##############ECHO OF PROBLEM################# ##############temp/mult_c_sinpostode.ode################# diff ( y , x , 1 ) = 2.0 * sin ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.1); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(cos(x) * c(-2.0)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = -1.990008330556052 y[1] (numeric) = -1.990008330556052 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) = -1.987912195913394 y[1] (numeric) = -1.987912195913394 absolute error = 2.220446049250313e-16 relative error = 1.116973905494893e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = -1.985617271707733 y[1] (numeric) = -1.985617271707733 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = -1.983123787429576 y[1] (numeric) = -1.983123787429576 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) = -1.980431992425274 y[1] (numeric) = -1.980431992425274 absolute error = 2.220446049250313e-16 relative error = 1.121192779021467e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = -1.977542155872084 y[1] (numeric) = -1.977542155872084 absolute error = 2.220446049250313e-16 relative error = 1.122831208759294e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = -1.974454566751254 y[1] (numeric) = -1.974454566751253 absolute error = 4.440892098500626e-16 relative error = 2.249174112832397e-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) = -1.971169533819121 y[1] (numeric) = -1.971169533819121 absolute error = 6.661338147750939e-16 relative error = 3.379383677285567e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = -1.967687385576243 y[1] (numeric) = -1.967687385576242 absolute error = 4.440892098500626e-16 relative error = 2.256909370387664e-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) = -1.964008470234541 y[1] (numeric) = -1.96400847023454 absolute error = 4.440892098500626e-16 relative error = 2.261136937953377e-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) = -1.960133155682483 y[1] (numeric) = -1.960133155682483 absolute error = 4.440892098500626e-16 relative error = 2.265607357146299e-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) = -1.956061829448297 y[1] (numeric) = -1.956061829448296 absolute error = 4.440892098500626e-16 relative error = 2.27032296814113e-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) = -1.951794898661211 y[1] (numeric) = -1.951794898661211 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] = 0.2300000000000001 y[1] (closed_form) = -1.94733279001075 y[1] (numeric) = -1.94733279001075 absolute error = 2.220446049250313e-16 relative error = 1.140249915494956e-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) = -1.942675949704059 y[1] (numeric) = -1.942675949704059 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] = 0.2500000000000001 y[1] (closed_form) = -1.937824843421289 y[1] (numeric) = -1.937824843421289 absolute error = 2.220446049250313e-16 relative error = 1.145844556998272e-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) = -1.932779956269026 y[1] (numeric) = -1.932779956269026 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] = 0.2700000000000001 y[1] (closed_form) = -1.927541792731781 y[1] (numeric) = -1.927541792731781 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = -1.922110876621542 y[1] (numeric) = -1.922110876621542 absolute error = 2.220446049250313e-16 relative error = 1.155212259738704e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = -1.916487751025394 y[1] (numeric) = -1.916487751025395 absolute error = 6.661338147750939e-16 relative error = 3.475805229742204e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = -1.910672978251212 y[1] (numeric) = -1.910672978251213 absolute error = 8.881784197001252e-16 relative error = 4.64851091636336e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = -1.904667139771427 y[1] (numeric) = -1.904667139771427 absolute error = 6.661338147750939e-16 relative error = 3.49737652771725e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = -1.898470836164882 y[1] (numeric) = -1.898470836164883 absolute error = 8.881784197001252e-16 relative error = 4.678388536609509e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = -1.892084687056774 y[1] (numeric) = -1.892084687056775 absolute error = 1.110223024625157e-15 relative error = 5.86772374524187e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = -1.885509331056692 y[1] (numeric) = -1.885509331056693 absolute error = 1.110223024625157e-15 relative error = 5.888186318351214e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = -1.878745425694758 y[1] (numeric) = -1.878745425694759 absolute error = 8.881784197001252e-16 relative error = 4.727508088924171e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (closed_form) = -1.87179364735587 y[1] (numeric) = -1.87179364735587 absolute error = 6.661338147750939e-16 relative error = 3.558799420631045e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (closed_form) = -1.864654691212069 y[1] (numeric) = -1.86465469121207 absolute error = 8.881784197001252e-16 relative error = 4.763232698719078e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (closed_form) = -1.85732927115302 y[1] (numeric) = -1.857329271153021 absolute error = 8.881784197001252e-16 relative error = 4.782019179338884e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = -1.849818119714626 y[1] (numeric) = -1.849818119714626 absolute error = 4.440892098500626e-16 relative error = 2.400718238821084e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (closed_form) = -1.84212198800577 y[1] (numeric) = -1.84212198800577 absolute error = 4.440892098500626e-16 relative error = 2.410748108657132e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = -1.83424164563321 y[1] (numeric) = -1.834241645633211 absolute error = 6.661338147750939e-16 relative error = 3.631657891755771e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = -1.826177880624616 y[1] (numeric) = -1.826177880624617 absolute error = 8.881784197001252e-16 relative error = 4.863592036260659e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = -1.81793149934977 y[1] (numeric) = -1.817931499349771 absolute error = 1.110223024625157e-15 relative error = 6.107067428130578e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = -1.809503326439927 y[1] (numeric) = -1.809503326439927 absolute error = 8.881784197001252e-16 relative error = 4.908409985891296e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = -1.800894204705354 y[1] (numeric) = -1.800894204705354 absolute error = 6.661338147750939e-16 relative error = 3.698905871508875e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (closed_form) = -1.79210499505105 y[1] (numeric) = -1.792104995051051 absolute error = 8.881784197001252e-16 relative error = 4.956062407910562e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = -1.783136576390658 y[1] (numeric) = -1.783136576390658 absolute error = 6.661338147750939e-16 relative error = 3.735741970609178e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (closed_form) = -1.773989845558568 y[1] (numeric) = -1.773989845558569 absolute error = 6.661338147750939e-16 relative error = 3.755003538734188e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = -1.764665717220243 y[1] (numeric) = -1.764665717220244 absolute error = 8.881784197001252e-16 relative error = 5.03312560012336e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (closed_form) = -1.755165123780745 y[1] (numeric) = -1.755165123780746 absolute error = 8.881784197001252e-16 relative error = 5.060369578145038e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (closed_form) = -1.745489015291502 y[1] (numeric) = -1.745489015291503 absolute error = 6.661338147750939e-16 relative error = 3.816316281221899e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (closed_form) = -1.7356383593553 y[1] (numeric) = -1.7356383593553 absolute error = 2.220446049250313e-16 relative error = 1.279325291056079e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (closed_form) = -1.725614141029522 y[1] (numeric) = -1.725614141029522 absolute error = 6.661338147750939e-16 relative error = 3.860270954766693e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (closed_form) = -1.715417362727648 y[1] (numeric) = -1.715417362727648 absolute error = 4.440892098500626e-16 relative error = 2.588811443204271e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (closed_form) = -1.705049044119011 y[1] (numeric) = -1.705049044119012 absolute error = 4.440892098500626e-16 relative error = 2.604553877096954e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (closed_form) = -1.694510222026832 y[1] (numeric) = -1.694510222026832 absolute error = 4.440892098500626e-16 relative error = 2.62075261675837e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = -1.683801950324537 y[1] (numeric) = -1.683801950324538 absolute error = 6.661338147750939e-16 relative error = 3.956129250513713e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = -1.672925299830373 y[1] (numeric) = -1.672925299830374 absolute error = 6.661338147750939e-16 relative error = 3.981850324354809e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = -1.661881358200326 y[1] (numeric) = -1.661881358200327 absolute error = 8.881784197001252e-16 relative error = 5.344415323738546e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = -1.650671229819356 y[1] (numeric) = -1.650671229819357 absolute error = 6.661338147750939e-16 relative error = 4.035532956178035e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = -1.639296035690958 y[1] (numeric) = -1.639296035690959 absolute error = 6.661338147750939e-16 relative error = 4.063535812153175e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = -1.627756913325067 y[1] (numeric) = -1.627756913325068 absolute error = 6.661338147750939e-16 relative error = 4.092342101710769e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (closed_form) = -1.616055016624303 y[1] (numeric) = -1.616055016624304 absolute error = 4.440892098500626e-16 relative error = 2.747983238699994e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = -1.604191515768585 y[1] (numeric) = -1.604191515768585 absolute error = 2.220446049250313e-16 relative error = 1.384152719562586e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = -1.592167597098111 y[1] (numeric) = -1.592167597098111 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = -1.579984462994729 y[1] (numeric) = -1.57998446299473 absolute error = 2.220446049250313e-16 relative error = 1.405359420460149e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (closed_form) = -1.567643331761698 y[1] (numeric) = -1.567643331761698 absolute error = 2.220446049250313e-16 relative error = 1.416422986187173e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (closed_form) = -1.555145437501855 y[1] (numeric) = -1.555145437501856 absolute error = 4.440892098500626e-16 relative error = 2.855612080651671e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (closed_form) = -1.542492029994213 y[1] (numeric) = -1.542492029994213 absolute error = 2.220446049250313e-16 relative error = 1.439518652980427e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = -1.529684374568976 y[1] (numeric) = -1.529684374568977 absolute error = 8.881784197001252e-16 relative error = 5.806285495662398e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = -1.516723751981016 y[1] (numeric) = -1.516723751981017 absolute error = 8.881784197001252e-16 relative error = 5.855901040252465e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (closed_form) = -1.503611458281789 y[1] (numeric) = -1.50361145828179 absolute error = 1.110223024625157e-15 relative error = 7.383709524891712e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (closed_form) = -1.49034880468974 y[1] (numeric) = -1.490348804689741 absolute error = 1.332267629550188e-15 relative error = 8.939300822451014e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (closed_form) = -1.476937117459175 y[1] (numeric) = -1.476937117459177 absolute error = 1.77635683940025e-15 relative error = 1.202730176120279e-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) = -1.463377737747641 y[1] (numeric) = -1.463377737747642 absolute error = 1.554312234475219e-15 relative error = 1.062140139474542e-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) = -1.44967202148181 y[1] (numeric) = -1.449672021481811 absolute error = 1.77635683940025e-15 relative error = 1.225350847003665e-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) = -1.435821339221886 y[1] (numeric) = -1.435821339221888 absolute error = 1.77635683940025e-15 relative error = 1.237171221012017e-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) = -1.421827076024554 y[1] (numeric) = -1.421827076024555 absolute error = 1.554312234475219e-15 relative error = 1.093179515768609e-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) = -1.407690631304471 y[1] (numeric) = -1.407690631304473 absolute error = 1.554312234475219e-15 relative error = 1.104157547056257e-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) = -1.39341341869433 y[1] (numeric) = -1.393413418694331 absolute error = 1.554312234475219e-15 relative error = 1.115470981994458e-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) = -1.378996865903493 y[1] (numeric) = -1.378996865903495 absolute error = 1.332267629550188e-15 relative error = 9.661136022070004e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (closed_form) = -1.364442414575226 y[1] (numeric) = -1.364442414575228 absolute error = 1.332267629550188e-15 relative error = 9.764190964152526e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = -1.349751520142533 y[1] (numeric) = -1.349751520142535 absolute error = 1.554312234475219e-15 relative error = 1.151554350026651e-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) = -1.334925651682615 y[1] (numeric) = -1.334925651682617 absolute error = 1.332267629550188e-15 relative error = 9.980088612957004e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = -1.319966291769963 y[1] (numeric) = -1.319966291769965 absolute error = 1.332267629550188e-15 relative error = 1.00931943327411e-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) = -1.304874936328103 y[1] (numeric) = -1.304874936328104 absolute error = 1.110223024625157e-15 relative error = 8.50827151105612e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (closed_form) = -1.289653094480001 y[1] (numeric) = -1.289653094480002 absolute error = 1.110223024625157e-15 relative error = 8.608695077592223e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (closed_form) = -1.274302288397159 y[1] (numeric) = -1.27430228839716 absolute error = 1.110223024625157e-15 relative error = 8.712399206483537e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (closed_form) = -1.258824053147393 y[1] (numeric) = -1.258824053147394 absolute error = 8.881784197001252e-16 relative error = 7.055620024732166e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = -1.243219936541328 y[1] (numeric) = -1.243219936541329 absolute error = 8.881784197001252e-16 relative error = 7.144177740352701e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = -1.227491498977622 y[1] (numeric) = -1.227491498977623 absolute error = 1.332267629550188e-15 relative error = 1.085357927659649e-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) = -1.211640313286924 y[1] (numeric) = -1.211640313286926 absolute error = 1.332267629550188e-15 relative error = 1.099557034328139e-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) = -1.195667964574595 y[1] (numeric) = -1.195667964574596 absolute error = 1.110223024625157e-15 relative error = 9.285379030959995e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = -1.179576050062195 y[1] (numeric) = -1.179576050062196 absolute error = 8.881784197001252e-16 relative error = 7.529641006642128e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = -1.163366178927766 y[1] (numeric) = -1.163366178927767 absolute error = 8.881784197001252e-16 relative error = 7.634555961724179e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = -1.147039972144912 y[1] (numeric) = -1.147039972144913 absolute error = 1.110223024625157e-15 relative error = 9.679026464518847e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = -1.130599062320707 y[1] (numeric) = -1.130599062320708 absolute error = 8.881784197001252e-16 relative error = 7.855821301293307e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = -1.114045093532433 y[1] (numeric) = -1.114045093532435 absolute error = 1.332267629550188e-15 relative error = 1.195883036768117e-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) = -1.097379721163174 y[1] (numeric) = -1.097379721163175 absolute error = 1.332267629550188e-15 relative error = 1.214044331107234e-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) = -1.080604611736278 y[1] (numeric) = -1.08060461173628 absolute error = 1.554312234475219e-15 relative error = 1.438372756875249e-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) = -1.063721442748712 y[1] (numeric) = -1.063721442748712 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = -1.046731902503302 y[1] (numeric) = -1.0467319025033 absolute error = 1.998401444325282e-15 relative error = 1.909181748971273e-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) = -1.029637689939915 y[1] (numeric) = -1.029637689939911 absolute error = 3.774758283725532e-15 relative error = 3.666103446490784e-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) = -1.012440514465563 y[1] (numeric) = -1.012440514465557 absolute error = 5.995204332975845e-15 relative error = 5.921537361768392e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = -0.9951420957834624 y[1] (numeric) = -0.9951420957834546 absolute error = 7.771561172376096e-15 relative error = 7.809498970353221e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = -0.9777441637210655 y[1] (numeric) = -0.9777441637210558 absolute error = 9.769962616701378e-15 relative error = 9.992350738785477e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = -0.9602484580570806 y[1] (numeric) = -0.9602484580570687 absolute error = 1.187938636348917e-14 relative error = 1.237115900974768e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = -0.9426567283474944 y[1] (numeric) = -0.9426567283474804 absolute error = 1.398881011027697e-14 relative error = 1.48397711378985e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = -0.9249707337506181 y[1] (numeric) = -0.9249707337506022 absolute error = 1.587618925213974e-14 relative error = 1.716399089489477e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y[1] (closed_form) = -0.9071922428511732 y[1] (numeric) = -0.9071922428511554 absolute error = 1.77635683940025e-14 relative error = 1.958082042034905e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = -0.8893230334834342 y[1] (numeric) = -0.8893230334834143 absolute error = 1.98729921407903e-14 relative error = 2.234620199023608e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = -0.871364892553447 y[1] (numeric) = -0.8713648925534251 absolute error = 2.187139358511558e-14 relative error = 2.510015467919952e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = -0.8533196158603393 y[1] (numeric) = -0.8533196158603154 absolute error = 2.398081733190338e-14 relative error = 2.810297207069978e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = -0.835189007916743 y[1] (numeric) = -0.835189007916717 absolute error = 2.597921877622866e-14 relative error = 3.110579584976822e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = -0.8169748817683435 y[1] (numeric) = -0.8169748817683156 absolute error = 2.797762022055394e-14 relative error = 3.424538605152258e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = -0.7986790588125774 y[1] (numeric) = -0.7986790588125475 absolute error = 2.986499936241671e-14 relative error = 3.73929916314796e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = -0.7803033686164936 y[1] (numeric) = -0.7803033686164618 absolute error = 3.186340080674199e-14 relative error = 4.083463187303288e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = -0.761849648733799 y[1] (numeric) = -0.761849648733765 absolute error = 3.397282455352979e-14 relative error = 4.459255787541929e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = -0.7433197445211035 y[1] (numeric) = -0.7433197445210676 absolute error = 3.586020369539256e-14 relative error = 4.824330842778313e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = -0.724715508953387 y[1] (numeric) = -0.7247155089533491 absolute error = 3.785860513971784e-14 relative error = 5.223926447274756e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = -0.7060388024387028 y[1] (numeric) = -0.7060388024386629 absolute error = 3.985700658404312e-14 relative error = 5.645158091364737e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = -0.6872914926321383 y[1] (numeric) = -0.6872914926320965 absolute error = 4.174438572590589e-14 relative error = 6.073752719684673e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = -0.6684754542490516 y[1] (numeric) = -0.6684754542490079 absolute error = 4.374278717023117e-14 relative error = 6.543663928449057e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = -0.6495925688776012 y[1] (numeric) = -0.6495925688775553 absolute error = 4.585221091701897e-14 relative error = 7.058610752928521e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = -0.6306447247905883 y[1] (numeric) = -0.6306447247905403 absolute error = 4.796163466380676e-14 relative error = 7.605174954842109e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = -0.6116338167566319 y[1] (numeric) = -0.6116338167565818 absolute error = 5.007105841059456e-14 relative error = 8.186443757493833e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = -0.592561745850693 y[1] (numeric) = -0.5925617458506407 absolute error = 5.229150445984487e-14 relative error = 8.824650734882351e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = -0.5734304192639689 y[1] (numeric) = -0.5734304192639145 absolute error = 5.440092820663267e-14 relative error = 9.486927511878321e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = -0.5542417501131753 y[1] (numeric) = -0.5542417501131188 absolute error = 5.651035195342047e-14 relative error = 1.01959753017309e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y[1] (closed_form) = -0.5349976572492372 y[1] (numeric) = -0.5349976572491786 absolute error = 5.861977570020827e-14 relative error = 1.095701540107853e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y[1] (closed_form) = -0.515700065065404 y[1] (numeric) = -0.5157000650653433 absolute error = 6.072919944699606e-14 relative error = 1.177606976630768e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = -0.4963509033048129 y[1] (numeric) = -0.49635090330475 absolute error = 6.294964549624638e-14 relative error = 1.26824883519127e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = -0.4769521068675157 y[1] (numeric) = -0.4769521068674506 absolute error = 6.511458039426543e-14 relative error = 1.365222617883361e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = -0.4575056156169905 y[1] (numeric) = -0.4575056156169232 absolute error = 6.733502644351574e-14 relative error = 1.47178579114724e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y[1] (closed_form) = -0.4380133741861571 y[1] (numeric) = -0.4380133741860876 absolute error = 6.94999613415348e-14 relative error = 1.586708658626417e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y[1] (closed_form) = -0.418477331782915 y[1] (numeric) = -0.4184773317828434 absolute error = 7.16093850883226e-14 relative error = 1.71118910511191e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y[1] (closed_form) = -0.3988994419952245 y[1] (numeric) = -0.3988994419951508 absolute error = 7.371880883511039e-14 relative error = 1.848054950049114e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y[1] (closed_form) = -0.3792816625957496 y[1] (numeric) = -0.3792816625956737 absolute error = 7.588374373312945e-14 relative error = 2.000722713926952e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y[1] (closed_form) = -0.3596259553460822 y[1] (numeric) = -0.3596259553460041 absolute error = 7.80486786311485e-14 relative error = 2.170273793392894e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y[1] (closed_form) = -0.3399342858005674 y[1] (numeric) = -0.3399342858004872 absolute error = 8.021361352916756e-14 relative error = 2.359679999334556e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y[1] (closed_form) = -0.3202086231097502 y[1] (numeric) = -0.3202086231096678 absolute error = 8.243405957841787e-14 relative error = 2.574385998036159e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = -0.3004509398234617 y[1] (numeric) = -0.3004509398233771 absolute error = 8.459899447643693e-14 relative error = 2.815734060480737e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = -0.2806632116935658 y[1] (numeric) = -0.280663211693479 absolute error = 8.681944052568724e-14 relative error = 3.093367313863657e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = -0.2608474174763857 y[1] (numeric) = -0.2608474174762967 absolute error = 8.903988657493755e-14 relative error = 3.413485455841181e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y[1] (closed_form) = -0.2410055387348302 y[1] (numeric) = -0.241005538734739 absolute error = 9.126033262418787e-14 relative error = 3.786648767628463e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y[1] (closed_form) = -0.2211395596402385 y[1] (numeric) = -0.221139559640145 absolute error = 9.345302309782255e-14 relative error = 4.225974911492854e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y[1] (closed_form) = -0.2012514667739651 y[1] (numeric) = -0.2012514667738695 absolute error = 9.561795799584161e-14 relative error = 4.75116825375661e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y[1] (closed_form) = -0.1813432489287233 y[1] (numeric) = -0.1813432489286254 absolute error = 9.786615962070755e-14 relative error = 5.396735759331946e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y[1] (closed_form) = -0.1614168969097075 y[1] (numeric) = -0.1614168969096075 absolute error = 1.00003338943111e-13 relative error = 6.195345150207559e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y[1] (closed_form) = -0.1414744033355143 y[1] (numeric) = -0.1414744033354122 absolute error = 1.0216827384113e-13 relative error = 7.221679076379092e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = -0.1215177624388826 y[1] (numeric) = -0.1215177624387783 absolute error = 1.043609643147647e-13 relative error = 8.588124256094091e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = -0.1015489698672715 y[1] (numeric) = -0.1015489698671649 absolute error = 1.065536547883994e-13 relative error = 1.049283463216508e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = -0.08157002248329744 y[1] (numeric) = -0.08157002248318868 absolute error = 1.087602230498419e-13 relative error = 1.333335700282687e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = -0.06158291816504987 y[1] (numeric) = -0.06158291816493891 absolute error = 1.109598524173805e-13 relative error = 1.801795948025625e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y[1] (closed_form) = -0.04158965560630474 y[1] (numeric) = -0.04158965560619157 absolute error = 1.13166420678823e-13 relative error = 2.721023269585999e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y[1] (closed_form) = -0.0215922341166569 y[1] (numeric) = -0.02159223411654154 absolute error = 1.153660500463616e-13 relative error = 5.342941792084624e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y[1] (closed_form) = -0.001592653421590872 y[1] (numeric) = -0.0015926534214733 absolute error = 1.175715341056316e-13 relative error = 7.38211669354853e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999937 y[1] (closed_form) = 0.01840708653749011 y[1] (numeric) = 0.01840708653760989 absolute error = 1.197757171222946e-13 relative error = 6.507043734397881e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999936 y[1] (closed_form) = 0.03840498580325653 y[1] (numeric) = 0.03840498580337851 absolute error = 1.219788159367852e-13 relative error = 3.176119282055353e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999935 y[1] (closed_form) = 0.05839904460244668 y[1] (numeric) = 0.05839904460257087 absolute error = 1.241923230921316e-13 relative error = 2.126615665334505e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y[1] (closed_form) = 0.07838726354584229 y[1] (numeric) = 0.07838726354596869 absolute error = 1.263988913535741e-13 relative error = 1.612492714197807e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y[1] (closed_form) = 0.09836764382820581 y[1] (numeric) = 0.09836764382833442 absolute error = 1.286054596150166e-13 relative error = 1.307395954706607e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y[1] (closed_form) = 0.1183381874281593 y[1] (numeric) = 0.1183381874282901 absolute error = 1.308120278764591e-13 relative error = 1.105408412274967e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y[1] (closed_form) = 0.1382968973079848 y[1] (numeric) = 0.1382968973081178 absolute error = 1.330324739257094e-13 relative error = 9.619339010147739e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999929 y[1] (closed_form) = 0.1582417776133265 y[1] (numeric) = 0.1582417776134618 absolute error = 1.352529199749597e-13 relative error = 8.547232090975274e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999928 y[1] (closed_form) = 0.1781708338727746 y[1] (numeric) = 0.178170833872912 absolute error = 1.374178548729788e-13 relative error = 7.712702011099298e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999927 y[1] (closed_form) = 0.1980820731973106 y[1] (numeric) = 0.1980820731974502 absolute error = 1.395827897709978e-13 relative error = 7.046714905490646e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999926 y[1] (closed_form) = 0.2179735044795948 y[1] (numeric) = 0.2179735044797365 absolute error = 1.417199690934012e-13 relative error = 6.501706224880561e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999925 y[1] (closed_form) = 0.237843138593075 y[1] (numeric) = 0.2378431385932189 absolute error = 1.439404151426515e-13 relative error = 6.051905301708901e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999924 y[1] (closed_form) = 0.2576889885908978 y[1] (numeric) = 0.2576889885910439 absolute error = 1.461053500406706e-13 relative error = 5.669832880310797e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y[1] (closed_form) = 0.2775090699046016 y[1] (numeric) = 0.2775090699047499 absolute error = 1.483257960899209e-13 relative error = 5.344899038467838e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y[1] (closed_form) = 0.2973014005425718 y[1] (numeric) = 0.2973014005427223 absolute error = 1.5049073098794e-13 relative error = 5.061891088077487e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y[1] (closed_form) = 0.3170640012882381 y[1] (numeric) = 0.3170640012883907 absolute error = 1.52655665885959e-13 relative error = 4.81466408251065e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y[1] (closed_form) = 0.3367948958979947 y[1] (numeric) = 0.3367948958981495 absolute error = 1.548206007839781e-13 relative error = 4.596880851509957e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999918 y[1] (closed_form) = 0.3564921112988229 y[1] (numeric) = 0.3564921112989798 absolute error = 1.569300245307659e-13 relative error = 4.402061632135871e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999917 y[1] (closed_form) = 0.3761536777855971 y[1] (numeric) = 0.3761536777857562 absolute error = 1.590949594287849e-13 relative error = 4.229520241975863e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999916 y[1] (closed_form) = 0.395777629218053 y[1] (numeric) = 0.3957776292182143 absolute error = 1.61259894326804e-13 relative error = 4.074507562375591e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999915 y[1] (closed_form) = 0.4153620032174008 y[1] (numeric) = 0.4153620032175643 absolute error = 1.634803403760543e-13 relative error = 3.935852078662298e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999914 y[1] (closed_form) = 0.4349048413625607 y[1] (numeric) = 0.4349048413627263 absolute error = 1.655897641228421e-13 relative error = 3.807494154446474e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999913 y[1] (closed_form) = 0.4544041893860038 y[1] (numeric) = 0.4544041893861716 absolute error = 1.678102101720924e-13 relative error = 3.69297233810365e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y[1] (closed_form) = 0.4738580973691772 y[1] (numeric) = 0.4738580973693471 absolute error = 1.699196339188802e-13 relative error = 3.58587591648767e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y[1] (closed_form) = 0.4932646199374942 y[1] (numeric) = 0.4932646199376662 absolute error = 1.72029057665668e-13 relative error = 3.487561254392567e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y[1] (closed_form) = 0.5126218164548698 y[1] (numeric) = 0.512621816455044 absolute error = 1.741939925636871e-13 relative error = 3.398099475522863e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999908 y[1] (closed_form) = 0.5319277512177835 y[1] (numeric) = 0.5319277512179598 absolute error = 1.763034163104749e-13 relative error = 3.314424109418051e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999907 y[1] (closed_form) = 0.551180493648847 y[1] (numeric) = 0.5511804936490252 absolute error = 1.781907954523376e-13 relative error = 3.232893716406837e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999906 y[1] (closed_form) = 0.5703781184898612 y[1] (numeric) = 0.5703781184900415 absolute error = 1.803002191991254e-13 relative error = 3.161064798146361e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999905 y[1] (closed_form) = 0.58951870599434 y[1] (numeric) = 0.5895187059945224 absolute error = 1.824096429459132e-13 relative error = 3.094212975621244e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999904 y[1] (closed_form) = 0.6086003421194832 y[1] (numeric) = 0.6086003421196676 absolute error = 1.844080443902385e-13 relative error = 3.030035174611102e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999903 y[1] (closed_form) = 0.6276211187175799 y[1] (numeric) = 0.6276211187177662 absolute error = 1.862954235321013e-13 relative error = 2.968278440227749e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999902 y[1] (closed_form) = 0.6465791337268205 y[1] (numeric) = 0.6465791337270087 absolute error = 1.88182802673964e-13 relative error = 2.910437297741056e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y[1] (closed_form) = 0.6654724913615027 y[1] (numeric) = 0.665472491361693 absolute error = 1.902922264207518e-13 relative error = 2.859505522631437e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y[1] (closed_form) = 0.6842993023016073 y[1] (numeric) = 0.6842993023017998 absolute error = 1.925126724700021e-13 relative error = 2.81328172953699e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y[1] (closed_form) = 0.7030576838817293 y[1] (numeric) = 0.7030576838819238 absolute error = 1.945110739143274e-13 relative error = 2.766644592238732e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999897 y[1] (closed_form) = 0.7217457602793426 y[1] (numeric) = 0.7217457602795392 absolute error = 1.966204976611152e-13 relative error = 2.724234882724018e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999896 y[1] (closed_form) = 0.7403616627023807 y[1] (numeric) = 0.7403616627025793 absolute error = 1.986188991054405e-13 relative error = 2.682728038354461e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999895 y[1] (closed_form) = 0.7589035295761146 y[1] (numeric) = 0.7589035295763153 absolute error = 2.007283228522283e-13 relative error = 2.644978116841083e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999894 y[1] (closed_form) = 0.7773695067293085 y[1] (numeric) = 0.7773695067295112 absolute error = 2.027267242965536e-13 relative error = 2.607855370472436e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999893 y[1] (closed_form) = 0.7957577475796351 y[1] (numeric) = 0.7957577475798399 absolute error = 2.047251257408789e-13 relative error = 2.572706660583171e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999892 y[1] (closed_form) = 0.8140664133183331 y[1] (numeric) = 0.8140664133185398 absolute error = 2.067235271852041e-13 relative error = 2.539393884861908e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999891 y[1] (closed_form) = 0.8322936730940858 y[1] (numeric) = 0.8322936730942944 absolute error = 2.086109063270669e-13 relative error = 2.506457913485601e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.00999999999989 y[1] (closed_form) = 0.850437704196105 y[1] (numeric) = 0.8504377041963154 absolute error = 2.103872631664672e-13 relative error = 2.473870362619216e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999889 y[1] (closed_form) = 0.8684966922364001 y[1] (numeric) = 0.8684966922366123 absolute error = 2.121636200058674e-13 relative error = 2.442883454852786e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999887 y[1] (closed_form) = 0.8864688313312163 y[1] (numeric) = 0.8864688313314306 absolute error = 2.142730437526552e-13 relative error = 2.417152596678215e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999886 y[1] (closed_form) = 0.9043523242816212 y[1] (numeric) = 0.9043523242818374 absolute error = 2.162714451969805e-13 relative error = 2.391451200932969e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999885 y[1] (closed_form) = 0.9221453827532221 y[1] (numeric) = 0.9221453827534404 absolute error = 2.182698466413058e-13 relative error = 2.366978686046488e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999884 y[1] (closed_form) = 0.9398462274549998 y[1] (numeric) = 0.93984622745522 absolute error = 2.201572257831685e-13 relative error = 2.342481348032115e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999883 y[1] (closed_form) = 0.9574530883172345 y[1] (numeric) = 0.9574530883174567 absolute error = 2.221556272274938e-13 relative error = 2.320276888113046e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999882 y[1] (closed_form) = 0.9749642046685125 y[1] (numeric) = 0.9749642046687367 absolute error = 2.241540286718191e-13 relative error = 2.299100085915784e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.089999999999881 y[1] (closed_form) = 0.9923778254117911 y[1] (numeric) = 0.992377825412017 absolute error = 2.259303855112194e-13 relative error = 2.276656931723244e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09999999999988 y[1] (closed_form) = 1.009692209199507 y[1] (numeric) = 1.009692209199735 absolute error = 2.280398092580072e-13 relative error = 2.258508159024017e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999879 y[1] (closed_form) = 1.026905624607711 y[1] (numeric) = 1.026905624607941 absolute error = 2.300382107023324e-13 relative error = 2.240110533917949e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999878 y[1] (closed_form) = 1.044016350309206 y[1] (numeric) = 1.044016350309438 absolute error = 2.318145675417327e-13 relative error = 2.220411274910362e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y[1] (closed_form) = 1.06102267524568 y[1] (numeric) = 1.061022675245914 absolute error = 2.33812968986058e-13 relative error = 2.203656664848548e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999875 y[1] (closed_form) = 1.077922898798813 y[1] (numeric) = 1.077922898799048 absolute error = 2.353672812205332e-13 relative error = 2.183526126801978e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999874 y[1] (closed_form) = 1.094715330960332 y[1] (numeric) = 1.094715330960569 absolute error = 2.369215934550084e-13 relative error = 2.164230158786308e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999873 y[1] (closed_form) = 1.111398292501014 y[1] (numeric) = 1.111398292501253 absolute error = 2.384759056894836e-13 relative error = 2.145728559226359e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999872 y[1] (closed_form) = 1.127970115138609 y[1] (numeric) = 1.127970115138849 absolute error = 2.398081733190338e-13 relative error = 2.126015309275861e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.179999999999871 y[1] (closed_form) = 1.144429141704662 y[1] (numeric) = 1.144429141704903 absolute error = 2.415845301584341e-13 relative error = 2.110961014140086e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18999999999987 y[1] (closed_form) = 1.160773726310232 y[1] (numeric) = 1.160773726310475 absolute error = 2.435829316027593e-13 relative error = 2.098453178958831e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999869 y[1] (closed_form) = 1.177002234510479 y[1] (numeric) = 1.177002234510724 absolute error = 2.453592884421596e-13 relative error = 2.084611917021599e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999868 y[1] (closed_form) = 1.193113043468107 y[1] (numeric) = 1.193113043468355 absolute error = 2.471356452815598e-13 relative error = 2.071351466942251e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999867 y[1] (closed_form) = 1.209104542115646 y[1] (numeric) = 1.209104542115895 absolute error = 2.489120021209601e-13 relative error = 2.058647482089705e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999865 y[1] (closed_form) = 1.224975131316558 y[1] (numeric) = 1.224975131316808 absolute error = 2.504663143554353e-13 relative error = 2.044664482994389e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999864 y[1] (closed_form) = 1.240723224025146 y[1] (numeric) = 1.240723224025399 absolute error = 2.522426711948356e-13 relative error = 2.033029335716885e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999863 y[1] (closed_form) = 1.256347245445265 y[1] (numeric) = 1.25634724544552 absolute error = 2.544631172440859e-13 relative error = 2.025420266304647e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999862 y[1] (closed_form) = 1.271845633187792 y[1] (numeric) = 1.271845633188048 absolute error = 2.557953848736361e-13 relative error = 2.011214082895444e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.269999999999861 y[1] (closed_form) = 1.287216837426868 y[1] (numeric) = 1.287216837427126 absolute error = 2.577937863179613e-13 relative error = 2.002722298391374e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27999999999986 y[1] (closed_form) = 1.302459321054879 y[1] (numeric) = 1.302459321055138 absolute error = 2.591260539475115e-13 relative error = 1.989513605212959e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999859 y[1] (closed_form) = 1.317571559836163 y[1] (numeric) = 1.317571559836423 absolute error = 2.602362769721367e-13 relative error = 1.97512063029424e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999858 y[1] (closed_form) = 1.332552042559436 y[1] (numeric) = 1.332552042559698 absolute error = 2.620126338115369e-13 relative error = 1.966246911514905e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999857 y[1] (closed_form) = 1.34739927118891 y[1] (numeric) = 1.347399271189174 absolute error = 2.637889906509372e-13 relative error = 1.957764088874537e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999856 y[1] (closed_form) = 1.362111761014094 y[1] (numeric) = 1.362111761014359 absolute error = 2.653433028854124e-13 relative error = 1.948028865765494e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999854 y[1] (closed_form) = 1.376688040798265 y[1] (numeric) = 1.376688040798532 absolute error = 2.666755705149626e-13 relative error = 1.937080606586313e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999853 y[1] (closed_form) = 1.391126652925593 y[1] (numeric) = 1.391126652925862 absolute error = 2.684519273543629e-13 relative error = 1.929744691396704e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999852 y[1] (closed_form) = 1.405426153546897 y[1] (numeric) = 1.405426153547168 absolute error = 2.702282841937631e-13 relative error = 1.922749790245354e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999851 y[1] (closed_form) = 1.419585112724031 y[1] (numeric) = 1.419585112724303 absolute error = 2.717825964282383e-13 relative error = 1.914521320294186e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36999999999985 y[1] (closed_form) = 1.433602114572877 y[1] (numeric) = 1.43360211457315 absolute error = 2.733369086627135e-13 relative error = 1.906644151010832e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999849 y[1] (closed_form) = 1.447475757404929 y[1] (numeric) = 1.447475757405204 absolute error = 2.748912208971888e-13 relative error = 1.899107598112874e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999848 y[1] (closed_form) = 1.461204653867467 y[1] (numeric) = 1.461204653867743 absolute error = 2.762234885267389e-13 relative error = 1.89038193791431e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999847 y[1] (closed_form) = 1.474787431082284 y[1] (numeric) = 1.474787431082562 absolute error = 2.777778007612142e-13 relative error = 1.883510768445896e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999846 y[1] (closed_form) = 1.488222730782979 y[1] (numeric) = 1.488222730783258 absolute error = 2.793321129956894e-13 relative error = 1.876950991393124e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y[1] (closed_form) = 1.501509209450776 y[1] (numeric) = 1.501509209451057 absolute error = 2.806643806252396e-13 relative error = 1.869215179358782e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y[1] (closed_form) = 1.514645538448883 y[1] (numeric) = 1.514645538449165 absolute error = 2.819966482547898e-13 relative error = 1.861799616454003e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y[1] (closed_form) = 1.527630404155345 y[1] (numeric) = 1.527630404155628 absolute error = 2.8377300509419e-13 relative error = 1.857602495487732e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y[1] (closed_form) = 1.540462508094412 y[1] (numeric) = 1.540462508094697 absolute error = 2.853273173286652e-13 relative error = 1.852218511190005e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y[1] (closed_form) = 1.553140567066385 y[1] (numeric) = 1.553140567066671 absolute error = 2.864375403532904e-13 relative error = 1.844247368377749e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y[1] (closed_form) = 1.56566331327593 y[1] (numeric) = 1.565663313276217 absolute error = 2.873257187729905e-13 relative error = 1.835169262360768e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999838 y[1] (closed_form) = 1.578029494458863 y[1] (numeric) = 1.578029494459152 absolute error = 2.884359417976157e-13 relative error = 1.827823515406003e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999837 y[1] (closed_form) = 1.59023787400737 y[1] (numeric) = 1.59023787400766 absolute error = 2.893241202173158e-13 relative error = 1.819376364670678e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999836 y[1] (closed_form) = 1.602287231093671 y[1] (numeric) = 1.602287231093961 absolute error = 2.90434343241941e-13 relative error = 1.81262346479351e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999835 y[1] (closed_form) = 1.614176360792097 y[1] (numeric) = 1.614176360792388 absolute error = 2.917666108714911e-13 relative error = 1.807526227978692e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y[1] (closed_form) = 1.625904074199586 y[1] (numeric) = 1.625904074199879 absolute error = 2.933209231059664e-13 relative error = 1.804048146262041e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999832 y[1] (closed_form) = 1.637469198554571 y[1] (numeric) = 1.637469198554866 absolute error = 2.946531907355165e-13 relative error = 1.799442645978399e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999831 y[1] (closed_form) = 1.648870577354254 y[1] (numeric) = 1.648870577354549 absolute error = 2.957634137601417e-13 relative error = 1.793733345856156e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54999999999983 y[1] (closed_form) = 1.660107070470255 y[1] (numeric) = 1.660107070470552 absolute error = 2.970956813896919e-13 relative error = 1.789617589578329e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999829 y[1] (closed_form) = 1.671177554262627 y[1] (numeric) = 1.671177554262925 absolute error = 2.97983859809392e-13 relative error = 1.783077202355505e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999828 y[1] (closed_form) = 1.682080921692217 y[1] (numeric) = 1.682080921692516 absolute error = 2.990940828340172e-13 relative error = 1.778119464865702e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999827 y[1] (closed_form) = 1.692816082431367 y[1] (numeric) = 1.692816082431667 absolute error = 3.002043058586423e-13 relative error = 1.773401782829611e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999826 y[1] (closed_form) = 1.703381962972949 y[1] (numeric) = 1.70338196297325 absolute error = 3.010924842783425e-13 relative error = 1.767615783325775e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999825 y[1] (closed_form) = 1.713777506737714 y[1] (numeric) = 1.713777506738016 absolute error = 3.024247519078926e-13 relative error = 1.764667529588352e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999824 y[1] (closed_form) = 1.724001674179948 y[1] (numeric) = 1.724001674180251 absolute error = 3.030908857226677e-13 relative error = 1.758066075352498e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y[1] (closed_form) = 1.734053442891428 y[1] (numeric) = 1.734053442891732 absolute error = 3.042011087472929e-13 relative error = 1.754277585816826e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999821 y[1] (closed_form) = 1.743931807703658 y[1] (numeric) = 1.743931807703964 absolute error = 3.05311331771918e-13 relative error = 1.750706824792307e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999982 y[1] (closed_form) = 1.75363578078839 y[1] (numeric) = 1.753635780788696 absolute error = 3.061995101916182e-13 relative error = 1.746083842187337e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999819 y[1] (closed_form) = 1.763164391756401 y[1] (numeric) = 1.763164391756709 absolute error = 3.075317778211684e-13 relative error = 1.74420365598931e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999818 y[1] (closed_form) = 1.772516687754536 y[1] (numeric) = 1.772516687754844 absolute error = 3.086420008457935e-13 relative error = 1.741264288105452e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999817 y[1] (closed_form) = 1.781691733560987 y[1] (numeric) = 1.781691733561296 absolute error = 3.095301792654936e-13 relative error = 1.737282457088408e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999816 y[1] (closed_form) = 1.79068861167882 y[1] (numeric) = 1.79068861167913 absolute error = 3.101963130802687e-13 relative error = 1.732273892050115e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999815 y[1] (closed_form) = 1.799506422427721 y[1] (numeric) = 1.799506422428032 absolute error = 3.110844914999689e-13 relative error = 1.728721207231278e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999814 y[1] (closed_form) = 1.808144284033963 y[1] (numeric) = 1.808144284034275 absolute error = 3.124167591295191e-13 relative error = 1.727830914204028e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999813 y[1] (closed_form) = 1.816601332718583 y[1] (numeric) = 1.816601332718897 absolute error = 3.135269821541442e-13 relative error = 1.725898668614011e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y[1] (closed_form) = 1.824876722783762 y[1] (numeric) = 1.824876722784076 absolute error = 3.144151605738443e-13 relative error = 1.722939180758573e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999981 y[1] (closed_form) = 1.832969626697387 y[1] (numeric) = 1.832969626697702 absolute error = 3.153033389935445e-13 relative error = 1.72017765270695e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999809 y[1] (closed_form) = 1.840879235175812 y[1] (numeric) = 1.840879235176128 absolute error = 3.159694728083196e-13 relative error = 1.716405219694615e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999808 y[1] (closed_form) = 1.848604757264781 y[1] (numeric) = 1.848604757265097 absolute error = 3.168576512280197e-13 relative error = 1.714036761956874e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999807 y[1] (closed_form) = 1.856145420418522 y[1] (numeric) = 1.856145420418839 absolute error = 3.170796958329447e-13 relative error = 1.708269688058438e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999806 y[1] (closed_form) = 1.863500470577004 y[1] (numeric) = 1.863500470577321 absolute error = 3.179678742526448e-13 relative error = 1.706293501252463e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999805 y[1] (closed_form) = 1.87066917224134 y[1] (numeric) = 1.870669172241658 absolute error = 3.186340080674199e-13 relative error = 1.703315651936729e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999804 y[1] (closed_form) = 1.877650808547337 y[1] (numeric) = 1.877650808547657 absolute error = 3.19300141882195e-13 relative error = 1.700529941076875e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999803 y[1] (closed_form) = 1.884444681337184 y[1] (numeric) = 1.884444681337504 absolute error = 3.199662756969701e-13 relative error = 1.697934032586858e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999802 y[1] (closed_form) = 1.891050111229263 y[1] (numeric) = 1.891050111229583 absolute error = 3.206324095117452e-13 relative error = 1.695525716678764e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y[1] (closed_form) = 1.897466437686088 y[1] (numeric) = 1.89746643768641 absolute error = 3.215205879314453e-13 relative error = 1.694473122399632e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999799 y[1] (closed_form) = 1.903693019080362 y[1] (numeric) = 1.903693019080684 absolute error = 3.224087663511455e-13 relative error = 1.693596410344012e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999798 y[1] (closed_form) = 1.909729232759133 y[1] (numeric) = 1.909729232759456 absolute error = 3.232969447708456e-13 relative error = 1.692894150778399e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999797 y[1] (closed_form) = 1.915574475106064 y[1] (numeric) = 1.915574475106388 absolute error = 3.237410339806956e-13 relative error = 1.69004671020567e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999796 y[1] (closed_form) = 1.921228161601791 y[1] (numeric) = 1.921228161602115 absolute error = 3.237410339806956e-13 relative error = 1.685073332002286e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999795 y[1] (closed_form) = 1.926689726882376 y[1] (numeric) = 1.926689726882701 absolute error = 3.244071677954707e-13 relative error = 1.683754074509972e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999794 y[1] (closed_form) = 1.931958624795843 y[1] (numeric) = 1.931958624796168 absolute error = 3.246292124003958e-13 relative error = 1.680311411610591e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999793 y[1] (closed_form) = 1.93703432845679 y[1] (numeric) = 1.937034328457115 absolute error = 3.250733016102458e-13 relative error = 1.678201035648282e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999792 y[1] (closed_form) = 1.941916330299081 y[1] (numeric) = 1.941916330299407 absolute error = 3.255173908200959e-13 relative error = 1.676268878020928e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.909999999999791 y[1] (closed_form) = 1.946604142126601 y[1] (numeric) = 1.946604142126927 absolute error = 3.26183524634871e-13 relative error = 1.675654117732053e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y[1] (closed_form) = 1.951097295162073 y[1] (numeric) = 1.951097295162399 absolute error = 3.266276138447211e-13 relative error = 1.674071378473153e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999788 y[1] (closed_form) = 1.955395340093937 y[1] (numeric) = 1.955395340094265 absolute error = 3.272937476594961e-13 relative error = 1.673798341177252e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999787 y[1] (closed_form) = 1.959497847121283 y[1] (numeric) = 1.959497847121611 absolute error = 3.279598814742712e-13 relative error = 1.673693502425023e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999786 y[1] (closed_form) = 1.963404405996827 y[1] (numeric) = 1.963404405997155 absolute error = 3.288480598939714e-13 relative error = 1.674887042575491e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999785 y[1] (closed_form) = 1.967114626067935 y[1] (numeric) = 1.967114626068264 absolute error = 3.290701044988964e-13 relative error = 1.672856782914957e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999784 y[1] (closed_form) = 1.970628136315694 y[1] (numeric) = 1.970628136316023 absolute error = 3.292921491038214e-13 relative error = 1.671000951602515e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999783 y[1] (closed_form) = 1.973944585392005 y[1] (numeric) = 1.973944585392335 absolute error = 3.297362383136715e-13 relative error = 1.670443237129624e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999782 y[1] (closed_form) = 1.977063641654726 y[1] (numeric) = 1.977063641655056 absolute error = 3.301803275235216e-13 relative error = 1.670054117464693e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.999999999999781 y[1] (closed_form) = 1.979984993200829 y[1] (numeric) = 1.979984993201159 absolute error = 3.301803275235216e-13 relative error = 1.667590050719296e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.00999999999978 y[1] (closed_form) = 1.982708347897594 y[1] (numeric) = 1.982708347897924 absolute error = 3.304023721284466e-13 relative error = 1.666419433189938e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y[1] (closed_form) = 1.98523343341182 y[1] (numeric) = 1.985233433412151 absolute error = 3.308464613382966e-13 relative error = 1.666536820154717e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999777 y[1] (closed_form) = 1.987559997237062 y[1] (numeric) = 1.987559997237393 absolute error = 3.310685059432217e-13 relative error = 1.665703205958287e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999776 y[1] (closed_form) = 1.989687806718873 y[1] (numeric) = 1.989687806719205 absolute error = 3.317346397579968e-13 relative error = 1.667269803020249e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999775 y[1] (closed_form) = 1.991616649078081 y[1] (numeric) = 1.991616649078413 absolute error = 3.317346397579968e-13 relative error = 1.665655084333406e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999774 y[1] (closed_form) = 1.993346331432056 y[1] (numeric) = 1.993346331432388 absolute error = 3.317346397579968e-13 relative error = 1.664209748838139e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999773 y[1] (closed_form) = 1.994876680814005 y[1] (numeric) = 1.994876680814337 absolute error = 3.321787289678468e-13 relative error = 1.66515921591856e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999772 y[1] (closed_form) = 1.996207544190263 y[1] (numeric) = 1.996207544190595 absolute error = 3.321787289678468e-13 relative error = 1.66404906110397e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.089999999999771 y[1] (closed_form) = 1.997338788475604 y[1] (numeric) = 1.997338788475936 absolute error = 3.321787289678468e-13 relative error = 1.663106584043112e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09999999999977 y[1] (closed_form) = 1.99827030054654 y[1] (numeric) = 1.998270300546872 absolute error = 3.326228181776969e-13 relative error = 1.664553679683486e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999769 y[1] (closed_form) = 1.999001987252641 y[1] (numeric) = 1.999001987252974 absolute error = 3.328448627826219e-13 relative error = 1.665055187063983e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y[1] (closed_form) = 1.999533775425847 y[1] (numeric) = 1.99953377542618 absolute error = 3.33510996597397e-13 relative error = 1.667943801181194e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999766 y[1] (closed_form) = 1.999865611887782 y[1] (numeric) = 1.999865611888116 absolute error = 3.337330412023221e-13 relative error = 1.668777337929688e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999765 y[1] (closed_form) = 1.999997463455078 y[1] (numeric) = 1.999997463455412 absolute error = 3.33510996597397e-13 relative error = 1.667557097903729e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999764 y[1] (closed_form) = 1.999929316942688 y[1] (numeric) = 1.999929316943021 absolute error = 3.33288951992472e-13 relative error = 1.6665036567491e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999763 y[1] (closed_form) = 1.999661179165205 y[1] (numeric) = 1.999661179165539 absolute error = 3.33288951992472e-13 relative error = 1.666727120899599e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999762 y[1] (closed_form) = 1.999193076936185 y[1] (numeric) = 1.999193076936518 absolute error = 3.33288951992472e-13 relative error = 1.667117377693433e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.179999999999761 y[1] (closed_form) = 1.99852505706546 y[1] (numeric) = 1.998525057065794 absolute error = 3.33288951992472e-13 relative error = 1.66767462241308e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18999999999976 y[1] (closed_form) = 1.997657186354461 y[1] (numeric) = 1.997657186354794 absolute error = 3.33288951992472e-13 relative error = 1.668399134091138e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999759 y[1] (closed_form) = 1.996589551589534 y[1] (numeric) = 1.996589551589868 absolute error = 3.33510996597397e-13 relative error = 1.670403395289135e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y[1] (closed_form) = 1.995322259533268 y[1] (numeric) = 1.995322259533602 absolute error = 3.339550858072471e-13 relative error = 1.673689972693251e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y[1] (closed_form) = 1.993855436913812 y[1] (numeric) = 1.993855436914146 absolute error = 3.337330412023221e-13 relative error = 1.673807614251565e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999755 y[1] (closed_form) = 1.992189230412205 y[1] (numeric) = 1.992189230412539 absolute error = 3.33510996597397e-13 relative error = 1.674092960177232e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999754 y[1] (closed_form) = 1.990323806647709 y[1] (numeric) = 1.990323806648043 absolute error = 3.337330412023221e-13 relative error = 1.676777618233019e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999753 y[1] (closed_form) = 1.988259352161146 y[1] (numeric) = 1.988259352161479 absolute error = 3.33288951992472e-13 relative error = 1.676285096459888e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999752 y[1] (closed_form) = 1.985996073396244 y[1] (numeric) = 1.985996073396577 absolute error = 3.33288951992472e-13 relative error = 1.678195422725665e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.269999999999751 y[1] (closed_form) = 1.983534196678994 y[1] (numeric) = 1.983534196679327 absolute error = 3.33288951992472e-13 relative error = 1.680278326184109e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27999999999975 y[1] (closed_form) = 1.980873968195015 y[1] (numeric) = 1.980873968195348 absolute error = 3.33066907387547e-13 relative error = 1.68141392504158e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999749 y[1] (closed_form) = 1.97801565396494 y[1] (numeric) = 1.978015653965273 absolute error = 3.326228181776969e-13 relative error = 1.681598512685949e-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) = 1.974959539817809 y[1] (numeric) = 1.974959539818142 absolute error = 3.324007735727719e-13 relative error = 1.683076371293338e-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) = 1.971705931362491 y[1] (numeric) = 1.971705931362823 absolute error = 3.319566843629218e-13 relative error = 1.683601388435915e-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) = 1.968255153957119 y[1] (numeric) = 1.968255153957451 absolute error = 3.319566843629218e-13 relative error = 1.686553106163765e-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) = 1.964607552676559 y[1] (numeric) = 1.964607552676891 absolute error = 3.317346397579968e-13 relative error = 1.688554232147002e-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) = 1.960763492277899 y[1] (numeric) = 1.96076349227823 absolute error = 3.312905505481467e-13 relative error = 1.689599749550992e-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) = 1.956723357163975 y[1] (numeric) = 1.956723357164306 absolute error = 3.310685059432217e-13 relative error = 1.691953564775063e-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) = 1.952487551344932 y[1] (numeric) = 1.952487551345263 absolute error = 3.306244167333716e-13 relative error = 1.693349678494122e-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) = 1.948056498397822 y[1] (numeric) = 1.948056498398152 absolute error = 3.301803275235216e-13 relative error = 1.69492172221431e-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) = 1.943430641424247 y[1] (numeric) = 1.943430641424577 absolute error = 3.297362383136715e-13 relative error = 1.696670986272109e-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) = 1.938610443006051 y[1] (numeric) = 1.93861044300638 absolute error = 3.295141937087465e-13 relative error = 1.699744241539289e-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) = 1.933596385159057 y[1] (numeric) = 1.933596385159386 absolute error = 3.290701044988964e-13 relative error = 1.701855190796849e-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) = 1.928388969284872 y[1] (numeric) = 1.9283889692852 absolute error = 3.284039706841213e-13 relative error = 1.702996521525984e-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) = 1.922988716120744 y[1] (numeric) = 1.922988716121072 absolute error = 3.279598814742712e-13 relative error = 1.705469609493428e-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) = 1.917396165687489 y[1] (numeric) = 1.917396165687816 absolute error = 3.270717030545711e-13 relative error = 1.705811813477255e-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) = 1.91161187723549 y[1] (numeric) = 1.911611877235817 absolute error = 3.266276138447211e-13 relative error = 1.708650263865692e-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) = 1.905636429188773 y[1] (numeric) = 1.905636429189099 absolute error = 3.26183524634871e-13 relative error = 1.711677629786533e-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) = 1.899470419087161 y[1] (numeric) = 1.899470419087487 absolute error = 3.252953462151709e-13 relative error = 1.712558105387605e-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) = 1.893114463526528 y[1] (numeric) = 1.893114463526852 absolute error = 3.244071677954707e-13 relative error = 1.713616234230017e-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) = 1.886569198097132 y[1] (numeric) = 1.886569198097456 absolute error = 3.235189893757706e-13 relative error = 1.714853553752942e-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) = 1.879835277320063 y[1] (numeric) = 1.879835277320386 absolute error = 3.230749001659206e-13 relative error = 1.718634095570883e-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) = 1.872913374581785 y[1] (numeric) = 1.872913374582107 absolute error = 3.221867217462204e-13 relative error = 1.720243584774248e-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) = 1.865804182066806 y[1] (numeric) = 1.865804182067127 absolute error = 3.210764987215953e-13 relative error = 1.720847781388985e-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) = 1.858508410688451 y[1] (numeric) = 1.858508410688771 absolute error = 3.201883203018951e-13 relative error = 1.722824166199426e-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) = 1.851026790017779 y[1] (numeric) = 1.851026790018098 absolute error = 3.1907809727727e-13 relative error = 1.723789731180526e-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) = 1.843360068210623 y[1] (numeric) = 1.843360068210941 absolute error = 3.184119634624949e-13 relative error = 1.727345454388529e-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) = 1.835509011932774 y[1] (numeric) = 1.835509011933091 absolute error = 3.173017404378697e-13 relative error = 1.72868527680915e-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) = 1.827474406283318 y[1] (numeric) = 1.827474406283634 absolute error = 3.166356066230946e-13 relative error = 1.732640443742586e-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) = 1.819257054716123 y[1] (numeric) = 1.819257054716439 absolute error = 3.157474282033945e-13 relative error = 1.735584465014834e-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) = 1.8108577789595 y[1] (numeric) = 1.810857778959815 absolute error = 3.153033389935445e-13 relative error = 1.741182232293883e-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) = 1.802277418934024 y[1] (numeric) = 1.802277418934338 absolute error = 3.141931159689193e-13 relative error = 1.74331161600389e-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) = 1.793516832668547 y[1] (numeric) = 1.79351683266886 absolute error = 3.135269821541442e-13 relative error = 1.748112849811686e-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) = 1.784576896214395 y[1] (numeric) = 1.784576896214708 absolute error = 3.124167591295191e-13 relative error = 1.750648906148261e-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) = 1.775458503557765 y[1] (numeric) = 1.775458503558077 absolute error = 3.113065361048939e-13 relative error = 1.753386719436585e-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) = 1.766162566530323 y[1] (numeric) = 1.766162566530633 absolute error = 3.101963130802687e-13 relative error = 1.756329337732813e-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) = 1.756690014718025 y[1] (numeric) = 1.756690014718334 absolute error = 3.093081346605686e-13 relative error = 1.760743967741043e-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) = 1.747041795368159 y[1] (numeric) = 1.747041795368467 absolute error = 3.081979116359435e-13 relative error = 1.76411298489282e-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) = 1.737218873294619 y[1] (numeric) = 1.737218873294927 absolute error = 3.073097332162433e-13 relative error = 1.768975331435545e-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) = 1.727222230781428 y[1] (numeric) = 1.727222230781734 absolute error = 3.064215547965432e-13 relative error = 1.774071392410879e-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) = 1.717052867484505 y[1] (numeric) = 1.717052867484811 absolute error = 3.055333763768431e-13 relative error = 1.779405760665085e-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) = 1.706711800331707 y[1] (numeric) = 1.706711800332011 absolute error = 3.044231533522179e-13 relative error = 1.783682243792139e-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) = 1.69620006342113 y[1] (numeric) = 1.696200063421434 absolute error = 3.033129303275928e-13 relative error = 1.788190773415191e-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) = 1.685518707917707 y[1] (numeric) = 1.68551870791801 absolute error = 3.022027073029676e-13 relative error = 1.792935942409737e-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) = 1.674668801948087 y[1] (numeric) = 1.674668801948388 absolute error = 3.013145288832675e-13 relative error = 1.799248475476215e-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) = 1.663651430493824 y[1] (numeric) = 1.663651430494124 absolute error = 2.999822612537173e-13 relative error = 1.803155731754897e-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) = 1.652467695282884 y[1] (numeric) = 1.652467695283183 absolute error = 2.990940828340172e-13 relative error = 1.809984447428582e-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) = 1.641118714679467 y[1] (numeric) = 1.641118714679765 absolute error = 2.97983859809392e-13 relative error = 1.815736163045295e-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) = 1.629605623572176 y[1] (numeric) = 1.629605623572473 absolute error = 2.968736367847669e-13 relative error = 1.821751425562739e-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) = 1.617929573260529 y[1] (numeric) = 1.617929573260824 absolute error = 2.953193245502916e-13 relative error = 1.825291591371002e-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) = 1.606091731339825 y[1] (numeric) = 1.60609173134012 absolute error = 2.942091015256665e-13 relative error = 1.831832489917826e-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) = 1.594093281584393 y[1] (numeric) = 1.594093281584686 absolute error = 2.926547892911913e-13 relative error = 1.835869912206877e-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) = 1.58193542382921 y[1] (numeric) = 1.581935423829501 absolute error = 2.913225216616411e-13 relative error = 1.84155760894759e-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) = 1.569619373849918 y[1] (numeric) = 1.569619373850208 absolute error = 2.899902540320909e-13 relative error = 1.847519588910342e-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) = 1.557146363241253 y[1] (numeric) = 1.557146363241542 absolute error = 2.888800310074657e-13 relative error = 1.855188682495794e-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) = 1.544517639293882 y[1] (numeric) = 1.54451763929417 absolute error = 2.873257187729905e-13 relative error = 1.860294188056985e-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) = 1.531734464869676 y[1] (numeric) = 1.531734464869962 absolute error = 2.864375403532904e-13 relative error = 1.870020861466098e-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) = 1.518798118275423 y[1] (numeric) = 1.518798118275708 absolute error = 2.846611835138901e-13 relative error = 1.874252937823754e-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) = 1.505709893135004 y[1] (numeric) = 1.505709893135287 absolute error = 2.833289158843399e-13 relative error = 1.881696581633181e-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) = 1.492471098260025 y[1] (numeric) = 1.492471098260307 absolute error = 2.819966482547898e-13 relative error = 1.889461367684448e-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) = 1.479083057518943 y[1] (numeric) = 1.479083057519223 absolute error = 2.804423360203145e-13 relative error = 1.896055360749901e-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) = 1.465547109704673 y[1] (numeric) = 1.465547109704952 absolute error = 2.784439345759893e-13 relative error = 1.899931655094317e-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) = 1.451864608400718 y[1] (numeric) = 1.451864608400995 absolute error = 2.771116669464391e-13 relative error = 1.908660527593462e-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) = 1.438036921845807 y[1] (numeric) = 1.438036921846082 absolute error = 2.751132655021138e-13 relative error = 1.913116842292126e-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) = 1.424065432797071 y[1] (numeric) = 1.424065432797344 absolute error = 2.735589532676386e-13 relative error = 1.920971796431637e-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) = 1.409951538391772 y[1] (numeric) = 1.409951538392044 absolute error = 2.720046410331634e-13 relative error = 1.929177235009219e-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) = 1.39569665000759 y[1] (numeric) = 1.39569665000786 absolute error = 2.704503287986881e-13 relative error = 1.937744342921633e-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) = 1.381302193121484 y[1] (numeric) = 1.381302193121753 absolute error = 2.688960165642129e-13 relative error = 1.946684931821894e-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) = 1.366769607167147 y[1] (numeric) = 1.366769607167414 absolute error = 2.673417043297377e-13 relative error = 1.956011480851165e-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) = 1.352100345391064 y[1] (numeric) = 1.35210034539133 absolute error = 2.655653474903374e-13 relative error = 1.964094960818375e-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) = 1.337295874707189 y[1] (numeric) = 1.337295874707453 absolute error = 2.640110352558622e-13 relative error = 1.974215581227822e-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) = 1.322357675550253 y[1] (numeric) = 1.322357675550515 absolute error = 2.62234678416462e-13 relative error = 1.983084329338824e-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) = 1.307287241727723 y[1] (numeric) = 1.307287241727983 absolute error = 2.604583215770617e-13 relative error = 1.992357251439536e-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) = 1.292086080270415 y[1] (numeric) = 1.29208608027068 absolute error = 2.653433028854124e-13 relative error = 2.053603911822035e-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) = 1.276755711281815 y[1] (numeric) = 1.276755711282086 absolute error = 2.702282841937631e-13 relative error = 2.116523010674171e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999681 y[1] (closed_form) = 1.261297667786047 y[1] (numeric) = 1.261297667786322 absolute error = 2.751132655021138e-13 relative error = 2.181192215989898e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999684 y[1] (closed_form) = 1.245713495574578 y[1] (numeric) = 1.245713495574858 absolute error = 2.802202914153895e-13 relative error = 2.249476243220273e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999687 y[1] (closed_form) = 1.230004753051642 y[1] (numeric) = 1.230004753051928 absolute error = 2.855493619335903e-13 relative error = 2.321530556895347e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999691 y[1] (closed_form) = 1.214173011078401 y[1] (numeric) = 1.214173011078692 absolute error = 2.90878432451791e-13 relative error = 2.395691798431916e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999694 y[1] (closed_form) = 1.198219852815861 y[1] (numeric) = 1.198219852816157 absolute error = 2.957634137601417e-13 relative error = 2.468356813360142e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999697 y[1] (closed_form) = 1.182146873566551 y[1] (numeric) = 1.182146873566853 absolute error = 3.013145288832675e-13 relative error = 2.548875572239158e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999701 y[1] (closed_form) = 1.165955680615004 y[1] (numeric) = 1.165955680615311 absolute error = 3.068656440063933e-13 relative error = 2.63188086055322e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999704 y[1] (closed_form) = 1.149647893067022 y[1] (numeric) = 1.149647893067335 absolute error = 3.124167591295191e-13 relative error = 2.717499514534453e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999707 y[1] (closed_form) = 1.13322514168777 y[1] (numeric) = 1.133225141688088 absolute error = 3.177458296477198e-13 relative error = 2.803907343376486e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.119999999999711 y[1] (closed_form) = 1.116689068738701 y[1] (numeric) = 1.116689068739024 absolute error = 3.230749001659206e-13 relative error = 2.89315002009318e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999714 y[1] (closed_form) = 1.100041327813328 y[1] (numeric) = 1.100041327813657 absolute error = 3.288480598939714e-13 relative error = 2.989415502667146e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999717 y[1] (closed_form) = 1.083283583671872 y[1] (numeric) = 1.083283583672206 absolute error = 3.343991750170971e-13 relative error = 3.086903374678916e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.149999999999721 y[1] (closed_form) = 1.066417512074782 y[1] (numeric) = 1.066417512075122 absolute error = 3.399502901402229e-13 relative error = 3.18777857913106e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999724 y[1] (closed_form) = 1.049444799615163 y[1] (numeric) = 1.049444799615508 absolute error = 3.452793606584237e-13 relative error = 3.290114551856748e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999727 y[1] (closed_form) = 1.032367143550116 y[1] (numeric) = 1.032367143550468 absolute error = 3.512745649913995e-13 relative error = 3.40261279319131e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.179999999999731 y[1] (closed_form) = 1.015186251631018 y[1] (numeric) = 1.015186251631375 absolute error = 3.568256801145253e-13 relative error = 3.514878964734226e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999734 y[1] (closed_form) = 0.9979038419327425 y[1] (numeric) = 0.9979038419331049 absolute error = 3.623767952376511e-13 relative error = 3.631379898646335e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999737 y[1] (closed_form) = 0.9805216426818572 y[1] (numeric) = 0.9805216426822253 absolute error = 3.681499549657019e-13 relative error = 3.754633645400858e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.209999999999741 y[1] (closed_form) = 0.9630413920838021 y[1] (numeric) = 0.9630413920841764 absolute error = 3.742561816011403e-13 relative error = 3.886189988068272e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999744 y[1] (closed_form) = 0.9454648381490706 y[1] (numeric) = 0.9454648381494506 absolute error = 3.800293413291911e-13 relative error = 4.019497351939303e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999747 y[1] (closed_form) = 0.9277937385184087 y[1] (numeric) = 0.9277937385187947 absolute error = 3.859135233597044e-13 relative error = 4.159475402107893e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999751 y[1] (closed_form) = 0.9100298602870539 y[1] (numeric) = 0.9100298602874455 absolute error = 3.915756607852927e-13 relative error = 4.302888046572193e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999754 y[1] (closed_form) = 0.892174979828026 y[1] (numeric) = 0.8921749798284235 absolute error = 3.975708651182686e-13 relative error = 4.456198325522462e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999757 y[1] (closed_form) = 0.8742308826144919 y[1] (numeric) = 0.8742308826148955 absolute error = 4.035660694512444e-13 relative error = 4.616241286790646e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999761 y[1] (closed_form) = 0.8561993630412196 y[1] (numeric) = 0.8561993630416291 absolute error = 4.095612737842202e-13 relative error = 4.783480243777091e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y[1] (closed_form) = 0.8380822242451401 y[1] (numeric) = 0.8380822242455558 absolute error = 4.156675004196586e-13 relative error = 4.95974605348598e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y[1] (closed_form) = 0.8198812779250357 y[1] (numeric) = 0.8198812779254574 absolute error = 4.216627047526345e-13 relative error = 5.142972721852887e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y[1] (closed_form) = 0.8015983441603708 y[1] (numeric) = 0.8015983441607987 absolute error = 4.278799536905353e-13 relative error = 5.337834799780126e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999774 y[1] (closed_form) = 0.7832352512292862 y[1] (numeric) = 0.7832352512297203 absolute error = 4.340972026284362e-13 relative error = 5.542360382108971e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y[1] (closed_form) = 0.7647938354257725 y[1] (numeric) = 0.7647938354262128 absolute error = 4.403144515663371e-13 relative error = 5.757296034181646e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999781 y[1] (closed_form) = 0.7462759408760422 y[1] (numeric) = 0.7462759408764889 absolute error = 4.466427228067005e-13 relative error = 5.984954067826349e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999784 y[1] (closed_form) = 0.7276834193541188 y[1] (numeric) = 0.7276834193545717 absolute error = 4.528599717446014e-13 relative error = 6.223310298131477e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999787 y[1] (closed_form) = 0.7090181300966609 y[1] (numeric) = 0.7090181300971199 absolute error = 4.589661983800397e-13 relative error = 6.473264630305978e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999791 y[1] (closed_form) = 0.6902819396170397 y[1] (numeric) = 0.6902819396175049 absolute error = 4.652944696204031e-13 relative error = 6.740643828499164e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y[1] (closed_form) = 0.6714767215186896 y[1] (numeric) = 0.6714767215191614 absolute error = 4.71733763163229e-13 relative error = 7.025318198616047e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = 0.6526043563077499 y[1] (numeric) = 0.652604356308228 absolute error = 4.780620344035924e-13 relative error = 7.325449635493266e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = 0.6336667312050144 y[1] (numeric) = 0.633666731205499 absolute error = 4.846123502488808e-13 relative error = 7.647748041424176e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = 0.6146657399572123 y[1] (numeric) = 0.614665739957703 absolute error = 4.907185768843192e-13 relative error = 7.983502983564348e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = 0.5956032826476341 y[1] (numeric) = 0.5956032826481312 absolute error = 4.971578704271451e-13 relative error = 8.34713113428674e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y[1] (closed_form) = 0.5764812655061256 y[1] (numeric) = 0.5764812655066291 absolute error = 5.03597163969971e-13 relative error = 8.735707369914867e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y[1] (closed_form) = 0.5573016007184658 y[1] (numeric) = 0.5573016007189757 absolute error = 5.099254352103344e-13 relative error = 9.149900781783963e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = 0.5380662062351506 y[1] (numeric) = 0.5380662062356669 absolute error = 5.163647287531603e-13 relative error = 9.596676445565398e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y[1] (closed_form) = 0.5187770055795988 y[1] (numeric) = 0.5187770055801217 absolute error = 5.229150445984487e-13 relative error = 1.007976527437307e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y[1] (closed_form) = 0.4994359276558018 y[1] (numeric) = 0.4994359276563312 absolute error = 5.293543381412746e-13 relative error = 1.059904401803652e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 0.4800449065554344 y[1] (numeric) = 0.4800449065559702 absolute error = 5.357381205328693e-13 relative error = 1.116016675142044e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y[1] (closed_form) = 0.4606058813644475 y[1] (numeric) = 0.4606058813649898 absolute error = 5.422329252269265e-13 relative error = 1.17721667734827e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y[1] (closed_form) = 0.4411207959691611 y[1] (numeric) = 0.4411207959697098 absolute error = 5.487277299209836e-13 relative error = 1.24393983447415e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 0.4215915988618772 y[1] (numeric) = 0.4215915988624324 absolute error = 5.551670234638095e-13 relative error = 1.316836068276813e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y[1] (closed_form) = 0.4020202429460322 y[1] (numeric) = 0.4020202429465938 absolute error = 5.616063170066354e-13 relative error = 1.396960294564138e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y[1] (closed_form) = 0.3824086853409084 y[1] (numeric) = 0.3824086853414765 absolute error = 5.681566328519239e-13 relative error = 1.485731508282626e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = 0.3627588871859233 y[1] (numeric) = 0.362758887186498 absolute error = 5.747069486972123e-13 relative error = 1.584267040720798e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y[1] (closed_form) = 0.3430728134445176 y[1] (numeric) = 0.3430728134450988 absolute error = 5.812572645425007e-13 relative error = 1.694267927285071e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y[1] (closed_form) = 0.3233524327076605 y[1] (numeric) = 0.3233524327082483 absolute error = 5.878075803877891e-13 relative error = 1.817854207762277e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y[1] (closed_form) = 0.3035997169969921 y[1] (numeric) = 0.3035997169975865 absolute error = 5.944134073843088e-13 relative error = 1.957885248589339e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y[1] (closed_form) = 0.2838166415676229 y[1] (numeric) = 0.283816641568224 absolute error = 6.01130256683291e-13 relative error = 2.118023289131424e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y[1] (closed_form) = 0.2640051847106099 y[1] (numeric) = 0.2640051847112177 absolute error = 6.077915948310419e-13 relative error = 2.302195676563226e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y[1] (closed_form) = 0.2441673275551295 y[1] (numeric) = 0.2441673275557439 absolute error = 6.14369666251946e-13 relative error = 2.516182948815009e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y[1] (closed_form) = 0.2243050538703657 y[1] (numeric) = 0.2243050538709866 absolute error = 6.209477376728501e-13 relative error = 2.768318087169445e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y[1] (closed_form) = 0.2044203498671351 y[1] (numeric) = 0.2044203498677626 absolute error = 6.275813202449854e-13 relative error = 3.070053058087846e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y[1] (closed_form) = 0.1845152039992674 y[1] (numeric) = 0.1845152039999016 absolute error = 6.342149028171207e-13 relative error = 3.437195900775953e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y[1] (closed_form) = 0.164591606764762 y[1] (numeric) = 0.1645916067654028 absolute error = 6.40848485389256e-13 relative error = 3.893567223662693e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y[1] (closed_form) = 0.1446515505067393 y[1] (numeric) = 0.1446515505073868 absolute error = 6.475098235370069e-13 relative error = 4.476342087372507e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y[1] (closed_form) = 0.1246970292142085 y[1] (numeric) = 0.1246970292148626 absolute error = 6.541434061091422e-13 relative error = 5.245861992312857e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y[1] (closed_form) = 0.1047300383226701 y[1] (numeric) = 0.1047300383233309 absolute error = 6.60818622044701e-13 relative error = 6.309733412001043e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y[1] (closed_form) = 0.08475257451457413 y[1] (numeric) = 0.08475257451524161 absolute error = 6.674799601924519e-13 relative error = 7.875630492825578e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y[1] (closed_form) = 0.06476663551965363 y[1] (numeric) = 0.0647666355203278 absolute error = 6.741690539158185e-13 relative error = 1.040920295622335e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y[1] (closed_form) = 0.04477421991515319 y[1] (numeric) = 0.04477421991583403 absolute error = 6.808442698513772e-13 relative error = 1.520616710110354e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y[1] (closed_form) = 0.02477732692597295 y[1] (numeric) = 0.02477732692666048 absolute error = 6.875264246808399e-13 relative error = 2.774820813943966e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y[1] (closed_form) = 0.004777956224747817 y[1] (numeric) = 0.004777956225442023 absolute error = 6.942051100633506e-13 relative error = 1.452933173534864e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y[1] (closed_form) = -0.01522189226811817 y[1] (numeric) = -0.01522189226741729 absolute error = 7.008872648928133e-13 relative error = 4.604468699077591e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y[1] (closed_form) = -0.03522021858444222 y[1] (numeric) = -0.03522021858373466 absolute error = 7.07565950275324e-13 relative error = 2.00897660126356e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y[1] (closed_form) = -0.0552150229082579 y[1] (numeric) = -0.05521502290754367 absolute error = 7.142272884230749e-13 relative error = 1.293537973550774e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y[1] (closed_form) = -0.07520430577579512 y[1] (numeric) = -0.07520430577507423 absolute error = 7.208955654647298e-13 relative error = 9.585828338259238e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y[1] (closed_form) = -0.09518606827542481 y[1] (numeric) = -0.09518606827469722 absolute error = 7.275846591880963e-13 relative error = 7.643814608276499e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y[1] (closed_form) = -0.1151583122475484 y[1] (numeric) = -0.1151583122468142 absolute error = 7.342459973358473e-13 relative error = 6.375970461927977e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y[1] (closed_form) = -0.1351190404844122 y[1] (numeric) = -0.1351190404836713 absolute error = 7.409073354835982e-13 relative error = 5.483367353907993e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y[1] (closed_form) = -0.1550662569298263 y[1] (numeric) = -0.1550662569290787 absolute error = 7.475686736313492e-13 relative error = 4.820962912451378e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y[1] (closed_form) = -0.1749979668787689 y[1] (numeric) = -0.1749979668780147 absolute error = 7.542577673547157e-13 relative error = 4.31009445885296e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y[1] (closed_form) = -0.1949121771768548 y[1] (numeric) = -0.1949121771760939 absolute error = 7.608635943512354e-13 relative error = 3.903622674435888e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y[1] (closed_form) = -0.2148068964196492 y[1] (numeric) = -0.2148068964188818 absolute error = 7.674694213477551e-13 relative error = 3.572834178696097e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y[1] (closed_form) = -0.2346801351518068 y[1] (numeric) = -0.2346801351510327 absolute error = 7.741030039198904e-13 relative error = 3.298545074635945e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y[1] (closed_form) = -0.2545299060660154 y[1] (numeric) = -0.2545299060652347 absolute error = 7.807088309164101e-13 relative error = 3.067257765434934e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y[1] (closed_form) = -0.2743542242017248 y[1] (numeric) = -0.2743542242009375 absolute error = 7.873146579129298e-13 relative error = 2.869701241902657e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y[1] (closed_form) = -0.2941511071436419 y[1] (numeric) = -0.294151107142848 absolute error = 7.939204849094494e-13 relative error = 2.699022596307131e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y[1] (closed_form) = -0.3139185752199696 y[1] (numeric) = -0.3139185752191692 absolute error = 8.004152896035066e-13 relative error = 2.549754467516419e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y[1] (closed_form) = -0.3336546517003733 y[1] (numeric) = -0.3336546516995663 absolute error = 8.070211166000263e-13 relative error = 2.418731800942319e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y[1] (closed_form) = -0.3533573629936516 y[1] (numeric) = -0.353357362992838 absolute error = 8.135714324453147e-13 relative error = 2.302404074879661e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y[1] (closed_form) = -0.3730247388450939 y[1] (numeric) = -0.3730247388442738 absolute error = 8.201217482906031e-13 relative error = 2.198572005786392e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y[1] (closed_form) = -0.3926548125335046 y[1] (numeric) = -0.392654812532678 absolute error = 8.266720641358916e-13 relative error = 2.10534046126164e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y[1] (closed_form) = -0.4122456210678732 y[1] (numeric) = -0.41224562106704 absolute error = 8.3322237998118e-13 relative error = 2.021179455643013e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y[1] (closed_form) = -0.4317952053836719 y[1] (numeric) = -0.4317952053828321 absolute error = 8.398282069776997e-13 relative error = 1.944968810460667e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = -0.4513016105387603 y[1] (numeric) = -0.451301610537914 absolute error = 8.463230116717568e-13 relative error = 1.875293577307254e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y[1] (closed_form) = -0.4707628859088782 y[1] (numeric) = -0.4707628859080255 absolute error = 8.527067940633515e-13 relative error = 1.811329693964879e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y[1] (closed_form) = -0.4901770853827063 y[1] (numeric) = -0.4901770853818471 absolute error = 8.592015987574086e-13 relative error = 1.752839176655078e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = -0.5095422675564756 y[1] (numeric) = -0.5095422675556099 absolute error = 8.656408923002346e-13 relative error = 1.698859834438152e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y[1] (closed_form) = -0.5288564959281064 y[1] (numeric) = -0.5288564959272343 absolute error = 8.720801858430605e-13 relative error = 1.648992103826994e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y[1] (closed_form) = -0.5481178390908567 y[1] (numeric) = -0.5481178390899781 absolute error = 8.785194793858864e-13 relative error = 1.602793079756453e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 Finished! diff ( y , x , 1 ) = 2.0 * sin ( x ) ; Iterations = 4900 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %