##############ECHO OF PROBLEM################# ##############temp/lin_exppostode.ode################# diff ( y , x , 1 ) = exp ( 0.1 * x + 0.2 ) ; ! /* BEGIN FIRST INPUT BLOCK */ max_terms=30; Digits=32; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(1.0); x_end=c(10.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(10.0) * exp(c(0.1) * c(x) + c(0.2))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 13.49858807576003 y[1] (numeric) = 13.49858807576003 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.009999999999999 y[1] (closed_form) = 13.51209341538016 y[1] (numeric) = 13.51209341538016 absolute error = 3.552713678800501e-15 relative error = 2.629284426613437e-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) = 13.52561226709482 y[1] (numeric) = 13.52561226709483 absolute error = 7.105427357601002e-15 relative error = 5.253312912781866e-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) = 13.53914464442288 y[1] (numeric) = 13.53914464442289 absolute error = 7.105427357601002e-15 relative error = 5.248062225650207e-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) = 13.55269056089671 y[1] (numeric) = 13.55269056089672 absolute error = 8.881784197001252e-15 relative error = 6.553520983226514e-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) = 13.56625003006224 y[1] (numeric) = 13.56625003006224 absolute error = 8.881784197001252e-15 relative error = 6.546970737911799e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999993 y[1] (closed_form) = 13.57982306547892 y[1] (numeric) = 13.57982306547893 absolute error = 8.881784197001252e-15 relative error = 6.540427039568369e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999992 y[1] (closed_form) = 13.5934096807198 y[1] (numeric) = 13.59340968071981 absolute error = 1.243449787580175e-14 relative error = 9.147445834313531e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999991 y[1] (closed_form) = 13.60700988937149 y[1] (numeric) = 13.6070098893715 absolute error = 1.4210854715202e-14 relative error = 1.044377481220336e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.08999999999999 y[1] (closed_form) = 13.62062370503421 y[1] (numeric) = 13.62062370503422 absolute error = 1.598721155460225e-14 relative error = 1.173750328973067e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.099999999999989 y[1] (closed_form) = 13.63425114132176 y[1] (numeric) = 13.63425114132178 absolute error = 1.953992523340276e-14 relative error = 1.433149868728945e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999988 y[1] (closed_form) = 13.6478922118616 y[1] (numeric) = 13.64789221186162 absolute error = 1.77635683940025e-14 relative error = 1.301561304723956e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 13.66154693029478 y[1] (numeric) = 13.6615469302948 absolute error = 2.309263891220326e-14 relative error = 1.690338512177916e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 13.67521531027603 y[1] (numeric) = 13.67521531027606 absolute error = 2.486899575160351e-14 relative error = 1.818545096903599e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 13.68889736547374 y[1] (numeric) = 13.68889736547376 absolute error = 2.664535259100376e-14 relative error = 1.946493707974531e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999983 y[1] (closed_form) = 13.70259310956994 y[1] (numeric) = 13.70259310956997 absolute error = 2.664535259100376e-14 relative error = 1.944548187189076e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999982 y[1] (closed_form) = 13.71630255626041 y[1] (numeric) = 13.71630255626043 absolute error = 2.664535259100376e-14 relative error = 1.94260461095197e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999981 y[1] (closed_form) = 13.73002571925456 y[1] (numeric) = 13.73002571925459 absolute error = 2.664535259100376e-14 relative error = 1.940662977319637e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.17999999999998 y[1] (closed_form) = 13.74376261227559 y[1] (numeric) = 13.74376261227561 absolute error = 2.842170943040401e-14 relative error = 2.06797150330714e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.189999999999979 y[1] (closed_form) = 13.75751324906036 y[1] (numeric) = 13.7575132490604 absolute error = 3.197442310920451e-14 relative error = 2.324142636125635e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999978 y[1] (closed_form) = 13.77127764335954 y[1] (numeric) = 13.77127764335958 absolute error = 3.552713678800501e-14 relative error = 2.579799616859519e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999977 y[1] (closed_form) = 13.78505580893751 y[1] (numeric) = 13.78505580893754 absolute error = 3.730349362740526e-14 relative error = 2.70608216204824e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 13.79884775957243 y[1] (numeric) = 13.79884775957247 absolute error = 3.907985046680551e-14 relative error = 2.832109691165723e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 13.81265350905626 y[1] (numeric) = 13.8126535090563 absolute error = 3.907985046680551e-14 relative error = 2.829278997057503e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 13.82647307119476 y[1] (numeric) = 13.8264730711948 absolute error = 3.907985046680551e-14 relative error = 2.826451132228516e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999972 y[1] (closed_form) = 13.84030645980748 y[1] (numeric) = 13.84030645980752 absolute error = 4.440892098500626e-14 relative error = 3.208666015739655e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999971 y[1] (closed_form) = 13.85415368872781 y[1] (numeric) = 13.85415368872785 absolute error = 4.618527782440651e-14 relative error = 3.333677311663171e-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) = 13.86801477180298 y[1] (numeric) = 13.86801477180303 absolute error = 4.618527782440651e-14 relative error = 3.330345300634689e-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) = 13.88188972289408 y[1] (numeric) = 13.88188972289413 absolute error = 5.151434834260726e-14 relative error = 3.710903153023147e-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) = 13.89577855587606 y[1] (numeric) = 13.89577855587612 absolute error = 5.506706202140776e-14 relative error = 3.962862663648432e-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) = 13.90968128463776 y[1] (numeric) = 13.90968128463781 absolute error = 5.506706202140776e-14 relative error = 3.958901781755803e-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) = 13.9235979230819 y[1] (numeric) = 13.92359792308195 absolute error = 5.861977570020827e-14 relative error = 4.210102591588853e-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) = 13.93752848512512 y[1] (numeric) = 13.93752848512518 absolute error = 6.217248937900877e-14 relative error = 4.460797295974147e-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) = 13.95147298469799 y[1] (numeric) = 13.95147298469805 absolute error = 6.394884621840902e-14 relative error = 4.583662692000213e-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) = 13.965431435745 y[1] (numeric) = 13.96543143574507 absolute error = 6.572520305780927e-14 relative error = 4.706278023719579e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999961 y[1] (closed_form) = 13.97940385222462 y[1] (numeric) = 13.97940385222468 absolute error = 6.572520305780927e-14 relative error = 4.701574098050688e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.35999999999996 y[1] (closed_form) = 13.99339024810925 y[1] (numeric) = 13.99339024810932 absolute error = 6.750155989720952e-14 relative error = 4.823817438117267e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.369999999999959 y[1] (closed_form) = 14.0073906373853 y[1] (numeric) = 14.00739063738537 absolute error = 7.283063041541027e-14 relative error = 5.199443086924952e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999958 y[1] (closed_form) = 14.02140503405315 y[1] (numeric) = 14.02140503405322 absolute error = 7.460698725481052e-14 relative error = 5.320935175441828e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999957 y[1] (closed_form) = 14.0354334521272 y[1] (numeric) = 14.03543345212728 absolute error = 7.638334409421077e-14 relative error = 5.442179206986597e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999956 y[1] (closed_form) = 14.04947590563588 y[1] (numeric) = 14.04947590563595 absolute error = 7.460698725481052e-14 relative error = 5.310303939870263e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999955 y[1] (closed_form) = 14.06353240862163 y[1] (numeric) = 14.0635324086217 absolute error = 7.283063041541027e-14 relative error = 5.178686854716639e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = 14.07760297514096 y[1] (numeric) = 14.07760297514104 absolute error = 7.283063041541027e-14 relative error = 5.173510756342452e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = 14.09168761926444 y[1] (numeric) = 14.09168761926451 absolute error = 7.283063041541027e-14 relative error = 5.168339831479452e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = 14.10578635507672 y[1] (numeric) = 14.10578635507679 absolute error = 7.460698725481052e-14 relative error = 5.289105149955658e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.44999999999995 y[1] (closed_form) = 14.11989919667652 y[1] (numeric) = 14.1198991966766 absolute error = 7.638334409421077e-14 relative error = 5.409623895345481e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.459999999999949 y[1] (closed_form) = 14.1340261581767 y[1] (numeric) = 14.13402615817678 absolute error = 7.460698725481052e-14 relative error = 5.278537510817433e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999948 y[1] (closed_form) = 14.14816725370421 y[1] (numeric) = 14.14816725370429 absolute error = 7.815970093361102e-14 relative error = 5.524369307490875e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999947 y[1] (closed_form) = 14.16232249740016 y[1] (numeric) = 14.16232249740024 absolute error = 7.993605777301127e-14 relative error = 5.644276056253166e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999946 y[1] (closed_form) = 14.17649190341979 y[1] (numeric) = 14.17649190341987 absolute error = 8.348877145181177e-14 relative error = 5.889240583678662e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999945 y[1] (closed_form) = 14.19067548593249 y[1] (numeric) = 14.19067548593258 absolute error = 8.348877145181177e-14 relative error = 5.883354286733982e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = 14.20487325912187 y[1] (numeric) = 14.20487325912196 absolute error = 8.348877145181177e-14 relative error = 5.877473873144077e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = 14.21908523718569 y[1] (numeric) = 14.21908523718578 absolute error = 8.526512829121202e-14 relative error = 5.996526982497229e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = 14.23331143433593 y[1] (numeric) = 14.23331143433602 absolute error = 8.526512829121202e-14 relative error = 5.990533452779053e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = 14.2475518647988 y[1] (numeric) = 14.24755186479889 absolute error = 8.704148513061227e-14 relative error = 6.109223953461386e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.549999999999939 y[1] (closed_form) = 14.26180654281471 y[1] (numeric) = 14.2618065428148 absolute error = 8.881784197001252e-14 relative error = 6.227671207246892e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999938 y[1] (closed_form) = 14.27607548263836 y[1] (numeric) = 14.27607548263845 absolute error = 8.881784197001252e-14 relative error = 6.221446648837563e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999937 y[1] (closed_form) = 14.29035869853868 y[1] (numeric) = 14.29035869853877 absolute error = 9.059419880941277e-14 relative error = 6.339532878112909e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999936 y[1] (closed_form) = 14.30465620479889 y[1] (numeric) = 14.30465620479898 absolute error = 9.237055564881302e-14 relative error = 6.457376837747754e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999935 y[1] (closed_form) = 14.31896801571649 y[1] (numeric) = 14.31896801571659 absolute error = 9.414691248821327e-14 relative error = 6.574978894070974e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999934 y[1] (closed_form) = 14.33329414560331 y[1] (numeric) = 14.3332941456034 absolute error = 9.592326932761353e-14 relative error = 6.692339412921187e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y[1] (closed_form) = 14.34763460878546 y[1] (numeric) = 14.34763460878556 absolute error = 9.414691248821327e-14 relative error = 6.561842077478364e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y[1] (closed_form) = 14.36198941960342 y[1] (numeric) = 14.36198941960351 absolute error = 9.414691248821327e-14 relative error = 6.555283515228559e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y[1] (closed_form) = 14.376358592412 y[1] (numeric) = 14.37635859241209 absolute error = 9.414691248821327e-14 relative error = 6.548731508262814e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y[1] (closed_form) = 14.39074214158036 y[1] (numeric) = 14.39074214158046 absolute error = 9.592326932761353e-14 relative error = 6.665623522671183e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999928 y[1] (closed_form) = 14.40514008149207 y[1] (numeric) = 14.40514008149216 absolute error = 9.237055564881302e-14 relative error = 6.412333037114442e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999927 y[1] (closed_form) = 14.41955242654506 y[1] (numeric) = 14.41955242654515 absolute error = 9.592326932761353e-14 relative error = 6.652305597989831e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999926 y[1] (closed_form) = 14.43397919115167 y[1] (numeric) = 14.43397919115177 absolute error = 9.769962616701378e-14 relative error = 6.768724332573908e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999925 y[1] (closed_form) = 14.44842038973868 y[1] (numeric) = 14.44842038973878 absolute error = 9.769962616701378e-14 relative error = 6.761958991475662e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999924 y[1] (closed_form) = 14.46287603674729 y[1] (numeric) = 14.46287603674738 absolute error = 9.592326932761353e-14 relative error = 6.632378586658118e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999923 y[1] (closed_form) = 14.47734614663313 y[1] (numeric) = 14.47734614663323 absolute error = 9.592326932761353e-14 relative error = 6.625749523155633e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y[1] (closed_form) = 14.49183073386633 y[1] (numeric) = 14.49183073386643 absolute error = 9.414691248821327e-14 relative error = 6.496550657895757e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y[1] (closed_form) = 14.50632981293147 y[1] (numeric) = 14.50632981293157 absolute error = 9.769962616701378e-14 relative error = 6.734965179126202e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y[1] (closed_form) = 14.52084339832764 y[1] (numeric) = 14.52084339832773 absolute error = 9.769962616701378e-14 relative error = 6.728233580307451e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y[1] (closed_form) = 14.53537150456841 y[1] (numeric) = 14.53537150456851 absolute error = 1.030286966852145e-13 relative error = 7.088136457525908e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999917 y[1] (closed_form) = 14.54991414618189 y[1] (numeric) = 14.549914146182 absolute error = 1.030286966852145e-13 relative error = 7.08105186395555e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999916 y[1] (closed_form) = 14.56447133771074 y[1] (numeric) = 14.56447133771084 absolute error = 1.048050535246148e-13 relative error = 7.195939426462434e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999915 y[1] (closed_form) = 14.57904309371214 y[1] (numeric) = 14.57904309371224 absolute error = 1.048050535246148e-13 relative error = 7.188747083806661e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999914 y[1] (closed_form) = 14.59362942875784 y[1] (numeric) = 14.59362942875795 absolute error = 1.083577672034153e-13 relative error = 7.42500470718327e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999913 y[1] (closed_form) = 14.60823035743419 y[1] (numeric) = 14.6082303574343 absolute error = 1.101341240428155e-13 relative error = 7.539183141835369e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999912 y[1] (closed_form) = 14.62284589434212 y[1] (numeric) = 14.62284589434223 absolute error = 1.101341240428155e-13 relative error = 7.531647727028889e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y[1] (closed_form) = 14.63747605409716 y[1] (numeric) = 14.63747605409727 absolute error = 1.101341240428155e-13 relative error = 7.524119843870763e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y[1] (closed_form) = 14.65212085132947 y[1] (numeric) = 14.65212085132958 absolute error = 1.13686837721616e-13 relative error = 7.759070435956758e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y[1] (closed_form) = 14.66678030068385 y[1] (numeric) = 14.66678030068397 absolute error = 1.154631945610163e-13 relative error = 7.872429544446965e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999907 y[1] (closed_form) = 14.68145441681976 y[1] (numeric) = 14.68145441681988 absolute error = 1.172395514004165e-13 relative error = 7.985554296725631e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999906 y[1] (closed_form) = 14.69614321441131 y[1] (numeric) = 14.69614321441143 absolute error = 1.20792265079217e-13 relative error = 8.219317362174719e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999905 y[1] (closed_form) = 14.71084670814729 y[1] (numeric) = 14.71084670814741 absolute error = 1.225686219186173e-13 relative error = 8.331853655353178e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999904 y[1] (closed_form) = 14.72556491273121 y[1] (numeric) = 14.72556491273134 absolute error = 1.261213355974178e-13 relative error = 8.564787588446108e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999903 y[1] (closed_form) = 14.74029784288127 y[1] (numeric) = 14.7402978428814 absolute error = 1.27897692436818e-13 relative error = 8.676737322413424e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999902 y[1] (closed_form) = 14.7550455133304 y[1] (numeric) = 14.75504551333053 absolute error = 1.296740492762183e-13 relative error = 8.788454712597439e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999901 y[1] (closed_form) = 14.76980793882628 y[1] (numeric) = 14.76980793882641 absolute error = 1.314504061156185e-13 relative error = 8.899940111615599e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y[1] (closed_form) = 14.78458513413132 y[1] (numeric) = 14.78458513413146 absolute error = 1.332267629550188e-13 relative error = 9.01119387161259e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y[1] (closed_form) = 14.79937711402273 y[1] (numeric) = 14.79937711402287 absolute error = 1.367794766338193e-13 relative error = 9.242245506685395e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y[1] (closed_form) = 14.81418389329249 y[1] (numeric) = 14.81418389329263 absolute error = 1.385558334732195e-13 relative error = 9.352917074018118e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999896 y[1] (closed_form) = 14.82900548674738 y[1] (numeric) = 14.82900548674752 absolute error = 1.403321903126198e-13 relative error = 9.46335817584221e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999895 y[1] (closed_form) = 14.84384190920899 y[1] (numeric) = 14.84384190920913 absolute error = 1.403321903126198e-13 relative error = 9.453899547768625e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999894 y[1] (closed_form) = 14.85869317551374 y[1] (numeric) = 14.85869317551389 absolute error = 1.474376176702208e-13 relative error = 9.922650392511597e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999893 y[1] (closed_form) = 14.87355930051291 y[1] (numeric) = 14.87355930051306 absolute error = 1.474376176702208e-13 relative error = 9.91273270179092e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999892 y[1] (closed_form) = 14.88844029907262 y[1] (numeric) = 14.88844029907277 absolute error = 1.49213974509621e-13 relative error = 1.002213606746406e-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) = 14.90333618607386 y[1] (numeric) = 14.90333618607401 absolute error = 1.509903313490213e-13 relative error = 1.013131083294701e-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) = 14.91824697641254 y[1] (numeric) = 14.91824697641269 absolute error = 1.509903313490213e-13 relative error = 1.012118458608135e-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) = 14.93317268499943 y[1] (numeric) = 14.93317268499959 absolute error = 1.56319401867222e-13 relative error = 1.046792970017998e-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) = 14.94811332676026 y[1] (numeric) = 14.94811332676042 absolute error = 1.598721155460225e-13 relative error = 1.069513670730726e-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) = 14.96306891663566 y[1] (numeric) = 14.96306891663582 absolute error = 1.598721155460225e-13 relative error = 1.068444691638623e-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) = 14.97803946958122 y[1] (numeric) = 14.97803946958138 absolute error = 1.63424829224823e-13 relative error = 1.09109626501333e-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) = 14.9930250005675 y[1] (numeric) = 14.99302500056766 absolute error = 1.63424829224823e-13 relative error = 1.090005714114645e-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) = 15.00802552458002 y[1] (numeric) = 15.00802552458019 absolute error = 1.687538997430238e-13 relative error = 1.12442439191378e-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) = 15.02304105661933 y[1] (numeric) = 15.0230410566195 absolute error = 1.669775429036235e-13 relative error = 1.111476313446213e-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) = 15.03807161170094 y[1] (numeric) = 15.03807161170111 absolute error = 1.687538997430238e-13 relative error = 1.122177790480253e-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) = 15.05311720485542 y[1] (numeric) = 15.05311720485559 absolute error = 1.687538997430238e-13 relative error = 1.121056173591685e-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) = 15.06817785112835 y[1] (numeric) = 15.06817785112852 absolute error = 1.687538997430238e-13 relative error = 1.119935677759385e-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) = 15.0832535655804 y[1] (numeric) = 15.08325356558057 absolute error = 1.723066134218243e-13 relative error = 1.142370329270494e-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) = 15.09834436328726 y[1] (numeric) = 15.09834436328743 absolute error = 1.70530256582424e-13 relative error = 1.12946328735938e-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) = 15.11345025933975 y[1] (numeric) = 15.11345025933992 absolute error = 1.723066134218243e-13 relative error = 1.140087871830213e-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) = 15.12857126884376 y[1] (numeric) = 15.12857126884393 absolute error = 1.758593271006248e-13 relative error = 1.162431825024977e-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) = 15.14370740692029 y[1] (numeric) = 15.14370740692047 absolute error = 1.77635683940025e-13 relative error = 1.172999973961792e-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) = 15.1588586887055 y[1] (numeric) = 15.15885868870567 absolute error = 1.77635683940025e-13 relative error = 1.171827560292366e-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) = 15.17402512935065 y[1] (numeric) = 15.17402512935083 absolute error = 1.794120407794253e-13 relative error = 1.182362881635105e-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) = 15.1892067440222 y[1] (numeric) = 15.18920674402238 absolute error = 1.794120407794253e-13 relative error = 1.181181109737899e-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) = 15.20440354790176 y[1] (numeric) = 15.20440354790194 absolute error = 1.794120407794253e-13 relative error = 1.180000519021902e-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) = 15.21961555618614 y[1] (numeric) = 15.21961555618632 absolute error = 1.829647544582258e-13 relative error = 1.202164100550216e-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) = 15.23484278408734 y[1] (numeric) = 15.23484278408752 absolute error = 1.811883976188255e-13 relative error = 1.189302706871877e-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) = 15.25008524683259 y[1] (numeric) = 15.25008524683277 absolute error = 1.811883976188255e-13 relative error = 1.188113998618191e-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) = 15.26534295966436 y[1] (numeric) = 15.26534295966454 absolute error = 1.811883976188255e-13 relative error = 1.186926478478603e-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) = 15.28061593784036 y[1] (numeric) = 15.28061593784055 absolute error = 1.829647544582258e-13 relative error = 1.197365048650549e-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) = 15.29590419663358 y[1] (numeric) = 15.29590419663376 absolute error = 1.865174681370263e-13 relative error = 1.219394850669085e-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) = 15.31120775133226 y[1] (numeric) = 15.31120775133245 absolute error = 1.84741111297626e-13 relative error = 1.206574388500158e-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) = 15.32652661723997 y[1] (numeric) = 15.32652661724016 absolute error = 1.865174681370263e-13 relative error = 1.216958498132401e-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) = 15.34186080967558 y[1] (numeric) = 15.34186080967577 absolute error = 1.900701818158268e-13 relative error = 1.23889914120428e-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) = 15.35721034397328 y[1] (numeric) = 15.35721034397347 absolute error = 1.900701818158268e-13 relative error = 1.237660861306215e-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) = 15.37257523548259 y[1] (numeric) = 15.37257523548279 absolute error = 1.918465386552271e-13 relative error = 1.247979181864153e-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) = 15.38795549956843 y[1] (numeric) = 15.38795549956863 absolute error = 1.989519660128281e-13 relative error = 1.292907079295933e-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) = 15.40335115161105 y[1] (numeric) = 15.40335115161125 absolute error = 2.007283228522283e-13 relative error = 1.303147093619521e-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) = 15.4187622070061 y[1] (numeric) = 15.4187622070063 absolute error = 1.989519660128281e-13 relative error = 1.290323849228485e-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) = 15.43418868116464 y[1] (numeric) = 15.43418868116484 absolute error = 2.025046796916286e-13 relative error = 1.312052637653435e-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) = 15.44963058951316 y[1] (numeric) = 15.44963058951336 absolute error = 2.007283228522283e-13 relative error = 1.299243510640817e-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) = 15.46508794749354 y[1] (numeric) = 15.46508794749375 absolute error = 2.025046796916286e-13 relative error = 1.309431154734874e-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) = 15.48056077056317 y[1] (numeric) = 15.48056077056337 absolute error = 2.060573933704291e-13 relative error = 1.331071893482402e-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) = 15.49604907419485 y[1] (numeric) = 15.49604907419507 absolute error = 2.113864638886298e-13 relative error = 1.364131352943673e-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) = 15.5115528738769 y[1] (numeric) = 15.51155287387712 absolute error = 2.184918912462308e-13 relative error = 1.40857522791412e-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) = 15.52707218511312 y[1] (numeric) = 15.52707218511334 absolute error = 2.202682480856311e-13 relative error = 1.418607741753255e-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) = 15.54260702342282 y[1] (numeric) = 15.54260702342304 absolute error = 2.255973186038318e-13 relative error = 1.451476694121231e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.419999999999844 y[1] (closed_form) = 15.55815740434083 y[1] (numeric) = 15.55815740434106 absolute error = 2.255973186038318e-13 relative error = 1.450025942923605e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.429999999999843 y[1] (closed_form) = 15.57372334341755 y[1] (numeric) = 15.57372334341778 absolute error = 2.255973186038318e-13 relative error = 1.448576641752042e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999841 y[1] (closed_form) = 15.58930485621891 y[1] (numeric) = 15.58930485621913 absolute error = 2.273736754432321e-13 relative error = 1.458523504032496e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.44999999999984 y[1] (closed_form) = 15.60490195832642 y[1] (numeric) = 15.60490195832665 absolute error = 2.273736754432321e-13 relative error = 1.457065709547189e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.459999999999839 y[1] (closed_form) = 15.62051466533719 y[1] (numeric) = 15.62051466533742 absolute error = 2.273736754432321e-13 relative error = 1.455609372127713e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999838 y[1] (closed_form) = 15.63614299286393 y[1] (numeric) = 15.63614299286416 absolute error = 2.309263891220326e-13 relative error = 1.476875654228946e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999837 y[1] (closed_form) = 15.65178695653496 y[1] (numeric) = 15.65178695653519 absolute error = 2.309263891220326e-13 relative error = 1.475399516766459e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999836 y[1] (closed_form) = 15.66744657199426 y[1] (numeric) = 15.66744657199449 absolute error = 2.327027459614328e-13 relative error = 1.485262738201333e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999835 y[1] (closed_form) = 15.68312185490143 y[1] (numeric) = 15.68312185490166 absolute error = 2.344791028008331e-13 relative error = 1.495104769128294e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999834 y[1] (closed_form) = 15.69881282093176 y[1] (numeric) = 15.698812820932 absolute error = 2.380318164796336e-13 relative error = 1.516240872445193e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y[1] (closed_form) = 15.71451948577623 y[1] (numeric) = 15.71451948577647 absolute error = 2.398081733190338e-13 relative error = 1.526029310257261e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999831 y[1] (closed_form) = 15.73024186514149 y[1] (numeric) = 15.73024186514173 absolute error = 2.451372438372346e-13 relative error = 1.558381911345326e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.53999999999983 y[1] (closed_form) = 15.74597997474992 y[1] (numeric) = 15.74597997475017 absolute error = 2.433608869978343e-13 relative error = 1.545542972797407e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.549999999999829 y[1] (closed_form) = 15.76173383033964 y[1] (numeric) = 15.76173383033989 absolute error = 2.433608869978343e-13 relative error = 1.54399820233857e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999828 y[1] (closed_form) = 15.77750344766451 y[1] (numeric) = 15.77750344766475 absolute error = 2.433608869978343e-13 relative error = 1.542454975878064e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999827 y[1] (closed_form) = 15.79328884249414 y[1] (numeric) = 15.79328884249438 absolute error = 2.469136006766348e-13 relative error = 1.563408376425548e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999826 y[1] (closed_form) = 15.80909003061392 y[1] (numeric) = 15.80909003061417 absolute error = 2.504663143554353e-13 relative error = 1.584318350204935e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999825 y[1] (closed_form) = 15.82490702782506 y[1] (numeric) = 15.82490702782531 absolute error = 2.522426711948356e-13 relative error = 1.593959893421903e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999824 y[1] (closed_form) = 15.84073984994454 y[1] (numeric) = 15.84073984994479 absolute error = 2.522426711948356e-13 relative error = 1.592366730242835e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999823 y[1] (closed_form) = 15.85658851280519 y[1] (numeric) = 15.85658851280544 absolute error = 2.557953848736361e-13 relative error = 1.613180443366272e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y[1] (closed_form) = 15.87245303225568 y[1] (numeric) = 15.87245303225593 absolute error = 2.575717417130363e-13 relative error = 1.622759514169639e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.62999999999982 y[1] (closed_form) = 15.88833342416052 y[1] (numeric) = 15.88833342416077 absolute error = 2.557953848736361e-13 relative error = 1.609957306690594e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.639999999999819 y[1] (closed_form) = 15.90422970440011 y[1] (numeric) = 15.90422970440036 absolute error = 2.593480985524366e-13 relative error = 1.630686322901163e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999818 y[1] (closed_form) = 15.92014188887072 y[1] (numeric) = 15.92014188887098 absolute error = 2.611244553918368e-13 relative error = 1.640214372551421e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999817 y[1] (closed_form) = 15.93606999348456 y[1] (numeric) = 15.93606999348482 absolute error = 2.611244553918368e-13 relative error = 1.638574978012755e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999816 y[1] (closed_form) = 15.95201403416971 y[1] (numeric) = 15.95201403416998 absolute error = 2.629008122312371e-13 relative error = 1.648072849410083e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999815 y[1] (closed_form) = 15.96797402687023 y[1] (numeric) = 15.9679740268705 absolute error = 2.646771690706373e-13 relative error = 1.657550097621964e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999814 y[1] (closed_form) = 15.98394998754611 y[1] (numeric) = 15.98394998754637 absolute error = 2.664535259100376e-13 relative error = 1.667006754385773e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999813 y[1] (closed_form) = 15.9999419321733 y[1] (numeric) = 15.99994193217357 absolute error = 2.664535259100376e-13 relative error = 1.665340580857e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999812 y[1] (closed_form) = 16.01594987674376 y[1] (numeric) = 16.01594987674403 absolute error = 2.700062395888381e-13 relative error = 1.685858420304532e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y[1] (closed_form) = 16.03197383726544 y[1] (numeric) = 16.03197383726571 absolute error = 2.664535259100376e-13 relative error = 1.662013228157103e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.729999999999809 y[1] (closed_form) = 16.04801382976228 y[1] (numeric) = 16.04801382976255 absolute error = 2.700062395888381e-13 relative error = 1.682490072934076e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999808 y[1] (closed_form) = 16.0640698702743 y[1] (numeric) = 16.06406987027457 absolute error = 2.664535259100376e-13 relative error = 1.658692523512336e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999807 y[1] (closed_form) = 16.08014197485752 y[1] (numeric) = 16.08014197485778 absolute error = 2.629008122312371e-13 relative error = 1.634940864591257e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999806 y[1] (closed_form) = 16.09623015958406 y[1] (numeric) = 16.09623015958432 absolute error = 2.593480985524366e-13 relative error = 1.611235028209477e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999805 y[1] (closed_form) = 16.11233444054209 y[1] (numeric) = 16.11233444054236 absolute error = 2.629008122312371e-13 relative error = 1.631674250564972e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999804 y[1] (closed_form) = 16.12845483383591 y[1] (numeric) = 16.12845483383618 absolute error = 2.629008122312371e-13 relative error = 1.630043391879655e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999803 y[1] (closed_form) = 16.14459135558591 y[1] (numeric) = 16.14459135558618 absolute error = 2.700062395888381e-13 relative error = 1.672425356838889e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999802 y[1] (closed_form) = 16.16074402192861 y[1] (numeric) = 16.16074402192888 absolute error = 2.664535259100376e-13 relative error = 1.648770165213217e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999801 y[1] (closed_form) = 16.17691284901668 y[1] (numeric) = 16.17691284901695 absolute error = 2.700062395888381e-13 relative error = 1.669083848747139e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y[1] (closed_form) = 16.19309785301895 y[1] (numeric) = 16.19309785301922 absolute error = 2.700062395888381e-13 relative error = 1.667415599162205e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999798 y[1] (closed_form) = 16.20929905012041 y[1] (numeric) = 16.20929905012068 absolute error = 2.700062395888381e-13 relative error = 1.66574901699301e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999797 y[1] (closed_form) = 16.22551645652229 y[1] (numeric) = 16.22551645652256 absolute error = 2.735589532676386e-13 relative error = 1.685979944001561e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999796 y[1] (closed_form) = 16.24175008844196 y[1] (numeric) = 16.24175008844223 absolute error = 2.700062395888381e-13 relative error = 1.662420848237169e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999795 y[1] (closed_form) = 16.25799996211308 y[1] (numeric) = 16.25799996211336 absolute error = 2.771116669464391e-13 relative error = 1.704463449330839e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999794 y[1] (closed_form) = 16.27426609378552 y[1] (numeric) = 16.27426609378579 absolute error = 2.735589532676386e-13 relative error = 1.680929583498082e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999793 y[1] (closed_form) = 16.29054849972541 y[1] (numeric) = 16.29054849972568 absolute error = 2.771116669464391e-13 relative error = 1.701057929087594e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999792 y[1] (closed_form) = 16.30684719621515 y[1] (numeric) = 16.30684719621543 absolute error = 2.806643806252396e-13 relative error = 1.72114435885793e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999791 y[1] (closed_form) = 16.32316219955345 y[1] (numeric) = 16.32316219955374 absolute error = 2.842170943040401e-13 relative error = 1.741188936490598e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.90999999999979 y[1] (closed_form) = 16.33949352605531 y[1] (numeric) = 16.3394935260556 absolute error = 2.913225216616411e-13 relative error = 1.782934833304912e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y[1] (closed_form) = 16.35584119205205 y[1] (numeric) = 16.35584119205234 absolute error = 2.842170943040401e-13 relative error = 1.737710038675066e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999787 y[1] (closed_form) = 16.37220521389136 y[1] (numeric) = 16.37220521389164 absolute error = 2.806643806252396e-13 relative error = 1.714273532236841e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999786 y[1] (closed_form) = 16.38858560793724 y[1] (numeric) = 16.38858560793752 absolute error = 2.842170943040401e-13 relative error = 1.734238091702004e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999785 y[1] (closed_form) = 16.40498239057009 y[1] (numeric) = 16.40498239057038 absolute error = 2.877698079828406e-13 relative error = 1.754161029445886e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999784 y[1] (closed_form) = 16.4213955781867 y[1] (numeric) = 16.42139557818699 absolute error = 2.877698079828406e-13 relative error = 1.752407745204668e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999783 y[1] (closed_form) = 16.43782518720026 y[1] (numeric) = 16.43782518720055 absolute error = 2.913225216616411e-13 relative error = 1.772269253042592e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999782 y[1] (closed_form) = 16.45427123404037 y[1] (numeric) = 16.45427123404066 absolute error = 2.913225216616411e-13 relative error = 1.770497869628872e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999781 y[1] (closed_form) = 16.47073373515309 y[1] (numeric) = 16.47073373515339 absolute error = 2.984279490192421e-13 relative error = 1.811867970291539e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.99999999999978 y[1] (closed_form) = 16.48721270700092 y[1] (numeric) = 16.48721270700122 absolute error = 2.984279490192421e-13 relative error = 1.81005700795333e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.009999999999779 y[1] (closed_form) = 16.50370816606283 y[1] (numeric) = 16.50370816606313 absolute error = 2.984279490192421e-13 relative error = 1.80824785567228e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y[1] (closed_form) = 16.52022012883428 y[1] (numeric) = 16.52022012883458 absolute error = 3.019806626980426e-13 relative error = 1.827945755825418e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999776 y[1] (closed_form) = 16.53674861182723 y[1] (numeric) = 16.53674861182754 absolute error = 3.126388037344441e-13 relative error = 1.890569972810991e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999775 y[1] (closed_form) = 16.55329363157018 y[1] (numeric) = 16.55329363157049 absolute error = 3.161915174132446e-13 relative error = 1.910142624487789e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999774 y[1] (closed_form) = 16.56985520460814 y[1] (numeric) = 16.56985520460844 absolute error = 3.090860900556436e-13 relative error = 1.865351786355294e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999773 y[1] (closed_form) = 16.58643334750268 y[1] (numeric) = 16.58643334750298 absolute error = 3.055333763768431e-13 relative error = 1.842067971911788e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999772 y[1] (closed_form) = 16.60302807683195 y[1] (numeric) = 16.60302807683225 absolute error = 3.055333763768431e-13 relative error = 1.840226824666928e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999771 y[1] (closed_form) = 16.61963940919068 y[1] (numeric) = 16.61963940919099 absolute error = 3.090860900556436e-13 relative error = 1.859764116691477e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.08999999999977 y[1] (closed_form) = 16.6362673611902 y[1] (numeric) = 16.63626736119052 absolute error = 3.161915174132446e-13 relative error = 1.900615748403213e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.099999999999769 y[1] (closed_form) = 16.65291194945848 y[1] (numeric) = 16.65291194945879 absolute error = 3.161915174132446e-13 relative error = 1.898716082645993e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999768 y[1] (closed_form) = 16.66957319064009 y[1] (numeric) = 16.66957319064041 absolute error = 3.197442310920451e-13 relative error = 1.918130880948892e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y[1] (closed_form) = 16.68625110139628 y[1] (numeric) = 16.6862511013966 absolute error = 3.197442310920451e-13 relative error = 1.916213708813775e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999765 y[1] (closed_form) = 16.70294569840496 y[1] (numeric) = 16.70294569840528 absolute error = 3.161915174132446e-13 relative error = 1.89302847008261e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999764 y[1] (closed_form) = 16.71965699836073 y[1] (numeric) = 16.71965699836105 absolute error = 3.197442310920451e-13 relative error = 1.912385111269891e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999763 y[1] (closed_form) = 16.7363850179749 y[1] (numeric) = 16.73638501797522 absolute error = 3.161915174132446e-13 relative error = 1.889246196676609e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999762 y[1] (closed_form) = 16.75312977397548 y[1] (numeric) = 16.7531297739758 absolute error = 3.232969447708456e-13 relative error = 1.929770431749768e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999761 y[1] (closed_form) = 16.76989128310722 y[1] (numeric) = 16.76989128310755 absolute error = 3.268496584496461e-13 relative error = 1.949026698693574e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.17999999999976 y[1] (closed_form) = 16.78666956213165 y[1] (numeric) = 16.78666956213198 absolute error = 3.268496584496461e-13 relative error = 1.947078646183473e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.189999999999759 y[1] (closed_form) = 16.80346462782704 y[1] (numeric) = 16.80346462782737 absolute error = 3.268496584496461e-13 relative error = 1.945132540752181e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999758 y[1] (closed_form) = 16.82027649698846 y[1] (numeric) = 16.82027649698878 absolute error = 3.232969447708456e-13 relative error = 1.922066767622574e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y[1] (closed_form) = 16.83710518642777 y[1] (numeric) = 16.8371051864281 absolute error = 3.304023721284466e-13 relative error = 1.962346665119018e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y[1] (closed_form) = 16.85395071297368 y[1] (numeric) = 16.853950712974 absolute error = 3.232969447708456e-13 relative error = 1.91822647565939e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999754 y[1] (closed_form) = 16.8708130934717 y[1] (numeric) = 16.87081309347202 absolute error = 3.232969447708456e-13 relative error = 1.916309207977344e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999753 y[1] (closed_form) = 16.88769234478422 y[1] (numeric) = 16.88769234478455 absolute error = 3.339550858072471e-13 relative error = 1.977505741987238e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999752 y[1] (closed_form) = 16.90458848379049 y[1] (numeric) = 16.90458848379083 absolute error = 3.375077994860476e-13 relative error = 1.996545493016158e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999751 y[1] (closed_form) = 16.92150152738666 y[1] (numeric) = 16.921501527387 absolute error = 3.375077994860476e-13 relative error = 1.994549945463214e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.26999999999975 y[1] (closed_form) = 16.93843149248577 y[1] (numeric) = 16.93843149248611 absolute error = 3.446132268436486e-13 relative error = 2.034504948091127e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.279999999999749 y[1] (closed_form) = 16.95537839601777 y[1] (numeric) = 16.95537839601812 absolute error = 3.481659405224491e-13 relative error = 2.053424774077712e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999748 y[1] (closed_form) = 16.97234225492959 y[1] (numeric) = 16.97234225492994 absolute error = 3.481659405224491e-13 relative error = 2.051372375673869e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999747 y[1] (closed_form) = 16.98932308618508 y[1] (numeric) = 16.98932308618543 absolute error = 3.481659405224491e-13 relative error = 2.049322028642573e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y[1] (closed_form) = 17.00632090676507 y[1] (numeric) = 17.00632090676541 absolute error = 3.481659405224491e-13 relative error = 2.047273730933477e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999744 y[1] (closed_form) = 17.02333573366738 y[1] (numeric) = 17.02333573366773 absolute error = 3.517186542012496e-13 relative error = 2.066097148666632e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999743 y[1] (closed_form) = 17.04036758390684 y[1] (numeric) = 17.04036758390719 absolute error = 3.517186542012496e-13 relative error = 2.064032084222277e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999742 y[1] (closed_form) = 17.05741647451531 y[1] (numeric) = 17.05741647451566 absolute error = 3.481659405224491e-13 relative error = 2.04114111326664e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999741 y[1] (closed_form) = 17.07448242254167 y[1] (numeric) = 17.07448242254203 absolute error = 3.517186542012496e-13 relative error = 2.059908145367334e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.35999999999974 y[1] (closed_form) = 17.09156544505188 y[1] (numeric) = 17.09156544505224 absolute error = 3.517186542012496e-13 relative error = 2.057849266832807e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.369999999999739 y[1] (closed_form) = 17.10866555912897 y[1] (numeric) = 17.10866555912932 absolute error = 3.517186542012496e-13 relative error = 2.055792446147718e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999738 y[1] (closed_form) = 17.12578278187303 y[1] (numeric) = 17.12578278187339 absolute error = 3.588240815588506e-13 relative error = 2.095227331381616e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999737 y[1] (closed_form) = 17.1429171304013 y[1] (numeric) = 17.14291713040166 absolute error = 3.623767952376511e-13 relative error = 2.11385724192186e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999736 y[1] (closed_form) = 17.16006862184813 y[1] (numeric) = 17.1600686218485 absolute error = 3.623767952376511e-13 relative error = 2.111744441256338e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = 17.17723727336502 y[1] (numeric) = 17.17723727336538 absolute error = 3.623767952376511e-13 relative error = 2.109633752335434e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999733 y[1] (closed_form) = 17.1944231021206 y[1] (numeric) = 17.19442310212098 absolute error = 3.730349362740526e-13 relative error = 2.169511207549882e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999732 y[1] (closed_form) = 17.21162612530073 y[1] (numeric) = 17.21162612530111 absolute error = 3.765876499528531e-13 relative error = 2.187984140552979e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999731 y[1] (closed_form) = 17.22884636010841 y[1] (numeric) = 17.22884636010879 absolute error = 3.765876499528531e-13 relative error = 2.185797250039923e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.44999999999973 y[1] (closed_form) = 17.24608382376389 y[1] (numeric) = 17.24608382376426 absolute error = 3.730349362740526e-13 relative error = 2.163012426972184e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.459999999999729 y[1] (closed_form) = 17.26333853350463 y[1] (numeric) = 17.263338533505 absolute error = 3.730349362740526e-13 relative error = 2.160850495691014e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999728 y[1] (closed_form) = 17.28061050658534 y[1] (numeric) = 17.28061050658572 absolute error = 3.801403636316536e-13 relative error = 2.19980864383691e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999727 y[1] (closed_form) = 17.297899760278 y[1] (numeric) = 17.29789976027838 absolute error = 3.836930773104541e-13 relative error = 2.218148345335813e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999726 y[1] (closed_form) = 17.31520631187186 y[1] (numeric) = 17.31520631187225 absolute error = 3.836930773104541e-13 relative error = 2.215931305695051e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999725 y[1] (closed_form) = 17.33253017867348 y[1] (numeric) = 17.33253017867385 absolute error = 3.765876499528531e-13 relative error = 2.172721732319377e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = 17.34987137800671 y[1] (numeric) = 17.34987137800709 absolute error = 3.801403636316536e-13 relative error = 2.191026984289534e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999722 y[1] (closed_form) = 17.36722992721278 y[1] (numeric) = 17.36722992721316 absolute error = 3.872457909892546e-13 relative error = 2.229749894555595e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999721 y[1] (closed_form) = 17.38460584365021 y[1] (numeric) = 17.3846058436506 absolute error = 3.836930773104541e-13 relative error = 2.207085284309735e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.53999999999972 y[1] (closed_form) = 17.40199914469494 y[1] (numeric) = 17.40199914469533 absolute error = 3.943512183468556e-13 relative error = 2.266125949483654e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.549999999999719 y[1] (closed_form) = 17.41940984774027 y[1] (numeric) = 17.41940984774066 absolute error = 3.943512183468556e-13 relative error = 2.263860956219552e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999718 y[1] (closed_form) = 17.43683797019689 y[1] (numeric) = 17.43683797019728 absolute error = 3.979039320256561e-13 relative error = 2.281972985616745e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999717 y[1] (closed_form) = 17.45428352949294 y[1] (numeric) = 17.45428352949333 absolute error = 3.979039320256561e-13 relative error = 2.279692153237387e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999716 y[1] (closed_form) = 17.47174654307397 y[1] (numeric) = 17.47174654307437 absolute error = 4.014566457044566e-13 relative error = 2.297747650555287e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999715 y[1] (closed_form) = 17.489227028403 y[1] (numeric) = 17.4892270284034 absolute error = 4.014566457044566e-13 relative error = 2.295451051395694e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999714 y[1] (closed_form) = 17.50672500296051 y[1] (numeric) = 17.50672500296091 absolute error = 4.014566457044566e-13 relative error = 2.293156747687346e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = 17.52424048424449 y[1] (numeric) = 17.52424048424489 absolute error = 4.014566457044566e-13 relative error = 2.290864737135935e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999711 y[1] (closed_form) = 17.54177348977041 y[1] (numeric) = 17.54177348977081 absolute error = 4.014566457044566e-13 relative error = 2.288575017449452e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.62999999999971 y[1] (closed_form) = 17.55932403707128 y[1] (numeric) = 17.55932403707169 absolute error = 4.121147867408581e-13 relative error = 2.346985486860431e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.639999999999709 y[1] (closed_form) = 17.57689214369766 y[1] (numeric) = 17.57689214369806 absolute error = 4.085620730620576e-13 relative error = 2.324427263488392e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999708 y[1] (closed_form) = 17.59447782721764 y[1] (numeric) = 17.59447782721804 absolute error = 4.050093593832571e-13 relative error = 2.301911789372522e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999707 y[1] (closed_form) = 17.61208110521692 y[1] (numeric) = 17.61208110521732 absolute error = 4.050093593832571e-13 relative error = 2.299611028155488e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999706 y[1] (closed_form) = 17.62970199529876 y[1] (numeric) = 17.62970199529917 absolute error = 4.085620730620576e-13 relative error = 2.317464431168531e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999705 y[1] (closed_form) = 17.64734051508407 y[1] (numeric) = 17.64734051508448 absolute error = 4.085620730620576e-13 relative error = 2.315148125083431e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999704 y[1] (closed_form) = 17.66499668221137 y[1] (numeric) = 17.66499668221179 absolute error = 4.156675004196586e-13 relative error = 2.353057336479634e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999703 y[1] (closed_form) = 17.68267051433683 y[1] (numeric) = 17.68267051433724 absolute error = 4.156675004196586e-13 relative error = 2.350705455279744e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.709999999999702 y[1] (closed_form) = 17.70036202913427 y[1] (numeric) = 17.70036202913468 absolute error = 4.121147867408581e-13 relative error = 2.328284506624946e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7199999999997 y[1] (closed_form) = 17.71807124429521 y[1] (numeric) = 17.71807124429563 absolute error = 4.121147867408581e-13 relative error = 2.325957385872624e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.729999999999699 y[1] (closed_form) = 17.73579817752888 y[1] (numeric) = 17.7357981775293 absolute error = 4.192202140984591e-13 relative error = 2.363695221958535e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999698 y[1] (closed_form) = 17.7535428465622 y[1] (numeric) = 17.75354284656262 absolute error = 4.227729277772596e-13 relative error = 2.381344002327544e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999697 y[1] (closed_form) = 17.77130526913984 y[1] (numeric) = 17.77130526914027 absolute error = 4.227729277772596e-13 relative error = 2.378963848600427e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999696 y[1] (closed_form) = 17.78908546302424 y[1] (numeric) = 17.78908546302466 absolute error = 4.192202140984591e-13 relative error = 2.356614762292504e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999695 y[1] (closed_form) = 17.80688344599559 y[1] (numeric) = 17.80688344599601 absolute error = 4.192202140984591e-13 relative error = 2.354259325444922e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999694 y[1] (closed_form) = 17.82469923585186 y[1] (numeric) = 17.82469923585229 absolute error = 4.263256414560601e-13 relative error = 2.391769060532401e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999693 y[1] (closed_form) = 17.84253285040885 y[1] (numeric) = 17.84253285040928 absolute error = 4.298783551348606e-13 relative error = 2.409289974349187e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999692 y[1] (closed_form) = 17.86038430750018 y[1] (numeric) = 17.86038430750061 absolute error = 4.298783551348606e-13 relative error = 2.406881888618377e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.809999999999691 y[1] (closed_form) = 17.87825362497731 y[1] (numeric) = 17.87825362497774 absolute error = 4.298783551348606e-13 relative error = 2.404476209769656e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.819999999999689 y[1] (closed_form) = 17.89614082070955 y[1] (numeric) = 17.89614082070998 absolute error = 4.334310688136611e-13 relative error = 2.421924777838647e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999688 y[1] (closed_form) = 17.91404591258411 y[1] (numeric) = 17.91404591258454 absolute error = 4.298783551348606e-13 relative error = 2.399672063098171e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999687 y[1] (closed_form) = 17.93196891850607 y[1] (numeric) = 17.93196891850651 absolute error = 4.405364961712621e-13 relative error = 2.4567101257722e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999686 y[1] (closed_form) = 17.94990985639844 y[1] (numeric) = 17.94990985639888 absolute error = 4.369837824924616e-13 relative error = 2.43446226743414e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999685 y[1] (closed_form) = 17.96786874420216 y[1] (numeric) = 17.9678687442026 absolute error = 4.369837824924616e-13 relative error = 2.432029021992198e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999684 y[1] (closed_form) = 17.98584559987613 y[1] (numeric) = 17.98584559987657 absolute error = 4.440892098500626e-13 relative error = 2.469103870507601e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999683 y[1] (closed_form) = 18.00384044139719 y[1] (numeric) = 18.00384044139764 absolute error = 4.440892098500626e-13 relative error = 2.466636000777615e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999682 y[1] (closed_form) = 18.0218532867602 y[1] (numeric) = 18.02185328676065 absolute error = 4.476419235288631e-13 relative error = 2.483883962465306e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.899999999999681 y[1] (closed_form) = 18.03988415397799 y[1] (numeric) = 18.03988415397845 absolute error = 4.547473508864641e-13 relative error = 2.520788642571118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.90999999999968 y[1] (closed_form) = 18.05793306108145 y[1] (numeric) = 18.0579330610819 absolute error = 4.583000645652646e-13 relative error = 2.537943091355208e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999678 y[1] (closed_form) = 18.07600002611947 y[1] (numeric) = 18.07600002611993 absolute error = 4.618527782440651e-13 relative error = 2.555060730121138e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999677 y[1] (closed_form) = 18.09408506715901 y[1] (numeric) = 18.09408506715948 absolute error = 4.654054919228656e-13 relative error = 2.572141615314843e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999676 y[1] (closed_form) = 18.11218820228514 y[1] (numeric) = 18.11218820228562 absolute error = 4.760636329592671e-13 relative error = 2.628415891235075e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999675 y[1] (closed_form) = 18.13030944960098 y[1] (numeric) = 18.13030944960145 absolute error = 4.725109192804666e-13 relative error = 2.606193350389097e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999674 y[1] (closed_form) = 18.14844882722777 y[1] (numeric) = 18.14844882722825 absolute error = 4.725109192804666e-13 relative error = 2.603588459701126e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999673 y[1] (closed_form) = 18.16660635330491 y[1] (numeric) = 18.16660635330539 absolute error = 4.725109192804666e-13 relative error = 2.600986172601831e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999672 y[1] (closed_form) = 18.18478204598992 y[1] (numeric) = 18.18478204599039 absolute error = 4.760636329592671e-13 relative error = 2.617923226988844e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999671 y[1] (closed_form) = 18.20297592345848 y[1] (numeric) = 18.20297592345896 absolute error = 4.796163466380676e-13 relative error = 2.634823825811789e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.99999999999967 y[1] (closed_form) = 18.22118800390449 y[1] (numeric) = 18.22118800390497 absolute error = 4.760636329592671e-13 relative error = 2.612692612892501e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999673 y[1] (closed_form) = 18.23941830554002 y[1] (numeric) = 18.2394183055405 absolute error = 4.725109192804666e-13 relative error = 2.590603008084674e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999676 y[1] (closed_form) = 18.25766684659538 y[1] (numeric) = 18.25766684659585 absolute error = 4.689582056016661e-13 relative error = 2.568554950322777e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.02999999999968 y[1] (closed_form) = 18.27593364531912 y[1] (numeric) = 18.27593364531958 absolute error = 4.654054919228656e-13 relative error = 2.546548378621776e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999683 y[1] (closed_form) = 18.29421871997802 y[1] (numeric) = 18.29421871997848 absolute error = 4.654054919228656e-13 relative error = 2.544003103093024e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999686 y[1] (closed_form) = 18.31252208885716 y[1] (numeric) = 18.31252208885762 absolute error = 4.583000645652646e-13 relative error = 2.502659449864265e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.05999999999969 y[1] (closed_form) = 18.33084377025992 y[1] (numeric) = 18.33084377026037 absolute error = 4.476419235288631e-13 relative error = 2.442014831063698e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999693 y[1] (closed_form) = 18.34918378250797 y[1] (numeric) = 18.34918378250841 absolute error = 4.405364961712621e-13 relative error = 2.400850639423099e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999696 y[1] (closed_form) = 18.36754214394134 y[1] (numeric) = 18.36754214394177 absolute error = 4.334310688136611e-13 relative error = 2.359766295441066e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.0899999999997 y[1] (closed_form) = 18.38591887291838 y[1] (numeric) = 18.38591887291881 absolute error = 4.263256414560601e-13 relative error = 2.318761680625157e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999703 y[1] (closed_form) = 18.40431398781583 y[1] (numeric) = 18.40431398781624 absolute error = 4.156675004196586e-13 relative error = 2.258532975990532e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999706 y[1] (closed_form) = 18.4227275070288 y[1] (numeric) = 18.42272750702921 absolute error = 4.121147867408581e-13 relative error = 2.236991165307225e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.11999999999971 y[1] (closed_form) = 18.44115944897081 y[1] (numeric) = 18.44115944897121 absolute error = 4.014566457044566e-13 relative error = 2.176959896775155e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999713 y[1] (closed_form) = 18.45960983207381 y[1] (numeric) = 18.4596098320742 absolute error = 3.943512183468556e-13 relative error = 2.136292272340802e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999716 y[1] (closed_form) = 18.47807867478817 y[1] (numeric) = 18.47807867478856 absolute error = 3.836930773104541e-13 relative error = 2.076477127646241e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.14999999999972 y[1] (closed_form) = 18.49656599558275 y[1] (numeric) = 18.49656599558313 absolute error = 3.801403636316536e-13 relative error = 2.055194265370321e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999723 y[1] (closed_form) = 18.51507181294487 y[1] (numeric) = 18.51507181294525 absolute error = 3.765876499528531e-13 relative error = 2.033951873141322e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999726 y[1] (closed_form) = 18.53359614538035 y[1] (numeric) = 18.53359614538071 absolute error = 3.659295089164516e-13 relative error = 1.974411798153175e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.17999999999973 y[1] (closed_form) = 18.55213901141351 y[1] (numeric) = 18.55213901141387 absolute error = 3.588240815588506e-13 relative error = 1.93413859899442e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999733 y[1] (closed_form) = 18.57070042958723 y[1] (numeric) = 18.57070042958759 absolute error = 3.517186542012496e-13 relative error = 1.893943933535668e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999736 y[1] (closed_form) = 18.58928041846293 y[1] (numeric) = 18.58928041846328 absolute error = 3.446132268436486e-13 relative error = 1.853827685020974e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.20999999999974 y[1] (closed_form) = 18.6078789966206 y[1] (numeric) = 18.60787899662094 absolute error = 3.375077994860476e-13 relative error = 1.813789736849336e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999743 y[1] (closed_form) = 18.62649618265881 y[1] (numeric) = 18.62649618265914 absolute error = 3.268496584496461e-13 relative error = 1.75475653200918e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999746 y[1] (closed_form) = 18.64513199519476 y[1] (numeric) = 18.64513199519508 absolute error = 3.232969447708456e-13 relative error = 1.733948275904756e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.23999999999975 y[1] (closed_form) = 18.66378645286426 y[1] (numeric) = 18.66378645286457 absolute error = 3.161915174132446e-13 relative error = 1.694144530702771e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999753 y[1] (closed_form) = 18.68245957432176 y[1] (numeric) = 18.68245957432207 absolute error = 3.055333763768431e-13 relative error = 1.635402314997034e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999756 y[1] (closed_form) = 18.7011513782404 y[1] (numeric) = 18.70115137824071 absolute error = 3.055333763768431e-13 relative error = 1.633767730110695e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.26999999999976 y[1] (closed_form) = 18.71986188331197 y[1] (numeric) = 18.71986188331227 absolute error = 2.948752353404416e-13 relative error = 1.57519984484133e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999763 y[1] (closed_form) = 18.73859110824699 y[1] (numeric) = 18.73859110824728 absolute error = 2.877698079828406e-13 relative error = 1.535706747217463e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999766 y[1] (closed_form) = 18.75733907177468 y[1] (numeric) = 18.75733907177496 absolute error = 2.771116669464391e-13 relative error = 1.477350629991148e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.29999999999977 y[1] (closed_form) = 18.776105792643 y[1] (numeric) = 18.77610579264327 absolute error = 2.700062395888381e-13 relative error = 1.438031094257223e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999773 y[1] (closed_form) = 18.79489128961868 y[1] (numeric) = 18.79489128961894 absolute error = 2.629008122312371e-13 relative error = 1.398788682414193e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999776 y[1] (closed_form) = 18.81369558148721 y[1] (numeric) = 18.81369558148747 absolute error = 2.593480985524366e-13 relative error = 1.37850693623233e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.32999999999978 y[1] (closed_form) = 18.8325186870529 y[1] (numeric) = 18.83251868705315 absolute error = 2.486899575160351e-13 relative error = 1.320534770991657e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999783 y[1] (closed_form) = 18.85136062513884 y[1] (numeric) = 18.85136062513908 absolute error = 2.380318164796336e-13 relative error = 1.262677114999387e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999786 y[1] (closed_form) = 18.87022141458698 y[1] (numeric) = 18.87022141458721 absolute error = 2.309263891220326e-13 relative error = 1.223760887847998e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.35999999999979 y[1] (closed_form) = 18.8891010742581 y[1] (numeric) = 18.88910107425832 absolute error = 2.238209617644316e-13 relative error = 1.184921192832478e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999793 y[1] (closed_form) = 18.90799962303187 y[1] (numeric) = 18.90799962303209 absolute error = 2.131628207280301e-13 relative error = 1.127368441812194e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.379999999999797 y[1] (closed_form) = 18.92691707980684 y[1] (numeric) = 18.92691707980705 absolute error = 2.096101070492296e-13 relative error = 1.107470942918976e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.3899999999998 y[1] (closed_form) = 18.94585346350047 y[1] (numeric) = 18.94585346350068 absolute error = 2.060573933704291e-13 relative error = 1.087612092890945e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999803 y[1] (closed_form) = 18.96480879304914 y[1] (numeric) = 18.96480879304934 absolute error = 1.953992523340276e-13 relative error = 1.030325454194107e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.409999999999807 y[1] (closed_form) = 18.98378308740818 y[1] (numeric) = 18.98378308740838 absolute error = 1.918465386552271e-13 relative error = 1.010581177481308e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.41999999999981 y[1] (closed_form) = 19.0027763655519 y[1] (numeric) = 19.00277636555209 absolute error = 1.882938249764265e-13 relative error = 9.908753402885081e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999813 y[1] (closed_form) = 19.02178864647356 y[1] (numeric) = 19.02178864647374 absolute error = 1.84741111297626e-13 relative error = 9.712078854996378e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = 19.04081994918545 y[1] (numeric) = 19.04081994918563 absolute error = 1.740829702612245e-13 relative error = 9.142619421107e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.44999999999982 y[1] (closed_form) = 19.05987029271888 y[1] (numeric) = 19.05987029271905 absolute error = 1.669775429036235e-13 relative error = 8.760686213452938e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999823 y[1] (closed_form) = 19.07893969612419 y[1] (numeric) = 19.07893969612436 absolute error = 1.63424829224823e-13 relative error = 8.565718631524481e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 19.09802817847079 y[1] (numeric) = 19.09802817847095 absolute error = 1.598721155460225e-13 relative error = 8.371132037926638e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.47999999999983 y[1] (closed_form) = 19.11713575884716 y[1] (numeric) = 19.11713575884731 absolute error = 1.527666881884215e-13 relative error = 7.991086641612781e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999833 y[1] (closed_form) = 19.13626245636088 y[1] (numeric) = 19.13626245636102 absolute error = 1.4210854715202e-13 relative error = 7.426139115519042e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 19.15540829013865 y[1] (numeric) = 19.15540829013878 absolute error = 1.314504061156185e-13 relative error = 6.862312936618021e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.50999999999984 y[1] (closed_form) = 19.17457327932631 y[1] (numeric) = 19.17457327932643 absolute error = 1.20792265079217e-13 relative error = 6.299606427719211e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999843 y[1] (closed_form) = 19.19375744308884 y[1] (numeric) = 19.19375744308896 absolute error = 1.172395514004165e-13 relative error = 6.108212617984884e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.529999999999847 y[1] (closed_form) = 19.21296080061041 y[1] (numeric) = 19.21296080061052 absolute error = 1.101341240428155e-13 relative error = 5.732282764003581e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.53999999999985 y[1] (closed_form) = 19.23218337109439 y[1] (numeric) = 19.23218337109449 absolute error = 9.947598300641403e-14 relative error = 5.172370764513641e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999853 y[1] (closed_form) = 19.25142517376334 y[1] (numeric) = 19.25142517376344 absolute error = 9.237055564881302e-14 relative error = 4.798115194853186e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999857 y[1] (closed_form) = 19.27068622785907 y[1] (numeric) = 19.27068622785916 absolute error = 8.526512829121202e-14 relative error = 4.424602594999793e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.56999999999986 y[1] (closed_form) = 19.28996655264264 y[1] (numeric) = 19.28996655264271 absolute error = 7.460698725481052e-14 relative error = 3.867657678472734e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999863 y[1] (closed_form) = 19.30926616739436 y[1] (numeric) = 19.30926616739443 absolute error = 6.750155989720952e-14 relative error = 3.495811767885446e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999867 y[1] (closed_form) = 19.32858509141386 y[1] (numeric) = 19.32858509141392 absolute error = 6.394884621840902e-14 relative error = 3.308511508523009e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.59999999999987 y[1] (closed_form) = 19.34792334402006 y[1] (numeric) = 19.34792334402012 absolute error = 6.039613253960852e-14 relative error = 3.121582170123461e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999873 y[1] (closed_form) = 19.36728094455123 y[1] (numeric) = 19.36728094455128 absolute error = 5.329070518200751e-14 relative error = 2.751584248433195e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999877 y[1] (closed_form) = 19.38665791236494 y[1] (numeric) = 19.386657912365 absolute error = 5.684341886080801e-14 relative error = 2.932089642152963e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.62999999999988 y[1] (closed_form) = 19.40605426683819 y[1] (numeric) = 19.40605426683823 absolute error = 4.618527782440651e-14 relative error = 2.379941702179494e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999883 y[1] (closed_form) = 19.42547002736731 y[1] (numeric) = 19.42547002736736 absolute error = 4.263256414560601e-14 relative error = 2.19467349235533e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999887 y[1] (closed_form) = 19.44490521336809 y[1] (numeric) = 19.44490521336813 absolute error = 3.907985046680551e-14 relative error = 2.009773256181196e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.65999999999989 y[1] (closed_form) = 19.4643598442757 y[1] (numeric) = 19.46435984427574 absolute error = 3.552713678800501e-14 relative error = 1.825240443160694e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999893 y[1] (closed_form) = 19.48383393954477 y[1] (numeric) = 19.4838339395448 absolute error = 2.842170943040401e-14 relative error = 1.4587328920269e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999897 y[1] (closed_form) = 19.50332751864941 y[1] (numeric) = 19.50332751864944 absolute error = 2.131628207280301e-14 relative error = 1.092956166193692e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.6899999999999 y[1] (closed_form) = 19.5228406010832 y[1] (numeric) = 19.52284060108321 absolute error = 1.06581410364015e-14 relative error = 5.459318781617339e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999903 y[1] (closed_form) = 19.54237320635921 y[1] (numeric) = 19.54237320635921 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999907 y[1] (closed_form) = 19.56192535401005 y[1] (numeric) = 19.56192535401005 absolute error = 3.552713678800501e-15 relative error = 1.81613701847207e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.71999999999991 y[1] (closed_form) = 19.58149706358788 y[1] (numeric) = 19.58149706358787 absolute error = 1.06581410364015e-14 relative error = 5.442965367658478e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999913 y[1] (closed_form) = 19.60108835466441 y[1] (numeric) = 19.60108835466439 absolute error = 1.77635683940025e-14 relative error = 9.06254187144428e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999917 y[1] (closed_form) = 19.62069924683092 y[1] (numeric) = 19.62069924683089 absolute error = 3.197442310920451e-14 relative error = 1.62962709468007e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.74999999999992 y[1] (closed_form) = 19.64032975969832 y[1] (numeric) = 19.64032975969828 absolute error = 3.907985046680551e-14 relative error = 1.989775678155711e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999923 y[1] (closed_form) = 19.65997991289711 y[1] (numeric) = 19.65997991289706 absolute error = 4.263256414560601e-14 relative error = 2.168494796764197e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999927 y[1] (closed_form) = 19.67964972607745 y[1] (numeric) = 19.6796497260774 absolute error = 4.973799150320701e-14 relative error = 2.527381950162423e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.77999999999993 y[1] (closed_form) = 19.69933921890916 y[1] (numeric) = 19.69933921890911 absolute error = 5.329070518200751e-14 relative error = 2.705202676587975e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999933 y[1] (closed_form) = 19.71904841108173 y[1] (numeric) = 19.71904841108167 absolute error = 6.394884621840902e-14 relative error = 3.242998591274363e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999937 y[1] (closed_form) = 19.73877732230435 y[1] (numeric) = 19.73877732230428 absolute error = 7.105427357601002e-14 relative error = 3.599730237380021e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.80999999999994 y[1] (closed_form) = 19.75852597230594 y[1] (numeric) = 19.75852597230586 absolute error = 7.815970093361102e-14 relative error = 3.955745537048749e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999943 y[1] (closed_form) = 19.77829438083515 y[1] (numeric) = 19.77829438083507 absolute error = 8.171241461241152e-14 relative error = 4.131418667303765e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999947 y[1] (closed_form) = 19.79808256766039 y[1] (numeric) = 19.7980825676603 absolute error = 9.237055564881302e-14 relative error = 4.665631398047492e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.83999999999995 y[1] (closed_form) = 19.81789055256985 y[1] (numeric) = 19.81789055256975 absolute error = 9.947598300641403e-14 relative error = 5.019504106279095e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999953 y[1] (closed_form) = 19.83771835537151 y[1] (numeric) = 19.8377183553714 absolute error = 1.030286966852145e-13 relative error = 5.19357593648451e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999957 y[1] (closed_form) = 19.85756599589318 y[1] (numeric) = 19.85756599589307 absolute error = 1.101341240428155e-13 relative error = 5.546204608640999e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.86999999999996 y[1] (closed_form) = 19.8774334939825 y[1] (numeric) = 19.87743349398238 absolute error = 1.13686837721616e-13 relative error = 5.719392181894734e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999963 y[1] (closed_form) = 19.89732086950697 y[1] (numeric) = 19.89732086950685 absolute error = 1.172395514004165e-13 relative error = 5.892228012470183e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999967 y[1] (closed_form) = 19.91722814235396 y[1] (numeric) = 19.91722814235384 absolute error = 1.243449787580175e-13 relative error = 6.243086531383254e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.89999999999997 y[1] (closed_form) = 19.93715533243077 y[1] (numeric) = 19.93715533243063 absolute error = 1.314504061156185e-13 relative error = 6.593237797660872e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999973 y[1] (closed_form) = 19.95710245966456 y[1] (numeric) = 19.95710245966442 absolute error = 1.35003119794419e-13 relative error = 6.76466536498847e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999977 y[1] (closed_form) = 19.97706954400248 y[1] (numeric) = 19.97706954400234 absolute error = 1.385558334732195e-13 relative error = 6.935743661903447e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.92999999999998 y[1] (closed_form) = 19.9970566054116 y[1] (numeric) = 19.99705660541146 absolute error = 1.385558334732195e-13 relative error = 6.928811384957703e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 20.017063663879 y[1] (numeric) = 20.01706366387885 absolute error = 1.4210854715202e-13 relative error = 7.099370294178383e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999987 y[1] (closed_form) = 20.03709073941172 y[1] (numeric) = 20.03709073941157 absolute error = 1.527666881884215e-13 relative error = 7.624195057815398e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.95999999999999 y[1] (closed_form) = 20.05713785203687 y[1] (numeric) = 20.0571378520367 absolute error = 1.669775429036235e-13 relative error = 8.325093247871677e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 20.07720502180153 y[1] (numeric) = 20.07720502180134 absolute error = 1.811883976188255e-13 relative error = 9.024582725637153e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999997 y[1] (closed_form) = 20.09729226877288 y[1] (numeric) = 20.09729226877269 absolute error = 1.918465386552271e-13 relative error = 9.545889868622634e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (closed_form) = 20.11739961303818 y[1] (numeric) = 20.11739961303799 absolute error = 1.953992523340276e-13 relative error = 9.712947801036292e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.000000000000004 y[1] (closed_form) = 20.13752707470477 y[1] (numeric) = 20.13752707470457 absolute error = 2.060573933704291e-13 relative error = 1.023250732853204e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.010000000000007 y[1] (closed_form) = 20.15767467390011 y[1] (numeric) = 20.1576746738999 absolute error = 2.131628207280301e-13 relative error = 1.057477234732984e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.02000000000001 y[1] (closed_form) = 20.17784243077181 y[1] (numeric) = 20.17784243077159 absolute error = 2.202682480856311e-13 relative error = 1.091634295596022e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.030000000000014 y[1] (closed_form) = 20.19803036548762 y[1] (numeric) = 20.19803036548739 absolute error = 2.273736754432321e-13 relative error = 1.125722020062637e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.040000000000017 y[1] (closed_form) = 20.21823849823548 y[1] (numeric) = 20.21823849823525 absolute error = 2.273736754432321e-13 relative error = 1.12459686071601e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.05000000000002 y[1] (closed_form) = 20.23846684922352 y[1] (numeric) = 20.23846684922329 absolute error = 2.344791028008331e-13 relative error = 1.158581351777786e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.060000000000024 y[1] (closed_form) = 20.25871543868009 y[1] (numeric) = 20.25871543867985 absolute error = 2.380318164796336e-13 relative error = 1.174960066940661e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.070000000000027 y[1] (closed_form) = 20.2789842868538 y[1] (numeric) = 20.27898428685355 absolute error = 2.486899575160351e-13 relative error = 1.226343262553108e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.08000000000003 y[1] (closed_form) = 20.29927341401348 y[1] (numeric) = 20.29927341401322 absolute error = 2.593480985524366e-13 relative error = 1.277622569354612e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.090000000000034 y[1] (closed_form) = 20.31958284044826 y[1] (numeric) = 20.319582840448 absolute error = 2.664535259100376e-13 relative error = 1.311313957585949e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.100000000000037 y[1] (closed_form) = 20.33991258646758 y[1] (numeric) = 20.3399125864673 absolute error = 2.771116669464391e-13 relative error = 1.362403431029518e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.11000000000004 y[1] (closed_form) = 20.36026267240118 y[1] (numeric) = 20.36026267240089 absolute error = 2.877698079828406e-13 relative error = 1.413389466595239e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.120000000000044 y[1] (closed_form) = 20.38063311859915 y[1] (numeric) = 20.38063311859886 absolute error = 2.948752353404416e-13 relative error = 1.446840407873991e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.130000000000047 y[1] (closed_form) = 20.40102394543194 y[1] (numeric) = 20.40102394543164 absolute error = 2.984279490192421e-13 relative error = 1.462808679689159e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.14000000000005 y[1] (closed_form) = 20.42143517329037 y[1] (numeric) = 20.42143517329006 absolute error = 3.090860900556436e-13 relative error = 1.513537552247571e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.150000000000054 y[1] (closed_form) = 20.44186682258568 y[1] (numeric) = 20.44186682258536 absolute error = 3.161915174132446e-13 relative error = 1.546783961354708e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.160000000000057 y[1] (closed_form) = 20.46231891374951 y[1] (numeric) = 20.46231891374919 absolute error = 3.232969447708456e-13 relative error = 1.579962398854064e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.17000000000006 y[1] (closed_form) = 20.48279146723397 y[1] (numeric) = 20.48279146723364 absolute error = 3.304023721284466e-13 relative error = 1.613072967407722e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.180000000000064 y[1] (closed_form) = 20.50328450351159 y[1] (numeric) = 20.50328450351126 absolute error = 3.375077994860476e-13 relative error = 1.646115769540449e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.190000000000067 y[1] (closed_form) = 20.52379804307543 y[1] (numeric) = 20.52379804307509 absolute error = 3.410605131648481e-13 relative error = 1.661780692097188e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.20000000000007 y[1] (closed_form) = 20.54433210643902 y[1] (numeric) = 20.54433210643868 absolute error = 3.446132268436486e-13 relative error = 1.677412655997902e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.210000000000074 y[1] (closed_form) = 20.56488671413643 y[1] (numeric) = 20.56488671413608 absolute error = 3.552713678800501e-13 relative error = 1.727562970895601e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.220000000000077 y[1] (closed_form) = 20.58546188672227 y[1] (numeric) = 20.58546188672191 absolute error = 3.659295089164516e-13 relative error = 1.777611359560885e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.23000000000008 y[1] (closed_form) = 20.60605764477171 y[1] (numeric) = 20.60605764477135 absolute error = 3.623767952376511e-13 relative error = 1.758593523733034e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.240000000000084 y[1] (closed_form) = 20.62667400888051 y[1] (numeric) = 20.62667400888014 absolute error = 3.765876499528531e-13 relative error = 1.82573133114296e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.250000000000087 y[1] (closed_form) = 20.64731099966505 y[1] (numeric) = 20.64731099966466 absolute error = 3.872457909892546e-13 relative error = 1.875526508006475e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.26000000000009 y[1] (closed_form) = 20.6679686377623 y[1] (numeric) = 20.6679686377619 absolute error = 3.943512183468556e-13 relative error = 1.908030853241858e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.270000000000094 y[1] (closed_form) = 20.68864694382991 y[1] (numeric) = 20.68864694382951 absolute error = 4.014566457044566e-13 relative error = 1.940468348628209e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.280000000000097 y[1] (closed_form) = 20.70934593854619 y[1] (numeric) = 20.70934593854578 absolute error = 4.050093593832571e-13 relative error = 1.955683972758481e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.2900000000001 y[1] (closed_form) = 20.73006564261013 y[1] (numeric) = 20.73006564260972 absolute error = 4.085620730620576e-13 relative error = 1.970867242322034e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.300000000000104 y[1] (closed_form) = 20.75080607674144 y[1] (numeric) = 20.75080607674102 absolute error = 4.156675004196586e-13 relative error = 2.003139053405544e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.310000000000107 y[1] (closed_form) = 20.77156726168056 y[1] (numeric) = 20.77156726168014 absolute error = 4.263256414560601e-13 relative error = 2.052448118551683e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.32000000000011 y[1] (closed_form) = 20.79234921818868 y[1] (numeric) = 20.79234921818824 absolute error = 4.369837824924616e-13 relative error = 2.101656613723081e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.330000000000114 y[1] (closed_form) = 20.81315196704774 y[1] (numeric) = 20.81315196704729 absolute error = 4.511946372076636e-13 relative error = 2.167834251736662e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.340000000000117 y[1] (closed_form) = 20.8339755290605 y[1] (numeric) = 20.83397552906004 absolute error = 4.547473508864641e-13 relative error = 2.182720001049031e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.35000000000012 y[1] (closed_form) = 20.85481992505053 y[1] (numeric) = 20.85481992505007 absolute error = 4.618527782440651e-13 relative error = 2.214609284107478e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.360000000000124 y[1] (closed_form) = 20.87568517586222 y[1] (numeric) = 20.87568517586175 absolute error = 4.760636329592671e-13 relative error = 2.280469498120817e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.370000000000127 y[1] (closed_form) = 20.89657130236083 y[1] (numeric) = 20.89657130236035 absolute error = 4.867217739956686e-13 relative error = 2.329194425980688e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.38000000000013 y[1] (closed_form) = 20.91747832543248 y[1] (numeric) = 20.91747832543199 absolute error = 4.938272013532696e-13 relative error = 2.36083524825672e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.390000000000134 y[1] (closed_form) = 20.93840626598421 y[1] (numeric) = 20.9384062659837 absolute error = 5.009326287108706e-13 relative error = 2.392410493651888e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.400000000000137 y[1] (closed_form) = 20.95935514494393 y[1] (numeric) = 20.95935514494343 absolute error = 4.973799150320701e-13 relative error = 2.373068787624671e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.41000000000014 y[1] (closed_form) = 20.98032498326056 y[1] (numeric) = 20.98032498326005 absolute error = 5.080380560684716e-13 relative error = 2.421497552939799e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.420000000000144 y[1] (closed_form) = 21.00131580190391 y[1] (numeric) = 21.0013158019034 absolute error = 5.115907697472721e-13 relative error = 2.435993889968042e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.430000000000147 y[1] (closed_form) = 21.02232762186482 y[1] (numeric) = 21.0223276218643 absolute error = 5.186961971048731e-13 relative error = 2.467358545803414e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.44000000000015 y[1] (closed_form) = 21.0433604641551 y[1] (numeric) = 21.04336046415457 absolute error = 5.293543381412746e-13 relative error = 2.515540894920124e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.450000000000154 y[1] (closed_form) = 21.0644143498076 y[1] (numeric) = 21.06441434980705 absolute error = 5.435651928564766e-13 relative error = 2.580490413024189e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.460000000000157 y[1] (closed_form) = 21.0854892998762 y[1] (numeric) = 21.08548929987565 absolute error = 5.506706202140776e-13 relative error = 2.611609398209748e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.470000000000161 y[1] (closed_form) = 21.10658533543586 y[1] (numeric) = 21.1065853354353 absolute error = 5.577760475716786e-13 relative error = 2.642663598622124e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.480000000000164 y[1] (closed_form) = 21.12770247758261 y[1] (numeric) = 21.12770247758204 absolute error = 5.684341886080801e-13 relative error = 2.690468541059838e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.490000000000167 y[1] (closed_form) = 21.14884074743361 y[1] (numeric) = 21.14884074743303 absolute error = 5.790923296444817e-13 relative error = 2.738175281379212e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.500000000000171 y[1] (closed_form) = 21.17000016612711 y[1] (numeric) = 21.17000016612653 absolute error = 5.755396159656812e-13 relative error = 2.718656643595917e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.510000000000174 y[1] (closed_form) = 21.19118075482254 y[1] (numeric) = 21.19118075482195 absolute error = 5.861977570020827e-13 relative error = 2.766234518898528e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.520000000000177 y[1] (closed_form) = 21.2123825347005 y[1] (numeric) = 21.2123825346999 absolute error = 5.933031843596837e-13 relative error = 2.796966269060642e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.530000000000181 y[1] (closed_form) = 21.23360552696276 y[1] (numeric) = 21.23360552696216 absolute error = 5.968558980384842e-13 relative error = 2.810902261891356e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.540000000000184 y[1] (closed_form) = 21.2548497528323 y[1] (numeric) = 21.2548497528317 absolute error = 6.004086117172847e-13 relative error = 2.824807602496825e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.550000000000187 y[1] (closed_form) = 21.27611523355338 y[1] (numeric) = 21.27611523355277 absolute error = 6.075140390748857e-13 relative error = 2.855380469630137e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.560000000000191 y[1] (closed_form) = 21.29740199039146 y[1] (numeric) = 21.29740199039086 absolute error = 6.075140390748857e-13 relative error = 2.852526516374963e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.570000000000194 y[1] (closed_form) = 21.31871004463331 y[1] (numeric) = 21.3187100446327 absolute error = 6.181721801112872e-13 relative error = 2.899669721184201e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.580000000000197 y[1] (closed_form) = 21.34003941758698 y[1] (numeric) = 21.34003941758636 absolute error = 6.217248937900877e-13 relative error = 2.913419612888368e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.590000000000201 y[1] (closed_form) = 21.36139013058185 y[1] (numeric) = 21.36139013058122 absolute error = 6.252776074688882e-13 relative error = 2.927139121782692e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.600000000000204 y[1] (closed_form) = 21.38276220496862 y[1] (numeric) = 21.38276220496799 absolute error = 6.359357485052897e-13 relative error = 2.974057993113349e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.610000000000207 y[1] (closed_form) = 21.40415566211939 y[1] (numeric) = 21.40415566211875 absolute error = 6.394884621840902e-13 relative error = 2.98768366423275e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.620000000000211 y[1] (closed_form) = 21.4255705234276 y[1] (numeric) = 21.42557052342695 absolute error = 6.465938895416912e-13 relative error = 3.01786077917822e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.630000000000214 y[1] (closed_form) = 21.44700681030811 y[1] (numeric) = 21.44700681030746 absolute error = 6.501466032204917e-13 relative error = 3.031409506094858e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.640000000000217 y[1] (closed_form) = 21.46846454419723 y[1] (numeric) = 21.46846454419656 absolute error = 6.679101716144942e-13 relative error = 3.111122224132352e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.650000000000221 y[1] (closed_form) = 21.48994374655268 y[1] (numeric) = 21.489943746552 absolute error = 6.785683126508957e-13 relative error = 3.157608603604412e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.660000000000224 y[1] (closed_form) = 21.51144443885366 y[1] (numeric) = 21.51144443885298 absolute error = 6.856737400084967e-13 relative error = 3.187483490276658e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.670000000000227 y[1] (closed_form) = 21.53296664260088 y[1] (numeric) = 21.53296664260018 absolute error = 6.963318810448982e-13 relative error = 3.233794453882975e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.680000000000231 y[1] (closed_form) = 21.55451037931654 y[1] (numeric) = 21.55451037931583 absolute error = 7.069900220812997e-13 relative error = 3.280009657559743e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.690000000000234 y[1] (closed_form) = 21.57607567054436 y[1] (numeric) = 21.57607567054365 absolute error = 7.105427357601002e-13 relative error = 3.293197273729126e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.700000000000237 y[1] (closed_form) = 21.59766253784966 y[1] (numeric) = 21.59766253784895 absolute error = 7.140954494389007e-13 relative error = 3.30635525111783e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.710000000000241 y[1] (closed_form) = 21.6192710028193 y[1] (numeric) = 21.61927100281858 absolute error = 7.212008767965017e-13 relative error = 3.33591672310529e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.720000000000244 y[1] (closed_form) = 21.64090108706174 y[1] (numeric) = 21.640901087061 absolute error = 7.389644451905042e-13 relative error = 3.414665785946882e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.730000000000247 y[1] (closed_form) = 21.66255281220707 y[1] (numeric) = 21.66255281220633 absolute error = 7.460698725481052e-13 relative error = 3.444053334876059e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.740000000000251 y[1] (closed_form) = 21.68422619990702 y[1] (numeric) = 21.68422619990627 absolute error = 7.531752999057062e-13 relative error = 3.473378726832022e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.750000000000254 y[1] (closed_form) = 21.70592127183497 y[1] (numeric) = 21.70592127183421 absolute error = 7.602807272633072e-13 relative error = 3.502642056708403e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.760000000000257 y[1] (closed_form) = 21.72763804968601 y[1] (numeric) = 21.72763804968524 absolute error = 7.744915819785092e-13 relative error = 3.564545673153375e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.770000000000261 y[1] (closed_form) = 21.74937655517691 y[1] (numeric) = 21.74937655517613 absolute error = 7.815970093361102e-13 relative error = 3.593652477133052e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.780000000000264 y[1] (closed_form) = 21.77113681004617 y[1] (numeric) = 21.77113681004538 absolute error = 7.958078640513122e-13 relative error = 3.65533445035397e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.790000000000267 y[1] (closed_form) = 21.79291883605406 y[1] (numeric) = 21.79291883605326 absolute error = 8.064660050877137e-13 relative error = 3.700587384162151e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.800000000000271 y[1] (closed_form) = 21.8147226549826 y[1] (numeric) = 21.81472265498179 absolute error = 8.135714324453147e-13 relative error = 3.729460352591238e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.810000000000274 y[1] (closed_form) = 21.83654828863562 y[1] (numeric) = 21.83654828863479 absolute error = 8.206768598029157e-13 relative error = 3.758271907057857e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.820000000000277 y[1] (closed_form) = 21.85839575883874 y[1] (numeric) = 21.85839575883791 absolute error = 8.313350008393172e-13 relative error = 3.803275455396381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.830000000000281 y[1] (closed_form) = 21.88026508743944 y[1] (numeric) = 21.88026508743861 absolute error = 8.348877145181177e-13 relative error = 3.815711149666977e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.840000000000284 y[1] (closed_form) = 21.90215629630706 y[1] (numeric) = 21.90215629630621 absolute error = 8.455458555545192e-13 relative error = 3.860559865044373e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.850000000000287 y[1] (closed_form) = 21.92406940733279 y[1] (numeric) = 21.92406940733193 absolute error = 8.526512829121202e-13 relative error = 3.889110488890078e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.860000000000291 y[1] (closed_form) = 21.94600444242976 y[1] (numeric) = 21.9460044424289 absolute error = 8.562039965909207e-13 relative error = 3.901411752818026e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.870000000000294 y[1] (closed_form) = 21.967961423533 y[1] (numeric) = 21.96796142353213 absolute error = 8.633094239485217e-13 relative error = 3.929856791462264e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.880000000000297 y[1] (closed_form) = 21.98994037259949 y[1] (numeric) = 21.98994037259862 absolute error = 8.668621376273222e-13 relative error = 3.94208498494827e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.890000000000301 y[1] (closed_form) = 22.01194131160819 y[1] (numeric) = 22.01194131160732 absolute error = 8.704148513061227e-13 relative error = 3.954284808342196e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.900000000000304 y[1] (closed_form) = 22.03396426256004 y[1] (numeric) = 22.03396426255916 absolute error = 8.810729923425242e-13 relative error = 3.998703918384933e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.910000000000307 y[1] (closed_form) = 22.05600924747798 y[1] (numeric) = 22.0560092474771 absolute error = 8.846257060213247e-13 relative error = 4.010814903527836e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.920000000000311 y[1] (closed_form) = 22.07807628840701 y[1] (numeric) = 22.07807628840613 absolute error = 8.846257060213247e-13 relative error = 4.006806093363457e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.930000000000314 y[1] (closed_form) = 22.10016540741417 y[1] (numeric) = 22.10016540741328 absolute error = 8.952838470577262e-13 relative error = 4.051027811571836e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.940000000000317 y[1] (closed_form) = 22.12227662658858 y[1] (numeric) = 22.12227662658768 absolute error = 8.988365607365267e-13 relative error = 4.06303824831583e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.950000000000321 y[1] (closed_form) = 22.14440996804146 y[1] (numeric) = 22.14440996804055 absolute error = 9.094947017729282e-13 relative error = 4.107107405821604e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.960000000000324 y[1] (closed_form) = 22.16656545390614 y[1] (numeric) = 22.16656545390523 absolute error = 9.130474154517287e-13 relative error = 4.119029704219846e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.970000000000327 y[1] (closed_form) = 22.18874310633814 y[1] (numeric) = 22.18874310633721 absolute error = 9.237055564881302e-13 relative error = 4.16294673412248e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.980000000000331 y[1] (closed_form) = 22.21094294751509 y[1] (numeric) = 22.21094294751416 absolute error = 9.272582701669307e-13 relative error = 4.174781198430256e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 5.990000000000334 y[1] (closed_form) = 22.23316499963683 y[1] (numeric) = 22.2331649996359 absolute error = 9.308109838457312e-13 relative error = 4.186587846853723e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.000000000000338 y[1] (closed_form) = 22.25540928492543 y[1] (numeric) = 22.25540928492449 absolute error = 9.379164112033322e-13 relative error = 4.214330094745211e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.010000000000341 y[1] (closed_form) = 22.27767582562517 y[1] (numeric) = 22.27767582562422 absolute error = 9.450218385609332e-13 relative error = 4.242012703470217e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.020000000000344 y[1] (closed_form) = 22.29996464400259 y[1] (numeric) = 22.29996464400163 absolute error = 9.521272659185342e-13 relative error = 4.269635764532936e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.030000000000348 y[1] (closed_form) = 22.32227576234651 y[1] (numeric) = 22.32227576234554 absolute error = 9.627854069549358e-13 relative error = 4.313114922533903e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.040000000000351 y[1] (closed_form) = 22.34460920296805 y[1] (numeric) = 22.34460920296707 absolute error = 9.769962616701378e-13 relative error = 4.372402545936505e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.050000000000354 y[1] (closed_form) = 22.36696498820066 y[1] (numeric) = 22.36696498819968 absolute error = 9.876544027065393e-13 relative error = 4.415683590632706e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.060000000000358 y[1] (closed_form) = 22.38934314040013 y[1] (numeric) = 22.38934314039913 absolute error = 9.947598300641403e-13 relative error = 4.443005870364997e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.070000000000361 y[1] (closed_form) = 22.41174368194459 y[1] (numeric) = 22.41174368194359 absolute error = 1.001865257421741e-12 relative error = 4.470269121580516e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.080000000000364 y[1] (closed_form) = 22.43416663523461 y[1] (numeric) = 22.4341666352336 absolute error = 1.008970684779342e-12 relative error = 4.497473434982314e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.090000000000368 y[1] (closed_form) = 22.45661202269314 y[1] (numeric) = 22.45661202269212 absolute error = 1.016076112136943e-12 relative error = 4.524618901151097e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.100000000000371 y[1] (closed_form) = 22.47907986676555 y[1] (numeric) = 22.47907986676453 absolute error = 1.016076112136943e-12 relative error = 4.520096543805481e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.110000000000374 y[1] (closed_form) = 22.5015701899197 y[1] (numeric) = 22.50157018991868 absolute error = 1.023181539494544e-12 relative error = 4.54715618002921e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.120000000000378 y[1] (closed_form) = 22.52408301464593 y[1] (numeric) = 22.52408301464489 absolute error = 1.033839680530946e-12 relative error = 4.58993016434324e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.130000000000381 y[1] (closed_form) = 22.54661836345704 y[1] (numeric) = 22.546618363456 absolute error = 1.040945107888547e-12 relative error = 4.616856910017526e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.140000000000384 y[1] (closed_form) = 22.56917625888839 y[1] (numeric) = 22.56917625888735 absolute error = 1.048050535246148e-12 relative error = 4.643725243775325e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.150000000000388 y[1] (closed_form) = 22.59175672349789 y[1] (numeric) = 22.59175672349683 absolute error = 1.06226138996135e-12 relative error = 4.701986671344075e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.160000000000391 y[1] (closed_form) = 22.61435977986599 y[1] (numeric) = 22.61435977986492 absolute error = 1.072919530997751e-12 relative error = 4.744417005132255e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.170000000000394 y[1] (closed_form) = 22.63698545059576 y[1] (numeric) = 22.63698545059468 absolute error = 1.080024958355352e-12 relative error = 4.771063535436112e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.180000000000398 y[1] (closed_form) = 22.65963375831286 y[1] (numeric) = 22.65963375831177 absolute error = 1.090683099391754e-12 relative error = 4.813330661143754e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.190000000000401 y[1] (closed_form) = 22.68230472566561 y[1] (numeric) = 22.68230472566452 absolute error = 1.090683099391754e-12 relative error = 4.808519736345919e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.200000000000404 y[1] (closed_form) = 22.70499837532498 y[1] (numeric) = 22.70499837532388 absolute error = 1.097788526749355e-12 relative error = 4.835008171339022e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.210000000000408 y[1] (closed_form) = 22.72771472998461 y[1] (numeric) = 22.7277147299835 absolute error = 1.104893954106956e-12 relative error = 4.861438852227727e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.220000000000411 y[1] (closed_form) = 22.75045381236087 y[1] (numeric) = 22.75045381235975 absolute error = 1.111999381464557e-12 relative error = 4.887811868000544e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.230000000000414 y[1] (closed_form) = 22.77321564519283 y[1] (numeric) = 22.77321564519172 absolute error = 1.115552095143357e-12 relative error = 4.89852690337492e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.240000000000418 y[1] (closed_form) = 22.79600025124234 y[1] (numeric) = 22.79600025124122 absolute error = 1.122657522500958e-12 relative error = 4.924800448007433e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.250000000000421 y[1] (closed_form) = 22.818807653294 y[1] (numeric) = 22.81880765329287 absolute error = 1.13331566353736e-12 relative error = 4.966585812706828e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.260000000000424 y[1] (closed_form) = 22.84163787415521 y[1] (numeric) = 22.84163787415407 absolute error = 1.13686837721616e-12 relative error = 4.977175382429562e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.270000000000428 y[1] (closed_form) = 22.8644909366562 y[1] (numeric) = 22.86449093665506 absolute error = 1.140421090894961e-12 relative error = 4.987738821976767e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.280000000000431 y[1] (closed_form) = 22.88736686365004 y[1] (numeric) = 22.88736686364889 absolute error = 1.143973804573761e-12 relative error = 4.998276173003688e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.290000000000434 y[1] (closed_form) = 22.91026567801264 y[1] (numeric) = 22.91026567801149 absolute error = 1.151079231931362e-12 relative error = 5.024294559080875e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.300000000000438 y[1] (closed_form) = 22.93318740264283 y[1] (numeric) = 22.93318740264168 absolute error = 1.154631945610163e-12 relative error = 5.034764358473355e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.310000000000441 y[1] (closed_form) = 22.95613206046234 y[1] (numeric) = 22.95613206046118 absolute error = 1.158184659288963e-12 relative error = 5.045208209460168e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.320000000000444 y[1] (closed_form) = 22.97909967441582 y[1] (numeric) = 22.97909967441465 absolute error = 1.168842800325365e-12 relative error = 5.086547414330233e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.330000000000448 y[1] (closed_form) = 23.00209026747089 y[1] (numeric) = 23.00209026746971 absolute error = 1.175948227682966e-12 relative error = 5.11235376441405e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.340000000000451 y[1] (closed_form) = 23.02510386261814 y[1] (numeric) = 23.02510386261695 absolute error = 1.186606368719367e-12 relative error = 5.153533186210091e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.350000000000454 y[1] (closed_form) = 23.04814048287117 y[1] (numeric) = 23.04814048286998 absolute error = 1.197264509755769e-12 relative error = 5.194625183083847e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.360000000000458 y[1] (closed_form) = 23.07120015126661 y[1] (numeric) = 23.0712001512654 absolute error = 1.20792265079217e-12 relative error = 5.2356298886595e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.370000000000461 y[1] (closed_form) = 23.09428289086412 y[1] (numeric) = 23.0942828908629 absolute error = 1.218580791828572e-12 relative error = 5.276547436381455e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.380000000000464 y[1] (closed_form) = 23.11738872474645 y[1] (numeric) = 23.11738872474523 absolute error = 1.225686219186173e-12 relative error = 5.302009815122906e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.390000000000468 y[1] (closed_form) = 23.14051767601942 y[1] (numeric) = 23.1405176760182 absolute error = 1.229238932864973e-12 relative error = 5.312063239358023e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.400000000000471 y[1] (closed_form) = 23.16366976781201 y[1] (numeric) = 23.16366976781077 absolute error = 1.236344360222574e-12 relative error = 5.337428708902531e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.410000000000474 y[1] (closed_form) = 23.18684502327629 y[1] (numeric) = 23.18684502327504 absolute error = 1.250555214937776e-12 relative error = 5.393382384202754e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.420000000000478 y[1] (closed_form) = 23.21004346558752 y[1] (numeric) = 23.21004346558627 absolute error = 1.250555214937776e-12 relative error = 5.387991697611069e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.430000000000481 y[1] (closed_form) = 23.23326511794416 y[1] (numeric) = 23.2332651179429 absolute error = 1.261213355974178e-12 relative error = 5.428480885366742e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.440000000000484 y[1] (closed_form) = 23.25651000356785 y[1] (numeric) = 23.25651000356658 absolute error = 1.271871497010579e-12 relative error = 5.468883752615751e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.450000000000488 y[1] (closed_form) = 23.27977814570348 y[1] (numeric) = 23.2797781457022 absolute error = 1.282529638046981e-12 relative error = 5.509200431464098e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.460000000000491 y[1] (closed_form) = 23.3030695676192 y[1] (numeric) = 23.3030695676179 absolute error = 1.296740492762183e-12 relative error = 5.564676743548282e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.470000000000494 y[1] (closed_form) = 23.32638429260643 y[1] (numeric) = 23.32638429260512 absolute error = 1.307398633798584e-12 relative error = 5.604806203132733e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.480000000000498 y[1] (closed_form) = 23.34972234397989 y[1] (numeric) = 23.34972234397857 absolute error = 1.318056774834986e-12 relative error = 5.644849884798788e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.490000000000501 y[1] (closed_form) = 23.37308374507764 y[1] (numeric) = 23.37308374507632 absolute error = 1.325162202192587e-12 relative error = 5.669607898750909e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.500000000000504 y[1] (closed_form) = 23.39646851926109 y[1] (numeric) = 23.39646851925975 absolute error = 1.335820343228988e-12 relative error = 5.70949561096914e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.510000000000508 y[1] (closed_form) = 23.419876689915 y[1] (numeric) = 23.41987668991366 absolute error = 1.342925770586589e-12 relative error = 5.734128272182048e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.520000000000511 y[1] (closed_form) = 23.44330828044756 y[1] (numeric) = 23.44330828044621 absolute error = 1.353583911622991e-12 relative error = 5.773860478352031e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.530000000000515 y[1] (closed_form) = 23.46676331429035 y[1] (numeric) = 23.46676331428899 absolute error = 1.364242052659392e-12 relative error = 5.813507531431152e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.540000000000518 y[1] (closed_form) = 23.49024181489841 y[1] (numeric) = 23.49024181489704 absolute error = 1.371347480016993e-12 relative error = 5.837945351193584e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.550000000000521 y[1] (closed_form) = 23.51374380575025 y[1] (numeric) = 23.51374380574887 absolute error = 1.374900193695794e-12 relative error = 5.847219417945535e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.560000000000525 y[1] (closed_form) = 23.53726931034785 y[1] (numeric) = 23.53726931034646 absolute error = 1.382005621053395e-12 relative error = 5.871563106285293e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.570000000000528 y[1] (closed_form) = 23.56081835221671 y[1] (numeric) = 23.56081835221532 absolute error = 1.389111048410996e-12 relative error = 5.895852290208339e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.580000000000531 y[1] (closed_form) = 23.5843909549059 y[1] (numeric) = 23.58439095490451 absolute error = 1.392663762089796e-12 relative error = 5.90502321960577e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.590000000000535 y[1] (closed_form) = 23.607987141988 y[1] (numeric) = 23.60798714198661 absolute error = 1.396216475768597e-12 relative error = 5.914169926352404e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.600000000000538 y[1] (closed_form) = 23.63160693705922 y[1] (numeric) = 23.63160693705781 absolute error = 1.410427330483799e-12 relative error = 5.968393661253559e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.610000000000541 y[1] (closed_form) = 23.65525036373934 y[1] (numeric) = 23.65525036373792 absolute error = 1.4210854715202e-12 relative error = 6.007484383672191e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.620000000000545 y[1] (closed_form) = 23.6789174456718 y[1] (numeric) = 23.67891744567038 absolute error = 1.424638185199001e-12 relative error = 6.016483601784787e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.630000000000548 y[1] (closed_form) = 23.70260820652367 y[1] (numeric) = 23.70260820652225 absolute error = 1.428190898877801e-12 relative error = 6.025458828976973e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.640000000000551 y[1] (closed_form) = 23.72632266998573 y[1] (numeric) = 23.7263226699843 absolute error = 1.431743612556602e-12 relative error = 6.034410104216385e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.650000000000555 y[1] (closed_form) = 23.75006085977244 y[1] (numeric) = 23.750060859771 absolute error = 1.438849039914203e-12 relative error = 6.058296222521718e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.660000000000558 y[1] (closed_form) = 23.77382279962198 y[1] (numeric) = 23.77382279962053 absolute error = 1.449507180950604e-12 relative error = 6.09707236891516e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.670000000000561 y[1] (closed_form) = 23.7976085132963 y[1] (numeric) = 23.79760851329484 absolute error = 1.460165321987006e-12 relative error = 6.135764949537581e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.680000000000565 y[1] (closed_form) = 23.82141802458113 y[1] (numeric) = 23.82141802457965 absolute error = 1.474376176702208e-12 relative error = 6.189288039783404e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.690000000000568 y[1] (closed_form) = 23.84525135728595 y[1] (numeric) = 23.84525135728448 absolute error = 1.477928890381008e-12 relative error = 6.19800088594757e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.700000000000571 y[1] (closed_form) = 23.86910853524413 y[1] (numeric) = 23.86910853524265 absolute error = 1.485034317738609e-12 relative error = 6.221574281024654e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.710000000000575 y[1] (closed_form) = 23.89298958231283 y[1] (numeric) = 23.89298958231133 absolute error = 1.495692458775011e-12 relative error = 6.259963633358888e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.720000000000578 y[1] (closed_form) = 23.9168945223731 y[1] (numeric) = 23.9168945223716 absolute error = 1.502797886132612e-12 relative error = 6.283415619560545e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.730000000000581 y[1] (closed_form) = 23.94082337932989 y[1] (numeric) = 23.94082337932838 absolute error = 1.509903313490213e-12 relative error = 6.306814471526648e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.740000000000585 y[1] (closed_form) = 23.96477617711205 y[1] (numeric) = 23.96477617711054 absolute error = 1.513456027169013e-12 relative error = 6.315335540727745e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.750000000000588 y[1] (closed_form) = 23.98875293967239 y[1] (numeric) = 23.98875293967087 absolute error = 1.520561454526614e-12 relative error = 6.338643189792176e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.760000000000591 y[1] (closed_form) = 24.01275369098767 y[1] (numeric) = 24.01275369098613 absolute error = 1.531219595563016e-12 relative error = 6.376693049317808e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.770000000000595 y[1] (closed_form) = 24.03677845505863 y[1] (numeric) = 24.03677845505709 absolute error = 1.538325022920617e-12 relative error = 6.399880191086383e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.780000000000598 y[1] (closed_form) = 24.06082725591006 y[1] (numeric) = 24.06082725590851 absolute error = 1.545430450278218e-12 relative error = 6.42301461143076e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.790000000000601 y[1] (closed_form) = 24.08490011759075 y[1] (numeric) = 24.08490011758919 absolute error = 1.552535877635819e-12 relative error = 6.446096392577118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.800000000000605 y[1] (closed_form) = 24.10899706417356 y[1] (numeric) = 24.108997064172 absolute error = 1.55964130499342e-12 relative error = 6.469125616639929e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.810000000000608 y[1] (closed_form) = 24.13311811975544 y[1] (numeric) = 24.13311811975388 absolute error = 1.566746732351021e-12 relative error = 6.492102365622108e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.820000000000611 y[1] (closed_form) = 24.15726330845746 y[1] (numeric) = 24.15726330845589 absolute error = 1.573852159708622e-12 relative error = 6.515026721415154e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.830000000000615 y[1] (closed_form) = 24.18143265442479 y[1] (numeric) = 24.18143265442321 absolute error = 1.580957587066223e-12 relative error = 6.537898765799282e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.840000000000618 y[1] (closed_form) = 24.2056261818268 y[1] (numeric) = 24.20562618182522 absolute error = 1.584510300745023e-12 relative error = 6.546041357668527e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.850000000000621 y[1] (closed_form) = 24.22984391485701 y[1] (numeric) = 24.22984391485542 absolute error = 1.588063014423824e-12 relative error = 6.554161141129233e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.860000000000625 y[1] (closed_form) = 24.25408587773315 y[1] (numeric) = 24.25408587773155 absolute error = 1.595168441781425e-12 relative error = 6.576906051305338e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.870000000000628 y[1] (closed_form) = 24.27835209469718 y[1] (numeric) = 24.27835209469558 absolute error = 1.605826582817826e-12 relative error = 6.614232203875843e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.880000000000631 y[1] (closed_form) = 24.30264259001534 y[1] (numeric) = 24.30264259001373 absolute error = 1.616484723854228e-12 relative error = 6.651477171121939e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.890000000000635 y[1] (closed_form) = 24.32695738797811 y[1] (numeric) = 24.32695738797649 absolute error = 1.620037437533028e-12 relative error = 6.659433038402156e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.900000000000638 y[1] (closed_form) = 24.3512965129003 y[1] (numeric) = 24.35129651289867 absolute error = 1.627142864890629e-12 relative error = 6.681955780172267e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.910000000000641 y[1] (closed_form) = 24.37565998912103 y[1] (numeric) = 24.3756599891194 absolute error = 1.63424829224823e-12 relative error = 6.704426846196588e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.920000000000645 y[1] (closed_form) = 24.40004784100378 y[1] (numeric) = 24.40004784100213 absolute error = 1.644906433284632e-12 relative error = 6.74140659068873e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.930000000000648 y[1] (closed_form) = 24.4244600929364 y[1] (numeric) = 24.42446009293475 absolute error = 1.652011860642233e-12 relative error = 6.76375999451467e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.940000000000651 y[1] (closed_form) = 24.44889676933116 y[1] (numeric) = 24.4488967693295 absolute error = 1.659117287999834e-12 relative error = 6.786061979209797e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.950000000000655 y[1] (closed_form) = 24.47335789462471 y[1] (numeric) = 24.47335789462305 absolute error = 1.666222715357435e-12 relative error = 6.808312625229909e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.960000000000658 y[1] (closed_form) = 24.49784349327821 y[1] (numeric) = 24.49784349327653 absolute error = 1.676880856393836e-12 relative error = 6.845014161568728e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.970000000000661 y[1] (closed_form) = 24.52235358977724 y[1] (numeric) = 24.52235358977555 absolute error = 1.687538997430238e-12 relative error = 6.881635530015893e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.980000000000665 y[1] (closed_form) = 24.5468882086319 y[1] (numeric) = 24.5468882086302 absolute error = 1.70174985214544e-12 relative error = 6.932650027497255e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 6.990000000000668 y[1] (closed_form) = 24.57144737437681 y[1] (numeric) = 24.5714473743751 absolute error = 1.70530256582424e-12 relative error = 6.940179550035525e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.000000000000671 y[1] (closed_form) = 24.59603111157115 y[1] (numeric) = 24.59603111156944 absolute error = 1.712407993181841e-12 relative error = 6.962131351249766e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.010000000000675 y[1] (closed_form) = 24.62063944479865 y[1] (numeric) = 24.62063944479693 absolute error = 1.719513420539442e-12 relative error = 6.984032337562648e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.020000000000678 y[1] (closed_form) = 24.64527239866764 y[1] (numeric) = 24.64527239866592 absolute error = 1.726618847897043e-12 relative error = 7.005882588623312e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.030000000000681 y[1] (closed_form) = 24.66992999781109 y[1] (numeric) = 24.66992999780935 absolute error = 1.737276988933445e-12 relative error = 7.042083172054358e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.040000000000685 y[1] (closed_form) = 24.69461226688659 y[1] (numeric) = 24.69461226688485 absolute error = 1.747935129969846e-12 relative error = 7.07820439162627e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.050000000000688 y[1] (closed_form) = 24.71931923057642 y[1] (numeric) = 24.71931923057467 absolute error = 1.755040557327447e-12 relative error = 7.099874154934494e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.060000000000692 y[1] (closed_form) = 24.74405091358754 y[1] (numeric) = 24.74405091358577 absolute error = 1.765698698363849e-12 relative error = 7.135851379105684e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.070000000000695 y[1] (closed_form) = 24.76880734065163 y[1] (numeric) = 24.76880734064985 absolute error = 1.77280412572145e-12 relative error = 7.157406092831316e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.080000000000698 y[1] (closed_form) = 24.79358853652513 y[1] (numeric) = 24.79358853652334 absolute error = 1.790567694115452e-12 relative error = 7.221898078519956e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.090000000000702 y[1] (closed_form) = 24.81839452598922 y[1] (numeric) = 24.81839452598743 absolute error = 1.794120407794253e-12 relative error = 7.228994631040672e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.100000000000705 y[1] (closed_form) = 24.84322533384992 y[1] (numeric) = 24.84322533384811 absolute error = 1.804778548830654e-12 relative error = 7.264670849205596e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.110000000000708 y[1] (closed_form) = 24.86808098493801 y[1] (numeric) = 24.8680809849362 absolute error = 1.815436689867056e-12 relative error = 7.300268528828668e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.120000000000712 y[1] (closed_form) = 24.89296150410917 y[1] (numeric) = 24.89296150410735 absolute error = 1.822542117224657e-12 relative error = 7.321515830584494e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.130000000000715 y[1] (closed_form) = 24.91786691624391 y[1] (numeric) = 24.91786691624207 absolute error = 1.833200258261058e-12 relative error = 7.356971061860833e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.140000000000718 y[1] (closed_form) = 24.94279724624763 y[1] (numeric) = 24.94279724624579 absolute error = 1.840305685618659e-12 relative error = 7.378104658632518e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.150000000000722 y[1] (closed_form) = 24.96775251905068 y[1] (numeric) = 24.96775251904883 absolute error = 1.850963826655061e-12 relative error = 7.413417868679826e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.160000000000725 y[1] (closed_form) = 24.99273275960833 y[1] (numeric) = 24.99273275960647 absolute error = 1.861621967691462e-12 relative error = 7.448653116877629e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.170000000000728 y[1] (closed_form) = 25.01773799290083 y[1] (numeric) = 25.01773799289895 absolute error = 1.879385536085465e-12 relative error = 7.51221208175883e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.180000000000732 y[1] (closed_form) = 25.0427682439334 y[1] (numeric) = 25.04276824393152 absolute error = 1.882938249764265e-12 relative error = 7.518890209832959e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.190000000000735 y[1] (closed_form) = 25.0678235377363 y[1] (numeric) = 25.06782353773441 absolute error = 1.893596390800667e-12 relative error = 7.553892295236989e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.200000000000738 y[1] (closed_form) = 25.09290389936483 y[1] (numeric) = 25.09290389936293 absolute error = 1.904254531837068e-12 relative error = 7.588816900084928e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.210000000000742 y[1] (closed_form) = 25.11800935389935 y[1] (numeric) = 25.11800935389744 absolute error = 1.911359959194669e-12 relative error = 7.609520054971823e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.220000000000745 y[1] (closed_form) = 25.14313992644531 y[1] (numeric) = 25.1431399264434 absolute error = 1.91491267287347e-12 relative error = 7.616044290710816e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.230000000000748 y[1] (closed_form) = 25.1682956421333 y[1] (numeric) = 25.16829564213138 absolute error = 1.918465386552271e-12 relative error = 7.622547882585419e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.240000000000752 y[1] (closed_form) = 25.19347652611903 y[1] (numeric) = 25.1934765261171 absolute error = 1.929123527588672e-12 relative error = 7.657234306621704e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.250000000000755 y[1] (closed_form) = 25.21868260358339 y[1] (numeric) = 25.21868260358145 absolute error = 1.939781668625074e-12 relative error = 7.691843777554998e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.260000000000758 y[1] (closed_form) = 25.24391389973244 y[1] (numeric) = 25.24391389973049 absolute error = 1.957545237019076e-12 relative error = 7.754523505326262e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.270000000000762 y[1] (closed_form) = 25.26917043979751 y[1] (numeric) = 25.26917043979554 absolute error = 1.964650664376677e-12 relative error = 7.774891815532115e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.280000000000765 y[1] (closed_form) = 25.29445224903511 y[1] (numeric) = 25.29445224903314 absolute error = 1.975308805413079e-12 relative error = 7.809257089124865e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.290000000000768 y[1] (closed_form) = 25.31975935272708 y[1] (numeric) = 25.31975935272509 absolute error = 1.989519660128281e-12 relative error = 7.857577287416036e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.300000000000772 y[1] (closed_form) = 25.3450917761805 y[1] (numeric) = 25.34509177617851 absolute error = 1.993072373807081e-12 relative error = 7.863741001246579e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.310000000000775 y[1] (closed_form) = 25.37044954472782 y[1] (numeric) = 25.37044954472582 absolute error = 2.000177801164682e-12 relative error = 7.883887897368121e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.320000000000778 y[1] (closed_form) = 25.39583268372679 y[1] (numeric) = 25.39583268372478 absolute error = 2.007283228522283e-12 relative error = 7.903986663955757e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.330000000000782 y[1] (closed_form) = 25.42124121856057 y[1] (numeric) = 25.42124121855854 absolute error = 2.025046796916286e-12 relative error = 7.965963500782006e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.340000000000785 y[1] (closed_form) = 25.44667517463768 y[1] (numeric) = 25.44667517463565 absolute error = 2.028599510595086e-12 relative error = 7.971962925109213e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.350000000000788 y[1] (closed_form) = 25.47213457739208 y[1] (numeric) = 25.47213457739005 absolute error = 2.028599510595086e-12 relative error = 7.963994946837236e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.360000000000792 y[1] (closed_form) = 25.49761945228319 y[1] (numeric) = 25.49761945228116 absolute error = 2.032152224273887e-12 relative error = 7.969968443826299e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.370000000000795 y[1] (closed_form) = 25.52312982479588 y[1] (numeric) = 25.52312982479383 absolute error = 2.046363078989089e-12 relative error = 8.017680797913092e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.380000000000798 y[1] (closed_form) = 25.54866572044051 y[1] (numeric) = 25.54866572043846 absolute error = 2.05702122002549e-12 relative error = 8.05138414089369e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.390000000000802 y[1] (closed_form) = 25.57422716475299 y[1] (numeric) = 25.57422716475094 absolute error = 2.05346850634669e-12 relative error = 8.029445007733521e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.400000000000805 y[1] (closed_form) = 25.59981418329478 y[1] (numeric) = 25.59981418329271 absolute error = 2.067679361061892e-12 relative error = 8.076931130270316e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.410000000000808 y[1] (closed_form) = 25.62542680165287 y[1] (numeric) = 25.6254268016508 absolute error = 2.067679361061892e-12 relative error = 8.068858236259791e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.420000000000812 y[1] (closed_form) = 25.65106504543991 y[1] (numeric) = 25.65106504543783 absolute error = 2.078337502098293e-12 relative error = 8.102343892608728e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.430000000000815 y[1] (closed_form) = 25.67672894029413 y[1] (numeric) = 25.67672894029204 absolute error = 2.081890215777094e-12 relative error = 8.108081915800469e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.440000000000818 y[1] (closed_form) = 25.70241851187943 y[1] (numeric) = 25.70241851187733 absolute error = 2.096101070492296e-12 relative error = 8.15526783801881e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.450000000000822 y[1] (closed_form) = 25.72813378588538 y[1] (numeric) = 25.72813378588328 absolute error = 2.099653784171096e-12 relative error = 8.160925318737964e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.460000000000825 y[1] (closed_form) = 25.75387478802725 y[1] (numeric) = 25.75387478802515 absolute error = 2.103206497849897e-12 relative error = 8.166563343033951e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.470000000000828 y[1] (closed_form) = 25.77964154404608 y[1] (numeric) = 25.77964154404396 absolute error = 2.117417352565099e-12 relative error = 8.213525191757857e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.480000000000832 y[1] (closed_form) = 25.80543407970858 y[1] (numeric) = 25.80543407970646 absolute error = 2.120970066243899e-12 relative error = 8.219083080302329e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.490000000000835 y[1] (closed_form) = 25.83125242080732 y[1] (numeric) = 25.83125242080519 absolute error = 2.131628207280301e-12 relative error = 8.25212874913976e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.500000000000838 y[1] (closed_form) = 25.85709659316063 y[1] (numeric) = 25.85709659315849 absolute error = 2.142286348316702e-12 relative error = 8.28510014880538e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.510000000000842 y[1] (closed_form) = 25.88296662261269 y[1] (numeric) = 25.88296662261054 absolute error = 2.152944489353104e-12 relative error = 8.317997394750648e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.520000000000845 y[1] (closed_form) = 25.90886253503353 y[1] (numeric) = 25.90886253503136 absolute error = 2.163602630389505e-12 relative error = 8.350820602270432e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.530000000000848 y[1] (closed_form) = 25.93478435631906 y[1] (numeric) = 25.93478435631689 absolute error = 2.170708057747106e-12 relative error = 8.369871242897797e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.540000000000852 y[1] (closed_form) = 25.96073211239111 y[1] (numeric) = 25.96073211238894 absolute error = 2.177813485104707e-12 relative error = 8.388875458813551e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.550000000000855 y[1] (closed_form) = 25.98670582919744 y[1] (numeric) = 25.98670582919525 absolute error = 2.188471626141109e-12 relative error = 8.421504597486322e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.560000000000858 y[1] (closed_form) = 26.01270553271176 y[1] (numeric) = 26.01270553270956 absolute error = 2.19557705349871e-12 relative error = 8.440402520751659e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.570000000000862 y[1] (closed_form) = 26.03873124893379 y[1] (numeric) = 26.03873124893157 absolute error = 2.213340621892712e-12 relative error = 8.500186129396541e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.580000000000865 y[1] (closed_form) = 26.06478300388922 y[1] (numeric) = 26.06478300388701 absolute error = 2.213340621892712e-12 relative error = 8.491690191943863e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.590000000000868 y[1] (closed_form) = 26.09086082362984 y[1] (numeric) = 26.09086082362762 absolute error = 2.223998762929114e-12 relative error = 8.524052839662897e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.600000000000872 y[1] (closed_form) = 26.11696473423346 y[1] (numeric) = 26.11696473423122 absolute error = 2.234656903965515e-12 relative error = 8.556342311234902e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.610000000000875 y[1] (closed_form) = 26.14309476180398 y[1] (numeric) = 26.14309476180174 absolute error = 2.241762331323116e-12 relative error = 8.574969228962183e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.620000000000879 y[1] (closed_form) = 26.16925093247144 y[1] (numeric) = 26.1692509324692 absolute error = 2.245315045001917e-12 relative error = 8.579974454736398e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.630000000000882 y[1] (closed_form) = 26.19543327239203 y[1] (numeric) = 26.19543327238977 absolute error = 2.259525899717119e-12 relative error = 8.625648128135697e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.640000000000885 y[1] (closed_form) = 26.22164180774806 y[1] (numeric) = 26.22164180774579 absolute error = 2.27018404075352e-12 relative error = 8.65767314418397e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.650000000000889 y[1] (closed_form) = 26.24787656474809 y[1] (numeric) = 26.24787656474581 absolute error = 2.273736754432321e-12 relative error = 8.662555040684842e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.660000000000892 y[1] (closed_form) = 26.27413756962687 y[1] (numeric) = 26.27413756962458 absolute error = 2.284394895468722e-12 relative error = 8.69446195680083e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.670000000000895 y[1] (closed_form) = 26.30042484864541 y[1] (numeric) = 26.30042484864311 absolute error = 2.295053036505124e-12 relative error = 8.726296437083334e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.680000000000899 y[1] (closed_form) = 26.32673842809098 y[1] (numeric) = 26.32673842808868 absolute error = 2.302158463862725e-12 relative error = 8.744563897084536e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.690000000000902 y[1] (closed_form) = 26.35307833427719 y[1] (numeric) = 26.35307833427487 absolute error = 2.312816604899126e-12 relative error = 8.776267332271648e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.700000000000905 y[1] (closed_form) = 26.37944459354392 y[1] (numeric) = 26.3794445935416 absolute error = 2.319922032256727e-12 relative error = 8.794430921508116e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.710000000000909 y[1] (closed_form) = 26.40583723225744 y[1] (numeric) = 26.40583723225511 absolute error = 2.323474745935528e-12 relative error = 8.79909516028208e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.720000000000912 y[1] (closed_form) = 26.43225627681039 y[1] (numeric) = 26.43225627680806 absolute error = 2.330580173293129e-12 relative error = 8.817182115995896e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.730000000000915 y[1] (closed_form) = 26.45870175362183 y[1] (numeric) = 26.45870175361949 absolute error = 2.34123831432953e-12 relative error = 8.848651517866128e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.740000000000919 y[1] (closed_form) = 26.48517368913722 y[1] (numeric) = 26.48517368913488 absolute error = 2.34123831432953e-12 relative error = 8.839807289199612e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.750000000000922 y[1] (closed_form) = 26.51167210982851 y[1] (numeric) = 26.51167210982616 absolute error = 2.348343741687131e-12 relative error = 8.857773029021974e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.760000000000925 y[1] (closed_form) = 26.53819704219412 y[1] (numeric) = 26.53819704219177 absolute error = 2.355449169044732e-12 relative error = 8.875694024351809e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.770000000000929 y[1] (closed_form) = 26.56474851275899 y[1] (numeric) = 26.56474851275662 absolute error = 2.362554596402333e-12 relative error = 8.893570346685585e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.780000000000932 y[1] (closed_form) = 26.59132654807457 y[1] (numeric) = 26.59132654807221 absolute error = 2.366107310081134e-12 relative error = 8.898041644531866e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.790000000000935 y[1] (closed_form) = 26.61793117471893 y[1] (numeric) = 26.61793117471655 absolute error = 2.373212737438735e-12 relative error = 8.915842188715084e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.800000000000939 y[1] (closed_form) = 26.64456241929667 y[1] (numeric) = 26.64456241929429 absolute error = 2.380318164796336e-12 relative error = 8.933598260455756e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.810000000000942 y[1] (closed_form) = 26.67122030843906 y[1] (numeric) = 26.67122030843667 absolute error = 2.387423592153937e-12 relative error = 8.951309930871555e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.820000000000945 y[1] (closed_form) = 26.69790486880398 y[1] (numeric) = 26.69790486880158 absolute error = 2.394529019511538e-12 relative error = 8.96897727098242e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.830000000000949 y[1] (closed_form) = 26.72461612707599 y[1] (numeric) = 26.72461612707359 absolute error = 2.398081733190338e-12 relative error = 8.973306564208145e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.840000000000952 y[1] (closed_form) = 26.75135410996635 y[1] (numeric) = 26.75135410996394 absolute error = 2.40873987422674e-12 relative error = 9.004179243881159e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.850000000000955 y[1] (closed_form) = 26.77811884421306 y[1] (numeric) = 26.77811884421064 absolute error = 2.419398015263141e-12 relative error = 9.034981244718728e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.860000000000959 y[1] (closed_form) = 26.80491035658083 y[1] (numeric) = 26.80491035657841 absolute error = 2.422950728941942e-12 relative error = 9.039204745361465e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.870000000000962 y[1] (closed_form) = 26.83172867386121 y[1] (numeric) = 26.83172867385878 absolute error = 2.430056156299543e-12 relative error = 9.056651495834638e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.880000000000965 y[1] (closed_form) = 26.85857382287249 y[1] (numeric) = 26.85857382287004 absolute error = 2.444267011014745e-12 relative error = 9.100509308998498e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.890000000000969 y[1] (closed_form) = 26.88544583045983 y[1] (numeric) = 26.88544583045737 absolute error = 2.454925152051146e-12 relative error = 9.131056139191272e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.900000000000972 y[1] (closed_form) = 26.91234472349524 y[1] (numeric) = 26.91234472349278 absolute error = 2.465583293087548e-12 relative error = 9.161532814846205e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.910000000000975 y[1] (closed_form) = 26.93927052887762 y[1] (numeric) = 26.93927052887515 absolute error = 2.469136006766348e-12 relative error = 9.165563722742795e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.920000000000979 y[1] (closed_form) = 26.96622327353277 y[1] (numeric) = 26.96622327353029 absolute error = 2.47979414780275e-12 relative error = 9.195926780880202e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.930000000000982 y[1] (closed_form) = 26.99320298441344 y[1] (numeric) = 26.99320298441095 absolute error = 2.490452288839151e-12 relative error = 9.226219986850768e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.940000000000985 y[1] (closed_form) = 27.02020968849935 y[1] (numeric) = 27.02020968849686 absolute error = 2.494005002517952e-12 relative error = 9.230146735609822e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.950000000000989 y[1] (closed_form) = 27.0472434127972 y[1] (numeric) = 27.04724341279469 absolute error = 2.508215857233154e-12 relative error = 9.273462063961795e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.960000000000992 y[1] (closed_form) = 27.07430418434071 y[1] (numeric) = 27.0743041843382 absolute error = 2.515321284590755e-12 relative error = 9.29043741055983e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.970000000000995 y[1] (closed_form) = 27.10139203019067 y[1] (numeric) = 27.10139203018814 absolute error = 2.529532139305957e-12 relative error = 9.333587501660743e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.980000000000999 y[1] (closed_form) = 27.12850697743491 y[1] (numeric) = 27.12850697743237 absolute error = 2.540190280342358e-12 relative error = 9.363546185771488e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 7.990000000001002 y[1] (closed_form) = 27.15564905318839 y[1] (numeric) = 27.15564905318584 absolute error = 2.55084842137876e-12 relative error = 9.393435658203354e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.000000000001005 y[1] (closed_form) = 27.18281828459319 y[1] (numeric) = 27.18281828459062 absolute error = 2.561506562415161e-12 relative error = 9.423256027381769e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.010000000001 y[1] (closed_form) = 27.21001469881851 y[1] (numeric) = 27.21001469881596 absolute error = 2.547295707699959e-12 relative error = 9.361610921182507e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.020000000000994 y[1] (closed_form) = 27.2372383230608 y[1] (numeric) = 27.23723832305827 absolute error = 2.529532139305957e-12 relative error = 9.287036039789292e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.030000000000989 y[1] (closed_form) = 27.26448918454368 y[1] (numeric) = 27.26448918454117 absolute error = 2.515321284590755e-12 relative error = 9.225631434227265e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.040000000000983 y[1] (closed_form) = 27.29176731051802 y[1] (numeric) = 27.29176731051552 absolute error = 2.497557716196752e-12 relative error = 9.151322769904368e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.050000000000978 y[1] (closed_form) = 27.31907272826194 y[1] (numeric) = 27.31907272825946 absolute error = 2.48334686148155e-12 relative error = 9.090157950026228e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.060000000000972 y[1] (closed_form) = 27.34640546508087 y[1] (numeric) = 27.3464054650784 absolute error = 2.469136006766348e-12 relative error = 9.029106256466626e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.070000000000967 y[1] (closed_form) = 27.37376554830755 y[1] (numeric) = 27.37376554830509 absolute error = 2.458477865729947e-12 relative error = 8.98114605895698e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.080000000000961 y[1] (closed_form) = 27.40115300530205 y[1] (numeric) = 27.40115300529961 absolute error = 2.440714297335944e-12 relative error = 8.907341588376492e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.090000000000956 y[1] (closed_form) = 27.42856786345183 y[1] (numeric) = 27.42856786344941 absolute error = 2.422950728941942e-12 relative error = 8.833675680787141e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.10000000000095 y[1] (closed_form) = 27.45601015017177 y[1] (numeric) = 27.45601015016937 absolute error = 2.40873987422674e-12 relative error = 8.773087790440191e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.110000000000944 y[1] (closed_form) = 27.48347989290415 y[1] (numeric) = 27.48347989290176 absolute error = 2.394529019511538e-12 relative error = 8.712612190459081e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.120000000000939 y[1] (closed_form) = 27.51097711911871 y[1] (numeric) = 27.51097711911633 absolute error = 2.383870878475136e-12 relative error = 8.665162520957747e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.130000000000933 y[1] (closed_form) = 27.53850185631268 y[1] (numeric) = 27.53850185631032 absolute error = 2.366107310081134e-12 relative error = 8.591997206045353e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.140000000000928 y[1] (closed_form) = 27.56605413201081 y[1] (numeric) = 27.56605413200846 absolute error = 2.348343741687131e-12 relative error = 8.51896949211944e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.150000000000922 y[1] (closed_form) = 27.59363397376536 y[1] (numeric) = 27.59363397376303 absolute error = 2.327027459614328e-12 relative error = 8.433204056510819e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.160000000000917 y[1] (closed_form) = 27.62124140915619 y[1] (numeric) = 27.62124140915388 absolute error = 2.309263891220326e-12 relative error = 8.360463807592753e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.170000000000911 y[1] (closed_form) = 27.64887646579072 y[1] (numeric) = 27.64887646578843 absolute error = 2.295053036505124e-12 relative error = 8.300709937869397e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.180000000000906 y[1] (closed_form) = 27.67653917130403 y[1] (numeric) = 27.67653917130175 absolute error = 2.277289468111121e-12 relative error = 8.228230610828292e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.1900000000009 y[1] (closed_form) = 27.70422955335881 y[1] (numeric) = 27.70422955335655 absolute error = 2.263078613395919e-12 relative error = 8.16871160064997e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.200000000000895 y[1] (closed_form) = 27.73194763964546 y[1] (numeric) = 27.73194763964321 absolute error = 2.248867758680717e-12 relative error = 8.109303348985652e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.210000000000889 y[1] (closed_form) = 27.75969345788206 y[1] (numeric) = 27.75969345787983 absolute error = 2.227551476607914e-12 relative error = 8.024409491364269e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.220000000000883 y[1] (closed_form) = 27.78746703581443 y[1] (numeric) = 27.78746703581221 absolute error = 2.216893335571513e-12 relative error = 7.978033164067187e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.230000000000878 y[1] (closed_form) = 27.81526840121614 y[1] (numeric) = 27.81526840121394 absolute error = 2.202682480856311e-12 relative error = 7.918968996035302e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.240000000000872 y[1] (closed_form) = 27.84309758188858 y[1] (numeric) = 27.84309758188639 absolute error = 2.188471626141109e-12 relative error = 7.860014927235211e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.250000000000867 y[1] (closed_form) = 27.87095460566093 y[1] (numeric) = 27.87095460565875 absolute error = 2.177813485104707e-12 relative error = 7.81391780768918e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.260000000000861 y[1] (closed_form) = 27.8988395003902 y[1] (numeric) = 27.89883950038804 absolute error = 2.160049916710705e-12 relative error = 7.742436443209382e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.270000000000856 y[1] (closed_form) = 27.92675229396129 y[1] (numeric) = 27.92675229395915 absolute error = 2.138733634637902e-12 relative error = 7.658368621332201e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.28000000000085 y[1] (closed_form) = 27.954693014287 y[1] (numeric) = 27.95469301428488 absolute error = 2.120970066243899e-12 relative error = 7.587169943736888e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.290000000000845 y[1] (closed_form) = 27.98266168930806 y[1] (numeric) = 27.98266168930595 absolute error = 2.106759211528697e-12 relative error = 7.528802066508462e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.300000000000839 y[1] (closed_form) = 28.01065834699315 y[1] (numeric) = 28.01065834699105 absolute error = 2.096101070492296e-12 relative error = 7.483226722221276e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.310000000000834 y[1] (closed_form) = 28.0386830153389 y[1] (numeric) = 28.03868301533683 absolute error = 2.078337502098293e-12 relative error = 7.412393445731075e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.320000000000828 y[1] (closed_form) = 28.06673572237002 y[1] (numeric) = 28.06673572236796 absolute error = 2.060573933704291e-12 relative error = 7.341694289236322e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.330000000000823 y[1] (closed_form) = 28.0948164961392 y[1] (numeric) = 28.09481649613715 absolute error = 2.049915792667889e-12 relative error = 7.296419939064523e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.340000000000817 y[1] (closed_form) = 28.1229253647272 y[1] (numeric) = 28.12292536472517 absolute error = 2.028599510595086e-12 relative error = 7.213330349834194e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.350000000000811 y[1] (closed_form) = 28.15106235624292 y[1] (numeric) = 28.1510623562409 absolute error = 2.021494083237485e-12 relative error = 7.180880272495962e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.360000000000806 y[1] (closed_form) = 28.17922749882335 y[1] (numeric) = 28.17922749882134 absolute error = 2.007283228522283e-12 relative error = 7.123272732036743e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.3700000000008 y[1] (closed_form) = 28.20742082063362 y[1] (numeric) = 28.20742082063163 absolute error = 1.989519660128281e-12 relative error = 7.053178214269611e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.380000000000795 y[1] (closed_form) = 28.23564234986706 y[1] (numeric) = 28.23564234986508 absolute error = 1.975308805413079e-12 relative error = 6.995799071744436e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.390000000000789 y[1] (closed_form) = 28.2638921147452 y[1] (numeric) = 28.26389211474324 absolute error = 1.961097950697877e-12 relative error = 6.938527584015142e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.400000000000784 y[1] (closed_form) = 28.29217014351782 y[1] (numeric) = 28.29217014351587 absolute error = 1.946887095982675e-12 relative error = 6.881363593201553e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.410000000000778 y[1] (closed_form) = 28.32047646446293 y[1] (numeric) = 28.320476464461 absolute error = 1.929123527588672e-12 relative error = 6.811762259753549e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.420000000000773 y[1] (closed_form) = 28.34881110588687 y[1] (numeric) = 28.34881110588495 absolute error = 1.91491267287347e-12 relative error = 6.754825328374432e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.430000000000767 y[1] (closed_form) = 28.37717409612427 y[1] (numeric) = 28.37717409612238 absolute error = 1.897149104479467e-12 relative error = 6.685475791398757e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.440000000000762 y[1] (closed_form) = 28.40556546353815 y[1] (numeric) = 28.40556546353626 absolute error = 1.882938249764265e-12 relative error = 6.62876524032319e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.450000000000756 y[1] (closed_form) = 28.43398523651984 y[1] (numeric) = 28.43398523651797 absolute error = 1.868727395049063e-12 relative error = 6.57216137486391e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.46000000000075 y[1] (closed_form) = 28.46243344348915 y[1] (numeric) = 28.4624334434873 absolute error = 1.850963826655061e-12 relative error = 6.503181923394093e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.470000000000745 y[1] (closed_form) = 28.49091011289427 y[1] (numeric) = 28.49091011289244 absolute error = 1.833200258261058e-12 relative error = 6.434333796277705e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.480000000000739 y[1] (closed_form) = 28.51941527321187 y[1] (numeric) = 28.51941527321006 absolute error = 1.808331262509455e-12 relative error = 6.340702448440485e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.490000000000734 y[1] (closed_form) = 28.54794895294713 y[1] (numeric) = 28.54794895294534 absolute error = 1.790567694115452e-12 relative error = 6.272141291364486e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.500000000000728 y[1] (closed_form) = 28.57651118063372 y[1] (numeric) = 28.57651118063194 absolute error = 1.779909553079051e-12 relative error = 6.228575426258802e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.510000000000723 y[1] (closed_form) = 28.60510198483387 y[1] (numeric) = 28.60510198483212 absolute error = 1.755040557327447e-12 relative error = 6.135410942628177e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.520000000000717 y[1] (closed_form) = 28.63372139413839 y[1] (numeric) = 28.63372139413665 absolute error = 1.737276988933445e-12 relative error = 6.067241365591701e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.530000000000712 y[1] (closed_form) = 28.66236943716669 y[1] (numeric) = 28.66236943716497 absolute error = 1.715960706860642e-12 relative error = 5.986806884972825e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.540000000000706 y[1] (closed_form) = 28.69104614256682 y[1] (numeric) = 28.69104614256511 absolute error = 1.70530256582424e-12 relative error = 5.943675101111797e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.550000000000701 y[1] (closed_form) = 28.71975153901548 y[1] (numeric) = 28.71975153901379 absolute error = 1.691091711109038e-12 relative error = 5.888253276884058e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.560000000000695 y[1] (closed_form) = 28.74848565521807 y[1] (numeric) = 28.74848565521639 absolute error = 1.680433570072637e-12 relative error = 5.845294219063068e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.57000000000069 y[1] (closed_form) = 28.77724851990871 y[1] (numeric) = 28.77724851990705 absolute error = 1.662670001678634e-12 relative error = 5.777724025729437e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.580000000000684 y[1] (closed_form) = 28.80604016185027 y[1] (numeric) = 28.80604016184862 absolute error = 1.644906433284632e-12 relative error = 5.710283065782465e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.590000000000678 y[1] (closed_form) = 28.83486060983439 y[1] (numeric) = 28.83486060983277 absolute error = 1.627142864890629e-12 relative error = 5.642971148387232e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.600000000000673 y[1] (closed_form) = 28.86370989268153 y[1] (numeric) = 28.86370989267991 absolute error = 1.612932010175427e-12 relative error = 5.588096665925785e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.610000000000667 y[1] (closed_form) = 28.89258803924096 y[1] (numeric) = 28.89258803923936 absolute error = 1.602273869139026e-12 relative error = 5.545622520775468e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.620000000000662 y[1] (closed_form) = 28.92149507839084 y[1] (numeric) = 28.92149507838925 absolute error = 1.588063014423824e-12 relative error = 5.490943708544205e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.630000000000656 y[1] (closed_form) = 28.95043103903821 y[1] (numeric) = 28.95043103903664 absolute error = 1.566746732351021e-12 relative error = 5.41182523409873e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.640000000000651 y[1] (closed_form) = 28.97939595011903 y[1] (numeric) = 28.97939595011747 absolute error = 1.552535877635819e-12 relative error = 5.357378325994549e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.650000000000645 y[1] (closed_form) = 29.00838984059821 y[1] (numeric) = 29.00838984059667 absolute error = 1.541877736599417e-12 relative error = 5.315282044512198e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.66000000000064 y[1] (closed_form) = 29.03741273946966 y[1] (numeric) = 29.03741273946813 absolute error = 1.531219595563016e-12 relative error = 5.273264561486487e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.670000000000634 y[1] (closed_form) = 29.06646467575626 y[1] (numeric) = 29.06646467575474 absolute error = 1.513456027169013e-12 relative error = 5.206880313970058e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.680000000000629 y[1] (closed_form) = 29.09554567850996 y[1] (numeric) = 29.09554567850846 absolute error = 1.495692458775011e-12 relative error = 5.140623500592164e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.690000000000623 y[1] (closed_form) = 29.12465577681176 y[1] (numeric) = 29.12465577681028 absolute error = 1.481481604059809e-12 relative error = 5.086692235653213e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.700000000000617 y[1] (closed_form) = 29.15379499977177 y[1] (numeric) = 29.15379499977031 absolute error = 1.463718035665806e-12 relative error = 5.020677533327189e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.710000000000612 y[1] (closed_form) = 29.18296337652921 y[1] (numeric) = 29.18296337652776 absolute error = 1.445954467271804e-12 relative error = 4.954789712804603e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.720000000000606 y[1] (closed_form) = 29.21216093625245 y[1] (numeric) = 29.21216093625102 absolute error = 1.424638185199001e-12 relative error = 4.876866823744687e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.730000000000601 y[1] (closed_form) = 29.24138770813907 y[1] (numeric) = 29.24138770813765 absolute error = 1.4175327578414e-12 relative error = 4.847693180603884e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.740000000000595 y[1] (closed_form) = 29.27064372141583 y[1] (numeric) = 29.27064372141442 absolute error = 1.406874616804998e-12 relative error = 4.806435520157899e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.75000000000059 y[1] (closed_form) = 29.29992900533875 y[1] (numeric) = 29.29992900533735 absolute error = 1.392663762089796e-12 relative error = 4.753130158902565e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.760000000000584 y[1] (closed_form) = 29.32924358919312 y[1] (numeric) = 29.32924358919174 absolute error = 1.378452907374594e-12 relative error = 4.699926553450257e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.770000000000579 y[1] (closed_form) = 29.35858750229352 y[1] (numeric) = 29.35858750229215 absolute error = 1.367794766338193e-12 relative error = 4.658925659251623e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.780000000000573 y[1] (closed_form) = 29.38796077398386 y[1] (numeric) = 29.38796077398252 absolute error = 1.342925770586589e-12 relative error = 4.569645988419294e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.790000000000568 y[1] (closed_form) = 29.41736343363744 y[1] (numeric) = 29.41736343363612 absolute error = 1.321609488513786e-12 relative error = 4.492617060992574e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.800000000000562 y[1] (closed_form) = 29.44679551065689 y[1] (numeric) = 29.44679551065559 absolute error = 1.307398633798584e-12 relative error = 4.439867262722806e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.810000000000556 y[1] (closed_form) = 29.47625703447432 y[1] (numeric) = 29.47625703447303 absolute error = 1.289635065404582e-12 relative error = 4.375165625324387e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.820000000000551 y[1] (closed_form) = 29.50574803455123 y[1] (numeric) = 29.50574803454996 absolute error = 1.271871497010579e-12 relative error = 4.310588891090705e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.830000000000545 y[1] (closed_form) = 29.53526854037864 y[1] (numeric) = 29.53526854037739 absolute error = 1.250555214937776e-12 relative error = 4.234108158617556e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.84000000000054 y[1] (closed_form) = 29.56481858147705 y[1] (numeric) = 29.56481858147581 absolute error = 1.239897073901375e-12 relative error = 4.193826085840403e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.850000000000534 y[1] (closed_form) = 29.5943981873965 y[1] (numeric) = 29.59439818739527 absolute error = 1.222133505507372e-12 relative error = 4.129610941126852e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.860000000000529 y[1] (closed_form) = 29.6240073877166 y[1] (numeric) = 29.62400738771539 absolute error = 1.20792265079217e-12 relative error = 4.077512657160041e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.870000000000523 y[1] (closed_form) = 29.65364621204657 y[1] (numeric) = 29.65364621204537 absolute error = 1.193711796076968e-12 relative error = 4.025514392196505e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.880000000000518 y[1] (closed_form) = 29.68331469002521 y[1] (numeric) = 29.68331469002403 absolute error = 1.179500941361766e-12 relative error = 3.973615998344437e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.890000000000512 y[1] (closed_form) = 29.71301285132103 y[1] (numeric) = 29.71301285131986 absolute error = 1.161737372967764e-12 relative error = 3.909860567761689e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.900000000000507 y[1] (closed_form) = 29.74274072563216 y[1] (numeric) = 29.74274072563102 absolute error = 1.143973804573761e-12 relative error = 3.846228614661223e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.910000000000501 y[1] (closed_form) = 29.7724983426865 y[1] (numeric) = 29.77249834268537 absolute error = 1.129762949858559e-12 relative error = 3.794652826426577e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.920000000000496 y[1] (closed_form) = 29.80228573224167 y[1] (numeric) = 29.80228573224055 absolute error = 1.115552095143357e-12 relative error = 3.743176295825171e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.93000000000049 y[1] (closed_form) = 29.83210292408505 y[1] (numeric) = 29.83210292408395 absolute error = 1.097788526749355e-12 relative error = 3.679889847333061e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.940000000000484 y[1] (closed_form) = 29.86194994803384 y[1] (numeric) = 29.86194994803276 absolute error = 1.080024958355352e-12 relative error = 3.616726169037273e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.950000000000479 y[1] (closed_form) = 29.89182683393507 y[1] (numeric) = 29.891826833934 absolute error = 1.06226138996135e-12 relative error = 3.553685078743345e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.960000000000473 y[1] (closed_form) = 29.92173361166562 y[1] (numeric) = 29.92173361166457 absolute error = 1.040945107888547e-12 relative error = 3.478893039415044e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.970000000000468 y[1] (closed_form) = 29.95167031113228 y[1] (numeric) = 29.95167031113125 absolute error = 1.030286966852145e-12 relative error = 3.439831422253648e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.980000000000462 y[1] (closed_form) = 29.98163696227174 y[1] (numeric) = 29.98163696227073 absolute error = 1.008970684779342e-12 relative error = 3.365295517549658e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 8.990000000000457 y[1] (closed_form) = 30.01163359505067 y[1] (numeric) = 30.01163359504967 absolute error = 9.983125437429408e-13 relative error = 3.326418538934769e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.000000000000451 y[1] (closed_form) = 30.04166023946569 y[1] (numeric) = 30.04166023946471 absolute error = 9.734435479913373e-13 relative error = 3.240312087387653e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.010000000000446 y[1] (closed_form) = 30.07171692554345 y[1] (numeric) = 30.07171692554249 absolute error = 9.556799795973347e-13 relative error = 3.178002712527409e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.02000000000044 y[1] (closed_form) = 30.10180368334065 y[1] (numeric) = 30.10180368333971 absolute error = 9.379164112033322e-13 relative error = 3.11581465705461e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.030000000000435 y[1] (closed_form) = 30.13192054294403 y[1] (numeric) = 30.13192054294312 absolute error = 9.166001291305292e-13 relative error = 3.041957208881492e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.040000000000429 y[1] (closed_form) = 30.16206753447048 y[1] (numeric) = 30.16206753446957 absolute error = 9.059419880941277e-13 relative error = 3.003580530607788e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.050000000000423 y[1] (closed_form) = 30.19224468806696 y[1] (numeric) = 30.19224468806607 absolute error = 8.917311333789257e-13 relative error = 2.953510554090631e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.060000000000418 y[1] (closed_form) = 30.22245203391066 y[1] (numeric) = 30.22245203390978 absolute error = 8.775202786637237e-13 relative error = 2.903537666894516e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.070000000000412 y[1] (closed_form) = 30.2526896022089 y[1] (numeric) = 30.25268960220804 absolute error = 8.633094239485217e-13 relative error = 2.853661724957794e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.080000000000407 y[1] (closed_form) = 30.28295742319927 y[1] (numeric) = 30.28295742319842 absolute error = 8.490985692333197e-13 relative error = 2.803882584409802e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.090000000000401 y[1] (closed_form) = 30.31325552714959 y[1] (numeric) = 30.31325552714875 absolute error = 8.348877145181177e-13 relative error = 2.754200101570627e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.100000000000396 y[1] (closed_form) = 30.34358394435796 y[1] (numeric) = 30.34358394435714 absolute error = 8.206768598029157e-13 relative error = 2.704614132950868e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.11000000000039 y[1] (closed_form) = 30.3739427051528 y[1] (numeric) = 30.37394270515199 absolute error = 8.064660050877137e-13 relative error = 2.655124535251397e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.120000000000385 y[1] (closed_form) = 30.40433183989288 y[1] (numeric) = 30.40433183989209 absolute error = 7.887024366937112e-13 relative error = 2.594046272244903e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.130000000000379 y[1] (closed_form) = 30.43475137896733 y[1] (numeric) = 30.43475137896656 absolute error = 7.673861546209082e-13 relative error = 2.521414238169952e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.140000000000374 y[1] (closed_form) = 30.4652013527957 y[1] (numeric) = 30.46520135279494 absolute error = 7.567280135845067e-13 relative error = 2.483909444160178e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.150000000000368 y[1] (closed_form) = 30.49568179182796 y[1] (numeric) = 30.49568179182722 absolute error = 7.354117315117037e-13 relative error = 2.411527430446807e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.160000000000363 y[1] (closed_form) = 30.52619272654454 y[1] (numeric) = 30.52619272654383 absolute error = 7.176481631177012e-13 relative error = 2.350925873876367e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.170000000000357 y[1] (closed_form) = 30.55673418745641 y[1] (numeric) = 30.55673418745571 absolute error = 7.034373084024992e-13 relative error = 2.302069665191058e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.180000000000351 y[1] (closed_form) = 30.587306205105 y[1] (numeric) = 30.58730620510432 absolute error = 6.821210263296962e-13 relative error = 2.230078784171751e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.190000000000346 y[1] (closed_form) = 30.61790881006235 y[1] (numeric) = 30.61790881006169 absolute error = 6.643574579356937e-13 relative error = 2.16983289765811e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.20000000000034 y[1] (closed_form) = 30.64854203293106 y[1] (numeric) = 30.64854203293042 absolute error = 6.394884621840902e-13 relative error = 2.086521641052212e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.210000000000335 y[1] (closed_form) = 30.67920590434436 y[1] (numeric) = 30.67920590434373 absolute error = 6.323830348264892e-13 relative error = 2.061275760520711e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.220000000000329 y[1] (closed_form) = 30.70990045496612 y[1] (numeric) = 30.70990045496551 absolute error = 6.146194664324867e-13 relative error = 2.001372382609257e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.230000000000324 y[1] (closed_form) = 30.74062571549089 y[1] (numeric) = 30.7406257154903 absolute error = 5.933031843596837e-13 relative error = 1.930029628709557e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.240000000000318 y[1] (closed_form) = 30.77138171664394 y[1] (numeric) = 30.77138171664336 absolute error = 5.790923296444817e-13 relative error = 1.881918514342358e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.250000000000313 y[1] (closed_form) = 30.80216848918128 y[1] (numeric) = 30.80216848918071 absolute error = 5.648814749292796e-13 relative error = 1.833901646008087e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.260000000000307 y[1] (closed_form) = 30.83298606388966 y[1] (numeric) = 30.83298606388912 absolute error = 5.471179065352771e-13 relative error = 1.774456438963073e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.270000000000302 y[1] (closed_form) = 30.86383447158669 y[1] (numeric) = 30.86383447158616 absolute error = 5.222489107836736e-13 relative error = 1.69210637539045e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.280000000000296 y[1] (closed_form) = 30.89471374312075 y[1] (numeric) = 30.89471374312024 absolute error = 5.044853423896711e-13 relative error = 1.632918002038468e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.29000000000029 y[1] (closed_form) = 30.92562390937113 y[1] (numeric) = 30.92562390937064 absolute error = 4.938272013532696e-13 relative error = 1.596822113598909e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.300000000000285 y[1] (closed_form) = 30.956565001248 y[1] (numeric) = 30.95656500124752 absolute error = 4.796163466380676e-13 relative error = 1.549320302878346e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.310000000000279 y[1] (closed_form) = 30.98753704969245 y[1] (numeric) = 30.98753704969199 absolute error = 4.583000645652646e-13 relative error = 1.4789819011118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.320000000000274 y[1] (closed_form) = 31.01854008567653 y[1] (numeric) = 31.01854008567608 absolute error = 4.440892098500626e-13 relative error = 1.43168959152636e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.330000000000268 y[1] (closed_form) = 31.04957414020328 y[1] (numeric) = 31.04957414020285 absolute error = 4.263256414560601e-13 relative error = 1.373048272839432e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.340000000000263 y[1] (closed_form) = 31.08063924430676 y[1] (numeric) = 31.08063924430635 absolute error = 4.121147867408581e-13 relative error = 1.325953380499881e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.350000000000257 y[1] (closed_form) = 31.11173542905208 y[1] (numeric) = 31.11173542905168 absolute error = 3.943512183468556e-13 relative error = 1.267532051518448e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.360000000000252 y[1] (closed_form) = 31.14286272553541 y[1] (numeric) = 31.14286272553503 absolute error = 3.765876499528531e-13 relative error = 1.209226182164918e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.370000000000246 y[1] (closed_form) = 31.17402116488406 y[1] (numeric) = 31.1740211648837 absolute error = 3.588240815588506e-13 relative error = 1.151035599998397e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.380000000000241 y[1] (closed_form) = 31.20521077825648 y[1] (numeric) = 31.20521077825613 absolute error = 3.481659405224491e-13 relative error = 1.115730135574178e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.390000000000235 y[1] (closed_form) = 31.23643159684228 y[1] (numeric) = 31.23643159684195 absolute error = 3.268496584496461e-13 relative error = 1.046373230681982e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.40000000000023 y[1] (closed_form) = 31.26768365186228 y[1] (numeric) = 31.26768365186198 absolute error = 3.019806626980426e-13 relative error = 9.657916015152497e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.410000000000224 y[1] (closed_form) = 31.29896697456853 y[1] (numeric) = 31.29896697456825 absolute error = 2.806643806252396e-13 relative error = 8.967209072851792e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.420000000000218 y[1] (closed_form) = 31.33028159624437 y[1] (numeric) = 31.33028159624411 absolute error = 2.593480985524366e-13 relative error = 8.277873205695196e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.430000000000213 y[1] (closed_form) = 31.36162754820441 y[1] (numeric) = 31.36162754820416 absolute error = 2.522426711948356e-13 relative error = 8.043035101004429e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.440000000000207 y[1] (closed_form) = 31.39300486179462 y[1] (numeric) = 31.39300486179439 absolute error = 2.309263891220326e-13 relative error = 7.355982332327501e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.450000000000202 y[1] (closed_form) = 31.4244135683923 y[1] (numeric) = 31.42441356839209 absolute error = 2.167155344068306e-13 relative error = 6.896406640498459e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.460000000000196 y[1] (closed_form) = 31.45585369940617 y[1] (numeric) = 31.45585369940598 absolute error = 1.953992523340276e-13 relative error = 6.21185659754376e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.470000000000191 y[1] (closed_form) = 31.48732528627637 y[1] (numeric) = 31.48732528627619 absolute error = 1.77635683940025e-13 relative error = 5.641498041672244e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.480000000000185 y[1] (closed_form) = 31.51882836047447 y[1] (numeric) = 31.51882836047431 absolute error = 1.63424829224823e-13 relative error = 5.184990614364414e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.49000000000018 y[1] (closed_form) = 31.55036295350356 y[1] (numeric) = 31.55036295350341 absolute error = 1.456612608308205e-13 relative error = 4.616785583274736e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.500000000000174 y[1] (closed_form) = 31.58192909689823 y[1] (numeric) = 31.5819290968981 absolute error = 1.27897692436818e-13 relative error = 4.049711214422912e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.510000000000169 y[1] (closed_form) = 31.61352682222463 y[1] (numeric) = 31.61352682222451 absolute error = 1.13686837721616e-13 relative error = 3.596145357679392e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.520000000000163 y[1] (closed_form) = 31.64515616108048 y[1] (numeric) = 31.64515616108039 absolute error = 9.237055564881302e-14 relative error = 2.918947695458588e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.530000000000157 y[1] (closed_form) = 31.67681714509514 y[1] (numeric) = 31.67681714509506 absolute error = 7.815970093361102e-14 relative error = 2.467410174942824e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.540000000000152 y[1] (closed_form) = 31.70850980592958 y[1] (numeric) = 31.70850980592952 absolute error = 6.394884621840902e-14 relative error = 2.016772362050594e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.550000000000146 y[1] (closed_form) = 31.74023417527647 y[1] (numeric) = 31.74023417527642 absolute error = 4.973799150320701e-14 relative error = 1.567032909352307e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.560000000000141 y[1] (closed_form) = 31.77199028486017 y[1] (numeric) = 31.77199028486014 absolute error = 3.197442310920451e-14 relative error = 1.006371424091767e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.570000000000135 y[1] (closed_form) = 31.80377816643681 y[1] (numeric) = 31.8037781664368 absolute error = 1.77635683940025e-14 relative error = 5.585364198253894e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.58000000000013 y[1] (closed_form) = 31.83559785179428 y[1] (numeric) = 31.83559785179427 absolute error = 7.105427357601002e-15 relative error = 2.231912650322832e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.590000000000124 y[1] (closed_form) = 31.86744937275224 y[1] (numeric) = 31.86744937275225 absolute error = 1.06581410364015e-14 relative error = 3.344522779885414e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.600000000000119 y[1] (closed_form) = 31.89933276116223 y[1] (numeric) = 31.89933276116225 absolute error = 2.486899575160351e-14 relative error = 7.796086500555827e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.610000000000113 y[1] (closed_form) = 31.93124804890763 y[1] (numeric) = 31.93124804890768 absolute error = 4.973799150320701e-14 relative error = 1.557658862159901e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.620000000000108 y[1] (closed_form) = 31.96319526790376 y[1] (numeric) = 31.96319526790382 absolute error = 6.394884621840902e-14 relative error = 2.000702548115521e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.630000000000102 y[1] (closed_form) = 31.99517445009781 y[1] (numeric) = 31.9951744500979 absolute error = 8.881784197001252e-14 relative error = 2.775976174424047e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.640000000000096 y[1] (closed_form) = 32.02718562746897 y[1] (numeric) = 32.02718562746907 absolute error = 9.947598300641403e-14 relative error = 3.105985776068184e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.650000000000091 y[1] (closed_form) = 32.05922883202844 y[1] (numeric) = 32.05922883202855 absolute error = 1.13686837721616e-13 relative error = 3.546150106019967e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.660000000000085 y[1] (closed_form) = 32.09130409581941 y[1] (numeric) = 32.09130409581954 absolute error = 1.27897692436818e-13 relative error = 3.98543144444789e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.67000000000008 y[1] (closed_form) = 32.12341145091715 y[1] (numeric) = 32.1234114509173 absolute error = 1.56319401867222e-13 relative error = 4.86621422840067e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.680000000000074 y[1] (closed_form) = 32.15555092942901 y[1] (numeric) = 32.15555092942918 absolute error = 1.70530256582424e-13 relative error = 5.303291396147513e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.690000000000069 y[1] (closed_form) = 32.18772256349448 y[1] (numeric) = 32.18772256349467 absolute error = 1.918465386552271e-13 relative error = 5.960239599952582e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.700000000000063 y[1] (closed_form) = 32.21992638528521 y[1] (numeric) = 32.21992638528541 absolute error = 2.060573933704291e-13 relative error = 6.395340290551848e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.710000000000058 y[1] (closed_form) = 32.25216242700499 y[1] (numeric) = 32.25216242700522 absolute error = 2.273736754432321e-13 relative error = 7.049873817231253e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.720000000000052 y[1] (closed_form) = 32.2844307208899 y[1] (numeric) = 32.28443072089014 absolute error = 2.415845301584341e-13 relative error = 7.483004183874763e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.730000000000047 y[1] (closed_form) = 32.31673129920821 y[1] (numeric) = 32.31673129920848 absolute error = 2.629008122312371e-13 relative error = 8.135130059941376e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.740000000000041 y[1] (closed_form) = 32.34906419426053 y[1] (numeric) = 32.34906419426081 absolute error = 2.771116669464391e-13 relative error = 8.566296239122895e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.750000000000036 y[1] (closed_form) = 32.38142943837973 y[1] (numeric) = 32.38142943838002 absolute error = 2.984279490192421e-13 relative error = 9.216021472651041e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.76000000000003 y[1] (closed_form) = 32.41382706393106 y[1] (numeric) = 32.41382706393138 absolute error = 3.197442310920451e-13 relative error = 9.864439347485905e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.770000000000024 y[1] (closed_form) = 32.44625710331216 y[1] (numeric) = 32.4462571033125 absolute error = 3.410605131648481e-13 relative error = 1.051155182796207e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.780000000000019 y[1] (closed_form) = 32.47871958895307 y[1] (numeric) = 32.47871958895342 absolute error = 3.552713678800501e-13 relative error = 1.093858909391514e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.790000000000013 y[1] (closed_form) = 32.51121455331627 y[1] (numeric) = 32.51121455331664 absolute error = 3.694822225952521e-13 relative error = 1.136476221118486e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.800000000000008 y[1] (closed_form) = 32.54374202889673 y[1] (numeric) = 32.54374202889713 absolute error = 3.979039320256561e-13 relative error = 1.222674183172738e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.810000000000002 y[1] (closed_form) = 32.57630204822194 y[1] (numeric) = 32.57630204822237 absolute error = 4.263256414560601e-13 relative error = 1.30869870013171e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.819999999999997 y[1] (closed_form) = 32.60889464385191 y[1] (numeric) = 32.60889464385235 absolute error = 4.405364961712621e-13 relative error = 1.350970344081629e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.829999999999991 y[1] (closed_form) = 32.64151984837924 y[1] (numeric) = 32.64151984837969 absolute error = 4.547473508864641e-13 relative error = 1.393156179610441e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.839999999999986 y[1] (closed_form) = 32.67417769442914 y[1] (numeric) = 32.67417769442961 absolute error = 4.689582056016661e-13 relative error = 1.435256336019811e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.84999999999998 y[1] (closed_form) = 32.70686821465945 y[1] (numeric) = 32.70686821465995 absolute error = 4.973799150320701e-13 relative error = 1.520720087804496e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.859999999999975 y[1] (closed_form) = 32.73959144176071 y[1] (numeric) = 32.73959144176123 absolute error = 5.258016244624741e-13 relative error = 1.606011563698966e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.869999999999969 y[1] (closed_form) = 32.77234740845614 y[1] (numeric) = 32.77234740845667 absolute error = 5.258016244624741e-13 relative error = 1.604406354873448e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.879999999999963 y[1] (closed_form) = 32.80513614750171 y[1] (numeric) = 32.80513614750226 absolute error = 5.542233338928781e-13 relative error = 1.689440736965469e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.889999999999958 y[1] (closed_form) = 32.83795769168615 y[1] (numeric) = 32.83795769168673 absolute error = 5.755396159656812e-13 relative error = 1.752665684539192e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.899999999999952 y[1] (closed_form) = 32.87081207383103 y[1] (numeric) = 32.87081207383162 absolute error = 5.897504706808832e-13 relative error = 1.794146336744728e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.909999999999947 y[1] (closed_form) = 32.90369932679071 y[1] (numeric) = 32.90369932679133 absolute error = 6.110667527536862e-13 relative error = 1.857136933706861e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.919999999999941 y[1] (closed_form) = 32.93661948345247 y[1] (numeric) = 32.93661948345311 absolute error = 6.394884621840902e-13 relative error = 1.941572851777859e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.929999999999936 y[1] (closed_form) = 32.96957257673646 y[1] (numeric) = 32.96957257673711 absolute error = 6.536993168992922e-13 relative error = 1.982735188264305e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.93999999999993 y[1] (closed_form) = 33.00255863959577 y[1] (numeric) = 33.00255863959644 absolute error = 6.750155989720952e-13 relative error = 2.045343230334347e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.949999999999925 y[1] (closed_form) = 33.03557770501646 y[1] (numeric) = 33.03557770501717 absolute error = 7.034373084024992e-13 relative error = 2.129332547726816e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.959999999999919 y[1] (closed_form) = 33.06862980601763 y[1] (numeric) = 33.06862980601834 absolute error = 7.176481631177012e-13 relative error = 2.170178103318656e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.969999999999914 y[1] (closed_form) = 33.10171497565135 y[1] (numeric) = 33.10171497565208 absolute error = 7.318590178329032e-13 relative error = 2.2109398814268e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.979999999999908 y[1] (closed_form) = 33.1348332470028 y[1] (numeric) = 33.13483324700354 absolute error = 7.460698725481052e-13 relative error = 2.251618008717731e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.989999999999903 y[1] (closed_form) = 33.16798465319025 y[1] (numeric) = 33.16798465319102 absolute error = 7.673861546209082e-13 relative error = 2.313635159461211e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 9.999999999999897 y[1] (closed_form) = 33.20116922736513 y[1] (numeric) = 33.20116922736592 absolute error = 7.815970093361102e-13 relative error = 2.354124952599262e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = exp ( 0.1 * x + 0.2 ) ; Iterations = 9001 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %