.140479999999961 y[1] (numeric) = 1.140479999999998 absolute error = 3.708144902248023e-14 relative error = 3.251389680001534e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = 1.15177999999996 y[1] (numeric) = 1.151779999999998 absolute error = 3.819167204710538e-14 relative error = 3.315882551104093e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = 1.163119999999958 y[1] (numeric) = 1.163119999999998 absolute error = 3.952393967665557e-14 relative error = 3.398096471271837e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y[1] (closed_form) = 1.174499999999957 y[1] (numeric) = 1.174499999999997 absolute error = 4.063416270128073e-14 relative error = 3.459698825141101e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y[1] (closed_form) = 1.185919999999955 y[1] (numeric) = 1.185919999999997 absolute error = 4.196643033083092e-14 relative error = 3.538723550562643e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y[1] (closed_form) = 1.197379999999954 y[1] (numeric) = 1.197379999999997 absolute error = 4.329869796038111e-14 relative error = 3.616120025420733e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y[1] (closed_form) = 1.208879999999953 y[1] (numeric) = 1.208879999999997 absolute error = 4.440892098500626e-14 relative error = 3.673559078238369e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y[1] (closed_form) = 1.220419999999951 y[1] (numeric) = 1.220419999999997 absolute error = 4.596323321948148e-14 relative error = 3.766181578430649e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y[1] (closed_form) = 1.23199999999995 y[1] (numeric) = 1.231999999999997 absolute error = 4.707345624410664e-14 relative error = 3.820897422411409e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y[1] (closed_form) = 1.243619999999948 y[1] (numeric) = 1.243619999999997 absolute error = 4.840572387365683e-14 relative error = 3.892324333289819e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = 1.255279999999947 y[1] (numeric) = 1.255279999999996 absolute error = 4.951594689828198e-14 relative error = 3.94461370357881e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = 1.266979999999945 y[1] (numeric) = 1.266979999999996 absolute error = 5.10702591327572e-14 relative error = 4.030865454289682e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = 1.278719999999944 y[1] (numeric) = 1.278719999999996 absolute error = 5.195843755245733e-14 relative error = 4.063316250035943e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y[1] (closed_form) = 1.290499999999942 y[1] (numeric) = 1.290499999999996 absolute error = 5.373479439185758e-14 relative error = 4.163874032689654e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y[1] (closed_form) = 1.302319999999941 y[1] (numeric) = 1.302319999999995 absolute error = 5.46229728115577e-14 relative error = 4.194281959238911e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y[1] (closed_form) = 1.314179999999939 y[1] (numeric) = 1.314179999999996 absolute error = 5.639932965095795e-14 relative error = 4.29159853680322e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y[1] (closed_form) = 1.326079999999938 y[1] (numeric) = 1.326079999999995 absolute error = 5.728750807065808e-14 relative error = 4.320064254845919e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y[1] (closed_form) = 1.338019999999936 y[1] (numeric) = 1.338019999999995 absolute error = 5.906386491005833e-14 relative error = 4.414273696212399e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y[1] (closed_form) = 1.349999999999935 y[1] (numeric) = 1.349999999999995 absolute error = 5.972999872483342e-14 relative error = 4.424444349987874e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = 1.362019999999933 y[1] (numeric) = 1.362019999999995 absolute error = 6.17284001691587e-14 relative error = 4.532121420328757e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = 1.374079999999932 y[1] (numeric) = 1.374079999999994 absolute error = 6.261657858885883e-14 relative error = 4.556982023525701e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = 1.38617999999993 y[1] (numeric) = 1.386179999999994 absolute error = 6.439293542825908e-14 relative error = 4.645351644682677e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = 1.398319999999929 y[1] (numeric) = 1.398319999999994 absolute error = 6.52811138479592e-14 relative error = 4.668538950166095e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y[1] (closed_form) = 1.410499999999927 y[1] (numeric) = 1.410499999999994 absolute error = 6.705747068735946e-14 relative error = 4.754163111475572e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y[1] (closed_form) = 1.422719999999925 y[1] (numeric) = 1.422719999999993 absolute error = 6.794564910705958e-14 relative error = 4.775756937912108e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y[1] (closed_form) = 1.434979999999924 y[1] (numeric) = 1.434979999999993 absolute error = 6.94999613415348e-14 relative error = 4.843270382969693e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999937 y[1] (closed_form) = 1.447279999999922 y[1] (numeric) = 1.447279999999993 absolute error = 7.061018436615996e-14 relative error = 4.878819880476739e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999936 y[1] (closed_form) = 1.459619999999921 y[1] (numeric) = 1.459619999999993 absolute error = 7.216449660063518e-14 relative error = 4.944060550049951e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999935 y[1] (closed_form) = 1.471999999999919 y[1] (numeric) = 1.471999999999992 absolute error = 7.371880883511039e-14 relative error = 5.008071252385494e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y[1] (closed_form) = 1.484419999999917 y[1] (numeric) = 1.484419999999992 absolute error = 7.505107646466058e-14 relative error = 5.05591924554134e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y[1] (closed_form) = 1.496879999999916 y[1] (numeric) = 1.496879999999992 absolute error = 7.638334409421077e-14 relative error = 5.102836840242042e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y[1] (closed_form) = 1.509379999999914 y[1] (numeric) = 1.509379999999992 absolute error = 7.771561172376096e-14 relative error = 5.148843347849142e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y[1] (closed_form) = 1.521919999999912 y[1] (numeric) = 1.521919999999992 absolute error = 7.926992395823618e-14 relative error = 5.208547358484069e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999929 y[1] (closed_form) = 1.534499999999911 y[1] (numeric) = 1.534499999999991 absolute error = 8.038014698286133e-14 relative error = 5.238197913513588e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999928 y[1] (closed_form) = 1.547119999999909 y[1] (numeric) = 1.547119999999991 absolute error = 8.193445921733655e-14 relative error = 5.295934330713931e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999927 y[1] (closed_form) = 1.559779999999907 y[1] (numeric) = 1.55977999999999 absolute error = 8.326672684688674e-14 relative error = 5.338363541454032e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999926 y[1] (closed_form) = 1.572479999999906 y[1] (numeric) = 1.57247999999999 absolute error = 8.482103908136196e-14 relative error = 5.394093348174035e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999925 y[1] (closed_form) = 1.585219999999904 y[1] (numeric) = 1.58521999999999 absolute error = 8.615330671091215e-14 relative error = 5.434785500493142e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999924 y[1] (closed_form) = 1.597999999999902 y[1] (numeric) = 1.59799999999999 absolute error = 8.770761894538737e-14 relative error = 5.488586917734214e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y[1] (closed_form) = 1.6108199999999 y[1] (numeric) = 1.610819999999989 absolute error = 8.881784197001252e-14 relative error = 5.513827862207944e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y[1] (closed_form) = 1.623679999999899 y[1] (numeric) = 1.623679999999989 absolute error = 9.059419880941277e-14 relative error = 5.579559938498868e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y[1] (closed_form) = 1.636579999999897 y[1] (numeric) = 1.636579999999989 absolute error = 9.170442183403793e-14 relative error = 5.603418215671932e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y[1] (closed_form) = 1.649519999999895 y[1] (numeric) = 1.649519999999989 absolute error = 9.370282327836321e-14 relative error = 5.680611528103277e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999918 y[1] (closed_form) = 1.662499999999894 y[1] (numeric) = 1.662499999999988 absolute error = 9.436895709313831e-14 relative error = 5.676328246204172e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999917 y[1] (closed_form) = 1.675519999999892 y[1] (numeric) = 1.675519999999988 absolute error = 9.636735853746359e-14 relative error = 5.751489599495668e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999916 y[1] (closed_form) = 1.68857999999989 y[1] (numeric) = 1.688579999999987 absolute error = 9.747758156208874e-14 relative error = 5.772754714736353e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999915 y[1] (closed_form) = 1.701679999999888 y[1] (numeric) = 1.701679999999987 absolute error = 9.925393840148899e-14 relative error = 5.832702881945813e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999914 y[1] (closed_form) = 1.714819999999886 y[1] (numeric) = 1.714819999999987 absolute error = 1.003641614261142e-13 relative error = 5.852751975491352e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999913 y[1] (closed_form) = 1.727999999999885 y[1] (numeric) = 1.727999999999987 absolute error = 1.021405182655144e-13 relative error = 5.910909621847294e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y[1] (closed_form) = 1.741219999999883 y[1] (numeric) = 1.741219999999986 absolute error = 1.032507412901396e-13 relative error = 5.929792977920453e-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) = 1.754479999999881 y[1] (numeric) = 1.754479999999986 absolute error = 1.048050535246148e-13 relative error = 5.97356786766574e-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) = 1.767779999999879 y[1] (numeric) = 1.767779999999985 absolute error = 1.06137321154165e-13 relative error = 6.00398924946386e-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) = 1.781119999999877 y[1] (numeric) = 1.781119999999985 absolute error = 1.076916333886402e-13 relative error = 6.046287357878616e-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) = 1.794499999999875 y[1] (numeric) = 1.794499999999984 absolute error = 1.090239010181904e-13 relative error = 6.075447256517021e-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) = 1.807919999999874 y[1] (numeric) = 1.807919999999984 absolute error = 1.105782132526656e-13 relative error = 6.116322251685546e-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) = 1.821379999999872 y[1] (numeric) = 1.821379999999984 absolute error = 1.121325254871408e-13 relative error = 6.156459689199876e-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) = 1.83487999999987 y[1] (numeric) = 1.834879999999983 absolute error = 1.13464793116691e-13 relative error = 6.183771860650236e-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) = 1.848419999999868 y[1] (numeric) = 1.848419999999983 absolute error = 1.150191053511662e-13 relative error = 6.222563343351318e-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) = 1.861999999999866 y[1] (numeric) = 1.861999999999983 absolute error = 1.165734175856414e-13 relative error = 6.260656153901709e-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) = 1.875619999999864 y[1] (numeric) = 1.875619999999982 absolute error = 1.181277298201167e-13 relative error = 6.298063030897795e-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) = 1.889279999999862 y[1] (numeric) = 1.889279999999982 absolute error = 1.194599974496668e-13 relative error = 6.323043564197767e-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) = 1.90297999999986 y[1] (numeric) = 1.902979999999981 absolute error = 1.210143096841421e-13 relative error = 6.35920029028949e-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) = 1.916719999999859 y[1] (numeric) = 1.916719999999981 absolute error = 1.223465773136923e-13 relative error = 6.383122068622505e-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) = 1.930499999999856 y[1] (numeric) = 1.930499999999981 absolute error = 1.243449787580175e-13 relative error = 6.441076340742128e-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) = 1.944319999999855 y[1] (numeric) = 1.94431999999998 absolute error = 1.254552017826427e-13 relative error = 6.452394759229554e-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) = 1.958179999999853 y[1] (numeric) = 1.95817999999998 absolute error = 1.27453603226968e-13 relative error = 6.508778724477707e-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) = 1.972079999999851 y[1] (numeric) = 1.972079999999979 absolute error = 1.283417816466681e-13 relative error = 6.5079399236683e-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) = 1.986019999999849 y[1] (numeric) = 1.986019999999979 absolute error = 1.305622276959184e-13 relative error = 6.574064092805126e-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) = 1.999999999999847 y[1] (numeric) = 1.999999999999978 absolute error = 1.314504061156185e-13 relative error = 6.57252030578143e-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) = 2.014019999999845 y[1] (numeric) = 2.014019999999977 absolute error = 1.323385845353187e-13 relative error = 6.570867445970191e-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) = 2.028079999999843 y[1] (numeric) = 2.028079999999977 absolute error = 1.34559030584569e-13 relative error = 6.634798951943681e-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) = 2.042179999999841 y[1] (numeric) = 2.042179999999977 absolute error = 1.354472090042691e-13 relative error = 6.632481417126778e-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) = 2.056319999999839 y[1] (numeric) = 2.056319999999976 absolute error = 1.372235658436693e-13 relative error = 6.67325931001401e-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) = 2.070499999999837 y[1] (numeric) = 2.070499999999976 absolute error = 1.385558334732195e-13 relative error = 6.691902123797654e-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) = 2.084719999999835 y[1] (numeric) = 2.084719999999975 absolute error = 1.403321903126198e-13 relative error = 6.731464672120519e-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) = 2.098979999999833 y[1] (numeric) = 2.098979999999975 absolute error = 1.4166445794217e-13 relative error = 6.749204753841448e-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) = 2.113279999999831 y[1] (numeric) = 2.113279999999974 absolute error = 1.434408147815702e-13 relative error = 6.787591553489443e-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) = 2.127619999999829 y[1] (numeric) = 2.127619999999974 absolute error = 1.447730824111204e-13 relative error = 6.804461436305922e-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) = 2.141999999999827 y[1] (numeric) = 2.141999999999973 absolute error = 1.465494392505207e-13 relative error = 6.841710515897877e-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) = 2.156419999999825 y[1] (numeric) = 2.156419999999973 absolute error = 1.478817068800709e-13 relative error = 6.85774138990006e-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) = 2.170879999999823 y[1] (numeric) = 2.170879999999972 absolute error = 1.49213974509621e-13 relative error = 6.873432640663382e-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) = 2.18537999999982 y[1] (numeric) = 2.185379999999971 absolute error = 1.509903313490213e-13 relative error = 6.90911106302033e-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) = 2.199919999999818 y[1] (numeric) = 2.199919999999971 absolute error = 1.527666881884215e-13 relative error = 6.944192888306582e-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) = 2.214499999999816 y[1] (numeric) = 2.214499999999971 absolute error = 1.545430450278218e-13 relative error = 6.978687966937666e-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) = 2.229119999999814 y[1] (numeric) = 2.22911999999997 absolute error = 1.55875312657372e-13 relative error = 6.992683779131898e-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) = 2.243779999999812 y[1] (numeric) = 2.24377999999997 absolute error = 1.576516694967722e-13 relative error = 7.026164307409168e-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) = 2.25847999999981 y[1] (numeric) = 2.258479999999969 absolute error = 1.594280263361725e-13 relative error = 7.059085151791731e-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) = 2.273219999999808 y[1] (numeric) = 2.273219999999969 absolute error = 1.612043831755727e-13 relative error = 7.091455432188101e-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) = 2.287999999999806 y[1] (numeric) = 2.287999999999968 absolute error = 1.625366508051229e-13 relative error = 7.103874598126605e-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) = 2.302819999999803 y[1] (numeric) = 2.302819999999968 absolute error = 1.647570968543732e-13 relative error = 7.154579900052427e-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) = 2.317679999999801 y[1] (numeric) = 2.317679999999967 absolute error = 1.660893644839234e-13 relative error = 7.166190521725935e-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) = 2.332579999999799 y[1] (numeric) = 2.332579999999967 absolute error = 1.678657213233237e-13 relative error = 7.196568663168599e-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) = 2.347519999999797 y[1] (numeric) = 2.347519999999966 absolute error = 1.691979889528739e-13 relative error = 7.207520658094009e-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) = 2.362499999999795 y[1] (numeric) = 2.362499999999966 absolute error = 1.714184350021242e-13 relative error = 7.255806772577315e-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) = 2.377519999999793 y[1] (numeric) = 2.377519999999965 absolute error = 1.723066134218243e-13 relative error = 7.247325508169829e-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) = 2.39257999999979 y[1] (numeric) = 2.392579999999965 absolute error = 1.745270594710746e-13 relative error = 7.294513014030457e-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) = 2.407679999999788 y[1] (numeric) = 2.407679999999964 absolute error = 1.754152378907747e-13 relative error = 7.28565415216267e-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) = 2.422819999999786 y[1] (numeric) = 2.422819999999963 absolute error = 1.77635683940025e-13 relative error = 7.331773880851271e-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) = 2.437999999999784 y[1] (numeric) = 2.437999999999962 absolute error = 1.785238623597252e-13 relative error = 7.322553829357711e-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) = 2.453219999999781 y[1] (numeric) = 2.453219999999962 absolute error = 1.807443084089755e-13 relative error = 7.367635532442733e-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) = 2.468479999999779 y[1] (numeric) = 2.468479999999961 absolute error = 1.820765760385257e-13 relative error = 7.376060411206165e-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) = 2.483779999999777 y[1] (numeric) = 2.483779999999961 absolute error = 1.84297022087776e-13 relative error = 7.420021986157893e-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) = 2.499119999999775 y[1] (numeric) = 2.49911999999996 absolute error = 1.856292897173262e-13 relative error = 7.427786169425353e-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) = 2.514499999999773 y[1] (numeric) = 2.51449999999996 absolute error = 1.874056465567264e-13 relative error = 7.45299847113714e-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) = 2.52991999999977 y[1] (numeric) = 2.529919999999959 absolute error = 1.891820033961267e-13 relative error = 7.477785993080566e-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) = 2.545379999999768 y[1] (numeric) = 2.545379999999959 absolute error = 1.909583602355269e-13 relative error = 7.502155286658351e-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) = 2.560879999999766 y[1] (numeric) = 2.560879999999958 absolute error = 1.927347170749272e-13 relative error = 7.52611278447037e-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) = 2.576419999999763 y[1] (numeric) = 2.576419999999958 absolute error = 1.940669847044774e-13 relative error = 7.53242812524725e-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) = 2.591999999999761 y[1] (numeric) = 2.591999999999957 absolute error = 1.962874307537277e-13 relative error = 7.572817544511798e-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) = 2.607619999999758 y[1] (numeric) = 2.607619999999956 absolute error = 1.980637875931279e-13 relative error = 7.595577100695128e-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) = 2.623279999999756 y[1] (numeric) = 2.623279999999956 absolute error = 1.998401444325282e-13 relative error = 7.617949453834388e-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) = 2.638979999999754 y[1] (numeric) = 2.638979999999955 absolute error = 2.007283228522283e-13 relative error = 7.606284354267445e-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) = 2.654719999999752 y[1] (numeric) = 2.654719999999954 absolute error = 2.029487689014786e-13 relative error = 7.644827661730714e-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) = 2.670499999999749 y[1] (numeric) = 2.670499999999953 absolute error = 2.042810365310288e-13 relative error = 7.649542652351544e-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) = 2.686319999999747 y[1] (numeric) = 2.686319999999953 absolute error = 2.065014825802791e-13 relative error = 7.687151291741065e-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) = 2.702179999999744 y[1] (numeric) = 2.702179999999952 absolute error = 2.078337502098293e-13 relative error = 7.69133626219752e-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) = 2.718079999999742 y[1] (numeric) = 2.718079999999952 absolute error = 2.100541962590796e-13 relative error = 7.728035828934378e-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) = 2.734019999999739 y[1] (numeric) = 2.734019999999951 absolute error = 2.118305530984799e-13 relative error = 7.747951847407848e-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) = 2.749999999999737 y[1] (numeric) = 2.749999999999951 absolute error = 2.140509991477302e-13 relative error = 7.783672696281841e-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) = 2.766019999999735 y[1] (numeric) = 2.76601999999995 absolute error = 2.153832667772804e-13 relative error = 7.786757390666049e-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) = 2.782079999999732 y[1] (numeric) = 2.78207999999995 absolute error = 2.176037128265307e-13 relative error = 7.821619537416308e-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) = 2.79817999999973 y[1] (numeric) = 2.798179999999949 absolute error = 2.189359804560809e-13 relative error = 7.824227907286236e-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) = 2.814319999999727 y[1] (numeric) = 2.814319999999948 absolute error = 2.211564265053312e-13 relative error = 7.858254445313703e-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) = 2.830499999999725 y[1] (numeric) = 2.830499999999947 absolute error = 2.224886941348814e-13 relative error = 7.860402548486239e-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) = 2.846719999999722 y[1] (numeric) = 2.846719999999947 absolute error = 2.247091401841317e-13 relative error = 7.893615816945594e-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) = 2.86297999999972 y[1] (numeric) = 2.862979999999946 absolute error = 2.264854970235319e-13 relative error = 7.910830568971985e-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) = 2.879279999999717 y[1] (numeric) = 2.879279999999945 absolute error = 2.282618538629322e-13 relative error = 7.927740749873393e-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) = 2.895619999999715 y[1] (numeric) = 2.895619999999945 absolute error = 2.295941214924824e-13 relative error = 7.929014217767006e-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) = 2.911999999999712 y[1] (numeric) = 2.911999999999944 absolute error = 2.318145675417327e-13 relative error = 7.960665094153694e-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) = 2.92841999999971 y[1] (numeric) = 2.928419999999943 absolute error = 2.331468351712829e-13 relative error = 7.961523113873896e-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) = 2.944879999999707 y[1] (numeric) = 2.944879999999942 absolute error = 2.349231920106831e-13 relative error = 7.977343457482358e-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) = 2.961379999999705 y[1] (numeric) = 2.961379999999942 absolute error = 2.366995488500834e-13 relative error = 7.992879969814984e-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) = 2.977919999999703 y[1] (numeric) = 2.977919999999941 absolute error = 2.384759056894836e-13 relative error = 8.008136742743507e-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) = 2.9944999999997 y[1] (numeric) = 2.99449999999994 absolute error = 2.406963517387339e-13 relative error = 8.037947962556623e-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) = 3.011119999999697 y[1] (numeric) = 3.01111999999994 absolute error = 2.424727085781342e-13 relative error = 8.052575406432111e-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) = 3.027779999999694 y[1] (numeric) = 3.027779999999939 absolute error = 2.446931546273845e-13 relative error = 8.081602845233445e-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) = 3.044479999999692 y[1] (numeric) = 3.044479999999938 absolute error = 2.464695114667848e-13 relative error = 8.095619332917599e-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) = 3.06121999999969 y[1] (numeric) = 3.061219999999938 absolute error = 2.48245868306185e-13 relative error = 8.109376925089022e-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) = 3.077999999999687 y[1] (numeric) = 3.077999999999937 absolute error = 2.500222251455853e-13 relative error = 8.122879309474032e-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) = 3.094819999999684 y[1] (numeric) = 3.094819999999936 absolute error = 2.522426711948356e-13 relative error = 8.150479549533134e-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) = 3.111679999999682 y[1] (numeric) = 3.111679999999935 absolute error = 2.535749388243858e-13 relative error = 8.149132906481762e-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) = 3.128579999999679 y[1] (numeric) = 3.128579999999935 absolute error = 2.562394740834861e-13 relative error = 8.190280385462811e-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) = 3.145519999999677 y[1] (numeric) = 3.145519999999934 absolute error = 2.571276525031863e-13 relative error = 8.174408444492888e-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) = 3.162499999999674 y[1] (numeric) = 3.162499999999933 absolute error = 2.597921877622866e-13 relative error = 8.214772735567224e-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) = 3.179519999999671 y[1] (numeric) = 3.179519999999932 absolute error = 2.606803661819868e-13 relative error = 8.198733336541795e-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) = 3.196579999999669 y[1] (numeric) = 3.196579999999932 absolute error = 2.629008122312371e-13 relative error = 8.224440252747134e-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) = 3.213679999999666 y[1] (numeric) = 3.21367999999993 absolute error = 2.642330798607873e-13 relative error = 8.222134122277723e-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) = 3.230819999999663 y[1] (numeric) = 3.23081999999993 absolute error = 2.668976151198876e-13 relative error = 8.260986842966042e-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) = 3.24799999999966 y[1] (numeric) = 3.247999999999929 absolute error = 2.682298827494378e-13 relative error = 8.258309197951535e-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) = 3.265219999999658 y[1] (numeric) = 3.265219999999928 absolute error = 2.704503287986881e-13 relative error = 8.282759777249817e-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) = 3.282479999999655 y[1] (numeric) = 3.282479999999927 absolute error = 2.722266856380884e-13 relative error = 8.293323512652537e-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) = 3.299779999999652 y[1] (numeric) = 3.299779999999927 absolute error = 2.744471316873387e-13 relative error = 8.317134223716963e-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) = 3.31711999999965 y[1] (numeric) = 3.317119999999926 absolute error = 2.762234885267389e-13 relative error = 8.327208196470677e-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) = 3.334499999999647 y[1] (numeric) = 3.334499999999925 absolute error = 2.784439345759893e-13 relative error = 8.350395398890951e-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) = 3.351919999999645 y[1] (numeric) = 3.351919999999924 absolute error = 2.797762022055394e-13 relative error = 8.346744618176123e-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) = 3.369379999999642 y[1] (numeric) = 3.369379999999924 absolute error = 2.819966482547898e-13 relative error = 8.369392833542663e-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) = 3.386879999999639 y[1] (numeric) = 3.386879999999923 absolute error = 2.8377300509419e-13 relative error = 8.378596380569145e-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) = 3.404419999999636 y[1] (numeric) = 3.404419999999922 absolute error = 2.859934511434403e-13 relative error = 8.400651245835441e-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) = 3.421999999999633 y[1] (numeric) = 3.421999999999921 absolute error = 2.877698079828406e-13 relative error = 8.409404090674209e-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) = 3.43961999999963 y[1] (numeric) = 3.43961999999992 absolute error = 2.899902540320909e-13 relative error = 8.43088056332159e-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) = 3.457279999999628 y[1] (numeric) = 3.45727999999992 absolute error = 2.917666108714911e-13 relative error = 8.439195288536727e-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) = 3.474979999999625 y[1] (numeric) = 3.474979999999918 absolute error = 2.935429677108914e-13 relative error = 8.447328264074127e-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) = 3.492719999999622 y[1] (numeric) = 3.492719999999918 absolute error = 2.957634137601417e-13 relative error = 8.467996683392134e-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) = 3.510499999999619 y[1] (numeric) = 3.510499999999916 absolute error = 2.970956813896919e-13 relative error = 8.463058863117051e-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) = 3.528319999999616 y[1] (numeric) = 3.528319999999916 absolute error = 2.997602166487923e-13 relative error = 8.495834183090674e-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) = 3.546179999999614 y[1] (numeric) = 3.546179999999914 absolute error = 3.006483950684924e-13 relative error = 8.478091779563506e-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) = 3.564079999999611 y[1] (numeric) = 3.564079999999914 absolute error = 3.033129303275928e-13 relative error = 8.510272786458943e-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) = 3.582019999999608 y[1] (numeric) = 3.582019999999913 absolute error = 3.04645197957143e-13 relative error = 8.504843578683991e-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) = 3.599999999999605 y[1] (numeric) = 3.599999999999913 absolute error = 3.073097332162433e-13 relative error = 8.536381478229917e-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) = 3.618019999999603 y[1] (numeric) = 3.618019999999911 absolute error = 3.086420008457935e-13 relative error = 8.530688079276163e-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) = 3.636079999999599 y[1] (numeric) = 3.636079999999911 absolute error = 3.11750625314744e-13 relative error = 8.57381095341077e-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) = 3.654179999999597 y[1] (numeric) = 3.65417999999991 absolute error = 3.130828929442941e-13 relative error = 8.567801611971187e-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) = 3.672319999999594 y[1] (numeric) = 3.672319999999909 absolute error = 3.153033389935445e-13 relative error = 8.585944007972599e-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) = 3.690499999999591 y[1] (numeric) = 3.690499999999908 absolute error = 3.170796958329447e-13 relative error = 8.591781488496949e-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) = 3.708719999999588 y[1] (numeric) = 3.708719999999907 absolute error = 3.19300141882195e-13 relative error = 8.609443200948859e-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) = 3.726979999999585 y[1] (numeric) = 3.726979999999906 absolute error = 3.210764987215953e-13 relative error = 8.614924113400958e-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) = 3.745279999999582 y[1] (numeric) = 3.745279999999905 absolute error = 3.232969447708456e-13 relative error = 8.632116818258759e-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) = 3.763619999999579 y[1] (numeric) = 3.763619999999904 absolute error = 3.250733016102458e-13 relative error = 8.63725088107413e-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) = 3.781999999999576 y[1] (numeric) = 3.781999999999903 absolute error = 3.268496584496461e-13 relative error = 8.642243745364428e-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) = 3.800419999999573 y[1] (numeric) = 3.800419999999902 absolute error = 3.290701044988964e-13 relative error = 8.658782568740648e-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) = 3.81887999999957 y[1] (numeric) = 3.818879999999901 absolute error = 3.308464613382966e-13 relative error = 8.663442196097648e-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) = 3.837379999999567 y[1] (numeric) = 3.8373799999999 absolute error = 3.33066907387547e-13 relative error = 8.679539357258977e-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) = 3.855919999999564 y[1] (numeric) = 3.855919999999899 absolute error = 3.352873534367973e-13 relative error = 8.695391850371253e-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) = 3.874499999999562 y[1] (numeric) = 3.874499999999899 absolute error = 3.370637102761975e-13 relative error = 8.699540851109451e-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) = 3.893119999999558 y[1] (numeric) = 3.893119999999898 absolute error = 3.392841563254478e-13 relative error = 8.714967849064153e-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) = 3.911779999999555 y[1] (numeric) = 3.911779999999897 absolute error = 3.415046023746982e-13 relative error = 8.730158709711103e-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) = 3.930479999999552 y[1] (numeric) = 3.930479999999896 absolute error = 3.437250484239485e-13 relative error = 8.745116332457807e-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) = 3.949219999999549 y[1] (numeric) = 3.949219999999895 absolute error = 3.459454944731988e-13 relative error = 8.759843576028639e-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) = 3.967999999999546 y[1] (numeric) = 3.967999999999894 absolute error = 3.47721851312599e-13 relative error = 8.763151494774163e-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) = 3.986819999999543 y[1] (numeric) = 3.986819999999893 absolute error = 3.499422973618493e-13 relative error = 8.777479228103838e-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) = 4.00567999999954 y[1] (numeric) = 4.005679999999892 absolute error = 3.526068326209497e-13 relative error = 8.80267102267256e-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) = 4.024579999999537 y[1] (numeric) = 4.024579999999892 absolute error = 3.552713678800501e-13 relative error = 8.827538970031432e-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) = 4.043519999999534 y[1] (numeric) = 4.043519999999891 absolute error = 3.570477247194503e-13 relative error = 8.830121397185905e-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) = 4.062499999999531 y[1] (numeric) = 4.062499999999891 absolute error = 3.597122599785507e-13 relative error = 8.854455630242271e-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) = 4.081519999999528 y[1] (numeric) = 4.081519999999889 absolute error = 3.61488616817951e-13 relative error = 8.856715557390207e-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) = 4.100579999999525 y[1] (numeric) = 4.100579999999889 absolute error = 3.641531520770513e-13 relative error = 8.880527927197946e-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) = 4.119679999999521 y[1] (numeric) = 4.119679999999888 absolute error = 3.668176873361517e-13 relative error = 8.904033501053343e-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) = 4.138819999999519 y[1] (numeric) = 4.138819999999887 absolute error = 3.68594044175552e-13 relative error = 8.905776143335415e-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) = 4.157999999999515 y[1] (numeric) = 4.157999999999886 absolute error = 3.703704010149522e-13 relative error = 8.907417051827691e-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) = 4.177219999999512 y[1] (numeric) = 4.177219999999886 absolute error = 3.739231146937527e-13 relative error = 8.95148243793232e-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) = 4.196479999999509 y[1] (numeric) = 4.196479999999884 absolute error = 3.748112931134528e-13 relative error = 8.931563908644785e-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) = 4.215779999999506 y[1] (numeric) = 4.215779999999883 absolute error = 3.774758283725532e-13 relative error = 8.953878721674221e-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) = 4.235119999999503 y[1] (numeric) = 4.235119999999882 absolute error = 3.792521852119535e-13 relative error = 8.954933631443689e-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) = 4.254499999999499 y[1] (numeric) = 4.254499999999881 absolute error = 3.819167204710538e-13 relative error = 8.976770959480522e-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) = 4.273919999999496 y[1] (numeric) = 4.27391999999988 absolute error = 3.845812557301542e-13 relative error = 8.998326026930771e-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) = 4.293379999999493 y[1] (numeric) = 4.293379999999879 absolute error = 3.863576125695545e-13 relative error = 8.998914900838037e-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) = 4.31287999999949 y[1] (numeric) = 4.312879999999878 absolute error = 3.881339694089547e-13 relative error = 8.999414994365728e-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) = 4.332419999999487 y[1] (numeric) = 4.332419999999877 absolute error = 3.89910326248355e-13 relative error = 8.999827492449972e-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) = 4.351999999999483 y[1] (numeric) = 4.351999999999876 absolute error = 3.925748615074554e-13 relative error = 9.020562075080468e-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) = 4.37161999999948 y[1] (numeric) = 4.371619999999875 absolute error = 3.943512183468556e-13 relative error = 9.020711277441828e-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) = 4.391279999999478 y[1] (numeric) = 4.391279999999874 absolute error = 3.961275751862559e-13 relative error = 9.020776975877261e-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) = 4.410979999999475 y[1] (numeric) = 4.410979999999872 absolute error = 3.979039320256561e-13 relative error = 9.02076028514533e-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) = 4.430719999999471 y[1] (numeric) = 4.430719999999872 absolute error = 4.014566457044566e-13 relative error = 9.060754137126801e-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) = 4.450499999999467 y[1] (numeric) = 4.45049999999987 absolute error = 4.032330025438569e-13 relative error = 9.060397765282668e-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) = 4.470319999999464 y[1] (numeric) = 4.47031999999987 absolute error = 4.050093593832571e-13 relative error = 9.059963478751088e-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) = 4.49017999999946 y[1] (numeric) = 4.490179999999868 absolute error = 4.076738946423575e-13 relative error = 9.079232784485398e-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) = 4.510079999999458 y[1] (numeric) = 4.510079999999867 absolute error = 4.094502514817577e-13 relative error = 9.078558506319333e-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) = 4.530019999999455 y[1] (numeric) = 4.530019999999865 absolute error = 4.103384299014579e-13 relative error = 9.058203493616081e-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) = 4.549999999999451 y[1] (numeric) = 4.549999999999865 absolute error = 4.138911435802584e-13 relative error = 9.096508650116667e-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) = 4.570019999999448 y[1] (numeric) = 4.570019999999863 absolute error = 4.147793219999585e-13 relative error = 9.076094240287977e-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) = 4.590079999999444 y[1] (numeric) = 4.590079999999862 absolute error = 4.174438572590589e-13 relative error = 9.094478903616264e-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) = 4.610179999999441 y[1] (numeric) = 4.61017999999986 absolute error = 4.192202140984591e-13 relative error = 9.093358916539266e-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) = 4.630319999999438 y[1] (numeric) = 4.630319999999859 absolute error = 4.209965709378594e-13 relative error = 9.092170107852384e-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) = 4.650499999999434 y[1] (numeric) = 4.650499999999858 absolute error = 4.236611061969597e-13 relative error = 9.110011959940034e-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) = 4.670719999999431 y[1] (numeric) = 4.670719999999857 absolute error = 4.263256414560601e-13 relative error = 9.127621468555427e-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) = 4.690979999999428 y[1] (numeric) = 4.690979999999856 absolute error = 4.281019982954604e-13 relative error = 9.126067437838417e-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) = 4.711279999999425 y[1] (numeric) = 4.711279999999856 absolute error = 4.307665335545607e-13 relative error = 9.143301471248011e-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) = 4.73161999999942 y[1] (numeric) = 4.731619999999854 absolute error = 4.334310688136611e-13 relative error = 9.160310185807697e-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) = 4.751999999999418 y[1] (numeric) = 4.751999999999853 absolute error = 4.352074256530614e-13 relative error = 9.158405421993153e-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) = 4.772419999999414 y[1] (numeric) = 4.772419999999852 absolute error = 4.378719609121617e-13 relative error = 9.175050831909502e-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) = 4.792879999999411 y[1] (numeric) = 4.792879999999851 absolute error = 4.405364961712621e-13 relative error = 9.191477695484057e-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) = 4.813379999999407 y[1] (numeric) = 4.81337999999985 absolute error = 4.432010314303625e-13 relative error = 9.207688390079676e-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) = 4.833919999999404 y[1] (numeric) = 4.833919999999849 absolute error = 4.449773882697627e-13 relative error = 9.205311388475969e-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) = 4.854499999999401 y[1] (numeric) = 4.854499999999848 absolute error = 4.46753745109163e-13 relative error = 9.202878671525762e-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) = 4.875119999999397 y[1] (numeric) = 4.875119999999847 absolute error = 4.503064587879635e-13 relative error = 9.236828196803754e-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) = 4.895779999999394 y[1] (numeric) = 4.895779999999846 absolute error = 4.520828156273637e-13 relative error = 9.23413257187659e-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) = 4.916479999999391 y[1] (numeric) = 4.916479999999845 absolute error = 4.53859172466764e-13 relative error = 9.231384495956868e-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) = 4.937219999999387 y[1] (numeric) = 4.937219999999844 absolute error = 4.565237077258644e-13 relative error = 9.24657413941289e-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) = 4.957999999999384 y[1] (numeric) = 4.957999999999842 absolute error = 4.583000645652646e-13 relative error = 9.243647933951626e-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) = 4.97881999999938 y[1] (numeric) = 4.978819999999842 absolute error = 4.618527782440651e-13 relative error = 9.276350184262991e-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) = 4.999679999999376 y[1] (numeric) = 4.99967999999984 absolute error = 4.636291350834654e-13 relative error = 9.2731761849463e-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) = 5.020579999999373 y[1] (numeric) = 5.020579999999839 absolute error = 4.662936703425657e-13 relative error = 9.287645458146747e-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) = 5.04151999999937 y[1] (numeric) = 5.041519999999838 absolute error = 4.68070027181966e-13 relative error = 9.28430368583333e-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) = 5.062499999999366 y[1] (numeric) = 5.062499999999837 absolute error = 4.707345624410664e-13 relative error = 9.298460492664205e-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) = 5.083519999999362 y[1] (numeric) = 5.083519999999835 absolute error = 4.725109192804666e-13 relative error = 9.294955449777436e-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) = 5.104579999999359 y[1] (numeric) = 5.104579999999834 absolute error = 4.75175454539567e-13 relative error = 9.308806102355662e-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) = 5.125679999999355 y[1] (numeric) = 5.125679999999832 absolute error = 4.769518113789672e-13 relative error = 9.305142173897458e-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) = 5.146819999999352 y[1] (numeric) = 5.146819999999831 absolute error = 4.796163466380676e-13 relative error = 9.318692836316949e-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) = 5.167999999999348 y[1] (numeric) = 5.16799999999983 absolute error = 4.813927034774679e-13 relative error = 9.314874293295831e-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) = 5.189219999999345 y[1] (numeric) = 5.189219999999828 absolute error = 4.831690603168681e-13 relative error = 9.311015149038374e-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) = 5.210479999999341 y[1] (numeric) = 5.210479999999827 absolute error = 4.858335955759685e-13 relative error = 9.324161988454612e-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) = 5.231779999999338 y[1] (numeric) = 5.231779999999826 absolute error = 4.876099524153688e-13 relative error = 9.320153989950465e-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) = 5.253119999999334 y[1] (numeric) = 5.253119999999824 absolute error = 4.902744876744691e-13 relative error = 9.333015192391023e-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) = 5.27449999999933 y[1] (numeric) = 5.274499999999823 absolute error = 4.929390229335695e-13 relative error = 9.345701449116164e-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) = 5.295919999999326 y[1] (numeric) = 5.295919999999821 absolute error = 4.947153797729698e-13 relative error = 9.341443597581396e-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) = 5.317379999999323 y[1] (numeric) = 5.31737999999982 absolute error = 4.9649173661237e-13 relative error = 9.337149810854842e-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) = 5.338879999999319 y[1] (numeric) = 5.338879999999818 absolute error = 4.991562718714704e-13 relative error = 9.349456662662095e-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) = 5.360419999999316 y[1] (numeric) = 5.360419999999817 absolute error = 5.018208071305708e-13 relative error = 9.36159493343124e-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) = 5.381999999999312 y[1] (numeric) = 5.381999999999817 absolute error = 5.044853423896711e-13 relative error = 9.373566376620877e-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) = 5.403619999999308 y[1] (numeric) = 5.403619999999815 absolute error = 5.071498776487715e-13 relative error = 9.385372725114579e-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) = 5.425279999999304 y[1] (numeric) = 5.425279999999814 absolute error = 5.098144129078719e-13 relative error = 9.397015691502322e-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) = 5.446979999999301 y[1] (numeric) = 5.446979999999813 absolute error = 5.124789481669723e-13 relative error = 9.408496968357475e-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) = 5.468719999999298 y[1] (numeric) = 5.468719999999812 absolute error = 5.142553050063725e-13 relative error = 9.403577162598169e-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) = 5.490499999999294 y[1] (numeric) = 5.490499999999811 absolute error = 5.169198402654729e-13 relative error = 9.414804485302602e-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) = 5.51231999999929 y[1] (numeric) = 5.51231999999981 absolute error = 5.195843755245733e-13 relative error = 9.425874686604555e-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) = 5.534179999999287 y[1] (numeric) = 5.534179999999808 absolute error = 5.213607323639735e-13 relative error = 9.420740423405829e-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) = 5.556079999999282 y[1] (numeric) = 5.556079999999808 absolute error = 5.258016244624741e-13 relative error = 9.463535882538446e-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) = 5.578019999999279 y[1] (numeric) = 5.578019999999806 absolute error = 5.266898028821743e-13 relative error = 9.44223582708994e-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) = 5.599999999999275 y[1] (numeric) = 5.599999999999805 absolute error = 5.302425165609748e-13 relative error = 9.46861636716149e-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) = 5.622019999999281 y[1] (numeric) = 5.622019999999804 absolute error = 5.222489107836736e-13 relative error = 9.28934636987667e-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) = 5.644079999999287 y[1] (numeric) = 5.644079999999803 absolute error = 5.160316618457728e-13 relative error = 9.142883549592458e-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) = 5.666179999999294 y[1] (numeric) = 5.666179999999801 absolute error = 5.071498776487715e-13 relative error = 8.950472410845309e-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) = 5.688319999999299 y[1] (numeric) = 5.6883199999998 absolute error = 5.009326287108706e-13 relative error = 8.806336997759134e-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) = 5.710499999999305 y[1] (numeric) = 5.710499999999798 absolute error = 4.929390229335695e-13 relative error = 8.632151701840986e-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) = 5.732719999999311 y[1] (numeric) = 5.732719999999797 absolute error = 4.858335955759685e-13 relative error = 8.474748384292742e-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) = 5.754979999999318 y[1] (numeric) = 5.754979999999795 absolute error = 4.778399897986674e-13 relative error = 8.303069511948331e-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) = 5.777279999999324 y[1] (numeric) = 5.777279999999794 absolute error = 4.698463840213662e-13 relative error = 8.132657306230981e-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) = 5.79961999999933 y[1] (numeric) = 5.799619999999793 absolute error = 4.627409566637652e-13 relative error = 7.978815106227971e-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) = 5.821999999999337 y[1] (numeric) = 5.821999999999792 absolute error = 4.556355293061642e-13 relative error = 7.826099781968674e-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) = 5.844419999999343 y[1] (numeric) = 5.844419999999791 absolute error = 4.476419235288631e-13 relative error = 7.659304490931751e-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) = 5.86687999999935 y[1] (numeric) = 5.86687999999979 absolute error = 4.405364961712621e-13 relative error = 7.508871771219301e-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) = 5.889379999999356 y[1] (numeric) = 5.889379999999789 absolute error = 4.32542890393961e-13 relative error = 7.344455450217312e-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) = 5.911919999999363 y[1] (numeric) = 5.911919999999788 absolute error = 4.2543746303636e-13 relative error = 7.196265562396072e-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) = 5.934499999999368 y[1] (numeric) = 5.934499999999787 absolute error = 4.18332035678759e-13 relative error = 7.049153857592106e-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) = 5.957119999999374 y[1] (numeric) = 5.957119999999786 absolute error = 4.11226608321158e-13 relative error = 6.90311103891144e-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) = 5.979779999999382 y[1] (numeric) = 5.979779999999785 absolute error = 4.032330025438569e-13 relative error = 6.743274878739662e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.179999999999731 y[1] (closed_form) = 6.002479999999387 y[1] (numeric) = 6.002479999999784 absolute error = 3.961275751862559e-13 relative error = 6.599398501724225e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999734 y[1] (closed_form) = 6.025219999999394 y[1] (numeric) = 6.025219999999782 absolute error = 3.881339694089547e-13 relative error = 6.44182236348206e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999737 y[1] (closed_form) = 6.047999999999401 y[1] (numeric) = 6.047999999999782 absolute error = 3.801403636316536e-13 relative error = 6.285389610312355e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.209999999999741 y[1] (closed_form) = 6.070819999999408 y[1] (numeric) = 6.07081999999978 absolute error = 3.721467578543525e-13 relative error = 6.130090463139885e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999744 y[1] (closed_form) = 6.093679999999415 y[1] (numeric) = 6.093679999999779 absolute error = 3.641531520770513e-13 relative error = 5.975915244599098e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999747 y[1] (closed_form) = 6.116579999999421 y[1] (numeric) = 6.116579999999778 absolute error = 3.570477247194503e-13 relative error = 5.837375211629442e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999751 y[1] (closed_form) = 6.139519999999427 y[1] (numeric) = 6.139519999999776 absolute error = 3.490541189421492e-13 relative error = 5.685364962443021e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999754 y[1] (closed_form) = 6.162499999999435 y[1] (numeric) = 6.162499999999776 absolute error = 3.410605131648481e-13 relative error = 5.534450517888509e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999757 y[1] (closed_form) = 6.185519999999441 y[1] (numeric) = 6.185519999999775 absolute error = 3.339550858072471e-13 relative error = 5.398981586144371e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999761 y[1] (closed_form) = 6.208579999999447 y[1] (numeric) = 6.208579999999774 absolute error = 3.268496584496461e-13 relative error = 5.26448331904679e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y[1] (closed_form) = 6.231679999999455 y[1] (numeric) = 6.231679999999773 absolute error = 3.18856052672345e-13 relative error = 5.116694898845462e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y[1] (closed_form) = 6.25481999999946 y[1] (numeric) = 6.254819999999772 absolute error = 3.11750625314744e-13 relative error = 4.984166216050515e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y[1] (closed_form) = 6.277999999999468 y[1] (numeric) = 6.277999999999771 absolute error = 3.037570195374428e-13 relative error = 4.83843611878733e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999774 y[1] (closed_form) = 6.301219999999475 y[1] (numeric) = 6.301219999999771 absolute error = 2.957634137601417e-13 relative error = 4.693748413167075e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y[1] (closed_form) = 6.324479999999482 y[1] (numeric) = 6.324479999999769 absolute error = 2.877698079828406e-13 relative error = 4.550094363218228e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999781 y[1] (closed_form) = 6.347779999999489 y[1] (numeric) = 6.347779999999769 absolute error = 2.806643806252396e-13 relative error = 4.421457275224759e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999784 y[1] (closed_form) = 6.371119999999495 y[1] (numeric) = 6.371119999999768 absolute error = 2.726707748479384e-13 relative error = 4.279793424828916e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999787 y[1] (closed_form) = 6.394499999999502 y[1] (numeric) = 6.394499999999767 absolute error = 2.646771690706373e-13 relative error = 4.139137838308827e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999791 y[1] (closed_form) = 6.417919999999509 y[1] (numeric) = 6.417919999999766 absolute error = 2.566835632933362e-13 relative error = 3.999482126504472e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y[1] (closed_form) = 6.441379999999516 y[1] (numeric) = 6.441379999999765 absolute error = 2.486899575160351e-13 relative error = 3.86081798490469e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = 6.464879999999523 y[1] (numeric) = 6.464879999999764 absolute error = 2.406963517387339e-13 relative error = 3.723137192627732e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = 6.488419999999531 y[1] (numeric) = 6.488419999999763 absolute error = 2.327027459614328e-13 relative error = 3.586431611416179e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = 6.511999999999538 y[1] (numeric) = 6.511999999999762 absolute error = 2.247091401841317e-13 relative error = 3.450693184646002e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = 6.535619999999545 y[1] (numeric) = 6.535619999999763 absolute error = 2.176037128265307e-13 relative error = 3.329503747564054e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y[1] (closed_form) = 6.559279999999552 y[1] (numeric) = 6.559279999999761 absolute error = 2.096101070492296e-13 relative error = 3.195626761614749e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y[1] (closed_form) = 6.582979999999559 y[1] (numeric) = 6.582979999999761 absolute error = 2.025046796916286e-13 relative error = 3.076185552616629e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = 6.606719999999566 y[1] (numeric) = 6.60671999999976 absolute error = 1.945110739143274e-13 relative error = 2.944139813921889e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y[1] (closed_form) = 6.630499999999573 y[1] (numeric) = 6.63049999999976 absolute error = 1.865174681370263e-13 relative error = 2.813022670040545e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y[1] (closed_form) = 6.654319999999581 y[1] (numeric) = 6.654319999999759 absolute error = 1.77635683940025e-13 relative error = 2.669479134457559e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 6.678179999999588 y[1] (numeric) = 6.678179999999759 absolute error = 1.70530256582424e-13 relative error = 2.553543878458421e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y[1] (closed_form) = 6.702079999999595 y[1] (numeric) = 6.702079999999757 absolute error = 1.616484723854228e-13 relative error = 2.411914993336883e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y[1] (closed_form) = 6.726019999999602 y[1] (numeric) = 6.726019999999757 absolute error = 1.545430450278218e-13 relative error = 2.297689347159701e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 6.74999999999961 y[1] (numeric) = 6.749999999999756 absolute error = 1.456612608308205e-13 relative error = 2.15794460490117e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y[1] (closed_form) = 6.774019999999617 y[1] (numeric) = 6.774019999999755 absolute error = 1.376676550535194e-13 relative error = 2.032288878000466e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y[1] (closed_form) = 6.798079999999625 y[1] (numeric) = 6.798079999999755 absolute error = 1.296740492762183e-13 relative error = 1.907509903917362e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = 6.822179999999632 y[1] (numeric) = 6.822179999999753 absolute error = 1.216804434989172e-13 relative error = 1.783600601258303e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y[1] (closed_form) = 6.84631999999964 y[1] (numeric) = 6.846319999999753 absolute error = 1.127986593019159e-13 relative error = 1.647580879975254e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y[1] (closed_form) = 6.870499999999647 y[1] (numeric) = 6.870499999999753 absolute error = 1.056932319443149e-13 relative error = 1.53836302953672e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y[1] (closed_form) = 6.894719999999655 y[1] (numeric) = 6.894719999999752 absolute error = 9.681144774731365e-14 relative error = 1.404138931636361e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y[1] (closed_form) = 6.918979999999662 y[1] (numeric) = 6.918979999999752 absolute error = 8.970602038971265e-14 relative error = 1.296520880096734e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y[1] (closed_form) = 6.943279999999669 y[1] (numeric) = 6.943279999999751 absolute error = 8.171241461241152e-14 relative error = 1.176856105650577e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y[1] (closed_form) = 6.967619999999677 y[1] (numeric) = 6.967619999999751 absolute error = 7.371880883511039e-14 relative error = 1.058019938445464e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y[1] (closed_form) = 6.991999999999685 y[1] (numeric) = 6.99199999999975 absolute error = 6.572520305780927e-14 relative error = 9.400057645568112e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y[1] (closed_form) = 7.016419999999693 y[1] (numeric) = 7.01641999999975 absolute error = 5.684341886080801e-14 relative error = 8.101484640430662e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y[1] (closed_form) = 7.0408799999997 y[1] (numeric) = 7.040879999999749 absolute error = 4.884981308350689e-14 relative error = 6.938026650576202e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y[1] (closed_form) = 7.065379999999708 y[1] (numeric) = 7.065379999999749 absolute error = 4.085620730620576e-14 relative error = 5.782591637846435e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y[1] (closed_form) = 7.089919999999716 y[1] (numeric) = 7.089919999999748 absolute error = 3.197442310920451e-14 relative error = 4.509842580622319e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y[1] (closed_form) = 7.114499999999723 y[1] (numeric) = 7.114499999999747 absolute error = 2.398081733190338e-14 relative error = 3.37069608994368e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y[1] (closed_form) = 7.139119999999731 y[1] (numeric) = 7.139119999999747 absolute error = 1.598721155460225e-14 relative error = 2.239381261920637e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y[1] (closed_form) = 7.163779999999739 y[1] (numeric) = 7.163779999999746 absolute error = 7.105427357601002e-15 relative error = 9.918544898923837e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y[1] (closed_form) = 7.188479999999747 y[1] (numeric) = 7.188479999999746 absolute error = 8.881784197001252e-16 relative error = 1.235558031322556e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y[1] (closed_form) = 7.213219999999755 y[1] (numeric) = 7.213219999999746 absolute error = 8.881784197001252e-15 relative error = 1.231320297592692e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y[1] (closed_form) = 7.237999999999762 y[1] (numeric) = 7.237999999999746 absolute error = 1.687538997430238e-14 relative error = 2.331499029331712e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y[1] (closed_form) = 7.26281999999977 y[1] (numeric) = 7.262819999999746 absolute error = 2.486899575160351e-14 relative error = 3.424151466180394e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y[1] (closed_form) = 7.287679999999779 y[1] (numeric) = 7.287679999999745 absolute error = 3.375077994860476e-14 relative error = 4.631210474198343e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y[1] (closed_form) = 7.312579999999786 y[1] (numeric) = 7.312579999999745 absolute error = 4.174438572590589e-14 relative error = 5.70857149267524e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y[1] (closed_form) = 7.337519999999794 y[1] (numeric) = 7.337519999999745 absolute error = 4.973799150320701e-14 relative error = 6.778583431896391e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y[1] (closed_form) = 7.362499999999803 y[1] (numeric) = 7.362499999999744 absolute error = 5.861977570020827e-14 relative error = 7.961938974561608e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y[1] (closed_form) = 7.38751999999981 y[1] (numeric) = 7.387519999999745 absolute error = 6.572520305780927e-14 relative error = 8.896788510597732e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y[1] (closed_form) = 7.412579999999818 y[1] (numeric) = 7.412579999999743 absolute error = 7.460698725481052e-14 relative error = 1.006491494929058e-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) = 7.437679999999826 y[1] (numeric) = 7.437679999999744 absolute error = 8.260059303211165e-14 relative error = 1.110569331190823e-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) = 7.462819999999835 y[1] (numeric) = 7.462819999999743 absolute error = 9.14823772291129e-14 relative error = 1.22584193681631e-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) = 7.487999999999843 y[1] (numeric) = 7.487999999999743 absolute error = 1.003641614261142e-13 relative error = 1.340333352378689e-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) = 7.513219999999851 y[1] (numeric) = 7.513219999999742 absolute error = 1.092459456231154e-13 relative error = 1.454049603540394e-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) = 7.53847999999986 y[1] (numeric) = 7.538479999999742 absolute error = 1.172395514004165e-13 relative error = 1.555214730296011e-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) = 7.563779999999867 y[1] (numeric) = 7.563779999999741 absolute error = 1.261213355974178e-13 relative error = 1.667437915928544e-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) = 7.589119999999876 y[1] (numeric) = 7.589119999999742 absolute error = 1.341149413747189e-13 relative error = 1.767200167802342e-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) = 7.614499999999884 y[1] (numeric) = 7.614499999999741 absolute error = 1.429967255717202e-13 relative error = 1.87795292628173e-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) = 7.639919999999893 y[1] (numeric) = 7.639919999999742 absolute error = 1.509903313490213e-13 relative error = 1.97633393214881e-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) = 7.6653799999999 y[1] (numeric) = 7.665379999999741 absolute error = 1.589839371263224e-13 relative error = 2.074051607700133e-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) = 7.690879999999909 y[1] (numeric) = 7.690879999999741 absolute error = 1.678657213233237e-13 relative error = 2.182659478802499e-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) = 7.716419999999918 y[1] (numeric) = 7.716419999999741 absolute error = 1.767475055203249e-13 relative error = 2.290537652438914e-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) = 7.741999999999926 y[1] (numeric) = 7.741999999999742 absolute error = 1.84741111297626e-13 relative error = 2.386219469098783e-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) = 7.767619999999934 y[1] (numeric) = 7.767619999999741 absolute error = 1.936228954946273e-13 relative error = 2.492692684433957e-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) = 7.793279999999942 y[1] (numeric) = 7.793279999999741 absolute error = 2.016165012719284e-13 relative error = 2.587055787446748e-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) = 7.818979999999951 y[1] (numeric) = 7.81897999999974 absolute error = 2.104982854689297e-13 relative error = 2.692145081186178e-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) = 7.84471999999996 y[1] (numeric) = 7.84471999999974 absolute error = 2.193800696659309e-13 relative error = 2.796531548174212e-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) = 7.870499999999969 y[1] (numeric) = 7.87049999999974 absolute error = 2.282618538629322e-13 relative error = 2.900220492509156e-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) = 7.896319999999977 y[1] (numeric) = 7.89631999999974 absolute error = 2.371436380599334e-13 relative error = 3.003217170275953e-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) = 7.922179999999986 y[1] (numeric) = 7.92217999999974 absolute error = 2.460254222569347e-13 relative error = 3.105526790062017e-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) = 7.948079999999994 y[1] (numeric) = 7.94807999999974 absolute error = 2.540190280342358e-13 relative error = 3.195979759064277e-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) = 7.974020000000003 y[1] (numeric) = 7.974019999999739 absolute error = 2.637889906509372e-13 relative error = 3.308105455603787e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) * 2.0 ; 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 %