##############ECHO OF PROBLEM################# ##############temp/add_full_linpostode.ode################# diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) + ( 0.1 * x + 0.2 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(1.0); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_display_interval=c(0.1); glob_look_poles=true; glob_type_given_pole=3; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(c(0.05) * c(x) * c(x) + c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = -2.82020331334295 y[1] (numeric) = -2.82020331334295 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] = 1.009999999999999 y[1] (closed_form) = -2.813290319856589 y[1] (numeric) = -2.813290319856588 absolute error = 4.440892098500626e-16 relative error = 1.578540283296111e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = -2.806339729733046 y[1] (numeric) = -2.806339729733045 absolute error = 8.881784197001252e-16 relative error = 3.164899852608413e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = -2.799351578392607 y[1] (numeric) = -2.799351578392605 absolute error = 2.220446049250313e-15 relative error = 7.932001347702446e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = -2.792325901503606 y[1] (numeric) = -2.792325901503604 absolute error = 2.664535259100376e-15 relative error = 9.542350546064776e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999994 y[1] (closed_form) = -2.78526273498211 y[1] (numeric) = -2.785262734982107 absolute error = 3.108624468950438e-15 relative error = 1.116097389990178e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999993 y[1] (closed_form) = -2.778162114991588 y[1] (numeric) = -2.778162114991583 absolute error = 4.884981308350689e-15 relative error = 1.758349983246201e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999992 y[1] (closed_form) = -2.771024077942594 y[1] (numeric) = -2.771024077942589 absolute error = 5.329070518200751e-15 relative error = 1.923141181132368e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999991 y[1] (closed_form) = -2.763848660492435 y[1] (numeric) = -2.763848660492428 absolute error = 6.661338147750939e-15 relative error = 2.410167475148255e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.08999999999999 y[1] (closed_form) = -2.756635899544838 y[1] (numeric) = -2.75663589954483 absolute error = 7.549516567451064e-15 relative error = 2.738670191699093e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.099999999999989 y[1] (closed_form) = -2.749385832249625 y[1] (numeric) = -2.749385832249617 absolute error = 8.43769498715119e-15 relative error = 3.068938119989957e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999988 y[1] (closed_form) = -2.742098496002374 y[1] (numeric) = -2.742098496002365 absolute error = 8.881784197001252e-15 relative error = 3.239046376324465e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = -2.734773928444082 y[1] (numeric) = -2.734773928444072 absolute error = 1.021405182655144e-14 relative error = 3.734879772077762e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = -2.727412167460829 y[1] (numeric) = -2.727412167460819 absolute error = 1.021405182655144e-14 relative error = 3.744960863784859e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = -2.720013251183436 y[1] (numeric) = -2.720013251183425 absolute error = 1.110223024625157e-14 relative error = 4.081682411444561e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999983 y[1] (closed_form) = -2.71257721798712 y[1] (numeric) = -2.712577217987107 absolute error = 1.243449787580175e-14 relative error = 4.584016187022623e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999982 y[1] (closed_form) = -2.70510410649115 y[1] (numeric) = -2.705104106491136 absolute error = 1.332267629550188e-14 relative error = 4.925014258613143e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999981 y[1] (closed_form) = -2.697593955558502 y[1] (numeric) = -2.697593955558487 absolute error = 1.509903313490213e-14 relative error = 5.59722233355022e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.17999999999998 y[1] (closed_form) = -2.690046804295504 y[1] (numeric) = -2.690046804295488 absolute error = 1.598721155460225e-14 relative error = 5.943097915275545e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.189999999999979 y[1] (closed_form) = -2.682462692051488 y[1] (numeric) = -2.682462692051471 absolute error = 1.643130076445232e-14 relative error = 6.125453603936621e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999978 y[1] (closed_form) = -2.674841658418434 y[1] (numeric) = -2.674841658418417 absolute error = 1.687538997430238e-14 relative error = 6.308930444982066e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999977 y[1] (closed_form) = -2.667183743230616 y[1] (numeric) = -2.667183743230599 absolute error = 1.731947918415244e-14 relative error = 6.493545571470186e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = -2.659488986564241 y[1] (numeric) = -2.659488986564222 absolute error = 1.865174681370263e-14 relative error = 7.013282216219508e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = -2.651757428737087 y[1] (numeric) = -2.651757428737068 absolute error = 1.909583602355269e-14 relative error = 7.201200161301022e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = -2.643989110308144 y[1] (numeric) = -2.643989110308125 absolute error = 1.953992523340276e-14 relative error = 7.39031986070679e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999972 y[1] (closed_form) = -2.636184072077249 y[1] (numeric) = -2.636184072077228 absolute error = 2.042810365310288e-14 relative error = 7.749118837898915e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999971 y[1] (closed_form) = -2.628342355084714 y[1] (numeric) = -2.628342355084693 absolute error = 2.131628207280301e-14 relative error = 8.110161916907495e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.26999999999997 y[1] (closed_form) = -2.620464000610962 y[1] (numeric) = -2.62046400061094 absolute error = 2.131628207280301e-14 relative error = 8.134544900381425e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.279999999999969 y[1] (closed_form) = -2.612549050176151 y[1] (numeric) = -2.612549050176129 absolute error = 2.131628207280301e-14 relative error = 8.159189229907763e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999968 y[1] (closed_form) = -2.604597545539804 y[1] (numeric) = -2.604597545539781 absolute error = 2.264854970235319e-14 relative error = 8.695604332860289e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999967 y[1] (closed_form) = -2.596609528700431 y[1] (numeric) = -2.596609528700408 absolute error = 2.353672812205332e-14 relative error = 9.064407975824204e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999966 y[1] (closed_form) = -2.588585041895153 y[1] (numeric) = -2.588585041895129 absolute error = 2.442490654175344e-14 relative error = 9.435620675560844e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = -2.580524127599318 y[1] (numeric) = -2.580524127599293 absolute error = 2.486899575160351e-14 relative error = 9.63718784320739e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = -2.572426828526123 y[1] (numeric) = -2.572426828526098 absolute error = 2.531308496145357e-14 relative error = 9.840157426734952e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = -2.564293187626229 y[1] (numeric) = -2.564293187626202 absolute error = 2.664535259100376e-14 relative error = 1.039091501688596e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999961 y[1] (closed_form) = -2.556123248087369 y[1] (numeric) = -2.556123248087341 absolute error = 2.797762022055394e-14 relative error = 1.094533303176532e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.35999999999996 y[1] (closed_form) = -2.547917053333968 y[1] (numeric) = -2.547917053333939 absolute error = 2.886579864025407e-14 relative error = 1.132917517957775e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.369999999999959 y[1] (closed_form) = -2.539674647026746 y[1] (numeric) = -2.539674647026716 absolute error = 2.97539770599542e-14 relative error = 1.171566487651788e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999958 y[1] (closed_form) = -2.531396073062326 y[1] (numeric) = -2.531396073062296 absolute error = 3.064215547965432e-14 relative error = 1.210484436067934e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999957 y[1] (closed_form) = -2.523081375572842 y[1] (numeric) = -2.52308137557281 absolute error = 3.197442310920451e-14 relative error = 1.267276728319752e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999956 y[1] (closed_form) = -2.514730598925536 y[1] (numeric) = -2.514730598925504 absolute error = 3.286260152890463e-14 relative error = 1.306804058571752e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999955 y[1] (closed_form) = -2.506343787722367 y[1] (numeric) = -2.506343787722333 absolute error = 3.419486915845482e-14 relative error = 1.364332751395183e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = -2.4979209867996 y[1] (numeric) = -2.497920986799565 absolute error = 3.508304757815495e-14 relative error = 1.404489884329938e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = -2.48946224122741 y[1] (numeric) = -2.489462241227375 absolute error = 3.552713678800501e-14 relative error = 1.427100849317909e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = -2.480967596309474 y[1] (numeric) = -2.480967596309437 absolute error = 3.730349362740526e-14 relative error = 1.503586491129328e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.44999999999995 y[1] (closed_form) = -2.472437097582561 y[1] (numeric) = -2.472437097582524 absolute error = 3.774758283725532e-14 relative error = 1.526735821678263e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.459999999999949 y[1] (closed_form) = -2.463870790816126 y[1] (numeric) = -2.463870790816088 absolute error = 3.819167204710538e-14 relative error = 1.550067973915745e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999948 y[1] (closed_form) = -2.455268722011896 y[1] (numeric) = -2.455268722011856 absolute error = 3.996802888650564e-14 relative error = 1.627847433895343e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999947 y[1] (closed_form) = -2.446630937403454 y[1] (numeric) = -2.446630937403413 absolute error = 4.130029651605582e-14 relative error = 1.688047669334499e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999946 y[1] (closed_form) = -2.437957483455828 y[1] (numeric) = -2.437957483455786 absolute error = 4.263256414560601e-14 relative error = 1.748700066958261e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999945 y[1] (closed_form) = -2.429248406865067 y[1] (numeric) = -2.429248406865025 absolute error = 4.263256414560601e-14 relative error = 1.754969315823206e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = -2.420503754557827 y[1] (numeric) = -2.420503754557783 absolute error = 4.352074256530614e-14 relative error = 1.798003514076616e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = -2.411723573690942 y[1] (numeric) = -2.411723573690897 absolute error = 4.485301019485632e-14 relative error = 1.859790677677564e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = -2.402907911651004 y[1] (numeric) = -2.402907911650959 absolute error = 4.574118861455645e-14 relative error = 1.903576428908102e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = -2.394056816053937 y[1] (numeric) = -2.39405681605389 absolute error = 4.662936703425657e-14 relative error = 1.947713467849714e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.549999999999939 y[1] (closed_form) = -2.385170334744565 y[1] (numeric) = -2.385170334744517 absolute error = 4.707345624410664e-14 relative error = 1.973588869456901e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999938 y[1] (closed_form) = -2.376248515796183 y[1] (numeric) = -2.376248515796135 absolute error = 4.796163466380676e-14 relative error = 2.018376207075159e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999937 y[1] (closed_form) = -2.367291407510126 y[1] (numeric) = -2.367291407510077 absolute error = 4.840572387365683e-14 relative error = 2.044772507520276e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999936 y[1] (closed_form) = -2.358299058415333 y[1] (numeric) = -2.358299058415283 absolute error = 5.018208071305708e-14 relative error = 2.12789300551123e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999935 y[1] (closed_form) = -2.349271517267907 y[1] (numeric) = -2.349271517267856 absolute error = 5.151434834260726e-14 relative error = 2.192779675059273e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999934 y[1] (closed_form) = -2.340208833050683 y[1] (numeric) = -2.340208833050631 absolute error = 5.240252676230739e-14 relative error = 2.2392243812701e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y[1] (closed_form) = -2.331111054972782 y[1] (numeric) = -2.331111054972729 absolute error = 5.284661597215745e-14 relative error = 2.267014085812161e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y[1] (closed_form) = -2.321978232469171 y[1] (numeric) = -2.321978232469116 absolute error = 5.417888360170764e-14 relative error = 2.333307127694057e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y[1] (closed_form) = -2.312810415200212 y[1] (numeric) = -2.312810415200157 absolute error = 5.506706202140776e-14 relative error = 2.380958753017411e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y[1] (closed_form) = -2.303607653051226 y[1] (numeric) = -2.30360765305117 absolute error = 5.639932965095795e-14 relative error = 2.44830449214104e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999928 y[1] (closed_form) = -2.294369996132033 y[1] (numeric) = -2.294369996131976 absolute error = 5.773159728050814e-14 relative error = 2.51622874156457e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999927 y[1] (closed_form) = -2.285097494776509 y[1] (numeric) = -2.28509749477645 absolute error = 5.81756864903582e-14 relative error = 2.545873277763495e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999926 y[1] (closed_form) = -2.275790199542127 y[1] (numeric) = -2.275790199542068 absolute error = 5.906386491005833e-14 relative error = 2.595312385207634e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999925 y[1] (closed_form) = -2.266448161209506 y[1] (numeric) = -2.266448161209445 absolute error = 6.039613253960852e-14 relative error = 2.664792143641075e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999924 y[1] (closed_form) = -2.257071430781954 y[1] (numeric) = -2.257071430781892 absolute error = 6.17284001691587e-14 relative error = 2.734889083584436e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999923 y[1] (closed_form) = -2.247660059485004 y[1] (numeric) = -2.247660059484942 absolute error = 6.261657858885883e-14 relative error = 2.78585626525774e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y[1] (closed_form) = -2.238214098765963 y[1] (numeric) = -2.238214098765898 absolute error = 6.439293542825908e-14 relative error = 2.876978366982947e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y[1] (closed_form) = -2.228733600293435 y[1] (numeric) = -2.22873360029337 absolute error = 6.439293542825908e-14 relative error = 2.889216343298325e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y[1] (closed_form) = -2.219218615956869 y[1] (numeric) = -2.219218615956803 absolute error = 6.616929226765933e-14 relative error = 2.981648215812612e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y[1] (closed_form) = -2.209669197866085 y[1] (numeric) = -2.209669197866018 absolute error = 6.750155989720952e-14 relative error = 3.054826485448451e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999917 y[1] (closed_form) = -2.200085398350806 y[1] (numeric) = -2.200085398350738 absolute error = 6.794564910705958e-14 relative error = 3.088318715173145e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999916 y[1] (closed_form) = -2.190467269960188 y[1] (numeric) = -2.190467269960119 absolute error = 6.927791673660977e-14 relative error = 3.162700383004074e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999915 y[1] (closed_form) = -2.180814865462349 y[1] (numeric) = -2.180814865462278 absolute error = 7.061018436615996e-14 relative error = 3.237789024846457e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999914 y[1] (closed_form) = -2.171128237843887 y[1] (numeric) = -2.171128237843815 absolute error = 7.238654120556021e-14 relative error = 3.334051851190795e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999913 y[1] (closed_form) = -2.161407440309412 y[1] (numeric) = -2.161407440309339 absolute error = 7.327471962526033e-14 relative error = 3.390139140761486e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999912 y[1] (closed_form) = -2.151652526281062 y[1] (numeric) = -2.151652526280987 absolute error = 7.460698725481052e-14 relative error = 3.467427307315368e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y[1] (closed_form) = -2.141863549398022 y[1] (numeric) = -2.141863549397947 absolute error = 7.549516567451064e-14 relative error = 3.52474207312267e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y[1] (closed_form) = -2.132040563516044 y[1] (numeric) = -2.132040563515968 absolute error = 7.682743330406083e-14 relative error = 3.603469587715594e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y[1] (closed_form) = -2.122183622706962 y[1] (numeric) = -2.122183622706883 absolute error = 7.860379014346108e-14 relative error = 3.703910882282544e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999907 y[1] (closed_form) = -2.1122927812582 y[1] (numeric) = -2.11229278125812 absolute error = 8.038014698286133e-14 relative error = 3.805350645329688e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999906 y[1] (closed_form) = -2.102368093672291 y[1] (numeric) = -2.10236809367221 absolute error = 8.08242361927114e-14 relative error = 3.84443791912445e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999905 y[1] (closed_form) = -2.092409614666384 y[1] (numeric) = -2.092409614666302 absolute error = 8.215650382226158e-14 relative error = 3.92640634254401e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999904 y[1] (closed_form) = -2.082417399171746 y[1] (numeric) = -2.082417399171663 absolute error = 8.304468224196171e-14 relative error = 3.987898020588554e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999903 y[1] (closed_form) = -2.072391502333277 y[1] (numeric) = -2.072391502333192 absolute error = 8.43769498715119e-14 relative error = 4.071477313843116e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999902 y[1] (closed_form) = -2.062331979509007 y[1] (numeric) = -2.062331979508921 absolute error = 8.526512829121202e-14 relative error = 4.13440363328467e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999901 y[1] (closed_form) = -2.052238886269598 y[1] (numeric) = -2.052238886269512 absolute error = 8.615330671091215e-14 relative error = 4.198015508200168e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y[1] (closed_form) = -2.04211227839785 y[1] (numeric) = -2.042112278397762 absolute error = 8.79296635503124e-14 relative error = 4.305819248062996e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y[1] (closed_form) = -2.031952211888189 y[1] (numeric) = -2.0319522118881 absolute error = 8.837375276016246e-14 relative error = 4.349204289506458e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y[1] (closed_form) = -2.021758742946174 y[1] (numeric) = -2.021758742946083 absolute error = 9.103828801926284e-14 relative error = 4.502925402790584e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999896 y[1] (closed_form) = -2.011531927987981 y[1] (numeric) = -2.011531927987889 absolute error = 9.237055564881302e-14 relative error = 4.592050186407229e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999895 y[1] (closed_form) = -2.001271823639904 y[1] (numeric) = -2.001271823639811 absolute error = 9.281464485866309e-14 relative error = 4.637783021891161e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999894 y[1] (closed_form) = -1.990978486737838 y[1] (numeric) = -1.990978486737744 absolute error = 9.392486788328824e-14 relative error = 4.717522992284135e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999893 y[1] (closed_form) = -1.980651974326774 y[1] (numeric) = -1.980651974326678 absolute error = 9.592326932761353e-14 relative error = 4.843014854248585e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999892 y[1] (closed_form) = -1.970292343660278 y[1] (numeric) = -1.970292343660182 absolute error = 9.614531393253856e-14 relative error = 4.87974864450451e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999891 y[1] (closed_form) = -1.959899652199987 y[1] (numeric) = -1.959899652199889 absolute error = 9.769962616701378e-14 relative error = 4.984930022174655e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.99999999999989 y[1] (closed_form) = -1.949473957615077 y[1] (numeric) = -1.949473957614978 absolute error = 9.947598300641403e-14 relative error = 5.102708995821094e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.009999999999889 y[1] (closed_form) = -1.939015317781757 y[1] (numeric) = -1.939015317781657 absolute error = 9.992007221626409e-14 relative error = 5.153134753498138e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999888 y[1] (closed_form) = -1.928523790782743 y[1] (numeric) = -1.928523790782642 absolute error = 1.012523398458143e-13 relative error = 5.250251012185765e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.029999999999887 y[1] (closed_form) = -1.917999434906734 y[1] (numeric) = -1.917999434906632 absolute error = 1.023625628704394e-13 relative error = 5.336944370654467e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999885 y[1] (closed_form) = -1.907442308647889 y[1] (numeric) = -1.907442308647785 absolute error = 1.039168751049147e-13 relative error = 5.447969494740696e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999884 y[1] (closed_form) = -1.896852470705299 y[1] (numeric) = -1.896852470705194 absolute error = 1.052491427344648e-13 relative error = 5.548620378227436e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999883 y[1] (closed_form) = -1.886229979982463 y[1] (numeric) = -1.886229979982357 absolute error = 1.06137321154165e-13 relative error = 5.626955476296256e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999882 y[1] (closed_form) = -1.875574895586752 y[1] (numeric) = -1.875574895586644 absolute error = 1.072475441787901e-13 relative error = 5.718115785786255e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999881 y[1] (closed_form) = -1.864887276828881 y[1] (numeric) = -1.864887276828773 absolute error = 1.083577672034153e-13 relative error = 5.810419136306757e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.08999999999988 y[1] (closed_form) = -1.854167183222375 y[1] (numeric) = -1.854167183222266 absolute error = 1.096900348329655e-13 relative error = 5.915865399059327e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.099999999999879 y[1] (closed_form) = -1.843414674483032 y[1] (numeric) = -1.843414674482921 absolute error = 1.112443470674407e-13 relative error = 6.034689243137227e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999878 y[1] (closed_form) = -1.832629810528385 y[1] (numeric) = -1.832629810528273 absolute error = 1.119104808822158e-13 relative error = 6.106551374385299e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999877 y[1] (closed_form) = -1.821812651477164 y[1] (numeric) = -1.821812651477051 absolute error = 1.127986593019159e-13 relative error = 6.191561970461474e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.129999999999876 y[1] (closed_form) = -1.810963257648756 y[1] (numeric) = -1.810963257648642 absolute error = 1.145750161413162e-13 relative error = 6.326744380781825e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999874 y[1] (closed_form) = -1.80008168956266 y[1] (numeric) = -1.800081689562544 absolute error = 1.154631945610163e-13 relative error = 6.41433081790131e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999873 y[1] (closed_form) = -1.789168007937943 y[1] (numeric) = -1.789168007937826 absolute error = 1.170175067954915e-13 relative error = 6.540330828425489e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999872 y[1] (closed_form) = -1.778222273692694 y[1] (numeric) = -1.778222273692576 absolute error = 1.181277298201167e-13 relative error = 6.643023854088279e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999871 y[1] (closed_form) = -1.767244547943476 y[1] (numeric) = -1.767244547943357 absolute error = 1.192379528447418e-13 relative error = 6.747111087907884e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.17999999999987 y[1] (closed_form) = -1.756234892004773 y[1] (numeric) = -1.756234892004653 absolute error = 1.201261312644419e-13 relative error = 6.839980905248719e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.189999999999869 y[1] (closed_form) = -1.745193367388444 y[1] (numeric) = -1.745193367388323 absolute error = 1.212363542890671e-13 relative error = 6.946872281006233e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999868 y[1] (closed_form) = -1.734120035803164 y[1] (numeric) = -1.734120035803042 absolute error = 1.223465773136923e-13 relative error = 7.055254237751021e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999867 y[1] (closed_form) = -1.723014959153871 y[1] (numeric) = -1.723014959153747 absolute error = 1.239008895481675e-13 relative error = 7.190935220261355e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999866 y[1] (closed_form) = -1.711878199541207 y[1] (numeric) = -1.711878199541082 absolute error = 1.254552017826427e-13 relative error = 7.328512146265159e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.229999999999865 y[1] (closed_form) = -1.700709819260963 y[1] (numeric) = -1.700709819260836 absolute error = 1.267874694121929e-13 relative error = 7.454973680771003e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999863 y[1] (closed_form) = -1.689509880803514 y[1] (numeric) = -1.689509880803386 absolute error = 1.27675647831893e-13 relative error = 7.556963666360551e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999862 y[1] (closed_form) = -1.67827844685326 y[1] (numeric) = -1.67827844685313 absolute error = 1.294520046712933e-13 relative error = 7.713380632040726e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999861 y[1] (closed_form) = -1.667015580288058 y[1] (numeric) = -1.667015580287928 absolute error = 1.307842723008434e-13 relative error = 7.84541391498237e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.26999999999986 y[1] (closed_form) = -1.655721344178661 y[1] (numeric) = -1.655721344178529 absolute error = 1.314504061156185e-13 relative error = 7.939162382473602e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.279999999999859 y[1] (closed_form) = -1.644395801788146 y[1] (numeric) = -1.644395801788013 absolute error = 1.330047183500938e-13 relative error = 8.08836401828939e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999858 y[1] (closed_form) = -1.633039016571348 y[1] (numeric) = -1.633039016571213 absolute error = 1.341149413747189e-13 relative error = 8.212598720164102e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999857 y[1] (closed_form) = -1.621651052174284 y[1] (numeric) = -1.621651052174149 absolute error = 1.354472090042691e-13 relative error = 8.352426301741279e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999856 y[1] (closed_form) = -1.610231972433588 y[1] (numeric) = -1.610231972433451 absolute error = 1.370015212387443e-13 relative error = 8.508185378513518e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999855 y[1] (closed_form) = -1.598781841375928 y[1] (numeric) = -1.598781841375789 absolute error = 1.381117442633695e-13 relative error = 8.638560977431988e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.329999999999854 y[1] (closed_form) = -1.587300723217435 y[1] (numeric) = -1.587300723217296 absolute error = 1.389999226830696e-13 relative error = 8.756999896107828e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999852 y[1] (closed_form) = -1.575788682363126 y[1] (numeric) = -1.575788682362986 absolute error = 1.403321903126198e-13 relative error = 8.905520891428862e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999851 y[1] (closed_form) = -1.564245783406319 y[1] (numeric) = -1.564245783406178 absolute error = 1.41886502547095e-13 relative error = 9.070601567365031e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.35999999999985 y[1] (closed_form) = -1.552672091128057 y[1] (numeric) = -1.552672091127914 absolute error = 1.432187701766452e-13 relative error = 9.224019095531818e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.369999999999849 y[1] (closed_form) = -1.541067670496521 y[1] (numeric) = -1.541067670496377 absolute error = 1.443289932012704e-13 relative error = 9.365519500825592e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999848 y[1] (closed_form) = -1.529432586666448 y[1] (numeric) = -1.529432586666302 absolute error = 1.458833054357456e-13 relative error = 9.538393957834577e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999847 y[1] (closed_form) = -1.517766904978543 y[1] (numeric) = -1.517766904978396 absolute error = 1.467714838554457e-13 relative error = 9.670225604077238e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999846 y[1] (closed_form) = -1.506070690958893 y[1] (numeric) = -1.506070690958744 absolute error = 1.481037514849959e-13 relative error = 9.833784853133319e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999845 y[1] (closed_form) = -1.494344010318374 y[1] (numeric) = -1.494344010318224 absolute error = 1.494360191145461e-13 relative error = 1.000010828046939e-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) = -1.482586928952062 y[1] (numeric) = -1.482586928951912 absolute error = 1.507682867440963e-13 relative error = 1.016927127845811e-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) = -1.470799512938642 y[1] (numeric) = -1.47079951293849 absolute error = 1.518785097687214e-13 relative error = 1.032625510361163e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999841 y[1] (closed_form) = -1.458981828539806 y[1] (numeric) = -1.458981828539652 absolute error = 1.536548666081217e-13 relative error = 1.053165047037661e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.44999999999984 y[1] (closed_form) = -1.447133942199664 y[1] (numeric) = -1.447133942199509 absolute error = 1.554312234475219e-13 relative error = 1.074062454863468e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.459999999999839 y[1] (closed_form) = -1.435255920544144 y[1] (numeric) = -1.435255920543988 absolute error = 1.56097357262297e-13 relative error = 1.087592498507975e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999838 y[1] (closed_form) = -1.423347830380391 y[1] (numeric) = -1.423347830380234 absolute error = 1.576516694967722e-13 relative error = 1.107611689369278e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999837 y[1] (closed_form) = -1.411409738696165 y[1] (numeric) = -1.411409738696007 absolute error = 1.585398479164724e-13 relative error = 1.123273019661382e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999836 y[1] (closed_form) = -1.399441712659243 y[1] (numeric) = -1.399441712659083 absolute error = 1.600941601509476e-13 relative error = 1.143985910257984e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999835 y[1] (closed_form) = -1.387443819616806 y[1] (numeric) = -1.387443819616645 absolute error = 1.614264277804978e-13 relative error = 1.163480823498004e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999834 y[1] (closed_form) = -1.375416127094842 y[1] (numeric) = -1.37541612709468 absolute error = 1.627586954100479e-13 relative error = 1.183341479017171e-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) = -1.363358702797534 y[1] (numeric) = -1.36335870279737 absolute error = 1.638689184346731e-13 relative error = 1.201950140476043e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999831 y[1] (closed_form) = -1.351271614606648 y[1] (numeric) = -1.351271614606483 absolute error = 1.649791414592983e-13 relative error = 1.220917687280239e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.53999999999983 y[1] (closed_form) = -1.339154930580928 y[1] (numeric) = -1.339154930580761 absolute error = 1.667554982986985e-13 relative error = 1.245229319555727e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.549999999999829 y[1] (closed_form) = -1.327008718955478 y[1] (numeric) = -1.32700871895531 absolute error = 1.678657213233237e-13 relative error = 1.264993356301796e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999828 y[1] (closed_form) = -1.314833048141151 y[1] (numeric) = -1.314833048140982 absolute error = 1.687538997430238e-13 relative error = 1.283462565696839e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999827 y[1] (closed_form) = -1.302627986723935 y[1] (numeric) = -1.302627986723764 absolute error = 1.70530256582424e-13 relative error = 1.309124771772345e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999826 y[1] (closed_form) = -1.29039360346433 y[1] (numeric) = -1.290393603464158 absolute error = 1.718625242119742e-13 relative error = 1.331861253423557e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999825 y[1] (closed_form) = -1.278129967296733 y[1] (numeric) = -1.278129967296559 absolute error = 1.731947918415244e-13 relative error = 1.355064009709705e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999824 y[1] (closed_form) = -1.265837147328818 y[1] (numeric) = -1.265837147328643 absolute error = 1.751931932858497e-13 relative error = 1.384010523435373e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999823 y[1] (closed_form) = -1.253515212840913 y[1] (numeric) = -1.253515212840737 absolute error = 1.763034163104749e-13 relative error = 1.406472091478718e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y[1] (closed_form) = -1.241164233285376 y[1] (numeric) = -1.241164233285199 absolute error = 1.77191594730175e-13 relative error = 1.427624080506629e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.62999999999982 y[1] (closed_form) = -1.228784278285972 y[1] (numeric) = -1.228784278285793 absolute error = 1.787459069646502e-13 relative error = 1.454656526155937e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.639999999999819 y[1] (closed_form) = -1.216375417637241 y[1] (numeric) = -1.216375417637062 absolute error = 1.796340853843503e-13 relative error = 1.47679805740634e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999818 y[1] (closed_form) = -1.20393772130388 y[1] (numeric) = -1.203937721303699 absolute error = 1.814104422237506e-13 relative error = 1.506809189658754e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999817 y[1] (closed_form) = -1.191471259420101 y[1] (numeric) = -1.191471259419917 absolute error = 1.834088436680759e-13 relative error = 1.539347610930561e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999816 y[1] (closed_form) = -1.178976102289008 y[1] (numeric) = -1.178976102288823 absolute error = 1.84519066692701e-13 relative error = 1.56507893870328e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999815 y[1] (closed_form) = -1.166452320381963 y[1] (numeric) = -1.166452320381777 absolute error = 1.856292897173262e-13 relative error = 1.591400578264018e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999814 y[1] (closed_form) = -1.15389998433795 y[1] (numeric) = -1.153899984337763 absolute error = 1.869615573468764e-13 relative error = 1.620257906963622e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999813 y[1] (closed_form) = -1.141319164962941 y[1] (numeric) = -1.141319164962753 absolute error = 1.880717803715015e-13 relative error = 1.647845634639879e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999812 y[1] (closed_form) = -1.128709933229257 y[1] (numeric) = -1.128709933229068 absolute error = 1.889599587912016e-13 relative error = 1.674123290920142e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y[1] (closed_form) = -1.116072360274929 y[1] (numeric) = -1.116072360274738 absolute error = 1.905142710256769e-13 relative error = 1.70700644337027e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.729999999999809 y[1] (closed_form) = -1.103406517403061 y[1] (numeric) = -1.103406517402869 absolute error = 1.920685832601521e-13 relative error = 1.740687409679235e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999808 y[1] (closed_form) = -1.090712476081186 y[1] (numeric) = -1.090712476080993 absolute error = 1.931788062847772e-13 relative error = 1.771124934582652e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999807 y[1] (closed_form) = -1.077990307940621 y[1] (numeric) = -1.077990307940426 absolute error = 1.945110739143274e-13 relative error = 1.804386110724121e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999806 y[1] (closed_form) = -1.065240084775826 y[1] (numeric) = -1.06524008477563 absolute error = 1.960653861488026e-13 relative error = 1.840574617411845e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999805 y[1] (closed_form) = -1.052461878543755 y[1] (numeric) = -1.052461878543557 absolute error = 1.978417429882029e-13 relative error = 1.879799611002993e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999804 y[1] (closed_form) = -1.03965576136321 y[1] (numeric) = -1.039655761363011 absolute error = 1.991740106177531e-13 relative error = 1.915768834451449e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999803 y[1] (closed_form) = -1.026821805514192 y[1] (numeric) = -1.026821805513992 absolute error = 2.005062782473033e-13 relative error = 1.95268816040479e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999802 y[1] (closed_form) = -1.01396008343725 y[1] (numeric) = -1.013960083437048 absolute error = 2.020605904817785e-13 relative error = 1.99278643984493e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999801 y[1] (closed_form) = -1.001070667732826 y[1] (numeric) = -1.001070667732623 absolute error = 2.029487689014786e-13 relative error = 2.02731710600518e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y[1] (closed_form) = -0.9881536311606087 y[1] (numeric) = -0.9881536311604044 absolute error = 2.042810365310288e-13 relative error = 2.067300367971083e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999798 y[1] (closed_form) = -0.9752090466388716 y[1] (numeric) = -0.9752090466386659 absolute error = 2.057243264630415e-13 relative error = 2.10954079201875e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999797 y[1] (closed_form) = -0.9622369872438215 y[1] (numeric) = -0.962236987243614 absolute error = 2.075006833024418e-13 relative error = 2.156440524041746e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999796 y[1] (closed_form) = -0.9492375262089368 y[1] (numeric) = -0.9492375262087281 absolute error = 2.086109063270669e-13 relative error = 2.197668134341641e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999795 y[1] (closed_form) = -0.9362107369243129 y[1] (numeric) = -0.9362107369241025 absolute error = 2.103872631664672e-13 relative error = 2.247221217069589e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999794 y[1] (closed_form) = -0.9231566929359977 y[1] (numeric) = -0.9231566929357858 absolute error = 2.118305530984799e-13 relative error = 2.294632695829526e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999793 y[1] (closed_form) = -0.9100754679453313 y[1] (numeric) = -0.9100754679451185 absolute error = 2.128297538206425e-13 relative error = 2.338594559648402e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999792 y[1] (closed_form) = -0.8969671358082842 y[1] (numeric) = -0.8969671358080701 absolute error = 2.141620214501927e-13 relative error = 2.387623948531903e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999791 y[1] (closed_form) = -0.8838317705347898 y[1] (numeric) = -0.8838317705345741 absolute error = 2.157163336846679e-13 relative error = 2.44069449499583e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.90999999999979 y[1] (closed_form) = -0.8706694462880795 y[1] (numeric) = -0.8706694462878624 absolute error = 2.171596236166806e-13 relative error = 2.494168418824114e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y[1] (closed_form) = -0.8574802373840162 y[1] (numeric) = -0.8574802373837977 absolute error = 2.184918912462308e-13 relative error = 2.548069118336786e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999787 y[1] (closed_form) = -0.8442642182904241 y[1] (numeric) = -0.8442642182902041 absolute error = 2.199351811782435e-13 relative error = 2.605051551558075e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999786 y[1] (closed_form) = -0.8310214636264193 y[1] (numeric) = -0.8310214636261977 absolute error = 2.216005157151812e-13 relative error = 2.666603997785555e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999785 y[1] (closed_form) = -0.8177520481617373 y[1] (numeric) = -0.8177520481615141 absolute error = 2.231548279496565e-13 relative error = 2.728881308842901e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999784 y[1] (closed_form) = -0.8044560468160613 y[1] (numeric) = -0.8044560468158366 absolute error = 2.247091401841317e-13 relative error = 2.793305377882396e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999783 y[1] (closed_form) = -0.791133534658347 y[1] (numeric) = -0.7911335346581209 absolute error = 2.261524301161444e-13 relative error = 2.858587333348331e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999782 y[1] (closed_form) = -0.7777845869061477 y[1] (numeric) = -0.77778458690592 absolute error = 2.277067423506196e-13 relative error = 2.927632485703861e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999781 y[1] (closed_form) = -0.7644092789249362 y[1] (numeric) = -0.764409278924707 absolute error = 2.291500322826323e-13 relative error = 2.997740066746815e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99999999999978 y[1] (closed_form) = -0.7510076862274282 y[1] (numeric) = -0.7510076862271975 absolute error = 2.307043445171075e-13 relative error = 3.071930537435847e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.009999999999779 y[1] (closed_form) = -0.7375798844729007 y[1] (numeric) = -0.7375798844726684 absolute error = 2.322586567515827e-13 relative error = 3.148928836604086e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y[1] (closed_form) = -0.7241259494665129 y[1] (numeric) = -0.7241259494662792 absolute error = 2.337019466835955e-13 relative error = 3.227365996975682e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999776 y[1] (closed_form) = -0.7106459571586228 y[1] (numeric) = -0.7106459571583877 absolute error = 2.350342143131456e-13 relative error = 3.307332039893444e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999775 y[1] (closed_form) = -0.6971399836441046 y[1] (numeric) = -0.6971399836438679 absolute error = 2.366995488500834e-13 relative error = 3.395294408632289e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999774 y[1] (closed_form) = -0.683608105161662 y[1] (numeric) = -0.6836081051614241 absolute error = 2.37920794177171e-13 relative error = 3.480368245793497e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999773 y[1] (closed_form) = -0.6700503980931445 y[1] (numeric) = -0.670050398092905 absolute error = 2.394751064116463e-13 relative error = 3.573986480616292e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999772 y[1] (closed_form) = -0.6564669389628581 y[1] (numeric) = -0.6564669389626173 absolute error = 2.408073740411965e-13 relative error = 3.668233078449377e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999771 y[1] (closed_form) = -0.6428578044368778 y[1] (numeric) = -0.6428578044366354 absolute error = 2.423616862756717e-13 relative error = 3.770066795532995e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.08999999999977 y[1] (closed_form) = -0.6292230713223563 y[1] (numeric) = -0.6292230713221124 absolute error = 2.439159985101469e-13 relative error = 3.876463048272219e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.099999999999769 y[1] (closed_form) = -0.6155628165668345 y[1] (numeric) = -0.6155628165665888 absolute error = 2.456923553495471e-13 relative error = 3.991344973041775e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999768 y[1] (closed_form) = -0.6018771172575468 y[1] (numeric) = -0.6018771172572995 absolute error = 2.472466675840224e-13 relative error = 4.107926028332857e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y[1] (closed_form) = -0.5881660506207287 y[1] (numeric) = -0.5881660506204802 absolute error = 2.4846791291111e-13 relative error = 4.224451796374275e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999765 y[1] (closed_form) = -0.5744296940209235 y[1] (numeric) = -0.5744296940206732 absolute error = 2.502442697505103e-13 relative error = 4.356395088123616e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999764 y[1] (closed_form) = -0.5606681249602807 y[1] (numeric) = -0.5606681249600292 absolute error = 2.515765373800605e-13 relative error = 4.487084715184814e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999763 y[1] (closed_form) = -0.5468814210778647 y[1] (numeric) = -0.5468814210776117 absolute error = 2.530198273120732e-13 relative error = 4.626593948161357e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999762 y[1] (closed_form) = -0.533069660148952 y[1] (numeric) = -0.5330696601486975 absolute error = 2.544631172440859e-13 relative error = 4.773543427194544e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999761 y[1] (closed_form) = -0.519232920084332 y[1] (numeric) = -0.5192329200840761 absolute error = 2.559064071760986e-13 relative error = 4.928547425970895e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.17999999999976 y[1] (closed_form) = -0.5053712789296074 y[1] (numeric) = -0.5053712789293499 absolute error = 2.575717417130363e-13 relative error = 5.096683417755388e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.189999999999759 y[1] (closed_form) = -0.4914848148644895 y[1] (numeric) = -0.4914848148642304 absolute error = 2.590705427962803e-13 relative error = 5.271181020469785e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999758 y[1] (closed_form) = -0.4775736062020963 y[1] (numeric) = -0.4775736062018355 absolute error = 2.608468996356805e-13 relative error = 5.461920345851297e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y[1] (closed_form) = -0.4636377313882467 y[1] (numeric) = -0.4636377313879845 absolute error = 2.62234678416462e-13 relative error = 5.656025397917165e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y[1] (closed_form) = -0.4496772690007553 y[1] (numeric) = -0.4496772690004917 absolute error = 2.636224571972434e-13 relative error = 5.86248128092062e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999754 y[1] (closed_form) = -0.4356922977487248 y[1] (numeric) = -0.4356922977484595 absolute error = 2.652322805829499e-13 relative error = 6.087605448924331e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999753 y[1] (closed_form) = -0.4216828964718369 y[1] (numeric) = -0.4216828964715701 absolute error = 2.667865928174251e-13 relative error = 6.326711257430454e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999752 y[1] (closed_form) = -0.4076491441396441 y[1] (numeric) = -0.4076491441393758 absolute error = 2.683409050519003e-13 relative error = 6.582643651030887e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999751 y[1] (closed_form) = -0.3935911198508582 y[1] (numeric) = -0.3935911198505882 absolute error = 2.699507284376068e-13 relative error = 6.858659020048474e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.26999999999975 y[1] (closed_form) = -0.3795089028326379 y[1] (numeric) = -0.3795089028323664 absolute error = 2.71505040672082e-13 relative error = 7.154115190594482e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.279999999999749 y[1] (closed_form) = -0.3654025724398773 y[1] (numeric) = -0.3654025724396043 absolute error = 2.73003841755326e-13 relative error = 7.471316907607309e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999748 y[1] (closed_form) = -0.3512722081544901 y[1] (numeric) = -0.3512722081542156 absolute error = 2.745581539898012e-13 relative error = 7.816108067081985e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999747 y[1] (closed_form) = -0.3371178895846954 y[1] (numeric) = -0.3371178895844192 absolute error = 2.761679773755077e-13 relative error = 8.192029729295188e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y[1] (closed_form) = -0.3229396964643003 y[1] (numeric) = -0.3229396964640224 absolute error = 2.779443342149079e-13 relative error = 8.606694601437255e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999744 y[1] (closed_form) = -0.3087377086519827 y[1] (numeric) = -0.3087377086517035 absolute error = 2.791655795419956e-13 relative error = 9.042160115811394e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999743 y[1] (closed_form) = -0.2945120061305737 y[1] (numeric) = -0.2945120061302928 absolute error = 2.808864252301646e-13 relative error = 9.537350579372709e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999742 y[1] (closed_form) = -0.2802626690063346 y[1] (numeric) = -0.280262669006053 absolute error = 2.815525590449397e-13 relative error = 1.004602432579331e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999741 y[1] (closed_form) = -0.2659897775082412 y[1] (numeric) = -0.2659897775079579 absolute error = 2.832734047331087e-13 relative error = 1.064978539351318e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.35999999999974 y[1] (closed_form) = -0.2516934119872556 y[1] (numeric) = -0.2516934119869707 absolute error = 2.848832281188152e-13 relative error = 1.131866050324909e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.369999999999739 y[1] (closed_form) = -0.237373652915607 y[1] (numeric) = -0.2373736529153208 absolute error = 2.861599845971341e-13 relative error = 1.205525470423089e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999738 y[1] (closed_form) = -0.2230305808860673 y[1] (numeric) = -0.2230305808857794 absolute error = 2.879363414365343e-13 relative error = 1.291017313825782e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999737 y[1] (closed_form) = -0.2086642766112237 y[1] (numeric) = -0.2086642766109341 absolute error = 2.895739203978565e-13 relative error = 1.38775033801009e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999736 y[1] (closed_form) = -0.1942748209227541 y[1] (numeric) = -0.1942748209224629 absolute error = 2.911559882079473e-13 relative error = 1.498681027345867e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = -0.1798622947706989 y[1] (numeric) = -0.1798622947704063 absolute error = 2.926547892911913e-13 relative error = 1.627104722889742e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999733 y[1] (closed_form) = -0.1654267792227333 y[1] (numeric) = -0.1654267792224388 absolute error = 2.945144128574384e-13 relative error = 1.780330936993577e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999732 y[1] (closed_form) = -0.1509683554634353 y[1] (numeric) = -0.1509683554631395 absolute error = 2.958466804869886e-13 relative error = 1.959660218718107e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999731 y[1] (closed_form) = -0.136487104793559 y[1] (numeric) = -0.1364871047932611 absolute error = 2.978173263556982e-13 relative error = 2.182018050761325e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.44999999999973 y[1] (closed_form) = -0.121983108629298 y[1] (numeric) = -0.1219831086289988 absolute error = 2.991773495608641e-13 relative error = 2.452612930779233e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.459999999999729 y[1] (closed_form) = -0.1074564485015577 y[1] (numeric) = -0.1074564485012568 absolute error = 3.009120730368409e-13 relative error = 2.800316567623012e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999728 y[1] (closed_form) = -0.09290720605521741 y[1] (numeric) = -0.092907206054915 absolute error = 3.024108741200848e-13 relative error = 3.254977594960217e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999727 y[1] (closed_form) = -0.07833546304839833 y[1] (numeric) = -0.07833546304809418 absolute error = 3.041594753838694e-13 relative error = 3.882781355309655e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999726 y[1] (closed_form) = -0.0637413013517254 y[1] (numeric) = -0.06374130135141994 absolute error = 3.05463987437804e-13 relative error = 4.792245858807454e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999725 y[1] (closed_form) = -0.04912480294759325 y[1] (numeric) = -0.04912480294728606 absolute error = 3.071917720198769e-13 relative error = 6.253292707302901e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = -0.0344860499294255 y[1] (numeric) = -0.03448604992911662 absolute error = 3.088779232385264e-13 relative error = 8.956604884312187e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999722 y[1] (closed_form) = -0.01982512450093732 y[1] (numeric) = -0.01982512450062714 absolute error = 3.10178965845509e-13 relative error = 1.564575121991511e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999721 y[1] (closed_form) = -0.005142108975396686 y[1] (numeric) = -0.005142108975084731 absolute error = 3.119553226849092e-13 relative error = 6.066680503612694e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.53999999999972 y[1] (closed_form) = 0.009562914225119012 y[1] (numeric) = 0.009562914225432697 absolute error = 3.136848419904581e-13 relative error = 3.280222269133176e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.549999999999719 y[1] (closed_form) = 0.02428986257046284 y[1] (numeric) = 0.02428986257077823 absolute error = 3.153935446142953e-13 relative error = 1.298457509586006e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999718 y[1] (closed_form) = 0.03903865342316193 y[1] (numeric) = 0.03903865342347874 absolute error = 3.168160178645962e-13 relative error = 8.115444311832408e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999717 y[1] (closed_form) = 0.05380920403916001 y[1] (numeric) = 0.05380920403947862 absolute error = 3.186131913857082e-13 relative error = 5.921165292722697e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999716 y[1] (closed_form) = 0.06860143156856435 y[1] (numeric) = 0.06860143156888444 absolute error = 3.200911757872404e-13 relative error = 4.665954754418241e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999715 y[1] (closed_form) = 0.08341525305638897 y[1] (numeric) = 0.08341525305671066 absolute error = 3.216871213851391e-13 relative error = 3.856454420484436e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999714 y[1] (closed_form) = 0.0982505854433029 y[1] (numeric) = 0.09825058544362622 absolute error = 3.233247003464612e-13 relative error = 3.290817035721797e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = 0.1131073455663767 y[1] (numeric) = 0.1131073455667019 absolute error = 3.252398350639396e-13 relative error = 2.875497019537724e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999711 y[1] (closed_form) = 0.1279854501598325 y[1] (numeric) = 0.1279854501601592 absolute error = 3.266831249959523e-13 relative error = 2.552502058538525e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.62999999999971 y[1] (closed_form) = 0.1428848158557907 y[1] (numeric) = 0.1428848158561193 absolute error = 3.285427485621994e-13 relative error = 2.29935382982743e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.639999999999709 y[1] (closed_form) = 0.1578053591850235 y[1] (numeric) = 0.1578053591853533 absolute error = 3.298750161917496e-13 relative error = 2.090391719871681e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999708 y[1] (closed_form) = 0.1727469965777026 y[1] (numeric) = 0.1727469965780342 absolute error = 3.31568106304303e-13 relative error = 1.919385649956361e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999707 y[1] (closed_form) = 0.1877096443641548 y[1] (numeric) = 0.1877096443644881 absolute error = 3.332334408412407e-13 relative error = 1.77526009369434e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999706 y[1] (closed_form) = 0.202693218775613 y[1] (numeric) = 0.2026932187759477 absolute error = 3.347599975001003e-13 relative error = 1.651559926485202e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999705 y[1] (closed_form) = 0.2176976359449696 y[1] (numeric) = 0.2176976359453063 absolute error = 3.366751322175787e-13 relative error = 1.546526358709217e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999704 y[1] (closed_form) = 0.232722811907534 y[1] (numeric) = 0.2327228119078722 absolute error = 3.382294444520539e-13 relative error = 1.453357501483096e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999703 y[1] (closed_form) = 0.247768662601785 y[1] (numeric) = 0.2477686626021249 absolute error = 3.399225345646073e-13 relative error = 1.371935138992668e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y[1] (closed_form) = 0.2628351038701298 y[1] (numeric) = 0.2628351038704713 absolute error = 3.415601135259294e-13 relative error = 1.299522432493259e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7199999999997 y[1] (closed_form) = 0.2779220514596599 y[1] (numeric) = 0.2779220514600031 absolute error = 3.432254480628671e-13 relative error = 1.234970187720732e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.729999999999699 y[1] (closed_form) = 0.2930294210229103 y[1] (numeric) = 0.2930294210232552 absolute error = 3.449462937510361e-13 relative error = 1.177172901433903e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999698 y[1] (closed_form) = 0.3081571281186184 y[1] (numeric) = 0.3081571281189651 absolute error = 3.466671394392051e-13 relative error = 1.124968750700984e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999697 y[1] (closed_form) = 0.3233050882124837 y[1] (numeric) = 0.323305088212832 absolute error = 3.483324739761429e-13 relative error = 1.077411048189908e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999696 y[1] (closed_form) = 0.338473216677929 y[1] (numeric) = 0.3384732166782788 absolute error = 3.498867862106181e-13 relative error = 1.033720746488339e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999695 y[1] (closed_form) = 0.3536614287968611 y[1] (numeric) = 0.3536614287972129 absolute error = 3.517186542012496e-13 relative error = 9.945066822745676e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999694 y[1] (closed_form) = 0.368869639760435 y[1] (numeric) = 0.3688696397607885 absolute error = 3.535505221918811e-13 relative error = 9.584701045645747e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999693 y[1] (closed_form) = 0.3840977646698156 y[1] (numeric) = 0.3840977646701708 absolute error = 3.551603455775876e-13 relative error = 9.246613186694704e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999692 y[1] (closed_form) = 0.3993457185369425 y[1] (numeric) = 0.3993457185372993 absolute error = 3.568256801145253e-13 relative error = 8.935257436133406e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y[1] (closed_form) = 0.4146134162852948 y[1] (numeric) = 0.414613416285653 absolute error = 3.582134588953068e-13 relative error = 8.639697723838746e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.819999999999689 y[1] (closed_form) = 0.4299007727506561 y[1] (numeric) = 0.4299007727510162 absolute error = 3.601563491884008e-13 relative error = 8.377662288997389e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999688 y[1] (closed_form) = 0.4452077026818828 y[1] (numeric) = 0.4452077026822446 absolute error = 3.617661725741073e-13 relative error = 8.12578422149633e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999687 y[1] (closed_form) = 0.4605341207416691 y[1] (numeric) = 0.4605341207420327 absolute error = 3.635980405647388e-13 relative error = 7.895137931999062e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999686 y[1] (closed_form) = 0.4758799415073167 y[1] (numeric) = 0.4758799415076821 absolute error = 3.654299085553703e-13 relative error = 7.679035754226084e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999685 y[1] (closed_form) = 0.4912450794715029 y[1] (numeric) = 0.4912450794718701 absolute error = 3.672062653947705e-13 relative error = 7.475011572427814e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999684 y[1] (closed_form) = 0.5066294490430503 y[1] (numeric) = 0.506629449043419 absolute error = 3.687050664780145e-13 relative error = 7.277608263286806e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999683 y[1] (closed_form) = 0.5220329645476969 y[1] (numeric) = 0.5220329645480671 absolute error = 3.702593787124897e-13 relative error = 7.092643642404693e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999682 y[1] (closed_form) = 0.537455540228867 y[1] (numeric) = 0.5374555402292394 absolute error = 3.723688024592775e-13 relative error = 6.92836475926381e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y[1] (closed_form) = 0.5528970902484446 y[1] (numeric) = 0.5528970902488186 absolute error = 3.740341369962152e-13 relative error = 6.764986533536337e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y[1] (closed_form) = 0.5683575286875436 y[1] (numeric) = 0.5683575286879192 absolute error = 3.755884492306905e-13 relative error = 6.608313082400839e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999678 y[1] (closed_form) = 0.5838367695472826 y[1] (numeric) = 0.5838367695476598 absolute error = 3.772537837676282e-13 relative error = 6.461631117549473e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999677 y[1] (closed_form) = 0.5993347267495585 y[1] (numeric) = 0.5993347267499373 absolute error = 3.788080960021034e-13 relative error = 6.320476339766549e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999676 y[1] (closed_form) = 0.6148513141378206 y[1] (numeric) = 0.6148513141382015 absolute error = 3.809175197488912e-13 relative error = 6.19527861435956e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999675 y[1] (closed_form) = 0.6303864454778477 y[1] (numeric) = 0.6303864454782303 absolute error = 3.825828542858289e-13 relative error = 6.069020947869876e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999674 y[1] (closed_form) = 0.6459400344585224 y[1] (numeric) = 0.6459400344589066 absolute error = 3.841371665203042e-13 relative error = 5.946947797442498e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999673 y[1] (closed_form) = 0.6615119946926086 y[1] (numeric) = 0.6615119946929943 absolute error = 3.856914787547794e-13 relative error = 5.830453292596796e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999672 y[1] (closed_form) = 0.6771022397175286 y[1] (numeric) = 0.6771022397179163 absolute error = 3.876898801991047e-13 relative error = 5.725721426661355e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999671 y[1] (closed_form) = 0.6927106829961427 y[1] (numeric) = 0.692710682996532 absolute error = 3.893552147360424e-13 relative error = 5.620747944177591e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y[1] (closed_form) = 0.7083372379175261 y[1] (numeric) = 0.708337237917917 absolute error = 3.909095269705176e-13 relative error = 5.518692312714928e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999673 y[1] (closed_form) = 0.7239818177977563 y[1] (numeric) = 0.723981817798142 absolute error = 3.856914787547794e-13 relative error = 5.327364158508771e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999676 y[1] (closed_form) = 0.7396443358806727 y[1] (numeric) = 0.739644335881053 absolute error = 3.803624082365786e-13 relative error = 5.142504171058004e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.02999999999968 y[1] (closed_form) = 0.7553247053386776 y[1] (numeric) = 0.7553247053390529 absolute error = 3.753664046257654e-13 relative error = 4.969603165005124e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999683 y[1] (closed_form) = 0.7710228392735115 y[1] (numeric) = 0.7710228392738812 absolute error = 3.697042672001771e-13 relative error = 4.794984640773123e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999686 y[1] (closed_form) = 0.7867386507170334 y[1] (numeric) = 0.786738650717398 absolute error = 3.645972412869014e-13 relative error = 4.634286633237195e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.05999999999969 y[1] (closed_form) = 0.8024720526320062 y[1] (numeric) = 0.8024720526323654 absolute error = 3.592681707687007e-13 relative error = 4.477017854894096e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999693 y[1] (closed_form) = 0.8182229579128777 y[1] (numeric) = 0.8182229579132315 absolute error = 3.538280779480374e-13 relative error = 4.324347960738986e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999696 y[1] (closed_form) = 0.8339912793865658 y[1] (numeric) = 0.8339912793869144 absolute error = 3.486100297322992e-13 relative error = 4.180020083527922e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.0899999999997 y[1] (closed_form) = 0.8497769298132427 y[1] (numeric) = 0.8497769298135861 absolute error = 3.433919815165609e-13 relative error = 4.040966157930751e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999703 y[1] (closed_form) = 0.8655798218871203 y[1] (numeric) = 0.8655798218874583 absolute error = 3.379518886958977e-13 relative error = 3.904341115058592e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999706 y[1] (closed_form) = 0.881399868237235 y[1] (numeric) = 0.8813998682375678 absolute error = 3.327338404801594e-13 relative error = 3.77506115522361e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.11999999999971 y[1] (closed_form) = 0.8972369814282354 y[1] (numeric) = 0.8972369814285629 absolute error = 3.275157922644212e-13 relative error = 3.650270765066734e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999713 y[1] (closed_form) = 0.9130910739611685 y[1] (numeric) = 0.9130910739614908 absolute error = 3.222977440486829e-13 relative error = 3.529743672232957e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999716 y[1] (closed_form) = 0.9289620582742673 y[1] (numeric) = 0.9289620582745842 absolute error = 3.169686735304822e-13 relative error = 3.412073407167079e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.14999999999972 y[1] (closed_form) = 0.9448498467437383 y[1] (numeric) = 0.9448498467440501 absolute error = 3.118616476172065e-13 relative error = 3.300647702827955e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999723 y[1] (closed_form) = 0.9607543516845515 y[1] (numeric) = 0.960754351684858 absolute error = 3.065325770990057e-13 relative error = 3.190540605530881e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999726 y[1] (closed_form) = 0.9766754853512278 y[1] (numeric) = 0.976675485351529 absolute error = 3.01203506580805e-13 relative error = 3.083967101646741e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.17999999999973 y[1] (closed_form) = 0.9926131599386304 y[1] (numeric) = 0.9926131599389263 absolute error = 2.958744360626042e-13 relative error = 2.980762778531941e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999733 y[1] (closed_form) = 1.008567287582753 y[1] (numeric) = 1.008567287583044 absolute error = 2.91100477056716e-13 relative error = 2.886277203719352e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999736 y[1] (closed_form) = 1.024537780361515 y[1] (numeric) = 1.0245377803618 absolute error = 2.855493619335903e-13 relative error = 2.787104266987913e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.20999999999974 y[1] (closed_form) = 1.040524550295545 y[1] (numeric) = 1.040524550295825 absolute error = 2.802202914153895e-13 relative error = 2.693067562277097e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999743 y[1] (closed_form) = 1.05652750934898 y[1] (numeric) = 1.056527509349255 absolute error = 2.744471316873387e-13 relative error = 2.597633561443656e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999746 y[1] (closed_form) = 1.072546569430256 y[1] (numeric) = 1.072546569430525 absolute error = 2.688960165642129e-13 relative error = 2.507080104755286e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.23999999999975 y[1] (closed_form) = 1.088581642392898 y[1] (numeric) = 1.088581642393161 absolute error = 2.633449014410871e-13 relative error = 2.419156186229706e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999753 y[1] (closed_form) = 1.104632640036313 y[1] (numeric) = 1.104632640036572 absolute error = 2.582378755278114e-13 relative error = 2.337771546559788e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999756 y[1] (closed_form) = 1.120699474106592 y[1] (numeric) = 1.120699474106845 absolute error = 2.529088050096107e-13 relative error = 2.256704949480114e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.26999999999976 y[1] (closed_form) = 1.136782056297292 y[1] (numeric) = 1.13678205629754 absolute error = 2.473576898864849e-13 relative error = 2.175946466749961e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999763 y[1] (closed_form) = 1.152880298250241 y[1] (numeric) = 1.152880298250483 absolute error = 2.415845301584341e-13 relative error = 2.095486673899222e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999766 y[1] (closed_form) = 1.168994111556327 y[1] (numeric) = 1.168994111556564 absolute error = 2.362554596402333e-13 relative error = 2.021014967523636e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.29999999999977 y[1] (closed_form) = 1.185123407756298 y[1] (numeric) = 1.185123407756528 absolute error = 2.309263891220326e-13 relative error = 1.94854297544614e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999773 y[1] (closed_form) = 1.201268098341552 y[1] (numeric) = 1.201268098341777 absolute error = 2.253752739989068e-13 relative error = 1.876144670037068e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999776 y[1] (closed_form) = 1.217428094754942 y[1] (numeric) = 1.217428094755162 absolute error = 2.202682480856311e-13 relative error = 1.809291645515781e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.32999999999978 y[1] (closed_form) = 1.233603308391566 y[1] (numeric) = 1.233603308391781 absolute error = 2.151612221723553e-13 relative error = 1.74416865380244e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999783 y[1] (closed_form) = 1.249793650599568 y[1] (numeric) = 1.249793650599778 absolute error = 2.098321516541546e-13 relative error = 1.678934370913879e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999786 y[1] (closed_form) = 1.265999032680936 y[1] (numeric) = 1.26599903268114 absolute error = 2.042810365310288e-13 relative error = 1.613595518303314e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.35999999999979 y[1] (closed_form) = 1.282219365892295 y[1] (numeric) = 1.282219365892494 absolute error = 1.98729921407903e-13 relative error = 1.549890188014802e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999793 y[1] (closed_form) = 1.298454561445715 y[1] (numeric) = 1.298454561445908 absolute error = 1.934008508897023e-13 relative error = 1.489469532721788e-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) = 1.314704530509502 y[1] (numeric) = 1.31470453050969 absolute error = 1.880717803715015e-13 relative error = 1.430525080023996e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.3899999999998 y[1] (closed_form) = 1.330969184209 y[1] (numeric) = 1.330969184209183 absolute error = 1.825206652483757e-13 relative error = 1.371336522391752e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999803 y[1] (closed_form) = 1.347248433627394 y[1] (numeric) = 1.347248433627571 absolute error = 1.77191594730175e-13 relative error = 1.315210990842247e-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) = 1.363542189806505 y[1] (numeric) = 1.363542189806677 absolute error = 1.718625242119742e-13 relative error = 1.260412222641696e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.41999999999981 y[1] (closed_form) = 1.379850363747595 y[1] (numeric) = 1.379850363747761 absolute error = 1.663114090888484e-13 relative error = 1.205285829958809e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999813 y[1] (closed_form) = 1.396172866412164 y[1] (numeric) = 1.396172866412325 absolute error = 1.605382493607976e-13 relative error = 1.149845074509599e-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) = 1.412509608722756 y[1] (numeric) = 1.412509608722911 absolute error = 1.549871342376719e-13 relative error = 1.097246583531683e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.44999999999982 y[1] (closed_form) = 1.428860501563757 y[1] (numeric) = 1.428860501563906 absolute error = 1.494360191145461e-13 relative error = 1.045840506830457e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999823 y[1] (closed_form) = 1.445225455782197 y[1] (numeric) = 1.445225455782341 absolute error = 1.443289932012704e-13 relative error = 9.986607461405072e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 1.461604382188557 y[1] (numeric) = 1.461604382188695 absolute error = 1.383337888682945e-13 relative error = 9.46451656508844e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.47999999999983 y[1] (closed_form) = 1.477997191557564 y[1] (numeric) = 1.477997191557697 absolute error = 1.332267629550188e-13 relative error = 9.014006502584749e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999833 y[1] (closed_form) = 1.494403794629002 y[1] (numeric) = 1.49440379462913 absolute error = 1.272315586220429e-13 relative error = 8.513867475398723e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 1.51082410210851 y[1] (numeric) = 1.510824102108632 absolute error = 1.219024881038422e-13 relative error = 8.068608909118854e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.50999999999984 y[1] (closed_form) = 1.527258024668388 y[1] (numeric) = 1.527258024668505 absolute error = 1.165734175856414e-13 relative error = 7.632856773560114e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999843 y[1] (closed_form) = 1.5437054729484 y[1] (numeric) = 1.54370547294851 absolute error = 1.108002578575906e-13 relative error = 7.177551663787763e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = 1.560166357556577 y[1] (numeric) = 1.560166357556683 absolute error = 1.052491427344648e-13 relative error = 6.746020526894237e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.53999999999985 y[1] (closed_form) = 1.576640589070027 y[1] (numeric) = 1.576640589070127 absolute error = 1.001421168211891e-13 relative error = 6.351613520254316e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999853 y[1] (closed_form) = 1.593128078035732 y[1] (numeric) = 1.593128078035826 absolute error = 9.459100169806334e-14 relative error = 5.937438615399369e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999857 y[1] (closed_form) = 1.609628734971358 y[1] (numeric) = 1.609628734971448 absolute error = 8.926193117986259e-14 relative error = 5.545498116461676e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.56999999999986 y[1] (closed_form) = 1.626142470366062 y[1] (numeric) = 1.626142470366145 absolute error = 8.348877145181177e-14 relative error = 5.134160934436303e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999863 y[1] (closed_form) = 1.642669194681289 y[1] (numeric) = 1.642669194681367 absolute error = 7.793765632868599e-14 relative error = 4.74457404942128e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999867 y[1] (closed_form) = 1.659208818351591 y[1] (numeric) = 1.659208818351663 absolute error = 7.194245199571014e-14 relative error = 4.335949230741452e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.59999999999987 y[1] (closed_form) = 1.67576125178542 y[1] (numeric) = 1.675761251785487 absolute error = 6.661338147750939e-14 relative error = 3.97511169365785e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999873 y[1] (closed_form) = 1.692326405365942 y[1] (numeric) = 1.692326405366004 absolute error = 6.128431095930864e-14 relative error = 3.621305604225726e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999877 y[1] (closed_form) = 1.708904189451844 y[1] (numeric) = 1.708904189451899 absolute error = 5.551115123125783e-14 relative error = 3.248347775954826e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.62999999999988 y[1] (closed_form) = 1.725494514378135 y[1] (numeric) = 1.725494514378185 absolute error = 5.018208071305708e-14 relative error = 2.90827239929781e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999883 y[1] (closed_form) = 1.742097290456958 y[1] (numeric) = 1.742097290457002 absolute error = 4.440892098500626e-14 relative error = 2.549164230280024e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999887 y[1] (closed_form) = 1.758712427978396 y[1] (numeric) = 1.758712427978435 absolute error = 3.885780586188048e-14 relative error = 2.209446254186464e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.65999999999989 y[1] (closed_form) = 1.775339837211278 y[1] (numeric) = 1.775339837211312 absolute error = 3.352873534367973e-14 relative error = 1.88858125306009e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999893 y[1] (closed_form) = 1.791979428403989 y[1] (numeric) = 1.791979428404017 absolute error = 2.775557561562891e-14 relative error = 1.548878027040141e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999897 y[1] (closed_form) = 1.808631111785276 y[1] (numeric) = 1.808631111785298 absolute error = 2.19824158875781e-14 relative error = 1.215417325530774e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.6899999999999 y[1] (closed_form) = 1.825294797565054 y[1] (numeric) = 1.82529479756507 absolute error = 1.620925615952729e-14 relative error = 8.880349728246888e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999903 y[1] (closed_form) = 1.84197039593522 y[1] (numeric) = 1.841970395935231 absolute error = 1.110223024625157e-14 relative error = 6.02736627621784e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999907 y[1] (closed_form) = 1.858657817070455 y[1] (numeric) = 1.858657817070461 absolute error = 5.773159728050814e-15 relative error = 3.106090682764968e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.71999999999991 y[1] (closed_form) = 1.875356971129037 y[1] (numeric) = 1.875356971129037 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999913 y[1] (closed_form) = 1.892067768253647 y[1] (numeric) = 1.892067768253641 absolute error = 5.551115123125783e-15 relative error = 2.933888107110132e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999917 y[1] (closed_form) = 1.908790118572177 y[1] (numeric) = 1.908790118572166 absolute error = 1.154631945610163e-14 relative error = 6.049025161937952e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.74999999999992 y[1] (closed_form) = 1.925523932198543 y[1] (numeric) = 1.925523932198526 absolute error = 1.709743457922741e-14 relative error = 8.879367476729173e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999923 y[1] (closed_form) = 1.942269119233489 y[1] (numeric) = 1.942269119233466 absolute error = 2.264854970235319e-14 relative error = 1.166087102867155e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999927 y[1] (closed_form) = 1.959025589765399 y[1] (numeric) = 1.959025589765371 absolute error = 2.797762022055394e-14 relative error = 1.428139599947971e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.77999999999993 y[1] (closed_form) = 1.975793253871106 y[1] (numeric) = 1.975793253871072 absolute error = 3.397282455352979e-14 relative error = 1.719452401559119e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999933 y[1] (closed_form) = 1.992572021616701 y[1] (numeric) = 1.992572021616661 absolute error = 3.930189507173054e-14 relative error = 1.972420301266823e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999937 y[1] (closed_form) = 2.00936180305834 y[1] (numeric) = 2.009361803058296 absolute error = 4.440892098500626e-14 relative error = 2.210100785105691e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.80999999999994 y[1] (closed_form) = 2.02616250824306 y[1] (numeric) = 2.02616250824301 absolute error = 4.973799150320701e-14 relative error = 2.454787871202699e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999943 y[1] (closed_form) = 2.04297404720958 y[1] (numeric) = 2.042974047209525 absolute error = 5.506706202140776e-14 relative error = 2.695436199819658e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999947 y[1] (closed_form) = 2.059796329989117 y[1] (numeric) = 2.059796329989056 absolute error = 6.039613253960852e-14 relative error = 2.932140991819692e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.83999999999995 y[1] (closed_form) = 2.076629266606194 y[1] (numeric) = 2.076629266606127 absolute error = 6.661338147750939e-14 relative error = 3.207764743987005e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999953 y[1] (closed_form) = 2.093472767079449 y[1] (numeric) = 2.093472767079376 absolute error = 7.238654120556021e-14 relative error = 3.457725476245141e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999957 y[1] (closed_form) = 2.110326741422444 y[1] (numeric) = 2.110326741422366 absolute error = 7.815970093361102e-14 relative error = 3.703677700682894e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.86999999999996 y[1] (closed_form) = 2.127191099644479 y[1] (numeric) = 2.127191099644395 absolute error = 8.393286066166183e-14 relative error = 3.945713230733698e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999963 y[1] (closed_form) = 2.144065751751396 y[1] (numeric) = 2.144065751751306 absolute error = 9.015010959956271e-14 relative error = 4.204633627766449e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999967 y[1] (closed_form) = 2.160950607746395 y[1] (numeric) = 2.1609506077463 absolute error = 9.547918011776346e-14 relative error = 4.41838789722901e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.89999999999997 y[1] (closed_form) = 2.177845577630839 y[1] (numeric) = 2.177845577630737 absolute error = 1.021405182655144e-13 relative error = 4.689979827524207e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999973 y[1] (closed_form) = 2.194750571405066 y[1] (numeric) = 2.194750571404959 absolute error = 1.074695887837152e-13 relative error = 4.896665260458903e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999977 y[1] (closed_form) = 2.211665499069201 y[1] (numeric) = 2.211665499069088 absolute error = 1.127986593019159e-13 relative error = 5.100168147009041e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.92999999999998 y[1] (closed_form) = 2.22859027062396 y[1] (numeric) = 2.228590270623842 absolute error = 1.176836406102666e-13 relative error = 5.28063153471982e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 2.245524796071469 y[1] (numeric) = 2.245524796071344 absolute error = 1.243449787580175e-13 relative error = 5.537457389718354e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999987 y[1] (closed_form) = 2.262468985416064 y[1] (numeric) = 2.262468985415934 absolute error = 1.301181384860683e-13 relative error = 5.751156781587431e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.95999999999999 y[1] (closed_form) = 2.279422748665112 y[1] (numeric) = 2.279422748664975 absolute error = 1.363353874239692e-13 relative error = 5.981136562044523e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 2.296385995829807 y[1] (numeric) = 2.296385995829666 absolute error = 1.4166445794217e-13 relative error = 6.16901767383314e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999997 y[1] (closed_form) = 2.313358636925996 y[1] (numeric) = 2.313358636925848 absolute error = 1.474376176702208e-13 relative error = 6.373314336861178e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (closed_form) = 2.330340581974973 y[1] (numeric) = 2.33034058197482 absolute error = 1.527666881884215e-13 relative error = 6.555551981116476e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) + ( 0.1 * x + 0.2 ) ; Iterations = 4000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %