##############ECHO OF PROBLEM################# ##############temp/sin_lg_hpostode.ode################# diff ( y , x , 1 ) = sin ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=16; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.0); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=false; glob_max_h=c(1.0); glob_min_h=c(1.0); glob_display_interval=c(1.0); 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(2.0) - cos(c(x))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 1 y[1] (numeric) = 1 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] = 0.01 y[1] (closed_form) = 1.000049999583335 y[1] (numeric) = 1.000049999583335 absolute error = 2.220446049250313e-16 relative error = 2.220335033423778e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.02000000000000001 y[1] (closed_form) = 1.000199993333422 y[1] (numeric) = 1.000199993333422 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] = 0.03000000000000002 y[1] (closed_form) = 1.000449966251012 y[1] (numeric) = 1.000449966251012 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] = 0.04000000000000003 y[1] (closed_form) = 1.000799893339022 y[1] (numeric) = 1.000799893339022 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] = 0.05000000000000004 y[1] (closed_form) = 1.001249739605034 y[1] (numeric) = 1.001249739605034 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] = 0.06000000000000005 y[1] (closed_form) = 1.001799460064796 y[1] (numeric) = 1.001799460064796 absolute error = 2.220446049250313e-16 relative error = 2.21645762227372e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07000000000000005 y[1] (closed_form) = 1.00244899974672 y[1] (numeric) = 1.002448999746721 absolute error = 2.220446049250313e-16 relative error = 2.215021462250282e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.08000000000000006 y[1] (closed_form) = 1.003198293697381 y[1] (numeric) = 1.003198293697381 absolute error = 2.220446049250313e-16 relative error = 2.213367051359958e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000007 y[1] (closed_form) = 1.004047266988006 y[1] (numeric) = 1.004047266988006 absolute error = 2.220446049250313e-16 relative error = 2.211495536371833e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1000000000000001 y[1] (closed_form) = 1.004995834721974 y[1] (numeric) = 1.004995834721975 absolute error = 4.440892098500626e-16 relative error = 4.41881642198962e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1100000000000001 y[1] (closed_form) = 1.006043902043303 y[1] (numeric) = 1.006043902043303 absolute error = 2.220446049250313e-16 relative error = 2.20710651368248e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1200000000000001 y[1] (closed_form) = 1.007191364146134 y[1] (numeric) = 1.007191364146134 absolute error = 2.220446049250313e-16 relative error = 2.204592025203413e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1300000000000001 y[1] (closed_form) = 1.008438106285212 y[1] (numeric) = 1.008438106285212 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] = 0.1400000000000001 y[1] (closed_form) = 1.009784003787363 y[1] (numeric) = 1.009784003787363 absolute error = 4.440892098500626e-16 relative error = 4.397863386471088e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1500000000000001 y[1] (closed_form) = 1.011228922063958 y[1] (numeric) = 1.011228922063958 absolute error = 4.440892098500626e-16 relative error = 4.391579395728311e-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) = 1.012772716624373 y[1] (numeric) = 1.012772716624374 absolute error = 6.661338147750939e-16 relative error = 6.577327803570325e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 1.014415233090439 y[1] (numeric) = 1.01441523309044 absolute error = 4.440892098500626e-16 relative error = 4.377785302938862e-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) = 1.016156307211879 y[1] (numeric) = 1.016156307211879 absolute error = 4.440892098500626e-16 relative error = 4.370284440476987e-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) = 1.01799576488273 y[1] (numeric) = 1.01799576488273 absolute error = 8.881784197001252e-16 relative error = 8.724775193956146e-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) = 1.019933422158758 y[1] (numeric) = 1.019933422158759 absolute error = 1.110223024625157e-15 relative error = 1.088524996342697e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000002 y[1] (closed_form) = 1.021969085275852 y[1] (numeric) = 1.021969085275853 absolute error = 1.110223024625157e-15 relative error = 1.086356760317738e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000002 y[1] (closed_form) = 1.024102550669395 y[1] (numeric) = 1.024102550669396 absolute error = 1.554312234475219e-15 relative error = 1.517731045059167e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000002 y[1] (closed_form) = 1.026333604994625 y[1] (numeric) = 1.026333604994627 absolute error = 1.77635683940025e-15 relative error = 1.730779184034954e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000002 y[1] (closed_form) = 1.028662025147971 y[1] (numeric) = 1.028662025147973 absolute error = 1.998401444325282e-15 relative error = 1.942719178379134e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000002 y[1] (closed_form) = 1.031087578289355 y[1] (numeric) = 1.031087578289357 absolute error = 1.77635683940025e-15 relative error = 1.722799184863955e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000002 y[1] (closed_form) = 1.033610021865487 y[1] (numeric) = 1.033610021865489 absolute error = 1.998401444325282e-15 relative error = 1.933419183299436e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000002 y[1] (closed_form) = 1.03622910363411 y[1] (numeric) = 1.036229103634111 absolute error = 1.554312234475219e-15 relative error = 1.499969677578216e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000002 y[1] (closed_form) = 1.038944561689229 y[1] (numeric) = 1.038944561689231 absolute error = 1.77635683940025e-15 relative error = 1.709770573813925e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000002 y[1] (closed_form) = 1.041756124487303 y[1] (numeric) = 1.041756124487305 absolute error = 1.998401444325282e-15 relative error = 1.918300643837144e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 1.044663510874394 y[1] (numeric) = 1.044663510874396 absolute error = 2.220446049250313e-15 relative error = 2.125513168725284e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 1.047666430114287 y[1] (numeric) = 1.047666430114289 absolute error = 1.998401444325282e-15 relative error = 1.907478742167278e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 1.050764581917559 y[1] (numeric) = 1.050764581917561 absolute error = 1.77635683940025e-15 relative error = 1.690537414345033e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 1.053957656471613 y[1] (numeric) = 1.053957656471615 absolute error = 1.554312234475219e-15 relative error = 1.474738785691513e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 1.057245334471654 y[1] (numeric) = 1.057245334471656 absolute error = 1.77635683940025e-15 relative error = 1.680174677988023e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000003 y[1] (closed_form) = 1.060627287152621 y[1] (numeric) = 1.060627287152623 absolute error = 1.77635683940025e-15 relative error = 1.674817215168101e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000003 y[1] (closed_form) = 1.064103176322065 y[1] (numeric) = 1.064103176322067 absolute error = 1.554312234475219e-15 relative error = 1.460678126953345e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000003 y[1] (closed_form) = 1.067672654393966 y[1] (numeric) = 1.067672654393967 absolute error = 1.110223024625157e-15 relative error = 1.039853385825774e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000003 y[1] (closed_form) = 1.07133536442349 y[1] (numeric) = 1.071335364423491 absolute error = 1.110223024625157e-15 relative error = 1.036298307227628e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000003 y[1] (closed_form) = 1.075090940142687 y[1] (numeric) = 1.075090940142688 absolute error = 1.332267629550188e-15 relative error = 1.239213893266897e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000003 y[1] (closed_form) = 1.078939005997115 y[1] (numeric) = 1.078939005997116 absolute error = 1.110223024625157e-15 relative error = 1.028995168822477e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 1.082879177183395 y[1] (numeric) = 1.082879177183396 absolute error = 8.881784197001252e-16 relative error = 8.202008482703556e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 1.086911059687692 y[1] (numeric) = 1.086911059687693 absolute error = 8.881784197001252e-16 relative error = 8.17158323842367e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 1.091034250325115 y[1] (numeric) = 1.091034250325116 absolute error = 8.881784197001252e-16 relative error = 8.140701535588447e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 1.095248336780037 y[1] (numeric) = 1.095248336780038 absolute error = 8.881784197001252e-16 relative error = 8.109379305804888e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 1.099552897647323 y[1] (numeric) = 1.099552897647324 absolute error = 8.881784197001252e-16 relative error = 8.077632477714634e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000004 y[1] (closed_form) = 1.103947502474475 y[1] (numeric) = 1.103947502474476 absolute error = 1.332267629550188e-15 relative error = 1.206821544107793e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000004 y[1] (closed_form) = 1.108431711804671 y[1] (numeric) = 1.108431711804672 absolute error = 1.332267629550188e-15 relative error = 1.201939294375729e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000004 y[1] (closed_form) = 1.113005077220716 y[1] (numeric) = 1.113005077220717 absolute error = 1.332267629550188e-15 relative error = 1.197000496059724e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000004 y[1] (closed_form) = 1.117667141389879 y[1] (numeric) = 1.11766714138988 absolute error = 1.332267629550188e-15 relative error = 1.192007512982302e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (closed_form) = 1.122417438109627 y[1] (numeric) = 1.122417438109629 absolute error = 1.332267629550188e-15 relative error = 1.186962697046109e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (closed_form) = 1.127255492354249 y[1] (numeric) = 1.12725549235425 absolute error = 1.554312234475219e-15 relative error = 1.378846450531877e-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) = 1.13218082032235 y[1] (numeric) = 1.132180820322352 absolute error = 1.332267629550188e-15 relative error = 1.176726902307769e-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) = 1.137192929485239 y[1] (numeric) = 1.137192929485241 absolute error = 1.77635683940025e-15 relative error = 1.56205406606277e-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) = 1.142291318636176 y[1] (numeric) = 1.142291318636178 absolute error = 1.554312234475219e-15 relative error = 1.360696881011904e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (closed_form) = 1.147475477940494 y[1] (numeric) = 1.147475477940496 absolute error = 1.554312234475219e-15 relative error = 1.354549412476266e-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) = 1.152744888986584 y[1] (numeric) = 1.152744888986585 absolute error = 1.110223024625157e-15 relative error = 9.631125110441305e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = 1.158099024837731 y[1] (numeric) = 1.158099024837733 absolute error = 1.332267629550188e-15 relative error = 1.150391806725561e-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) = 1.163537350084813 y[1] (numeric) = 1.163537350084815 absolute error = 1.110223024625157e-15 relative error = 9.541791026684527e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = 1.169059320899837 y[1] (numeric) = 1.169059320899838 absolute error = 1.332267629550188e-15 relative error = 1.139606524436012e-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) = 1.174664385090322 y[1] (numeric) = 1.174664385090323 absolute error = 1.554312234475219e-15 relative error = 1.323196867295594e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 1.180351982154521 y[1] (numeric) = 1.180351982154522 absolute error = 1.332267629550188e-15 relative error = 1.128703683047469e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = 1.186121543337466 y[1] (numeric) = 1.186121543337468 absolute error = 1.332267629550188e-15 relative error = 1.123213415213335e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (closed_form) = 1.191972491687848 y[1] (numeric) = 1.19197249168785 absolute error = 1.110223024625157e-15 relative error = 9.314166496015913e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = 1.197904242115708 y[1] (numeric) = 1.197904242115709 absolute error = 8.881784197001252e-16 relative error = 7.414435882883654e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = 1.203916201450944 y[1] (numeric) = 1.203916201450945 absolute error = 8.881784197001252e-16 relative error = 7.377410642283109e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = 1.210007768502635 y[1] (numeric) = 1.210007768502636 absolute error = 6.661338147750939e-16 relative error = 5.505202793858287e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (closed_form) = 1.216178334119151 y[1] (numeric) = 1.216178334119152 absolute error = 8.881784197001252e-16 relative error = 7.303027810830158e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (closed_form) = 1.222427281249072 y[1] (numeric) = 1.222427281249073 absolute error = 4.440892098500626e-16 relative error = 3.632847668421582e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (closed_form) = 1.228753985002894 y[1] (numeric) = 1.228753985002894 absolute error = 2.220446049250313e-16 relative error = 1.807071290389414e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 1.235157812715512 y[1] (numeric) = 1.235157812715512 absolute error = 2.220446049250313e-16 relative error = 1.797702306856345e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = 1.241638124009492 y[1] (numeric) = 1.241638124009492 absolute error = 2.220446049250313e-16 relative error = 1.788319806160638e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (closed_form) = 1.248194270859105 y[1] (numeric) = 1.248194270859105 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] = 0.7300000000000005 y[1] (closed_form) = 1.25482559765513 y[1] (numeric) = 1.25482559765513 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] = 0.7400000000000005 y[1] (closed_form) = 1.261531441270412 y[1] (numeric) = 1.261531441270413 absolute error = 6.661338147750939e-16 relative error = 5.280358403943311e-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) = 1.268311131126179 y[1] (numeric) = 1.26831113112618 absolute error = 6.661338147750939e-16 relative error = 5.252132528267016e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 1.275163989259095 y[1] (numeric) = 1.275163989259096 absolute error = 6.661338147750939e-16 relative error = 5.223907045572513e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = 1.282089330389057 y[1] (numeric) = 1.282089330389057 absolute error = 4.440892098500626e-16 relative error = 3.463793039407803e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (closed_form) = 1.289086461987723 y[1] (numeric) = 1.289086461987724 absolute error = 6.661338147750939e-16 relative error = 5.167487475959841e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = 1.296154684347764 y[1] (numeric) = 1.296154684347765 absolute error = 4.440892098500626e-16 relative error = 3.426205338088424e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (closed_form) = 1.303293290652835 y[1] (numeric) = 1.303293290652836 absolute error = 4.440892098500626e-16 relative error = 3.407438778631424e-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) = 1.310501567048253 y[1] (numeric) = 1.310501567048254 absolute error = 4.440892098500626e-16 relative error = 3.388696519076432e-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) = 1.317778792712387 y[1] (numeric) = 1.317778792712387 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] = 0.8300000000000006 y[1] (closed_form) = 1.325124239928734 y[1] (numeric) = 1.325124239928733 absolute error = 4.440892098500626e-16 relative error = 3.351302439942886e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (closed_form) = 1.332537174158692 y[1] (numeric) = 1.332537174158692 absolute error = 2.220446049250313e-16 relative error = 1.666329534597944e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = 1.340016854115018 y[1] (numeric) = 1.340016854115017 absolute error = 8.881784197001252e-16 relative error = 6.628113795529095e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (closed_form) = 1.347562531835949 y[1] (numeric) = 1.347562531835948 absolute error = 8.881784197001252e-16 relative error = 6.59099966581923e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (closed_form) = 1.355173452759999 y[1] (numeric) = 1.355173452759998 absolute error = 1.110223024625157e-15 relative error = 8.19247914253362e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (closed_form) = 1.36284885580142 y[1] (numeric) = 1.362848855801419 absolute error = 1.554312234475219e-15 relative error = 1.140487610096139e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (closed_form) = 1.370587973426304 y[1] (numeric) = 1.370587973426302 absolute error = 1.554312234475219e-15 relative error = 1.134047769724425e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = 1.378390031729336 y[1] (numeric) = 1.378390031729335 absolute error = 1.332267629550188e-15 relative error = 9.665389322924203e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = 1.386254250511189 y[1] (numeric) = 1.386254250511188 absolute error = 1.332267629550188e-15 relative error = 9.610557580320541e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (closed_form) = 1.394179843356538 y[1] (numeric) = 1.394179843356536 absolute error = 1.77635683940025e-15 relative error = 1.274123168445477e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = 1.402166017712702 y[1] (numeric) = 1.402166017712701 absolute error = 1.332267629550188e-15 relative error = 9.501497060408461e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = 1.410211974968902 y[1] (numeric) = 1.410211974968901 absolute error = 1.77635683940025e-15 relative error = 1.25963817562918e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = 1.418316910536117 y[1] (numeric) = 1.418316910536116 absolute error = 1.554312234475219e-15 relative error = 1.09588500491593e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = 1.426480013927544 y[1] (numeric) = 1.426480013927543 absolute error = 1.332267629550188e-15 relative error = 9.339546411744248e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = 1.434700468839646 y[1] (numeric) = 1.434700468839645 absolute error = 1.77635683940025e-15 relative error = 1.238137770204347e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 1.442977453233783 y[1] (numeric) = 1.442977453233782 absolute error = 1.77635683940025e-15 relative error = 1.231035755561771e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = 1.451310139418413 y[1] (numeric) = 1.451310139418411 absolute error = 1.998401444325282e-15 relative error = 1.376963744721101e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (closed_form) = 1.459697694131861 y[1] (numeric) = 1.459697694131859 absolute error = 1.554312234475219e-15 relative error = 1.064817900804885e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 1.468139278625644 y[1] (numeric) = 1.468139278625644 absolute error = 6.661338147750939e-16 relative error = 4.537265806270613e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = 1.476634048748349 y[1] (numeric) = 1.476634048748349 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] = 1.029999999999997 y[1] (closed_form) = 1.485181155030042 y[1] (numeric) = 1.485181155030043 absolute error = 8.881784197001252e-16 relative error = 5.980269926614839e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 1.493779742767218 y[1] (numeric) = 1.49377974276722 absolute error = 1.77635683940025e-15 relative error = 1.189169185083177e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = 1.502428952108269 y[1] (numeric) = 1.502428952108271 absolute error = 2.664535259100376e-15 relative error = 1.773485032594315e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = 1.511127918139467 y[1] (numeric) = 1.511127918139471 absolute error = 3.33066907387547e-15 relative error = 2.204094725465902e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = 1.51987577097146 y[1] (numeric) = 1.519875770971464 absolute error = 4.218847493575595e-15 relative error = 2.775784425380393e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = 1.528671635826253 y[1] (numeric) = 1.528671635826258 absolute error = 4.884981308350689e-15 relative error = 3.1955726749063e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = 1.537514633124691 y[1] (numeric) = 1.537514633124697 absolute error = 5.995204332975845e-15 relative error = 3.899282780022582e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y[1] (closed_form) = 1.546403878574413 y[1] (numeric) = 1.546403878574421 absolute error = 7.105427357601002e-15 relative error = 4.594806994503465e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = 1.555338483258283 y[1] (numeric) = 1.555338483258291 absolute error = 7.993605777301127e-15 relative error = 5.139463765183319e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 1.564317553723277 y[1] (numeric) = 1.564317553723285 absolute error = 8.881784197001252e-15 relative error = 5.677737346781967e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 1.57334019206983 y[1] (numeric) = 1.57334019206984 absolute error = 9.769962616701378e-15 relative error = 6.209694931805158e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 1.582405496041629 y[1] (numeric) = 1.582405496041639 absolute error = 1.06581410364015e-14 relative error = 6.735404460527176e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 1.591512559115828 y[1] (numeric) = 1.59151255911584 absolute error = 1.176836406102666e-14 relative error = 7.394452524813645e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 1.600660470593711 y[1] (numeric) = 1.600660470593724 absolute error = 1.243449787580175e-14 relative error = 7.76835444133233e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 1.609848315691753 y[1] (numeric) = 1.609848315691766 absolute error = 1.332267629550188e-14 relative error = 8.275733909611921e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = 1.619075175633101 y[1] (numeric) = 1.619075175633115 absolute error = 1.398881011027697e-14 relative error = 8.640000366139259e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = 1.628340127739448 y[1] (numeric) = 1.628340127739464 absolute error = 1.532107773982716e-14 relative error = 9.409015646563183e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = 1.637642245523307 y[1] (numeric) = 1.637642245523323 absolute error = 1.598721155460225e-14 relative error = 9.762334599211295e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = 1.646980598780649 y[1] (numeric) = 1.646980598780666 absolute error = 1.709743457922741e-14 relative error = 1.038107831499994e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 1.656354253683931 y[1] (numeric) = 1.656354253683949 absolute error = 1.820765760385257e-14 relative error = 1.099261076750734e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 1.665762272875474 y[1] (numeric) = 1.665762272875493 absolute error = 1.909583602355269e-14 relative error = 1.146372224566538e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 1.675203715561199 y[1] (numeric) = 1.675203715561219 absolute error = 1.998401444325282e-14 relative error = 1.192930403485769e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = 1.684677637604706 y[1] (numeric) = 1.684677637604727 absolute error = 2.109423746787797e-14 relative error = 1.252123076665872e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = 1.694183091621684 y[1] (numeric) = 1.694183091621706 absolute error = 2.220446049250313e-14 relative error = 1.310629329398446e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = 1.703719127074653 y[1] (numeric) = 1.703719127074677 absolute error = 2.331468351712829e-14 relative error = 1.368458165822229e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = 1.713284790368016 y[1] (numeric) = 1.71328479036804 absolute error = 2.420286193682841e-14 relative error = 1.412658425084694e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = 1.722879124943412 y[1] (numeric) = 1.722879124943437 absolute error = 2.509104035652854e-14 relative error = 1.45634362813193e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y[1] (closed_form) = 1.732501171375382 y[1] (numeric) = 1.732501171375407 absolute error = 2.575717417130363e-14 relative error = 1.48670457468469e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y[1] (closed_form) = 1.742149967467298 y[1] (numeric) = 1.742149967467325 absolute error = 2.686739719592879e-14 relative error = 1.542197726811548e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = 1.751824548347594 y[1] (numeric) = 1.751824548347622 absolute error = 2.797762022055394e-14 relative error = 1.597056066313479e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = 1.761523946566242 y[1] (numeric) = 1.761523946566272 absolute error = 2.930988785010413e-14 relative error = 1.663893806680188e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = 1.771247192191505 y[1] (numeric) = 1.771247192191535 absolute error = 3.042011087472929e-14 relative error = 1.717440174857328e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y[1] (closed_form) = 1.780993312906922 y[1] (numeric) = 1.780993312906953 absolute error = 3.153033389935445e-14 relative error = 1.770379128930637e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y[1] (closed_form) = 1.790761334108542 y[1] (numeric) = 1.790761334108575 absolute error = 3.26405569239796e-14 relative error = 1.822719549628224e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y[1] (closed_form) = 1.800550279002388 y[1] (numeric) = 1.800550279002421 absolute error = 3.33066907387547e-14 relative error = 1.849806202424327e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y[1] (closed_form) = 1.810359168702125 y[1] (numeric) = 1.810359168702159 absolute error = 3.419486915845482e-14 relative error = 1.888844476257695e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y[1] (closed_form) = 1.820187022326959 y[1] (numeric) = 1.820187022326994 absolute error = 3.508304757815495e-14 relative error = 1.927441913815217e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y[1] (closed_form) = 1.830032857099716 y[1] (numeric) = 1.830032857099753 absolute error = 3.641531520770513e-14 relative error = 1.989872207290151e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y[1] (closed_form) = 1.839895688445125 y[1] (numeric) = 1.839895688445162 absolute error = 3.730349362740526e-14 relative error = 2.027478724021035e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = 1.849774530088269 y[1] (numeric) = 1.849774530088308 absolute error = 3.863576125695545e-14 relative error = 2.088674085868822e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = 1.859668394153217 y[1] (numeric) = 1.859668394153257 absolute error = 3.952393967665557e-14 relative error = 2.12532190152387e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = 1.869576291261807 y[1] (numeric) = 1.869576291261848 absolute error = 4.063416270128073e-14 relative error = 2.173442340449027e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y[1] (closed_form) = 1.879497230632585 y[1] (numeric) = 1.879497230632627 absolute error = 4.174438572590589e-14 relative error = 2.221040023126606e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y[1] (closed_form) = 1.889430220179881 y[1] (numeric) = 1.889430220179923 absolute error = 4.263256414560601e-14 relative error = 2.256371454752493e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y[1] (closed_form) = 1.899374266613018 y[1] (numeric) = 1.899374266613061 absolute error = 4.329869796038111e-14 relative error = 2.279629598098734e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y[1] (closed_form) = 1.909328375535638 y[1] (numeric) = 1.909328375535683 absolute error = 4.485301019485632e-14 relative error = 2.349151186855083e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y[1] (closed_form) = 1.919291551545146 y[1] (numeric) = 1.919291551545192 absolute error = 4.596323321948148e-14 relative error = 2.394802039454521e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y[1] (closed_form) = 1.929262798332243 y[1] (numeric) = 1.92926279833229 absolute error = 4.685141163918161e-14 relative error = 2.428461880863636e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = 1.939241118780559 y[1] (numeric) = 1.939241118780607 absolute error = 4.818367926873179e-14 relative error = 2.484666749384463e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = 1.949225515066364 y[1] (numeric) = 1.949225515066414 absolute error = 4.973799150320701e-14 relative error = 2.551679686047697e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = 1.959214988758351 y[1] (numeric) = 1.959214988758402 absolute error = 5.084821452783217e-14 relative error = 2.595336133073233e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = 1.969208540917475 y[1] (numeric) = 1.969208540917527 absolute error = 5.195843755245733e-14 relative error = 2.638544190360323e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y[1] (closed_form) = 1.979205172196848 y[1] (numeric) = 1.979205172196901 absolute error = 5.306866057708248e-14 relative error = 2.681311736780586e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y[1] (closed_form) = 1.989203882941672 y[1] (numeric) = 1.989203882941726 absolute error = 5.395683899678261e-14 relative error = 2.712484097758257e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y[1] (closed_form) = 1.999203673289205 y[1] (numeric) = 1.99920367328926 absolute error = 5.506706202140776e-14 relative error = 2.754449822053812e-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) = 2.009203543268745 y[1] (numeric) = 2.009203543268802 absolute error = 5.684341886080801e-14 relative error = 2.829151832388781e-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) = 2.019202492901628 y[1] (numeric) = 2.019202492901685 absolute error = 5.684341886080801e-14 relative error = 2.815142070230067e-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) = 2.029199522301223 y[1] (numeric) = 2.029199522301282 absolute error = 5.861977570020827e-14 relative error = 2.888812808004717e-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) = 2.039193631772921 y[1] (numeric) = 2.039193631772981 absolute error = 5.995204332975845e-14 relative error = 2.939987767499783e-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) = 2.049183821914103 y[1] (numeric) = 2.049183821914164 absolute error = 6.084022174945858e-14 relative error = 2.96899775895307e-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) = 2.05916909371408 y[1] (numeric) = 2.059169093714142 absolute error = 6.217248937900877e-14 relative error = 3.019299851032125e-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) = 2.069148448653992 y[1] (numeric) = 2.069148448654056 absolute error = 6.350475700855895e-14 relative error = 3.069125226363996e-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) = 2.079120888806663 y[1] (numeric) = 2.079120888806728 absolute error = 6.439293542825908e-14 relative error = 3.097123201201551e-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) = 2.089085416936387 y[1] (numeric) = 2.089085416936454 absolute error = 6.616929226765933e-14 relative error = 3.16738088980084e-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) = 2.099041036598655 y[1] (numeric) = 2.099041036598723 absolute error = 6.750155989720952e-14 relative error = 3.215828500741983e-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) = 2.108986752239797 y[1] (numeric) = 2.108986752239866 absolute error = 6.883382752675971e-14 relative error = 3.263834040382494e-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) = 2.118921569296537 y[1] (numeric) = 2.118921569296607 absolute error = 6.927791673660977e-14 relative error = 3.269489429927763e-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) = 2.128844494295449 y[1] (numeric) = 2.128844494295519 absolute error = 6.972200594645983e-14 relative error = 3.275110330195097e-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) = 2.138754534952301 y[1] (numeric) = 2.138754534952372 absolute error = 7.149836278586008e-14 relative error = 3.342990587157523e-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) = 2.148650700271286 y[1] (numeric) = 2.148650700271358 absolute error = 7.238654120556021e-14 relative error = 3.368930147483757e-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) = 2.158532000644119 y[1] (numeric) = 2.158532000644193 absolute error = 7.416289804496046e-14 relative error = 3.435802574287979e-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) = 2.168397447948997 y[1] (numeric) = 2.168397447949073 absolute error = 7.549516567451064e-14 relative error = 3.48161107392552e-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) = 2.178246055649411 y[1] (numeric) = 2.178246055649488 absolute error = 7.638334409421077e-14 relative error = 3.506644435145699e-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) = 2.188076838892798 y[1] (numeric) = 2.188076838892875 absolute error = 7.682743330406083e-14 relative error = 3.511185344977955e-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) = 2.197888814609026 y[1] (numeric) = 2.197888814609104 absolute error = 7.815970093361102e-14 relative error = 3.556126243242861e-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) = 2.2076810016087 y[1] (numeric) = 2.207681001608779 absolute error = 7.904787935331115e-14 relative error = 3.580584300707859e-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) = 2.21745242068128 y[1] (numeric) = 2.217452420681361 absolute error = 8.038014698286133e-14 relative error = 3.62488711068559e-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) = 2.227202094693002 y[1] (numeric) = 2.227202094693083 absolute error = 8.126832540256146e-14 relative error = 3.648897672833928e-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) = 2.236929048684589 y[1] (numeric) = 2.23692904868467 absolute error = 8.171241461241152e-14 relative error = 3.652883611148148e-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) = 2.246632309968747 y[1] (numeric) = 2.24663230996883 absolute error = 8.260059303211165e-14 relative error = 3.676640483874315e-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) = 2.256310908227435 y[1] (numeric) = 2.256310908227519 absolute error = 8.348877145181177e-14 relative error = 3.700233471698313e-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) = 2.265963875608892 y[1] (numeric) = 2.265963875608977 absolute error = 8.526512829121202e-14 relative error = 3.762863530571521e-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) = 2.275590246824423 y[1] (numeric) = 2.27559024682451 absolute error = 8.659739592076221e-14 relative error = 3.805491609994748e-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) = 2.285189059244931 y[1] (numeric) = 2.285189059245018 absolute error = 8.704148513061227e-14 relative error = 3.808940217811668e-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) = 2.29475935299717 y[1] (numeric) = 2.294759352997258 absolute error = 8.79296635503124e-14 relative error = 3.831759676040454e-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) = 2.304300171059741 y[1] (numeric) = 2.304300171059831 absolute error = 8.970602038971265e-14 relative error = 3.892983280405568e-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) = 2.31381055935879 y[1] (numeric) = 2.31381055935888 absolute error = 9.015010959956271e-14 relative error = 3.896175044881175e-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) = 2.32328956686341 y[1] (numeric) = 2.323289566863501 absolute error = 9.103828801926284e-14 relative error = 3.918508020598154e-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) = 2.332736245680751 y[1] (numeric) = 2.332736245680844 absolute error = 9.237055564881302e-14 relative error = 3.959751378658626e-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) = 2.342149651150804 y[1] (numeric) = 2.342149651150897 absolute error = 9.325873406851315e-14 relative error = 3.981758126458356e-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) = 2.351528841940865 y[1] (numeric) = 2.351528841940959 absolute error = 9.414691248821327e-14 relative error = 4.00364693849589e-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) = 2.360872880139671 y[1] (numeric) = 2.360872880139767 absolute error = 9.547918011776346e-14 relative error = 4.044232153326054e-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) = 2.370180831351191 y[1] (numeric) = 2.370180831351287 absolute error = 9.636735853746359e-14 relative error = 4.065823048721838e-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) = 2.379451764788057 y[1] (numeric) = 2.379451764788155 absolute error = 9.769962616701378e-14 relative error = 4.105972124033205e-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) = 2.388684753364654 y[1] (numeric) = 2.388684753364753 absolute error = 9.85878045867139e-14 relative error = 4.127284039798264e-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) = 2.397878873789818 y[1] (numeric) = 2.397878873789917 absolute error = 9.947598300641403e-14 relative error = 4.148499079488259e-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) = 2.407033206659166 y[1] (numeric) = 2.407033206659267 absolute error = 1.008082506359642e-13 relative error = 4.188070623914686e-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) = 2.416146836547043 y[1] (numeric) = 2.416146836547144 absolute error = 1.016964290556643e-13 relative error = 4.209033470871351e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.00999999999989 y[1] (closed_form) = 2.425218852098053 y[1] (numeric) = 2.425218852098155 absolute error = 1.021405182655144e-13 relative error = 4.211600044967192e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999889 y[1] (closed_form) = 2.4342483461182 y[1] (numeric) = 2.434248346118304 absolute error = 1.039168751049147e-13 relative error = 4.268951246105468e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999887 y[1] (closed_form) = 2.443234415665608 y[1] (numeric) = 2.443234415665713 absolute error = 1.048050535246148e-13 relative error = 4.289602866291602e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999886 y[1] (closed_form) = 2.452176162140811 y[1] (numeric) = 2.452176162140916 absolute error = 1.056932319443149e-13 relative error = 4.310181037403205e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999885 y[1] (closed_form) = 2.461072691376611 y[1] (numeric) = 2.461072691376718 absolute error = 1.06581410364015e-13 relative error = 4.330689245281832e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999884 y[1] (closed_form) = 2.4699231137275 y[1] (numeric) = 2.469923113727607 absolute error = 1.074695887837152e-13 relative error = 4.351130939518467e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999883 y[1] (closed_form) = 2.478726544158617 y[1] (numeric) = 2.478726544158726 absolute error = 1.083577672034153e-13 relative error = 4.371509534150585e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999882 y[1] (closed_form) = 2.487482102334256 y[1] (numeric) = 2.487482102334365 absolute error = 1.092459456231154e-13 relative error = 4.391828408357145e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.089999999999881 y[1] (closed_form) = 2.496188912705895 y[1] (numeric) = 2.496188912706005 absolute error = 1.096900348329655e-13 relative error = 4.394300218009554e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09999999999988 y[1] (closed_form) = 2.504846104599753 y[1] (numeric) = 2.504846104599864 absolute error = 1.105782132526656e-13 relative error = 4.414571140702265e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999879 y[1] (closed_form) = 2.513452812303855 y[1] (numeric) = 2.513452812303967 absolute error = 1.119104808822158e-13 relative error = 4.452459991864241e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999878 y[1] (closed_form) = 2.522008175154603 y[1] (numeric) = 2.522008175154716 absolute error = 1.13242748511766e-13 relative error = 4.490181658702356e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y[1] (closed_form) = 2.53051133762284 y[1] (numeric) = 2.530511337622954 absolute error = 1.13686837721616e-13 relative error = 4.492642891235308e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999875 y[1] (closed_form) = 2.538961449399406 y[1] (numeric) = 2.538961449399522 absolute error = 1.154631945610163e-13 relative error = 4.547654498193709e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999874 y[1] (closed_form) = 2.547357665480166 y[1] (numeric) = 2.547357665480282 absolute error = 1.159072837708663e-13 relative error = 4.55009853314094e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999873 y[1] (closed_form) = 2.555699146250507 y[1] (numeric) = 2.555699146250624 absolute error = 1.167954621905665e-13 relative error = 4.570000438506947e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999872 y[1] (closed_form) = 2.563985057569305 y[1] (numeric) = 2.563985057569422 absolute error = 1.176836406102666e-13 relative error = 4.589872326394617e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.179999999999871 y[1] (closed_form) = 2.572214570852331 y[1] (numeric) = 2.57221457085245 absolute error = 1.190159082398168e-13 relative error = 4.626982118384454e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18999999999987 y[1] (closed_form) = 2.580386863155116 y[1] (numeric) = 2.580386863155235 absolute error = 1.190159082398168e-13 relative error = 4.6123280946444e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999869 y[1] (closed_form) = 2.58850111725524 y[1] (numeric) = 2.58850111725536 absolute error = 1.20348175869367e-13 relative error = 4.649338378380928e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999868 y[1] (closed_form) = 2.596556521734054 y[1] (numeric) = 2.596556521734175 absolute error = 1.20792265079217e-13 relative error = 4.652017549710358e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999867 y[1] (closed_form) = 2.604552271057823 y[1] (numeric) = 2.604552271057945 absolute error = 1.221245327087672e-13 relative error = 4.688887762623673e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999865 y[1] (closed_form) = 2.612487565658279 y[1] (numeric) = 2.612487565658402 absolute error = 1.230127111284673e-13 relative error = 4.708642932716556e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999864 y[1] (closed_form) = 2.620361612012573 y[1] (numeric) = 2.620361612012697 absolute error = 1.239008895481675e-13 relative error = 4.728388974260892e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999863 y[1] (closed_form) = 2.628173622722633 y[1] (numeric) = 2.628173622722756 absolute error = 1.234568003383174e-13 relative error = 4.697437006099447e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999862 y[1] (closed_form) = 2.635922816593896 y[1] (numeric) = 2.635922816594021 absolute error = 1.243449787580175e-13 relative error = 4.717322448716249e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.269999999999861 y[1] (closed_form) = 2.643608418713434 y[1] (numeric) = 2.643608418713559 absolute error = 1.247890679678676e-13 relative error = 4.72040666403229e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27999999999986 y[1] (closed_form) = 2.651229660527439 y[1] (numeric) = 2.651229660527564 absolute error = 1.252331571777177e-13 relative error = 4.723587663575082e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999859 y[1] (closed_form) = 2.658785779918082 y[1] (numeric) = 2.658785779918207 absolute error = 1.256772463875677e-13 relative error = 4.726866200985921e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999858 y[1] (closed_form) = 2.666276021279718 y[1] (numeric) = 2.666276021279845 absolute error = 1.270095140171179e-13 relative error = 4.763554598377922e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999857 y[1] (closed_form) = 2.673699635594455 y[1] (numeric) = 2.673699635594582 absolute error = 1.27453603226968e-13 relative error = 4.766937973518132e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999856 y[1] (closed_form) = 2.681055880507047 y[1] (numeric) = 2.681055880507175 absolute error = 1.283417816466681e-13 relative error = 4.78698644738415e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999854 y[1] (closed_form) = 2.688344020399133 y[1] (numeric) = 2.688344020399261 absolute error = 1.283417816466681e-13 relative error = 4.774008857230016e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999853 y[1] (closed_form) = 2.695563326462797 y[1] (numeric) = 2.695563326462926 absolute error = 1.296740492762183e-13 relative error = 4.810647481481381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999852 y[1] (closed_form) = 2.702713076773449 y[1] (numeric) = 2.70271307677358 absolute error = 1.310063169057685e-13 relative error = 4.84721511993298e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999851 y[1] (closed_form) = 2.709792556362016 y[1] (numeric) = 2.709792556362147 absolute error = 1.314504061156185e-13 relative error = 4.850939818511235e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36999999999985 y[1] (closed_form) = 2.716801057286438 y[1] (numeric) = 2.71680105728657 absolute error = 1.323385845353187e-13 relative error = 4.871117970908752e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999849 y[1] (closed_form) = 2.723737878702464 y[1] (numeric) = 2.723737878702597 absolute error = 1.327826737451687e-13 relative error = 4.875016600658496e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999848 y[1] (closed_form) = 2.730602326933733 y[1] (numeric) = 2.730602326933867 absolute error = 1.336708521648688e-13 relative error = 4.895288151130064e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999847 y[1] (closed_form) = 2.737393715541142 y[1] (numeric) = 2.737393715541276 absolute error = 1.34559030584569e-13 relative error = 4.915589227104244e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999846 y[1] (closed_form) = 2.744111365391489 y[1] (numeric) = 2.744111365391625 absolute error = 1.354472090042691e-13 relative error = 4.935922452438278e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y[1] (closed_form) = 2.750754604725388 y[1] (numeric) = 2.750754604725524 absolute error = 1.363353874239692e-13 relative error = 4.956290437168232e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y[1] (closed_form) = 2.757322769224441 y[1] (numeric) = 2.757322769224579 absolute error = 1.372235658436693e-13 relative error = 4.976695778066872e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y[1] (closed_form) = 2.763815202077672 y[1] (numeric) = 2.76381520207781 absolute error = 1.381117442633695e-13 relative error = 4.997141059197637e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y[1] (closed_form) = 2.770231254047206 y[1] (numeric) = 2.770231254047345 absolute error = 1.385558334732195e-13 relative error = 5.001598089357866e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y[1] (closed_form) = 2.776570283533192 y[1] (numeric) = 2.776570283533332 absolute error = 1.394440118929197e-13 relative error = 5.022167553975144e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y[1] (closed_form) = 2.782831656637965 y[1] (numeric) = 2.782831656638105 absolute error = 1.403321903126198e-13 relative error = 5.042784028199534e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999838 y[1] (closed_form) = 2.789014747229432 y[1] (numeric) = 2.789014747229573 absolute error = 1.412203687323199e-13 relative error = 5.063450054274767e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999837 y[1] (closed_form) = 2.795118937003685 y[1] (numeric) = 2.795118937003827 absolute error = 1.4166445794217e-13 relative error = 5.068280138877797e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999836 y[1] (closed_form) = 2.801143615546835 y[1] (numeric) = 2.801143615546978 absolute error = 1.425526363618701e-13 relative error = 5.089087027551108e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999835 y[1] (closed_form) = 2.807088180396049 y[1] (numeric) = 2.807088180396192 absolute error = 1.429967255717202e-13 relative error = 5.094130158445715e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y[1] (closed_form) = 2.812952037099793 y[1] (numeric) = 2.812952037099937 absolute error = 1.443289932012704e-13 relative error = 5.130872880082103e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999832 y[1] (closed_form) = 2.818734599277286 y[1] (numeric) = 2.818734599277431 absolute error = 1.456612608308205e-13 relative error = 5.167611766931431e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999831 y[1] (closed_form) = 2.824435288677127 y[1] (numeric) = 2.824435288677273 absolute error = 1.461053500406706e-13 relative error = 5.172904850268372e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54999999999983 y[1] (closed_form) = 2.830053535235128 y[1] (numeric) = 2.830053535235275 absolute error = 1.474376176702208e-13 relative error = 5.20971125933034e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999829 y[1] (closed_form) = 2.835588777131314 y[1] (numeric) = 2.835588777131463 absolute error = 1.49213974509621e-13 relative error = 5.262186665182695e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999828 y[1] (closed_form) = 2.841040460846108 y[1] (numeric) = 2.841040460846258 absolute error = 1.501021529293212e-13 relative error = 5.283351469222592e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999827 y[1] (closed_form) = 2.846408041215684 y[1] (numeric) = 2.846408041215835 absolute error = 1.509903313490213e-13 relative error = 5.304591933506984e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999826 y[1] (closed_form) = 2.851690981486474 y[1] (numeric) = 2.851690981486627 absolute error = 1.523225989785715e-13 relative error = 5.341483350316299e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999825 y[1] (closed_form) = 2.856888753368857 y[1] (numeric) = 2.85688875336901 absolute error = 1.536548666081217e-13 relative error = 5.378398666273971e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999824 y[1] (closed_form) = 2.862000837089974 y[1] (numeric) = 2.862000837090128 absolute error = 1.536548666081217e-13 relative error = 5.368791812246808e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y[1] (closed_form) = 2.867026721445714 y[1] (numeric) = 2.867026721445869 absolute error = 1.549871342376719e-13 relative error = 5.405848961167643e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999821 y[1] (closed_form) = 2.871965903851829 y[1] (numeric) = 2.871965903851985 absolute error = 1.55875312657372e-13 relative error = 5.427477827933639e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999982 y[1] (closed_form) = 2.876817890394195 y[1] (numeric) = 2.876817890394352 absolute error = 1.567634910770721e-13 relative error = 5.449197587393746e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999819 y[1] (closed_form) = 2.881582195878201 y[1] (numeric) = 2.881582195878358 absolute error = 1.572075802869222e-13 relative error = 5.455599375641306e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999818 y[1] (closed_form) = 2.886258343877268 y[1] (numeric) = 2.886258343877425 absolute error = 1.572075802869222e-13 relative error = 5.446760530650789e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999817 y[1] (closed_form) = 2.890845866780493 y[1] (numeric) = 2.890845866780651 absolute error = 1.576516694967722e-13 relative error = 5.453478904164038e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999816 y[1] (closed_form) = 2.89534430583941 y[1] (numeric) = 2.895344305839568 absolute error = 1.585398479164724e-13 relative error = 5.475682031899448e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999815 y[1] (closed_form) = 2.899753211213861 y[1] (numeric) = 2.899753211214019 absolute error = 1.585398479164724e-13 relative error = 5.4673565772208e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999814 y[1] (closed_form) = 2.904072142016981 y[1] (numeric) = 2.904072142017141 absolute error = 1.594280263361725e-13 relative error = 5.489809431023433e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999813 y[1] (closed_form) = 2.908300666359292 y[1] (numeric) = 2.908300666359452 absolute error = 1.598721155460225e-13 relative error = 5.497097236034946e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y[1] (closed_form) = 2.912438361391881 y[1] (numeric) = 2.912438361392041 absolute error = 1.603162047558726e-13 relative error = 5.504535542488049e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999981 y[1] (closed_form) = 2.916484813348693 y[1] (numeric) = 2.916484813348854 absolute error = 1.607602939657227e-13 relative error = 5.512125186797682e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999809 y[1] (closed_form) = 2.920439617587906 y[1] (numeric) = 2.920439617588067 absolute error = 1.607602939657227e-13 relative error = 5.504660770849981e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999808 y[1] (closed_form) = 2.92430237863239 y[1] (numeric) = 2.924302378632552 absolute error = 1.620925615952729e-13 relative error = 5.542948047358862e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999807 y[1] (closed_form) = 2.928072710209261 y[1] (numeric) = 2.928072710209423 absolute error = 1.620925615952729e-13 relative error = 5.535810672669005e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999806 y[1] (closed_form) = 2.931750235288502 y[1] (numeric) = 2.931750235288664 absolute error = 1.625366508051229e-13 relative error = 5.54401424953338e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999805 y[1] (closed_form) = 2.93533458612067 y[1] (numeric) = 2.935334586120833 absolute error = 1.63424829224823e-13 relative error = 5.567502593999168e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999804 y[1] (closed_form) = 2.938825404273669 y[1] (numeric) = 2.938825404273833 absolute error = 1.643130076445232e-13 relative error = 5.591111585110758e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999803 y[1] (closed_form) = 2.942222340668592 y[1] (numeric) = 2.942222340668756 absolute error = 1.643130076445232e-13 relative error = 5.584656379408247e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999802 y[1] (closed_form) = 2.945525055614631 y[1] (numeric) = 2.945525055614795 absolute error = 1.643130076445232e-13 relative error = 5.578394498166529e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y[1] (closed_form) = 2.948733218843044 y[1] (numeric) = 2.948733218843208 absolute error = 1.643130076445232e-13 relative error = 5.572325315648342e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999799 y[1] (closed_form) = 2.951846509540181 y[1] (numeric) = 2.951846509540346 absolute error = 1.647570968543732e-13 relative error = 5.581492679984841e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999798 y[1] (closed_form) = 2.954864616379567 y[1] (numeric) = 2.954864616379731 absolute error = 1.643130076445232e-13 relative error = 5.560762639807399e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999797 y[1] (closed_form) = 2.957787237553032 y[1] (numeric) = 2.957787237553197 absolute error = 1.647570968543732e-13 relative error = 5.570282228639144e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999796 y[1] (closed_form) = 2.960614080800895 y[1] (numeric) = 2.960614080801061 absolute error = 1.656452752740734e-13 relative error = 5.594963435060862e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999795 y[1] (closed_form) = 2.963344863441188 y[1] (numeric) = 2.963344863441354 absolute error = 1.656452752740734e-13 relative error = 5.589807562313809e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999794 y[1] (closed_form) = 2.965979312397922 y[1] (numeric) = 2.965979312398087 absolute error = 1.652011860642233e-13 relative error = 5.569869802317069e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999793 y[1] (closed_form) = 2.968517164228395 y[1] (numeric) = 2.968517164228561 absolute error = 1.665334536937735e-13 relative error = 5.60998789902771e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999792 y[1] (closed_form) = 2.970958165149541 y[1] (numeric) = 2.970958165149708 absolute error = 1.669775429036235e-13 relative error = 5.62032629278773e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.909999999999791 y[1] (closed_form) = 2.9733020710633 y[1] (numeric) = 2.973302071063468 absolute error = 1.674216321134736e-13 relative error = 5.630831584279661e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y[1] (closed_form) = 2.975548647581037 y[1] (numeric) = 2.975548647581204 absolute error = 1.674216321134736e-13 relative error = 5.626580235869393e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999788 y[1] (closed_form) = 2.977697670046969 y[1] (numeric) = 2.977697670047136 absolute error = 1.674216321134736e-13 relative error = 5.622519498792259e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999787 y[1] (closed_form) = 2.979748923560642 y[1] (numeric) = 2.979748923560809 absolute error = 1.678657213233237e-13 relative error = 5.633552545183339e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999786 y[1] (closed_form) = 2.981702202998413 y[1] (numeric) = 2.981702202998581 absolute error = 1.683098105331737e-13 relative error = 5.644755883532588e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999785 y[1] (closed_form) = 2.983557313033967 y[1] (numeric) = 2.983557313034135 absolute error = 1.678657213233237e-13 relative error = 5.626361544656291e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999784 y[1] (closed_form) = 2.985314068157847 y[1] (numeric) = 2.985314068158015 absolute error = 1.678657213233237e-13 relative error = 5.623050623511411e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999783 y[1] (closed_form) = 2.986972292696003 y[1] (numeric) = 2.986972292696171 absolute error = 1.678657213233237e-13 relative error = 5.619928974025073e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999782 y[1] (closed_form) = 2.988531820827363 y[1] (numeric) = 2.988531820827531 absolute error = 1.678657213233237e-13 relative error = 5.61699628404327e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.999999999999781 y[1] (closed_form) = 2.989992496600415 y[1] (numeric) = 2.989992496600582 absolute error = 1.674216321134736e-13 relative error = 5.599399741097343e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.00999999999978 y[1] (closed_form) = 2.991354173948797 y[1] (numeric) = 2.991354173948965 absolute error = 1.678657213233237e-13 relative error = 5.611696628411244e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y[1] (closed_form) = 2.99261671670591 y[1] (numeric) = 2.992616716706078 absolute error = 1.678657213233237e-13 relative error = 5.609329132803215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999777 y[1] (closed_form) = 2.993779998618531 y[1] (numeric) = 2.993779998618699 absolute error = 1.683098105331737e-13 relative error = 5.62198326566547e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999776 y[1] (closed_form) = 2.994843903359437 y[1] (numeric) = 2.994843903359605 absolute error = 1.687538997430238e-13 relative error = 5.634814540875596e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999775 y[1] (closed_form) = 2.995808324539041 y[1] (numeric) = 2.99580832453921 absolute error = 1.687538997430238e-13 relative error = 5.633000561509209e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999774 y[1] (closed_form) = 2.996673165716028 y[1] (numeric) = 2.996673165716197 absolute error = 1.691979889528739e-13 relative error = 5.646194282666976e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999773 y[1] (closed_form) = 2.997438340407002 y[1] (numeric) = 2.997438340407171 absolute error = 1.687538997430238e-13 relative error = 5.62993731908126e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999772 y[1] (closed_form) = 2.998103772095131 y[1] (numeric) = 2.9981037720953 absolute error = 1.687538997430238e-13 relative error = 5.628687749693714e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.089999999999771 y[1] (closed_form) = 2.998669394237802 y[1] (numeric) = 2.99866939423797 absolute error = 1.683098105331737e-13 relative error = 5.612816499764707e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09999999999977 y[1] (closed_form) = 2.99913515027327 y[1] (numeric) = 2.999135150273438 absolute error = 1.683098105331737e-13 relative error = 5.611944847428365e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999769 y[1] (closed_form) = 2.999500993626321 y[1] (numeric) = 2.999500993626489 absolute error = 1.683098105331737e-13 relative error = 5.611260369335349e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y[1] (closed_form) = 2.999766887712923 y[1] (numeric) = 2.999766887713092 absolute error = 1.683098105331737e-13 relative error = 5.610762997037286e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999766 y[1] (closed_form) = 2.999932805943891 y[1] (numeric) = 2.99993280594406 absolute error = 1.687538997430238e-13 relative error = 5.62525598602291e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999765 y[1] (closed_form) = 2.999998731727539 y[1] (numeric) = 2.999998731727707 absolute error = 1.678657213233237e-13 relative error = 5.595526409661472e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999764 y[1] (closed_form) = 2.999964658471344 y[1] (numeric) = 2.999964658471512 absolute error = 1.678657213233237e-13 relative error = 5.595589963011797e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999763 y[1] (closed_form) = 2.999830589582603 y[1] (numeric) = 2.999830589582771 absolute error = 1.683098105331737e-13 relative error = 5.610643851611381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999762 y[1] (closed_form) = 2.999596538468093 y[1] (numeric) = 2.999596538468261 absolute error = 1.678657213233237e-13 relative error = 5.596276671563751e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.179999999999761 y[1] (closed_form) = 2.99926252853273 y[1] (numeric) = 2.999262528532899 absolute error = 1.683098105331737e-13 relative error = 5.611706508916797e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18999999999976 y[1] (closed_form) = 2.99882859317723 y[1] (numeric) = 2.998828593177399 absolute error = 1.687538997430238e-13 relative error = 5.627327287960485e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999759 y[1] (closed_form) = 2.998294775794767 y[1] (numeric) = 2.998294775794936 absolute error = 1.691979889528739e-13 relative error = 5.643140571727943e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y[1] (closed_form) = 2.997661129766634 y[1] (numeric) = 2.997661129766803 absolute error = 1.687538997430238e-13 relative error = 5.629518896158925e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y[1] (closed_form) = 2.996927718456906 y[1] (numeric) = 2.996927718457074 absolute error = 1.683098105331737e-13 relative error = 5.616078409119427e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999755 y[1] (closed_form) = 2.996094615206102 y[1] (numeric) = 2.996094615206271 absolute error = 1.683098105331737e-13 relative error = 5.617640033093402e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999754 y[1] (closed_form) = 2.995161903323854 y[1] (numeric) = 2.995161903324022 absolute error = 1.678657213233237e-13 relative error = 5.604562515870551e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999753 y[1] (closed_form) = 2.994129676080573 y[1] (numeric) = 2.99412967608074 absolute error = 1.674216321134736e-13 relative error = 5.591662694203504e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999752 y[1] (closed_form) = 2.992998036698122 y[1] (numeric) = 2.992998036698289 absolute error = 1.669775429036235e-13 relative error = 5.578939272804647e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.269999999999751 y[1] (closed_form) = 2.991767098339497 y[1] (numeric) = 2.991767098339664 absolute error = 1.669775429036235e-13 relative error = 5.581234682215074e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27999999999975 y[1] (closed_form) = 2.990436984097507 y[1] (numeric) = 2.990436984097674 absolute error = 1.665334536937735e-13 relative error = 5.568866843854664e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999749 y[1] (closed_form) = 2.98900782698247 y[1] (numeric) = 2.989007826982637 absolute error = 1.669775429036235e-13 relative error = 5.586386940719203e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999748 y[1] (closed_form) = 2.987479769908905 y[1] (numeric) = 2.987479769909072 absolute error = 1.669775429036235e-13 relative error = 5.589244305032234e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y[1] (closed_form) = 2.985852965681246 y[1] (numeric) = 2.985852965681413 absolute error = 1.669775429036235e-13 relative error = 5.59228953410726e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999745 y[1] (closed_form) = 2.98412757697856 y[1] (numeric) = 2.984127576978727 absolute error = 1.669775429036235e-13 relative error = 5.595522932457497e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999744 y[1] (closed_form) = 2.98230377633828 y[1] (numeric) = 2.982303776338446 absolute error = 1.660893644839234e-13 relative error = 5.569163202007898e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y[1] (closed_form) = 2.980381746138949 y[1] (numeric) = 2.980381746139115 absolute error = 1.660893644839234e-13 relative error = 5.572754721742955e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y[1] (closed_form) = 2.978361678581988 y[1] (numeric) = 2.978361678582153 absolute error = 1.656452752740734e-13 relative error = 5.561623911067036e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y[1] (closed_form) = 2.976243775672466 y[1] (numeric) = 2.976243775672632 absolute error = 1.660893644839234e-13 relative error = 5.580502707524233e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y[1] (closed_form) = 2.974028249198911 y[1] (numeric) = 2.974028249199077 absolute error = 1.660893644839234e-13 relative error = 5.584659948292741e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y[1] (closed_form) = 2.971715320712124 y[1] (numeric) = 2.971715320712289 absolute error = 1.656452752740734e-13 relative error = 5.574062701079292e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y[1] (closed_form) = 2.969305221503025 y[1] (numeric) = 2.969305221503191 absolute error = 1.656452752740734e-13 relative error = 5.578587006634023e-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) = 2.966798192579528 y[1] (numeric) = 2.966798192579693 absolute error = 1.652011860642233e-13 relative error = 5.568332435870422e-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) = 2.964194484642436 y[1] (numeric) = 2.9641944846426 absolute error = 1.643130076445232e-13 relative error = 5.543260015354353e-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) = 2.961494358060372 y[1] (numeric) = 2.961494358060536 absolute error = 1.638689184346731e-13 relative error = 5.533318609527891e-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) = 2.958698082843744 y[1] (numeric) = 2.958698082843908 absolute error = 1.63424829224823e-13 relative error = 5.523538551380265e-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) = 2.955805938617745 y[1] (numeric) = 2.955805938617909 absolute error = 1.63424829224823e-13 relative error = 5.528943124772499e-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) = 2.952818214594386 y[1] (numeric) = 2.95281821459455 absolute error = 1.63424829224823e-13 relative error = 5.534537426553767e-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) = 2.949735209543581 y[1] (numeric) = 2.949735209543743 absolute error = 1.625366508051229e-13 relative error = 5.510211570152176e-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) = 2.946557231763264 y[1] (numeric) = 2.946557231763427 absolute error = 1.62980740014973e-13 relative error = 5.531226010412256e-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) = 2.943284599048566 y[1] (numeric) = 2.943284599048729 absolute error = 1.625366508051229e-13 relative error = 5.522287951958973e-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) = 2.939917638660031 y[1] (numeric) = 2.939917638660193 absolute error = 1.616484723854228e-13 relative error = 5.498401392601584e-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) = 2.936456687290892 y[1] (numeric) = 2.936456687291054 absolute error = 1.612043831755727e-13 relative error = 5.489758588072219e-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) = 2.932902091033403 y[1] (numeric) = 2.932902091033564 absolute error = 1.612043831755727e-13 relative error = 5.496412023722641e-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) = 2.929254205344225 y[1] (numeric) = 2.929254205344387 absolute error = 1.612043831755727e-13 relative error = 5.503256865910315e-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) = 2.92551339500889 y[1] (numeric) = 2.925513395009051 absolute error = 1.612043831755727e-13 relative error = 5.510293798367068e-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) = 2.921680034105312 y[1] (numeric) = 2.921680034105472 absolute error = 1.603162047558726e-13 relative error = 5.487123945280519e-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) = 2.917754505966387 y[1] (numeric) = 2.917754505966547 absolute error = 1.598721155460225e-13 relative error = 5.47928604751041e-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) = 2.913737203141659 y[1] (numeric) = 2.913737203141818 absolute error = 1.594280263361725e-13 relative error = 5.471599366074383e-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) = 2.909628527358062 y[1] (numeric) = 2.90962852735822 absolute error = 1.585398479164724e-13 relative error = 5.448800299618532e-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) = 2.90542888947975 y[1] (numeric) = 2.905428889479908 absolute error = 1.580957587066223e-13 relative error = 5.441391433776619e-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) = 2.901138709467012 y[1] (numeric) = 2.90113870946717 absolute error = 1.580957587066223e-13 relative error = 5.449438118581623e-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) = 2.896758416334273 y[1] (numeric) = 2.896758416334431 absolute error = 1.572075802869222e-13 relative error = 5.427017296315023e-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) = 2.892288448107198 y[1] (numeric) = 2.892288448107355 absolute error = 1.572075802869222e-13 relative error = 5.435404632266316e-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) = 2.887729251778882 y[1] (numeric) = 2.887729251779039 absolute error = 1.567634910770721e-13 relative error = 5.42860765012868e-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) = 2.883081283265161 y[1] (numeric) = 2.883081283265318 absolute error = 1.56319401867222e-13 relative error = 5.421956112530633e-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) = 2.878345007359012 y[1] (numeric) = 2.878345007359168 absolute error = 1.554312234475219e-13 relative error = 5.400020603858597e-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) = 2.87352089768408 y[1] (numeric) = 2.873520897684235 absolute error = 1.549871342376719e-13 relative error = 5.393631706753345e-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) = 2.86860943664731 y[1] (numeric) = 2.868609436647464 absolute error = 1.540989558179717e-13 relative error = 5.371904374618354e-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) = 2.863611115390714 y[1] (numeric) = 2.863611115390868 absolute error = 1.540989558179717e-13 relative error = 5.381280823703826e-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) = 2.858526433742253 y[1] (numeric) = 2.858526433742405 absolute error = 1.527666881884215e-13 relative error = 5.344246125736411e-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) = 2.853355900165853 y[1] (numeric) = 2.853355900166006 absolute error = 1.523225989785715e-13 relative error = 5.338366621903619e-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) = 2.848100031710565 y[1] (numeric) = 2.848100031710717 absolute error = 1.518785097687214e-13 relative error = 5.33262554256226e-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) = 2.842759353958854 y[1] (numeric) = 2.842759353959005 absolute error = 1.509903313490213e-13 relative error = 5.311400387751805e-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) = 2.837334400974044 y[1] (numeric) = 2.837334400974194 absolute error = 1.505462421391712e-13 relative error = 5.305904093909037e-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) = 2.831825715246912 y[1] (numeric) = 2.831825715247062 absolute error = 1.496580637194711e-13 relative error = 5.284861385137261e-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) = 2.826233847641442 y[1] (numeric) = 2.826233847641591 absolute error = 1.49213974509621e-13 relative error = 5.279604680771324e-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) = 2.820559357339733 y[1] (numeric) = 2.820559357339882 absolute error = 1.483257960899209e-13 relative error = 5.258736913440366e-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) = 2.814802811786088 y[1] (numeric) = 2.814802811786236 absolute error = 1.483257960899209e-13 relative error = 5.269491541960027e-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) = 2.808964786630264 y[1] (numeric) = 2.808964786630412 absolute error = 1.474376176702208e-13 relative error = 5.248823992809546e-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) = 2.803045865669913 y[1] (numeric) = 2.803045865670059 absolute error = 1.465494392505207e-13 relative error = 5.228221237667695e-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) = 2.797046640792197 y[1] (numeric) = 2.797046640792343 absolute error = 1.461053500406706e-13 relative error = 5.223557873861187e-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) = 2.790967711914605 y[1] (numeric) = 2.79096771191475 absolute error = 1.452171716209705e-13 relative error = 5.203111845437705e-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) = 2.784809686924959 y[1] (numeric) = 2.784809686925103 absolute error = 1.438849039914203e-13 relative error = 5.166776913588691e-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) = 2.778573181620627 y[1] (numeric) = 2.77857318162077 absolute error = 1.429967255717202e-13 relative error = 5.14640847027524e-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) = 2.772258819646941 y[1] (numeric) = 2.772258819647083 absolute error = 1.4166445794217e-13 relative error = 5.110073306943669e-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) = 2.765867232434838 y[1] (numeric) = 2.765867232434979 absolute error = 1.4166445794217e-13 relative error = 5.121882073040088e-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) = 2.759399059137712 y[1] (numeric) = 2.759399059137852 absolute error = 1.403321903126198e-13 relative error = 5.085606949379492e-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) = 2.752854946567502 y[1] (numeric) = 2.752854946567642 absolute error = 1.398881011027697e-13 relative error = 5.08156455091084e-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) = 2.746235549130013 y[1] (numeric) = 2.746235549130152 absolute error = 1.389999226830696e-13 relative error = 5.061471246598048e-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) = 2.739541528759471 y[1] (numeric) = 2.739541528759609 absolute error = 1.372235658436693e-13 relative error = 5.008997469215493e-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) = 2.732773554852336 y[1] (numeric) = 2.732773554852472 absolute error = 1.358912982141192e-13 relative error = 4.972651245575375e-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) = 2.725932304200359 y[1] (numeric) = 2.725932304200494 absolute error = 1.34559030584569e-13 relative error = 4.93625723490009e-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) = 2.719018460922904 y[1] (numeric) = 2.719018460923038 absolute error = 1.341149413747189e-13 relative error = 4.932476307247907e-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) = 2.712032716398535 y[1] (numeric) = 2.712032716398669 absolute error = 1.332267629550188e-13 relative error = 4.912431997942056e-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) = 2.704975769195886 y[1] (numeric) = 2.704975769196019 absolute error = 1.332267629550188e-13 relative error = 4.925247925404648e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y[1] (closed_form) = 2.697848325003795 y[1] (numeric) = 2.697848325003927 absolute error = 1.318944953254686e-13 relative error = 4.888877336174303e-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) = 2.690651096560742 y[1] (numeric) = 2.690651096560873 absolute error = 1.314504061156185e-13 relative error = 4.885449707085462e-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) = 2.683384803583574 y[1] (numeric) = 2.683384803583704 absolute error = 1.305622276959184e-13 relative error = 4.865579752913439e-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) = 2.676050172695532 y[1] (numeric) = 2.676050172695662 absolute error = 1.301181384860683e-13 relative error = 4.862320587771452e-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) = 2.668647937353595 y[1] (numeric) = 2.668647937353724 absolute error = 1.287858708565182e-13 relative error = 4.825884638204867e-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) = 2.661178837775126 y[1] (numeric) = 2.661178837775255 absolute error = 1.283417816466681e-13 relative error = 4.822741704723912e-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) = 2.653643620863861 y[1] (numeric) = 2.653643620863988 absolute error = 1.270095140171179e-13 relative error = 4.786231015292532e-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) = 2.646043040135208 y[1] (numeric) = 2.646043040135337 absolute error = 1.292299600663682e-13 relative error = 4.883894861353609e-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) = 2.638377855640908 y[1] (numeric) = 2.63837785564104 absolute error = 1.318944953254686e-13 relative error = 4.999075285728137e-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) = 2.630648833893023 y[1] (numeric) = 2.630648833893158 absolute error = 1.35003119794419e-13 relative error = 5.131932398389781e-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) = 2.622856747787289 y[1] (numeric) = 2.622856747787427 absolute error = 1.381117442633695e-13 relative error = 5.265699103844851e-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) = 2.615002376525821 y[1] (numeric) = 2.615002376525962 absolute error = 1.407762795224698e-13 relative error = 5.38340923840762e-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) = 2.607086505539201 y[1] (numeric) = 2.607086505539344 absolute error = 1.429967255717202e-13 relative error = 5.484924465218135e-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) = 2.59910992640793 y[1] (numeric) = 2.599109926408076 absolute error = 1.461053500406706e-13 relative error = 5.621360934225425e-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) = 2.591073436783276 y[1] (numeric) = 2.591073436783424 absolute error = 1.483257960899209e-13 relative error = 5.724492173176768e-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) = 2.582977840307502 y[1] (numeric) = 2.582977840307653 absolute error = 1.509903313490213e-13 relative error = 5.845591432989064e-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) = 2.574823946533511 y[1] (numeric) = 2.574823946533665 absolute error = 1.536548666081217e-13 relative error = 5.967587291355877e-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) = 2.566612570843885 y[1] (numeric) = 2.566612570844042 absolute error = 1.567634910770721e-13 relative error = 6.107797213255654e-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) = 2.55834453436935 y[1] (numeric) = 2.55834453436951 absolute error = 1.594280263361725e-13 relative error = 6.231687100559839e-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) = 2.550020663906664 y[1] (numeric) = 2.550020663906826 absolute error = 1.625366508051229e-13 relative error = 6.373934654949608e-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) = 2.541641791835936 y[1] (numeric) = 2.541641791836101 absolute error = 1.652011860642233e-13 relative error = 6.499782408161123e-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) = 2.533208756037391 y[1] (numeric) = 2.533208756037559 absolute error = 1.678657213233237e-13 relative error = 6.62660433820346e-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) = 2.524722399807581 y[1] (numeric) = 2.524722399807752 absolute error = 1.70530256582424e-13 relative error = 6.75441611305151e-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) = 2.516183571775058 y[1] (numeric) = 2.516183571775232 absolute error = 1.736388810513745e-13 relative error = 6.90088286876779e-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) = 2.507593125815509 y[1] (numeric) = 2.507593125815686 absolute error = 1.767475055203249e-13 relative error = 7.04849218562297e-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) = 2.498951920966371 y[1] (numeric) = 2.49895192096655 absolute error = 1.794120407794253e-13 relative error = 7.17949150098273e-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) = 2.490260821340929 y[1] (numeric) = 2.49026082134111 absolute error = 1.816324868286756e-13 relative error = 7.2937133842419e-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) = 2.481520696041901 y[1] (numeric) = 2.481520696042086 absolute error = 1.84741111297626e-13 relative error = 7.444673404992896e-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) = 2.472732419074535 y[1] (numeric) = 2.472732419074724 absolute error = 1.882938249764265e-13 relative error = 7.614807955925087e-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) = 2.463896869259204 y[1] (numeric) = 2.463896869259396 absolute error = 1.91402449445377e-13 relative error = 7.768281693662125e-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) = 2.455014930143527 y[1] (numeric) = 2.455014930143722 absolute error = 1.949551631241775e-13 relative error = 7.941098880110675e-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) = 2.446087489914013 y[1] (numeric) = 2.446087489914211 absolute error = 1.98507876802978e-13 relative error = 8.115322024313862e-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) = 2.437115441307246 y[1] (numeric) = 2.437115441307447 absolute error = 2.016165012719284e-13 relative error = 8.272751378727601e-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) = 2.42809968152061 y[1] (numeric) = 2.428099681520814 absolute error = 2.047251257408789e-13 relative error = 8.431495926586865e-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) = 2.41904111212257 y[1] (numeric) = 2.419041112122777 absolute error = 2.073896609999792e-13 relative error = 8.573217708483124e-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) = 2.409940638962518 y[1] (numeric) = 2.409940638962728 absolute error = 2.100541962590796e-13 relative error = 8.716156442322505e-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) = 2.400799172080185 y[1] (numeric) = 2.400799172080399 absolute error = 2.131628207280301e-13 relative error = 8.878827650683251e-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) = 2.391617625614643 y[1] (numeric) = 2.391617625614859 absolute error = 2.162714451969805e-13 relative error = 9.042893934242478e-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) = 2.382396917712886 y[1] (numeric) = 2.382396917713105 absolute error = 2.193800696659309e-13 relative error = 9.208376154068272e-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) = 2.373137970438021 y[1] (numeric) = 2.373137970438244 absolute error = 2.224886941348814e-13 relative error = 9.375295364466971e-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) = 2.363841709677059 y[1] (numeric) = 2.363841709677285 absolute error = 2.260414078136819e-13 relative error = 9.562459571142898e-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) = 2.35450906504833 y[1] (numeric) = 2.354509065048559 absolute error = 2.287059430727822e-13 relative error = 9.713529944217379e-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) = 2.34514096980852 y[1] (numeric) = 2.345140969808752 absolute error = 2.318145675417327e-13 relative error = 9.884888393752307e-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) = 2.335738360759345 y[1] (numeric) = 2.335738360759581 absolute error = 2.358113704303832e-13 relative error = 1.009579559046679e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = 2.326302178153875 y[1] (numeric) = 2.326302178154114 absolute error = 2.393640841091838e-13 relative error = 1.028946653435798e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = 2.316833365602507 y[1] (numeric) = 2.31683336560275 absolute error = 2.429167977879843e-13 relative error = 1.048486271798888e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = 2.307332869978606 y[1] (numeric) = 2.307332869978852 absolute error = 2.460254222569347e-13 relative error = 1.066276242401105e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = 2.297801641323817 y[1] (numeric) = 2.297801641324067 absolute error = 2.495781359357352e-13 relative error = 1.086160491172543e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y[1] (closed_form) = 2.288240632753063 y[1] (numeric) = 2.288240632753316 absolute error = 2.526867604046856e-13 relative error = 1.104284037211022e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y[1] (closed_form) = 2.278650800359233 y[1] (numeric) = 2.278650800359488 absolute error = 2.55351295663786e-13 relative error = 1.120624957643924e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = 2.269033103117575 y[1] (numeric) = 2.269033103117835 absolute error = 2.593480985524366e-13 relative error = 1.142989488324789e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y[1] (closed_form) = 2.2593885027898 y[1] (numeric) = 2.259388502790062 absolute error = 2.629008122312371e-13 relative error = 1.163592768161022e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y[1] (closed_form) = 2.249717963827901 y[1] (numeric) = 2.249717963828167 absolute error = 2.660094367001875e-13 relative error = 1.182412377805668e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 2.240022453277717 y[1] (numeric) = 2.240022453277987 absolute error = 2.69562150378988e-13 relative error = 1.203390394522835e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y[1] (closed_form) = 2.230302940682224 y[1] (numeric) = 2.230302940682496 absolute error = 2.726707748479384e-13 relative error = 1.222572816787533e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y[1] (closed_form) = 2.220560397984581 y[1] (numeric) = 2.220560397984856 absolute error = 2.757793993168889e-13 relative error = 1.241936042663785e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 2.210795799430938 y[1] (numeric) = 2.210795799431218 absolute error = 2.793321129956894e-13 relative error = 1.263491241785378e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y[1] (closed_form) = 2.201010121473016 y[1] (numeric) = 2.201010121473299 absolute error = 2.828848266744899e-13 relative error = 1.28525000368999e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y[1] (closed_form) = 2.191204342670454 y[1] (numeric) = 2.19120434267074 absolute error = 2.859934511434403e-13 relative error = 1.305188409744094e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = 2.181379443592962 y[1] (numeric) = 2.181379443593251 absolute error = 2.891020756123908e-13 relative error = 1.325317685841071e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y[1] (closed_form) = 2.171536406722259 y[1] (numeric) = 2.171536406722551 absolute error = 2.922107000813412e-13 relative error = 1.345640345594792e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y[1] (closed_form) = 2.16167621635383 y[1] (numeric) = 2.161676216354126 absolute error = 2.957634137601417e-13 relative error = 1.36821329449151e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y[1] (closed_form) = 2.151799858498496 y[1] (numeric) = 2.151799858498795 absolute error = 2.993161274389422e-13 relative error = 1.391003565023942e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y[1] (closed_form) = 2.141908320783811 y[1] (numeric) = 2.141908320784114 absolute error = 3.024247519078926e-13 relative error = 1.41194069313491e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y[1] (closed_form) = 2.132002592355305 y[1] (numeric) = 2.132002592355611 absolute error = 3.059774655866931e-13 relative error = 1.435164603851012e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y[1] (closed_form) = 2.122083663777565 y[1] (numeric) = 2.122083663777873 absolute error = 3.086420008457935e-13 relative error = 1.454428994078271e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y[1] (closed_form) = 2.112152526935183 y[1] (numeric) = 2.112152526935494 absolute error = 3.11750625314744e-13 relative error = 1.475985381449258e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y[1] (closed_form) = 2.102210174933568 y[1] (numeric) = 2.102210174933882 absolute error = 3.148592497836944e-13 relative error = 1.497753428929362e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y[1] (closed_form) = 2.092257601999634 y[1] (numeric) = 2.092257601999953 absolute error = 3.18856052672345e-13 relative error = 1.523980853827964e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y[1] (closed_form) = 2.082295803382381 y[1] (numeric) = 2.082295803382703 absolute error = 3.224087663511455e-13 relative error = 1.548333170664034e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y[1] (closed_form) = 2.07232577525337 y[1] (numeric) = 2.072325775253695 absolute error = 3.255173908200959e-13 relative error = 1.57078290830165e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y[1] (closed_form) = 2.062348514607104 y[1] (numeric) = 2.062348514607434 absolute error = 3.295141937087465e-13 relative error = 1.597761927117938e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y[1] (closed_form) = 2.052365019161335 y[1] (numeric) = 2.052365019161667 absolute error = 3.321787289678468e-13 relative error = 1.618516812879544e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y[1] (closed_form) = 2.042376287257287 y[1] (numeric) = 2.042376287257623 absolute error = 3.357314426466473e-13 relative error = 1.643827558816314e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y[1] (closed_form) = 2.032383317759827 y[1] (numeric) = 2.032383317760166 absolute error = 3.392841563254478e-13 relative error = 1.669390578837364e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y[1] (closed_form) = 2.022387109957577 y[1] (numeric) = 2.022387109957918 absolute error = 3.419486915845482e-13 relative error = 1.690817202606287e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y[1] (closed_form) = 2.012388663462986 y[1] (numeric) = 2.012388663463332 absolute error = 3.455014052633487e-13 relative error = 1.716872150674901e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y[1] (closed_form) = 2.002388978112374 y[1] (numeric) = 2.002388978112722 absolute error = 3.481659405224491e-13 relative error = 1.738752781443396e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y[1] (closed_form) = 1.992389053865941 y[1] (numeric) = 1.992389053866293 absolute error = 3.514966095963246e-13 relative error = 1.764196650821267e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y[1] (closed_form) = 1.982389890707779 y[1] (numeric) = 1.982389890708134 absolute error = 3.550493232751251e-13 relative error = 1.791016615547614e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y[1] (closed_form) = 1.972392488545871 y[1] (numeric) = 1.972392488546229 absolute error = 3.583799923490005e-13 relative error = 1.816981125360161e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y[1] (closed_form) = 1.962397847112102 y[1] (numeric) = 1.962397847112464 absolute error = 3.61932706027801e-13 relative error = 1.84433909036553e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y[1] (closed_form) = 1.952406965862288 y[1] (numeric) = 1.952406965862653 absolute error = 3.650413304967515e-13 relative error = 1.869698976081709e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y[1] (closed_form) = 1.942420843876226 y[1] (numeric) = 1.942420843876594 absolute error = 3.68594044175552e-13 relative error = 1.897601363461477e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y[1] (closed_form) = 1.932440479757794 y[1] (numeric) = 1.932440479758166 absolute error = 3.725908470642025e-13 relative error = 1.928084466078365e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y[1] (closed_form) = 1.922466871535087 y[1] (numeric) = 1.922466871535463 absolute error = 3.75921516138078e-13 relative error = 1.955412193074127e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y[1] (closed_form) = 1.912501016560616 y[1] (numeric) = 1.912501016560995 absolute error = 3.792521852119535e-13 relative error = 1.98301690784975e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y[1] (closed_form) = 1.902543911411573 y[1] (numeric) = 1.902543911411955 absolute error = 3.823608096809039e-13 relative error = 2.009734479122825e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y[1] (closed_form) = 1.892596551790175 y[1] (numeric) = 1.892596551790561 absolute error = 3.852473895449293e-13 relative error = 2.035549463410626e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y[1] (closed_form) = 1.882659932424097 y[1] (numeric) = 1.882659932424485 absolute error = 3.881339694089547e-13 relative error = 2.061625483839754e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y[1] (closed_form) = 1.872735046966992 y[1] (numeric) = 1.872735046967384 absolute error = 3.919087276926803e-13 relative error = 2.0927078196534e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y[1] (closed_form) = 1.862822887899138 y[1] (numeric) = 1.862822887899533 absolute error = 3.956834859764058e-13 relative error = 2.124106851739681e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y[1] (closed_form) = 1.852924446428179 y[1] (numeric) = 1.852924446428578 absolute error = 3.987921104453562e-13 relative error = 2.152230822007311e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y[1] (closed_form) = 1.843040712390015 y[1] (numeric) = 1.843040712390417 absolute error = 4.019007349143067e-13 relative error = 2.180639484589196e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y[1] (closed_form) = 1.833172674149813 y[1] (numeric) = 1.833172674150219 absolute error = 4.056754931980322e-13 relative error = 2.212969344997333e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y[1] (closed_form) = 1.823321318503174 y[1] (numeric) = 1.823321318503583 absolute error = 4.090061622719077e-13 relative error = 2.243193002359423e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y[1] (closed_form) = 1.813487630577453 y[1] (numeric) = 1.813487630577866 absolute error = 4.125588759507082e-13 relative error = 2.274947283866175e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y[1] (closed_form) = 1.803672593733248 y[1] (numeric) = 1.803672593733663 absolute error = 4.154454558147336e-13 relative error = 2.303330755582659e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y[1] (closed_form) = 1.793877189466063 y[1] (numeric) = 1.793877189466482 absolute error = 4.18554080283684e-13 relative error = 2.333237095278881e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y[1] (closed_form) = 1.784102397308164 y[1] (numeric) = 1.784102397308586 absolute error = 4.218847493575595e-13 relative error = 2.364689100771878e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 1.77434919473062 y[1] (numeric) = 1.774349194731045 absolute error = 4.247713292215849e-13 relative error = 2.393955656998358e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y[1] (closed_form) = 1.764618557045561 y[1] (numeric) = 1.764618557045989 absolute error = 4.278799536905353e-13 relative error = 2.424773059209577e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y[1] (closed_form) = 1.754911457308647 y[1] (numeric) = 1.754911457309078 absolute error = 4.312106227644108e-13 relative error = 2.457164553622099e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 1.745228866221762 y[1] (numeric) = 1.745228866222197 absolute error = 4.343192472333612e-13 relative error = 2.488609119637225e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y[1] (closed_form) = 1.735571752035947 y[1] (numeric) = 1.735571752036384 absolute error = 4.376499163072367e-13 relative error = 2.521646920064485e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y[1] (closed_form) = 1.725941080454572 y[1] (numeric) = 1.725941080455012 absolute error = 4.407585407761871e-13 relative error = 2.553728778853226e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 Finished! diff ( y , x , 1 ) = sin ( x ) ; Iterations = 5000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %