##############ECHO OF PROBLEM################# ##############temp/expt_lin_cpostode.ode################# diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , 2.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(5.0)/c(3.0) * expt((c(0.2) * c(x) + c(0.3)),c(3.0))) ; } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.05461333333333335 y[1] (numeric) = 0.05461333333333335 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) = 0.05564374666666667 y[1] (numeric) = 0.05564374666666669 absolute error = 2.775557561562891e-17 relative error = 4.988085324645449e-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) = 0.05668704 y[1] (numeric) = 0.05668704000000003 absolute error = 2.775557561562891e-17 relative error = 4.896282398168773e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 0.05774329333333334 y[1] (numeric) = 0.05774329333333336 absolute error = 2.081668171172169e-17 relative error = 3.605038872922214e-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) = 0.05881258666666668 y[1] (numeric) = 0.05881258666666669 absolute error = 1.387778780781446e-17 relative error = 2.359662887549885e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 0.05989500000000001 y[1] (numeric) = 0.05989500000000003 absolute error = 2.081668171172169e-17 relative error = 3.475529127927486e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 0.06099061333333335 y[1] (numeric) = 0.06099061333333337 absolute error = 2.081668171172169e-17 relative error = 3.413095978876588e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 0.06209950666666668 y[1] (numeric) = 0.06209950666666671 absolute error = 3.469446951953614e-17 relative error = 5.586915481594186e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 0.06322176000000002 y[1] (numeric) = 0.06322176000000004 absolute error = 2.775557561562891e-17 relative error = 4.390193442199159e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 0.06435745333333336 y[1] (numeric) = 0.06435745333333337 absolute error = 1.387778780781446e-17 relative error = 2.156360621657256e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 0.06550666666666669 y[1] (numeric) = 0.06550666666666669 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] = 0.2100000000000001 y[1] (closed_form) = 0.06666948000000002 y[1] (numeric) = 0.06666948000000004 absolute error = 2.775557561562891e-17 relative error = 4.163160656964612e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (closed_form) = 0.06784597333333335 y[1] (numeric) = 0.06784597333333338 absolute error = 2.775557561562891e-17 relative error = 4.090968741691313e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (closed_form) = 0.06903622666666669 y[1] (numeric) = 0.06903622666666673 absolute error = 4.163336342344337e-17 relative error = 6.030654546701282e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = 0.07024032000000002 y[1] (numeric) = 0.07024032000000008 absolute error = 5.551115123125783e-17 relative error = 7.903032222982157e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = 0.07145833333333336 y[1] (numeric) = 0.07145833333333342 absolute error = 5.551115123125783e-17 relative error = 7.768324370555028e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 0.0726903466666667 y[1] (numeric) = 0.07269034666666677 absolute error = 6.938893903907228e-17 relative error = 9.545825851851615e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 0.07393644000000003 y[1] (numeric) = 0.0739364400000001 absolute error = 6.938893903907228e-17 relative error = 9.384944560364585e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 0.07519669333333337 y[1] (numeric) = 0.07519669333333343 absolute error = 5.551115123125783e-17 relative error = 7.382126629582888e-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) = 0.07647118666666669 y[1] (numeric) = 0.07647118666666675 absolute error = 5.551115123125783e-17 relative error = 7.259093738564252e-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) = 0.07776000000000004 y[1] (numeric) = 0.07776000000000008 absolute error = 4.163336342344337e-17 relative error = 5.35408480239755e-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) = 0.07906321333333337 y[1] (numeric) = 0.07906321333333342 absolute error = 5.551115123125783e-17 relative error = 7.021109931014416e-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) = 0.0803809066666667 y[1] (numeric) = 0.08038090666666675 absolute error = 5.551115123125783e-17 relative error = 6.906012078397947e-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) = 0.08171316000000003 y[1] (numeric) = 0.08171316000000009 absolute error = 5.551115123125783e-17 relative error = 6.793416290748981e-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) = 0.08306005333333337 y[1] (numeric) = 0.08306005333333343 absolute error = 5.551115123125783e-17 relative error = 6.683254946692924e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = 0.08442166666666671 y[1] (numeric) = 0.08442166666666674 absolute error = 2.775557561562891e-17 relative error = 3.287731303057536e-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) = 0.08579808000000004 y[1] (numeric) = 0.08579808000000008 absolute error = 4.163336342344337e-17 relative error = 4.852481946384272e-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) = 0.08718937333333338 y[1] (numeric) = 0.08718937333333343 absolute error = 5.551115123125783e-17 relative error = 6.36673359481933e-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) = 0.08859562666666672 y[1] (numeric) = 0.08859562666666677 absolute error = 5.551115123125783e-17 relative error = 6.265676232542908e-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) = 0.09001692000000004 y[1] (numeric) = 0.09001692000000011 absolute error = 6.938893903907228e-17 relative error = 7.708432930061621e-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) = 0.09145333333333337 y[1] (numeric) = 0.09145333333333346 absolute error = 8.326672684688674e-17 relative error = 9.104832356781605e-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) = 0.09290494666666671 y[1] (numeric) = 0.09290494666666681 absolute error = 9.71445146547012e-17 relative error = 1.045633393485985e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 0.09437184000000005 y[1] (numeric) = 0.09437184000000017 absolute error = 1.110223024625157e-16 relative error = 1.176434648964305e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 0.09585409333333339 y[1] (numeric) = 0.0958540933333335 absolute error = 1.110223024625157e-16 relative error = 1.158242685332537e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 0.09735178666666672 y[1] (numeric) = 0.09735178666666683 absolute error = 1.110223024625157e-16 relative error = 1.140423881922752e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 0.09886500000000005 y[1] (numeric) = 0.09886500000000015 absolute error = 9.71445146547012e-17 relative error = 9.825976296434648e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (closed_form) = 0.1003938133333334 y[1] (numeric) = 0.1003938133333335 absolute error = 1.110223024625157e-16 relative error = 1.105867969113723e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = 0.1019383066666667 y[1] (numeric) = 0.1019383066666668 absolute error = 1.110223024625157e-16 relative error = 1.089112680923307e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (closed_form) = 0.1034985600000001 y[1] (numeric) = 0.1034985600000002 absolute error = 1.249000902703301e-16 relative error = 1.206780947197044e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = 0.1050746533333334 y[1] (numeric) = 0.1050746533333335 absolute error = 9.71445146547012e-17 relative error = 9.245285287454146e-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) = 0.1066666666666667 y[1] (numeric) = 0.1066666666666668 absolute error = 8.326672684688674e-17 relative error = 7.806255641895627e-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) = 0.1082746800000001 y[1] (numeric) = 0.1082746800000002 absolute error = 1.110223024625157e-16 relative error = 1.025376408062491e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (closed_form) = 0.1098987733333334 y[1] (numeric) = 0.1098987733333335 absolute error = 1.110223024625157e-16 relative error = 1.010223309097131e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (closed_form) = 0.1115390266666667 y[1] (numeric) = 0.1115390266666669 absolute error = 1.249000902703301e-16 relative error = 1.119788239174731e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (closed_form) = 0.1131955200000001 y[1] (numeric) = 0.1131955200000002 absolute error = 1.110223024625157e-16 relative error = 9.808012054056165e-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) = 0.1148683333333334 y[1] (numeric) = 0.1148683333333335 absolute error = 1.387778780781446e-16 relative error = 1.208147398425541e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (closed_form) = 0.1165575466666668 y[1] (numeric) = 0.1165575466666669 absolute error = 1.249000902703301e-16 relative error = 1.071574461218899e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = 0.1182632400000001 y[1] (numeric) = 0.1182632400000002 absolute error = 1.249000902703301e-16 relative error = 1.056119300218141e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = 0.1199854933333334 y[1] (numeric) = 0.1199854933333335 absolute error = 1.110223024625157e-16 relative error = 9.252977120665996e-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) = 0.1217243866666667 y[1] (numeric) = 0.1217243866666669 absolute error = 1.387778780781446e-16 relative error = 1.140099218229602e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = 0.1234800000000001 y[1] (numeric) = 0.1234800000000002 absolute error = 8.326672684688674e-17 relative error = 6.743337127217904e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 0.1252524133333334 y[1] (numeric) = 0.1252524133333335 absolute error = 1.110223024625157e-16 relative error = 8.863885294333829e-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) = 0.1270417066666668 y[1] (numeric) = 0.1270417066666668 absolute error = 5.551115123125783e-17 relative error = 4.369521843476844e-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) = 0.12884796 y[1] (numeric) = 0.1288479600000002 absolute error = 1.387778780781446e-16 relative error = 1.077066940587531e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = 0.1306712533333334 y[1] (numeric) = 0.1306712533333335 absolute error = 1.110223024625157e-16 relative error = 8.496306542595516e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = 0.1325116666666667 y[1] (numeric) = 0.1325116666666668 absolute error = 1.110223024625157e-16 relative error = 8.378303982983809e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = 0.1343692800000001 y[1] (numeric) = 0.1343692800000002 absolute error = 1.387778780781446e-16 relative error = 1.032809568363725e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (closed_form) = 0.1362441733333334 y[1] (numeric) = 0.1362441733333336 absolute error = 1.942890293094024e-16 relative error = 1.426035510774154e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (closed_form) = 0.1381364266666667 y[1] (numeric) = 0.1381364266666669 absolute error = 1.665334536937735e-16 relative error = 1.205572329561057e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (closed_form) = 0.1400461200000001 y[1] (numeric) = 0.1400461200000002 absolute error = 1.665334536937735e-16 relative error = 1.189132934877263e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 0.1419733333333334 y[1] (numeric) = 0.1419733333333335 absolute error = 1.387778780781446e-16 relative error = 9.774925672296053e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = 0.1439181466666667 y[1] (numeric) = 0.1439181466666669 absolute error = 1.387778780781446e-16 relative error = 9.642833881093002e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (closed_form) = 0.1458806400000001 y[1] (numeric) = 0.1458806400000002 absolute error = 1.110223024625157e-16 relative error = 7.610489127448001e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (closed_form) = 0.1478608933333334 y[1] (numeric) = 0.1478608933333335 absolute error = 1.387778780781446e-16 relative error = 9.385705371418773e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (closed_form) = 0.1498589866666667 y[1] (numeric) = 0.1498589866666669 absolute error = 1.110223024625157e-16 relative error = 7.408451433711078e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (closed_form) = 0.1518750000000001 y[1] (numeric) = 0.1518750000000002 absolute error = 5.551115123125783e-17 relative error = 3.655055225103392e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 0.1539090133333335 y[1] (numeric) = 0.1539090133333335 absolute error = 8.326672684688674e-17 relative error = 5.41012673939694e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = 0.1559611066666668 y[1] (numeric) = 0.1559611066666669 absolute error = 8.326672684688674e-17 relative error = 5.338941780199816e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (closed_form) = 0.1580313600000001 y[1] (numeric) = 0.1580313600000002 absolute error = 8.326672684688674e-17 relative error = 5.269000206470834e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = 0.1601198533333335 y[1] (numeric) = 0.1601198533333336 absolute error = 8.326672684688674e-17 relative error = 5.2002749886077e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (closed_form) = 0.1622266666666668 y[1] (numeric) = 0.1622266666666669 absolute error = 5.551115123125783e-17 relative error = 3.421826532706775e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (closed_form) = 0.1643518800000001 y[1] (numeric) = 0.1643518800000002 absolute error = 5.551115123125783e-17 relative error = 3.377579327431957e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (closed_form) = 0.1664955733333335 y[1] (numeric) = 0.1664955733333335 absolute error = 2.775557561562891e-17 relative error = 1.667045859535298e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = 0.1686578266666668 y[1] (numeric) = 0.1686578266666669 absolute error = 5.551115123125783e-17 relative error = 3.29134747721903e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (closed_form) = 0.1708387200000002 y[1] (numeric) = 0.1708387200000002 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] = 0.8500000000000006 y[1] (closed_form) = 0.1730383333333335 y[1] (numeric) = 0.1730383333333335 absolute error = 2.775557561562891e-17 relative error = 1.604013115530984e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (closed_form) = 0.1752567466666668 y[1] (numeric) = 0.1752567466666668 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] = 0.8700000000000007 y[1] (closed_form) = 0.1774940400000002 y[1] (numeric) = 0.1774940400000001 absolute error = 5.551115123125783e-17 relative error = 3.127493815074454e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (closed_form) = 0.1797502933333335 y[1] (numeric) = 0.1797502933333335 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] = 0.8900000000000007 y[1] (closed_form) = 0.1820255866666668 y[1] (numeric) = 0.1820255866666668 absolute error = 2.775557561562891e-17 relative error = 1.524817259150282e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = 0.1843200000000002 y[1] (numeric) = 0.1843200000000002 absolute error = 2.775557561562891e-17 relative error = 1.50583635067431e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = 0.1866336133333335 y[1] (numeric) = 0.1866336133333335 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] = 0.9200000000000007 y[1] (closed_form) = 0.1889665066666668 y[1] (numeric) = 0.1889665066666668 absolute error = 2.775557561562891e-17 relative error = 1.468809267061766e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = 0.1913187600000002 y[1] (numeric) = 0.1913187600000001 absolute error = 2.775557561562891e-17 relative error = 1.450750340198153e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = 0.1936904533333335 y[1] (numeric) = 0.1936904533333335 absolute error = 5.551115123125783e-17 relative error = 2.865972497659725e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = 0.1960816666666669 y[1] (numeric) = 0.1960816666666668 absolute error = 1.110223024625157e-16 relative error = 5.662044001862261e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = 0.1984924800000002 y[1] (numeric) = 0.1984924800000001 absolute error = 8.326672684688674e-17 relative error = 4.194956244533126e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = 0.2009229733333335 y[1] (numeric) = 0.2009229733333334 absolute error = 1.110223024625157e-16 relative error = 5.525615145975785e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 0.2033732266666669 y[1] (numeric) = 0.2033732266666667 absolute error = 1.387778780781446e-16 relative error = 6.823802737102879e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = 0.2058433200000002 y[1] (numeric) = 0.2058433200000001 absolute error = 1.110223024625157e-16 relative error = 5.393534386372875e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (closed_form) = 0.2083333333333335 y[1] (numeric) = 0.2083333333333335 absolute error = 2.775557561562891e-17 relative error = 1.332267629550187e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 0.2108433466666665 y[1] (numeric) = 0.2108433466666668 absolute error = 2.775557561562891e-16 relative error = 1.316407468124151e-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) = 0.2133734399999996 y[1] (numeric) = 0.2133734400000002 absolute error = 5.828670879282072e-16 relative error = 2.731675919590594e-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) = 0.2159236933333326 y[1] (numeric) = 0.2159236933333335 absolute error = 8.326672684688674e-16 relative error = 3.856303380210506e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 0.2184941866666657 y[1] (numeric) = 0.2184941866666668 absolute error = 1.110223024625157e-15 relative error = 5.081247430710413e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = 0.2210849999999987 y[1] (numeric) = 0.2210850000000001 absolute error = 1.443289932012704e-15 relative error = 6.528212823179826e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = 0.2236962133333317 y[1] (numeric) = 0.2236962133333334 absolute error = 1.720845688168993e-15 relative error = 7.692779696743213e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = 0.2263279066666648 y[1] (numeric) = 0.2263279066666668 absolute error = 1.998401444325282e-15 relative error = 8.829673166502277e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = 0.2289801599999978 y[1] (numeric) = 0.2289801600000002 absolute error = 2.331468351712829e-15 relative error = 1.018196664598737e-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) = 0.2316530533333308 y[1] (numeric) = 0.2316530533333335 absolute error = 2.692290834716005e-15 relative error = 1.162208223019624e-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) = 0.2343466666666638 y[1] (numeric) = 0.2343466666666668 absolute error = 3.025357742103552e-15 relative error = 1.290975367875336e-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) = 0.2370610799999968 y[1] (numeric) = 0.2370610800000001 absolute error = 3.302913498259841e-15 relative error = 1.393275310422059e-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) = 0.2397963733333298 y[1] (numeric) = 0.2397963733333334 absolute error = 3.552713678800501e-15 relative error = 1.481554382752085e-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) = 0.2425526266666629 y[1] (numeric) = 0.2425526266666667 absolute error = 3.83026943495679e-15 relative error = 1.579149847847528e-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) = 0.2453299199999959 y[1] (numeric) = 0.24532992 absolute error = 4.135580766728708e-15 relative error = 1.685722135615899e-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) = 0.2481283333333289 y[1] (numeric) = 0.2481283333333333 absolute error = 4.440892098500626e-15 relative error = 1.789756147088149e-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) = 0.2509479466666619 y[1] (numeric) = 0.2509479466666666 absolute error = 4.718447854656915e-15 relative error = 1.880249636361641e-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) = 0.2537888399999949 y[1] (numeric) = 0.2537888399999998 absolute error = 4.996003610813204e-15 relative error = 1.968567101222144e-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) = 0.2566510933333278 y[1] (numeric) = 0.2566510933333332 absolute error = 5.384581669432009e-15 relative error = 2.098016259934158e-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) = 0.2595347866666608 y[1] (numeric) = 0.2595347866666665 absolute error = 5.717648576819556e-15 relative error = 2.203037461857914e-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) = 0.2624399999999937 y[1] (numeric) = 0.2624399999999998 absolute error = 6.050715484207103e-15 relative error = 2.305561455649767e-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) = 0.2653668133333267 y[1] (numeric) = 0.2653668133333331 absolute error = 6.439293542825908e-15 relative error = 2.426563239743745e-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) = 0.2683153066666596 y[1] (numeric) = 0.2683153066666664 absolute error = 6.716849298982197e-15 relative error = 2.503341826609559e-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) = 0.2712855599999927 y[1] (numeric) = 0.2712855599999996 absolute error = 6.938893903907228e-15 relative error = 2.557782251258569e-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) = 0.2742776533333256 y[1] (numeric) = 0.2742776533333329 absolute error = 7.271960811294775e-15 relative error = 2.651313631613024e-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) = 0.2772916666666586 y[1] (numeric) = 0.2772916666666662 absolute error = 7.605027718682322e-15 relative error = 2.742609545430219e-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) = 0.2803276799999915 y[1] (numeric) = 0.2803276799999994 absolute error = 7.938094626069869e-15 relative error = 2.831719873709978e-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) = 0.2833857733333244 y[1] (numeric) = 0.2833857733333326 absolute error = 8.160139230994901e-15 relative error = 2.879516192718951e-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) = 0.2864660266666573 y[1] (numeric) = 0.2864660266666658 absolute error = 8.493206138382448e-15 relative error = 2.96482142654405e-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) = 0.2895685199999903 y[1] (numeric) = 0.2895685199999991 absolute error = 8.826273045769994e-15 relative error = 3.048077548543706e-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) = 0.2926933333333231 y[1] (numeric) = 0.2926933333333324 absolute error = 9.214851104388799e-15 relative error = 3.148295521269971e-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) = 0.295840546666656 y[1] (numeric) = 0.2958405466666655 absolute error = 9.492406860545088e-15 relative error = 3.208622674443892e-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) = 0.299010239999989 y[1] (numeric) = 0.2990102399999988 absolute error = 9.769962616701378e-15 relative error = 3.267434124229905e-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) = 0.3022024933333219 y[1] (numeric) = 0.3022024933333321 absolute error = 1.021405182655144e-14 relative error = 3.379870137366998e-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) = 0.3054173866666548 y[1] (numeric) = 0.3054173866666653 absolute error = 1.054711873393899e-14 relative error = 3.453345878258905e-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) = 0.3086549999999876 y[1] (numeric) = 0.3086549999999986 absolute error = 1.099120794378905e-14 relative error = 3.561001099541394e-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) = 0.3119154133333206 y[1] (numeric) = 0.3119154133333319 absolute error = 1.137978600240785e-14 relative error = 3.648356418426534e-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) = 0.3151987066666534 y[1] (numeric) = 0.3151987066666652 absolute error = 1.176836406102666e-14 relative error = 3.73363335956597e-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) = 0.3185049599999863 y[1] (numeric) = 0.3185049599999984 absolute error = 1.210143096841421e-14 relative error = 3.799448199618218e-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) = 0.3218342533333192 y[1] (numeric) = 0.3218342533333317 absolute error = 1.249000902703301e-14 relative error = 3.880882441092212e-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) = 0.325186666666652 y[1] (numeric) = 0.3251866666666649 absolute error = 1.287858708565182e-14 relative error = 3.960367507580999e-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) = 0.3285622799999849 y[1] (numeric) = 0.3285622799999982 absolute error = 1.332267629550188e-14 relative error = 4.054840469058862e-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) = 0.3319611733333178 y[1] (numeric) = 0.3319611733333315 absolute error = 1.371125435412068e-14 relative error = 4.13037892848794e-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) = 0.3353834266666506 y[1] (numeric) = 0.3353834266666648 absolute error = 1.415534356397075e-14 relative error = 4.220644921145802e-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) = 0.3388291199999834 y[1] (numeric) = 0.3388291199999979 absolute error = 1.443289932012704e-14 relative error = 4.259639584734553e-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) = 0.3422983333333163 y[1] (numeric) = 0.342298333333331 absolute error = 1.471045507628332e-14 relative error = 4.297553813082367e-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) = 0.3457911466666491 y[1] (numeric) = 0.3457911466666642 absolute error = 1.509903313490213e-14 relative error = 4.366518136873514e-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) = 0.3493076399999819 y[1] (numeric) = 0.3493076399999973 absolute error = 1.537658889105842e-14 relative error = 4.402019060063849e-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) = 0.3528478933333148 y[1] (numeric) = 0.3528478933333306 absolute error = 1.576516694967722e-14 relative error = 4.467978198975611e-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) = 0.3564119866666476 y[1] (numeric) = 0.3564119866666638 absolute error = 1.626476731075854e-14 relative error = 4.563473709982429e-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) = 0.3599999999999804 y[1] (numeric) = 0.3599999999999971 absolute error = 1.670885652060861e-14 relative error = 4.641349033502643e-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) = 0.3636120133333134 y[1] (numeric) = 0.3636120133333304 absolute error = 1.69864122767649e-14 relative error = 4.671576200424904e-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) = 0.3672481066666462 y[1] (numeric) = 0.3672481066666636 absolute error = 1.743050148661496e-14 relative error = 4.746246793434595e-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) = 0.370908359999979 y[1] (numeric) = 0.3709083599999969 absolute error = 1.793010184769628e-14 relative error = 4.834105612420624e-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) = 0.3745928533333118 y[1] (numeric) = 0.3745928533333301 absolute error = 1.837419105754634e-14 relative error = 4.905109879711728e-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) = 0.3783016666666446 y[1] (numeric) = 0.3783016666666633 absolute error = 1.870725796493389e-14 relative error = 4.945063586362289e-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) = 0.3820348799999773 y[1] (numeric) = 0.3820348799999964 absolute error = 1.904032487232143e-14 relative error = 4.983923162283655e-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) = 0.3857925733333101 y[1] (numeric) = 0.3857925733333296 absolute error = 1.94844140821715e-14 relative error = 5.050489674755275e-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) = 0.3895748266666429 y[1] (numeric) = 0.3895748266666626 absolute error = 1.970645868709653e-14 relative error = 5.05845278959958e-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) = 0.3933817199999756 y[1] (numeric) = 0.3933817199999958 absolute error = 2.020605904817785e-14 relative error = 5.136501779538485e-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) = 0.3972133333333084 y[1] (numeric) = 0.397213333333329 absolute error = 2.065014825802791e-14 relative error = 5.198755058078583e-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) = 0.4010697466666411 y[1] (numeric) = 0.4010697466666622 absolute error = 2.109423746787797e-14 relative error = 5.259493552728863e-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) = 0.4049510399999739 y[1] (numeric) = 0.4049510399999954 absolute error = 2.153832667772804e-14 relative error = 5.318748330101689e-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) = 0.4088572933333066 y[1] (numeric) = 0.4088572933333286 absolute error = 2.19824158875781e-14 relative error = 5.37654977568364e-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) = 0.4127885866666393 y[1] (numeric) = 0.4127885866666617 absolute error = 2.242650509742816e-14 relative error = 5.432927610360363e-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) = 0.416744999999972 y[1] (numeric) = 0.4167449999999949 absolute error = 2.287059430727822e-14 relative error = 5.487910906496721e-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) = 0.4207266133333048 y[1] (numeric) = 0.4207266133333281 absolute error = 2.325917236589703e-14 relative error = 5.528333989053083e-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) = 0.4247335066666375 y[1] (numeric) = 0.4247335066666613 absolute error = 2.381428387820961e-14 relative error = 5.606876666055178e-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) = 0.4287657599999701 y[1] (numeric) = 0.4287657599999945 absolute error = 2.436939539052219e-14 relative error = 5.683615079367318e-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) = 0.4328234533333029 y[1] (numeric) = 0.4328234533333277 absolute error = 2.475797344914099e-14 relative error = 5.720109032556446e-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) = 0.4369066666666356 y[1] (numeric) = 0.4369066666666608 absolute error = 2.520206265899105e-14 relative error = 5.768294370802196e-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) = 0.4410154799999683 y[1] (numeric) = 0.4410154799999939 absolute error = 2.564615186884112e-14 relative error = 5.815249811376907e-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) = 0.4451499733333009 y[1] (numeric) = 0.445149973333327 absolute error = 2.609024107869118e-14 relative error = 5.86100025645883e-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) = 0.4493102266666336 y[1] (numeric) = 0.4493102266666601 absolute error = 2.647881913730998e-14 relative error = 5.893215325578597e-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) = 0.4534963199999663 y[1] (numeric) = 0.4534963199999932 absolute error = 2.69784194983913e-14 relative error = 5.948983113775501e-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) = 0.457708333333299 y[1] (numeric) = 0.4577083333333263 absolute error = 2.731148640577885e-14 relative error = 5.967006588427324e-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) = 0.4619463466666315 y[1] (numeric) = 0.4619463466666595 absolute error = 2.792210906932269e-14 relative error = 6.044448510266707e-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) = 0.4662104399999642 y[1] (numeric) = 0.4662104399999926 absolute error = 2.836619827917275e-14 relative error = 6.084419362032075e-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) = 0.4705006933332969 y[1] (numeric) = 0.4705006933333257 absolute error = 2.875477633779155e-14 relative error = 6.111526878754677e-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) = 0.4748171866666295 y[1] (numeric) = 0.4748171866666587 absolute error = 2.919886554764162e-14 relative error = 6.149496346715483e-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) = 0.4791599999999621 y[1] (numeric) = 0.4791599999999917 absolute error = 2.958744360626042e-14 relative error = 6.174856750618324e-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) = 0.4835292133332947 y[1] (numeric) = 0.4835292133333248 absolute error = 3.0142555118573e-14 relative error = 6.233864322442885e-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) = 0.4879249066666274 y[1] (numeric) = 0.4879249066666579 absolute error = 3.05311331771918e-14 relative error = 6.257342627940916e-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) = 0.49234715999996 y[1] (numeric) = 0.492347159999991 absolute error = 3.103073353827313e-14 relative error = 6.302612477398194e-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) = 0.4967960533332925 y[1] (numeric) = 0.4967960533333242 absolute error = 3.164135620181696e-14 relative error = 6.369083649017897e-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) = 0.5012716666666251 y[1] (numeric) = 0.5012716666666572 absolute error = 3.208544541166702e-14 relative error = 6.400809689689825e-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) = 0.5057740799999577 y[1] (numeric) = 0.5057740799999904 absolute error = 3.26405569239796e-14 relative error = 6.453584360033304e-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) = 0.5103033733332903 y[1] (numeric) = 0.5103033733333235 absolute error = 3.319566843629218e-14 relative error = 6.505085047637214e-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) = 0.5148596266666229 y[1] (numeric) = 0.5148596266666566 absolute error = 3.375077994860476e-14 relative error = 6.555336289838618e-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) = 0.5194429199999555 y[1] (numeric) = 0.5194429199999897 absolute error = 3.419486915845482e-14 relative error = 6.582988783148252e-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) = 0.524053333333288 y[1] (numeric) = 0.5240533333333228 absolute error = 3.486100297322992e-14 relative error = 6.652186095543634e-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) = 0.5286909466666205 y[1] (numeric) = 0.5286909466666559 absolute error = 3.541611448554249e-14 relative error = 6.698831275405785e-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) = 0.5333558399999532 y[1] (numeric) = 0.5333558399999889 absolute error = 3.574918139293004e-14 relative error = 6.702688657713616e-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) = 0.5380480933332857 y[1] (numeric) = 0.538048093333322 absolute error = 3.630429290524262e-14 relative error = 6.747406664027425e-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) = 0.5427677866666182 y[1] (numeric) = 0.5427677866666549 absolute error = 3.674838211509268e-14 relative error = 6.77055326749973e-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) = 0.5475149999999507 y[1] (numeric) = 0.5475149999999879 absolute error = 3.719247132494274e-14 relative error = 6.792959339003697e-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) = 0.5522898133332832 y[1] (numeric) = 0.5522898133333211 absolute error = 3.785860513971784e-14 relative error = 6.854844001417748e-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) = 0.5570923066666158 y[1] (numeric) = 0.5570923066666542 absolute error = 3.841371665203042e-14 relative error = 6.895395285905209e-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) = 0.5619225599999482 y[1] (numeric) = 0.5619225599999873 absolute error = 3.907985046680551e-14 relative error = 6.954668356224941e-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) = 0.5667806533332808 y[1] (numeric) = 0.5667806533333204 absolute error = 3.963496197911809e-14 relative error = 6.992998392944752e-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) = 0.5716666666666133 y[1] (numeric) = 0.5716666666666534 absolute error = 4.019007349143067e-14 relative error = 7.03033355535296e-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) = 0.5765806799999458 y[1] (numeric) = 0.5765806799999864 absolute error = 4.063416270128073e-14 relative error = 7.047437437772724e-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) = 0.5815227733332783 y[1] (numeric) = 0.5815227733333194 absolute error = 4.107825191113079e-14 relative error = 7.063911130370867e-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) = 0.5864930266666106 y[1] (numeric) = 0.5864930266666524 absolute error = 4.174438572590589e-14 relative error = 7.117626950002135e-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) = 0.5914915199999431 y[1] (numeric) = 0.5914915199999855 absolute error = 4.241051954068098e-14 relative error = 7.170097644119236e-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) = 0.5965183333332756 y[1] (numeric) = 0.5965183333333185 absolute error = 4.285460875053104e-14 relative error = 7.184122659074774e-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) = 0.6015735466666081 y[1] (numeric) = 0.6015735466666515 absolute error = 4.340972026284362e-14 relative error = 7.216028780417978e-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) = 0.6066572399999405 y[1] (numeric) = 0.6066572399999846 absolute error = 4.407585407761871e-14 relative error = 7.265363564707979e-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) = 0.6117694933332729 y[1] (numeric) = 0.6117694933333174 absolute error = 4.451994328746878e-14 relative error = 7.277241472911383e-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) = 0.6169103866666054 y[1] (numeric) = 0.6169103866666504 absolute error = 4.507505479978136e-14 relative error = 7.306580627267198e-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) = 0.6220799999999378 y[1] (numeric) = 0.6220799999999835 absolute error = 4.574118861455645e-14 relative error = 7.352943128626708e-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) = 0.6272784133332703 y[1] (numeric) = 0.6272784133333166 absolute error = 4.629630012686903e-14 relative error = 7.380502683147811e-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) = 0.6325057066666027 y[1] (numeric) = 0.6325057066666494 absolute error = 4.674038933671909e-14 relative error = 7.389718202393423e-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) = 0.637761959999935 y[1] (numeric) = 0.6377619599999824 absolute error = 4.740652315149418e-14 relative error = 7.433262898197787e-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) = 0.6430472533332674 y[1] (numeric) = 0.6430472533333155 absolute error = 4.807265696626928e-14 relative error = 7.475758074866547e-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) = 0.6483616666665998 y[1] (numeric) = 0.6483616666666484 absolute error = 4.862776847858186e-14 relative error = 7.500099246858653e-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) = 0.6537052799999321 y[1] (numeric) = 0.6537052799999812 absolute error = 4.907185768843192e-14 relative error = 7.506725001278407e-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) = 0.6590781733332645 y[1] (numeric) = 0.6590781733333141 absolute error = 4.96269692007445e-14 relative error = 7.529754619206681e-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) = 0.6644804266665969 y[1] (numeric) = 0.6644804266666472 absolute error = 5.029310301551959e-14 relative error = 7.568786227130534e-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) = 0.6699121199999293 y[1] (numeric) = 0.6699121199999802 absolute error = 5.095923683029469e-14 relative error = 7.606853990087546e-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) = 0.6753733333332617 y[1] (numeric) = 0.6753733333333133 absolute error = 5.162537064506978e-14 relative error = 7.643975279609587e-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) = 0.6808641466665939 y[1] (numeric) = 0.6808641466666464 absolute error = 5.25135490647699e-14 relative error = 7.712779314620716e-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) = 0.6863846399999263 y[1] (numeric) = 0.6863846399999793 absolute error = 5.306866057708248e-14 relative error = 7.731621234573108e-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) = 0.6919348933332585 y[1] (numeric) = 0.6919348933333122 absolute error = 5.362377208939506e-14 relative error = 7.749829153877935e-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) = 0.6975149866665908 y[1] (numeric) = 0.6975149866666451 absolute error = 5.428990590417015e-14 relative error = 7.783331819667481e-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) = 0.7031249999999233 y[1] (numeric) = 0.7031249999999781 absolute error = 5.484501741648273e-14 relative error = 7.800180254789507e-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) = 0.7087650133332556 y[1] (numeric) = 0.7087650133333112 absolute error = 5.562217353372034e-14 relative error = 7.847759481260856e-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) = 0.7144351066665878 y[1] (numeric) = 0.7144351066666441 absolute error = 5.628830734849544e-14 relative error = 7.878715200758469e-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) = 0.7201353599999201 y[1] (numeric) = 0.7201353599999771 absolute error = 5.706546346573305e-14 relative error = 7.924269052104229e-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) = 0.7258658533332524 y[1] (numeric) = 0.7258658533333101 absolute error = 5.773159728050814e-14 relative error = 7.95348024919461e-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) = 0.7316266666665846 y[1] (numeric) = 0.7316266666666431 absolute error = 5.850875339774575e-14 relative error = 7.997077753374077e-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) = 0.7374178799999169 y[1] (numeric) = 0.737417879999976 absolute error = 5.906386491005833e-14 relative error = 8.009551505594763e-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) = 0.7432395733332491 y[1] (numeric) = 0.7432395733333089 absolute error = 5.984102102729594e-14 relative error = 8.051377129843003e-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) = 0.7490918266665814 y[1] (numeric) = 0.7490918266666416 absolute error = 6.0285110237146e-14 relative error = 8.047759712639173e-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) = 0.7549747199999136 y[1] (numeric) = 0.7549747199999745 absolute error = 6.084022174945858e-14 relative error = 8.058577345406419e-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) = 0.7608883333332459 y[1] (numeric) = 0.7608883333333072 absolute error = 6.128431095930864e-14 relative error = 8.054310767368275e-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) = 0.7668327466665781 y[1] (numeric) = 0.7668327466666399 absolute error = 6.183942247162122e-14 relative error = 8.064264696628723e-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) = 0.7728080399999103 y[1] (numeric) = 0.7728080399999727 absolute error = 6.23945339839338e-14 relative error = 8.073742864261742e-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) = 0.7788142933332425 y[1] (numeric) = 0.7788142933333057 absolute error = 6.317169010117141e-14 relative error = 8.111264860176523e-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) = 0.7848515866665747 y[1] (numeric) = 0.7848515866666385 absolute error = 6.372680161348399e-14 relative error = 8.119599003952422e-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) = 0.7909199999999069 y[1] (numeric) = 0.7909199999999712 absolute error = 6.428191312579656e-14 relative error = 8.127486108051905e-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) = 0.797019613333239 y[1] (numeric) = 0.7970196133333038 absolute error = 6.483702463810914e-14 relative error = 8.134934643195582e-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) = 0.8031505066665713 y[1] (numeric) = 0.8031505066666367 absolute error = 6.539213615042172e-14 relative error = 8.14195292260076e-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) = 0.8093127599999034 y[1] (numeric) = 0.8093127599999694 absolute error = 6.605826996519681e-14 relative error = 8.162267201273917e-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) = 0.8155064533332356 y[1] (numeric) = 0.8155064533333024 absolute error = 6.683542608243442e-14 relative error = 8.195572923948876e-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) = 0.8217316666665677 y[1] (numeric) = 0.8217316666666353 absolute error = 6.761258219967203e-14 relative error = 8.228060928204079e-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) = 0.8279884799998998 y[1] (numeric) = 0.8279884799999679 absolute error = 6.816769371198461e-14 relative error = 8.232927795323053e-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) = 0.8342769733332319 y[1] (numeric) = 0.8342769733333006 absolute error = 6.872280522429719e-14 relative error = 8.237408848733443e-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) = 0.840597226666564 y[1] (numeric) = 0.8405972266666336 absolute error = 6.961098364399732e-14 relative error = 8.281134107477801e-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) = 0.8469493199998962 y[1] (numeric) = 0.8469493199999664 absolute error = 7.016609515630989e-14 relative error = 8.284568332414328e-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) = 0.8533333333332282 y[1] (numeric) = 0.8533333333332993 absolute error = 7.105427357601002e-14 relative error = 8.3266726846897e-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) = 0.8597493466665606 y[1] (numeric) = 0.8597493466666319 absolute error = 7.138734048339757e-14 relative error = 8.303273594819485e-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) = 0.8661974399998925 y[1] (numeric) = 0.8661974399999647 absolute error = 7.216449660063518e-14 relative error = 8.331183315508775e-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) = 0.8726776933332246 y[1] (numeric) = 0.8726776933332976 absolute error = 7.294165271787278e-14 relative error = 8.358372544079757e-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) = 0.8791901866665568 y[1] (numeric) = 0.8791901866666304 absolute error = 7.360778653264788e-14 relative error = 8.372225674143528e-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) = 0.8857349999998887 y[1] (numeric) = 0.8857349999999631 absolute error = 7.438494264988549e-14 relative error = 8.398103569340134e-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) = 0.8923122133332209 y[1] (numeric) = 0.8923122133332957 absolute error = 7.482903185973555e-14 relative error = 8.385969702265159e-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) = 0.8989219066665529 y[1] (numeric) = 0.8989219066666284 absolute error = 7.549516567451064e-14 relative error = 8.398412043874564e-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) = 0.9055641599998848 y[1] (numeric) = 0.9055641599999611 absolute error = 7.627232179174825e-14 relative error = 8.422630351421809e-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) = 0.912239053333217 y[1] (numeric) = 0.912239053333294 absolute error = 7.704947790898586e-14 relative error = 8.446193750142125e-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) = 0.918946666666549 y[1] (numeric) = 0.9189466666666269 absolute error = 7.793765632868599e-14 relative error = 8.481194736948386e-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) = 0.9256870799998811 y[1] (numeric) = 0.9256870799999596 absolute error = 7.849276784099857e-14 relative error = 8.479406220189295e-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) = 0.9324603733332131 y[1] (numeric) = 0.9324603733332922 absolute error = 7.915890165577366e-14 relative error = 8.489251009435268e-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) = 0.939266626666545 y[1] (numeric) = 0.9392666266666251 absolute error = 8.004708007547379e-14 relative error = 8.522295778735446e-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) = 0.9461059199998769 y[1] (numeric) = 0.9461059199999577 absolute error = 8.08242361927114e-14 relative error = 8.542831672876745e-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) = 0.9529783333332089 y[1] (numeric) = 0.9529783333332904 absolute error = 8.149037000748649e-14 relative error = 8.551125157532136e-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) = 0.9598839466665409 y[1] (numeric) = 0.9598839466666231 absolute error = 8.22675261247241e-14 relative error = 8.570570058018009e-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) = 0.9668228399998728 y[1] (numeric) = 0.9668228399999558 absolute error = 8.293365993949919e-14 relative error = 8.577958288564025e-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) = 0.9737950933332048 y[1] (numeric) = 0.9737950933332887 absolute error = 8.393286066166183e-14 relative error = 8.619150089816935e-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) = 0.9808007866665368 y[1] (numeric) = 0.9808007866666214 absolute error = 8.459899447643693e-14 relative error = 8.62550230653514e-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) = 0.9878399999998687 y[1] (numeric) = 0.9878399999999542 absolute error = 8.548717289613705e-14 relative error = 8.653949313264133e-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) = 0.9949128133332007 y[1] (numeric) = 0.9949128133332868 absolute error = 8.615330671091215e-14 relative error = 8.659382566626873e-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) = 1.002019306666533 y[1] (numeric) = 1.00201930666662 absolute error = 8.704148513061227e-14 relative error = 8.68660758844832e-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) = 1.009159559999865 y[1] (numeric) = 1.009159559999953 absolute error = 8.79296635503124e-14 relative error = 8.713157664613928e-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) = 1.016333653333196 y[1] (numeric) = 1.016333653333285 absolute error = 8.903988657493755e-14 relative error = 8.76089129617226e-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) = 1.023541666666528 y[1] (numeric) = 1.023541666666618 absolute error = 8.992806499463768e-14 relative error = 8.785970119566849e-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) = 1.03078367999986 y[1] (numeric) = 1.030783679999951 absolute error = 9.081624341433781e-14 relative error = 8.810407574007198e-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) = 1.038059773333192 y[1] (numeric) = 1.038059773333284 absolute error = 9.192646643896296e-14 relative error = 8.855604349621282e-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) = 1.045370026666524 y[1] (numeric) = 1.045370026666616 absolute error = 9.237055564881302e-14 relative error = 8.836158804300545e-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) = 1.052714519999856 y[1] (numeric) = 1.052714519999949 absolute error = 9.325873406851315e-14 relative error = 8.858881709784522e-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) = 1.060093333333187 y[1] (numeric) = 1.060093333333281 absolute error = 9.348077867343818e-14 relative error = 8.818164942091676e-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) = 1.067506546666519 y[1] (numeric) = 1.067506546666614 absolute error = 9.414691248821327e-14 relative error = 8.819328816502707e-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) = 1.074954239999851 y[1] (numeric) = 1.074954239999946 absolute error = 9.50350909079134e-14 relative error = 8.840849905194715e-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) = 1.082436493333183 y[1] (numeric) = 1.082436493333279 absolute error = 9.592326932761353e-14 relative error = 8.861791885104852e-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) = 1.089953386666515 y[1] (numeric) = 1.089953386666611 absolute error = 9.636735853746359e-14 relative error = 8.841420166800986e-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) = 1.097504999999847 y[1] (numeric) = 1.097504999999944 absolute error = 9.747758156208874e-14 relative error = 8.881743733477511e-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) = 1.105091413333178 y[1] (numeric) = 1.105091413333277 absolute error = 9.85878045867139e-14 relative error = 8.921235238753075e-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) = 1.11271270666651 y[1] (numeric) = 1.11271270666661 absolute error = 9.925393840148899e-14 relative error = 8.919996851553548e-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) = 1.120368959999842 y[1] (numeric) = 1.120368959999942 absolute error = 1.003641614261142e-13 relative error = 8.958134776076651e-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) = 1.128060253333174 y[1] (numeric) = 1.128060253333275 absolute error = 1.012523398458143e-13 relative error = 8.975791811353652e-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) = 1.135786666666506 y[1] (numeric) = 1.135786666666607 absolute error = 1.016964290556643e-13 relative error = 8.95383191582446e-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) = 1.143548279999837 y[1] (numeric) = 1.14354827999994 absolute error = 1.025846074753645e-13 relative error = 8.97072815109993e-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) = 1.151345173333169 y[1] (numeric) = 1.151345173333272 absolute error = 1.032507412901396e-13 relative error = 8.967835509417775e-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) = 1.159177426666501 y[1] (numeric) = 1.159177426666605 absolute error = 1.039168751049147e-13 relative error = 8.964708310767673e-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) = 1.167045119999832 y[1] (numeric) = 1.167045119999937 absolute error = 1.050270981295398e-13 relative error = 8.999403393208559e-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) = 1.174948333333164 y[1] (numeric) = 1.17494833333327 absolute error = 1.054711873393899e-13 relative error = 8.976665981574087e-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) = 1.182887146666496 y[1] (numeric) = 1.182887146666602 absolute error = 1.0635936575909e-13 relative error = 8.991505745820488e-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) = 1.190861639999828 y[1] (numeric) = 1.190861639999935 absolute error = 1.070254995738651e-13 relative error = 8.987232099766064e-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) = 1.198871893333159 y[1] (numeric) = 1.198871893333267 absolute error = 1.079136779935652e-13 relative error = 9.001268491960271e-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) = 1.206917986666491 y[1] (numeric) = 1.2069179866666 absolute error = 1.085798118083403e-13 relative error = 8.996453197970633e-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) = 1.214999999999823 y[1] (numeric) = 1.214999999999932 absolute error = 1.094679902280404e-13 relative error = 9.009711129881187e-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) = 1.223118013333154 y[1] (numeric) = 1.223118013333264 absolute error = 1.103561686477406e-13 relative error = 9.022528279753299e-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) = 1.231272106666486 y[1] (numeric) = 1.231272106666597 absolute error = 1.112443470674407e-13 relative error = 9.034911654794223e-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) = 1.239462359999818 y[1] (numeric) = 1.239462359999929 absolute error = 1.114663916723657e-13 relative error = 8.993124379540022e-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) = 1.247688853333149 y[1] (numeric) = 1.247688853333262 absolute error = 1.123545700920658e-13 relative error = 9.005015135938359e-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) = 1.255951666666481 y[1] (numeric) = 1.255951666666594 absolute error = 1.13464793116691e-13 relative error = 9.034168760478399e-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) = 1.264250879999812 y[1] (numeric) = 1.264250879999927 absolute error = 1.143529715363911e-13 relative error = 9.045117021109616e-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) = 1.272586573333144 y[1] (numeric) = 1.272586573333259 absolute error = 1.150191053511662e-13 relative error = 9.038214590769217e-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) = 1.280958826666476 y[1] (numeric) = 1.280958826666591 absolute error = 1.156852391659413e-13 relative error = 9.031144230216728e-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) = 1.289367719999807 y[1] (numeric) = 1.289367719999924 absolute error = 1.167954621905665e-13 relative error = 9.058351653986184e-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) = 1.297813333333139 y[1] (numeric) = 1.297813333333257 absolute error = 1.183497744250417e-13 relative error = 9.119167709664933e-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) = 1.30629574666647 y[1] (numeric) = 1.306295746666589 absolute error = 1.190159082398168e-13 relative error = 9.110946624723605e-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) = 1.314815039999802 y[1] (numeric) = 1.314815039999922 absolute error = 1.20348175869367e-13 relative error = 9.153239977341995e-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) = 1.323371293333133 y[1] (numeric) = 1.323371293333255 absolute error = 1.214583988939921e-13 relative error = 9.177953270248044e-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) = 1.331964586666465 y[1] (numeric) = 1.331964586666587 absolute error = 1.223465773136923e-13 relative error = 9.185422686040893e-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) = 1.340594999999796 y[1] (numeric) = 1.34059499999992 absolute error = 1.234568003383174e-13 relative error = 9.209104937608762e-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) = 1.349262613333128 y[1] (numeric) = 1.349262613333252 absolute error = 1.243449787580175e-13 relative error = 9.215772936214697e-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) = 1.357967506666459 y[1] (numeric) = 1.357967506666584 absolute error = 1.250111125727926e-13 relative error = 9.205751386472428e-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) = 1.366709759999791 y[1] (numeric) = 1.366709759999917 absolute error = 1.256772463875677e-13 relative error = 9.195606123979605e-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) = 1.375489453333122 y[1] (numeric) = 1.375489453333249 absolute error = 1.270095140171179e-13 relative error = 9.233768656629472e-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) = 1.384306666666454 y[1] (numeric) = 1.384306666666581 absolute error = 1.27453603226968e-13 relative error = 9.207035283149272e-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) = 1.393161479999785 y[1] (numeric) = 1.393161479999914 absolute error = 1.285638262515931e-13 relative error = 9.228207074144267e-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) = 1.402053973333117 y[1] (numeric) = 1.402053973333246 absolute error = 1.292299600663682e-13 relative error = 9.217188676349498e-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) = 1.410984226666448 y[1] (numeric) = 1.410984226666578 absolute error = 1.303401830909934e-13 relative error = 9.237536510165777e-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) = 1.419952319999779 y[1] (numeric) = 1.419952319999911 absolute error = 1.316724507205436e-13 relative error = 9.273019161697205e-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) = 1.428958333333111 y[1] (numeric) = 1.428958333333243 absolute error = 1.325606291402437e-13 relative error = 9.276731591679091e-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) = 1.438002346666442 y[1] (numeric) = 1.438002346666576 absolute error = 1.336708521648688e-13 relative error = 9.295593465111015e-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) = 1.447084439999774 y[1] (numeric) = 1.447084439999908 absolute error = 1.34781075189494e-13 relative error = 9.31397446229987e-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) = 1.456204693333105 y[1] (numeric) = 1.456204693333241 absolute error = 1.356692536091941e-13 relative error = 9.316633453409695e-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) = 1.465363186666436 y[1] (numeric) = 1.465363186666573 absolute error = 1.370015212387443e-13 relative error = 9.349321894076644e-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) = 1.474559999999768 y[1] (numeric) = 1.474559999999906 absolute error = 1.383337888682945e-13 relative error = 9.38136046470244e-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) = 1.483795213333099 y[1] (numeric) = 1.483795213333238 absolute error = 1.394440118929197e-13 relative error = 9.397793620029404e-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) = 1.49306890666643 y[1] (numeric) = 1.493068906666571 absolute error = 1.405542349175448e-13 relative error = 9.413780856997401e-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) = 1.502381159999762 y[1] (numeric) = 1.502381159999903 absolute error = 1.4166445794217e-13 relative error = 9.429328702590523e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y[1] (closed_form) = 1.511732053333093 y[1] (numeric) = 1.511732053333236 absolute error = 1.427746809667951e-13 relative error = 9.444443587208663e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y[1] (closed_form) = 1.521121666666424 y[1] (numeric) = 1.521121666666568 absolute error = 1.438849039914203e-13 relative error = 9.459131846221586e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y[1] (closed_form) = 1.530550079999756 y[1] (numeric) = 1.530550079999901 absolute error = 1.449951270160454e-13 relative error = 9.473399721495465e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y[1] (closed_form) = 1.540017373333087 y[1] (numeric) = 1.540017373333233 absolute error = 1.465494392505207e-13 relative error = 9.516089999253784e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y[1] (closed_form) = 1.549523626666418 y[1] (numeric) = 1.549523626666566 absolute error = 1.474376176702208e-13 relative error = 9.515028692231822e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y[1] (closed_form) = 1.559068919999749 y[1] (numeric) = 1.559068919999898 absolute error = 1.483257960899209e-13 relative error = 9.513742092296006e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999737 y[1] (closed_form) = 1.568653333333081 y[1] (numeric) = 1.56865333333323 absolute error = 1.48991929904696e-13 relative error = 9.498078813125483e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = 1.578276946666412 y[1] (numeric) = 1.578276946666562 absolute error = 1.501021529293212e-13 relative error = 9.510507851385799e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y[1] (closed_form) = 1.587939839999743 y[1] (numeric) = 1.587939839999894 absolute error = 1.509903313490213e-13 relative error = 9.508567487609967e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y[1] (closed_form) = 1.597642093333074 y[1] (numeric) = 1.597642093333226 absolute error = 1.518785097687214e-13 relative error = 9.506416387156243e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y[1] (closed_form) = 1.607383786666405 y[1] (numeric) = 1.607383786666559 absolute error = 1.532107773982716e-13 relative error = 9.531686126809789e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y[1] (closed_form) = 1.617164999999737 y[1] (numeric) = 1.617164999999891 absolute error = 1.543210004228968e-13 relative error = 9.542687383348136e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y[1] (closed_form) = 1.626985813333068 y[1] (numeric) = 1.626985813333223 absolute error = 1.554312234475219e-13 relative error = 9.553323831945599e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999729 y[1] (closed_form) = 1.636846306666399 y[1] (numeric) = 1.636846306666556 absolute error = 1.56319401867222e-13 relative error = 9.550035408369042e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999728 y[1] (closed_form) = 1.64674655999973 y[1] (numeric) = 1.646746559999888 absolute error = 1.574296248918472e-13 relative error = 9.560039699847497e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999727 y[1] (closed_form) = 1.656686653333061 y[1] (numeric) = 1.65668665333322 absolute error = 1.583178033115473e-13 relative error = 9.556291347734966e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999726 y[1] (closed_form) = 1.666666666666393 y[1] (numeric) = 1.666666666666552 absolute error = 1.594280263361725e-13 relative error = 9.565681580171922e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = 1.676686679999724 y[1] (numeric) = 1.676686679999884 absolute error = 1.605382493607976e-13 relative error = 9.574731598680327e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y[1] (closed_form) = 1.686746773333055 y[1] (numeric) = 1.686746773333216 absolute error = 1.616484723854228e-13 relative error = 9.583446367945396e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y[1] (closed_form) = 1.696847026666386 y[1] (numeric) = 1.696847026666549 absolute error = 1.627586954100479e-13 relative error = 9.591830780986933e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y[1] (closed_form) = 1.706987519999717 y[1] (numeric) = 1.706987519999881 absolute error = 1.638689184346731e-13 relative error = 9.599889660277088e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y[1] (closed_form) = 1.717168333333048 y[1] (numeric) = 1.717168333333213 absolute error = 1.649791414592983e-13 relative error = 9.607627758838961e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y[1] (closed_form) = 1.727389546666379 y[1] (numeric) = 1.727389546666545 absolute error = 1.658673198789984e-13 relative error = 9.602195416725728e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999718 y[1] (closed_form) = 1.73765123999971 y[1] (numeric) = 1.737651239999877 absolute error = 1.669775429036235e-13 relative error = 9.609381851772016e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999717 y[1] (closed_form) = 1.747953493333041 y[1] (numeric) = 1.747953493333209 absolute error = 1.680877659282487e-13 relative error = 9.616260762621021e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999716 y[1] (closed_form) = 1.758296386666372 y[1] (numeric) = 1.758296386666542 absolute error = 1.691979889528739e-13 relative error = 9.62283664096378e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999715 y[1] (closed_form) = 1.768679999999703 y[1] (numeric) = 1.768679999999874 absolute error = 1.707523011873491e-13 relative error = 9.654222425050192e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = 1.779104413333034 y[1] (numeric) = 1.779104413333206 absolute error = 1.716404796070492e-13 relative error = 9.647577641915469e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y[1] (closed_form) = 1.789569706666365 y[1] (numeric) = 1.789569706666538 absolute error = 1.731947918415244e-13 relative error = 9.678013166872054e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y[1] (closed_form) = 1.800075959999696 y[1] (numeric) = 1.800075959999871 absolute error = 1.743050148661496e-13 relative error = 9.683203305830438e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y[1] (closed_form) = 1.810623253333027 y[1] (numeric) = 1.810623253333203 absolute error = 1.756372824956998e-13 relative error = 9.700377048200587e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y[1] (closed_form) = 1.821211666666358 y[1] (numeric) = 1.821211666666535 absolute error = 1.77191594730175e-13 relative error = 9.729324601489942e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999708 y[1] (closed_form) = 1.831841279999689 y[1] (numeric) = 1.831841279999867 absolute error = 1.778577285449501e-13 relative error = 9.709232480282366e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999707 y[1] (closed_form) = 1.84251217333302 y[1] (numeric) = 1.8425121733332 absolute error = 1.796340853843503e-13 relative error = 9.749411047819592e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999706 y[1] (closed_form) = 1.853224426666351 y[1] (numeric) = 1.853224426666532 absolute error = 1.807443084089755e-13 relative error = 9.752963850908498e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999705 y[1] (closed_form) = 1.863978119999682 y[1] (numeric) = 1.863978119999864 absolute error = 1.820765760385257e-13 relative error = 9.768171315152388e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999704 y[1] (closed_form) = 1.874773333333013 y[1] (numeric) = 1.874773333333196 absolute error = 1.831867990631508e-13 relative error = 9.771143839424969e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y[1] (closed_form) = 1.885610146666344 y[1] (numeric) = 1.885610146666528 absolute error = 1.84741111297626e-13 relative error = 9.797418179162765e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y[1] (closed_form) = 1.896488639999675 y[1] (numeric) = 1.896488639999861 absolute error = 1.860733789271762e-13 relative error = 9.81146815238546e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y[1] (closed_form) = 1.907408893333006 y[1] (numeric) = 1.907408893333193 absolute error = 1.871836019518014e-13 relative error = 9.813501583539167e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y[1] (closed_form) = 1.918370986666337 y[1] (numeric) = 1.918370986666525 absolute error = 1.885158695813516e-13 relative error = 9.826872429349364e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y[1] (closed_form) = 1.929374999999667 y[1] (numeric) = 1.929374999999857 absolute error = 1.900701818158268e-13 relative error = 9.851386164735191e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999697 y[1] (closed_form) = 1.940421013332998 y[1] (numeric) = 1.940421013333189 absolute error = 1.91180404840452e-13 relative error = 9.852521876789388e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999696 y[1] (closed_form) = 1.951509106666329 y[1] (numeric) = 1.951509106666521 absolute error = 1.922906278650771e-13 relative error = 9.853432259588997e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999695 y[1] (closed_form) = 1.96263935999966 y[1] (numeric) = 1.962639359999854 absolute error = 1.936228954946273e-13 relative error = 9.865434243337546e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999694 y[1] (closed_form) = 1.973811853332991 y[1] (numeric) = 1.973811853333186 absolute error = 1.949551631241775e-13 relative error = 9.877089490316669e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999693 y[1] (closed_form) = 1.985026666666322 y[1] (numeric) = 1.985026666666518 absolute error = 1.962874307537277e-13 relative error = 9.888402712663565e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y[1] (closed_form) = 1.996283879999652 y[1] (numeric) = 1.99628387999985 absolute error = 1.978417429882029e-13 relative error = 9.910501455746732e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y[1] (closed_form) = 2.007583573332983 y[1] (numeric) = 2.007583573333182 absolute error = 1.98507876802978e-13 relative error = 9.887901028868049e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y[1] (closed_form) = 2.018925826666314 y[1] (numeric) = 2.018925826666514 absolute error = 2.002842336423782e-13 relative error = 9.920336398543731e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y[1] (closed_form) = 2.030310719999644 y[1] (numeric) = 2.030310719999846 absolute error = 2.020605904817785e-13 relative error = 9.952200345069048e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y[1] (closed_form) = 2.041738333332975 y[1] (numeric) = 2.041738333333179 absolute error = 2.033928581113287e-13 relative error = 9.96174949506414e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999686 y[1] (closed_form) = 2.053208746666306 y[1] (numeric) = 2.053208746666511 absolute error = 2.051692149507289e-13 relative error = 9.992613526698252e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999685 y[1] (closed_form) = 2.064722039999637 y[1] (numeric) = 2.064722039999843 absolute error = 2.060573933704291e-13 relative error = 9.979909613909352e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999684 y[1] (closed_form) = 2.076278293332968 y[1] (numeric) = 2.076278293333175 absolute error = 2.073896609999792e-13 relative error = 9.988529074638873e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999683 y[1] (closed_form) = 2.087877586666298 y[1] (numeric) = 2.087877586666507 absolute error = 2.087219286295294e-13 relative error = 9.996847035596302e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y[1] (closed_form) = 2.099519999999629 y[1] (numeric) = 2.099519999999838 absolute error = 2.096101070492296e-13 relative error = 9.983715661163819e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y[1] (closed_form) = 2.11120561333296 y[1] (numeric) = 2.11120561333317 absolute error = 2.104982854689297e-13 relative error = 9.970525094266688e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y[1] (closed_form) = 2.12293450666629 y[1] (numeric) = 2.122934506666502 absolute error = 2.122746423083299e-13 relative error = 9.99911403963523e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y[1] (closed_form) = 2.134706759999621 y[1] (numeric) = 2.134706759999834 absolute error = 2.136069099378801e-13 relative error = 1.00063818572401e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y[1] (closed_form) = 2.146522453332952 y[1] (numeric) = 2.146522453333164 absolute error = 2.1271873151818e-13 relative error = 9.909923429307111e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y[1] (closed_form) = 2.158381666666282 y[1] (numeric) = 2.158381666666497 absolute error = 2.144950883575802e-13 relative error = 9.937773827039479e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999675 y[1] (closed_form) = 2.170284479999613 y[1] (numeric) = 2.170284479999828 absolute error = 2.153832667772804e-13 relative error = 9.924195134884749e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999674 y[1] (closed_form) = 2.182230973332943 y[1] (numeric) = 2.18223097333316 absolute error = 2.171596236166806e-13 relative error = 9.951266674810804e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999673 y[1] (closed_form) = 2.194221226666274 y[1] (numeric) = 2.194221226666492 absolute error = 2.184918912462308e-13 relative error = 9.95760539506721e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999672 y[1] (closed_form) = 2.206255319999604 y[1] (numeric) = 2.206255319999824 absolute error = 2.202682480856311e-13 relative error = 9.983805867295113e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y[1] (closed_form) = 2.218333333332935 y[1] (numeric) = 2.218333333333157 absolute error = 2.211564265053312e-13 relative error = 9.969485792879228e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999674 y[1] (closed_form) = 2.230455346666271 y[1] (numeric) = 2.230455346666489 absolute error = 2.180478020363807e-13 relative error = 9.775932181842772e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999677 y[1] (closed_form) = 2.242621439999607 y[1] (numeric) = 2.242621439999821 absolute error = 2.136069099378801e-13 relative error = 9.524875938844032e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999681 y[1] (closed_form) = 2.254831693332943 y[1] (numeric) = 2.254831693333153 absolute error = 2.100541962590796e-13 relative error = 9.315737262349343e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999684 y[1] (closed_form) = 2.267086186666279 y[1] (numeric) = 2.267086186666485 absolute error = 2.065014825802791e-13 relative error = 9.108673670846934e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999687 y[1] (closed_form) = 2.279384999999615 y[1] (numeric) = 2.279384999999817 absolute error = 2.020605904817785e-13 relative error = 8.864697735652933e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999691 y[1] (closed_form) = 2.291728213332951 y[1] (numeric) = 2.291728213333149 absolute error = 1.980637875931279e-13 relative error = 8.642551347966168e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999694 y[1] (closed_form) = 2.304115906666287 y[1] (numeric) = 2.30411590666648 absolute error = 1.927347170749272e-13 relative error = 8.364801289609846e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999697 y[1] (closed_form) = 2.316548159999623 y[1] (numeric) = 2.316548159999812 absolute error = 1.882938249764265e-13 relative error = 8.128206796117598e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999701 y[1] (closed_form) = 2.32902505333296 y[1] (numeric) = 2.329025053333143 absolute error = 1.838529328779259e-13 relative error = 7.893986911597302e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999704 y[1] (closed_form) = 2.341546666666296 y[1] (numeric) = 2.341546666666475 absolute error = 1.798561299892754e-13 relative error = 7.681082446472867e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999707 y[1] (closed_form) = 2.354113079999632 y[1] (numeric) = 2.354113079999808 absolute error = 1.758593271006248e-13 relative error = 7.470300751255853e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.119999999999711 y[1] (closed_form) = 2.366724373332968 y[1] (numeric) = 2.36672437333314 absolute error = 1.714184350021242e-13 relative error = 7.242855861611046e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999714 y[1] (closed_form) = 2.379380626666304 y[1] (numeric) = 2.379380626666471 absolute error = 1.669775429036235e-13 relative error = 7.017689437001593e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999717 y[1] (closed_form) = 2.392081919999641 y[1] (numeric) = 2.392081919999804 absolute error = 1.63424829224823e-13 relative error = 6.831907714299668e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.149999999999721 y[1] (closed_form) = 2.404828333332977 y[1] (numeric) = 2.404828333333136 absolute error = 1.594280263361725e-13 relative error = 6.629497171434805e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999724 y[1] (closed_form) = 2.417619946666314 y[1] (numeric) = 2.417619946666469 absolute error = 1.549871342376719e-13 relative error = 6.410731945332663e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999727 y[1] (closed_form) = 2.43045683999965 y[1] (numeric) = 2.4304568399998 absolute error = 1.505462421391712e-13 relative error = 6.1941541055793e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.179999999999731 y[1] (closed_form) = 2.443339093332986 y[1] (numeric) = 2.443339093333133 absolute error = 1.465494392505207e-13 relative error = 5.997916525397665e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999734 y[1] (closed_form) = 2.456266786666323 y[1] (numeric) = 2.456266786666465 absolute error = 1.4210854715202e-13 relative error = 5.785550165944784e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999737 y[1] (closed_form) = 2.469239999999659 y[1] (numeric) = 2.469239999999797 absolute error = 1.376676550535194e-13 relative error = 5.57530475180778e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.209999999999741 y[1] (closed_form) = 2.482258813332995 y[1] (numeric) = 2.48225881333313 absolute error = 1.341149413747189e-13 relative error = 5.402939478121509e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999744 y[1] (closed_form) = 2.495323306666332 y[1] (numeric) = 2.495323306666462 absolute error = 1.296740492762183e-13 relative error = 5.196683288686084e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999747 y[1] (closed_form) = 2.508433559999669 y[1] (numeric) = 2.508433559999794 absolute error = 1.252331571777177e-13 relative error = 4.992484520009938e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999751 y[1] (closed_form) = 2.521589653333005 y[1] (numeric) = 2.521589653333126 absolute error = 1.212363542890671e-13 relative error = 4.807933524347168e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999754 y[1] (closed_form) = 2.534791666666342 y[1] (numeric) = 2.534791666666458 absolute error = 1.163513729807164e-13 relative error = 4.590174984034768e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999757 y[1] (closed_form) = 2.548039679999678 y[1] (numeric) = 2.54803967999979 absolute error = 1.123545700920658e-13 relative error = 4.409451350933438e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999761 y[1] (closed_form) = 2.561333773333015 y[1] (numeric) = 2.561333773333122 absolute error = 1.070254995738651e-13 relative error = 4.178506553427235e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y[1] (closed_form) = 2.574674026666352 y[1] (numeric) = 2.574674026666453 absolute error = 1.016964290556643e-13 relative error = 3.949875906711938e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y[1] (closed_form) = 2.588060519999688 y[1] (numeric) = 2.588060519999786 absolute error = 9.769962616701378e-14 relative error = 3.775013196639836e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y[1] (closed_form) = 2.601493333333025 y[1] (numeric) = 2.601493333333118 absolute error = 9.325873406851315e-14 relative error = 3.584815416345132e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999774 y[1] (closed_form) = 2.614972546666362 y[1] (numeric) = 2.61497254666645 absolute error = 8.837375276016246e-14 relative error = 3.37952889305946e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y[1] (closed_form) = 2.628498239999699 y[1] (numeric) = 2.628498239999782 absolute error = 8.348877145181177e-14 relative error = 3.176291700762993e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999781 y[1] (closed_form) = 2.642070493333036 y[1] (numeric) = 2.642070493333115 absolute error = 7.904787935331115e-14 relative error = 2.991891380369277e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999784 y[1] (closed_form) = 2.655689386666372 y[1] (numeric) = 2.655689386666446 absolute error = 7.371880883511039e-14 relative error = 2.775882194854421e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999787 y[1] (closed_form) = 2.669354999999709 y[1] (numeric) = 2.669354999999778 absolute error = 6.883382752675971e-14 relative error = 2.578668911657205e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999791 y[1] (closed_form) = 2.683067413333046 y[1] (numeric) = 2.68306741333311 absolute error = 6.394884621840902e-14 relative error = 2.383423014294241e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y[1] (closed_form) = 2.696826706666383 y[1] (numeric) = 2.696826706666442 absolute error = 5.906386491005833e-14 relative error = 2.190124592138465e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = 2.71063295999972 y[1] (numeric) = 2.710632959999775 absolute error = 5.46229728115577e-14 relative error = 2.015137188162994e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = 2.724486253333057 y[1] (numeric) = 2.724486253333107 absolute error = 4.929390229335695e-14 relative error = 1.809291650235057e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = 2.738386666666394 y[1] (numeric) = 2.738386666666439 absolute error = 4.485301019485632e-14 relative error = 1.637935604231474e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = 2.752334279999731 y[1] (numeric) = 2.752334279999771 absolute error = 3.952393967665557e-14 relative error = 1.436015238550872e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y[1] (closed_form) = 2.766329173333068 y[1] (numeric) = 2.766329173333103 absolute error = 3.508304757815495e-14 relative error = 1.268216664753762e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y[1] (closed_form) = 2.780371426666405 y[1] (numeric) = 2.780371426666435 absolute error = 2.97539770599542e-14 relative error = 1.070143966183268e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = 2.794461119999743 y[1] (numeric) = 2.794461119999768 absolute error = 2.486899575160351e-14 relative error = 8.899388713486841e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y[1] (closed_form) = 2.80859833333308 y[1] (numeric) = 2.8085983333331 absolute error = 1.953992523340276e-14 relative error = 6.95718038478429e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y[1] (closed_form) = 2.822783146666417 y[1] (numeric) = 2.822783146666432 absolute error = 1.465494392505207e-14 relative error = 5.19166480866903e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 2.837015639999755 y[1] (numeric) = 2.837015639999764 absolute error = 9.325873406851315e-15 relative error = 3.28721254665065e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y[1] (closed_form) = 2.851295893333092 y[1] (numeric) = 2.851295893333096 absolute error = 3.996802888650564e-15 relative error = 1.401749603748913e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y[1] (closed_form) = 2.865623986666429 y[1] (numeric) = 2.865623986666428 absolute error = 8.881784197001252e-16 relative error = 3.099424152759623e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 2.879999999999767 y[1] (numeric) = 2.879999999999761 absolute error = 5.773159728050814e-15 relative error = 2.004569350017806e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y[1] (closed_form) = 2.894424013333104 y[1] (numeric) = 2.894424013333093 absolute error = 1.110223024625157e-14 relative error = 3.835730423431181e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y[1] (closed_form) = 2.908896106666441 y[1] (numeric) = 2.908896106666426 absolute error = 1.509903313490213e-14 relative error = 5.190640222694455e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = 2.923416359999779 y[1] (numeric) = 2.923416359999758 absolute error = 2.042810365310288e-14 relative error = 6.987750336426394e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y[1] (closed_form) = 2.937984853333116 y[1] (numeric) = 2.93798485333309 absolute error = 2.620126338115369e-14 relative error = 8.91810703224988e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y[1] (closed_form) = 2.952601666666454 y[1] (numeric) = 2.952601666666422 absolute error = 3.197442310920451e-14 relative error = 1.082923696419378e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y[1] (closed_form) = 2.967266879999791 y[1] (numeric) = 2.967266879999754 absolute error = 3.730349362740526e-14 relative error = 1.257166784654297e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y[1] (closed_form) = 2.981980573333129 y[1] (numeric) = 2.981980573333086 absolute error = 4.263256414560601e-14 relative error = 1.429672766041972e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y[1] (closed_form) = 2.996742826666466 y[1] (numeric) = 2.99674282666642 absolute error = 4.662936703425657e-14 relative error = 1.556001623473524e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y[1] (closed_form) = 3.011553719999804 y[1] (numeric) = 3.011553719999752 absolute error = 5.195843755245733e-14 relative error = 1.725303361098958e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y[1] (closed_form) = 3.026413333333142 y[1] (numeric) = 3.026413333333084 absolute error = 5.773159728050814e-14 relative error = 1.907591294442435e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y[1] (closed_form) = 3.041321746666479 y[1] (numeric) = 3.041321746666418 absolute error = 6.084022174945858e-14 relative error = 2.000453316593159e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y[1] (closed_form) = 3.056279039999817 y[1] (numeric) = 3.056279039999751 absolute error = 6.616929226765933e-14 relative error = 2.165027846006604e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y[1] (closed_form) = 3.071285293333155 y[1] (numeric) = 3.071285293333083 absolute error = 7.149836278586008e-14 relative error = 2.327962268469873e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y[1] (closed_form) = 3.086340586666493 y[1] (numeric) = 3.086340586666416 absolute error = 7.682743330406083e-14 relative error = 2.489272688697035e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y[1] (closed_form) = 3.10144499999983 y[1] (numeric) = 3.101444999999748 absolute error = 8.215650382226158e-14 relative error = 2.648975036547999e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y[1] (closed_form) = 3.116598613333168 y[1] (numeric) = 3.116598613333081 absolute error = 8.704148513061227e-14 relative error = 2.79283590637045e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y[1] (closed_form) = 3.131801506666506 y[1] (numeric) = 3.131801506666414 absolute error = 9.192646643896296e-14 relative error = 2.935258388607445e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y[1] (closed_form) = 3.147053759999844 y[1] (numeric) = 3.147053759999747 absolute error = 9.681144774731365e-14 relative error = 3.076256560273011e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y[1] (closed_form) = 3.162355453333182 y[1] (numeric) = 3.16235545333308 absolute error = 1.016964290556643e-13 relative error = 3.215844346291762e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y[1] (closed_form) = 3.17770666666652 y[1] (numeric) = 3.177706666666413 absolute error = 1.06581410364015e-13 relative error = 3.354035521340965e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y[1] (closed_form) = 3.193107479999858 y[1] (numeric) = 3.193107479999746 absolute error = 1.119104808822158e-13 relative error = 3.504751455538877e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y[1] (closed_form) = 3.208557973333196 y[1] (numeric) = 3.208557973333079 absolute error = 1.172395514004165e-13 relative error = 3.653963941895766e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y[1] (closed_form) = 3.224058226666534 y[1] (numeric) = 3.224058226666412 absolute error = 1.221245327087672e-13 relative error = 3.787913372614118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y[1] (closed_form) = 3.239608319999872 y[1] (numeric) = 3.239608319999744 absolute error = 1.27897692436818e-13 relative error = 3.947936904817651e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y[1] (closed_form) = 3.25520833333321 y[1] (numeric) = 3.255208333333076 absolute error = 1.336708521648688e-13 relative error = 4.106368578504927e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y[1] (closed_form) = 3.270858346666548 y[1] (numeric) = 3.270858346666409 absolute error = 1.389999226830696e-13 relative error = 4.249646666133662e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y[1] (closed_form) = 3.286558439999887 y[1] (numeric) = 3.286558439999742 absolute error = 1.443289932012704e-13 relative error = 4.391493285032696e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y[1] (closed_form) = 3.302308693333225 y[1] (numeric) = 3.302308693333075 absolute error = 1.496580637194711e-13 relative error = 4.531922288840052e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y[1] (closed_form) = 3.318109186666563 y[1] (numeric) = 3.318109186666408 absolute error = 1.549871342376719e-13 relative error = 4.670947383542099e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y[1] (closed_form) = 3.333959999999901 y[1] (numeric) = 3.333959999999741 absolute error = 1.603162047558726e-13 relative error = 4.808582129236024e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y[1] (closed_form) = 3.34986121333324 y[1] (numeric) = 3.349861213333075 absolute error = 1.656452752740734e-13 relative error = 4.944839941868815e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y[1] (closed_form) = 3.365812906666578 y[1] (numeric) = 3.365812906666408 absolute error = 1.70530256582424e-13 relative error = 5.066539980420753e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y[1] (closed_form) = 3.381815159999916 y[1] (numeric) = 3.381815159999741 absolute error = 1.758593271006248e-13 relative error = 5.200146039342645e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y[1] (closed_form) = 3.397868053333255 y[1] (numeric) = 3.397868053333074 absolute error = 1.811883976188255e-13 relative error = 5.332414171912373e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y[1] (closed_form) = 3.413971666666593 y[1] (numeric) = 3.413971666666407 absolute error = 1.865174681370263e-13 relative error = 5.46335723749993e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y[1] (closed_form) = 3.430126079999932 y[1] (numeric) = 3.43012607999974 absolute error = 1.918465386552271e-13 relative error = 5.592987959650476e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y[1] (closed_form) = 3.446331373333271 y[1] (numeric) = 3.446331373333073 absolute error = 1.980637875931279e-13 relative error = 5.747090634571272e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y[1] (closed_form) = 3.462587626666609 y[1] (numeric) = 3.462587626666406 absolute error = 2.029487689014786e-13 relative error = 5.861187954883756e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y[1] (closed_form) = 3.478894919999948 y[1] (numeric) = 3.478894919999739 absolute error = 2.087219286295294e-13 relative error = 5.999661772754336e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y[1] (closed_form) = 3.495253333333287 y[1] (numeric) = 3.495253333333073 absolute error = 2.140509991477302e-13 relative error = 6.124048208648673e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y[1] (closed_form) = 3.511662946666625 y[1] (numeric) = 3.511662946666406 absolute error = 2.193800696659309e-13 relative error = 6.247184681382165e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y[1] (closed_form) = 3.528123839999964 y[1] (numeric) = 3.528123839999739 absolute error = 2.251532293939817e-13 relative error = 6.381670247549589e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y[1] (closed_form) = 3.544636093333302 y[1] (numeric) = 3.544636093333072 absolute error = 2.304822999121825e-13 relative error = 6.502283840805834e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 3.561199786666641 y[1] (numeric) = 3.561199786666405 absolute error = 2.362554596402333e-13 relative error = 6.634153481778495e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y[1] (closed_form) = 3.57781499999998 y[1] (numeric) = 3.577814999999738 absolute error = 2.420286193682841e-13 relative error = 6.764704697372153e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y[1] (closed_form) = 3.594481813333319 y[1] (numeric) = 3.594481813333071 absolute error = 2.478017790963349e-13 relative error = 6.893950003506558e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 3.611200306666658 y[1] (numeric) = 3.611200306666404 absolute error = 2.531308496145357e-13 relative error = 7.009604234559611e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y[1] (closed_form) = 3.627970559999997 y[1] (numeric) = 3.627970559999738 absolute error = 2.584599201327364e-13 relative error = 7.124090889335571e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y[1] (closed_form) = 3.644792653333335 y[1] (numeric) = 3.644792653333071 absolute error = 2.637889906509372e-13 relative error = 7.237421048072232e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , 2.0 ) ; Iterations = 4900 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %