##############ECHO OF PROBLEM################# ##############temp/multpostode.ode################# diff ( y , x , 1 ) = x * x ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.1); x_end=c(10.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(c(1.0) + c(x) * c(x) * c(x) / c(3.0)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 1.000333333333333 y[1] (numeric) = 1.000333333333333 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 1.000443666666667 y[1] (numeric) = 1.000443666666667 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 1.000576 y[1] (numeric) = 1.000576 absolute error = 2.220446049250313e-16 relative error = 2.219167808592564e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 1.000732333333333 y[1] (numeric) = 1.000732333333333 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] = 0.14 y[1] (closed_form) = 1.000914666666667 y[1] (numeric) = 1.000914666666667 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 1.001125 y[1] (numeric) = 1.001125 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 1.001365333333333 y[1] (numeric) = 1.001365333333333 absolute error = 2.220446049250313e-16 relative error = 2.217418533812148e-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) = 1.001637666666667 y[1] (numeric) = 1.001637666666667 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 1.001944 y[1] (numeric) = 1.001944 absolute error = 2.220446049250313e-16 relative error = 2.216137877217003e-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) = 1.002286333333333 y[1] (numeric) = 1.002286333333334 absolute error = 6.661338147750939e-16 relative error = 6.646142849815311e-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) = 1.002666666666667 y[1] (numeric) = 1.002666666666667 absolute error = 8.881784197001252e-16 relative error = 8.858162430519867e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (closed_form) = 1.003087 y[1] (numeric) = 1.003087000000001 absolute error = 8.881784197001252e-16 relative error = 8.854450508282185e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (closed_form) = 1.003549333333333 y[1] (numeric) = 1.003549333333334 absolute error = 8.881784197001252e-16 relative error = 8.850371279207584e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (closed_form) = 1.004055666666667 y[1] (numeric) = 1.004055666666667 absolute error = 6.661338147750939e-16 relative error = 6.634431106659364e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = 1.004608 y[1] (numeric) = 1.004608000000001 absolute error = 6.661338147750939e-16 relative error = 6.630783497394944e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = 1.005208333333333 y[1] (numeric) = 1.005208333333334 absolute error = 4.440892098500626e-16 relative error = 4.417882294881452e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 1.005858666666667 y[1] (numeric) = 1.005858666666667 absolute error = 4.440892098500626e-16 relative error = 4.415025933233124e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 1.006561 y[1] (numeric) = 1.006561 absolute error = 2.220446049250313e-16 relative error = 2.205972662610923e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 1.007317333333333 y[1] (numeric) = 1.007317333333334 absolute error = 2.220446049250313e-16 relative error = 2.204316331877852e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 1.008129666666667 y[1] (numeric) = 1.008129666666667 absolute error = 4.440892098500626e-16 relative error = 4.405080264311859e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 1.009 y[1] (numeric) = 1.009000000000001 absolute error = 4.440892098500626e-16 relative error = 4.401280573340561e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 1.009930333333333 y[1] (numeric) = 1.009930333333334 absolute error = 4.440892098500626e-16 relative error = 4.397226176822717e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 1.010922666666667 y[1] (numeric) = 1.010922666666667 absolute error = 6.661338147750939e-16 relative error = 6.589364713440929e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 1.011979 y[1] (numeric) = 1.011979 absolute error = 4.440892098500626e-16 relative error = 4.388324360980442e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 1.013101333333333 y[1] (numeric) = 1.013101333333334 absolute error = 2.220446049250313e-16 relative error = 2.191731445012062e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = 1.014291666666667 y[1] (numeric) = 1.014291666666667 absolute error = 2.220446049250313e-16 relative error = 2.18915931405363e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (closed_form) = 1.015552 y[1] (numeric) = 1.015552 absolute error = 2.220446049250313e-16 relative error = 2.186442495559374e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (closed_form) = 1.016884333333333 y[1] (numeric) = 1.016884333333334 absolute error = 4.440892098500626e-16 relative error = 4.367155587837056e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (closed_form) = 1.018290666666667 y[1] (numeric) = 1.018290666666667 absolute error = 4.440892098500626e-16 relative error = 4.361124228937212e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = 1.019773 y[1] (numeric) = 1.019773 absolute error = 4.440892098500626e-16 relative error = 4.354784935961852e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (closed_form) = 1.021333333333333 y[1] (numeric) = 1.021333333333334 absolute error = 4.440892098500626e-16 relative error = 4.348131950229072e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 1.022973666666667 y[1] (numeric) = 1.022973666666667 absolute error = 4.440892098500626e-16 relative error = 4.341159741649224e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 1.024696 y[1] (numeric) = 1.024696 absolute error = 4.440892098500626e-16 relative error = 4.333863017422363e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 1.026502333333333 y[1] (numeric) = 1.026502333333334 absolute error = 6.661338147750939e-16 relative error = 6.489355095881521e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 1.028394666666667 y[1] (numeric) = 1.028394666666667 absolute error = 4.440892098500626e-16 relative error = 4.318276088395984e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 1.030375 y[1] (numeric) = 1.030375000000001 absolute error = 8.881784197001252e-16 relative error = 8.619953120952325e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (closed_form) = 1.032445333333333 y[1] (numeric) = 1.032445333333335 absolute error = 1.110223024625157e-15 relative error = 1.075333471691631e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = 1.034607666666667 y[1] (numeric) = 1.034607666666668 absolute error = 8.881784197001252e-16 relative error = 8.584688170364017e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (closed_form) = 1.036864 y[1] (numeric) = 1.036864000000001 absolute error = 1.110223024625157e-15 relative error = 1.070750864747119e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = 1.039216333333334 y[1] (numeric) = 1.039216333333334 absolute error = 8.881784197001252e-16 relative error = 8.546617207711244e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (closed_form) = 1.041666666666667 y[1] (numeric) = 1.041666666666668 absolute error = 1.110223024625157e-15 relative error = 1.06581410364015e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (closed_form) = 1.044217 y[1] (numeric) = 1.044217000000001 absolute error = 1.110223024625157e-15 relative error = 1.063211022828738e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (closed_form) = 1.046869333333333 y[1] (numeric) = 1.046869333333335 absolute error = 1.110223024625157e-15 relative error = 1.060517286422078e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (closed_form) = 1.049625666666667 y[1] (numeric) = 1.049625666666668 absolute error = 1.110223024625157e-15 relative error = 1.057732351525788e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (closed_form) = 1.052488 y[1] (numeric) = 1.052488000000001 absolute error = 1.110223024625157e-15 relative error = 1.054855755718979e-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) = 1.055458333333333 y[1] (numeric) = 1.055458333333335 absolute error = 1.554312234475219e-15 relative error = 1.472641965473343e-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) = 1.058538666666667 y[1] (numeric) = 1.058538666666668 absolute error = 1.554312234475219e-15 relative error = 1.468356597090346e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = 1.061731 y[1] (numeric) = 1.061731000000002 absolute error = 1.77635683940025e-15 relative error = 1.673076174097064e-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) = 1.065037333333333 y[1] (numeric) = 1.065037333333335 absolute error = 1.998401444325282e-15 relative error = 1.87636750541948e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = 1.068459666666667 y[1] (numeric) = 1.068459666666669 absolute error = 1.77635683940025e-15 relative error = 1.662539911255658e-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) = 1.072 y[1] (numeric) = 1.072000000000002 absolute error = 1.77635683940025e-15 relative error = 1.657049290485308e-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) = 1.075660333333333 y[1] (numeric) = 1.075660333333336 absolute error = 2.220446049250313e-15 relative error = 2.064263206926517e-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) = 1.079442666666667 y[1] (numeric) = 1.079442666666669 absolute error = 2.220446049250313e-15 relative error = 2.0570300932305e-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) = 1.083349 y[1] (numeric) = 1.083349000000002 absolute error = 2.220446049250313e-15 relative error = 2.049612866444989e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = 1.087381333333334 y[1] (numeric) = 1.087381333333336 absolute error = 1.998401444325282e-15 relative error = 1.837811063207462e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = 1.091541666666667 y[1] (numeric) = 1.091541666666669 absolute error = 1.998401444325282e-15 relative error = 1.830806377211389e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = 1.095832 y[1] (numeric) = 1.095832000000003 absolute error = 2.442490654175344e-15 relative error = 2.228891521853116e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (closed_form) = 1.100254333333333 y[1] (numeric) = 1.100254333333336 absolute error = 2.886579864025407e-15 relative error = 2.623556914591026e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (closed_form) = 1.104810666666667 y[1] (numeric) = 1.104810666666669 absolute error = 2.664535259100376e-15 relative error = 2.411757362136597e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (closed_form) = 1.109503 y[1] (numeric) = 1.109503000000003 absolute error = 2.886579864025407e-15 relative error = 2.601687299651652e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 1.114333333333334 y[1] (numeric) = 1.114333333333336 absolute error = 2.664535259100376e-15 relative error = 2.391147405713768e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = 1.119303666666667 y[1] (numeric) = 1.11930366666667 absolute error = 2.664535259100376e-15 relative error = 2.380529375942699e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (closed_form) = 1.124416 y[1] (numeric) = 1.124416000000003 absolute error = 2.664535259100376e-15 relative error = 2.369705926543535e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (closed_form) = 1.129672333333334 y[1] (numeric) = 1.129672333333336 absolute error = 2.442490654175344e-15 relative error = 2.162123106058787e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (closed_form) = 1.135074666666667 y[1] (numeric) = 1.135074666666669 absolute error = 2.442490654175344e-15 relative error = 2.151832585029952e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (closed_form) = 1.140625 y[1] (numeric) = 1.140625000000003 absolute error = 2.220446049250313e-15 relative error = 1.94669242674e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 1.146325333333334 y[1] (numeric) = 1.146325333333336 absolute error = 2.220446049250313e-15 relative error = 1.93701210701992e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = 1.152177666666667 y[1] (numeric) = 1.152177666666669 absolute error = 2.442490654175344e-15 relative error = 2.119890642596507e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (closed_form) = 1.158184 y[1] (numeric) = 1.158184000000003 absolute error = 2.220446049250313e-15 relative error = 1.917179005451908e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = 1.164346333333334 y[1] (numeric) = 1.164346333333336 absolute error = 1.998401444325282e-15 relative error = 1.716329057011915e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (closed_form) = 1.170666666666667 y[1] (numeric) = 1.170666666666669 absolute error = 1.998401444325282e-15 relative error = 1.70706273717991e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (closed_form) = 1.177147 y[1] (numeric) = 1.177147000000002 absolute error = 1.998401444325282e-15 relative error = 1.697665155095567e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (closed_form) = 1.183789333333334 y[1] (numeric) = 1.183789333333335 absolute error = 1.554312234475219e-15 relative error = 1.312997330444396e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = 1.190595666666667 y[1] (numeric) = 1.190595666666669 absolute error = 1.77635683940025e-15 relative error = 1.491990008978909e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (closed_form) = 1.197568 y[1] (numeric) = 1.197568000000002 absolute error = 1.77635683940025e-15 relative error = 1.483303527983588e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = 1.204708333333334 y[1] (numeric) = 1.204708333333336 absolute error = 1.77635683940025e-15 relative error = 1.474511954678034e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (closed_form) = 1.212018666666667 y[1] (numeric) = 1.212018666666669 absolute error = 1.77635683940025e-15 relative error = 1.465618383820477e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (closed_form) = 1.219501000000001 y[1] (numeric) = 1.219501000000002 absolute error = 1.554312234475219e-15 relative error = 1.274547732617865e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (closed_form) = 1.227157333333334 y[1] (numeric) = 1.227157333333335 absolute error = 1.554312234475219e-15 relative error = 1.266595726770611e-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) = 1.234989666666667 y[1] (numeric) = 1.234989666666669 absolute error = 1.554312234475219e-15 relative error = 1.258562947065321e-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) = 1.243000000000001 y[1] (numeric) = 1.243000000000002 absolute error = 1.554312234475219e-15 relative error = 1.250452320575397e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = 1.251190333333334 y[1] (numeric) = 1.251190333333336 absolute error = 1.77635683940025e-15 relative error = 1.41973350662629e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (closed_form) = 1.259562666666667 y[1] (numeric) = 1.259562666666669 absolute error = 1.554312234475219e-15 relative error = 1.234009450747364e-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) = 1.268119000000001 y[1] (numeric) = 1.268119000000002 absolute error = 1.332267629550188e-15 relative error = 1.050585654461598e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = 1.276861333333334 y[1] (numeric) = 1.276861333333335 absolute error = 1.332267629550188e-15 relative error = 1.04339257111985e-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) = 1.285791666666667 y[1] (numeric) = 1.285791666666669 absolute error = 1.554312234475219e-15 relative error = 1.20883676163859e-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) = 1.294912000000001 y[1] (numeric) = 1.294912000000002 absolute error = 1.554312234475219e-15 relative error = 1.2003226740313e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = 1.304224333333334 y[1] (numeric) = 1.304224333333336 absolute error = 1.554312234475219e-15 relative error = 1.191752212215448e-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) = 1.313730666666667 y[1] (numeric) = 1.313730666666669 absolute error = 1.554312234475219e-15 relative error = 1.183128531526923e-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) = 1.323433000000001 y[1] (numeric) = 1.323433000000002 absolute error = 1.332267629550188e-15 relative error = 1.006675539713901e-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) = 1.333333333333334 y[1] (numeric) = 1.333333333333335 absolute error = 1.554312234475219e-15 relative error = 1.165734175856414e-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) = 1.343433666666666 y[1] (numeric) = 1.343433666666669 absolute error = 2.664535259100376e-15 relative error = 1.983376868700658e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = 1.353735999999998 y[1] (numeric) = 1.353736000000002 absolute error = 3.552713678800501e-15 relative error = 2.624377041609668e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = 1.36424233333333 y[1] (numeric) = 1.364242333333335 absolute error = 4.662936703425657e-15 relative error = 3.417968046800337e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 1.374954666666663 y[1] (numeric) = 1.374954666666668 absolute error = 5.551115123125783e-15 relative error = 4.037307743813468e-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) = 1.385874999999995 y[1] (numeric) = 1.385875000000002 absolute error = 6.883382752675971e-15 relative error = 4.966813567367907e-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) = 1.397005333333327 y[1] (numeric) = 1.397005333333335 absolute error = 7.993605777301127e-15 relative error = 5.721957952893402e-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) = 1.408347666666659 y[1] (numeric) = 1.408347666666668 absolute error = 9.547918011776346e-15 relative error = 6.779517755281829e-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) = 1.419903999999991 y[1] (numeric) = 1.419904000000001 absolute error = 1.043609643147647e-14 relative error = 7.34986057612102e-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) = 1.431676333333322 y[1] (numeric) = 1.431676333333334 absolute error = 1.13242748511766e-14 relative error = 7.909800970733853e-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) = 1.443666666666654 y[1] (numeric) = 1.443666666666667 absolute error = 1.287858708565182e-14 relative error = 8.920748385351139e-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) = 1.455876999999986 y[1] (numeric) = 1.455877 absolute error = 1.443289932012704e-14 relative error = 9.913543053518378e-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) = 1.468309333333318 y[1] (numeric) = 1.468309333333333 absolute error = 1.576516694967722e-14 relative error = 1.073695207936025e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 1.480965666666649 y[1] (numeric) = 1.480965666666666 absolute error = 1.709743457922741e-14 relative error = 1.154478794752227e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 1.493847999999981 y[1] (numeric) = 1.493847999999999 absolute error = 1.865174681370263e-14 relative error = 1.248570591767226e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 1.506958333333313 y[1] (numeric) = 1.506958333333332 absolute error = 1.976196983832779e-14 relative error = 1.31138130372957e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 1.520298666666644 y[1] (numeric) = 1.520298666666665 absolute error = 2.131628207280301e-14 relative error = 1.402111475868118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 1.533870999999975 y[1] (numeric) = 1.533870999999998 absolute error = 2.287059430727822e-14 relative error = 1.491037662702965e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = 1.547677333333306 y[1] (numeric) = 1.547677333333331 absolute error = 2.464695114667848e-14 relative error = 1.592512251477843e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = 1.561719666666638 y[1] (numeric) = 1.561719666666664 absolute error = 2.620126338115369e-14 relative error = 1.67771873149796e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = 1.575999999999969 y[1] (numeric) = 1.575999999999997 absolute error = 2.819966482547898e-14 relative error = 1.789318834104031e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = 1.5905203333333 y[1] (numeric) = 1.59052033333333 absolute error = 2.997602166487923e-14 relative error = 1.884667617046907e-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) = 1.605282666666632 y[1] (numeric) = 1.605282666666663 absolute error = 3.130828929442941e-14 relative error = 1.950328745493842e-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) = 1.620288999999963 y[1] (numeric) = 1.620288999999996 absolute error = 3.286260152890463e-14 relative error = 2.028193830168901e-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) = 1.635541333333294 y[1] (numeric) = 1.635541333333329 absolute error = 3.508304757815495e-14 relative error = 2.145041941963912e-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) = 1.651041666666625 y[1] (numeric) = 1.651041666666662 absolute error = 3.708144902248023e-14 relative error = 2.245942653727566e-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) = 1.666791999999956 y[1] (numeric) = 1.666791999999994 absolute error = 3.863576125695545e-14 relative error = 2.317971363970818e-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) = 1.682794333333286 y[1] (numeric) = 1.682794333333327 absolute error = 4.063416270128073e-14 relative error = 2.414683832503311e-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) = 1.699050666666617 y[1] (numeric) = 1.69905066666666 absolute error = 4.241051954068098e-14 relative error = 2.496130361073137e-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) = 1.715562999999948 y[1] (numeric) = 1.715562999999992 absolute error = 4.39648317751562e-14 relative error = 2.562705757536012e-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) = 1.732333333333278 y[1] (numeric) = 1.732333333333324 absolute error = 4.574118861455645e-14 relative error = 2.640438057411462e-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) = 1.749363666666609 y[1] (numeric) = 1.749363666666657 absolute error = 4.729550084903167e-14 relative error = 2.703583122836469e-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) = 1.76665599999994 y[1] (numeric) = 1.766655999999989 absolute error = 4.929390229335695e-14 relative error = 2.790237731248111e-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) = 1.78421233333327 y[1] (numeric) = 1.784212333333322 absolute error = 5.151434834260726e-14 relative error = 2.887231938721555e-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) = 1.802034666666601 y[1] (numeric) = 1.802034666666654 absolute error = 5.329070518200751e-14 relative error = 2.957251942360495e-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) = 1.820124999999931 y[1] (numeric) = 1.820124999999986 absolute error = 5.551115123125783e-14 relative error = 3.049853786484991e-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) = 1.838485333333261 y[1] (numeric) = 1.838485333333318 absolute error = 5.706546346573305e-14 relative error = 3.10393901061319e-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) = 1.857117666666591 y[1] (numeric) = 1.857117666666651 absolute error = 5.928590951498336e-14 relative error = 3.192361506171971e-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) = 1.876023999999922 y[1] (numeric) = 1.876023999999983 absolute error = 6.150635556423367e-14 relative error = 3.278548438838535e-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) = 1.895206333333252 y[1] (numeric) = 1.895206333333315 absolute error = 6.350475700855895e-14 relative error = 3.350809666030824e-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) = 1.914666666666581 y[1] (numeric) = 1.914666666666647 absolute error = 6.59472476627343e-14 relative error = 3.444320038095608e-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) = 1.934406999999911 y[1] (numeric) = 1.93440699999998 absolute error = 6.816769371198461e-14 relative error = 3.523958180051444e-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) = 1.954429333333242 y[1] (numeric) = 1.954429333333312 absolute error = 6.994405055138486e-14 relative error = 3.578745435226181e-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) = 1.974735666666571 y[1] (numeric) = 1.974735666666644 absolute error = 7.238654120556021e-14 relative error = 3.665631933804661e-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) = 1.995327999999901 y[1] (numeric) = 1.995327999999976 absolute error = 7.482903185973555e-14 relative error = 3.750212088425525e-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) = 2.016208333333231 y[1] (numeric) = 2.016208333333308 absolute error = 7.72715225139109e-14 relative error = 3.832516771030515e-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) = 2.03737866666656 y[1] (numeric) = 2.03737866666664 absolute error = 8.038014698286133e-14 relative error = 3.945272830130033e-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) = 2.05884099999989 y[1] (numeric) = 2.058840999999972 absolute error = 8.260059303211165e-14 relative error = 4.01199475977582e-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) = 2.080597333333219 y[1] (numeric) = 2.080597333333305 absolute error = 8.570921750106208e-14 relative error = 4.119452434544445e-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) = 2.102649666666548 y[1] (numeric) = 2.102649666666636 absolute error = 8.79296635503124e-14 relative error = 4.181850402578588e-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) = 2.124999999999877 y[1] (numeric) = 2.124999999999968 absolute error = 9.059419880941277e-14 relative error = 4.263256414560847e-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) = 2.147650333333207 y[1] (numeric) = 2.1476503333333 absolute error = 9.325873406851315e-14 relative error = 4.342361166576556e-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) = 2.170602666666536 y[1] (numeric) = 2.170602666666632 absolute error = 9.592326932761353e-14 relative error = 4.419199828724341e-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) = 2.193858999999865 y[1] (numeric) = 2.193858999999963 absolute error = 9.85878045867139e-14 relative error = 4.493807696243012e-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) = 2.217421333333194 y[1] (numeric) = 2.217421333333295 absolute error = 1.012523398458143e-13 relative error = 4.566220155084975e-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) = 2.241291666666522 y[1] (numeric) = 2.241291666666627 absolute error = 1.043609643147647e-13 relative error = 4.656286634482561e-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) = 2.265471999999852 y[1] (numeric) = 2.265471999999959 absolute error = 1.074695887837152e-13 relative error = 4.743805652143227e-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) = 2.28996433333318 y[1] (numeric) = 2.289964333333291 absolute error = 1.105782132526656e-13 relative error = 4.828818145464841e-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) = 2.314770666666509 y[1] (numeric) = 2.314770666666622 absolute error = 1.13242748511766e-13 relative error = 4.892180039366334e-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) = 2.339892999999837 y[1] (numeric) = 2.339892999999953 absolute error = 1.159072837708663e-13 relative error = 4.953529232784336e-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) = 2.365333333333166 y[1] (numeric) = 2.365333333333285 absolute error = 1.185718190299667e-13 relative error = 5.012901030015858e-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) = 2.391093666666494 y[1] (numeric) = 2.391093666666617 absolute error = 1.225686219186173e-13 relative error = 5.126048537006684e-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) = 2.417175999999823 y[1] (numeric) = 2.417175999999948 absolute error = 1.256772463875677e-13 relative error = 5.199341975411676e-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) = 2.443582333333151 y[1] (numeric) = 2.443582333333279 absolute error = 1.283417816466681e-13 relative error = 5.252197967547278e-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) = 2.470314666666479 y[1] (numeric) = 2.47031466666661 absolute error = 1.318944953254686e-13 relative error = 5.339177923574054e-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) = 2.497374999999807 y[1] (numeric) = 2.497374999999941 absolute error = 1.341149413747189e-13 relative error = 5.370236403212544e-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) = 2.524765333333135 y[1] (numeric) = 2.524765333333272 absolute error = 1.372235658436693e-13 relative error = 5.435101790728015e-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) = 2.552487666666463 y[1] (numeric) = 2.552487666666603 absolute error = 1.398881011027697e-13 relative error = 5.480461391825761e-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) = 2.58054399999979 y[1] (numeric) = 2.580543999999933 absolute error = 1.429967255717202e-13 relative error = 5.541340336445796e-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) = 2.608936333333118 y[1] (numeric) = 2.608936333333264 absolute error = 1.456612608308205e-13 relative error = 5.583166556031936e-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) = 2.637666666666446 y[1] (numeric) = 2.637666666666595 absolute error = 1.48769885299771e-13 relative error = 5.640207960310253e-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) = 2.666736999999773 y[1] (numeric) = 2.666736999999925 absolute error = 1.518785097687214e-13 relative error = 5.695293902950848e-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) = 2.696149333333101 y[1] (numeric) = 2.696149333333255 absolute error = 1.545430450278218e-13 relative error = 5.731991292810504e-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) = 2.725905666666428 y[1] (numeric) = 2.725905666666585 absolute error = 1.572075802869222e-13 relative error = 5.767168769239726e-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) = 2.756007999999755 y[1] (numeric) = 2.756007999999916 absolute error = 1.607602939657227e-13 relative error = 5.83308517122363e-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) = 2.786458333333083 y[1] (numeric) = 2.786458333333246 absolute error = 1.638689184346731e-13 relative error = 5.880903241020574e-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) = 2.817258666666409 y[1] (numeric) = 2.817258666666577 absolute error = 1.678657213233237e-13 relative error = 5.958477413149817e-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) = 2.848410999999737 y[1] (numeric) = 2.848410999999908 absolute error = 1.714184350021242e-13 relative error = 6.018037249615313e-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) = 2.879917333333063 y[1] (numeric) = 2.879917333333239 absolute error = 1.754152378907747e-13 relative error = 6.09098170494215e-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) = 2.91177966666639 y[1] (numeric) = 2.911779666666569 absolute error = 1.789679515695752e-13 relative error = 6.146342514111665e-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) = 2.943999999999717 y[1] (numeric) = 2.943999999999899 absolute error = 1.825206652483757e-13 relative error = 6.199750857622055e-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) = 2.976580333333043 y[1] (numeric) = 2.976580333333229 absolute error = 1.860733789271762e-13 relative error = 6.251246668650111e-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) = 3.00952266666637 y[1] (numeric) = 3.009522666666559 absolute error = 1.896260926059767e-13 relative error = 6.300869393883795e-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) = 3.042828999999696 y[1] (numeric) = 3.04282899999989 absolute error = 1.936228954946273e-13 relative error = 6.363252601268315e-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) = 3.076501333333022 y[1] (numeric) = 3.07650133333322 absolute error = 1.971756091734278e-13 relative error = 6.409085770159947e-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) = 3.110541666666349 y[1] (numeric) = 3.11054166666655 absolute error = 2.007283228522283e-13 relative error = 6.453162965257889e-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) = 3.144951999999674 y[1] (numeric) = 3.144951999999879 absolute error = 2.047251257408789e-13 relative error = 6.509642301087586e-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) = 3.179734333333001 y[1] (numeric) = 3.179734333333209 absolute error = 2.087219286295294e-13 relative error = 6.564131048355443e-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) = 3.214890666666327 y[1] (numeric) = 3.21489066666654 absolute error = 2.131628207280301e-13 relative error = 6.630484294169442e-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) = 3.250422999999652 y[1] (numeric) = 3.250422999999869 absolute error = 2.171596236166806e-13 relative error = 6.680965019528346e-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) = 3.286333333332978 y[1] (numeric) = 3.286333333333199 absolute error = 2.207123372954811e-13 relative error = 6.716066658753575e-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) = 3.322623666666304 y[1] (numeric) = 3.322623666666528 absolute error = 2.242650509742816e-13 relative error = 6.749637439358098e-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) = 3.359295999999629 y[1] (numeric) = 3.359295999999857 absolute error = 2.282618538629322e-13 relative error = 6.79493125532723e-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) = 3.396352333332954 y[1] (numeric) = 3.396352333333187 absolute error = 2.327027459614328e-13 relative error = 6.85154904800686e-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) = 3.43379466666628 y[1] (numeric) = 3.433794666666516 absolute error = 2.366995488500834e-13 relative error = 6.893235380317151e-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) = 3.471624999999605 y[1] (numeric) = 3.471624999999845 absolute error = 2.402522625288839e-13 relative error = 6.920455479175062e-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) = 3.50984533333293 y[1] (numeric) = 3.509845333333174 absolute error = 2.442490654175344e-13 relative error = 6.958969476458294e-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) = 3.548457666666255 y[1] (numeric) = 3.548457666666503 absolute error = 2.48245868306185e-13 relative error = 6.995880791764097e-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) = 3.58746399999958 y[1] (numeric) = 3.587463999999833 absolute error = 2.531308496145357e-13 relative error = 7.055982990061095e-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) = 3.626866333332904 y[1] (numeric) = 3.626866333333163 absolute error = 2.584599201327364e-13 relative error = 7.126259872257962e-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) = 3.666666666666229 y[1] (numeric) = 3.666666666666491 absolute error = 2.62456723021387e-13 relative error = 7.157910627856865e-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) = 3.706866999999554 y[1] (numeric) = 3.70686699999982 absolute error = 2.655653474903374e-13 relative error = 7.164145557161057e-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) = 3.747469333332878 y[1] (numeric) = 3.747469333333149 absolute error = 2.708944180085382e-13 relative error = 7.228729414781187e-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) = 3.788475666666203 y[1] (numeric) = 3.788475666666478 absolute error = 2.748912208971888e-13 relative error = 7.25598486261596e-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) = 3.829887999999527 y[1] (numeric) = 3.829887999999807 absolute error = 2.793321129956894e-13 relative error = 7.293479939771707e-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) = 3.871708333332851 y[1] (numeric) = 3.871708333333136 absolute error = 2.851052727237402e-13 relative error = 7.363810705191095e-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) = 3.913938666666175 y[1] (numeric) = 3.913938666666465 absolute error = 2.895461648222408e-13 relative error = 7.397820698832545e-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) = 3.956580999999499 y[1] (numeric) = 3.956580999999793 absolute error = 2.944311461305915e-13 relative error = 7.441554871001726e-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) = 3.999637333332823 y[1] (numeric) = 3.999637333333121 absolute error = 2.97983859809392e-13 relative error = 7.450271986562533e-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) = 4.043109666666146 y[1] (numeric) = 4.04310966666645 absolute error = 3.04645197957143e-13 relative error = 7.534922944802195e-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) = 4.08699999999947 y[1] (numeric) = 4.086999999999779 absolute error = 3.090860900556436e-13 relative error = 7.562664302806059e-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) = 4.131310333332793 y[1] (numeric) = 4.131310333333109 absolute error = 3.153033389935445e-13 relative error = 7.632041980714247e-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) = 4.176042666666117 y[1] (numeric) = 4.176042666666437 absolute error = 3.197442310920451e-13 relative error = 7.656632285974901e-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) = 4.221198999999439 y[1] (numeric) = 4.221198999999765 absolute error = 3.25961480029946e-13 relative error = 7.722011685068372e-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) = 4.266781333332762 y[1] (numeric) = 4.266781333333093 absolute error = 3.304023721284466e-13 relative error = 7.743597487579025e-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) = 4.312791666666085 y[1] (numeric) = 4.312791666666421 absolute error = 3.357314426466473e-13 relative error = 7.78455043960372e-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) = 4.359231999999407 y[1] (numeric) = 4.359231999999748 absolute error = 3.410605131648481e-13 relative error = 7.823866983103778e-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) = 4.406104333332731 y[1] (numeric) = 4.406104333333077 absolute error = 3.455014052633487e-13 relative error = 7.841425874770765e-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) = 4.453410666666054 y[1] (numeric) = 4.453410666666403 absolute error = 3.490541189421492e-13 relative error = 7.837905485672642e-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) = 4.501152999999375 y[1] (numeric) = 4.501152999999731 absolute error = 3.561595462997502e-13 relative error = 7.912629193004541e-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) = 4.549333333332697 y[1] (numeric) = 4.549333333333059 absolute error = 3.61488616817951e-13 relative error = 7.945969009774359e-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) = 4.597953666666021 y[1] (numeric) = 4.597953666666386 absolute error = 3.650413304967515e-13 relative error = 7.93921289688513e-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) = 4.647015999999342 y[1] (numeric) = 4.647015999999713 absolute error = 3.712585794346523e-13 relative error = 7.989182293211491e-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) = 4.696522333332664 y[1] (numeric) = 4.696522333333041 absolute error = 3.765876499528531e-13 relative error = 8.018436264639787e-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) = 4.746474666665986 y[1] (numeric) = 4.746474666666369 absolute error = 3.836930773104541e-13 relative error = 8.083748555640506e-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) = 4.796874999999307 y[1] (numeric) = 4.796874999999698 absolute error = 3.907985046680551e-13 relative error = 8.146939510996463e-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) = 4.84772533333263 y[1] (numeric) = 4.847725333333025 absolute error = 3.952393967665557e-13 relative error = 8.153089739819138e-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) = 4.899027666665951 y[1] (numeric) = 4.899027666666352 absolute error = 4.005684672847565e-13 relative error = 8.17648918397239e-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) = 4.950783999999272 y[1] (numeric) = 4.950783999999679 absolute error = 4.067857162226574e-13 relative error = 8.216591881663938e-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) = 5.002996333332592 y[1] (numeric) = 5.002996333333006 absolute error = 4.138911435802584e-13 relative error = 8.272865219242676e-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) = 5.055666666665914 y[1] (numeric) = 5.055666666666331 absolute error = 4.165556788393587e-13 relative error = 8.239381792828261e-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) = 5.108796999999234 y[1] (numeric) = 5.108796999999657 absolute error = 4.227729277772596e-13 relative error = 8.275391012352281e-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) = 5.162389333332556 y[1] (numeric) = 5.162389333332984 absolute error = 4.281019982954604e-13 relative error = 8.292710422503161e-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) = 5.216445666665877 y[1] (numeric) = 5.216445666666311 absolute error = 4.343192472333612e-13 relative error = 8.325961295997915e-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) = 5.270967999999197 y[1] (numeric) = 5.270967999999637 absolute error = 4.405364961712621e-13 relative error = 8.357791133835933e-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) = 5.325958333332517 y[1] (numeric) = 5.325958333332965 absolute error = 4.476419235288631e-13 relative error = 8.404908478673135e-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) = 5.381418666665837 y[1] (numeric) = 5.381418666666292 absolute error = 4.547473508864641e-13 relative error = 8.450324701612775e-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) = 5.437350999999157 y[1] (numeric) = 5.437350999999619 absolute error = 4.618527782440651e-13 relative error = 8.494076954828496e-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) = 5.493757333332478 y[1] (numeric) = 5.493757333332945 absolute error = 4.671818487622659e-13 relative error = 8.503867579438139e-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) = 5.550639666665798 y[1] (numeric) = 5.550639666666271 absolute error = 4.733990977001667e-13 relative error = 8.52873049106666e-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) = 5.607999999999117 y[1] (numeric) = 5.607999999999596 absolute error = 4.796163466380676e-13 relative error = 8.552359961450484e-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) = 5.665840333332437 y[1] (numeric) = 5.665840333332922 absolute error = 4.849454171562684e-13 relative error = 8.559108422157768e-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) = 5.724162666665756 y[1] (numeric) = 5.724162666666247 absolute error = 4.911626660941693e-13 relative error = 8.580515521587449e-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) = 5.782968999999076 y[1] (numeric) = 5.782968999999573 absolute error = 4.973799150320701e-13 relative error = 8.600770902146452e-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) = 5.842261333332394 y[1] (numeric) = 5.842261333332899 absolute error = 5.044853423896711e-13 relative error = 8.635104005214286e-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) = 5.902041666665713 y[1] (numeric) = 5.902041666666223 absolute error = 5.098144129078719e-13 relative error = 8.637933137396594e-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) = 5.962311999999033 y[1] (numeric) = 5.962311999999549 absolute error = 5.160316618457728e-13 relative error = 8.654891958788075e-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) = 6.02307433333235 y[1] (numeric) = 6.023074333332874 absolute error = 5.240252676230739e-13 relative error = 8.700295540486042e-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) = 6.084330666665669 y[1] (numeric) = 6.084330666666199 absolute error = 5.302425165609748e-13 relative error = 8.714886576859209e-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) = 6.146082999998988 y[1] (numeric) = 6.146082999999526 absolute error = 5.373479439185758e-13 relative error = 8.742933408459733e-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) = 6.208333333332306 y[1] (numeric) = 6.208333333332851 absolute error = 5.444533712761768e-13 relative error = 8.769718731966715e-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) = 6.271083666665625 y[1] (numeric) = 6.271083666666177 absolute error = 5.524469770534779e-13 relative error = 8.809434005641604e-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) = 6.334335999998943 y[1] (numeric) = 6.334335999999503 absolute error = 5.60440582830779e-13 relative error = 8.847661109718092e-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) = 6.398092333332261 y[1] (numeric) = 6.398092333332829 absolute error = 5.684341886080801e-13 relative error = 8.884432405682831e-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) = 6.462354666665578 y[1] (numeric) = 6.462354666666154 absolute error = 5.755396159656812e-13 relative error = 8.906035735464298e-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) = 6.527124999998896 y[1] (numeric) = 6.527124999999478 absolute error = 5.81756864903582e-13 relative error = 8.912911349233858e-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) = 6.592405333332213 y[1] (numeric) = 6.592405333332802 absolute error = 5.88862292261183e-13 relative error = 8.932434558958397e-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) = 6.65819766666553 y[1] (numeric) = 6.658197666666126 absolute error = 5.95967719618784e-13 relative error = 8.95088655301591e-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) = 6.724503999998848 y[1] (numeric) = 6.72450399999945 absolute error = 6.021849685566849e-13 relative error = 8.955083803307845e-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) = 6.791326333332165 y[1] (numeric) = 6.791326333332775 absolute error = 6.10178574333986e-13 relative error = 8.984674633277442e-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) = 6.858666666665481 y[1] (numeric) = 6.8586666666661 absolute error = 6.190603585309873e-13 relative error = 9.025957793513233e-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) = 6.926526999998798 y[1] (numeric) = 6.926526999999424 absolute error = 6.252776074688882e-13 relative error = 9.02728896413739e-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) = 6.994909333332115 y[1] (numeric) = 6.994909333332746 absolute error = 6.31494856406789e-13 relative error = 9.027920539264065e-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) = 7.063815666665431 y[1] (numeric) = 7.063815666666071 absolute error = 6.394884621840902e-13 relative error = 9.05301741099891e-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) = 7.133247999998748 y[1] (numeric) = 7.133247999999395 absolute error = 6.474820679613913e-13 relative error = 9.076960004215541e-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) = 7.203208333332063 y[1] (numeric) = 7.203208333332719 absolute error = 6.554756737386924e-13 relative error = 9.099773925815113e-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) = 7.273698666665379 y[1] (numeric) = 7.273698666666042 absolute error = 6.625811010962934e-13 relative error = 9.109273444785872e-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) = 7.344720999998695 y[1] (numeric) = 7.344720999999365 absolute error = 6.696865284538944e-13 relative error = 9.117930122247169e-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) = 7.416277333332011 y[1] (numeric) = 7.416277333332689 absolute error = 6.776801342311956e-13 relative error = 9.137739916836755e-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) = 7.488369666665325 y[1] (numeric) = 7.488369666666011 absolute error = 6.856737400084967e-13 relative error = 9.156515643996467e-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) = 7.560999999998642 y[1] (numeric) = 7.560999999999334 absolute error = 6.918909889463976e-13 relative error = 9.150786786754687e-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) = 7.634170333331956 y[1] (numeric) = 7.634170333332657 absolute error = 7.007727731433988e-13 relative error = 9.179422812767454e-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) = 7.707882666665273 y[1] (numeric) = 7.70788266666598 absolute error = 7.069900220812997e-13 relative error = 9.172298705828261e-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) = 7.782138999998587 y[1] (numeric) = 7.782138999999303 absolute error = 7.158718062783009e-13 relative error = 9.198907990186644e-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) = 7.856941333331901 y[1] (numeric) = 7.856941333332625 absolute error = 7.247535904753022e-13 relative error = 9.22437319724717e-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) = 7.932291666665216 y[1] (numeric) = 7.932291666665948 absolute error = 7.318590178329032e-13 relative error = 9.226325109910906e-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) = 8.00819199999853 y[1] (numeric) = 8.008191999999271 absolute error = 7.407408020299044e-13 relative error = 9.249788242215477e-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) = 8.084644333331845 y[1] (numeric) = 8.084644333332596 absolute error = 7.513989430663059e-13 relative error = 9.294149650695138e-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) = 8.16165066666516 y[1] (numeric) = 8.161650666665921 absolute error = 7.602807272633072e-13 relative error = 9.315281409538163e-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) = 8.239212999998472 y[1] (numeric) = 8.239212999999243 absolute error = 7.709388682997087e-13 relative error = 9.356947906309155e-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) = 8.317333333331785 y[1] (numeric) = 8.317333333332565 absolute error = 7.7982065249671e-13 relative error = 9.375849460927242e-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) = 8.396013666665098 y[1] (numeric) = 8.396013666665887 absolute error = 7.887024366937112e-13 relative error = 9.393772664105064e-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) = 8.475255999998414 y[1] (numeric) = 8.475255999999208 absolute error = 7.94031507211912e-13 relative error = 9.368820330761225e-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) = 8.555062333331726 y[1] (numeric) = 8.555062333332531 absolute error = 8.046896482483135e-13 relative error = 9.406005671205099e-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) = 8.635434666665038 y[1] (numeric) = 8.635434666665853 absolute error = 8.15347789284715e-13 relative error = 9.441884754593346e-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) = 8.716374999998354 y[1] (numeric) = 8.716374999999177 absolute error = 8.22453216642316e-13 relative error = 9.435725478108401e-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) = 8.797885333331664 y[1] (numeric) = 8.797885333332498 absolute error = 8.348877145181177e-13 relative error = 9.489640781689466e-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) = 8.879967666664978 y[1] (numeric) = 8.87996766666582 absolute error = 8.419931418757187e-13 relative error = 9.481939275933686e-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) = 8.962623999998289 y[1] (numeric) = 8.962623999999142 absolute error = 8.526512829121202e-13 relative error = 9.513411283484424e-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) = 9.045856333331603 y[1] (numeric) = 9.045856333332463 absolute error = 8.597567102697212e-13 relative error = 9.504425878418428e-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) = 9.129666666664916 y[1] (numeric) = 9.129666666665788 absolute error = 8.72191208145523e-13 relative error = 9.553374071477859e-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) = 9.214056999998226 y[1] (numeric) = 9.214056999999109 absolute error = 8.828493491819245e-13 relative error = 9.5815485966941e-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) = 9.299029333331537 y[1] (numeric) = 9.299029333332431 absolute error = 8.93507490218326e-13 relative error = 9.608610298879566e-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) = 9.384585666664849 y[1] (numeric) = 9.384585666665751 absolute error = 9.023892744153272e-13 relative error = 9.615653865473465e-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) = 9.470727999998161 y[1] (numeric) = 9.47072799999907 absolute error = 9.094947017729282e-13 relative error = 9.603218483025854e-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) = 9.557458333331471 y[1] (numeric) = 9.557458333332393 absolute error = 9.2192919964873e-13 relative error = 9.646175452667345e-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) = 9.644778666664783 y[1] (numeric) = 9.644778666665715 absolute error = 9.325873406851315e-13 relative error = 9.669349322742159e-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) = 9.732690999998093 y[1] (numeric) = 9.732690999999038 absolute error = 9.450218385609332e-13 relative error = 9.709769256633323e-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) = 9.821197333331403 y[1] (numeric) = 9.821197333332357 absolute error = 9.539036227579345e-13 relative error = 9.712701928109669e-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) = 9.910299666664717 y[1] (numeric) = 9.910299666665678 absolute error = 9.610090501155355e-13 relative error = 9.697073574354995e-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) = 9.999999999998026 y[1] (numeric) = 9.999999999998998 absolute error = 9.71667191151937e-13 relative error = 9.716671911521288e-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) = 10.09030033333134 y[1] (numeric) = 10.09030033333232 absolute error = 9.805489753489383e-13 relative error = 9.717738253140853e-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) = 10.18120266666465 y[1] (numeric) = 10.18120266666564 absolute error = 9.912071163853398e-13 relative error = 9.735658436804878e-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) = 10.27270899999796 y[1] (numeric) = 10.27270899999895 absolute error = 9.983125437429408e-13 relative error = 9.718103995188994e-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) = 10.36482133333127 y[1] (numeric) = 10.36482133333227 absolute error = 1.005417971100542e-12 relative error = 9.700292352047705e-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) = 10.45754166666458 y[1] (numeric) = 10.45754166666559 absolute error = 1.016076112136943e-12 relative error = 9.716204290879196e-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) = 10.55087199999788 y[1] (numeric) = 10.55087199999891 absolute error = 1.028510610012745e-12 relative error = 9.748110014157611e-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) = 10.64481433333119 y[1] (numeric) = 10.64481433333223 absolute error = 1.035616037370346e-12 relative error = 9.728831381563982e-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) = 10.7393706666645 y[1] (numeric) = 10.73937066666555 absolute error = 1.046274178406748e-12 relative error = 9.742416114329961e-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) = 10.83454299999781 y[1] (numeric) = 10.83454299999887 absolute error = 1.06048503312195e-12 relative error = 9.787999670333708e-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) = 10.93033333333112 y[1] (numeric) = 10.93033333333219 absolute error = 1.069366817318951e-12 relative error = 9.783478551912117e-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) = 11.02674366666443 y[1] (numeric) = 11.02674366666551 absolute error = 1.080024958355352e-12 relative error = 9.7945956757881e-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) = 11.12377599999773 y[1] (numeric) = 11.12377599999883 absolute error = 1.094235813070554e-12 relative error = 9.836909814354201e-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) = 11.22143233333104 y[1] (numeric) = 11.22143233333215 absolute error = 1.106670310946356e-12 relative error = 9.86211276843163e-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) = 11.31971466666435 y[1] (numeric) = 11.31971466666547 absolute error = 1.115552095143357e-12 relative error = 9.854948892206342e-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) = 11.41862499999766 y[1] (numeric) = 11.41862499999879 absolute error = 1.127986593019159e-12 relative error = 9.878480053591305e-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) = 11.51816533333097 y[1] (numeric) = 11.5181653333321 absolute error = 1.13686837721616e-12 relative error = 9.870221031871457e-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) = 11.61833766666427 y[1] (numeric) = 11.61833766666542 absolute error = 1.151079231931362e-12 relative error = 9.907434823779289e-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) = 11.71914399999758 y[1] (numeric) = 11.71914399999874 absolute error = 1.158184659288963e-12 relative error = 9.882843484892773e-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) = 11.82058633333089 y[1] (numeric) = 11.82058633333206 absolute error = 1.168842800325365e-12 relative error = 9.888196468135775e-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) = 11.92266666666419 y[1] (numeric) = 11.92266666666537 absolute error = 1.179500941361766e-12 relative error = 9.892928942311655e-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) = 12.0253869999975 y[1] (numeric) = 12.02538699999869 absolute error = 1.188382725558768e-12 relative error = 9.882282587321426e-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) = 12.12874933333081 y[1] (numeric) = 12.12874933333201 absolute error = 1.199040866595169e-12 relative error = 9.885939874279581e-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) = 12.23275566666411 y[1] (numeric) = 12.23275566666532 absolute error = 1.211475364470971e-12 relative error = 9.903536026411468e-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) = 12.33740799999742 y[1] (numeric) = 12.33740799999864 absolute error = 1.225686219186173e-12 relative error = 9.934714157029007e-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) = 12.44270833333073 y[1] (numeric) = 12.44270833333196 absolute error = 1.236344360222574e-12 relative error = 9.936296239547259e-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) = 12.54865866666403 y[1] (numeric) = 12.54865866666528 absolute error = 1.247002501258976e-12 relative error = 9.937337004565144e-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) = 12.65526099999734 y[1] (numeric) = 12.6552609999986 absolute error = 1.259436999134778e-12 relative error = 9.951884825884213e-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) = 12.76251733333064 y[1] (numeric) = 12.76251733333192 absolute error = 1.27364785384998e-12 relative error = 9.979597446059608e-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) = 12.87042966666395 y[1] (numeric) = 12.87042966666523 absolute error = 1.287858708565182e-12 relative error = 1.000633810929327e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999748 y[1] (closed_form) = 12.97899999999725 y[1] (numeric) = 12.97899999999855 absolute error = 1.298516849601583e-12 relative error = 1.000475267433437e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y[1] (closed_form) = 13.08823033333056 y[1] (numeric) = 13.08823033333187 absolute error = 1.309174990637985e-12 relative error = 1.000268911301196e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999745 y[1] (closed_form) = 13.19812266666386 y[1] (numeric) = 13.19812266666518 absolute error = 1.321609488513786e-12 relative error = 1.001361725370184e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999744 y[1] (closed_form) = 13.30867899999716 y[1] (numeric) = 13.3086789999985 absolute error = 1.335820343228988e-12 relative error = 1.003721213224298e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y[1] (closed_form) = 13.41990133333047 y[1] (numeric) = 13.41990133333181 absolute error = 1.34825484110479e-12 relative error = 1.004668221931099e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y[1] (closed_form) = 13.53179166666377 y[1] (numeric) = 13.53179166666513 absolute error = 1.360689338980592e-12 relative error = 1.005550020647093e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y[1] (closed_form) = 13.64435199999708 y[1] (numeric) = 13.64435199999845 absolute error = 1.371347480016993e-12 relative error = 1.005066037593641e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y[1] (closed_form) = 13.75758433333038 y[1] (numeric) = 13.75758433333176 absolute error = 1.383781977892795e-12 relative error = 1.005832088225197e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y[1] (closed_form) = 13.87149066666368 y[1] (numeric) = 13.87149066666508 absolute error = 1.394440118929197e-12 relative error = 1.005256141850962e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y[1] (closed_form) = 13.98607299999698 y[1] (numeric) = 13.98607299999839 absolute error = 1.408650973644399e-12 relative error = 1.007181196354904e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999737 y[1] (closed_form) = 14.10133333333029 y[1] (numeric) = 14.10133333333171 absolute error = 1.4193091146808e-12 relative error = 1.006507031023856e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = 14.21727366666359 y[1] (numeric) = 14.21727366666502 absolute error = 1.433519969396002e-12 relative error = 1.0082945598475e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y[1] (closed_form) = 14.33389599999689 y[1] (numeric) = 14.33389599999834 absolute error = 1.445954467271804e-12 relative error = 1.008765842358642e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y[1] (closed_form) = 14.45120233333019 y[1] (numeric) = 14.45120233333165 absolute error = 1.458388965147606e-12 relative error = 1.009181749385643e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y[1] (closed_form) = 14.5691946666635 y[1] (numeric) = 14.56919466666497 absolute error = 1.470823463023407e-12 relative error = 1.009543421359365e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y[1] (closed_form) = 14.6878749999968 y[1] (numeric) = 14.68787499999828 absolute error = 1.481481604059809e-12 relative error = 1.008642573592253e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y[1] (closed_form) = 14.8072453333301 y[1] (numeric) = 14.8072453333316 absolute error = 1.493916101935611e-12 relative error = 1.008908860700043e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999729 y[1] (closed_form) = 14.9273076666634 y[1] (numeric) = 14.92730766666491 absolute error = 1.504574242972012e-12 relative error = 1.007934100756911e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999728 y[1] (closed_form) = 15.0480639999967 y[1] (numeric) = 15.04806399999822 absolute error = 1.518785097687214e-12 relative error = 1.009289366185276e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999727 y[1] (closed_form) = 15.16951633333 y[1] (numeric) = 15.16951633333153 absolute error = 1.529443238723616e-12 relative error = 1.008234676120272e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999726 y[1] (closed_form) = 15.29166666666331 y[1] (numeric) = 15.29166666666485 absolute error = 1.541877736599417e-12 relative error = 1.008312416305018e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = 15.41451699999661 y[1] (numeric) = 15.41451699999816 absolute error = 1.556088591314619e-12 relative error = 1.009495523807176e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y[1] (closed_form) = 15.53806933332991 y[1] (numeric) = 15.53806933333147 absolute error = 1.566746732351021e-12 relative error = 1.008327803628906e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y[1] (closed_form) = 15.66232566666321 y[1] (numeric) = 15.66232566666478 absolute error = 1.579181230226823e-12 relative error = 1.008267395172393e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y[1] (closed_form) = 15.78728799999651 y[1] (numeric) = 15.7872879999981 absolute error = 1.591615728102624e-12 relative error = 1.008162851088152e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y[1] (closed_form) = 15.91295833332981 y[1] (numeric) = 15.91295833333141 absolute error = 1.604050225978426e-12 relative error = 1.008015098373463e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y[1] (closed_form) = 16.03933866666311 y[1] (numeric) = 16.03933866666473 absolute error = 1.620037437533028e-12 relative error = 1.010040046663637e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999718 y[1] (closed_form) = 16.1664309999964 y[1] (numeric) = 16.16643099999804 absolute error = 1.641353719605831e-12 relative error = 1.015285142160441e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999717 y[1] (closed_form) = 16.2942373333297 y[1] (numeric) = 16.29423733333136 absolute error = 1.652011860642233e-12 relative error = 1.01386264778595e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999716 y[1] (closed_form) = 16.422759666663 y[1] (numeric) = 16.42275966666467 absolute error = 1.666222715357435e-12 relative error = 1.014581440133807e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999715 y[1] (closed_form) = 16.5519999999963 y[1] (numeric) = 16.55199999999798 absolute error = 1.683986283751437e-12 relative error = 1.017391423243e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = 16.6819603333296 y[1] (numeric) = 16.6819603333313 absolute error = 1.698197138466639e-12 relative error = 1.017984160454895e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y[1] (closed_form) = 16.8126426666629 y[1] (numeric) = 16.81264266666461 absolute error = 1.712407993181841e-12 relative error = 1.01852399241037e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y[1] (closed_form) = 16.9440489999962 y[1] (numeric) = 16.94404899999792 absolute error = 1.726618847897043e-12 relative error = 1.01901195392992e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y[1] (closed_form) = 17.07618133332949 y[1] (numeric) = 17.07618133333124 absolute error = 1.744382416291046e-12 relative error = 1.021529569310874e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y[1] (closed_form) = 17.20904166666279 y[1] (numeric) = 17.20904166666455 absolute error = 1.762145984685048e-12 relative error = 1.023965203186568e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999708 y[1] (closed_form) = 17.34263199999609 y[1] (numeric) = 17.34263199999786 absolute error = 1.77635683940025e-12 relative error = 1.024271771090254e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999707 y[1] (closed_form) = 17.47695433332938 y[1] (numeric) = 17.47695433333118 absolute error = 1.790567694115452e-12 relative error = 1.02453073914644e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999706 y[1] (closed_form) = 17.61201066666268 y[1] (numeric) = 17.61201066666449 absolute error = 1.804778548830654e-12 relative error = 1.024743047792307e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999705 y[1] (closed_form) = 17.74780299999598 y[1] (numeric) = 17.7478029999978 absolute error = 1.818989403545856e-12 relative error = 1.024909620388658e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999704 y[1] (closed_form) = 17.88433333332927 y[1] (numeric) = 17.8843333333311 absolute error = 1.829647544582258e-12 relative error = 1.023044868646305e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y[1] (closed_form) = 18.02160366666257 y[1] (numeric) = 18.02160366666442 absolute error = 1.84385839929746e-12 relative error = 1.023137803606423e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y[1] (closed_form) = 18.15961599999587 y[1] (numeric) = 18.15961599999772 absolute error = 1.850963826655061e-12 relative error = 1.019274761457226e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y[1] (closed_form) = 18.29837233332916 y[1] (numeric) = 18.29837233333103 absolute error = 1.865174681370263e-12 relative error = 1.019311798554335e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y[1] (closed_form) = 18.43787466666246 y[1] (numeric) = 18.43787466666434 absolute error = 1.882938249764265e-12 relative error = 1.021233891544348e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y[1] (closed_form) = 18.57812499999575 y[1] (numeric) = 18.57812499999765 absolute error = 1.897149104479467e-12 relative error = 1.021173613849568e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999697 y[1] (closed_form) = 18.71912533332905 y[1] (numeric) = 18.71912533333096 absolute error = 1.91491267287347e-12 relative error = 1.022971233310781e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999696 y[1] (closed_form) = 18.86087766666234 y[1] (numeric) = 18.86087766666428 absolute error = 1.932676241267473e-12 relative error = 1.024701117002411e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999695 y[1] (closed_form) = 19.00338399999564 y[1] (numeric) = 19.00338399999759 absolute error = 1.950439809661475e-12 relative error = 1.026364467329568e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999694 y[1] (closed_form) = 19.14664633332893 y[1] (numeric) = 19.1466463333309 absolute error = 1.968203378055478e-12 relative error = 1.027962466006064e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999693 y[1] (closed_form) = 19.29066666666223 y[1] (numeric) = 19.29066666666421 absolute error = 1.98241423277068e-12 relative error = 1.027654599515034e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y[1] (closed_form) = 19.43544699999552 y[1] (numeric) = 19.43544699999752 absolute error = 2.003730514843483e-12 relative error = 1.030967034019822e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y[1] (closed_form) = 19.58098933332881 y[1] (numeric) = 19.58098933333083 absolute error = 2.021494083237485e-12 relative error = 1.032375866625237e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y[1] (closed_form) = 19.7272956666621 y[1] (numeric) = 19.72729566666414 absolute error = 2.039257651631488e-12 relative error = 1.033723874822693e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y[1] (closed_form) = 19.8743679999954 y[1] (numeric) = 19.87436799999745 absolute error = 2.049915792667889e-12 relative error = 1.031436970810022e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y[1] (closed_form) = 20.0222083333287 y[1] (numeric) = 20.02220833333077 absolute error = 2.074784788419493e-12 relative error = 1.036241734117727e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999686 y[1] (closed_form) = 20.17081866666199 y[1] (numeric) = 20.17081866666408 absolute error = 2.092548356813495e-12 relative error = 1.037413697180287e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999685 y[1] (closed_form) = 20.32020099999528 y[1] (numeric) = 20.32020099999739 absolute error = 2.113864638886298e-12 relative error = 1.040277425841796e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999684 y[1] (closed_form) = 20.47035733332857 y[1] (numeric) = 20.4703573333307 absolute error = 2.1280754936015e-12 relative error = 1.039588835186916e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999683 y[1] (closed_form) = 20.62128966666186 y[1] (numeric) = 20.621289666664 absolute error = 2.142286348316702e-12 relative error = 1.038871177771245e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y[1] (closed_form) = 20.77299999999515 y[1] (numeric) = 20.77299999999731 absolute error = 2.156497203031904e-12 relative error = 1.038125067651474e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y[1] (closed_form) = 20.92549033332845 y[1] (numeric) = 20.92549033333063 absolute error = 2.177813485104707e-12 relative error = 1.040746692389836e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y[1] (closed_form) = 21.07876266666174 y[1] (numeric) = 21.07876266666393 absolute error = 2.192024339819909e-12 relative error = 1.039920784006371e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y[1] (closed_form) = 21.23281899999503 y[1] (numeric) = 21.23281899999724 absolute error = 2.209787908213912e-12 relative error = 1.040741650091036e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y[1] (closed_form) = 21.38766133332832 y[1] (numeric) = 21.38766133333054 absolute error = 2.223998762929114e-12 relative error = 1.039851308784034e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y[1] (closed_form) = 21.54329166666161 y[1] (numeric) = 21.54329166666385 absolute error = 2.238209617644316e-12 relative error = 1.038935763520279e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999675 y[1] (closed_form) = 21.6997119999949 y[1] (numeric) = 21.69971199999716 absolute error = 2.252420472359518e-12 relative error = 1.037995560659997e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999674 y[1] (closed_form) = 21.85692433332819 y[1] (numeric) = 21.85692433333046 absolute error = 2.273736754432321e-12 relative error = 1.040282118269151e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999673 y[1] (closed_form) = 22.01493066666148 y[1] (numeric) = 22.01493066666377 absolute error = 2.291500322826323e-12 relative error = 1.04088464211994e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999672 y[1] (closed_form) = 22.17373299999477 y[1] (numeric) = 22.17373299999708 absolute error = 2.305711177541525e-12 relative error = 1.039838974133074e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y[1] (closed_form) = 22.33333333332806 y[1] (numeric) = 22.33333333333039 absolute error = 2.330580173293129e-12 relative error = 1.043543361176274e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999674 y[1] (closed_form) = 22.49373366666142 y[1] (numeric) = 22.4937336666637 absolute error = 2.273736754432321e-12 relative error = 1.010831188866741e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999677 y[1] (closed_form) = 22.65493599999479 y[1] (numeric) = 22.654935999997 absolute error = 2.213340621892712e-12 relative error = 9.769794193606291e-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) = 22.81694233332814 y[1] (numeric) = 22.81694233333031 absolute error = 2.167155344068306e-12 relative error = 9.498009472122807e-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) = 22.97975466666151 y[1] (numeric) = 22.97975466666362 absolute error = 2.110311925207498e-12 relative error = 9.183352719901267e-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) = 23.14337499999487 y[1] (numeric) = 23.14337499999693 absolute error = 2.05346850634669e-12 relative error = 8.872813521567812e-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) = 23.30780533332823 y[1] (numeric) = 23.30780533333024 absolute error = 2.003730514843483e-12 relative error = 8.596821906601021e-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) = 23.4730476666616 y[1] (numeric) = 23.47304766666354 absolute error = 1.946887095982675e-12 relative error = 8.294138552565579e-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) = 23.63910399999496 y[1] (numeric) = 23.63910399999686 absolute error = 1.893596390800667e-12 relative error = 8.010440627534236e-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) = 23.80597633332832 y[1] (numeric) = 23.80597633333016 absolute error = 1.84385839929746e-12 relative error = 7.745359289112885e-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) = 23.97366666666169 y[1] (numeric) = 23.97366666666348 absolute error = 1.787014980436652e-12 relative error = 7.454074528039194e-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) = 24.14217699999505 y[1] (numeric) = 24.14217699999679 absolute error = 1.730171561575844e-12 relative error = 7.166592977825481e-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) = 24.31150933332842 y[1] (numeric) = 24.31150933333009 absolute error = 1.673328142715036e-12 relative error = 6.882864077966094e-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) = 24.48166566666179 y[1] (numeric) = 24.48166566666341 absolute error = 1.620037437533028e-12 relative error = 6.617349732616987e-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) = 24.65264799999515 y[1] (numeric) = 24.65264799999672 absolute error = 1.56319401867222e-12 relative error = 6.340876723151719e-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) = 24.82445833332852 y[1] (numeric) = 24.82445833333003 absolute error = 1.506350599811412e-12 relative error = 6.068009942392315e-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) = 24.99709866666189 y[1] (numeric) = 24.99709866666334 absolute error = 1.453059894629405e-12 relative error = 5.812914186586464e-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) = 25.17057099999526 y[1] (numeric) = 25.17057099999666 absolute error = 1.396216475768597e-12 relative error = 5.54701947670897e-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) = 25.34487733332863 y[1] (numeric) = 25.34487733332997 absolute error = 1.342925770586589e-12 relative error = 5.298608286498337e-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) = 25.52001966666199 y[1] (numeric) = 25.52001966666328 absolute error = 1.286082351725781e-12 relative error = 5.039503764199098e-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) = 25.69599999999537 y[1] (numeric) = 25.69599999999659 absolute error = 1.229238932864973e-12 relative error = 4.783775423665921e-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) = 25.87282033332873 y[1] (numeric) = 25.87282033332991 absolute error = 1.179500941361766e-12 relative error = 4.558841773590342e-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) = 26.05048266666211 y[1] (numeric) = 26.05048266666322 absolute error = 1.119104808822158e-12 relative error = 4.295908153188744e-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) = 26.22898899999548 y[1] (numeric) = 26.22898899999654 absolute error = 1.058708676282549e-12 relative error = 4.036406726476311e-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) = 26.40834133332885 y[1] (numeric) = 26.40834133332985 absolute error = 1.001865257421741e-12 relative error = 3.793745486610057e-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) = 26.58854166666222 y[1] (numeric) = 26.58854166666316 absolute error = 9.450218385609332e-13 relative error = 3.554244720934956e-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) = 26.7695919999956 y[1] (numeric) = 26.76959199999648 absolute error = 8.810729923425242e-13 relative error = 3.291320212660205e-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) = 26.95149433332897 y[1] (numeric) = 26.95149433332979 absolute error = 8.242295734817162e-13 relative error = 3.058196192344152e-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) = 27.13425066666234 y[1] (numeric) = 27.13425066666311 absolute error = 7.673861546209082e-13 relative error = 2.828108887354437e-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) = 27.31786299999571 y[1] (numeric) = 27.31786299999642 absolute error = 7.069900220812997e-13 relative error = 2.588013645435628e-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) = 27.50233333332909 y[1] (numeric) = 27.50233333332973 absolute error = 6.394884621840902e-13 relative error = 2.32521529876564e-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) = 27.68766366666247 y[1] (numeric) = 27.68766366666305 absolute error = 5.755396159656812e-13 relative error = 2.078686099682234e-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) = 27.87385599999584 y[1] (numeric) = 27.87385599999635 absolute error = 5.080380560684716e-13 relative error = 1.822632850182434e-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) = 28.06091233332922 y[1] (numeric) = 28.06091233332966 absolute error = 4.405364961712621e-13 relative error = 1.569929341349379e-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) = 28.2488346666626 y[1] (numeric) = 28.24883466666298 absolute error = 3.836930773104541e-13 relative error = 1.358261612693224e-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) = 28.43762499999598 y[1] (numeric) = 28.4376249999963 absolute error = 3.232969447708456e-13 relative error = 1.136863380014651e-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) = 28.62728533332936 y[1] (numeric) = 28.62728533332962 absolute error = 2.593480985524366e-13 relative error = 9.059472301779525e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y[1] (closed_form) = 28.81781766666273 y[1] (numeric) = 28.81781766666293 absolute error = 1.989519660128281e-13 relative error = 6.903783218913946e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = 29.00922399999611 y[1] (numeric) = 29.00922399999624 absolute error = 1.35003119794419e-13 relative error = 4.653799763635082e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = 29.20150633332949 y[1] (numeric) = 29.20150633332956 absolute error = 6.394884621840902e-14 relative error = 2.189916009415591e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = 29.39466666666288 y[1] (numeric) = 29.39466666666288 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] = 4.409999999999807 y[1] (closed_form) = 29.58870699999626 y[1] (numeric) = 29.58870699999619 absolute error = 7.105427357601002e-14 relative error = 2.401398397571716e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y[1] (closed_form) = 29.78362933332964 y[1] (numeric) = 29.7836293333295 absolute error = 1.35003119794419e-13 relative error = 4.532796130501885e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y[1] (closed_form) = 29.97943566666302 y[1] (numeric) = 29.97943566666283 absolute error = 1.918465386552271e-13 relative error = 6.399271180029564e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = 30.1761279999964 y[1] (numeric) = 30.17612799999614 absolute error = 2.593480985524366e-13 relative error = 8.594479005141664e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y[1] (closed_form) = 30.37370833332978 y[1] (numeric) = 30.37370833332946 absolute error = 3.268496584496461e-13 relative error = 1.076094018098496e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y[1] (closed_form) = 30.57217866666317 y[1] (numeric) = 30.57217866666278 absolute error = 3.907985046680551e-13 relative error = 1.278281502044843e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 30.77154099999655 y[1] (numeric) = 30.7715409999961 absolute error = 4.511946372076636e-13 relative error = 1.466272479521628e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y[1] (closed_form) = 30.97179733332993 y[1] (numeric) = 30.97179733332942 absolute error = 5.186961971048731e-13 relative error = 1.674737153683633e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y[1] (closed_form) = 31.17294966666332 y[1] (numeric) = 31.17294966666274 absolute error = 5.861977570020827e-13 relative error = 1.880469327639433e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 31.37499999999671 y[1] (numeric) = 31.37499999999605 absolute error = 6.536993168992922e-13 relative error = 2.083503798882425e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y[1] (closed_form) = 31.57795033333009 y[1] (numeric) = 31.57795033332937 absolute error = 7.212008767965017e-13 relative error = 2.283874884796699e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y[1] (closed_form) = 31.78180266666348 y[1] (numeric) = 31.78180266666269 absolute error = 7.922551503725117e-13 relative error = 2.492794882285021e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = 31.98655899999687 y[1] (numeric) = 31.98655899999602 absolute error = 8.562039965909207e-13 relative error = 2.676761812957137e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y[1] (closed_form) = 32.19222133333025 y[1] (numeric) = 32.19222133332934 absolute error = 9.094947017729282e-13 relative error = 2.825200200867412e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y[1] (closed_form) = 32.39879166666364 y[1] (numeric) = 32.39879166666265 absolute error = 9.876544027065393e-13 relative error = 3.048429746603096e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y[1] (closed_form) = 32.60627199999703 y[1] (numeric) = 32.60627199999598 absolute error = 1.058708676282549e-12 relative error = 3.246947937754569e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y[1] (closed_form) = 32.81466433333043 y[1] (numeric) = 32.8146643333293 absolute error = 1.122657522500958e-12 relative error = 3.421206784555329e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y[1] (closed_form) = 33.02397066666381 y[1] (numeric) = 33.02397066666262 absolute error = 1.193711796076968e-12 relative error = 3.614682825775296e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y[1] (closed_form) = 33.23419299999721 y[1] (numeric) = 33.23419299999595 absolute error = 1.257660642295377e-12 relative error = 3.784237042540744e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y[1] (closed_form) = 33.4453333333306 y[1] (numeric) = 33.44533333332928 absolute error = 1.321609488513786e-12 relative error = 3.951551253330492e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y[1] (closed_form) = 33.65739366666399 y[1] (numeric) = 33.65739366666261 absolute error = 1.385558334732195e-12 relative error = 4.116653679291048e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y[1] (closed_form) = 33.87037599999739 y[1] (numeric) = 33.87037599999594 absolute error = 1.449507180950604e-12 relative error = 4.279572157541789e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y[1] (closed_form) = 34.08428233333078 y[1] (numeric) = 34.08428233332926 absolute error = 1.527666881884215e-12 relative error = 4.482027425263757e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y[1] (closed_form) = 34.29911466666417 y[1] (numeric) = 34.29911466666257 absolute error = 1.605826582817826e-12 relative error = 4.68183099891658e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y[1] (closed_form) = 34.51487499999757 y[1] (numeric) = 34.5148749999959 absolute error = 1.669775429036235e-12 relative error = 4.837842898276042e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y[1] (closed_form) = 34.73156533333096 y[1] (numeric) = 34.73156533332922 absolute error = 1.740829702612245e-12 relative error = 5.012240841738329e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y[1] (closed_form) = 34.94918766666436 y[1] (numeric) = 34.94918766666254 absolute error = 1.826094830903457e-12 relative error = 5.224999357124526e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y[1] (closed_form) = 35.16774399999775 y[1] (numeric) = 35.16774399999586 absolute error = 1.890043677121866e-12 relative error = 5.374367139165899e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y[1] (closed_form) = 35.38723633333115 y[1] (numeric) = 35.38723633332919 absolute error = 1.961097950697877e-12 relative error = 5.541822854503964e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y[1] (closed_form) = 35.60766666666455 y[1] (numeric) = 35.60766666666252 absolute error = 2.032152224273887e-12 relative error = 5.707063715512597e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y[1] (closed_form) = 35.82903699999795 y[1] (numeric) = 35.82903699999584 absolute error = 2.110311925207498e-12 relative error = 5.889948773135092e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y[1] (closed_form) = 36.05134933333135 y[1] (numeric) = 36.05134933332917 absolute error = 2.181366198783508e-12 relative error = 6.050719984471485e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y[1] (closed_form) = 36.27460566666475 y[1] (numeric) = 36.27460566666251 absolute error = 2.238209617644316e-12 relative error = 6.170183180519483e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y[1] (closed_form) = 36.49880799999815 y[1] (numeric) = 36.49880799999583 absolute error = 2.316369318577927e-12 relative error = 6.346424569750453e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y[1] (closed_form) = 36.72395833333155 y[1] (numeric) = 36.72395833332916 absolute error = 2.387423592153937e-12 relative error = 6.50099744282482e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y[1] (closed_form) = 36.95005866666495 y[1] (numeric) = 36.95005866666249 absolute error = 2.458477865729947e-12 relative error = 6.653515459632813e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y[1] (closed_form) = 37.17711099999836 y[1] (numeric) = 37.17711099999583 absolute error = 2.529532139305957e-12 relative error = 6.804004053209161e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y[1] (closed_form) = 37.40511733333176 y[1] (numeric) = 37.40511733332916 absolute error = 2.600586412881967e-12 relative error = 6.952488317860669e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y[1] (closed_form) = 37.63407966666516 y[1] (numeric) = 37.63407966666249 absolute error = 2.664535259100376e-12 relative error = 7.080112713532145e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y[1] (closed_form) = 37.86399999999856 y[1] (numeric) = 37.86399999999583 absolute error = 2.735589532676386e-12 relative error = 7.224776919175178e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y[1] (closed_form) = 38.09488033333196 y[1] (numeric) = 38.09488033332915 absolute error = 2.813749233609997e-12 relative error = 7.38616110351197e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y[1] (closed_form) = 38.32672266666537 y[1] (numeric) = 38.32672266666248 absolute error = 2.891908934543608e-12 relative error = 7.545411486640997e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y[1] (closed_form) = 38.55952899999878 y[1] (numeric) = 38.55952899999581 absolute error = 2.970068635477219e-12 relative error = 7.702554238868719e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y[1] (closed_form) = 38.79330133333219 y[1] (numeric) = 38.79330133332913 absolute error = 3.055333763768431e-12 relative error = 7.875931304519346e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y[1] (closed_form) = 39.02804166666559 y[1] (numeric) = 39.02804166666247 absolute error = 3.126388037344441e-12 relative error = 8.010619810357365e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y[1] (closed_form) = 39.263751999999 y[1] (numeric) = 39.2637519999958 absolute error = 3.204547738278052e-12 relative error = 8.161593263624254e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y[1] (closed_form) = 39.50043433333241 y[1] (numeric) = 39.50043433332912 absolute error = 3.282707439211663e-12 relative error = 8.310560363741503e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y[1] (closed_form) = 39.73809066666582 y[1] (numeric) = 39.73809066666245 absolute error = 3.367972567502875e-12 relative error = 8.475426249726911e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y[1] (closed_form) = 39.97672299999923 y[1] (numeric) = 39.97672299999579 absolute error = 3.439026841078885e-12 relative error = 8.602573155080649e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y[1] (closed_form) = 40.21633333333264 y[1] (numeric) = 40.21633333332911 absolute error = 3.531397396727698e-12 relative error = 8.781002901129122e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y[1] (closed_form) = 40.45692366666605 y[1] (numeric) = 40.45692366666245 absolute error = 3.602451670303708e-12 relative error = 8.904413247001034e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y[1] (closed_form) = 40.69849599999946 y[1] (numeric) = 40.69849599999578 absolute error = 3.680611371237319e-12 relative error = 9.043605373617167e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y[1] (closed_form) = 40.94105233333287 y[1] (numeric) = 40.94105233332911 absolute error = 3.75877107217093e-12 relative error = 9.180934191842111e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 41.18459466666629 y[1] (numeric) = 41.18459466666244 absolute error = 3.844036200462142e-12 relative error = 9.333674961655996e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y[1] (closed_form) = 41.42912499999969 y[1] (numeric) = 41.42912499999578 absolute error = 3.915090474038152e-12 relative error = 9.450092112826861e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y[1] (closed_form) = 41.67464533333312 y[1] (numeric) = 41.67464533332912 absolute error = 4.000355602329364e-12 relative error = 9.599015349339309e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 41.92115766666652 y[1] (numeric) = 41.92115766666245 absolute error = 4.078515303262975e-12 relative error = 9.729014011714648e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y[1] (closed_form) = 42.16866399999994 y[1] (numeric) = 42.16866399999579 absolute error = 4.156675004196586e-12 relative error = 9.857260368022549e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y[1] (closed_form) = 42.41716633333336 y[1] (numeric) = 42.41716633332912 absolute error = 4.241940132487798e-12 relative error = 1.000052690732027e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.000000000000004 y[1] (closed_form) = 42.66666666666678 y[1] (numeric) = 42.66666666666245 absolute error = 4.32720526077901e-12 relative error = 1.014188732995078e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.010000000000008 y[1] (closed_form) = 42.9171670000002 y[1] (numeric) = 42.91716699999578 absolute error = 4.419575816427823e-12 relative error = 1.029792068154872e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.020000000000011 y[1] (closed_form) = 43.16866933333362 y[1] (numeric) = 43.16866933332911 absolute error = 4.504840944719035e-12 relative error = 1.043544082847262e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.030000000000014 y[1] (closed_form) = 43.42117566666703 y[1] (numeric) = 43.42117566666246 absolute error = 4.568789790937444e-12 relative error = 1.052203152215602e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.040000000000018 y[1] (closed_form) = 43.67468800000045 y[1] (numeric) = 43.6746879999958 absolute error = 4.654054919228656e-12 relative error = 1.065618355242425e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.050000000000021 y[1] (closed_form) = 43.92920833333387 y[1] (numeric) = 43.92920833332914 absolute error = 4.732214620162267e-12 relative error = 1.077236490185374e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.060000000000024 y[1] (closed_form) = 44.18473866666729 y[1] (numeric) = 44.18473866666248 absolute error = 4.817479748453479e-12 relative error = 1.090304004012987e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.070000000000028 y[1] (closed_form) = 44.44128100000071 y[1] (numeric) = 44.4412809999958 absolute error = 4.909850304102292e-12 relative error = 1.104794954965905e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.080000000000031 y[1] (closed_form) = 44.69883733333413 y[1] (numeric) = 44.69883733332914 absolute error = 4.995115432393504e-12 relative error = 1.117504555016334e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.090000000000034 y[1] (closed_form) = 44.95740966666756 y[1] (numeric) = 44.95740966666247 absolute error = 5.087485988042317e-12 relative error = 1.131623468914913e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.100000000000038 y[1] (closed_form) = 45.21700000000098 y[1] (numeric) = 45.21699999999581 absolute error = 5.172751116333529e-12 relative error = 1.143983704432717e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.110000000000041 y[1] (closed_form) = 45.47761033333441 y[1] (numeric) = 45.47761033332914 absolute error = 5.272227099339943e-12 relative error = 1.159301700484355e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.120000000000045 y[1] (closed_form) = 45.73924266666783 y[1] (numeric) = 45.73924266666248 absolute error = 5.350386800273554e-12 relative error = 1.169758502401399e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.130000000000048 y[1] (closed_form) = 46.00189900000126 y[1] (numeric) = 46.00189899999582 absolute error = 5.435651928564766e-12 relative error = 1.181614682594868e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.140000000000051 y[1] (closed_form) = 46.26558133333469 y[1] (numeric) = 46.26558133332917 absolute error = 5.520917056855978e-12 relative error = 1.193309777538258e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.150000000000055 y[1] (closed_form) = 46.53029166666811 y[1] (numeric) = 46.53029166666251 absolute error = 5.60618218514719e-12 relative error = 1.204845700368384e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.160000000000058 y[1] (closed_form) = 46.79603200000154 y[1] (numeric) = 46.79603199999585 absolute error = 5.684341886080801e-12 relative error = 1.21470595756508e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.170000000000061 y[1] (closed_form) = 47.06280433333497 y[1] (numeric) = 47.0628043333292 absolute error = 5.776712441729615e-12 relative error = 1.227447561521089e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.180000000000065 y[1] (closed_form) = 47.3306106666684 y[1] (numeric) = 47.33061066666254 absolute error = 5.861977570020827e-12 relative error = 1.238517206402537e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.190000000000068 y[1] (closed_form) = 47.59945300000183 y[1] (numeric) = 47.59945299999588 absolute error = 5.95434812566964e-12 relative error = 1.250927846937529e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.200000000000071 y[1] (closed_form) = 47.86933333333526 y[1] (numeric) = 47.86933333332919 absolute error = 6.060929536033655e-12 relative error = 1.266140368788663e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.210000000000075 y[1] (closed_form) = 48.14025366666869 y[1] (numeric) = 48.14025366666253 absolute error = 6.160405519040069e-12 relative error = 1.279678657635617e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.220000000000078 y[1] (closed_form) = 48.41221600000213 y[1] (numeric) = 48.41221599999587 absolute error = 6.252776074688882e-12 relative error = 1.291569895228222e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.230000000000081 y[1] (closed_form) = 48.68522233333556 y[1] (numeric) = 48.68522233332922 absolute error = 6.338041202980094e-12 relative error = 1.301840866533403e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.240000000000085 y[1] (closed_form) = 48.95927466666899 y[1] (numeric) = 48.95927466666257 absolute error = 6.423306331271306e-12 relative error = 1.311969259145138e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.250000000000088 y[1] (closed_form) = 49.23437500000242 y[1] (numeric) = 49.23437499999591 absolute error = 6.515676886920119e-12 relative error = 1.323399938949118e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.260000000000091 y[1] (closed_form) = 49.51052533333586 y[1] (numeric) = 49.51052533332926 absolute error = 6.600942015211331e-12 relative error = 1.333240148588539e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.270000000000095 y[1] (closed_form) = 49.7877276666693 y[1] (numeric) = 49.7877276666626 absolute error = 6.700417998217745e-12 relative error = 1.345797109495998e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.280000000000098 y[1] (closed_form) = 50.06598400000272 y[1] (numeric) = 50.06598399999594 absolute error = 6.785683126508957e-12 relative error = 1.355347999653535e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.290000000000101 y[1] (closed_form) = 50.34529633333617 y[1] (numeric) = 50.34529633332927 absolute error = 6.892264536872972e-12 relative error = 1.368998702726724e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.300000000000105 y[1] (closed_form) = 50.62566666666961 y[1] (numeric) = 50.62566666666262 absolute error = 6.991740519879386e-12 relative error = 1.381066360254478e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.310000000000108 y[1] (closed_form) = 50.90709700000304 y[1] (numeric) = 50.90709699999596 absolute error = 7.077005648170598e-12 relative error = 1.390180557373007e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.320000000000111 y[1] (closed_form) = 51.18958933333648 y[1] (numeric) = 51.1895893333293 absolute error = 7.176481631177012e-12 relative error = 1.401941630053952e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.330000000000115 y[1] (closed_form) = 51.47314566666992 y[1] (numeric) = 51.47314566666267 absolute error = 7.254641332110623e-12 relative error = 1.409403143746113e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.340000000000118 y[1] (closed_form) = 51.75776800000336 y[1] (numeric) = 51.75776799999601 absolute error = 7.347011887759436e-12 relative error = 1.419499366309413e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.350000000000121 y[1] (closed_form) = 52.04345833333681 y[1] (numeric) = 52.04345833332935 absolute error = 7.453593298123451e-12 relative error = 1.432186395143729e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.360000000000125 y[1] (closed_form) = 52.33021866667025 y[1] (numeric) = 52.3302186666627 absolute error = 7.553069281129865e-12 relative error = 1.443347548238033e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.370000000000128 y[1] (closed_form) = 52.6180510000037 y[1] (numeric) = 52.61805099999604 absolute error = 7.652545264136279e-12 relative error = 1.454357415126558e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.380000000000131 y[1] (closed_form) = 52.90695733333714 y[1] (numeric) = 52.90695733332939 absolute error = 7.744915819785092e-12 relative error = 1.46387473598013e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.390000000000135 y[1] (closed_form) = 53.19693966667058 y[1] (numeric) = 53.19693966666274 absolute error = 7.837286375433905e-12 relative error = 1.473258880029933e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.400000000000138 y[1] (closed_form) = 53.48800000000403 y[1] (numeric) = 53.48799999999609 absolute error = 7.936762358440319e-12 relative error = 1.483839806767821e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.410000000000141 y[1] (closed_form) = 53.78014033333747 y[1] (numeric) = 53.78014033332943 absolute error = 8.036238341446733e-12 relative error = 1.494276194081478e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.420000000000145 y[1] (closed_form) = 54.07336266667091 y[1] (numeric) = 54.07336266666277 absolute error = 8.135714324453147e-12 relative error = 1.504569703682908e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.430000000000148 y[1] (closed_form) = 54.36766900000436 y[1] (numeric) = 54.36766899999613 absolute error = 8.235190307459561e-12 relative error = 1.51472197703729e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.440000000000151 y[1] (closed_form) = 54.66306133333782 y[1] (numeric) = 54.66306133332948 absolute error = 8.334666290465975e-12 relative error = 1.524734635632791e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.450000000000155 y[1] (closed_form) = 54.95954166667126 y[1] (numeric) = 54.95954166666283 absolute error = 8.434142273472389e-12 relative error = 1.534609281246435e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.460000000000158 y[1] (closed_form) = 55.25711200000472 y[1] (numeric) = 55.25711199999616 absolute error = 8.562039965909207e-12 relative error = 1.549491034911212e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.470000000000161 y[1] (closed_form) = 55.55577433333816 y[1] (numeric) = 55.5557743333295 absolute error = 8.65441052155802e-12 relative error = 1.557787759312112e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.480000000000165 y[1] (closed_form) = 55.85553066667162 y[1] (numeric) = 55.85553066666286 absolute error = 8.760991931922035e-12 relative error = 1.568509300216822e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.490000000000168 y[1] (closed_form) = 56.15638300000506 y[1] (numeric) = 56.15638299999621 absolute error = 8.853362487570848e-12 relative error = 1.576554972846106e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.500000000000171 y[1] (closed_form) = 56.45833333333852 y[1] (numeric) = 56.45833333332957 absolute error = 8.952838470577262e-12 relative error = 1.585742607334572e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.510000000000175 y[1] (closed_form) = 56.76138366667197 y[1] (numeric) = 56.76138366666292 absolute error = 9.052314453583676e-12 relative error = 1.594801583193053e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.520000000000178 y[1] (closed_form) = 57.06553600000543 y[1] (numeric) = 57.06553599999627 absolute error = 9.158895863947691e-12 relative error = 1.60497850470498e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.530000000000181 y[1] (closed_form) = 57.37079233333888 y[1] (numeric) = 57.37079233332963 absolute error = 9.251266419596504e-12 relative error = 1.612539420031764e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.540000000000185 y[1] (closed_form) = 57.67715466667234 y[1] (numeric) = 57.67715466666299 absolute error = 9.357847829960519e-12 relative error = 1.622453098465305e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.550000000000188 y[1] (closed_form) = 57.98462500000579 y[1] (numeric) = 57.98462499999634 absolute error = 9.450218385609332e-12 relative error = 1.629780029724843e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.560000000000191 y[1] (closed_form) = 58.29320533333925 y[1] (numeric) = 58.2932053333297 absolute error = 9.549694368615746e-12 relative error = 1.638217406987235e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.570000000000195 y[1] (closed_form) = 58.60289766667271 y[1] (numeric) = 58.60289766666306 absolute error = 9.649170351622161e-12 relative error = 1.646534682722628e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.580000000000198 y[1] (closed_form) = 58.91370400000617 y[1] (numeric) = 58.91370399999641 absolute error = 9.755751761986176e-12 relative error = 1.655939297584337e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.590000000000201 y[1] (closed_form) = 59.22562633333963 y[1] (numeric) = 59.22562633332978 absolute error = 9.848122317634989e-12 relative error = 1.662814380755857e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.600000000000205 y[1] (closed_form) = 59.53866666667309 y[1] (numeric) = 59.53866666666314 absolute error = 9.954703727999004e-12 relative error = 1.671972901867346e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.610000000000208 y[1] (closed_form) = 59.85282700000655 y[1] (numeric) = 59.85282699999649 absolute error = 1.005417971100542e-11 relative error = 1.679817013656568e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.620000000000211 y[1] (closed_form) = 60.16810933334001 y[1] (numeric) = 60.16810933332985 absolute error = 1.015365569401183e-11 relative error = 1.687547740242113e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.630000000000215 y[1] (closed_form) = 60.48451566667347 y[1] (numeric) = 60.48451566666321 absolute error = 1.026023710437585e-11 relative error = 1.696341119918922e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.640000000000218 y[1] (closed_form) = 60.80204800000694 y[1] (numeric) = 60.80204799999657 absolute error = 1.037392394209746e-11 relative error = 1.706180019149401e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.650000000000222 y[1] (closed_form) = 61.12070833334041 y[1] (numeric) = 61.12070833332993 absolute error = 1.048050535246148e-11 relative error = 1.714722495574307e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.660000000000225 y[1] (closed_form) = 61.44049866667388 y[1] (numeric) = 61.44049866666329 absolute error = 1.058708676282549e-11 relative error = 1.723144667210858e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.670000000000228 y[1] (closed_form) = 61.76142100000735 y[1] (numeric) = 61.76142099999664 absolute error = 1.070077360054711e-11 relative error = 1.732598348173666e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.680000000000232 y[1] (closed_form) = 62.0834773333408 y[1] (numeric) = 62.08347733332999 absolute error = 1.080024958355352e-11 relative error = 1.739633481798135e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.690000000000235 y[1] (closed_form) = 62.40666966667427 y[1] (numeric) = 62.40666966666335 absolute error = 1.091393642127514e-11 relative error = 1.74884134653692e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.700000000000238 y[1] (closed_form) = 62.73100000000775 y[1] (numeric) = 62.73099999999672 absolute error = 1.102762325899675e-11 relative error = 1.757922440100651e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.710000000000242 y[1] (closed_form) = 63.05647033334122 y[1] (numeric) = 63.05647033333008 absolute error = 1.114131009671837e-11 relative error = 1.766878170919025e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.720000000000245 y[1] (closed_form) = 63.38308266667468 y[1] (numeric) = 63.38308266666343 absolute error = 1.125499693443999e-11 relative error = 1.775709930933605e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.730000000000248 y[1] (closed_form) = 63.71083900000815 y[1] (numeric) = 63.71083899999678 absolute error = 1.13686837721616e-11 relative error = 1.784419095808823e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.740000000000252 y[1] (closed_form) = 64.03974133334162 y[1] (numeric) = 64.03974133333014 absolute error = 1.148237060988322e-11 relative error = 1.793007025140035e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.750000000000255 y[1] (closed_form) = 64.3697916666751 y[1] (numeric) = 64.3697916666635 absolute error = 1.159605744760484e-11 relative error = 1.801475062658659e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.760000000000258 y[1] (closed_form) = 64.70099200000857 y[1] (numeric) = 64.70099199999686 absolute error = 1.170974428532645e-11 relative error = 1.809824536434449e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.770000000000262 y[1] (closed_form) = 65.03334433334204 y[1] (numeric) = 65.03334433333022 absolute error = 1.182343112304807e-11 relative error = 1.818056759074943e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.780000000000265 y[1] (closed_form) = 65.36685066667552 y[1] (numeric) = 65.36685066666357 absolute error = 1.195132881548489e-11 relative error = 1.828347043431566e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.790000000000268 y[1] (closed_form) = 65.701513000009 y[1] (numeric) = 65.70151299999694 absolute error = 1.20650156532065e-11 relative error = 1.836337567021455e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.800000000000272 y[1] (closed_form) = 66.03733333334246 y[1] (numeric) = 66.0373333333303 absolute error = 1.216449163621292e-11 relative error = 1.842062818437737e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.810000000000275 y[1] (closed_form) = 66.37431366667595 y[1] (numeric) = 66.37431366666365 absolute error = 1.229238932864973e-11 relative error = 1.851979877393637e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.820000000000278 y[1] (closed_form) = 66.71245600000942 y[1] (numeric) = 66.71245599999703 absolute error = 1.239186531165615e-11 relative error = 1.857503988708555e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.830000000000282 y[1] (closed_form) = 67.05176233334291 y[1] (numeric) = 67.05176233333042 absolute error = 1.249134129466256e-11 relative error = 1.862940042136816e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.840000000000285 y[1] (closed_form) = 67.39223466667639 y[1] (numeric) = 67.3922346666638 absolute error = 1.259081727766898e-11 relative error = 1.868289030619546e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.850000000000288 y[1] (closed_form) = 67.73387500000986 y[1] (numeric) = 67.73387499999717 absolute error = 1.269029326067539e-11 relative error = 1.873551935523184e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.860000000000292 y[1] (closed_form) = 68.07668533334335 y[1] (numeric) = 68.07668533333054 absolute error = 1.280398009839701e-11 relative error = 1.880817204260345e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.870000000000295 y[1] (closed_form) = 68.42066766667683 y[1] (numeric) = 68.42066766666395 absolute error = 1.288924522668822e-11 relative error = 1.883823363063397e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.880000000000298 y[1] (closed_form) = 68.76582400001031 y[1] (numeric) = 68.76582399999731 absolute error = 1.300293206440983e-11 relative error = 1.89090034962831e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.890000000000302 y[1] (closed_form) = 69.1121563333438 y[1] (numeric) = 69.11215633333066 absolute error = 1.314504061156185e-11 relative error = 1.901986757316658e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.900000000000305 y[1] (closed_form) = 69.45966666667728 y[1] (numeric) = 69.45966666666403 absolute error = 1.324451659456827e-11 relative error = 1.906792420718917e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.910000000000308 y[1] (closed_form) = 69.80835700001077 y[1] (numeric) = 69.8083569999974 absolute error = 1.337241428700509e-11 relative error = 1.915589316477255e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.920000000000312 y[1] (closed_form) = 70.15822933334427 y[1] (numeric) = 70.15822933333075 absolute error = 1.351452283415711e-11 relative error = 1.926291892280415e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.930000000000315 y[1] (closed_form) = 70.50928566667774 y[1] (numeric) = 70.50928566666413 absolute error = 1.361399881716352e-11 relative error = 1.930809352050692e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.940000000000318 y[1] (closed_form) = 70.86152800001123 y[1] (numeric) = 70.86152799999751 absolute error = 1.372768565488514e-11 relative error = 1.937255100522664e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.950000000000322 y[1] (closed_form) = 71.21495833334471 y[1] (numeric) = 71.21495833333084 absolute error = 1.386979420203716e-11 relative error = 1.947595635331988e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.960000000000325 y[1] (closed_form) = 71.56957866667821 y[1] (numeric) = 71.56957866666421 absolute error = 1.399769189447397e-11 relative error = 1.955815886476792e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.970000000000328 y[1] (closed_form) = 71.92539100001171 y[1] (numeric) = 71.92539099999756 absolute error = 1.41540112963412e-11 relative error = 1.967874084457725e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.980000000000332 y[1] (closed_form) = 72.2823973333452 y[1] (numeric) = 72.28239733333092 absolute error = 1.428190898877801e-11 relative error = 1.975848825671075e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.990000000000335 y[1] (closed_form) = 72.64059966667868 y[1] (numeric) = 72.6405996666643 absolute error = 1.438138497178443e-11 relative error = 1.97979986918822e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.000000000000338 y[1] (closed_form) = 73.00000000001219 y[1] (numeric) = 72.99999999999768 absolute error = 1.450928266422125e-11 relative error = 1.987572967701209e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.010000000000342 y[1] (closed_form) = 73.36060033334567 y[1] (numeric) = 73.36060033333106 absolute error = 1.460875864722766e-11 relative error = 1.991363017866053e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.020000000000345 y[1] (closed_form) = 73.72240266667917 y[1] (numeric) = 73.72240266666444 absolute error = 1.473665633966448e-11 relative error = 1.998938695242105e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.030000000000348 y[1] (closed_form) = 74.08540900001266 y[1] (numeric) = 74.08540899999781 absolute error = 1.485034317738609e-11 relative error = 2.004489598941616e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.040000000000352 y[1] (closed_form) = 74.44962133334617 y[1] (numeric) = 74.44962133333122 absolute error = 1.494981916039251e-11 relative error = 2.008045023285625e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.050000000000355 y[1] (closed_form) = 74.81504166667968 y[1] (numeric) = 74.8150416666646 absolute error = 1.507771685282933e-11 relative error = 2.015332280372769e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.060000000000358 y[1] (closed_form) = 75.18167200001317 y[1] (numeric) = 75.18167199999797 absolute error = 1.519140369055094e-11 relative error = 2.020625943321436e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.070000000000362 y[1] (closed_form) = 75.54951433334666 y[1] (numeric) = 75.54951433333135 absolute error = 1.531930138298776e-11 relative error = 2.027716725668745e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.080000000000365 y[1] (closed_form) = 75.91857066668017 y[1] (numeric) = 75.91857066666468 absolute error = 1.548983163957018e-11 relative error = 2.040321821597268e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.090000000000368 y[1] (closed_form) = 76.28884300001367 y[1] (numeric) = 76.28884299999805 absolute error = 1.5617729332007e-11 relative error = 2.047183928586281e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.100000000000372 y[1] (closed_form) = 76.66033333334717 y[1] (numeric) = 76.66033333333141 absolute error = 1.575983787915902e-11 relative error = 2.055800854743154e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.110000000000375 y[1] (closed_form) = 77.03304366668068 y[1] (numeric) = 77.03304366666478 absolute error = 1.590194642631104e-11 relative error = 2.064301976060847e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.120000000000378 y[1] (closed_form) = 77.40697600001418 y[1] (numeric) = 77.40697599999817 absolute error = 1.601563326403266e-11 relative error = 2.069016785261024e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.130000000000382 y[1] (closed_form) = 77.78213233334769 y[1] (numeric) = 77.78213233333156 absolute error = 1.612932010175427e-11 relative error = 2.073653629426037e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.140000000000385 y[1] (closed_form) = 78.15851466668119 y[1] (numeric) = 78.15851466666494 absolute error = 1.624300693947589e-11 relative error = 2.078213360213747e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.150000000000388 y[1] (closed_form) = 78.53612500001469 y[1] (numeric) = 78.53612499999834 absolute error = 1.635669377719751e-11 relative error = 2.082696819736707e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.160000000000392 y[1] (closed_form) = 78.91496533334821 y[1] (numeric) = 78.91496533333171 absolute error = 1.649880232434953e-11 relative error = 2.090706402094483e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.170000000000395 y[1] (closed_form) = 79.29503766668171 y[1] (numeric) = 79.29503766666508 absolute error = 1.662670001678634e-11 relative error = 2.096814694341532e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.180000000000399 y[1] (closed_form) = 79.67634400001522 y[1] (numeric) = 79.67634399999847 absolute error = 1.675459770922316e-11 relative error = 2.10283214164796e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.190000000000402 y[1] (closed_form) = 80.05888633334872 y[1] (numeric) = 80.05888633333186 absolute error = 1.686828454694478e-11 relative error = 2.106984660854351e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.200000000000405 y[1] (closed_form) = 80.44266666668223 y[1] (numeric) = 80.44266666666525 absolute error = 1.698197138466639e-11 relative error = 2.111065195666865e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.210000000000409 y[1] (closed_form) = 80.82768700001576 y[1] (numeric) = 80.82768699999862 absolute error = 1.713829078653362e-11 relative error = 2.120349031703737e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.220000000000412 y[1] (closed_form) = 81.21394933334928 y[1] (numeric) = 81.21394933333201 absolute error = 1.726618847897043e-11 relative error = 2.126012664166836e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.230000000000415 y[1] (closed_form) = 81.60145566668278 y[1] (numeric) = 81.60145566666542 absolute error = 1.736566446197685e-11 relative error = 2.128107191238147e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.240000000000419 y[1] (closed_form) = 81.9902080000163 y[1] (numeric) = 81.99020799999879 absolute error = 1.750777300912887e-11 relative error = 2.135349261356355e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.250000000000422 y[1] (closed_form) = 82.38020833334981 y[1] (numeric) = 82.38020833333219 absolute error = 1.762145984685048e-11 relative error = 2.139040456846821e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.260000000000425 y[1] (closed_form) = 82.77145866668333 y[1] (numeric) = 82.77145866666557 absolute error = 1.77635683940025e-11 relative error = 2.146098266255708e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.270000000000429 y[1] (closed_form) = 83.16396100001684 y[1] (numeric) = 83.16396099999895 absolute error = 1.789146608643932e-11 relative error = 2.151348477309264e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.280000000000432 y[1] (closed_form) = 83.55771733335037 y[1] (numeric) = 83.55771733333235 absolute error = 1.801936377887614e-11 relative error = 2.156516998542285e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.290000000000435 y[1] (closed_form) = 83.95272966668388 y[1] (numeric) = 83.95272966666573 absolute error = 1.814726147131296e-11 relative error = 2.161604696281196e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.300000000000439 y[1] (closed_form) = 84.3490000000174 y[1] (numeric) = 84.34899999999912 absolute error = 1.827515916374978e-11 relative error = 2.166612427384558e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.310000000000442 y[1] (closed_form) = 84.74653033335092 y[1] (numeric) = 84.74653033333252 absolute error = 1.840305685618659e-11 relative error = 2.171541039355602e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.320000000000445 y[1] (closed_form) = 85.14532266668445 y[1] (numeric) = 85.1453226666659 absolute error = 1.854516540333861e-11 relative error = 2.178060382240461e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.330000000000449 y[1] (closed_form) = 85.54537900001797 y[1] (numeric) = 85.54537899999929 absolute error = 1.868727395049063e-11 relative error = 2.184486662977635e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.340000000000452 y[1] (closed_form) = 85.9467013333515 y[1] (numeric) = 85.94670133333267 absolute error = 1.882938249764265e-11 relative error = 2.190820846586225e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.350000000000455 y[1] (closed_form) = 86.34929166668502 y[1] (numeric) = 86.34929166666605 absolute error = 1.897149104479467e-11 relative error = 2.19706388768377e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.360000000000459 y[1] (closed_form) = 86.75315200001855 y[1] (numeric) = 86.75315199999946 absolute error = 1.908517788251629e-11 relative error = 2.19994057190132e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.370000000000462 y[1] (closed_form) = 87.15828433335207 y[1] (numeric) = 87.15828433333284 absolute error = 1.922728642966831e-11 relative error = 2.206019379194088e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.380000000000465 y[1] (closed_form) = 87.56469066668562 y[1] (numeric) = 87.56469066666624 absolute error = 1.938360583153553e-11 relative error = 2.213632650781477e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.390000000000469 y[1] (closed_form) = 87.97237300001912 y[1] (numeric) = 87.97237299999964 absolute error = 1.948308181454195e-11 relative error = 2.214681854101823e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.400000000000472 y[1] (closed_form) = 88.38133333335266 y[1] (numeric) = 88.38133333333303 absolute error = 1.962519036169397e-11 relative error = 2.220513045178055e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.410000000000475 y[1] (closed_form) = 88.79157366668619 y[1] (numeric) = 88.79157366666644 absolute error = 1.975308805413079e-11 relative error = 2.224657953274002e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.420000000000479 y[1] (closed_form) = 89.20309600001973 y[1] (numeric) = 89.20309599999982 absolute error = 1.990940745599801e-11 relative error = 2.231918884967132e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.430000000000482 y[1] (closed_form) = 89.61590233335328 y[1] (numeric) = 89.61590233333321 absolute error = 2.006572685786523e-11 relative error = 2.2390810487211e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.440000000000485 y[1] (closed_form) = 90.02999466668679 y[1] (numeric) = 90.0299946666666 absolute error = 2.019362455030205e-11 relative error = 2.24298853121827e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.450000000000489 y[1] (closed_form) = 90.44537500002032 y[1] (numeric) = 90.44537499999998 absolute error = 2.033573309745407e-11 relative error = 2.248399445239682e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.460000000000492 y[1] (closed_form) = 90.86204533335388 y[1] (numeric) = 90.8620453333334 absolute error = 2.047784164460609e-11 relative error = 2.253728888610988e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.470000000000495 y[1] (closed_form) = 91.28000766668741 y[1] (numeric) = 91.28000766666682 absolute error = 2.05915284823277e-11 relative error = 2.255864017619115e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.480000000000499 y[1] (closed_form) = 91.69926400002093 y[1] (numeric) = 91.69926400000021 absolute error = 2.071942617476452e-11 relative error = 2.259497543487349e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.490000000000502 y[1] (closed_form) = 92.11981633335448 y[1] (numeric) = 92.11981633333362 absolute error = 2.086153472191654e-11 relative error = 2.264608805387192e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.500000000000505 y[1] (closed_form) = 92.54166666668802 y[1] (numeric) = 92.54166666666703 absolute error = 2.098943241435336e-11 relative error = 2.268106159137165e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.510000000000509 y[1] (closed_form) = 92.96481700002154 y[1] (numeric) = 92.96481700000041 absolute error = 2.113154096150538e-11 relative error = 2.273068634287795e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.520000000000512 y[1] (closed_form) = 93.3892693333551 y[1] (numeric) = 93.38926933333381 absolute error = 2.12878603633726e-11 relative error = 2.279476059223154e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.530000000000515 y[1] (closed_form) = 93.81502566668864 y[1] (numeric) = 93.81502566666722 absolute error = 2.141575805580942e-11 relative error = 2.282764184481124e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.540000000000519 y[1] (closed_form) = 94.24208800002219 y[1] (numeric) = 94.24208800000063 absolute error = 2.155786660296144e-11 relative error = 2.287498829923671e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.550000000000522 y[1] (closed_form) = 94.67045833335573 y[1] (numeric) = 94.67045833333403 absolute error = 2.169997515011346e-11 relative error = 2.292159088709915e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.560000000000525 y[1] (closed_form) = 95.10013866668926 y[1] (numeric) = 95.10013866666742 absolute error = 2.184208369726548e-11 relative error = 2.29674572545246e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.570000000000529 y[1] (closed_form) = 95.53113100002281 y[1] (numeric) = 95.53113100000081 absolute error = 2.19984030991327e-11 relative error = 2.302747059398621e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.580000000000532 y[1] (closed_form) = 95.96343733335637 y[1] (numeric) = 95.96343733333421 absolute error = 2.215472250099992e-11 relative error = 2.308662873760886e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.590000000000535 y[1] (closed_form) = 96.39705966668993 y[1] (numeric) = 96.39705966666762 absolute error = 2.231104190286715e-11 relative error = 2.314494029175948e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.600000000000539 y[1] (closed_form) = 96.83200000002347 y[1] (numeric) = 96.83200000000105 absolute error = 2.242472874058876e-11 relative error = 2.315838642244643e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.610000000000542 y[1] (closed_form) = 97.26826033335702 y[1] (numeric) = 97.26826033333444 absolute error = 2.258104814245598e-11 relative error = 2.321522772697527e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.620000000000545 y[1] (closed_form) = 97.70584266669057 y[1] (numeric) = 97.70584266666785 absolute error = 2.2723156689608e-11 relative error = 2.325670202459108e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.630000000000549 y[1] (closed_form) = 98.14474900002411 y[1] (numeric) = 98.14474900000126 absolute error = 2.285105438204482e-11 relative error = 2.328301270813705e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.640000000000552 y[1] (closed_form) = 98.58498133335767 y[1] (numeric) = 98.58498133333467 absolute error = 2.300737378391204e-11 relative error = 2.333760525461211e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.650000000000555 y[1] (closed_form) = 99.02654166669123 y[1] (numeric) = 99.02654166666808 absolute error = 2.314948233106406e-11 relative error = 2.337704815440472e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.660000000000559 y[1] (closed_form) = 99.46943200002478 y[1] (numeric) = 99.46943200000146 absolute error = 2.332001258764649e-11 relative error = 2.344440107754981e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.670000000000562 y[1] (closed_form) = 99.91365433335834 y[1] (numeric) = 99.91365433333488 absolute error = 2.346212113479851e-11 relative error = 2.348239716717595e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.680000000000565 y[1] (closed_form) = 100.3592106666919 y[1] (numeric) = 100.3592106666683 absolute error = 2.361844053666573e-11 relative error = 2.35339042423382e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.690000000000569 y[1] (closed_form) = 100.8061030000255 y[1] (numeric) = 100.8061030000017 absolute error = 2.380318164796336e-11 relative error = 2.361283785363406e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.700000000000572 y[1] (closed_form) = 101.254333333359 y[1] (numeric) = 101.2543333333351 absolute error = 2.391686848568497e-11 relative error = 2.362058758210734e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.710000000000576 y[1] (closed_form) = 101.7039036666926 y[1] (numeric) = 101.7039036666685 absolute error = 2.404476617812179e-11 relative error = 2.364193045816816e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.720000000000579 y[1] (closed_form) = 102.1548160000261 y[1] (numeric) = 102.1548160000019 absolute error = 2.421529643470421e-11 relative error = 2.370450790562632e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.730000000000582 y[1] (closed_form) = 102.6070723333597 y[1] (numeric) = 102.6070723333353 absolute error = 2.435740498185623e-11 relative error = 2.373852447784648e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.740000000000586 y[1] (closed_form) = 103.0606746666933 y[1] (numeric) = 103.0606746666687 absolute error = 2.454214609315386e-11 relative error = 2.38132984987001e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.750000000000589 y[1] (closed_form) = 103.5156250000268 y[1] (numeric) = 103.5156250000021 absolute error = 2.468425464030588e-11 relative error = 2.384592146383648e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.760000000000592 y[1] (closed_form) = 103.9719253333604 y[1] (numeric) = 103.9719253333355 absolute error = 2.48547848968883e-11 relative error = 2.390528483260991e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.770000000000596 y[1] (closed_form) = 104.429577666694 y[1] (numeric) = 104.429577666669 absolute error = 2.499689344404032e-11 relative error = 2.393660302239512e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.780000000000599 y[1] (closed_form) = 104.8885840000275 y[1] (numeric) = 104.8885840000024 absolute error = 2.515321284590755e-11 relative error = 2.398088703905178e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.790000000000602 y[1] (closed_form) = 105.3489463333611 y[1] (numeric) = 105.3489463333358 absolute error = 2.532374310248997e-11 relative error = 2.403796524206018e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.800000000000606 y[1] (closed_form) = 105.8106666666947 y[1] (numeric) = 105.8106666666692 absolute error = 2.548006250435719e-11 relative error = 2.408080707460223e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.810000000000609 y[1] (closed_form) = 106.2737470000283 y[1] (numeric) = 106.2737470000026 absolute error = 2.560796019679401e-11 relative error = 2.409622406254971e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.820000000000612 y[1] (closed_form) = 106.7381893333618 y[1] (numeric) = 106.7381893333361 absolute error = 2.575006874394603e-11 relative error = 2.412451335812351e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.830000000000616 y[1] (closed_form) = 107.2039956666954 y[1] (numeric) = 107.2039956666695 absolute error = 2.590638814581325e-11 relative error = 2.416550613128078e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.840000000000619 y[1] (closed_form) = 107.671168000029 y[1] (numeric) = 107.6711680000029 absolute error = 2.606270754768047e-11 relative error = 2.420583711664897e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.850000000000622 y[1] (closed_form) = 108.1397083333625 y[1] (numeric) = 108.1397083333363 absolute error = 2.619060524011729e-11 relative error = 2.421923051556552e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.860000000000626 y[1] (closed_form) = 108.6096186666961 y[1] (numeric) = 108.6096186666698 absolute error = 2.634692464198451e-11 relative error = 2.425837137209606e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.870000000000629 y[1] (closed_form) = 109.0809010000297 y[1] (numeric) = 109.0809010000032 absolute error = 2.647482233442133e-11 relative error = 2.427081376456006e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.880000000000632 y[1] (closed_form) = 109.5535573333633 y[1] (numeric) = 109.5535573333366 absolute error = 2.664535259100376e-11 relative error = 2.432175936553475e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.890000000000636 y[1] (closed_form) = 110.0275896666968 y[1] (numeric) = 110.02758966667 absolute error = 2.680167199287098e-11 relative error = 2.435904673915011e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.900000000000639 y[1] (closed_form) = 110.5030000000304 y[1] (numeric) = 110.5030000000035 absolute error = 2.69295696853078e-11 relative error = 2.436998967023555e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.910000000000642 y[1] (closed_form) = 110.979790333364 y[1] (numeric) = 110.9797903333369 absolute error = 2.711431079660542e-11 relative error = 2.443175529090364e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.920000000000646 y[1] (closed_form) = 111.4579626666976 y[1] (numeric) = 111.4579626666703 absolute error = 2.725641934375744e-11 relative error = 2.445443886792071e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.930000000000649 y[1] (closed_form) = 111.9375190000312 y[1] (numeric) = 111.9375190000037 absolute error = 2.742694960033987e-11 relative error = 2.450201670123869e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.940000000000652 y[1] (closed_form) = 112.4184613333647 y[1] (numeric) = 112.4184613333372 absolute error = 2.755484729277669e-11 relative error = 2.451096284894505e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.950000000000656 y[1] (closed_form) = 112.9007916666983 y[1] (numeric) = 112.9007916666706 absolute error = 2.773958840407431e-11 relative error = 2.456987944421694e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.960000000000659 y[1] (closed_form) = 113.3845120000319 y[1] (numeric) = 113.384512000004 absolute error = 2.788169695122633e-11 relative error = 2.459039286707737e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.970000000000662 y[1] (closed_form) = 113.8696243333655 y[1] (numeric) = 113.8696243333375 absolute error = 2.803801635309355e-11 relative error = 2.462291108558439e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.980000000000666 y[1] (closed_form) = 114.3561306666991 y[1] (numeric) = 114.3561306666709 absolute error = 2.819433575496078e-11 relative error = 2.465485286235823e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.990000000000669 y[1] (closed_form) = 114.8440330000327 y[1] (numeric) = 114.8440330000043 absolute error = 2.83790768662584e-11 relative error = 2.471097202433698e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.000000000000672 y[1] (closed_form) = 115.3333333333663 y[1] (numeric) = 115.3333333333377 absolute error = 2.853539626812562e-11 relative error = 2.474167306484174e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.010000000000676 y[1] (closed_form) = 115.8240336666999 y[1] (numeric) = 115.8240336666712 absolute error = 2.867750481527764e-11 relative error = 2.475954593137487e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.020000000000679 y[1] (closed_form) = 116.3161360000335 y[1] (numeric) = 116.3161360000046 absolute error = 2.884803507186007e-11 relative error = 2.480140422808729e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.030000000000682 y[1] (closed_form) = 116.8096423333671 y[1] (numeric) = 116.8096423333381 absolute error = 2.899014361901209e-11 relative error = 2.481827958712186e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.040000000000686 y[1] (closed_form) = 117.3045546667007 y[1] (numeric) = 117.3045546666715 absolute error = 2.917488473030971e-11 relative error = 2.487105876937583e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.050000000000689 y[1] (closed_form) = 117.8008750000342 y[1] (numeric) = 117.8008750000049 absolute error = 2.933120413217694e-11 relative error = 2.489896966569086e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.060000000000692 y[1] (closed_form) = 118.2986053333678 y[1] (numeric) = 118.2986053333383 absolute error = 2.950173438875936e-11 relative error = 2.4938361957542e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.070000000000696 y[1] (closed_form) = 118.7977476667015 y[1] (numeric) = 118.7977476666718 absolute error = 2.964384293591138e-11 relative error = 2.495320283266653e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.080000000000699 y[1] (closed_form) = 119.298304000035 y[1] (numeric) = 119.2983040000052 absolute error = 2.98143731924938e-11 relative error = 2.49914476508275e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.090000000000702 y[1] (closed_form) = 119.8002763333686 y[1] (numeric) = 119.8002763333387 absolute error = 2.995648173964582e-11 relative error = 2.500535278924217e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.100000000000706 y[1] (closed_form) = 120.3036666667023 y[1] (numeric) = 120.3036666666721 absolute error = 3.015543370565865e-11 relative error = 2.506609693718097e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.110000000000709 y[1] (closed_form) = 120.8084770000359 y[1] (numeric) = 120.8084770000056 absolute error = 3.028333139809547e-11 relative error = 2.506722388205133e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.120000000000712 y[1] (closed_form) = 121.3147093333695 y[1] (numeric) = 121.314709333339 absolute error = 3.04680725093931e-11 relative error = 2.511490377120525e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.130000000000716 y[1] (closed_form) = 121.822365666703 y[1] (numeric) = 121.8223656666724 absolute error = 3.063860276597552e-11 relative error = 2.515022803760064e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.140000000000719 y[1] (closed_form) = 122.3314480000367 y[1] (numeric) = 122.3314480000058 absolute error = 3.082334387727315e-11 relative error = 2.519658222083982e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.150000000000722 y[1] (closed_form) = 122.8419583333703 y[1] (numeric) = 122.8419583333393 absolute error = 3.099387413385557e-11 relative error = 2.523069035560631e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.160000000000726 y[1] (closed_form) = 123.3538986667039 y[1] (numeric) = 123.3538986666727 absolute error = 3.116440439043799e-11 relative error = 2.526422328542908e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.170000000000729 y[1] (closed_form) = 123.8672710000375 y[1] (numeric) = 123.8672710000061 absolute error = 3.133493464702042e-11 relative error = 2.52971865724005e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.180000000000732 y[1] (closed_form) = 124.3820773333711 y[1] (numeric) = 124.3820773333396 absolute error = 3.150546490360284e-11 relative error = 2.532958572412433e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.190000000000736 y[1] (closed_form) = 124.8983196667047 y[1] (numeric) = 124.898319666673 absolute error = 3.170441686961567e-11 relative error = 2.538418207244097e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.200000000000739 y[1] (closed_form) = 125.4160000000383 y[1] (numeric) = 125.4160000000064 absolute error = 3.187494712619809e-11 relative error = 2.54153753318463e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.210000000000742 y[1] (closed_form) = 125.9351203333719 y[1] (numeric) = 125.9351203333399 absolute error = 3.204547738278052e-11 relative error = 2.5446021171815e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.220000000000746 y[1] (closed_form) = 126.4556826667056 y[1] (numeric) = 126.4556826666733 absolute error = 3.221600763936294e-11 relative error = 2.547612488422007e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.230000000000749 y[1] (closed_form) = 126.9776890000392 y[1] (numeric) = 126.9776890000068 absolute error = 3.238653789594537e-11 relative error = 2.550569170930129e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.240000000000753 y[1] (closed_form) = 127.5011413333728 y[1] (numeric) = 127.5011413333402 absolute error = 3.257127900724299e-11 relative error = 2.554587250484293e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.250000000000756 y[1] (closed_form) = 128.0260416667064 y[1] (numeric) = 128.0260416666736 absolute error = 3.271338755439501e-11 relative error = 2.555213543160122e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.260000000000759 y[1] (closed_form) = 128.55239200004 y[1] (numeric) = 128.552392000007 absolute error = 3.296918293926865e-11 relative error = 2.56464951187049e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.270000000000763 y[1] (closed_form) = 129.0801943333736 y[1] (numeric) = 129.0801943333405 absolute error = 3.313971319585107e-11 relative error = 2.567373977626776e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.280000000000766 y[1] (closed_form) = 129.6094506667073 y[1] (numeric) = 129.6094506666739 absolute error = 3.33670868712943e-11 relative error = 2.574433168233873e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.290000000000769 y[1] (closed_form) = 130.1401630000409 y[1] (numeric) = 130.1401630000073 absolute error = 3.356603883730713e-11 relative error = 2.579222129704616e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.300000000000773 y[1] (closed_form) = 130.6723333333745 y[1] (numeric) = 130.6723333333407 absolute error = 3.376499080331996e-11 relative error = 2.583943359852455e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.310000000000776 y[1] (closed_form) = 131.2059636667081 y[1] (numeric) = 131.2059636666742 absolute error = 3.393552105990238e-11 relative error = 2.586431295615955e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.320000000000779 y[1] (closed_form) = 131.7410560000418 y[1] (numeric) = 131.7410560000077 absolute error = 3.410605131648481e-11 relative error = 2.588870345511273e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.330000000000783 y[1] (closed_form) = 132.2776123333754 y[1] (numeric) = 132.2776123333411 absolute error = 3.424815986363683e-11 relative error = 2.589112341801438e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.340000000000786 y[1] (closed_form) = 132.815634666709 y[1] (numeric) = 132.8156346666746 absolute error = 3.444711182964966e-11 relative error = 2.593603675959697e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.350000000000789 y[1] (closed_form) = 133.3551250000426 y[1] (numeric) = 133.355125000008 absolute error = 3.461764208623208e-11 relative error = 2.595898889241865e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.360000000000793 y[1] (closed_form) = 133.8960853333763 y[1] (numeric) = 133.8960853333415 absolute error = 3.478817234281451e-11 relative error = 2.598147082209196e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.370000000000796 y[1] (closed_form) = 134.4385176667099 y[1] (numeric) = 134.4385176666749 absolute error = 3.501554601825774e-11 relative error = 2.604576919322013e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.380000000000799 y[1] (closed_form) = 134.9824240000436 y[1] (numeric) = 134.9824240000084 absolute error = 3.515765456540976e-11 relative error = 2.604609809451815e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.390000000000803 y[1] (closed_form) = 135.5278063333772 y[1] (numeric) = 135.5278063333419 absolute error = 3.532818482199218e-11 relative error = 2.606711181843405e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.400000000000806 y[1] (closed_form) = 136.0746666667108 y[1] (numeric) = 136.0746666666753 absolute error = 3.54702933691442e-11 relative error = 2.606678688842354e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.410000000000809 y[1] (closed_form) = 136.6230070000444 y[1] (numeric) = 136.6230070000088 absolute error = 3.561240191629622e-11 relative error = 2.60661821886885e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.420000000000813 y[1] (closed_form) = 137.1728293333781 y[1] (numeric) = 137.1728293333422 absolute error = 3.583977559173945e-11 relative error = 2.612745961857813e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.430000000000816 y[1] (closed_form) = 137.7241356667117 y[1] (numeric) = 137.7241356666757 absolute error = 3.601030584832188e-11 relative error = 2.614669220757772e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.440000000000819 y[1] (closed_form) = 138.2769280000454 y[1] (numeric) = 138.2769280000091 absolute error = 3.620925781433471e-11 relative error = 2.618604443853629e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.450000000000823 y[1] (closed_form) = 138.831208333379 y[1] (numeric) = 138.8312083333426 absolute error = 3.635136636148673e-11 relative error = 2.618385793646285e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.460000000000826 y[1] (closed_form) = 139.3869786667126 y[1] (numeric) = 139.3869786666761 absolute error = 3.652189661806915e-11 relative error = 2.620179945602842e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.470000000000829 y[1] (closed_form) = 139.9442410000463 y[1] (numeric) = 139.9442410000095 absolute error = 3.674927029351238e-11 relative error = 2.62599375514854e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.480000000000833 y[1] (closed_form) = 140.5029973333799 y[1] (numeric) = 140.502997333343 absolute error = 3.691980055009481e-11 relative error = 2.627687754055024e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.490000000000836 y[1] (closed_form) = 141.0632496667136 y[1] (numeric) = 141.0632496666765 absolute error = 3.711875251610763e-11 relative error = 2.631355268208207e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.500000000000839 y[1] (closed_form) = 141.6250000000472 y[1] (numeric) = 141.6250000000099 absolute error = 3.731770448212046e-11 relative error = 2.634965894588387e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.510000000000843 y[1] (closed_form) = 142.1882503333809 y[1] (numeric) = 142.1882503333433 absolute error = 3.751665644813329e-11 relative error = 2.638520156213335e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.520000000000846 y[1] (closed_form) = 142.7530026667145 y[1] (numeric) = 142.7530026666768 absolute error = 3.768718670471571e-11 relative error = 2.640027600169224e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.530000000000849 y[1] (closed_form) = 143.3192590000482 y[1] (numeric) = 143.3192590000102 absolute error = 3.791456038015895e-11 relative error = 2.645461652864547e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.540000000000853 y[1] (closed_form) = 143.8870213333818 y[1] (numeric) = 143.8870213333437 absolute error = 3.808509063674137e-11 relative error = 2.646874630096024e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.550000000000856 y[1] (closed_form) = 144.4562916667155 y[1] (numeric) = 144.4562916666771 absolute error = 3.83124643121846e-11 relative error = 2.652183845379181e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.560000000000859 y[1] (closed_form) = 145.0270720000491 y[1] (numeric) = 145.0270720000106 absolute error = 3.851141627819743e-11 relative error = 2.655463959045135e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.570000000000863 y[1] (closed_form) = 145.5993643333828 y[1] (numeric) = 145.5993643333441 absolute error = 3.871036824421026e-11 relative error = 2.658690745075926e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.580000000000866 y[1] (closed_form) = 146.1731706667164 y[1] (numeric) = 146.1731706666775 absolute error = 3.885247679136228e-11 relative error = 2.657975920899209e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.590000000000869 y[1] (closed_form) = 146.7484930000501 y[1] (numeric) = 146.7484930000111 absolute error = 3.90230070479447e-11 relative error = 2.659175999029264e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.600000000000873 y[1] (closed_form) = 147.3253333333837 y[1] (numeric) = 147.3253333333445 absolute error = 3.922195901395753e-11 relative error = 2.662268472537702e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.610000000000876 y[1] (closed_form) = 147.9036936667174 y[1] (numeric) = 147.903693666678 absolute error = 3.944933268940076e-11 relative error = 2.667231068501571e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.620000000000879 y[1] (closed_form) = 148.483576000051 y[1] (numeric) = 148.4835760000114 absolute error = 3.961986294598319e-11 relative error = 2.668299350897204e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.630000000000883 y[1] (closed_form) = 149.0649823333847 y[1] (numeric) = 149.0649823333449 absolute error = 3.981881491199601e-11 relative error = 2.67123869662031e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.640000000000886 y[1] (closed_form) = 149.6479146667184 y[1] (numeric) = 149.6479146666784 absolute error = 3.998934516857844e-11 relative error = 2.672228694775929e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.650000000000889 y[1] (closed_form) = 150.2323750000521 y[1] (numeric) = 150.2323750000119 absolute error = 4.018829713459127e-11 relative error = 2.675075670911635e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.660000000000893 y[1] (closed_form) = 150.8183653333857 y[1] (numeric) = 150.8183653333453 absolute error = 4.038724910060409e-11 relative error = 2.677873414907238e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.670000000000896 y[1] (closed_form) = 151.4058876667194 y[1] (numeric) = 151.4058876666787 absolute error = 4.067146619490813e-11 relative error = 2.686253937788454e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.680000000000899 y[1] (closed_form) = 151.9949440000531 y[1] (numeric) = 151.9949440000122 absolute error = 4.087041816092096e-11 relative error = 2.688932742454032e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.690000000000903 y[1] (closed_form) = 152.5855363333867 y[1] (numeric) = 152.5855363333457 absolute error = 4.104094841750339e-11 relative error = 2.689701095117713e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.700000000000906 y[1] (closed_form) = 153.1776666667204 y[1] (numeric) = 153.1776666666791 absolute error = 4.126832209294662e-11 relative error = 2.694147455760445e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.710000000000909 y[1] (closed_form) = 153.771337000054 y[1] (numeric) = 153.7713370000127 absolute error = 4.138200893066823e-11 relative error = 2.691139307103358e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.720000000000913 y[1] (closed_form) = 154.3665493333877 y[1] (numeric) = 154.3665493333461 absolute error = 4.160938260611147e-11 relative error = 2.695492176627403e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.730000000000916 y[1] (closed_form) = 154.9633056667214 y[1] (numeric) = 154.9633056666796 absolute error = 4.18367562815547e-11 relative error = 2.699784707195956e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.740000000000919 y[1] (closed_form) = 155.5616080000551 y[1] (numeric) = 155.5616080000131 absolute error = 4.200728653813712e-11 relative error = 2.700363353027454e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.750000000000923 y[1] (closed_form) = 156.1614583333888 y[1] (numeric) = 156.1614583333466 absolute error = 4.217781679471955e-11 relative error = 2.700910790975979e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.760000000000926 y[1] (closed_form) = 156.7628586667224 y[1] (numeric) = 156.7628586666801 absolute error = 4.231992534187157e-11 relative error = 2.699614290132566e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.770000000000929 y[1] (closed_form) = 157.3658110000561 y[1] (numeric) = 157.3658110000135 absolute error = 4.260414243617561e-11 relative error = 2.707331545869287e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.780000000000933 y[1] (closed_form) = 157.9703173333898 y[1] (numeric) = 157.970317333347 absolute error = 4.280309440218844e-11 relative error = 2.709565640224314e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.790000000000936 y[1] (closed_form) = 158.5763796667235 y[1] (numeric) = 158.5763796666805 absolute error = 4.297362465877086e-11 relative error = 2.709963788370474e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.80000000000094 y[1] (closed_form) = 159.1840000000572 y[1] (numeric) = 159.184000000014 absolute error = 4.314415491535328e-11 relative error = 2.710332377333011e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.810000000000943 y[1] (closed_form) = 159.7931803333908 y[1] (numeric) = 159.7931803333475 absolute error = 4.334310688136611e-11 relative error = 2.712450355574343e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.820000000000946 y[1] (closed_form) = 160.4039226667245 y[1] (numeric) = 160.403922666681 absolute error = 4.354205884737894e-11 relative error = 2.714525812304941e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.83000000000095 y[1] (closed_form) = 161.0162290000582 y[1] (numeric) = 161.0162290000145 absolute error = 4.374101081339177e-11 relative error = 2.716559137239263e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.840000000000953 y[1] (closed_form) = 161.6301013333919 y[1] (numeric) = 161.6301013333479 absolute error = 4.39399627794046e-11 relative error = 2.718550716538272e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.850000000000956 y[1] (closed_form) = 162.2455416667256 y[1] (numeric) = 162.2455416666814 absolute error = 4.416733645484783e-11 relative error = 2.722252704211346e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.86000000000096 y[1] (closed_form) = 162.8625520000593 y[1] (numeric) = 162.8625520000149 absolute error = 4.439471013029106e-11 relative error = 2.725900434758931e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.870000000000963 y[1] (closed_form) = 163.481134333393 y[1] (numeric) = 163.4811343333484 absolute error = 4.462208380573429e-11 relative error = 2.729494384026897e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.880000000000966 y[1] (closed_form) = 164.1012906667267 y[1] (numeric) = 164.1012906666818 absolute error = 4.487787919060793e-11 relative error = 2.734766984968474e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.89000000000097 y[1] (closed_form) = 164.7230230000604 y[1] (numeric) = 164.7230230000152 absolute error = 4.513367457548156e-11 relative error = 2.739973669343418e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.900000000000973 y[1] (closed_form) = 165.3463333333941 y[1] (numeric) = 165.3463333333487 absolute error = 4.533262654149439e-11 relative error = 2.741677158941802e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.910000000000976 y[1] (closed_form) = 165.9712236667278 y[1] (numeric) = 165.9712236666822 absolute error = 4.553157850750722e-11 relative error = 2.743341737296291e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.92000000000098 y[1] (closed_form) = 166.5976960000615 y[1] (numeric) = 166.5976960000157 absolute error = 4.578737389238086e-11 relative error = 2.748379779055526e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.930000000000983 y[1] (closed_form) = 167.2257523333951 y[1] (numeric) = 167.2257523333492 absolute error = 4.595790414896328e-11 relative error = 2.748255188431611e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.940000000000986 y[1] (closed_form) = 167.8553946667289 y[1] (numeric) = 167.8553946666827 absolute error = 4.621369953383692e-11 relative error = 2.753185241713121e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.95000000000099 y[1] (closed_form) = 168.4866250000625 y[1] (numeric) = 168.4866250000162 absolute error = 4.635580808098894e-11 relative error = 2.751304922926181e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.960000000000993 y[1] (closed_form) = 169.1194453333962 y[1] (numeric) = 169.1194453333497 absolute error = 4.658318175643217e-11 relative error = 2.754454501940903e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.970000000000996 y[1] (closed_form) = 169.7538576667299 y[1] (numeric) = 169.7538576666832 absolute error = 4.675371201301459e-11 relative error = 2.754206158001077e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.980000000001 y[1] (closed_form) = 170.3898640000637 y[1] (numeric) = 170.3898640000167 absolute error = 4.700950739788823e-11 relative error = 2.758938019803259e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.990000000001003 y[1] (closed_form) = 171.0274663333974 y[1] (numeric) = 171.0274663333502 absolute error = 4.720845936390106e-11 relative error = 2.760285255695356e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.000000000001005 y[1] (closed_form) = 171.666666666731 y[1] (numeric) = 171.6666666666837 absolute error = 4.735056791105308e-11 relative error = 2.758285509380699e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.010000000001 y[1] (closed_form) = 172.3074670000641 y[1] (numeric) = 172.3074670000172 absolute error = 4.695266397902742e-11 relative error = 2.724934954734721e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.020000000000994 y[1] (closed_form) = 172.9498693333973 y[1] (numeric) = 172.9498693333507 absolute error = 4.661160346586257e-11 relative error = 2.695093303366937e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.030000000000989 y[1] (closed_form) = 173.5938756667304 y[1] (numeric) = 173.5938756666842 absolute error = 4.627054295269772e-11 relative error = 2.66544788950556e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.040000000000983 y[1] (closed_form) = 174.2394880000636 y[1] (numeric) = 174.2394880000176 absolute error = 4.592948243953288e-11 relative error = 2.635997325676033e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.050000000000978 y[1] (closed_form) = 174.8867083333967 y[1] (numeric) = 174.8867083333512 absolute error = 4.553157850750722e-11 relative error = 2.603489935936568e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.060000000000972 y[1] (closed_form) = 175.5355386667298 y[1] (numeric) = 175.5355386666847 absolute error = 4.516209628491197e-11 relative error = 2.572817825264223e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.070000000000967 y[1] (closed_form) = 176.185981000063 y[1] (numeric) = 176.1859810000181 absolute error = 4.482103577174712e-11 relative error = 2.543961529591342e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.080000000000961 y[1] (closed_form) = 176.8380373333961 y[1] (numeric) = 176.8380373333516 absolute error = 4.445155354915187e-11 relative error = 2.513687338960142e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.090000000000956 y[1] (closed_form) = 177.4917096667292 y[1] (numeric) = 177.4917096666851 absolute error = 4.408207132655662e-11 relative error = 2.483612976027341e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.10000000000095 y[1] (closed_form) = 178.1470000000623 y[1] (numeric) = 178.1470000000186 absolute error = 4.368416739453096e-11 relative error = 2.452141624305527e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.110000000000944 y[1] (closed_form) = 178.8039103333955 y[1] (numeric) = 178.8039103333521 absolute error = 4.331468517193571e-11 relative error = 2.422468562973355e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.120000000000939 y[1] (closed_form) = 179.4624426667285 y[1] (numeric) = 179.4624426666856 absolute error = 4.294520294934046e-11 relative error = 2.392991107843774e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.130000000000933 y[1] (closed_form) = 180.1225990000617 y[1] (numeric) = 180.1225990000191 absolute error = 4.25757207267452e-11 relative error = 2.363707883580484e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.140000000000928 y[1] (closed_form) = 180.7843813333948 y[1] (numeric) = 180.7843813333526 absolute error = 4.217781679471955e-11 relative error = 2.333045392728758e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.150000000000922 y[1] (closed_form) = 181.4477916667279 y[1] (numeric) = 181.4477916666861 absolute error = 4.180833457212429e-11 relative error = 2.30415229571464e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.160000000000917 y[1] (closed_form) = 182.112832000061 y[1] (numeric) = 182.1128320000196 absolute error = 4.143885234952904e-11 relative error = 2.275449340632688e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.170000000000911 y[1] (closed_form) = 182.7795043333941 y[1] (numeric) = 182.7795043333531 absolute error = 4.104094841750339e-11 relative error = 2.245380222863704e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.180000000000906 y[1] (closed_form) = 183.4478106667273 y[1] (numeric) = 183.4478106666866 absolute error = 4.067146619490813e-11 relative error = 2.21705923047491e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.1900000000009 y[1] (closed_form) = 184.1177530000604 y[1] (numeric) = 184.1177530000201 absolute error = 4.030198397231288e-11 relative error = 2.188924387552115e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.200000000000895 y[1] (closed_form) = 184.7893333333935 y[1] (numeric) = 184.7893333333536 absolute error = 3.993250174971763e-11 relative error = 2.160974393347269e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.210000000000889 y[1] (closed_form) = 185.4625536667266 y[1] (numeric) = 185.4625536666871 absolute error = 3.950617610826157e-11 relative error = 2.130143003382428e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.220000000000883 y[1] (closed_form) = 186.1374160000597 y[1] (numeric) = 186.1374160000206 absolute error = 3.913669388566632e-11 relative error = 2.102569957544364e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.230000000000878 y[1] (closed_form) = 186.8139223333928 y[1] (numeric) = 186.813922333354 absolute error = 3.879563337250147e-11 relative error = 2.076699257096364e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.240000000000872 y[1] (closed_form) = 187.4920746667259 y[1] (numeric) = 187.4920746666875 absolute error = 3.839772944047581e-11 relative error = 2.047965467805997e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.250000000000867 y[1] (closed_form) = 188.171875000059 y[1] (numeric) = 188.171875000021 absolute error = 3.802824721788056e-11 relative error = 2.020931513695585e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.260000000000861 y[1] (closed_form) = 188.8533253333921 y[1] (numeric) = 188.8533253333545 absolute error = 3.765876499528531e-11 relative error = 1.994074762983624e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.270000000000856 y[1] (closed_form) = 189.5364276667252 y[1] (numeric) = 189.5364276666879 absolute error = 3.726086106325965e-11 relative error = 1.96589444688585e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.28000000000085 y[1] (closed_form) = 190.2211840000583 y[1] (numeric) = 190.2211840000214 absolute error = 3.6862957131234e-11 relative error = 1.937899678472336e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.290000000000845 y[1] (closed_form) = 190.9075963333914 y[1] (numeric) = 190.9075963333549 absolute error = 3.652189661806915e-11 relative error = 1.913066704495569e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.300000000000839 y[1] (closed_form) = 191.5956666667245 y[1] (numeric) = 191.5956666666883 absolute error = 3.612399268604349e-11 relative error = 1.885428481473968e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.310000000000834 y[1] (closed_form) = 192.2853970000575 y[1] (numeric) = 192.2853970000218 absolute error = 3.572608875401784e-11 relative error = 1.857972020309329e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.320000000000828 y[1] (closed_form) = 192.9767893333907 y[1] (numeric) = 192.9767893333553 absolute error = 3.535660653142259e-11 relative error = 1.832168866191456e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.330000000000823 y[1] (closed_form) = 193.6698456667237 y[1] (numeric) = 193.6698456666888 absolute error = 3.498712430882733e-11 relative error = 1.806534424002941e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.340000000000817 y[1] (closed_form) = 194.3645680000568 y[1] (numeric) = 194.3645680000222 absolute error = 3.458922037680168e-11 relative error = 1.779605240436187e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.350000000000811 y[1] (closed_form) = 195.0609583333899 y[1] (numeric) = 195.0609583333557 absolute error = 3.419131644477602e-11 relative error = 1.752852889522755e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.360000000000806 y[1] (closed_form) = 195.759018666723 y[1] (numeric) = 195.7590186666892 absolute error = 3.382183422218077e-11 relative error = 1.727728022572588e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.3700000000008 y[1] (closed_form) = 196.4587510000561 y[1] (numeric) = 196.4587510000226 absolute error = 3.345235199958552e-11 relative error = 1.702767213437897e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.380000000000795 y[1] (closed_form) = 197.1601573333892 y[1] (numeric) = 197.1601573333561 absolute error = 3.305444806755986e-11 relative error = 1.676527778970385e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.390000000000789 y[1] (closed_form) = 197.8632396667223 y[1] (numeric) = 197.8632396666896 absolute error = 3.26565441355342e-11 relative error = 1.650460398330705e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.400000000000784 y[1] (closed_form) = 198.5680000000553 y[1] (numeric) = 198.5680000000231 absolute error = 3.220179678464774e-11 relative error = 1.621701219966902e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.410000000000778 y[1] (closed_form) = 199.2744403333884 y[1] (numeric) = 199.2744403333566 absolute error = 3.180389285262208e-11 relative error = 1.595984552731089e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.420000000000773 y[1] (closed_form) = 199.9825626667215 y[1] (numeric) = 199.98256266669 absolute error = 3.143441063002683e-11 relative error = 1.571857576523483e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.430000000000767 y[1] (closed_form) = 200.6923690000545 y[1] (numeric) = 200.6923690000235 absolute error = 3.095124156970996e-11 relative error = 1.542223141015469e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.440000000000762 y[1] (closed_form) = 201.4038613333876 y[1] (numeric) = 201.403861333357 absolute error = 3.058175934711471e-11 relative error = 1.518429644032105e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.450000000000756 y[1] (closed_form) = 202.1170416667206 y[1] (numeric) = 202.1170416666905 absolute error = 3.018385541508906e-11 relative error = 1.493384979622871e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.46000000000075 y[1] (closed_form) = 202.8319120000537 y[1] (numeric) = 202.8319120000239 absolute error = 2.9757529773633e-11 relative error = 1.467102956344716e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.470000000000745 y[1] (closed_form) = 203.5484743333868 y[1] (numeric) = 203.5484743333574 absolute error = 2.941646926046815e-11 relative error = 1.445182498017041e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.480000000000739 y[1] (closed_form) = 204.2667306667198 y[1] (numeric) = 204.2667306666908 absolute error = 2.899014361901209e-11 relative error = 1.419229823887092e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.490000000000734 y[1] (closed_form) = 204.9866830000529 y[1] (numeric) = 204.9866830000243 absolute error = 2.859223968698643e-11 relative error = 1.394834009142879e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.500000000000728 y[1] (closed_form) = 205.7083333333859 y[1] (numeric) = 205.7083333333578 absolute error = 2.813749233609997e-11 relative error = 1.367834344877915e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.510000000000723 y[1] (closed_form) = 206.431683666719 y[1] (numeric) = 206.4316836666912 absolute error = 2.773958840407431e-11 relative error = 1.343766030066367e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.520000000000717 y[1] (closed_form) = 207.1567360000521 y[1] (numeric) = 207.1567360000247 absolute error = 2.734168447204866e-11 relative error = 1.31985495620291e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.530000000000712 y[1] (closed_form) = 207.8834923333851 y[1] (numeric) = 207.8834923333582 absolute error = 2.69153588305926e-11 relative error = 1.294732858702803e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.540000000000706 y[1] (closed_form) = 208.6119546667181 y[1] (numeric) = 208.6119546666916 absolute error = 2.648903318913653e-11 relative error = 1.269775417782545e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.550000000000701 y[1] (closed_form) = 209.3421250000513 y[1] (numeric) = 209.3421250000251 absolute error = 2.614797267597169e-11 relative error = 1.249054516665735e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.560000000000695 y[1] (closed_form) = 210.0740053333842 y[1] (numeric) = 210.0740053333586 absolute error = 2.566480361565482e-11 relative error = 1.221702969623737e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.57000000000069 y[1] (closed_form) = 210.8075976667173 y[1] (numeric) = 210.807597666692 absolute error = 2.523847797419876e-11 relative error = 1.197228100578249e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.580000000000684 y[1] (closed_form) = 211.5429040000504 y[1] (numeric) = 211.5429040000255 absolute error = 2.486899575160351e-11 relative error = 1.175600565245033e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.590000000000678 y[1] (closed_form) = 212.2799263333834 y[1] (numeric) = 212.2799263333589 absolute error = 2.449951352900825e-11 relative error = 1.154113530759947e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.600000000000673 y[1] (closed_form) = 213.0186666667164 y[1] (numeric) = 213.0186666666924 absolute error = 2.407318788755219e-11 relative error = 1.130097576153572e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.610000000000667 y[1] (closed_form) = 213.7591270000495 y[1] (numeric) = 213.7591270000258 absolute error = 2.361844053666573e-11 relative error = 1.104909103444283e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.620000000000662 y[1] (closed_form) = 214.5013093333825 y[1] (numeric) = 214.5013093333593 absolute error = 2.319211489520967e-11 relative error = 1.081210877793011e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.630000000000656 y[1] (closed_form) = 215.2452156667156 y[1] (numeric) = 215.2452156666928 absolute error = 2.276578925375361e-11 relative error = 1.057667608696308e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.640000000000651 y[1] (closed_form) = 215.9908480000486 y[1] (numeric) = 215.9908480000262 absolute error = 2.233946361229755e-11 relative error = 1.034278249247511e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.650000000000645 y[1] (closed_form) = 216.7382083333816 y[1] (numeric) = 216.7382083333597 absolute error = 2.194155968027189e-11 relative error = 1.012353098652634e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.66000000000064 y[1] (closed_form) = 217.4872986667147 y[1] (numeric) = 217.4872986666932 absolute error = 2.148681232938543e-11 relative error = 9.879571111098581e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.670000000000634 y[1] (closed_form) = 218.2381210000476 y[1] (numeric) = 218.2381210000266 absolute error = 2.106048668792937e-11 relative error = 9.650232778500129e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.680000000000629 y[1] (closed_form) = 218.9906773333807 y[1] (numeric) = 218.99067733336 absolute error = 2.071942617476452e-11 relative error = 9.461327955629033e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.690000000000623 y[1] (closed_form) = 219.7449696667137 y[1] (numeric) = 219.7449696666934 absolute error = 2.029310053330846e-11 relative error = 9.234841900630045e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.700000000000617 y[1] (closed_form) = 220.5010000000467 y[1] (numeric) = 220.5010000000268 absolute error = 1.992361831071321e-11 relative error = 9.035613584840425e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.710000000000612 y[1] (closed_form) = 221.2587703333798 y[1] (numeric) = 221.2587703333602 absolute error = 1.955413608811796e-11 relative error = 8.837677285585078e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.720000000000606 y[1] (closed_form) = 222.0182826667127 y[1] (numeric) = 222.0182826666937 absolute error = 1.907096702780109e-11 relative error = 8.589818279258496e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.730000000000601 y[1] (closed_form) = 222.7795390000458 y[1] (numeric) = 222.7795390000271 absolute error = 1.864464138634503e-11 relative error = 8.369099545690862e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.740000000000595 y[1] (closed_form) = 223.5425413333788 y[1] (numeric) = 223.5425413333605 absolute error = 1.827515916374978e-11 relative error = 8.175248905529454e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.75000000000059 y[1] (closed_form) = 224.3072916667118 y[1] (numeric) = 224.3072916666939 absolute error = 1.784883352229372e-11 relative error = 7.957313108133151e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.760000000000584 y[1] (closed_form) = 225.0737920000448 y[1] (numeric) = 225.0737920000274 absolute error = 1.745092959026806e-11 relative error = 7.753425858779945e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.770000000000579 y[1] (closed_form) = 225.8420443333779 y[1] (numeric) = 225.8420443333608 absolute error = 1.70530256582424e-11 relative error = 7.55086401585592e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.780000000000573 y[1] (closed_form) = 226.6120506667108 y[1] (numeric) = 226.6120506666942 absolute error = 1.659827830735594e-11 relative error = 7.324534709660176e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.790000000000568 y[1] (closed_form) = 227.3838130000438 y[1] (numeric) = 227.3838130000277 absolute error = 1.614353095646948e-11 relative error = 7.099683457443985e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.800000000000562 y[1] (closed_form) = 228.1573333333768 y[1] (numeric) = 228.1573333333611 absolute error = 1.571720531501342e-11 relative error = 6.888757457577703e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.810000000000556 y[1] (closed_form) = 228.9326136667098 y[1] (numeric) = 228.9326136666946 absolute error = 1.529087967355736e-11 relative error = 6.679205478262914e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.820000000000551 y[1] (closed_form) = 229.7096560000429 y[1] (numeric) = 229.709656000028 absolute error = 1.483613232267089e-11 relative error = 6.458645483613507e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.830000000000545 y[1] (closed_form) = 230.4884623333758 y[1] (numeric) = 230.4884623333615 absolute error = 1.435296326235402e-11 relative error = 6.227193811373544e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.84000000000054 y[1] (closed_form) = 231.2690346667089 y[1] (numeric) = 231.2690346666949 absolute error = 1.395505933032837e-11 relative error = 6.034123569737542e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.850000000000534 y[1] (closed_form) = 232.0513750000418 y[1] (numeric) = 232.0513750000284 absolute error = 1.34718902700115e-11 relative error = 5.805563647278138e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.860000000000529 y[1] (closed_form) = 232.8354853333748 y[1] (numeric) = 232.8354853333618 absolute error = 1.301714291912504e-11 relative error = 5.590704054619096e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.870000000000523 y[1] (closed_form) = 233.6213676667078 y[1] (numeric) = 233.6213676666952 absolute error = 1.256239556823857e-11 relative error = 5.377245965857246e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.880000000000518 y[1] (closed_form) = 234.4090240000408 y[1] (numeric) = 234.4090240000287 absolute error = 1.213606992678251e-11 relative error = 5.177304917570237e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.890000000000512 y[1] (closed_form) = 235.1984563333738 y[1] (numeric) = 235.1984563333621 absolute error = 1.168132257589605e-11 relative error = 4.966581310949918e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.900000000000507 y[1] (closed_form) = 235.9896666667068 y[1] (numeric) = 235.9896666666955 absolute error = 1.122657522500958e-11 relative error = 4.757231697295083e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.910000000000501 y[1] (closed_form) = 236.7826570000398 y[1] (numeric) = 236.782657000029 absolute error = 1.082867129298393e-11 relative error = 4.573253560957426e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.920000000000496 y[1] (closed_form) = 237.5774293333727 y[1] (numeric) = 237.5774293333624 absolute error = 1.037392394209746e-11 relative error = 4.366544402473769e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.93000000000049 y[1] (closed_form) = 238.3739856667057 y[1] (numeric) = 238.3739856666958 absolute error = 9.947598300641403e-12 relative error = 4.173105665376642e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.940000000000484 y[1] (closed_form) = 239.1723280000387 y[1] (numeric) = 239.1723280000292 absolute error = 9.492850949754938e-12 relative error = 3.969042334092011e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.950000000000479 y[1] (closed_form) = 239.9724583333717 y[1] (numeric) = 239.9724583333627 absolute error = 9.066525308298878e-12 relative error = 3.778152447687803e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.960000000000473 y[1] (closed_form) = 240.7743786667047 y[1] (numeric) = 240.774378666696 absolute error = 8.668621376273222e-12 relative error = 3.600308896767161e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.970000000000468 y[1] (closed_form) = 241.5780910000376 y[1] (numeric) = 241.5780910000294 absolute error = 8.185452315956354e-12 relative error = 3.388325606048058e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.980000000000462 y[1] (closed_form) = 242.3835973333706 y[1] (numeric) = 242.3835973333628 absolute error = 7.759126674500294e-12 relative error = 3.201176465678291e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.990000000000457 y[1] (closed_form) = 243.1908996667036 y[1] (numeric) = 243.1908996666963 absolute error = 7.275957614183426e-12 relative error = 2.991870840625708e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.000000000000451 y[1] (closed_form) = 244.0000000000366 y[1] (numeric) = 244.0000000000297 absolute error = 6.87805368215777e-12 relative error = 2.818874459900303e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.010000000000446 y[1] (closed_form) = 244.8109003333695 y[1] (numeric) = 244.8109003333631 absolute error = 6.394884621840902e-12 relative error = 2.612173156151426e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.02000000000044 y[1] (closed_form) = 245.6236026667025 y[1] (numeric) = 245.6236026666965 absolute error = 5.940137270954438e-12 relative error = 2.418390255033785e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.030000000000435 y[1] (closed_form) = 246.4381090000354 y[1] (numeric) = 246.4381090000299 absolute error = 5.513811629498377e-12 relative error = 2.237402182589213e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.040000000000429 y[1] (closed_form) = 247.2544213333684 y[1] (numeric) = 247.2544213333634 absolute error = 5.059064278611913e-12 relative error = 2.046096588012424e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.050000000000423 y[1] (closed_form) = 248.0725416667013 y[1] (numeric) = 248.0725416666968 absolute error = 4.547473508864641e-12 relative error = 1.833122472286519e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.060000000000418 y[1] (closed_form) = 248.8924720000343 y[1] (numeric) = 248.8924720000302 absolute error = 4.121147867408581e-12 relative error = 1.655794502056299e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.070000000000412 y[1] (closed_form) = 249.7142143333673 y[1] (numeric) = 249.7142143333636 absolute error = 3.666400516522117e-12 relative error = 1.4682386128118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.080000000000407 y[1] (closed_form) = 250.5377706667002 y[1] (numeric) = 250.537770666697 absolute error = 3.240074875066057e-12 relative error = 1.293248066526644e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.090000000000401 y[1] (closed_form) = 251.3631430000331 y[1] (numeric) = 251.3631430000303 absolute error = 2.813749233609997e-12 relative error = 1.119396105581647e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.100000000000396 y[1] (closed_form) = 252.1903333333661 y[1] (numeric) = 252.1903333333638 absolute error = 2.359001882723533e-12 relative error = 9.354053549725905e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.11000000000039 y[1] (closed_form) = 253.0193436666991 y[1] (numeric) = 253.0193436666972 absolute error = 1.932676241267473e-12 relative error = 7.638452512205453e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.120000000000385 y[1] (closed_form) = 253.850176000032 y[1] (numeric) = 253.8501760000306 absolute error = 1.4210854715202e-12 relative error = 5.598126792395926e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.130000000000379 y[1] (closed_form) = 254.6828323333649 y[1] (numeric) = 254.6828323333639 absolute error = 9.663381206337363e-13 relative error = 3.794280563712501e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.140000000000374 y[1] (closed_form) = 255.5173146666979 y[1] (numeric) = 255.5173146666974 absolute error = 5.115907697472721e-13 relative error = 2.002176527311278e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.150000000000368 y[1] (closed_form) = 256.3536250000308 y[1] (numeric) = 256.3536250000307 absolute error = 1.13686837721616e-13 relative error = 4.434766144680122e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.160000000000363 y[1] (closed_form) = 257.1917653333638 y[1] (numeric) = 257.191765333364 absolute error = 2.273736754432321e-13 relative error = 8.840628126196713e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.170000000000357 y[1] (closed_form) = 258.0317376666967 y[1] (numeric) = 258.0317376666974 absolute error = 6.821210263296962e-13 relative error = 2.643554752209597e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.180000000000351 y[1] (closed_form) = 258.8735440000297 y[1] (numeric) = 258.8735440000307 absolute error = 1.080024958355352e-12 relative error = 4.172017509658031e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.190000000000346 y[1] (closed_form) = 259.7171863333626 y[1] (numeric) = 259.7171863333641 absolute error = 1.534772309241816e-12 relative error = 5.909398337897609e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.20000000000034 y[1] (closed_form) = 260.5626666666955 y[1] (numeric) = 260.5626666666976 absolute error = 2.046363078989089e-12 relative error = 7.853631163541702e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.210000000000335 y[1] (closed_form) = 261.4099870000284 y[1] (numeric) = 261.409987000031 absolute error = 2.557953848736361e-12 relative error = 9.785218530063591e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.220000000000329 y[1] (closed_form) = 262.2591493333613 y[1] (numeric) = 262.2591493333644 absolute error = 3.069544618483633e-12 relative error = 1.170424225917812e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.230000000000324 y[1] (closed_form) = 263.1101556666943 y[1] (numeric) = 263.1101556666978 absolute error = 3.581135388230905e-12 relative error = 1.36107835866566e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.240000000000318 y[1] (closed_form) = 263.9630080000272 y[1] (numeric) = 263.9630080000313 absolute error = 4.092726157978177e-12 relative error = 1.55049231670286e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.250000000000313 y[1] (closed_form) = 264.8177083333601 y[1] (numeric) = 264.8177083333646 absolute error = 4.490630090003833e-12 relative error = 1.695743882939618e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.260000000000307 y[1] (closed_form) = 265.674258666693 y[1] (numeric) = 265.6742586666979 absolute error = 4.945377440890297e-12 relative error = 1.861443959873666e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.270000000000302 y[1] (closed_form) = 266.5326610000259 y[1] (numeric) = 266.5326610000313 absolute error = 5.343281372915953e-12 relative error = 2.004737938257943e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.280000000000296 y[1] (closed_form) = 267.3929173333588 y[1] (numeric) = 267.3929173333647 absolute error = 5.854872142663226e-12 relative error = 2.189613771767917e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.29000000000029 y[1] (closed_form) = 268.2550296666917 y[1] (numeric) = 268.255029666698 absolute error = 6.30961949354969e-12 relative error = 2.352097368459195e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.300000000000285 y[1] (closed_form) = 269.1190000000246 y[1] (numeric) = 269.1190000000313 absolute error = 6.650680006714538e-12 relative error = 2.471278507542734e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.310000000000279 y[1] (closed_form) = 269.9848303333576 y[1] (numeric) = 269.9848303333646 absolute error = 7.048583938740194e-12 relative error = 2.610733325289838e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.320000000000274 y[1] (closed_form) = 270.8525226666905 y[1] (numeric) = 270.852522666698 absolute error = 7.503331289626658e-12 relative error = 2.770264502524207e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.330000000000268 y[1] (closed_form) = 271.7220790000234 y[1] (numeric) = 271.7220790000314 absolute error = 8.01492205937393e-12 relative error = 2.949676407920182e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.340000000000263 y[1] (closed_form) = 272.5935013333562 y[1] (numeric) = 272.5935013333648 absolute error = 8.58335624798201e-12 relative error = 3.148775083044028e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.350000000000257 y[1] (closed_form) = 273.4667916666892 y[1] (numeric) = 273.4667916666983 absolute error = 9.094947017729282e-12 relative error = 3.325795780284181e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.360000000000252 y[1] (closed_form) = 274.3419520000221 y[1] (numeric) = 274.3419520000317 absolute error = 9.549694368615746e-12 relative error = 3.480945695325146e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.370000000000246 y[1] (closed_form) = 275.218984333355 y[1] (numeric) = 275.2189843333651 absolute error = 1.011812855722383e-11 relative error = 3.676391939942773e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.380000000000241 y[1] (closed_form) = 276.0978906666878 y[1] (numeric) = 276.0978906666984 absolute error = 1.057287590811029e-11 relative error = 3.829393945234492e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.390000000000235 y[1] (closed_form) = 276.9786730000207 y[1] (numeric) = 276.9786730000317 absolute error = 1.102762325899675e-11 relative error = 3.981397968137399e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.40000000000023 y[1] (closed_form) = 277.8613333333536 y[1] (numeric) = 277.8613333333651 absolute error = 1.148237060988322e-11 relative error = 4.132410390512191e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.410000000000224 y[1] (closed_form) = 278.7458736666865 y[1] (numeric) = 278.7458736666985 absolute error = 1.20508047984913e-11 relative error = 4.323222668724124e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.420000000000218 y[1] (closed_form) = 279.6322960000194 y[1] (numeric) = 279.6322960000319 absolute error = 1.250555214937776e-11 relative error = 4.472141568861165e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.430000000000213 y[1] (closed_form) = 280.5206023333523 y[1] (numeric) = 280.5206023333652 absolute error = 1.296029950026423e-11 relative error = 4.62008829029358e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.440000000000207 y[1] (closed_form) = 281.4107946666851 y[1] (numeric) = 281.4107946666986 absolute error = 1.34718902700115e-11 relative error = 4.787268479152755e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.450000000000202 y[1] (closed_form) = 282.302875000018 y[1] (numeric) = 282.302875000032 absolute error = 1.392663762089796e-11 relative error = 4.933225572320889e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.460000000000196 y[1] (closed_form) = 283.1968453333509 y[1] (numeric) = 283.1968453333653 absolute error = 1.443822839064524e-11 relative error = 5.098301280033682e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.470000000000191 y[1] (closed_form) = 284.0927076666838 y[1] (numeric) = 284.0927076666988 absolute error = 1.500666257925332e-11 relative error = 5.282311785651365e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.480000000000185 y[1] (closed_form) = 284.9904640000166 y[1] (numeric) = 284.9904640000323 absolute error = 1.56319401867222e-11 relative error = 5.485074822265383e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.49000000000018 y[1] (closed_form) = 285.8901163333496 y[1] (numeric) = 285.8901163333656 absolute error = 1.602984411874786e-11 relative error = 5.60699485674313e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.500000000000174 y[1] (closed_form) = 286.7916666666824 y[1] (numeric) = 286.791666666699 absolute error = 1.665512172621675e-11 relative error = 5.807393889716404e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.510000000000169 y[1] (closed_form) = 287.6951170000153 y[1] (numeric) = 287.6951170000323 absolute error = 1.70530256582424e-11 relative error = 5.927464406092613e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.520000000000163 y[1] (closed_form) = 288.6004693333481 y[1] (numeric) = 288.6004693333657 absolute error = 1.750777300912887e-11 relative error = 6.066439548615739e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.530000000000157 y[1] (closed_form) = 289.507725666681 y[1] (numeric) = 289.5077256666991 absolute error = 1.807620719773695e-11 relative error = 6.24377368725166e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.540000000000152 y[1] (closed_form) = 290.4168880000138 y[1] (numeric) = 290.4168880000324 absolute error = 1.858779796748422e-11 relative error = 6.40038466615734e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.550000000000146 y[1] (closed_form) = 291.3279583333467 y[1] (numeric) = 291.3279583333658 absolute error = 1.904254531837068e-11 relative error = 6.536463382131556e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.560000000000141 y[1] (closed_form) = 292.2409386666795 y[1] (numeric) = 292.2409386666992 absolute error = 1.961097950697877e-11 relative error = 6.710551778423627e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.570000000000135 y[1] (closed_form) = 293.1558310000124 y[1] (numeric) = 293.1558310000324 absolute error = 2.006572685786523e-11 relative error = 6.844730595812158e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.58000000000013 y[1] (closed_form) = 294.0726373333452 y[1] (numeric) = 294.0726373333658 absolute error = 2.063416104647331e-11 relative error = 7.016688541165941e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.590000000000124 y[1] (closed_form) = 294.9913596666781 y[1] (numeric) = 294.9913596666991 absolute error = 2.103206497849897e-11 relative error = 7.129722376365156e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.600000000000119 y[1] (closed_form) = 295.9120000000109 y[1] (numeric) = 295.9120000000325 absolute error = 2.154365574824624e-11 relative error = 7.280426528239964e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.610000000000113 y[1] (closed_form) = 296.8345603333437 y[1] (numeric) = 296.8345603333659 absolute error = 2.211208993685432e-11 relative error = 7.449297653218868e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.620000000000108 y[1] (closed_form) = 297.7590426666766 y[1] (numeric) = 297.7590426666991 absolute error = 2.250999386887997e-11 relative error = 7.559801934908341e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.630000000000102 y[1] (closed_form) = 298.6854490000094 y[1] (numeric) = 298.6854490000325 absolute error = 2.307842805748805e-11 relative error = 7.726666342385942e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.640000000000096 y[1] (closed_form) = 299.6137813333423 y[1] (numeric) = 299.6137813333659 absolute error = 2.364686224609613e-11 relative error = 7.892448117994703e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.650000000000091 y[1] (closed_form) = 300.5440416666751 y[1] (numeric) = 300.5440416666993 absolute error = 2.421529643470421e-11 relative error = 8.057154053168923e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.660000000000085 y[1] (closed_form) = 301.476232000008 y[1] (numeric) = 301.4762320000327 absolute error = 2.472688720445149e-11 relative error = 8.201935867518349e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.67000000000008 y[1] (closed_form) = 302.4103543333408 y[1] (numeric) = 302.4103543333661 absolute error = 2.529532139305957e-11 relative error = 8.36456855084302e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.680000000000074 y[1] (closed_form) = 303.3464106666736 y[1] (numeric) = 303.3464106666994 absolute error = 2.580691216280684e-11 relative error = 8.507406468430006e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.690000000000069 y[1] (closed_form) = 304.2844030000065 y[1] (numeric) = 304.2844030000326 absolute error = 2.614797267597169e-11 relative error = 8.59326748863008e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.700000000000063 y[1] (closed_form) = 305.2243333333393 y[1] (numeric) = 305.224333333366 absolute error = 2.671640686457977e-11 relative error = 8.753039632460248e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.710000000000058 y[1] (closed_form) = 306.1662036666721 y[1] (numeric) = 306.1662036666993 absolute error = 2.728484105318785e-11 relative error = 8.911774299848353e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.720000000000052 y[1] (closed_form) = 307.1100160000049 y[1] (numeric) = 307.1100160000327 absolute error = 2.773958840407431e-11 relative error = 9.032459691602461e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.730000000000047 y[1] (closed_form) = 308.0557723333378 y[1] (numeric) = 308.055772333366 absolute error = 2.825117917382158e-11 relative error = 9.170800131364474e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.740000000000041 y[1] (closed_form) = 309.0034746666706 y[1] (numeric) = 309.0034746666993 absolute error = 2.870592652470805e-11 relative error = 9.289839396037154e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.750000000000036 y[1] (closed_form) = 309.9531250000034 y[1] (numeric) = 309.9531250000326 absolute error = 2.927436071331613e-11 relative error = 9.444770306257055e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.76000000000003 y[1] (closed_form) = 310.9047253333362 y[1] (numeric) = 310.9047253333659 absolute error = 2.97859514830634e-11 relative error = 9.580411314472118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.770000000000024 y[1] (closed_form) = 311.858277666669 y[1] (numeric) = 311.8582776666992 absolute error = 3.018385541508906e-11 relative error = 9.67870907289214e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.780000000000019 y[1] (closed_form) = 312.8137840000018 y[1] (numeric) = 312.8137840000325 absolute error = 3.069544618483633e-11 relative error = 9.812689770996841e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.790000000000013 y[1] (closed_form) = 313.7712463333347 y[1] (numeric) = 313.7712463333658 absolute error = 3.115019353572279e-11 relative error = 9.9276762608867e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.800000000000008 y[1] (closed_form) = 314.7306666666674 y[1] (numeric) = 314.7306666666992 absolute error = 3.177547114319168e-11 relative error = 1.009608357511765e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.810000000000002 y[1] (closed_form) = 315.6920470000002 y[1] (numeric) = 315.6920470000326 absolute error = 3.234390533179976e-11 relative error = 1.024539757626512e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.819999999999997 y[1] (closed_form) = 316.655389333333 y[1] (numeric) = 316.655389333366 absolute error = 3.296918293926865e-11 relative error = 1.04116917159313e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.829999999999991 y[1] (closed_form) = 317.6206956666658 y[1] (numeric) = 317.6206956666994 absolute error = 3.353761712787673e-11 relative error = 1.05590150722022e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.839999999999986 y[1] (closed_form) = 318.5879679999986 y[1] (numeric) = 318.5879680000327 absolute error = 3.410605131648481e-11 relative error = 1.07053795943998e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.84999999999998 y[1] (closed_form) = 319.5572083333314 y[1] (numeric) = 319.5572083333661 absolute error = 3.467448550509289e-11 relative error = 1.085079122011975e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.859999999999975 y[1] (closed_form) = 320.5284186666642 y[1] (numeric) = 320.5284186666993 absolute error = 3.512923285597935e-11 relative error = 1.095978727942755e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.869999999999969 y[1] (closed_form) = 321.501600999997 y[1] (numeric) = 321.5016010000327 absolute error = 3.569766704458743e-11 relative error = 1.110341812717373e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.879999999999963 y[1] (closed_form) = 322.4767573333298 y[1] (numeric) = 322.476757333366 absolute error = 3.620925781433471e-11 relative error = 1.122848608183777e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.889999999999958 y[1] (closed_form) = 323.4538896666625 y[1] (numeric) = 323.4538896666993 absolute error = 3.677769200294279e-11 relative error = 1.137030444767391e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.899999999999952 y[1] (closed_form) = 324.4329999999953 y[1] (numeric) = 324.4330000000326 absolute error = 3.723243935382925e-11 relative error = 1.147615666526826e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.909999999999947 y[1] (closed_form) = 325.4140903333281 y[1] (numeric) = 325.4140903333659 absolute error = 3.774403012357652e-11 relative error = 1.159876945860413e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.919999999999941 y[1] (closed_form) = 326.3971626666609 y[1] (numeric) = 326.3971626666993 absolute error = 3.836930773104541e-11 relative error = 1.175540480118412e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.929999999999936 y[1] (closed_form) = 327.3822189999937 y[1] (numeric) = 327.3822190000325 absolute error = 3.888089850079268e-11 relative error = 1.187630122966252e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.93999999999993 y[1] (closed_form) = 328.3692613333264 y[1] (numeric) = 328.3692613333658 absolute error = 3.939248927053995e-11 relative error = 1.199639975757438e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.949999999999925 y[1] (closed_form) = 329.3582916666592 y[1] (numeric) = 329.3582916666991 absolute error = 3.990408004028723e-11 relative error = 1.211570531239997e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.959999999999919 y[1] (closed_form) = 330.349311999992 y[1] (numeric) = 330.3493120000324 absolute error = 4.04156708100345e-11 relative error = 1.223422278840268e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.969999999999914 y[1] (closed_form) = 331.3423243333247 y[1] (numeric) = 331.3423243333658 absolute error = 4.104094841750339e-11 relative error = 1.238626803867558e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.979999999999908 y[1] (closed_form) = 332.3373306666575 y[1] (numeric) = 332.337330666699 absolute error = 4.155253918725066e-11 relative error = 1.25031211822932e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.989999999999903 y[1] (closed_form) = 333.3343329999903 y[1] (numeric) = 333.3343330000324 absolute error = 4.212097337585874e-11 relative error = 1.263625411663189e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.999999999999897 y[1] (closed_form) = 334.333333333323 y[1] (numeric) = 334.3333333333657 absolute error = 4.268940756446682e-11 relative error = 1.276851671918289e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 Finished! diff ( y , x , 1 ) = x * x ; Iterations = 9901 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %