##############ECHO OF PROBLEM################# ##############temp/sub_sin_cospostode.ode################# diff ( y , x , 1 ) = neg ( sin ( x ) ) - cos ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(cos(c(x)) - sin(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) = 0.8951707486311977 y[1] (numeric) = 0.8951707486311977 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) = 0.8841777971195219 y[1] (numeric) = 0.884177797119522 absolute error = 1.110223024625157e-16 relative error = 1.25565585139329e-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) = 0.8730964285649468 y[1] (numeric) = 0.8730964285649468 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 0.8619277510950932 y[1] (numeric) = 0.861927751095093 absolute error = 2.220446049250313e-16 relative error = 2.57613941125483e-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) = 0.8506728815684006 y[1] (numeric) = 0.8506728815684006 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 0.839332945462443 y[1] (numeric) = 0.839332945462443 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 0.8279090767613809 y[1] (numeric) = 0.8279090767613809 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 0.8164024178425646 y[1] (numeric) = 0.8164024178425646 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 0.8048141193622972 y[1] (numeric) = 0.8048141193622972 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 0.7931453401407697 y[1] (numeric) = 0.7931453401407698 absolute error = 1.110223024625157e-16 relative error = 1.399772486122293e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 0.7813972470461803 y[1] (numeric) = 0.7813972470461803 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (closed_form) = 0.7695710148780486 y[1] (numeric) = 0.7695710148780485 absolute error = 1.110223024625157e-16 relative error = 1.44265181921007e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (closed_form) = 0.7576678262497361 y[1] (numeric) = 0.7576678262497361 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (closed_form) = 0.7456888714701863 y[1] (numeric) = 0.7456888714701864 absolute error = 1.110223024625157e-16 relative error = 1.488855563093307e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = 0.7336353484248949 y[1] (numeric) = 0.7336353484248949 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = 0.7215084624561217 y[1] (numeric) = 0.7215084624561218 absolute error = 1.110223024625157e-16 relative error = 1.538752602908901e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 0.709309426242358 y[1] (numeric) = 0.709309426242358 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 0.6970394596770593 y[1] (numeric) = 0.6970394596770593 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 0.684699789746657 y[1] (numeric) = 0.6846997897466571 absolute error = 1.110223024625157e-16 relative error = 1.621474171966586e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 0.6722916504078613 y[1] (numeric) = 0.6722916504078618 absolute error = 4.440892098500626e-16 relative error = 6.605603529073217e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 0.6598162824642663 y[1] (numeric) = 0.6598162824642665 absolute error = 2.220446049250313e-16 relative error = 3.365248946202788e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 0.6472749334422697 y[1] (numeric) = 0.6472749334422698 absolute error = 1.110223024625157e-16 relative error = 1.715226354774601e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 0.6346688574663228 y[1] (numeric) = 0.6346688574663231 absolute error = 2.220446049250313e-16 relative error = 3.498589891608374e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 0.6219993151335184 y[1] (numeric) = 0.6219993151335187 absolute error = 3.33066907387547e-16 relative error = 5.354779326662937e-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) = 0.6092675733875317 y[1] (numeric) = 0.6092675733875317 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = 0.5964749053919274 y[1] (numeric) = 0.5964749053919275 absolute error = 1.110223024625157e-16 relative error = 1.861307180887449e-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) = 0.5836225904028447 y[1] (numeric) = 0.5836225904028448 absolute error = 1.110223024625157e-16 relative error = 1.902296180582775e-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) = 0.5707119136410721 y[1] (numeric) = 0.5707119136410723 absolute error = 2.220446049250313e-16 relative error = 3.890660061893819e-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) = 0.5577441661635272 y[1] (numeric) = 0.5577441661635275 absolute error = 3.33066907387547e-16 relative error = 5.971678909320833e-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) = 0.5447206447341513 y[1] (numeric) = 0.5447206447341515 absolute error = 2.220446049250313e-16 relative error = 4.076302359228541e-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) = 0.5316426516942343 y[1] (numeric) = 0.5316426516942344 absolute error = 1.110223024625157e-16 relative error = 2.088288103084106e-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) = 0.5185114948321818 y[1] (numeric) = 0.5185114948321818 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 0.5053284872527377 y[1] (numeric) = 0.5053284872527376 absolute error = 1.110223024625157e-16 relative error = 2.197032331703642e-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) = 0.492094947245674 y[1] (numeric) = 0.4920949472456739 absolute error = 1.110223024625157e-16 relative error = 2.256115472916831e-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) = 0.4788121981539634 y[1] (numeric) = 0.4788121981539634 absolute error = 5.551115123125783e-17 relative error = 1.159351233015331e-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) = 0.4654815682414463 y[1] (numeric) = 0.4654815682414463 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (closed_form) = 0.4521043905600051 y[1] (numeric) = 0.4521043905600051 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = 0.4386820028162603 y[1] (numeric) = 0.4386820028162602 absolute error = 1.110223024625157e-16 relative error = 2.530815072188334e-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) = 0.4252157472378009 y[1] (numeric) = 0.4252157472378009 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = 0.411706970438963 y[1] (numeric) = 0.4117069704389631 absolute error = 5.551115123125783e-17 relative error = 1.348317012268986e-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) = 0.3981570232861693 y[1] (numeric) = 0.3981570232861693 absolute error = 5.551115123125783e-17 relative error = 1.394202487578878e-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) = 0.3845672607628433 y[1] (numeric) = 0.3845672607628434 absolute error = 1.110223024625157e-16 relative error = 2.886941083915654e-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) = 0.3709390418339127 y[1] (numeric) = 0.3709390418339128 absolute error = 5.551115123125783e-17 relative error = 1.496503332644959e-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) = 0.3572737293099135 y[1] (numeric) = 0.3572737293099136 absolute error = 1.110223024625157e-16 relative error = 3.107485755444685e-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) = 0.3435726897107105 y[1] (numeric) = 0.3435726897107106 absolute error = 5.551115123125783e-17 relative error = 1.615703252723563e-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) = 0.3298372931288461 y[1] (numeric) = 0.3298372931288461 absolute error = 5.551115123125783e-17 relative error = 1.682985896005798e-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) = 0.3160689130925322 y[1] (numeric) = 0.3160689130925322 absolute error = 5.551115123125783e-17 relative error = 1.756298988347722e-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) = 0.3022689264282989 y[1] (numeric) = 0.3022689264282989 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = 0.2884387131233128 y[1] (numeric) = 0.2884387131233129 absolute error = 5.551115123125783e-17 relative error = 1.924538860618401e-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) = 0.2745796561873791 y[1] (numeric) = 0.2745796561873792 absolute error = 1.110223024625157e-16 relative error = 4.043354995926997e-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) = 0.2606931415146424 y[1] (numeric) = 0.2606931415146424 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 0.2467805577449976 y[1] (numeric) = 0.2467805577449977 absolute error = 1.110223024625157e-16 relative error = 4.498826952860557e-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) = 0.2328432961252282 y[1] (numeric) = 0.2328432961252283 absolute error = 8.326672684688674e-17 relative error = 3.576084355123717e-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) = 0.2188827503698818 y[1] (numeric) = 0.2188827503698818 absolute error = 2.775557561562891e-17 relative error = 1.268056782397233e-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) = 0.2049003165218999 y[1] (numeric) = 0.2049003165219001 absolute error = 1.942890293094024e-16 relative error = 9.482124410902832e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = 0.1908973928130157 y[1] (numeric) = 0.1908973928130158 absolute error = 1.665334536937735e-16 relative error = 8.72371545990119e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = 0.1768753795239306 y[1] (numeric) = 0.1768753795239308 absolute error = 2.220446049250313e-16 relative error = 1.255373164556175e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (closed_form) = 0.162835678844289 y[1] (numeric) = 0.1628356788442892 absolute error = 1.942890293094024e-16 relative error = 1.193160065953301e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (closed_form) = 0.1487796947324587 y[1] (numeric) = 0.148779694732459 absolute error = 3.05311331771918e-16 relative error = 2.052103496521757e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (closed_form) = 0.134708832775138 y[1] (numeric) = 0.1347088327751382 absolute error = 1.665334536937735e-16 relative error = 1.236247469917274e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 0.1206245000467966 y[1] (numeric) = 0.1206245000467969 absolute error = 3.05311331771918e-16 relative error = 2.531088888687387e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = 0.1065281049689708 y[1] (numeric) = 0.106528104968971 absolute error = 1.942890293094024e-16 relative error = 1.823828832456884e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (closed_form) = 0.09242105716942106 y[1] (numeric) = 0.09242105716942135 absolute error = 2.914335439641036e-16 relative error = 3.153324068019089e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (closed_form) = 0.07830476734117175 y[1] (numeric) = 0.07830476734117205 absolute error = 2.914335439641036e-16 relative error = 3.721785452657506e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (closed_form) = 0.064180647101442 y[1] (numeric) = 0.06418064710144239 absolute error = 3.885780586188048e-16 relative error = 6.054442829232152e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (closed_form) = 0.05005010885048589 y[1] (numeric) = 0.05005010885048627 absolute error = 3.816391647148976e-16 relative error = 7.625141552737954e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 0.035914565630353 y[1] (numeric) = 0.03591456563035338 absolute error = 3.747002708109903e-16 relative error = 1.043310044920366e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = 0.02177543098358581 y[1] (numeric) = 0.02177543098358615 absolute error = 3.434752482434078e-16 relative error = 1.577352239330268e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (closed_form) = 0.007634118811866375 y[1] (numeric) = 0.007634118811866708 absolute error = 3.33066907387547e-16 relative error = 4.362872986333827e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = -0.006507956765372636 y[1] (numeric) = -0.006507956765372178 absolute error = 4.570996359198887e-16 relative error = 7.023704250034547e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (closed_form) = -0.02064938155235818 y[1] (numeric) = -0.02064938155235781 absolute error = 3.747002708109903e-16 relative error = 1.814583501500553e-12 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (closed_form) = -0.03478874141839627 y[1] (numeric) = -0.03478874141839597 absolute error = 3.05311331771918e-16 relative error = 8.776153414117751e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (closed_form) = -0.04892462243928319 y[1] (numeric) = -0.04892462243928281 absolute error = 3.816391647148976e-16 relative error = 7.800554111347967e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = -0.0630556110386965 y[1] (numeric) = -0.06305561103869611 absolute error = 3.885780586188048e-16 relative error = 6.162465991810609e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (closed_form) = -0.07718029412955207 y[1] (numeric) = -0.0771802941295517 absolute error = 3.747002708109903e-16 relative error = 4.854869692282228e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = -0.09129725925531151 y[1] (numeric) = -0.091297259255311 absolute error = 5.134781488891349e-16 relative error = 5.624244945329634e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (closed_form) = -0.1054050947312261 y[1] (numeric) = -0.1054050947312256 absolute error = 4.718447854656915e-16 relative error = 4.476489363904612e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (closed_form) = -0.1195023897855049 y[1] (numeric) = -0.1195023897855043 absolute error = 5.273559366969494e-16 relative error = 4.412932140047591e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (closed_form) = -0.1335877347003901 y[1] (numeric) = -0.1335877347003896 absolute error = 4.996003610813204e-16 relative error = 3.739867003522604e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (closed_form) = -0.147659720953128 y[1] (numeric) = -0.1476597209531275 absolute error = 4.440892098500626e-16 relative error = 3.007517601845063e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = -0.1617169413568199 y[1] (numeric) = -0.1617169413568195 absolute error = 3.885780586188048e-16 relative error = 2.40282839483977e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = -0.1757579902011398 y[1] (numeric) = -0.1757579902011394 absolute error = 3.608224830031759e-16 relative error = 2.052950665800433e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (closed_form) = -0.1897814633929042 y[1] (numeric) = -0.1897814633929037 absolute error = 5.273559366969494e-16 relative error = 2.778753663655577e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = -0.2037859585964799 y[1] (numeric) = -0.2037859585964794 absolute error = 4.163336342344337e-16 relative error = 2.042994704354598e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = -0.217770075374017 y[1] (numeric) = -0.2177700753740165 absolute error = 4.996003610813204e-16 relative error = 2.294164431101306e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = -0.2317324153254913 y[1] (numeric) = -0.2317324153254908 absolute error = 4.996003610813204e-16 relative error = 2.155936451012181e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = -0.2456715822285427 y[1] (numeric) = -0.2456715822285422 absolute error = 5.273559366969494e-16 relative error = 2.146589084147153e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = -0.2595861821780968 y[1] (numeric) = -0.2595861821780963 absolute error = 5.551115123125783e-16 relative error = 2.138447846702902e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = -0.2734748237257543 y[1] (numeric) = -0.2734748237257537 absolute error = 6.106226635438361e-16 relative error = 2.232829535183027e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = -0.287336118018934 y[1] (numeric) = -0.2873361180189333 absolute error = 6.661338147750939e-16 relative error = 2.318308674063729e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (closed_form) = -0.3011686789397576 y[1] (numeric) = -0.3011686789397572 absolute error = 4.440892098500626e-16 relative error = 1.474553102312785e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = -0.3149711232436592 y[1] (numeric) = -0.3149711232436601 absolute error = 8.881784197001252e-16 relative error = 2.819872534832463e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = -0.3287420706977112 y[1] (numeric) = -0.3287420706977137 absolute error = 2.498001805406602e-15 relative error = 7.598667855638088e-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) = -0.3424801442186445 y[1] (numeric) = -0.3424801442186484 absolute error = 3.941291737419306e-15 relative error = 1.150808829052328e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = -0.3561839700105549 y[1] (numeric) = -0.3561839700105604 absolute error = 5.495603971894525e-15 relative error = 1.542911650889756e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = -0.3698521777022833 y[1] (numeric) = -0.3698521777022903 absolute error = 6.994405055138486e-15 relative error = 1.891135290480488e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = -0.3834834004844506 y[1] (numeric) = -0.3834834004844591 absolute error = 8.493206138382448e-15 relative error = 2.214751962575973e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = -0.3970762752461379 y[1] (numeric) = -0.3970762752461479 absolute error = 9.992007221626409e-15 relative error = 2.516394920707012e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = -0.4106294427111964 y[1] (numeric) = -0.410629442711208 absolute error = 1.154631945610163e-14 relative error = 2.811858638257066e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = -0.4241415475741739 y[1] (numeric) = -0.4241415475741869 absolute error = 1.298960938811433e-14 relative error = 3.062564717464447e-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) = -0.4376112386358441 y[1] (numeric) = -0.4376112386358585 absolute error = 1.448841047135829e-14 relative error = 3.31079487732598e-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) = -0.4510371689383254 y[1] (numeric) = -0.4510371689383413 absolute error = 1.5931700403371e-14 relative error = 3.532236698113341e-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) = -0.4644179958997761 y[1] (numeric) = -0.4644179958997934 absolute error = 1.731947918415244e-14 relative error = 3.729286835794813e-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) = -0.4777523814486504 y[1] (numeric) = -0.4777523814486692 absolute error = 1.876276911616515e-14 relative error = 3.927299966411952e-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) = -0.4910389921575056 y[1] (numeric) = -0.4910389921575258 absolute error = 2.026157019940911e-14 relative error = 4.126265026405481e-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) = -0.5042764993763428 y[1] (numeric) = -0.5042764993763644 absolute error = 2.164934898019055e-14 relative error = 4.293150485292314e-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) = -0.5174635793654715 y[1] (numeric) = -0.5174635793654945 absolute error = 2.298161660974074e-14 relative error = 4.441204661769906e-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) = -0.5305989134278817 y[1] (numeric) = -0.5305989134279062 absolute error = 2.453592884421596e-14 relative error = 4.62419507904832e-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) = -0.5436811880411136 y[1] (numeric) = -0.5436811880411394 absolute error = 2.575717417130363e-14 relative error = 4.737551112280871e-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) = -0.5567090949886074 y[1] (numeric) = -0.5567090949886346 absolute error = 2.720046410331634e-14 relative error = 4.8859385176513e-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) = -0.5696813314905251 y[1] (numeric) = -0.569681331490554 absolute error = 2.886579864025407e-14 relative error = 5.067007999845992e-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) = -0.5825966003340266 y[1] (numeric) = -0.5825966003340569 absolute error = 3.030908857226677e-14 relative error = 5.202414252827655e-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) = -0.5954536100029904 y[1] (numeric) = -0.5954536100030221 absolute error = 3.175237850427948e-14 relative error = 5.332468889410212e-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) = -0.6082510748071634 y[1] (numeric) = -0.6082510748071965 absolute error = 3.308464613382966e-14 relative error = 5.439307467614198e-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) = -0.62098771501073 y[1] (numeric) = -0.6209877150107647 absolute error = 3.463895836830488e-14 relative error = 5.578042452531667e-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) = -0.6336622569602837 y[1] (numeric) = -0.6336622569603196 absolute error = 3.597122599785507e-14 relative error = 5.676719041214673e-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) = -0.6462734332121913 y[1] (numeric) = -0.6462734332122287 absolute error = 3.741451592986778e-14 relative error = 5.789270300638128e-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) = -0.6588199826593371 y[1] (numeric) = -0.658819982659376 absolute error = 3.896882816434299e-14 relative error = 5.914943260683247e-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) = -0.6713006506572319 y[1] (numeric) = -0.6713006506572723 absolute error = 4.04121180963557e-14 relative error = 6.019973026510628e-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) = -0.6837141891494763 y[1] (numeric) = -0.6837141891495181 absolute error = 4.174438572590589e-14 relative error = 6.105531578602293e-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) = -0.6960593567925657 y[1] (numeric) = -0.6960593567926089 absolute error = 4.318767565791859e-14 relative error = 6.204596667865647e-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) = -0.7083349190800234 y[1] (numeric) = -0.708334919080068 absolute error = 4.451994328746878e-14 relative error = 6.285154393530496e-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) = -0.7205396484658502 y[1] (numeric) = -0.7205396484658961 absolute error = 4.596323321948148e-14 relative error = 6.379001255148821e-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) = -0.7326723244872781 y[1] (numeric) = -0.7326723244873254 absolute error = 4.729550084903167e-14 relative error = 6.455205044373542e-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) = -0.7447317338868157 y[1] (numeric) = -0.7447317338868644 absolute error = 4.873879078104437e-14 relative error = 6.544476160116428e-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) = -0.7567166707335722 y[1] (numeric) = -0.7567166707336221 absolute error = 4.996003610813204e-14 relative error = 6.602211638829108e-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) = -0.7686259365438506 y[1] (numeric) = -0.7686259365439018 absolute error = 5.118128143521972e-14 relative error = 6.658802286240544e-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) = -0.7804583404009939 y[1] (numeric) = -0.7804583404010466 absolute error = 5.262457136723242e-14 relative error = 6.742777755465371e-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) = -0.7922126990744771 y[1] (numeric) = -0.7922126990745308 absolute error = 5.373479439185758e-14 relative error = 6.782874656595966e-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) = -0.8038878371382279 y[1] (numeric) = -0.8038878371382828 absolute error = 5.495603971894525e-14 relative error = 6.836282025933377e-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) = -0.8154825870881691 y[1] (numeric) = -0.8154825870882253 absolute error = 5.617728504603292e-14 relative error = 6.888839312513621e-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) = -0.8269957894589681 y[1] (numeric) = -0.8269957894590255 absolute error = 5.739853037312059e-14 relative error = 6.940607328928663e-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) = -0.8384262929399822 y[1] (numeric) = -0.8384262929400408 absolute error = 5.861977570020827e-14 relative error = 6.991643295757723e-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) = -0.8497729544903883 y[1] (numeric) = -0.8497729544904482 absolute error = 5.995204332975845e-14 relative error = 7.055066063583054e-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) = -0.8610346394534873 y[1] (numeric) = -0.8610346394535484 absolute error = 6.106226635438361e-14 relative error = 7.091731686095791e-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) = -0.8722102216701675 y[1] (numeric) = -0.8722102216702299 absolute error = 6.23945339839338e-14 relative error = 7.153611874033819e-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) = -0.88329858359152 y[1] (numeric) = -0.8832985835915836 absolute error = 6.361577931102147e-14 relative error = 7.202069661694429e-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) = -0.8942986163905932 y[1] (numeric) = -0.894298616390658 absolute error = 6.483702463810914e-14 relative error = 7.250041926688051e-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) = -0.9052092200732738 y[1] (numeric) = -0.9052092200733397 absolute error = 6.59472476627343e-14 relative error = 7.285304457835292e-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) = -0.9160293035882854 y[1] (numeric) = -0.9160293035883528 absolute error = 6.7390537594747e-14 relative error = 7.356810238576829e-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) = -0.9267577849362933 y[1] (numeric) = -0.926757784936362 absolute error = 6.861178292183467e-14 relative error = 7.40342126465667e-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) = -0.9373935912781035 y[1] (numeric) = -0.9373935912781732 absolute error = 6.972200594645983e-14 relative error = 7.437858184137605e-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) = -0.9479356590419444 y[1] (numeric) = -0.9479356590420153 absolute error = 7.083222897108499e-14 relative error = 7.472261254806408e-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) = -0.958382934029825 y[1] (numeric) = -0.9583829340298968 absolute error = 7.183142969324763e-14 relative error = 7.49506560923509e-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) = -0.9687343715229524 y[1] (numeric) = -0.9687343715230254 absolute error = 7.30526750203353e-14 relative error = 7.541042949213086e-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) = -0.9789889363862034 y[1] (numeric) = -0.9789889363862777 absolute error = 7.427392034742297e-14 relative error = 7.586798745815704e-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) = -0.9891456031716371 y[1] (numeric) = -0.9891456031717126 absolute error = 7.549516567451064e-14 relative error = 7.632361245143267e-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) = -0.9992033562210392 y[1] (numeric) = -0.9992033562211156 absolute error = 7.638334409421077e-14 relative error = 7.644424292477416e-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) = -1.009161189767486 y[1] (numeric) = -1.009161189767563 absolute error = 7.749356711883593e-14 relative error = 7.679007863618964e-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) = -1.01901810803592 y[1] (numeric) = -1.019018108035999 absolute error = 7.860379014346108e-14 relative error = 7.71367942567418e-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) = -1.02877312534273 y[1] (numeric) = -1.02877312534281 absolute error = 7.971401316808624e-14 relative error = 7.748454076454411e-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) = -1.038425266194314 y[1] (numeric) = -1.038425266194395 absolute error = 8.08242361927114e-14 relative error = 7.783346459675534e-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) = -1.04797356538463 y[1] (numeric) = -1.047973565384712 absolute error = 8.171241461241152e-14 relative error = 7.797182802260971e-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) = -1.057417068091716 y[1] (numeric) = -1.057417068091799 absolute error = 8.260059303211165e-14 relative error = 7.811543384785537e-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) = -1.066754829973171 y[1] (numeric) = -1.066754829973255 absolute error = 8.393286066166183e-14 relative error = 7.86805536786487e-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) = -1.075985917260588 y[1] (numeric) = -1.075985917260672 absolute error = 8.43769498715119e-14 relative error = 7.841826599955124e-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) = -1.085109406852931 y[1] (numeric) = -1.085109406853016 absolute error = 8.504308368628699e-14 relative error = 7.837281950483841e-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) = -1.094124386408843 y[1] (numeric) = -1.094124386408929 absolute error = 8.615330671091215e-14 relative error = 7.874178455494102e-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) = -1.103029954437881 y[1] (numeric) = -1.103029954437969 absolute error = 8.748557434046234e-14 relative error = 7.931386993478897e-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) = -1.111825220390665 y[1] (numeric) = -1.111825220390753 absolute error = 8.859579736508749e-14 relative error = 7.968500420772733e-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) = -1.120509304747927 y[1] (numeric) = -1.120509304748017 absolute error = 8.970602038971265e-14 relative error = 8.005825566070881e-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) = -1.12908133910847 y[1] (numeric) = -1.12908133910856 absolute error = 9.059419880941277e-14 relative error = 8.023708803915453e-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) = -1.137540466275999 y[1] (numeric) = -1.13754046627609 absolute error = 9.103828801926284e-14 relative error = 8.003081272114885e-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) = -1.145885840344848 y[1] (numeric) = -1.14588584034494 absolute error = 9.170442183403793e-14 relative error = 8.002928267831635e-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) = -1.154116626784564 y[1] (numeric) = -1.154116626784657 absolute error = 9.281464485866309e-14 relative error = 8.04205075159952e-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) = -1.162232002523363 y[1] (numeric) = -1.162232002523456 absolute error = 9.348077867343818e-14 relative error = 8.043211550747076e-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) = -1.170231156030433 y[1] (numeric) = -1.170231156030527 absolute error = 9.414691248821327e-14 relative error = 8.045155181782301e-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) = -1.178113287397089 y[1] (numeric) = -1.178113287397184 absolute error = 9.50350909079134e-14 relative error = 8.066719213216154e-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) = -1.185877608416763 y[1] (numeric) = -1.185877608416859 absolute error = 9.592326932761353e-14 relative error = 8.088800112827699e-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) = -1.193523342663823 y[1] (numeric) = -1.19352334266392 absolute error = 9.658940314238862e-14 relative error = 8.092795481218728e-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) = -1.201049725571217 y[1] (numeric) = -1.201049725571314 absolute error = 9.747758156208874e-14 relative error = 8.116032124792219e-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) = -1.208456004506925 y[1] (numeric) = -1.208456004507023 absolute error = 9.836575998178887e-14 relative error = 8.139788259972621e-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) = -1.215741438849226 y[1] (numeric) = -1.215741438849325 absolute error = 9.947598300641403e-14 relative error = 8.182330537369376e-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) = -1.222905300060756 y[1] (numeric) = -1.222905300060857 absolute error = 1.008082506359642e-13 relative error = 8.243340725643752e-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) = -1.229946871761364 y[1] (numeric) = -1.229946871761466 absolute error = 1.012523398458143e-13 relative error = 8.232253129829445e-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) = -1.236865449799749 y[1] (numeric) = -1.236865449799851 absolute error = 1.021405182655144e-13 relative error = 8.258013697613685e-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) = -1.243660342323872 y[1] (numeric) = -1.243660342323974 absolute error = 1.023625628704394e-13 relative error = 8.230749135183276e-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) = -1.250330869850142 y[1] (numeric) = -1.250330869850245 absolute error = 1.032507412901396e-13 relative error = 8.257873478123006e-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) = -1.256876365331366 y[1] (numeric) = -1.25687636533147 absolute error = 1.041389197098397e-13 relative error = 8.285534089296383e-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) = -1.263296174223451 y[1] (numeric) = -1.263296174223556 absolute error = 1.048050535246148e-13 relative error = 8.296158546434173e-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) = -1.269589654550856 y[1] (numeric) = -1.269589654550962 absolute error = 1.056932319443149e-13 relative error = 8.324991588065993e-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) = -1.275756176970795 y[1] (numeric) = -1.275756176970901 absolute error = 1.0635936575909e-13 relative error = 8.336966551996934e-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) = -1.281795124836163 y[1] (numeric) = -1.28179512483627 absolute error = 1.072475441787901e-13 relative error = 8.366980190574397e-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) = -1.287705894257206 y[1] (numeric) = -1.287705894257315 absolute error = 1.081357225984902e-13 relative error = 8.397548157599038e-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) = -1.293487894161909 y[1] (numeric) = -1.293487894162018 absolute error = 1.088018564132653e-13 relative error = 8.411509447002708e-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) = -1.299140546355098 y[1] (numeric) = -1.299140546355208 absolute error = 1.096900348329655e-13 relative error = 8.443276991139615e-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) = -1.304663285576265 y[1] (numeric) = -1.304663285576375 absolute error = 1.099120794378905e-13 relative error = 8.424555259048522e-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) = -1.310055559556091 y[1] (numeric) = -1.310055559556201 absolute error = 1.101341240428155e-13 relative error = 8.406828492078168e-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) = -1.31531682907167 y[1] (numeric) = -1.315316829071781 absolute error = 1.108002578575906e-13 relative error = 8.423845525932463e-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) = -1.320446568000436 y[1] (numeric) = -1.320446568000547 absolute error = 1.112443470674407e-13 relative error = 8.424751880411111e-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) = -1.32544426337277 y[1] (numeric) = -1.325444263372882 absolute error = 1.119104808822158e-13 relative error = 8.443243067606977e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.00999999999989 y[1] (closed_form) = -1.3303094154233 y[1] (numeric) = -1.330309415423412 absolute error = 1.119104808822158e-13 relative error = 8.412364791585437e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999889 y[1] (closed_form) = -1.335041537640876 y[1] (numeric) = -1.335041537640988 absolute error = 1.125766146969909e-13 relative error = 8.43244285087359e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999887 y[1] (closed_form) = -1.339640156817218 y[1] (numeric) = -1.339640156817331 absolute error = 1.13242748511766e-13 relative error = 8.453221406919719e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999886 y[1] (closed_form) = -1.344104813094241 y[1] (numeric) = -1.344104813094356 absolute error = 1.143529715363911e-13 relative error = 8.50774213605716e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999885 y[1] (closed_form) = -1.348435060010039 y[1] (numeric) = -1.348435060010154 absolute error = 1.145750161413162e-13 relative error = 8.49688795101954e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999884 y[1] (closed_form) = -1.352630464543528 y[1] (numeric) = -1.352630464543644 absolute error = 1.154631945610163e-13 relative error = 8.536196513951917e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999883 y[1] (closed_form) = -1.356690607157751 y[1] (numeric) = -1.356690607157867 absolute error = 1.156852391659413e-13 relative error = 8.527017033625694e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999882 y[1] (closed_form) = -1.36061508184183 y[1] (numeric) = -1.360615081841946 absolute error = 1.161293283757914e-13 relative error = 8.535061085651794e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.089999999999881 y[1] (closed_form) = -1.364403496151567 y[1] (numeric) = -1.364403496151684 absolute error = 1.167954621905665e-13 relative error = 8.560184910109028e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09999999999988 y[1] (closed_form) = -1.368055471248688 y[1] (numeric) = -1.368055471248805 absolute error = 1.170175067954915e-13 relative error = 8.553564475619118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999879 y[1] (closed_form) = -1.371570641938727 y[1] (numeric) = -1.371570641938844 absolute error = 1.176836406102666e-13 relative error = 8.580209944120689e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999878 y[1] (closed_form) = -1.374948656707543 y[1] (numeric) = -1.374948656707661 absolute error = 1.179056852151916e-13 relative error = 8.575279130606156e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y[1] (closed_form) = -1.378189177756475 y[1] (numeric) = -1.378189177756594 absolute error = 1.183497744250417e-13 relative error = 8.587338830921656e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999875 y[1] (closed_form) = -1.381291881036119 y[1] (numeric) = -1.381291881036238 absolute error = 1.187938636348917e-13 relative error = 8.600199948021371e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999874 y[1] (closed_form) = -1.384256456278732 y[1] (numeric) = -1.384256456278852 absolute error = 1.194599974496668e-13 relative error = 8.629903578041359e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999873 y[1] (closed_form) = -1.387082607029261 y[1] (numeric) = -1.38708260702938 absolute error = 1.194599974496668e-13 relative error = 8.612320336531104e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999872 y[1] (closed_form) = -1.389770050674985 y[1] (numeric) = -1.389770050675105 absolute error = 1.199040866595169e-13 relative error = 8.627620562213281e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.179999999999871 y[1] (closed_form) = -1.392318518473779 y[1] (numeric) = -1.392318518473899 absolute error = 1.201261312644419e-13 relative error = 8.627776594979207e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18999999999987 y[1] (closed_form) = -1.394727755580987 y[1] (numeric) = -1.394727755581108 absolute error = 1.20570220474292e-13 relative error = 8.64471363617965e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999869 y[1] (closed_form) = -1.396997521074907 y[1] (numeric) = -1.396997521075028 absolute error = 1.210143096841421e-13 relative error = 8.662457009302973e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999868 y[1] (closed_form) = -1.39912758798088 y[1] (numeric) = -1.399127587981001 absolute error = 1.214583988939921e-13 relative error = 8.681009504592225e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999867 y[1] (closed_form) = -1.401117743293991 y[1] (numeric) = -1.401117743294112 absolute error = 1.216804434989172e-13 relative error = 8.684526627494537e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999865 y[1] (closed_form) = -1.402967788000366 y[1] (numeric) = -1.402967788000488 absolute error = 1.221245327087672e-13 relative error = 8.704728202122867e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999864 y[1] (closed_form) = -1.404677537097077 y[1] (numeric) = -1.404677537097199 absolute error = 1.219024881038422e-13 relative error = 8.678325443700571e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999863 y[1] (closed_form) = -1.40624681961064 y[1] (numeric) = -1.406246819610762 absolute error = 1.221245327087672e-13 relative error = 8.684430855643176e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999862 y[1] (closed_form) = -1.40767547861411 y[1] (numeric) = -1.407675478614232 absolute error = 1.221245327087672e-13 relative error = 8.675616970255229e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.269999999999861 y[1] (closed_form) = -1.408963371242777 y[1] (numeric) = -1.408963371242899 absolute error = 1.225686219186173e-13 relative error = 8.699205701174869e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27999999999986 y[1] (closed_form) = -1.410110368708453 y[1] (numeric) = -1.410110368708575 absolute error = 1.223465773136923e-13 relative error = 8.676383071046548e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999859 y[1] (closed_form) = -1.411116356312345 y[1] (numeric) = -1.411116356312468 absolute error = 1.223465773136923e-13 relative error = 8.67019766062518e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999858 y[1] (closed_form) = -1.411981233456533 y[1] (numeric) = -1.411981233456655 absolute error = 1.223465773136923e-13 relative error = 8.664886927299137e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999857 y[1] (closed_form) = -1.412704913654022 y[1] (numeric) = -1.412704913654145 absolute error = 1.223465773136923e-13 relative error = 8.660448203385767e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999856 y[1] (closed_form) = -1.413287324537396 y[1] (numeric) = -1.413287324537519 absolute error = 1.227906665235423e-13 relative error = 8.688301691500325e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999854 y[1] (closed_form) = -1.413728407866052 y[1] (numeric) = -1.413728407866175 absolute error = 1.230127111284673e-13 relative error = 8.701297253702957e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999853 y[1] (closed_form) = -1.414028119532025 y[1] (numeric) = -1.414028119532148 absolute error = 1.227906665235423e-13 relative error = 8.683749978337073e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999852 y[1] (closed_form) = -1.414186429564397 y[1] (numeric) = -1.41418642956452 absolute error = 1.227906665235423e-13 relative error = 8.682777882500595e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999851 y[1] (closed_form) = -1.414203322132297 y[1] (numeric) = -1.41420332213242 absolute error = 1.225686219186173e-13 relative error = 8.666973128998993e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36999999999985 y[1] (closed_form) = -1.414078795546484 y[1] (numeric) = -1.414078795546606 absolute error = 1.221245327087672e-13 relative error = 8.636331517973937e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999849 y[1] (closed_form) = -1.41381286225951 y[1] (numeric) = -1.413812862259632 absolute error = 1.223465773136923e-13 relative error = 8.653661356437364e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999848 y[1] (closed_form) = -1.413405548864484 y[1] (numeric) = -1.413405548864606 absolute error = 1.223465773136923e-13 relative error = 8.656155157448211e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999847 y[1] (closed_form) = -1.412856896092406 y[1] (numeric) = -1.412856896092528 absolute error = 1.221245327087672e-13 relative error = 8.643800589184359e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999846 y[1] (closed_form) = -1.412166958808095 y[1] (numeric) = -1.412166958808218 absolute error = 1.225686219186173e-13 relative error = 8.679471018219284e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y[1] (closed_form) = -1.411335806004706 y[1] (numeric) = -1.411335806004828 absolute error = 1.221245327087672e-13 relative error = 8.65311658566112e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y[1] (closed_form) = -1.410363520796825 y[1] (numeric) = -1.410363520796947 absolute error = 1.219024881038422e-13 relative error = 8.643338139869777e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y[1] (closed_form) = -1.409250200412163 y[1] (numeric) = -1.409250200412286 absolute error = 1.221245327087672e-13 relative error = 8.665922678105666e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y[1] (closed_form) = -1.407995956181832 y[1] (numeric) = -1.407995956181954 absolute error = 1.219024881038422e-13 relative error = 8.657872032133834e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y[1] (closed_form) = -1.406600913529209 y[1] (numeric) = -1.40660091352933 absolute error = 1.216804434989172e-13 relative error = 8.650672861687317e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y[1] (closed_form) = -1.405065211957396 y[1] (numeric) = -1.405065211957518 absolute error = 1.216804434989172e-13 relative error = 8.660127833455087e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999838 y[1] (closed_form) = -1.403389005035271 y[1] (numeric) = -1.403389005035393 absolute error = 1.214583988939921e-13 relative error = 8.65464945629523e-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) = -1.40157246038213 y[1] (numeric) = -1.401572460382251 absolute error = 1.214583988939921e-13 relative error = 8.665866541133182e-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) = -1.399615759650923 y[1] (numeric) = -1.399615759651045 absolute error = 1.214583988939921e-13 relative error = 8.677981657214615e-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) = -1.397519098510095 y[1] (numeric) = -1.397519098510216 absolute error = 1.210143096841421e-13 relative error = 8.659224035875882e-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) = -1.39528268662401 y[1] (numeric) = -1.395282686624131 absolute error = 1.20348175869367e-13 relative error = 8.625361514415281e-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) = -1.392906747631995 y[1] (numeric) = -1.392906747632115 absolute error = 1.201261312644419e-13 relative error = 8.62413305619072e-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) = -1.390391519125969 y[1] (numeric) = -1.390391519126089 absolute error = 1.201261312644419e-13 relative error = 8.639734176453832e-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) = -1.387737252626685 y[1] (numeric) = -1.387737252626805 absolute error = 1.199040866595169e-13 relative error = 8.640258552731398e-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) = -1.384944213558583 y[1] (numeric) = -1.384944213558703 absolute error = 1.194599974496668e-13 relative error = 8.625618005415326e-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) = -1.382012681223242 y[1] (numeric) = -1.382012681223361 absolute error = 1.190159082398168e-13 relative error = 8.6117811983081e-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) = -1.378942948771451 y[1] (numeric) = -1.37894294877157 absolute error = 1.185718190299667e-13 relative error = 8.598747260400187e-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) = -1.375735323173899 y[1] (numeric) = -1.375735323174017 absolute error = 1.179056852151916e-13 relative error = 8.57037565504799e-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) = -1.372390125190471 y[1] (numeric) = -1.372390125190589 absolute error = 1.176836406102666e-13 relative error = 8.57508651877931e-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) = -1.36890768933818 y[1] (numeric) = -1.368907689338297 absolute error = 1.172395514004165e-13 relative error = 8.564459993434464e-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) = -1.365288363857706 y[1] (numeric) = -1.365288363857824 absolute error = 1.172395514004165e-13 relative error = 8.587164038309749e-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) = -1.361532510678584 y[1] (numeric) = -1.361532510678701 absolute error = 1.163513729807164e-13 relative error = 8.545618416612555e-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) = -1.357640505383001 y[1] (numeric) = -1.357640505383117 absolute error = 1.161293283757914e-13 relative error = 8.553761317178025e-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) = -1.353612737168242 y[1] (numeric) = -1.353612737168358 absolute error = 1.159072837708663e-13 relative error = 8.562809774776821e-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) = -1.349449608807774 y[1] (numeric) = -1.34944960880789 absolute error = 1.152411499560912e-13 relative error = 8.539863156350513e-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) = -1.345151536610963 y[1] (numeric) = -1.345151536611078 absolute error = 1.147970607462412e-13 relative error = 8.534135940956231e-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) = -1.340718950381446 y[1] (numeric) = -1.340718950381561 absolute error = 1.143529715363911e-13 relative error = 8.529227658328892e-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) = -1.336152293374153 y[1] (numeric) = -1.336152293374267 absolute error = 1.139088823265411e-13 relative error = 8.52514214819702e-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) = -1.33145202225098 y[1] (numeric) = -1.331452022251093 absolute error = 1.13686837721616e-13 relative error = 8.538560595628129e-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) = -1.326618607035121 y[1] (numeric) = -1.326618607035234 absolute error = 1.127986593019159e-13 relative error = 8.502719523436449e-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) = -1.32165253106407 y[1] (numeric) = -1.321652531064183 absolute error = 1.123545700920658e-13 relative error = 8.501067220868446e-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) = -1.316554290941287 y[1] (numeric) = -1.316554290941399 absolute error = 1.116884362772907e-13 relative error = 8.483390092286867e-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) = -1.311324396486534 y[1] (numeric) = -1.311324396486645 absolute error = 1.112443470674407e-13 relative error = 8.48335830291121e-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) = -1.305963370684899 y[1] (numeric) = -1.30596337068501 absolute error = 1.103561686477406e-13 relative error = 8.450173345203807e-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) = -1.300471749634496 y[1] (numeric) = -1.300471749634605 absolute error = 1.096900348329655e-13 relative error = 8.434634190538505e-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) = -1.294850082492851 y[1] (numeric) = -1.29485008249296 absolute error = 1.094679902280404e-13 relative error = 8.4541053600037e-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) = -1.289098931421995 y[1] (numeric) = -1.289098931422104 absolute error = 1.088018564132653e-13 relative error = 8.440147901856287e-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) = -1.283218871532243 y[1] (numeric) = -1.283218871532351 absolute error = 1.079136779935652e-13 relative error = 8.409608086943857e-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) = -1.277210490824683 y[1] (numeric) = -1.27721049082479 absolute error = 1.070254995738651e-13 relative error = 8.379628913379794e-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) = -1.271074390132379 y[1] (numeric) = -1.271074390132485 absolute error = 1.06581410364015e-13 relative error = 8.385143402418396e-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) = -1.264811183060287 y[1] (numeric) = -1.264811183060393 absolute error = 1.056932319443149e-13 relative error = 8.356443503969008e-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) = -1.258421495923895 y[1] (numeric) = -1.258421495924 absolute error = 1.050270981295398e-13 relative error = 8.345939613216166e-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) = -1.251905967686591 y[1] (numeric) = -1.251905967686696 absolute error = 1.048050535246148e-13 relative error = 8.371639422590581e-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) = -1.245265249895771 y[1] (numeric) = -1.245265249895875 absolute error = 1.043609643147647e-13 relative error = 8.380621263100353e-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) = -1.238500006617678 y[1] (numeric) = -1.238500006617782 absolute error = 1.041389197098397e-13 relative error = 8.40847146979363e-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) = -1.231610914371004 y[1] (numeric) = -1.231610914371107 absolute error = 1.036948304999896e-13 relative error = 8.419447188233764e-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) = -1.224598662059231 y[1] (numeric) = -1.224598662059334 absolute error = 1.025846074753645e-13 relative error = 8.376998167127074e-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) = -1.217463950901748 y[1] (numeric) = -1.21746395090185 absolute error = 1.019184736605894e-13 relative error = 8.371375069060618e-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) = -1.210207494363725 y[1] (numeric) = -1.210207494363826 absolute error = 1.008082506359642e-13 relative error = 8.329831959019956e-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) = -1.202830018084769 y[1] (numeric) = -1.202830018084869 absolute error = 1.001421168211891e-13 relative error = 8.325541873376465e-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) = -1.195332259806359 y[1] (numeric) = -1.195332259806458 absolute error = 9.903189379656396e-14 relative error = 8.284884222283678e-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) = -1.187714969298075 y[1] (numeric) = -1.187714969298173 absolute error = 9.836575998178887e-14 relative error = 8.281933167847655e-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) = -1.179978908282621 y[1] (numeric) = -1.179978908282718 absolute error = 9.747758156208874e-14 relative error = 8.260959655962052e-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) = -1.17212485035965 y[1] (numeric) = -1.172124850359747 absolute error = 9.658940314238862e-14 relative error = 8.240538805465261e-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) = -1.164153580928412 y[1] (numeric) = -1.164153580928508 absolute error = 9.570122472268849e-14 relative error = 8.220670046504243e-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) = -1.156065897109205 y[1] (numeric) = -1.1560658971093 absolute error = 9.481304630298837e-14 relative error = 8.201353101070852e-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) = -1.147862607663673 y[1] (numeric) = -1.147862607663766 absolute error = 9.370282327836321e-14 relative error = 8.163243810954284e-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) = -1.139544532913923 y[1] (numeric) = -1.139544532914016 absolute error = 9.303668946358812e-14 relative error = 8.164375044271813e-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) = -1.131112504660499 y[1] (numeric) = -1.131112504660591 absolute error = 9.214851104388799e-14 relative error = 8.146714908040573e-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) = -1.122567366099199 y[1] (numeric) = -1.122567366099291 absolute error = 9.126033262418787e-14 relative error = 8.129608554478799e-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) = -1.11390997173676 y[1] (numeric) = -1.11390997173685 absolute error = 9.015010959956271e-14 relative error = 8.093123491749031e-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) = -1.105141187305402 y[1] (numeric) = -1.105141187305491 absolute error = 8.926193117986259e-14 relative error = 8.076970816507571e-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) = -1.096261889676261 y[1] (numeric) = -1.096261889676349 absolute error = 8.815170815523743e-14 relative error = 8.041117636705372e-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) = -1.087272966771702 y[1] (numeric) = -1.087272966771789 absolute error = 8.72635297355373e-14 relative error = 8.025908157602554e-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) = -1.078175317476523 y[1] (numeric) = -1.078175317476609 absolute error = 8.637535131583718e-14 relative error = 8.011252893267798e-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) = -1.068969851548072 y[1] (numeric) = -1.068969851548158 absolute error = 8.548717289613705e-14 relative error = 7.997154716041365e-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) = -1.059657489525273 y[1] (numeric) = -1.059657489525357 absolute error = 8.459899447643693e-14 relative error = 7.983616905717086e-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) = -1.050239162636565 y[1] (numeric) = -1.050239162636649 absolute error = 8.37108160567368e-14 relative error = 7.970643167274928e-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) = -1.040715812706791 y[1] (numeric) = -1.040715812706873 absolute error = 8.260059303211165e-14 relative error = 7.936901892292414e-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) = -1.031088392063006 y[1] (numeric) = -1.031088392063088 absolute error = 8.171241461241152e-14 relative error = 7.924869995764475e-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) = -1.021357863439252 y[1] (numeric) = -1.021357863439333 absolute error = 8.08242361927114e-14 relative error = 7.913410087288043e-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) = -1.011525199880283 y[1] (numeric) = -1.011525199880362 absolute error = 7.949196856316121e-14 relative error = 7.858624636595244e-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) = -1.001591384644261 y[1] (numeric) = -1.001591384644339 absolute error = 7.815970093361102e-14 relative error = 7.803551641108744e-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) = -0.9915574111044312 y[1] (numeric) = -0.9915574111045083 absolute error = 7.716050021144838e-14 relative error = 7.781748121422877e-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) = -0.981424282649786 y[1] (numeric) = -0.981424282649862 absolute error = 7.605027718682322e-14 relative error = 7.74897040263688e-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) = -0.9711930125847268 y[1] (numeric) = -0.9711930125848017 absolute error = 7.494005416219807e-14 relative error = 7.71628844020954e-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) = -0.960864624027734 y[1] (numeric) = -0.9608646240278076 absolute error = 7.360778653264788e-14 relative error = 7.6605782637829e-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) = -0.9504401498090561 y[1] (numeric) = -0.9504401498091287 absolute error = 7.260858581048524e-14 relative error = 7.639469547353649e-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) = -0.9399206323674283 y[1] (numeric) = -0.9399206323674997 absolute error = 7.138734048339757e-14 relative error = 7.595039200660002e-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) = -0.9293071236458282 y[1] (numeric) = -0.9293071236458986 absolute error = 7.038813976123492e-14 relative error = 7.574260217127186e-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) = -0.9186006849862838 y[1] (numeric) = -0.9186006849863531 absolute error = 6.927791673660977e-14 relative error = 7.541679194115145e-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) = -0.9078023870237387 y[1] (numeric) = -0.9078023870238068 absolute error = 6.80566714095221e-14 relative error = 7.496859711136938e-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) = -0.8969133095789906 y[1] (numeric) = -0.8969133095790576 absolute error = 6.694644838489694e-14 relative error = 7.464093538351157e-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) = -0.8859345415507099 y[1] (numeric) = -0.8859345415507757 absolute error = 6.572520305780927e-14 relative error = 7.418742579193953e-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) = -0.8748671808065507 y[1] (numeric) = -0.8748671808066151 absolute error = 6.439293542825908e-14 relative error = 7.360309866566769e-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) = -0.8637123340733642 y[1] (numeric) = -0.8637123340734274 absolute error = 6.317169010117141e-14 relative error = 7.313973369263656e-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) = -0.8524711168265283 y[1] (numeric) = -0.8524711168265903 absolute error = 6.195044477408373e-14 relative error = 7.267160558436868e-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) = -0.8411446531784001 y[1] (numeric) = -0.8411446531784609 absolute error = 6.072919944699606e-14 relative error = 7.219828268243879e-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) = -0.8297340757659056 y[1] (numeric) = -0.829734075765965 absolute error = 5.939693181744587e-14 relative error = 7.158550378037462e-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) = -0.8182405256372772 y[1] (numeric) = -0.8182405256373355 absolute error = 5.828670879282072e-14 relative error = 7.123419943961439e-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) = -0.80666515213795 y[1] (numeric) = -0.8066651521380069 absolute error = 5.695444116327053e-14 relative error = 7.060481168960996e-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) = -0.7950091127956277 y[1] (numeric) = -0.7950091127956835 absolute error = 5.584421813864537e-14 relative error = 7.024349436985787e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y[1] (closed_form) = -0.7832735732045313 y[1] (numeric) = -0.7832735732045856 absolute error = 5.428990590417015e-14 relative error = 6.931155060173819e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y[1] (closed_form) = -0.77145970690884 y[1] (numeric) = -0.7714597069088932 absolute error = 5.3179682879545e-14 relative error = 6.893384372935113e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y[1] (closed_form) = -0.7595686952853391 y[1] (numeric) = -0.7595686952853908 absolute error = 5.173639294753229e-14 relative error = 6.811285571490942e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y[1] (closed_form) = -0.7476017274252814 y[1] (numeric) = -0.7476017274253317 absolute error = 5.029310301551959e-14 relative error = 6.72725880245456e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y[1] (closed_form) = -0.7355600000154805 y[1] (numeric) = -0.7355600000155295 absolute error = 4.89608353859694e-14 relative error = 6.656266706310699e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y[1] (closed_form) = -0.7234447172186427 y[1] (numeric) = -0.7234447172186903 absolute error = 4.762856775641922e-14 relative error = 6.583580835247802e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999737 y[1] (closed_form) = -0.7112570905529517 y[1] (numeric) = -0.7112570905529979 absolute error = 4.618527782440651e-14 relative error = 6.493471690876325e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = -0.6989983387709177 y[1] (numeric) = -0.6989983387709625 absolute error = 4.485301019485632e-14 relative error = 6.416754905844773e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y[1] (closed_form) = -0.6866696877375031 y[1] (numeric) = -0.6866696877375466 absolute error = 4.340972026284362e-14 relative error = 6.321776108375136e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y[1] (closed_form) = -0.6742723703075378 y[1] (numeric) = -0.6742723703075797 absolute error = 4.18554080283684e-14 relative error = 6.207492679742759e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y[1] (closed_form) = -0.6618076262024335 y[1] (numeric) = -0.661807626202474 absolute error = 4.052314039881821e-14 relative error = 6.123099643222155e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y[1] (closed_form) = -0.6492767018862133 y[1] (numeric) = -0.6492767018862525 absolute error = 3.919087276926803e-14 relative error = 6.036081790000265e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y[1] (closed_form) = -0.636680850440867 y[1] (numeric) = -0.6366808504409047 absolute error = 3.774758283725532e-14 relative error = 5.928807629618068e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999729 y[1] (closed_form) = -0.6240213314410419 y[1] (numeric) = -0.6240213314410782 absolute error = 3.630429290524262e-14 relative error = 5.817796776498927e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999728 y[1] (closed_form) = -0.6112994108280889 y[1] (numeric) = -0.6112994108281237 absolute error = 3.47499806707674e-14 relative error = 5.684608892996278e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999727 y[1] (closed_form) = -0.5985163607834675 y[1] (numeric) = -0.5985163607835009 absolute error = 3.341771304121721e-14 relative error = 5.583425154405619e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999726 y[1] (closed_form) = -0.5856734596015298 y[1] (numeric) = -0.5856734596015618 absolute error = 3.197442310920451e-14 relative error = 5.459428387101355e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = -0.5727719915616916 y[1] (numeric) = -0.5727719915617222 absolute error = 3.064215547965432e-14 relative error = 5.34979990835567e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y[1] (closed_form) = -0.5598132468000054 y[1] (numeric) = -0.559813246800035 absolute error = 2.953193245502916e-14 relative error = 5.27531862167233e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y[1] (closed_form) = -0.5467985211801489 y[1] (numeric) = -0.546798521180177 absolute error = 2.808864252301646e-14 relative error = 5.136927302289163e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y[1] (closed_form) = -0.5337291161638382 y[1] (numeric) = -0.5337291161638651 absolute error = 2.686739719592879e-14 relative error = 5.033901352251005e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y[1] (closed_form) = -0.5206063386806841 y[1] (numeric) = -0.5206063386807095 absolute error = 2.542410726391608e-14 relative error = 4.883556994013102e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y[1] (closed_form) = -0.507431500997499 y[1] (numeric) = -0.507431500997523 absolute error = 2.398081733190338e-14 relative error = 4.725922077120233e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999718 y[1] (closed_form) = -0.4942059205870723 y[1] (numeric) = -0.4942059205870948 absolute error = 2.253752739989068e-14 relative error = 4.560351558135548e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999717 y[1] (closed_form) = -0.4809309199964238 y[1] (numeric) = -0.480930919996445 absolute error = 2.120525977034049e-14 relative error = 4.409211154587061e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999716 y[1] (closed_form) = -0.4676078267145502 y[1] (numeric) = -0.4676078267145699 absolute error = 1.965094753586527e-14 relative error = 4.202441963799963e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999715 y[1] (closed_form) = -0.4542379730396769 y[1] (numeric) = -0.4542379730396952 absolute error = 1.826316875508383e-14 relative error = 4.020616909869965e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = -0.4408226959460301 y[1] (numeric) = -0.440822695946047 absolute error = 1.693090112553364e-14 relative error = 3.840750778314393e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y[1] (closed_form) = -0.4273633369501398 y[1] (numeric) = -0.4273633369501551 absolute error = 1.532107773982716e-14 relative error = 3.585023893056755e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y[1] (closed_form) = -0.4138612419766893 y[1] (numeric) = -0.4138612419767032 absolute error = 1.38222766565832e-14 relative error = 3.339833561259582e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y[1] (closed_form) = -0.4003177612239244 y[1] (numeric) = -0.4003177612239368 absolute error = 1.243449787580175e-14 relative error = 3.106156928382279e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y[1] (closed_form) = -0.3867342490286342 y[1] (numeric) = -0.3867342490286451 absolute error = 1.088018564132653e-14 relative error = 2.813349391385544e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999708 y[1] (closed_form) = -0.3731120637307185 y[1] (numeric) = -0.3731120637307279 absolute error = 9.381384558082573e-15 relative error = 2.51436109148518e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999707 y[1] (closed_form) = -0.3594525675373555 y[1] (numeric) = -0.3594525675373633 absolute error = 7.716050021144838e-15 relative error = 2.146611463651031e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999706 y[1] (closed_form) = -0.3457571263867815 y[1] (numeric) = -0.3457571263867878 absolute error = 6.38378239159465e-15 relative error = 1.846319831005718e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999705 y[1] (closed_form) = -0.3320271098116989 y[1] (numeric) = -0.3320271098117036 absolute error = 4.718447854656915e-15 relative error = 1.42110319164386e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999704 y[1] (closed_form) = -0.3182638908023234 y[1] (numeric) = -0.3182638908023267 absolute error = 3.275157922644212e-15 relative error = 1.029069906230249e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y[1] (closed_form) = -0.3044688456690868 y[1] (numeric) = -0.3044688456690885 absolute error = 1.665334536937735e-15 relative error = 5.469638554572214e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y[1] (closed_form) = -0.2906433539050064 y[1] (numeric) = -0.2906433539050066 absolute error = 2.220446049250313e-16 relative error = 7.639761994957028e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y[1] (closed_form) = -0.2767887980477376 y[1] (numeric) = -0.2767887980477363 absolute error = 1.332267629550188e-15 relative error = 4.81330038985325e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y[1] (closed_form) = -0.2629065635413205 y[1] (numeric) = -0.2629065635413176 absolute error = 2.831068712794149e-15 relative error = 1.076834550898991e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y[1] (closed_form) = -0.2489980385976374 y[1] (numeric) = -0.248998038597633 absolute error = 4.385380947269368e-15 relative error = 1.761211040845114e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999697 y[1] (closed_form) = -0.235064614057592 y[1] (numeric) = -0.2350646140575862 absolute error = 5.828670879282072e-15 relative error = 2.479603704985565e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999696 y[1] (closed_form) = -0.2211076832520277 y[1] (numeric) = -0.2211076832520202 absolute error = 7.466249840604178e-15 relative error = 3.37674825713489e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999695 y[1] (closed_form) = -0.2071286418623938 y[1] (numeric) = -0.2071286418623848 absolute error = 8.93729534823251e-15 relative error = 4.314852483882946e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999694 y[1] (closed_form) = -0.1931288877811803 y[1] (numeric) = -0.1931288877811698 absolute error = 1.049160758270773e-14 relative error = 5.432438255738817e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999693 y[1] (closed_form) = -0.1791098209721289 y[1] (numeric) = -0.1791098209721169 absolute error = 1.201816424156732e-14 relative error = 6.709941518749803e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y[1] (closed_form) = -0.1650728433302381 y[1] (numeric) = -0.1650728433302244 absolute error = 1.365574320288943e-14 relative error = 8.272555877389412e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y[1] (closed_form) = -0.1510193585415743 y[1] (numeric) = -0.1510193585415592 absolute error = 1.515454428613339e-14 relative error = 1.003483555517915e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y[1] (closed_form) = -0.1369507719429056 y[1] (numeric) = -0.1369507719428888 absolute error = 1.676436767183986e-14 relative error = 1.224116332752683e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y[1] (closed_form) = -0.1228684903811678 y[1] (numeric) = -0.1228684903811495 absolute error = 1.829092433069945e-14 relative error = 1.488658668626642e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y[1] (closed_form) = -0.1087739220727819 y[1] (numeric) = -0.1087739220727621 absolute error = 1.984523656517467e-14 relative error = 1.824448009872807e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999686 y[1] (closed_form) = -0.09466847646283338 y[1] (numeric) = -0.09466847646281203 absolute error = 2.135791543622645e-14 relative error = 2.256074697115414e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999685 y[1] (closed_form) = -0.08055356408412873 y[1] (numeric) = -0.08055356408410583 absolute error = 2.289834988289385e-14 relative error = 2.842624053105735e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999684 y[1] (closed_form) = -0.06643059641614346 y[1] (numeric) = -0.06643059641611895 absolute error = 2.450817326860033e-14 relative error = 3.689289964382216e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999683 y[1] (closed_form) = -0.05230098574387521 y[1] (numeric) = -0.05230098574384912 absolute error = 2.608330218478727e-14 relative error = 4.987153074422082e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y[1] (closed_form) = -0.03816614501661653 y[1] (numeric) = -0.03816614501658891 absolute error = 2.761679773755077e-14 relative error = 7.23594110055578e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y[1] (closed_form) = -0.0240274877066613 y[1] (numeric) = -0.02402748770663205 absolute error = 2.925090725192092e-14 relative error = 1.217393495692498e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y[1] (closed_form) = -0.009886427667958109 y[1] (numeric) = -0.009886427667927368 absolute error = 3.0741034717785e-14 relative error = 3.109417855492599e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y[1] (closed_form) = 0.004255621005273102 y[1] (numeric) = 0.004255621005305449 absolute error = 3.234652129480153e-14 relative error = 7.600893325491449e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y[1] (closed_form) = 0.01839724411995014 y[1] (numeric) = 0.01839724411998407 absolute error = 3.39346606370583e-14 relative error = 1.844551304304281e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y[1] (closed_form) = 0.03253702752554621 y[1] (numeric) = 0.0325370275255817 absolute error = 3.548550342458157e-14 relative error = 1.090619092254828e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999675 y[1] (closed_form) = 0.04667355725550382 y[1] (numeric) = 0.04667355725554086 absolute error = 3.703981565905679e-14 relative error = 7.935931571765723e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999674 y[1] (closed_form) = 0.0608054196686304 y[1] (numeric) = 0.06080541966866897 absolute error = 3.856637231791638e-14 relative error = 6.342587967995363e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999673 y[1] (closed_form) = 0.07493120159046118 y[1] (numeric) = 0.07493120159050122 absolute error = 4.003741782554471e-14 relative error = 5.3432237807116e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999672 y[1] (closed_form) = 0.08904949045457522 y[1] (numeric) = 0.08904949045461689 absolute error = 4.167499678686681e-14 relative error = 4.679981499515208e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y[1] (closed_form) = 0.1031588744438515 y[1] (numeric) = 0.1031588744438948 absolute error = 4.324318680914985e-14 relative error = 4.191901767277108e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999674 y[1] (closed_form) = 0.1172579426316552 y[1] (numeric) = 0.1172579426316937 absolute error = 3.84969833788773e-14 relative error = 3.283102407809479e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999677 y[1] (closed_form) = 0.1313452851229103 y[1] (numeric) = 0.1313452851229441 absolute error = 3.377853552422039e-14 relative error = 2.571735673085722e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999681 y[1] (closed_form) = 0.1454194931951072 y[1] (numeric) = 0.1454194931951363 absolute error = 2.911559882079473e-14 relative error = 2.002179912821644e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999684 y[1] (closed_form) = 0.159479159439167 y[1] (numeric) = 0.1594791594391914 absolute error = 2.436939539052219e-14 relative error = 1.528061439263971e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999687 y[1] (closed_form) = 0.1735228779001817 y[1] (numeric) = 0.1735228779002014 absolute error = 1.970645868709653e-14 relative error = 1.135669193916469e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999691 y[1] (closed_form) = 0.1875492442180084 y[1] (numeric) = 0.1875492442180234 absolute error = 1.493249968120836e-14 relative error = 7.961908747470463e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999694 y[1] (closed_form) = 0.2015568557677038 y[1] (numeric) = 0.201556855767714 absolute error = 1.02695629777827e-14 relative error = 5.095119656767453e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999697 y[1] (closed_form) = 0.2155443117997857 y[1] (numeric) = 0.2155443117997914 absolute error = 5.717648576819556e-15 relative error = 2.652655748174209e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999701 y[1] (closed_form) = 0.2295102135803075 y[1] (numeric) = 0.2295102135803085 absolute error = 9.159339953157541e-16 relative error = 3.990820195003048e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999704 y[1] (closed_form) = 0.2434531645307291 y[1] (numeric) = 0.2434531645307253 absolute error = 3.747002708109903e-15 relative error = 1.539106183044481e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999707 y[1] (closed_form) = 0.2573717703675745 y[1] (numeric) = 0.2573717703675661 absolute error = 8.43769498715119e-15 relative error = 3.278407330804229e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.119999999999711 y[1] (closed_form) = 0.271264639241859 y[1] (numeric) = 0.2712646392418459 absolute error = 1.310063169057685e-14 relative error = 4.82946532478063e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999714 y[1] (closed_form) = 0.2851303818782722 y[1] (numeric) = 0.2851303818782546 absolute error = 1.765254609153999e-14 relative error = 6.191043541293404e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999717 y[1] (closed_form) = 0.2989676117141056 y[1] (numeric) = 0.2989676117140833 absolute error = 2.231548279496565e-14 relative error = 7.464180707408977e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.149999999999721 y[1] (closed_form) = 0.3127749450379063 y[1] (numeric) = 0.3127749450378794 absolute error = 2.686739719592879e-14 relative error = 8.590009405220305e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999724 y[1] (closed_form) = 0.3265510011278481 y[1] (numeric) = 0.3265510011278167 absolute error = 3.141931159689193e-14 relative error = 9.621563396950343e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999727 y[1] (closed_form) = 0.3402944023898021 y[1] (numeric) = 0.340294402389766 absolute error = 3.613775945154885e-14 relative error = 1.061955741786008e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.179999999999731 y[1] (closed_form) = 0.3540037744950948 y[1] (numeric) = 0.3540037744950541 absolute error = 4.068967385251199e-14 relative error = 1.149413559517733e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999734 y[1] (closed_form) = 0.3676777465179401 y[1] (numeric) = 0.3676777465178948 absolute error = 4.529709940470639e-14 relative error = 1.231978269930356e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999737 y[1] (closed_form) = 0.3813149510725307 y[1] (numeric) = 0.3813149510724809 absolute error = 4.979350265443827e-14 relative error = 1.305836619161753e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.209999999999741 y[1] (closed_form) = 0.3949140244497754 y[1] (numeric) = 0.3949140244497211 absolute error = 5.428990590417015e-14 relative error = 1.374727220179406e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999744 y[1] (closed_form) = 0.4084736067536691 y[1] (numeric) = 0.4084736067536102 absolute error = 5.895284260759581e-14 relative error = 1.443247290225717e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999747 y[1] (closed_form) = 0.4219923420372809 y[1] (numeric) = 0.4219923420372174 absolute error = 6.350475700855895e-14 relative error = 1.504879370605939e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999751 y[1] (closed_form) = 0.435468878438348 y[1] (numeric) = 0.43546887843828 absolute error = 6.800116025829084e-14 relative error = 1.561561884793064e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999754 y[1] (closed_form) = 0.4489018683144608 y[1] (numeric) = 0.4489018683143882 absolute error = 7.260858581048524e-14 relative error = 1.617471232256536e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999757 y[1] (closed_form) = 0.4622899683778257 y[1] (numeric) = 0.4622899683777487 absolute error = 7.699396675775461e-14 relative error = 1.665490753085693e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999761 y[1] (closed_form) = 0.4756318398295933 y[1] (numeric) = 0.4756318398295118 absolute error = 8.143485885625523e-14 relative error = 1.712140610381157e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y[1] (closed_form) = 0.4889261484937363 y[1] (numeric) = 0.4889261484936504 absolute error = 8.593126210598712e-14 relative error = 1.757550958784279e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y[1] (closed_form) = 0.5021715649504671 y[1] (numeric) = 0.5021715649503767 absolute error = 9.037215420448774e-14 relative error = 1.799627069951717e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y[1] (closed_form) = 0.5153667646691777 y[1] (numeric) = 0.5153667646690829 absolute error = 9.481304630298837e-14 relative error = 1.839719842311725e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999774 y[1] (closed_form) = 0.5285104281408922 y[1] (numeric) = 0.528510428140793 absolute error = 9.925393840148899e-14 relative error = 1.877993945183415e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y[1] (closed_form) = 0.5416012410102164 y[1] (numeric) = 0.541601241010113 absolute error = 1.034727858950646e-13 relative error = 1.910497577554715e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999781 y[1] (closed_form) = 0.5546378942067726 y[1] (numeric) = 0.5546378942066648 absolute error = 1.078026556911027e-13 relative error = 1.943658318645519e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999784 y[1] (closed_form) = 0.5676190840761046 y[1] (numeric) = 0.5676190840759924 absolute error = 1.122435477896033e-13 relative error = 1.977444926332922e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999787 y[1] (closed_form) = 0.5805435125100433 y[1] (numeric) = 0.5805435125099266 absolute error = 1.16684439888104e-13 relative error = 2.009917213330074e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999791 y[1] (closed_form) = 0.5934098870765157 y[1] (numeric) = 0.5934098870763947 absolute error = 1.209032873816795e-13 relative error = 2.037432978700774e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y[1] (closed_form) = 0.606216921148787 y[1] (numeric) = 0.6062169211486618 absolute error = 1.252331571777177e-13 relative error = 2.065814278829426e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = 0.6189633340341223 y[1] (numeric) = 0.618963334033993 absolute error = 1.293409823688307e-13 relative error = 2.089638840573074e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = 0.6316478511018554 y[1] (numeric) = 0.6316478511017217 absolute error = 1.336708521648688e-13 relative error = 2.116224284333296e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = 0.6442692039108495 y[1] (numeric) = 0.6442692039107119 absolute error = 1.376676550535194e-13 relative error = 2.136803283749212e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = 0.656826130336342 y[1] (numeric) = 0.6568261303362001 absolute error = 1.41886502547095e-13 relative error = 2.160183585790641e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y[1] (closed_form) = 0.6693173746961538 y[1] (numeric) = 0.6693173746960079 absolute error = 1.458833054357456e-13 relative error = 2.17958342261728e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y[1] (closed_form) = 0.6817416878762588 y[1] (numeric) = 0.6817416878761087 absolute error = 1.501021529293212e-13 relative error = 2.201745259218559e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = 0.6940978274556922 y[1] (numeric) = 0.6940978274555378 absolute error = 1.543210004228968e-13 relative error = 2.223332134442502e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y[1] (closed_form) = 0.7063845578307929 y[1] (numeric) = 0.7063845578306345 absolute error = 1.584288256140098e-13 relative error = 2.242812698235114e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y[1] (closed_form) = 0.7186006503387623 y[1] (numeric) = 0.7186006503385998 absolute error = 1.625366508051229e-13 relative error = 2.261849481050427e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 0.7307448833805297 y[1] (numeric) = 0.730744883380363 absolute error = 1.66644475996236e-13 relative error = 2.280474072227711e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y[1] (closed_form) = 0.742816042542911 y[1] (numeric) = 0.7428160425427404 absolute error = 1.706412788848866e-13 relative error = 2.297221237989471e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y[1] (closed_form) = 0.7548129207200494 y[1] (numeric) = 0.7548129207198746 absolute error = 1.747491040759996e-13 relative error = 2.315131329618719e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 0.7667343182341242 y[1] (numeric) = 0.7667343182339454 absolute error = 1.787459069646502e-13 relative error = 2.331262638358516e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y[1] (closed_form) = 0.7785790429553188 y[1] (numeric) = 0.7785790429551361 absolute error = 1.826316875508383e-13 relative error = 2.345705156121434e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y[1] (closed_form) = 0.7903459104210315 y[1] (numeric) = 0.7903459104208448 absolute error = 1.867395127419513e-13 relative error = 2.362756740810765e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = 0.8020337439543214 y[1] (numeric) = 0.8020337439541307 absolute error = 1.906252933281394e-13 relative error = 2.376773979462342e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y[1] (closed_form) = 0.8136413747815751 y[1] (numeric) = 0.8136413747813805 absolute error = 1.945110739143274e-13 relative error = 2.390624173537692e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y[1] (closed_form) = 0.8251676421493828 y[1] (numeric) = 0.8251676421491844 absolute error = 1.983968545005155e-13 relative error = 2.404321793129632e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y[1] (closed_form) = 0.8366113934406127 y[1] (numeric) = 0.8366113934404107 absolute error = 2.020605904817785e-13 relative error = 2.415226377097168e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y[1] (closed_form) = 0.8479714842896726 y[1] (numeric) = 0.8479714842894667 absolute error = 2.059463710679665e-13 relative error = 2.42869453611973e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y[1] (closed_form) = 0.859246778696944 y[1] (numeric) = 0.8592467786967342 absolute error = 2.098321516541546e-13 relative error = 2.442047580002186e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y[1] (closed_form) = 0.8704361491423822 y[1] (numeric) = 0.8704361491421686 absolute error = 2.136069099378801e-13 relative error = 2.454021586170811e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y[1] (closed_form) = 0.8815384766982671 y[1] (numeric) = 0.8815384766980496 absolute error = 2.174926905240682e-13 relative error = 2.46719452721644e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y[1] (closed_form) = 0.8925526511410951 y[1] (numeric) = 0.892552651140874 absolute error = 2.210454042028687e-13 relative error = 2.476553107766476e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y[1] (closed_form) = 0.9034775710626003 y[1] (numeric) = 0.9034775710623755 absolute error = 2.248201624865942e-13 relative error = 2.48838675897818e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y[1] (closed_form) = 0.9143121439798947 y[1] (numeric) = 0.9143121439796661 absolute error = 2.285949207703197e-13 relative error = 2.500184671891949e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y[1] (closed_form) = 0.9250552864447152 y[1] (numeric) = 0.9250552864444831 absolute error = 2.321476344491202e-13 relative error = 2.509554162339185e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y[1] (closed_form) = 0.9357059241517681 y[1] (numeric) = 0.9357059241515325 absolute error = 2.355893258254582e-13 relative error = 2.517771019126801e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y[1] (closed_form) = 0.946262992046158 y[1] (numeric) = 0.9462629920459188 absolute error = 2.392530618067212e-13 relative error = 2.528399227463929e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y[1] (closed_form) = 0.9567254344298932 y[1] (numeric) = 0.9567254344296504 absolute error = 2.428057754855217e-13 relative error = 2.537883563534696e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y[1] (closed_form) = 0.9670922050674539 y[1] (numeric) = 0.9670922050672077 absolute error = 2.461364445593972e-13 relative error = 2.545118689507268e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y[1] (closed_form) = 0.9773622672904151 y[1] (numeric) = 0.9773622672901655 absolute error = 2.495781359357352e-13 relative error = 2.553588820526618e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y[1] (closed_form) = 0.9875345941011132 y[1] (numeric) = 0.9875345941008604 absolute error = 2.527977827071481e-13 relative error = 2.559887868406808e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y[1] (closed_form) = 0.9976081682753438 y[1] (numeric) = 0.9976081682750877 absolute error = 2.561284517810236e-13 relative error = 2.567425367254322e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y[1] (closed_form) = 1.007581982464084 y[1] (numeric) = 1.007581982463825 absolute error = 2.595701431573616e-13 relative error = 2.576168963666578e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y[1] (closed_form) = 1.017455039294227 y[1] (numeric) = 1.017455039293964 absolute error = 2.62678767626312e-13 relative error = 2.581723589560509e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y[1] (closed_form) = 1.027226351468317 y[1] (numeric) = 1.027226351468051 absolute error = 2.660094367001875e-13 relative error = 2.58958929859961e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y[1] (closed_form) = 1.036894941863278 y[1] (numeric) = 1.036894941863009 absolute error = 2.691180611691379e-13 relative error = 2.595422644125724e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y[1] (closed_form) = 1.04645984362813 y[1] (numeric) = 1.046459843627858 absolute error = 2.722266856380884e-13 relative error = 2.601405943053338e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y[1] (closed_form) = 1.055920100280666 y[1] (numeric) = 1.05592010028039 absolute error = 2.757793993168889e-13 relative error = 2.611744953463677e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y[1] (closed_form) = 1.065274765803104 y[1] (numeric) = 1.065274765802825 absolute error = 2.788880237858393e-13 relative error = 2.617991458528423e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y[1] (closed_form) = 1.074522904736688 y[1] (numeric) = 1.074522904736406 absolute error = 2.817746036498647e-13 relative error = 2.622322915665662e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y[1] (closed_form) = 1.083663592275231 y[1] (numeric) = 1.083663592274945 absolute error = 2.853273173286652e-13 relative error = 2.63298794351483e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y[1] (closed_form) = 1.092695914357596 y[1] (numeric) = 1.092695914357308 absolute error = 2.882138971926906e-13 relative error = 2.637640476235639e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y[1] (closed_form) = 1.101618967759102 y[1] (numeric) = 1.101618967758811 absolute error = 2.90656387846866e-13 relative error = 2.638447560848695e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y[1] (closed_form) = 1.110431860181845 y[1] (numeric) = 1.110431860181551 absolute error = 2.935429677108914e-13 relative error = 2.6435027509281e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y[1] (closed_form) = 1.119133710343927 y[1] (numeric) = 1.11913371034363 absolute error = 2.966515921798418e-13 relative error = 2.650725194299405e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y[1] (closed_form) = 1.127723648067582 y[1] (numeric) = 1.127723648067283 absolute error = 2.993161274389422e-13 relative error = 2.654162018787469e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y[1] (closed_form) = 1.136200814366197 y[1] (numeric) = 1.136200814365895 absolute error = 3.019806626980426e-13 relative error = 2.657810651777216e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y[1] (closed_form) = 1.144564361530206 y[1] (numeric) = 1.144564361529901 absolute error = 3.04867242562068e-13 relative error = 2.663609429132327e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y[1] (closed_form) = 1.152813453211863 y[1] (numeric) = 1.152813453211555 absolute error = 3.075317778211684e-13 relative error = 2.667662985406282e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y[1] (closed_form) = 1.160947264508873 y[1] (numeric) = 1.160947264508563 absolute error = 3.104183576851938e-13 relative error = 2.673836850087356e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y[1] (closed_form) = 1.168964982046885 y[1] (numeric) = 1.168964982046572 absolute error = 3.126388037344441e-13 relative error = 2.674492465865028e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y[1] (closed_form) = 1.176865804060826 y[1] (numeric) = 1.176865804060511 absolute error = 3.150812943886194e-13 relative error = 2.677291610491339e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y[1] (closed_form) = 1.18464894047508 y[1] (numeric) = 1.184648940474762 absolute error = 3.175237850427948e-13 relative error = 2.680319664283482e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y[1] (closed_form) = 1.19231361298249 y[1] (numeric) = 1.192313612982169 absolute error = 3.204103649068202e-13 relative error = 2.687299393532343e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 1.199859055122193 y[1] (numeric) = 1.19985905512187 absolute error = 3.228528555609955e-13 relative error = 2.690756503297101e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y[1] (closed_form) = 1.207284512356263 y[1] (numeric) = 1.207284512355937 absolute error = 3.252953462151709e-13 relative error = 2.694438161724533e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y[1] (closed_form) = 1.214589242145164 y[1] (numeric) = 1.214589242144836 absolute error = 3.277378368693462e-13 relative error = 2.698342991170475e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 1.221772514022005 y[1] (numeric) = 1.221772514021675 absolute error = 3.306244167333716e-13 relative error = 2.706104556608291e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y[1] (closed_form) = 1.228833609665585 y[1] (numeric) = 1.228833609665251 absolute error = 3.33066907387547e-13 relative error = 2.710431296538089e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y[1] (closed_form) = 1.235771822972221 y[1] (numeric) = 1.235771822971886 absolute error = 3.350653088318722e-13 relative error = 2.711384922387926e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 Finished! diff ( y , x , 1 ) = neg ( sin ( x ) ) - cos ( x ) ; Iterations = 4900 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %