##############ECHO OF PROBLEM################# ##############temp/mult_div_sinh_cosh_tanhpostode.ode################# diff ( y , x , 1 ) = sinh ( 0.1 ) * cosh ( 0.05 ) / tanh ( 0.02 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return((sinh(c(0.1)) * cosh(c(0.05)) / tanh(c(0.02))) * c(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.5015267822632982 y[1] (numeric) = 0.5015267822632982 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (closed_form) = 0.5516794604896281 y[1] (numeric) = 0.5516794604896277 absolute error = 4.440892098500626e-16 relative error = 8.049768781602333e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (closed_form) = 0.601832138715958 y[1] (numeric) = 0.6018321387159572 absolute error = 7.771561172376096e-16 relative error = 1.291317075382041e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (closed_form) = 0.6519848169422878 y[1] (numeric) = 0.6519848169422867 absolute error = 1.110223024625157e-15 relative error = 1.702835703800493e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (closed_form) = 0.7021374951686177 y[1] (numeric) = 0.7021374951686162 absolute error = 1.443289932012704e-15 relative error = 2.055565956730596e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (closed_form) = 0.7522901733949475 y[1] (numeric) = 0.7522901733949457 absolute error = 1.77635683940025e-15 relative error = 2.361265509270017e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 0.8024428516212774 y[1] (numeric) = 0.8024428516212753 absolute error = 2.109423746787797e-15 relative error = 2.628752617742011e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 0.8525955298476072 y[1] (numeric) = 0.8525955298476048 absolute error = 2.442490654175344e-15 relative error = 2.864770654629065e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 0.9027482080739371 y[1] (numeric) = 0.9027482080739343 absolute error = 2.775557561562891e-15 relative error = 3.074564465195335e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 0.952900886300267 y[1] (numeric) = 0.9529008863002638 absolute error = 3.219646771412954e-15 relative error = 3.378784528067294e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 1.003053564526597 y[1] (numeric) = 1.003053564526593 absolute error = 3.33066907387547e-15 relative error = 3.320529622410962e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (closed_form) = 1.053206242752927 y[1] (numeric) = 1.053206242752923 absolute error = 3.774758283725532e-15 relative error = 3.584063719427704e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (closed_form) = 1.103358920979256 y[1] (numeric) = 1.103358920979252 absolute error = 3.996802888650564e-15 relative error = 3.622395951721049e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (closed_form) = 1.153511599205586 y[1] (numeric) = 1.153511599205582 absolute error = 4.440892098500626e-15 relative error = 3.849889417288071e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (closed_form) = 1.203664277431916 y[1] (numeric) = 1.203664277431912 absolute error = 4.884981308350689e-15 relative error = 4.058425094057841e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = 1.253816955658246 y[1] (numeric) = 1.253816955658241 absolute error = 5.10702591327572e-15 relative error = 4.073183003490779e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = 1.303969633884576 y[1] (numeric) = 1.303969633884571 absolute error = 5.329070518200751e-15 relative error = 4.086805689121184e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = 1.354122312110906 y[1] (numeric) = 1.3541223121109 absolute error = 5.773159728050814e-15 relative error = 4.263396058404197e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = 1.404274990337236 y[1] (numeric) = 1.40427499033723 absolute error = 5.995204332975845e-15 relative error = 4.269252371671236e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = 1.454427668563566 y[1] (numeric) = 1.454427668563559 absolute error = 6.439293542825908e-15 relative error = 4.427372829881281e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 1.504580346789895 y[1] (numeric) = 1.504580346789889 absolute error = 6.661338147750939e-15 relative error = 4.427372829881282e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 1.554733025016225 y[1] (numeric) = 1.554733025016218 absolute error = 7.105427357601002e-15 relative error = 4.570191308264549e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 1.604885703242555 y[1] (numeric) = 1.604885703242548 absolute error = 7.327471962526033e-15 relative error = 4.565728230815072e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 1.655038381468885 y[1] (numeric) = 1.655038381468877 absolute error = 7.771561172376096e-15 relative error = 4.695698455934692e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 1.705191059695215 y[1] (numeric) = 1.705191059695207 absolute error = 8.215650382226158e-15 relative error = 4.818023373694336e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (closed_form) = 1.755343737921545 y[1] (numeric) = 1.755343737921536 absolute error = 8.43769498715119e-15 relative error = 4.806861929585392e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (closed_form) = 1.805496416147875 y[1] (numeric) = 1.805496416147866 absolute error = 8.881784197001252e-15 relative error = 4.919303144312535e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (closed_form) = 1.855649094374204 y[1] (numeric) = 1.855649094374195 absolute error = 9.103828801926284e-15 relative error = 4.906007730408987e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (closed_form) = 1.905801772600534 y[1] (numeric) = 1.905801772600525 absolute error = 9.547918011776346e-15 relative error = 5.009921886444607e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = 1.955954450826864 y[1] (numeric) = 1.955954450826854 absolute error = 9.769962616701378e-15 relative error = 4.994984731148112e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (closed_form) = 2.006107129053194 y[1] (numeric) = 2.006107129053184 absolute error = 9.769962616701378e-15 relative error = 4.87011011286941e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 2.056259807279524 y[1] (numeric) = 2.056259807279516 absolute error = 7.993605777301127e-15 relative error = 3.887449314042101e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 2.106412485505854 y[1] (numeric) = 2.106412485505848 absolute error = 6.217248937900877e-15 relative error = 2.95158188658752e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 2.156565163732183 y[1] (numeric) = 2.156565163732179 absolute error = 3.996802888650564e-15 relative error = 1.853318859020071e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 2.206717841958513 y[1] (numeric) = 2.206717841958511 absolute error = 2.220446049250313e-15 relative error = 1.006221097700291e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 2.256870520184843 y[1] (numeric) = 2.256870520184843 absolute error = 4.440892098500626e-16 relative error = 1.967721257725014e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (closed_form) = 2.307023198411173 y[1] (numeric) = 2.307023198411175 absolute error = 1.332267629550188e-15 relative error = 5.774834125932105e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = 2.357175876637503 y[1] (numeric) = 2.357175876637506 absolute error = 3.552713678800501e-15 relative error = 1.507190750597883e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (closed_form) = 2.407328554863833 y[1] (numeric) = 2.407328554863838 absolute error = 5.329070518200751e-15 relative error = 2.213686414940641e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = 2.457481233090163 y[1] (numeric) = 2.45748123309017 absolute error = 7.105427357601002e-15 relative error = 2.891345521555122e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (closed_form) = 2.507633911316493 y[1] (numeric) = 2.507633911316502 absolute error = 8.881784197001252e-15 relative error = 3.541898263905025e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (closed_form) = 2.557786589542823 y[1] (numeric) = 2.557786589542833 absolute error = 1.06581410364015e-14 relative error = 4.166939134005911e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (closed_form) = 2.607939267769152 y[1] (numeric) = 2.607939267769165 absolute error = 1.287858708565182e-14 relative error = 4.938223541021429e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (closed_form) = 2.658091945995482 y[1] (numeric) = 2.658091945995497 absolute error = 1.465494392505207e-14 relative error = 5.513332203248388e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (closed_form) = 2.708244624221812 y[1] (numeric) = 2.708244624221829 absolute error = 1.643130076445232e-14 relative error = 6.067140544652126e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (closed_form) = 2.758397302448142 y[1] (numeric) = 2.75839730244816 absolute error = 1.820765760385257e-14 relative error = 6.60081040091391e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (closed_form) = 2.808549980674472 y[1] (numeric) = 2.808549980674492 absolute error = 2.042810365310288e-14 relative error = 7.273541077662105e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (closed_form) = 2.858702658900802 y[1] (numeric) = 2.858702658900824 absolute error = 2.220446049250313e-14 relative error = 7.767320754177687e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (closed_form) = 2.908855337127132 y[1] (numeric) = 2.908855337127155 absolute error = 2.398081733190338e-14 relative error = 8.244073545296178e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (closed_form) = 2.959008015353461 y[1] (numeric) = 2.959008015353487 absolute error = 2.575717417130363e-14 relative error = 8.704665224851332e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (closed_form) = 3.009160693579791 y[1] (numeric) = 3.009160693579819 absolute error = 2.753353101070388e-14 relative error = 9.149903848421313e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (closed_form) = 3.059313371806121 y[1] (numeric) = 3.059313371806151 absolute error = 2.97539770599542e-14 relative error = 9.725704249247405e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (closed_form) = 3.109466050032451 y[1] (numeric) = 3.109466050032482 absolute error = 3.153033389935445e-14 relative error = 1.014011196521197e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (closed_form) = 3.159618728258781 y[1] (numeric) = 3.159618728258814 absolute error = 3.33066907387547e-14 relative error = 1.054136388066972e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (closed_form) = 3.209771406485111 y[1] (numeric) = 3.209771406485146 absolute error = 3.508304757815495e-14 relative error = 1.093007667376941e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (closed_form) = 3.25992408471144 y[1] (numeric) = 3.259924084711478 absolute error = 3.730349362740526e-14 relative error = 1.144305592953931e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (closed_form) = 3.31007676293777 y[1] (numeric) = 3.310076762937809 absolute error = 3.907985046680551e-14 relative error = 1.180632754635008e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (closed_form) = 3.3602294411641 y[1] (numeric) = 3.360229441164141 absolute error = 4.085620730620576e-14 relative error = 1.215875523430083e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (closed_form) = 3.41038211939043 y[1] (numeric) = 3.410382119390473 absolute error = 4.263256414560601e-14 relative error = 1.250081740201773e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (closed_form) = 3.46053479761676 y[1] (numeric) = 3.460534797616805 absolute error = 4.440892098500626e-14 relative error = 1.283296472429357e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (closed_form) = 3.51068747584309 y[1] (numeric) = 3.510687475843136 absolute error = 4.662936703425657e-14 relative error = 1.328211848964384e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (closed_form) = 3.56084015406942 y[1] (numeric) = 3.560840154069468 absolute error = 4.840572387365683e-14 relative error = 1.359390530864957e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (closed_form) = 3.61099283229575 y[1] (numeric) = 3.6109928322958 absolute error = 5.018208071305708e-14 relative error = 1.389703138268291e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (closed_form) = 3.66114551052208 y[1] (numeric) = 3.661145510522132 absolute error = 5.195843755245733e-14 relative error = 1.419185263277013e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (closed_form) = 3.711298188748409 y[1] (numeric) = 3.711298188748463 absolute error = 5.417888360170764e-14 relative error = 1.459836446609504e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (closed_form) = 3.761450866974739 y[1] (numeric) = 3.761450866974795 absolute error = 5.595524044110789e-14 relative error = 1.48759727084011e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (closed_form) = 3.811603545201069 y[1] (numeric) = 3.811603545201127 absolute error = 5.773159728050814e-14 relative error = 1.514627547064649e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (closed_form) = 3.861756223427399 y[1] (numeric) = 3.861756223427459 absolute error = 5.950795411990839e-14 relative error = 1.540955738192446e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (closed_form) = 3.911908901653729 y[1] (numeric) = 3.91190890165379 absolute error = 6.128431095930864e-14 relative error = 1.566608847496453e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (closed_form) = 3.962061579880058 y[1] (numeric) = 3.962061579880122 absolute error = 6.350475700855895e-14 relative error = 1.602821049805122e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (closed_form) = 4.012214258106389 y[1] (numeric) = 4.012214258106453 absolute error = 6.394884621840902e-14 relative error = 1.593854218757261e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (closed_form) = 4.062366936332718 y[1] (numeric) = 4.06236693633278 absolute error = 6.217248937900877e-14 relative error = 1.530449867119455e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (closed_form) = 4.112519614559048 y[1] (numeric) = 4.112519614559107 absolute error = 5.950795411990839e-14 relative error = 1.446995022449004e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (closed_form) = 4.162672292785378 y[1] (numeric) = 4.162672292785435 absolute error = 5.684341886080801e-14 relative error = 1.365551137891094e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (closed_form) = 4.212824971011708 y[1] (numeric) = 4.212824971011762 absolute error = 5.417888360170764e-14 relative error = 1.286046393441705e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (closed_form) = 4.262977649238038 y[1] (numeric) = 4.262977649238089 absolute error = 5.151434834260726e-14 relative error = 1.208412348861714e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (closed_form) = 4.313130327464368 y[1] (numeric) = 4.313130327464417 absolute error = 4.884981308350689e-14 relative error = 1.132583747178932e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (closed_form) = 4.363283005690698 y[1] (numeric) = 4.363283005690744 absolute error = 4.618527782440651e-14 relative error = 1.058498331741731e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (closed_form) = 4.413435683917028 y[1] (numeric) = 4.413435683917071 absolute error = 4.352074256530614e-14 relative error = 9.860966757462852e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (closed_form) = 4.463588362143358 y[1] (numeric) = 4.463588362143398 absolute error = 4.085620730620576e-14 relative error = 9.153220232563545e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (closed_form) = 4.513741040369687 y[1] (numeric) = 4.513741040369726 absolute error = 3.907985046680551e-14 relative error = 8.657973533990061e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (closed_form) = 4.563893718596017 y[1] (numeric) = 4.563893718596053 absolute error = 3.641531520770513e-14 relative error = 7.979001583522309e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (closed_form) = 4.614046396822347 y[1] (numeric) = 4.61404639682238 absolute error = 3.375077994860476e-14 relative error = 7.314789892847334e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (closed_form) = 4.664199075048677 y[1] (numeric) = 4.664199075048708 absolute error = 3.108624468950438e-14 relative error = 6.664862324552465e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (closed_form) = 4.714351753275007 y[1] (numeric) = 4.714351753275035 absolute error = 2.842170943040401e-14 relative error = 6.028763002391531e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (closed_form) = 4.764504431501337 y[1] (numeric) = 4.764504431501362 absolute error = 2.575717417130363e-14 relative error = 5.406055244907669e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (closed_form) = 4.814657109727666 y[1] (numeric) = 4.81465710972769 absolute error = 2.309263891220326e-14 relative error = 4.79632056570472e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (closed_form) = 4.864809787953996 y[1] (numeric) = 4.864809787954017 absolute error = 2.042810365310288e-14 relative error = 4.199157735557503e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (closed_form) = 4.914962466180326 y[1] (numeric) = 4.914962466180344 absolute error = 1.77635683940025e-14 relative error = 3.614181901943902e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (closed_form) = 4.965115144406655 y[1] (numeric) = 4.965115144406671 absolute error = 1.598721155460225e-14 relative error = 3.219907512640932e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y[1] (closed_form) = 5.015267822632985 y[1] (numeric) = 5.015267822632999 absolute error = 1.332267629550188e-14 relative error = 2.656423697928769e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (closed_form) = 5.065420500859309 y[1] (numeric) = 5.065420500859326 absolute error = 1.687538997430238e-14 relative error = 3.331488466049284e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y[1] (closed_form) = 5.115573179085634 y[1] (numeric) = 5.115573179085653 absolute error = 1.953992523340276e-14 relative error = 3.819694206172094e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y[1] (closed_form) = 5.165725857311958 y[1] (numeric) = 5.165725857311981 absolute error = 2.220446049250313e-14 relative error = 4.298420223185723e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y[1] (closed_form) = 5.215878535538282 y[1] (numeric) = 5.215878535538308 absolute error = 2.575717417130363e-14 relative error = 4.93822354102145e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y[1] (closed_form) = 5.266031213764607 y[1] (numeric) = 5.266031213764635 absolute error = 2.842170943040401e-14 relative error = 5.397178306902924e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y[1] (closed_form) = 5.316183891990931 y[1] (numeric) = 5.316183891990963 absolute error = 3.197442310920451e-14 relative error = 6.014544221725553e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y[1] (closed_form) = 5.366336570217255 y[1] (numeric) = 5.36633657021729 absolute error = 3.463895836830488e-14 relative error = 6.454861322069953e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y[1] (closed_form) = 5.41648924844358 y[1] (numeric) = 5.416489248443617 absolute error = 3.730349362740526e-14 relative error = 6.887024402037605e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y[1] (closed_form) = 5.466641926669904 y[1] (numeric) = 5.466641926669944 absolute error = 4.085620730620576e-14 relative error = 7.473730281634525e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y[1] (closed_form) = 5.516794604896228 y[1] (numeric) = 5.516794604896272 absolute error = 4.352074256530614e-14 relative error = 7.888773405970363e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y[1] (closed_form) = 5.566947283122553 y[1] (numeric) = 5.566947283122599 absolute error = 4.618527782440651e-14 relative error = 8.296338275813662e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y[1] (closed_form) = 5.617099961348877 y[1] (numeric) = 5.617099961348926 absolute error = 4.973799150320701e-14 relative error = 8.854745659762668e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y[1] (closed_form) = 5.667252639575201 y[1] (numeric) = 5.667252639575254 absolute error = 5.240252676230739e-14 relative error = 9.246548565061908e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y[1] (closed_form) = 5.717405317801525 y[1] (numeric) = 5.717405317801581 absolute error = 5.595524044110789e-14 relative error = 9.786824150264019e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y[1] (closed_form) = 5.76755799602785 y[1] (numeric) = 5.767557996027908 absolute error = 5.861977570020827e-14 relative error = 1.016370806164065e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y[1] (closed_form) = 5.817710674254174 y[1] (numeric) = 5.817710674254235 absolute error = 6.128431095930864e-14 relative error = 1.053409397454528e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y[1] (closed_form) = 5.867863352480498 y[1] (numeric) = 5.867863352480563 absolute error = 6.483702463810914e-14 relative error = 1.104951167799449e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y[1] (closed_form) = 5.918016030706823 y[1] (numeric) = 5.91801603070689 absolute error = 6.750155989720952e-14 relative error = 1.140611305325366e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y[1] (closed_form) = 5.968168708933147 y[1] (numeric) = 5.968168708933217 absolute error = 7.016609515630989e-14 relative error = 1.175672112808832e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y[1] (closed_form) = 6.018321387159471 y[1] (numeric) = 6.018321387159545 absolute error = 7.371880883511039e-14 relative error = 1.224906482933844e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y[1] (closed_form) = 6.068474065385796 y[1] (numeric) = 6.068474065385872 absolute error = 7.638334409421077e-14 relative error = 1.258691118577843e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y[1] (closed_form) = 6.118626743612119 y[1] (numeric) = 6.118626743612199 absolute error = 7.993605777301127e-14 relative error = 1.306437884227289e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y[1] (closed_form) = 6.168779421838444 y[1] (numeric) = 6.168779421838527 absolute error = 8.260059303211165e-14 relative error = 1.339010319281196e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y[1] (closed_form) = 6.218932100064769 y[1] (numeric) = 6.218932100064854 absolute error = 8.526512829121202e-14 relative error = 1.371057392479394e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y[1] (closed_form) = 6.269084778291092 y[1] (numeric) = 6.269084778291181 absolute error = 8.881784197001252e-14 relative error = 1.416759305562041e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y[1] (closed_form) = 6.319237456517417 y[1] (numeric) = 6.319237456517508 absolute error = 9.14823772291129e-14 relative error = 1.447680639612007e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y[1] (closed_form) = 6.369390134743742 y[1] (numeric) = 6.369390134743836 absolute error = 9.414691248821327e-14 relative error = 1.478115023519454e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y[1] (closed_form) = 6.419542812970065 y[1] (numeric) = 6.419542812970163 absolute error = 9.769962616701378e-14 relative error = 1.521909410271727e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y[1] (closed_form) = 6.46969549119639 y[1] (numeric) = 6.46969549119649 absolute error = 1.003641614261142e-13 relative error = 1.551296526439061e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y[1] (closed_form) = 6.519848169422714 y[1] (numeric) = 6.519848169422818 absolute error = 1.039168751049147e-13 relative error = 1.593854218757302e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y[1] (closed_form) = 6.570000847649038 y[1] (numeric) = 6.570000847649145 absolute error = 1.06581410364015e-13 relative error = 1.622243479651199e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y[1] (closed_form) = 6.620153525875363 y[1] (numeric) = 6.620153525875472 absolute error = 1.092459456231154e-13 relative error = 1.650202600228522e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y[1] (closed_form) = 6.670306204101687 y[1] (numeric) = 6.6703062041018 absolute error = 1.127986593019159e-13 relative error = 1.691056689909589e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y[1] (closed_form) = 6.720458882328011 y[1] (numeric) = 6.720458882328127 absolute error = 1.154631945610163e-13 relative error = 1.718084978759948e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y[1] (closed_form) = 6.770611560554335 y[1] (numeric) = 6.770611560554454 absolute error = 1.190159082398168e-13 relative error = 1.757830990234396e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y[1] (closed_form) = 6.82076423878066 y[1] (numeric) = 6.820764238780781 absolute error = 1.216804434989172e-13 relative error = 1.783970816746333e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y[1] (closed_form) = 6.870916917006984 y[1] (numeric) = 6.870916917007109 absolute error = 1.243449787580175e-13 relative error = 1.809729039951527e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y[1] (closed_form) = 6.921069595233308 y[1] (numeric) = 6.921069595233436 absolute error = 1.27897692436818e-13 relative error = 1.84794692029833e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y[1] (closed_form) = 6.971222273459633 y[1] (numeric) = 6.971222273459763 absolute error = 1.305622276959184e-13 relative error = 1.872874261849118e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y[1] (closed_form) = 7.021374951685957 y[1] (numeric) = 7.021374951686091 absolute error = 1.332267629550188e-13 relative error = 1.897445498520609e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y[1] (closed_form) = 7.071527629912281 y[1] (numeric) = 7.071527629912418 absolute error = 1.367794766338193e-13 relative error = 1.934228129934012e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y[1] (closed_form) = 7.121680308138606 y[1] (numeric) = 7.121680308138745 absolute error = 1.394440118929197e-13 relative error = 1.958021223356011e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y[1] (closed_form) = 7.171832986364929 y[1] (numeric) = 7.171832986365072 absolute error = 1.429967255717202e-13 relative error = 1.993865805904644e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y[1] (closed_form) = 7.221985664591254 y[1] (numeric) = 7.2219856645914 absolute error = 1.456612608308205e-13 relative error = 2.016914289168207e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y[1] (closed_form) = 7.272138342817579 y[1] (numeric) = 7.272138342817727 absolute error = 1.483257960899209e-13 relative error = 2.039644862317791e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y[1] (closed_form) = 7.322291021043903 y[1] (numeric) = 7.322291021044054 absolute error = 1.518785097687214e-13 relative error = 2.074193846328015e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y[1] (closed_form) = 7.372443699270227 y[1] (numeric) = 7.372443699270382 absolute error = 1.545430450278218e-13 relative error = 2.096225503127538e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y[1] (closed_form) = 7.422596377496552 y[1] (numeric) = 7.422596377496709 absolute error = 1.572075802869222e-13 relative error = 2.117959434835176e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y[1] (closed_form) = 7.472749055722876 y[1] (numeric) = 7.472749055723036 absolute error = 1.607602939657227e-13 relative error = 2.151287200559842e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y[1] (closed_form) = 7.5229017339492 y[1] (numeric) = 7.522901733949364 absolute error = 1.63424829224823e-13 relative error = 2.172364268528495e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y[1] (closed_form) = 7.573054412175524 y[1] (numeric) = 7.573054412175691 absolute error = 1.669775429036235e-13 relative error = 2.204890309980694e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y[1] (closed_form) = 7.623207090401849 y[1] (numeric) = 7.623207090402018 absolute error = 1.696420781627239e-13 relative error = 2.225337396071991e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y[1] (closed_form) = 7.673359768628173 y[1] (numeric) = 7.673359768628345 absolute error = 1.723066134218243e-13 relative error = 2.245517199992161e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y[1] (closed_form) = 7.723512446854497 y[1] (numeric) = 7.723512446854673 absolute error = 1.758593271006248e-13 relative error = 2.276934598224748e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y[1] (closed_form) = 7.773665125080822 y[1] (numeric) = 7.773665125081 absolute error = 1.785238623597252e-13 relative error = 2.296521132403026e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y[1] (closed_form) = 7.823817803307146 y[1] (numeric) = 7.823817803307327 absolute error = 1.811883976188255e-13 relative error = 2.315856557168762e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.569999999999938 y[1] (closed_form) = 7.87397048153347 y[1] (numeric) = 7.873970481533655 absolute error = 1.84741111297626e-13 relative error = 2.346225601567754e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.579999999999937 y[1] (closed_form) = 7.924123159759795 y[1] (numeric) = 7.924123159759982 absolute error = 1.874056465567264e-13 relative error = 2.365001688873388e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.589999999999936 y[1] (closed_form) = 7.974275837986118 y[1] (numeric) = 7.974275837986309 absolute error = 1.909583602355269e-13 relative error = 2.394679643835257e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.599999999999935 y[1] (closed_form) = 8.024428516212444 y[1] (numeric) = 8.024428516212641 absolute error = 1.971756091734278e-13 relative error = 2.457191920584213e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.609999999999933 y[1] (closed_form) = 8.074581194438768 y[1] (numeric) = 8.074581194438977 absolute error = 2.096101070492296e-13 relative error = 2.595925435657208e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.619999999999932 y[1] (closed_form) = 8.124733872665091 y[1] (numeric) = 8.124733872665313 absolute error = 2.220446049250313e-13 relative error = 2.732946191284858e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.629999999999931 y[1] (closed_form) = 8.174886550891415 y[1] (numeric) = 8.17488655089165 absolute error = 2.344791028008331e-13 relative error = 2.868285710647137e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.63999999999993 y[1] (closed_form) = 8.225039229117741 y[1] (numeric) = 8.225039229117986 absolute error = 2.451372438372346e-13 relative error = 2.980377807432406e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.649999999999929 y[1] (closed_form) = 8.275191907344064 y[1] (numeric) = 8.275191907344322 absolute error = 2.575717417130363e-13 relative error = 3.112577262219703e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.659999999999928 y[1] (closed_form) = 8.325344585570388 y[1] (numeric) = 8.325344585570658 absolute error = 2.700062395888381e-13 relative error = 3.243183952491491e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.669999999999927 y[1] (closed_form) = 8.375497263796714 y[1] (numeric) = 8.375497263796994 absolute error = 2.806643806252396e-13 relative error = 3.351017519143825e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.679999999999926 y[1] (closed_form) = 8.425649942023037 y[1] (numeric) = 8.42564994202333 absolute error = 2.930988785010413e-13 relative error = 3.478650080621163e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.689999999999925 y[1] (closed_form) = 8.475802620249361 y[1] (numeric) = 8.475802620249667 absolute error = 3.055333763768431e-13 relative error = 3.604772197583976e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.699999999999924 y[1] (closed_form) = 8.525955298475687 y[1] (numeric) = 8.525955298476003 absolute error = 3.161915174132446e-13 relative error = 3.70857582926543e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.709999999999922 y[1] (closed_form) = 8.57610797670201 y[1] (numeric) = 8.576107976702339 absolute error = 3.286260152890463e-13 relative error = 3.831878238727835e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.719999999999921 y[1] (closed_form) = 8.626260654928334 y[1] (numeric) = 8.626260654928675 absolute error = 3.410605131648481e-13 relative error = 3.953746899243002e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.72999999999992 y[1] (closed_form) = 8.67641333315466 y[1] (numeric) = 8.676413333155011 absolute error = 3.517186542012496e-13 relative error = 4.053733273140045e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.739999999999919 y[1] (closed_form) = 8.726566011380983 y[1] (numeric) = 8.726566011381347 absolute error = 3.641531520770513e-13 relative error = 4.172926115520485e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.749999999999918 y[1] (closed_form) = 8.776718689607307 y[1] (numeric) = 8.776718689607684 absolute error = 3.765876499528531e-13 relative error = 4.290756753988005e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.759999999999917 y[1] (closed_form) = 8.826871367833631 y[1] (numeric) = 8.82687136783402 absolute error = 3.890221478286549e-13 relative error = 4.407248407927486e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.769999999999916 y[1] (closed_form) = 8.877024046059956 y[1] (numeric) = 8.877024046060356 absolute error = 3.996802888650564e-13 relative error = 4.502413047337113e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.779999999999915 y[1] (closed_form) = 8.92717672428628 y[1] (numeric) = 8.927176724286692 absolute error = 4.121147867408581e-13 relative error = 4.616406725988796e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.789999999999914 y[1] (closed_form) = 8.977329402512604 y[1] (numeric) = 8.977329402513028 absolute error = 4.245492846166599e-13 relative error = 4.729126732253309e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.799999999999913 y[1] (closed_form) = 9.027482080738929 y[1] (numeric) = 9.027482080739365 absolute error = 4.352074256530614e-13 relative error = 4.820917081426521e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.809999999999911 y[1] (closed_form) = 9.077634758965253 y[1] (numeric) = 9.077634758965701 absolute error = 4.476419235288631e-13 relative error = 4.931261671293429e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.81999999999991 y[1] (closed_form) = 9.127787437191577 y[1] (numeric) = 9.127787437192037 absolute error = 4.600764214046649e-13 relative error = 5.04039368324971e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.829999999999909 y[1] (closed_form) = 9.177940115417902 y[1] (numeric) = 9.177940115418373 absolute error = 4.707345624410664e-13 relative error = 5.128978360299883e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.839999999999908 y[1] (closed_form) = 9.228092793644226 y[1] (numeric) = 9.228092793644709 absolute error = 4.831690603168681e-13 relative error = 5.235849607512041e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.849999999999907 y[1] (closed_form) = 9.27824547187055 y[1] (numeric) = 9.278245471871045 absolute error = 4.956035581926699e-13 relative error = 5.341565489889472e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.859999999999906 y[1] (closed_form) = 9.328398150096875 y[1] (numeric) = 9.328398150097382 absolute error = 5.062616992290714e-13 relative error = 5.427102178564429e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.869999999999905 y[1] (closed_form) = 9.378550828323199 y[1] (numeric) = 9.378550828323718 absolute error = 5.186961971048731e-13 relative error = 5.530664668771768e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.879999999999904 y[1] (closed_form) = 9.428703506549523 y[1] (numeric) = 9.428703506550054 absolute error = 5.311306949806749e-13 relative error = 5.63312543035988e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.889999999999903 y[1] (closed_form) = 9.478856184775848 y[1] (numeric) = 9.47885618477639 absolute error = 5.417888360170764e-13 relative error = 5.7157617486301e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.899999999999902 y[1] (closed_form) = 9.529008863002172 y[1] (numeric) = 9.529008863002726 absolute error = 5.542233338928781e-13 relative error = 5.816169780728557e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.9099999999999 y[1] (closed_form) = 9.579161541228496 y[1] (numeric) = 9.579161541229062 absolute error = 5.666578317686799e-13 relative error = 5.915526419820747e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.919999999999899 y[1] (closed_form) = 9.62931421945482 y[1] (numeric) = 9.629314219455399 absolute error = 5.790923296444817e-13 relative error = 6.013848093922393e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.929999999999898 y[1] (closed_form) = 9.679466897681145 y[1] (numeric) = 9.679466897681735 absolute error = 5.897504706808832e-13 relative error = 6.092799086096015e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.939999999999897 y[1] (closed_form) = 9.729619575907469 y[1] (numeric) = 9.729619575908071 absolute error = 6.021849685566849e-13 relative error = 6.189193358061174e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.949999999999896 y[1] (closed_form) = 9.779772254133793 y[1] (numeric) = 9.779772254134407 absolute error = 6.146194664324867e-13 relative error = 6.284598970826692e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.959999999999895 y[1] (closed_form) = 9.829924932360118 y[1] (numeric) = 9.829924932360743 absolute error = 6.252776074688882e-13 relative error = 6.360960147421614e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.969999999999894 y[1] (closed_form) = 9.880077610586442 y[1] (numeric) = 9.88007761058708 absolute error = 6.377121053446899e-13 relative error = 6.454525262649611e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.979999999999893 y[1] (closed_form) = 9.930230288812766 y[1] (numeric) = 9.930230288813416 absolute error = 6.501466032204917e-13 relative error = 6.547145275703588e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.989999999999892 y[1] (closed_form) = 9.980382967039091 y[1] (numeric) = 9.980382967039752 absolute error = 6.608047442568932e-13 relative error = 6.621035950616793e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 1.999999999999891 y[1] (closed_form) = 10.03053564526541 y[1] (numeric) = 10.03053564526609 absolute error = 6.732392421326949e-13 relative error = 6.711897210100394e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.00999999999989 y[1] (closed_form) = 10.08068832349174 y[1] (numeric) = 10.08068832349242 absolute error = 6.838973831690964e-13 relative error = 6.78423299305229e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.019999999999889 y[1] (closed_form) = 10.13084100171806 y[1] (numeric) = 10.13084100171876 absolute error = 6.963318810448982e-13 relative error = 6.87338672995469e-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) = 10.18099367994439 y[1] (numeric) = 10.1809936799451 absolute error = 7.087663789206999e-13 relative error = 6.961662104917164e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.039999999999886 y[1] (closed_form) = 10.23114635817071 y[1] (numeric) = 10.23114635817143 absolute error = 7.194245199571014e-13 relative error = 7.031709788635372e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.049999999999885 y[1] (closed_form) = 10.28129903639704 y[1] (numeric) = 10.28129903639777 absolute error = 7.318590178329032e-13 relative error = 7.11835163282416e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.059999999999884 y[1] (closed_form) = 10.33145171462336 y[1] (numeric) = 10.33145171462411 absolute error = 7.442935157087049e-13 relative error = 7.20415229405966e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.069999999999883 y[1] (closed_form) = 10.38160439284969 y[1] (numeric) = 10.38160439285044 absolute error = 7.549516567451064e-13 relative error = 7.272013343766771e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.079999999999882 y[1] (closed_form) = 10.43175707107601 y[1] (numeric) = 10.43175707107678 absolute error = 7.673861546209082e-13 relative error = 7.356250240418552e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.089999999999881 y[1] (closed_form) = 10.48190974930233 y[1] (numeric) = 10.48190974930311 absolute error = 7.7982065249671e-13 relative error = 7.439681042365529e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.09999999999988 y[1] (closed_form) = 10.53206242752866 y[1] (numeric) = 10.53206242752945 absolute error = 7.904787935331115e-13 relative error = 7.505451083037273e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.109999999999879 y[1] (closed_form) = 10.58221510575498 y[1] (numeric) = 10.58221510575579 absolute error = 8.029132914089132e-13 relative error = 7.587383958697462e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.119999999999878 y[1] (closed_form) = 10.63236778398131 y[1] (numeric) = 10.63236778398212 absolute error = 8.15347789284715e-13 relative error = 7.668543882700479e-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) = 10.68252046220763 y[1] (numeric) = 10.68252046220846 absolute error = 8.260059303211165e-13 relative error = 7.732313111342408e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.139999999999875 y[1] (closed_form) = 10.73267314043396 y[1] (numeric) = 10.73267314043479 absolute error = 8.384404281969182e-13 relative error = 7.81203729235173e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.149999999999874 y[1] (closed_form) = 10.78282581866028 y[1] (numeric) = 10.78282581866113 absolute error = 8.5087492607272e-13 relative error = 7.891019853072592e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.159999999999873 y[1] (closed_form) = 10.83297849688661 y[1] (numeric) = 10.83297849688747 absolute error = 8.615330671091215e-13 relative error = 7.952873416639069e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.169999999999872 y[1] (closed_form) = 10.88313117511293 y[1] (numeric) = 10.8831311751138 absolute error = 8.739675649849232e-13 relative error = 8.0304790130939e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.179999999999871 y[1] (closed_form) = 10.93328385333925 y[1] (numeric) = 10.93328385334014 absolute error = 8.86402062860725e-13 relative error = 8.107372631599602e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.18999999999987 y[1] (closed_form) = 10.98343653156558 y[1] (numeric) = 10.98343653156648 absolute error = 8.988365607365267e-13 relative error = 8.183564025278769e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.199999999999869 y[1] (closed_form) = 11.0335892097919 y[1] (numeric) = 11.03358920979281 absolute error = 9.094947017729282e-13 relative error = 8.242963232361282e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.209999999999868 y[1] (closed_form) = 11.08374188801823 y[1] (numeric) = 11.08374188801915 absolute error = 9.2192919964873e-13 relative error = 8.317851579035381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.219999999999867 y[1] (closed_form) = 11.13389456624455 y[1] (numeric) = 11.13389456624548 absolute error = 9.343636975245317e-13 relative error = 8.392065255919624e-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) = 11.18404724447088 y[1] (numeric) = 11.18404724447182 absolute error = 9.450218385609332e-13 relative error = 8.449730387433131e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.239999999999864 y[1] (closed_form) = 11.2341999226972 y[1] (numeric) = 11.23419992269816 absolute error = 9.57456336436735e-13 relative error = 8.522692697521988e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.249999999999863 y[1] (closed_form) = 11.28435260092352 y[1] (numeric) = 11.28435260092449 absolute error = 9.698908343125368e-13 relative error = 8.595006453743389e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.259999999999862 y[1] (closed_form) = 11.33450527914985 y[1] (numeric) = 11.33450527915083 absolute error = 9.805489753489383e-13 relative error = 8.651008149007497e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.269999999999861 y[1] (closed_form) = 11.38465795737617 y[1] (numeric) = 11.38465795737716 absolute error = 9.9298347322474e-13 relative error = 8.722119513317319e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.27999999999986 y[1] (closed_form) = 11.4348106356025 y[1] (numeric) = 11.4348106356035 absolute error = 1.005417971100542e-12 relative error = 8.792607093729687e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.289999999999859 y[1] (closed_form) = 11.48496331382882 y[1] (numeric) = 11.48496331382984 absolute error = 1.016076112136943e-12 relative error = 8.847012257440176e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.299999999999858 y[1] (closed_form) = 11.53511599205514 y[1] (numeric) = 11.53511599205617 absolute error = 1.028510610012745e-12 relative error = 8.916343890439729e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.309999999999857 y[1] (closed_form) = 11.58526867028147 y[1] (numeric) = 11.58526867028251 absolute error = 1.040945107888547e-12 relative error = 8.985075249560497e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.319999999999856 y[1] (closed_form) = 11.63542134850779 y[1] (numeric) = 11.63542134850885 absolute error = 1.053379605764349e-12 relative error = 9.053214096964707e-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) = 11.68557402673412 y[1] (numeric) = 11.68557402673518 absolute error = 1.06403774680075e-12 relative error = 9.105566781455982e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.339999999999853 y[1] (closed_form) = 11.73572670496044 y[1] (numeric) = 11.73572670496152 absolute error = 1.076472244676552e-12 relative error = 9.172608324472569e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.349999999999852 y[1] (closed_form) = 11.78587938318677 y[1] (numeric) = 11.78587938318785 absolute error = 1.088906742552354e-12 relative error = 9.239079301165611e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.359999999999851 y[1] (closed_form) = 11.83603206141309 y[1] (numeric) = 11.83603206141419 absolute error = 1.099564883588755e-12 relative error = 9.28997892100572e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.36999999999985 y[1] (closed_form) = 11.88618473963941 y[1] (numeric) = 11.88618473964053 absolute error = 1.111999381464557e-12 relative error = 9.355393726602057e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.379999999999849 y[1] (closed_form) = 11.93633741786574 y[1] (numeric) = 11.93633741786686 absolute error = 1.124433879340359e-12 relative error = 9.420258827949684e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.389999999999848 y[1] (closed_form) = 11.98649009609206 y[1] (numeric) = 11.9864900960932 absolute error = 1.13509202037676e-12 relative error = 9.469761467093961e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.399999999999847 y[1] (closed_form) = 12.03664277431839 y[1] (numeric) = 12.03664277431954 absolute error = 1.147526518252562e-12 relative error = 9.533609493678307e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.409999999999846 y[1] (closed_form) = 12.08679545254471 y[1] (numeric) = 12.08679545254587 absolute error = 1.159961016128364e-12 relative error = 9.596927661120876e-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) = 12.13694813077104 y[1] (numeric) = 12.13694813077221 absolute error = 1.170619157164765e-12 relative error = 9.645086594684144e-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) = 12.18710080899736 y[1] (numeric) = 12.18710080899854 absolute error = 1.183053655040567e-12 relative error = 9.707424871444033e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.439999999999842 y[1] (closed_form) = 12.23725348722368 y[1] (numeric) = 12.23725348722488 absolute error = 1.195488152916369e-12 relative error = 9.769252178722285e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.449999999999841 y[1] (closed_form) = 12.28740616545001 y[1] (numeric) = 12.28740616545122 absolute error = 1.20614629395277e-12 relative error = 9.816118045680283e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.45999999999984 y[1] (closed_form) = 12.33755884367633 y[1] (numeric) = 12.33755884367755 absolute error = 1.218580791828572e-12 relative error = 9.877000849752059e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.469999999999839 y[1] (closed_form) = 12.38771152190266 y[1] (numeric) = 12.38771152190389 absolute error = 1.231015289704374e-12 relative error = 9.937390675653215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.479999999999838 y[1] (closed_form) = 12.43786420012898 y[1] (numeric) = 12.43786420013022 absolute error = 1.243449787580175e-12 relative error = 9.99729348682936e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.489999999999837 y[1] (closed_form) = 12.48801687835531 y[1] (numeric) = 12.48801687835656 absolute error = 1.254107928616577e-12 relative error = 1.004249065990808e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.499999999999836 y[1] (closed_form) = 12.53816955658163 y[1] (numeric) = 12.5381695565829 absolute error = 1.266542426492379e-12 relative error = 1.01014938486578e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.509999999999835 y[1] (closed_form) = 12.58832223480795 y[1] (numeric) = 12.58832223480923 absolute error = 1.27897692436818e-12 relative error = 1.016002689247724e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.519999999999833 y[1] (closed_form) = 12.63847491303428 y[1] (numeric) = 12.63847491303557 absolute error = 1.289635065404582e-12 relative error = 1.020404023648897e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.529999999999832 y[1] (closed_form) = 12.6886275912606 y[1] (numeric) = 12.68862759126191 absolute error = 1.302069563280384e-12 relative error = 1.026170524680853e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.539999999999831 y[1] (closed_form) = 12.73878026948693 y[1] (numeric) = 12.73878026948824 absolute error = 1.314504061156185e-12 relative error = 1.031891620192872e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.54999999999983 y[1] (closed_form) = 12.78893294771325 y[1] (numeric) = 12.78893294771458 absolute error = 1.325162202192587e-12 relative error = 1.036178864656206e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.559999999999829 y[1] (closed_form) = 12.83908562593958 y[1] (numeric) = 12.83908562594091 absolute error = 1.337596700068389e-12 relative error = 1.041816169031509e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.569999999999828 y[1] (closed_form) = 12.8892383041659 y[1] (numeric) = 12.88923830416725 absolute error = 1.35003119794419e-12 relative error = 1.047409603333853e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.579999999999827 y[1] (closed_form) = 12.93939098239223 y[1] (numeric) = 12.93939098239359 absolute error = 1.360689338980592e-12 relative error = 1.051586848895904e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.589999999999826 y[1] (closed_form) = 12.98954366061855 y[1] (numeric) = 12.98954366061992 absolute error = 1.373123836856394e-12 relative error = 1.057099366022691e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.599999999999825 y[1] (closed_form) = 13.03969633884487 y[1] (numeric) = 13.03969633884626 absolute error = 1.385558334732195e-12 relative error = 1.06256947917158e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.609999999999824 y[1] (closed_form) = 13.0898490170712 y[1] (numeric) = 13.08984901707259 absolute error = 1.396216475768597e-12 relative error = 1.066640626601356e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.619999999999822 y[1] (closed_form) = 13.14000169529752 y[1] (numeric) = 13.14000169529893 absolute error = 1.408650973644399e-12 relative error = 1.072032566136213e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.629999999999821 y[1] (closed_form) = 13.19015437352385 y[1] (numeric) = 13.19015437352527 absolute error = 1.4210854715202e-12 relative error = 1.077383502328599e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.63999999999982 y[1] (closed_form) = 13.24030705175017 y[1] (numeric) = 13.2403070517516 absolute error = 1.433519969396002e-12 relative error = 1.082693901125588e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.649999999999819 y[1] (closed_form) = 13.2904597299765 y[1] (numeric) = 13.29045972997794 absolute error = 1.444178110432404e-12 relative error = 1.086627656058484e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.659999999999818 y[1] (closed_form) = 13.34061240820282 y[1] (numeric) = 13.34061240820428 absolute error = 1.456612608308205e-12 relative error = 1.091863374587339e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.669999999999817 y[1] (closed_form) = 13.39076508642914 y[1] (numeric) = 13.39076508643061 absolute error = 1.469047106184007e-12 relative error = 1.097059874250808e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.679999999999816 y[1] (closed_form) = 13.44091776465547 y[1] (numeric) = 13.44091776465695 absolute error = 1.479705247220409e-12 relative error = 1.100895990236228e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.689999999999815 y[1] (closed_form) = 13.49107044288179 y[1] (numeric) = 13.49107044288328 absolute error = 1.49213974509621e-12 relative error = 1.106020275717631e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.699999999999814 y[1] (closed_form) = 13.54122312110812 y[1] (numeric) = 13.54122312110962 absolute error = 1.504574242972012e-12 relative error = 1.111106603528802e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.709999999999813 y[1] (closed_form) = 13.59137579933444 y[1] (numeric) = 13.59137579933596 absolute error = 1.515232384008414e-12 relative error = 1.114848420336235e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.719999999999811 y[1] (closed_form) = 13.64152847756077 y[1] (numeric) = 13.64152847756229 absolute error = 1.527666881884215e-12 relative error = 1.119864892264167e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.72999999999981 y[1] (closed_form) = 13.69168115578709 y[1] (numeric) = 13.69168115578863 absolute error = 1.540101379760017e-12 relative error = 1.124844613482004e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.739999999999809 y[1] (closed_form) = 13.74183383401341 y[1] (numeric) = 13.74183383401497 absolute error = 1.550759520796419e-12 relative error = 1.128495322769819e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.749999999999808 y[1] (closed_form) = 13.79198651223974 y[1] (numeric) = 13.7919865122413 absolute error = 1.56319401867222e-12 relative error = 1.133407444449688e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.759999999999807 y[1] (closed_form) = 13.84213919046606 y[1] (numeric) = 13.84213919046764 absolute error = 1.575628516548022e-12 relative error = 1.13828397104492e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.769999999999806 y[1] (closed_form) = 13.89229186869239 y[1] (numeric) = 13.89229186869397 absolute error = 1.588063014423824e-12 relative error = 1.143125288061847e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.779999999999805 y[1] (closed_form) = 13.94244454691871 y[1] (numeric) = 13.94244454692031 absolute error = 1.598721155460225e-12 relative error = 1.14665771133624e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.789999999999804 y[1] (closed_form) = 13.99259722514504 y[1] (numeric) = 13.99259722514665 absolute error = 1.611155653336027e-12 relative error = 1.151434310165622e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.799999999999803 y[1] (closed_form) = 14.04274990337136 y[1] (numeric) = 14.04274990337298 absolute error = 1.623590151211829e-12 relative error = 1.156176790431937e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.809999999999802 y[1] (closed_form) = 14.09290258159768 y[1] (numeric) = 14.09290258159932 absolute error = 1.63424829224823e-12 relative error = 1.159625054374681e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.8199999999998 y[1] (closed_form) = 14.14305525982401 y[1] (numeric) = 14.14305525982565 absolute error = 1.646682790124032e-12 relative error = 1.164304854836948e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.829999999999799 y[1] (closed_form) = 14.19320793805033 y[1] (numeric) = 14.19320793805199 absolute error = 1.659117287999834e-12 relative error = 1.168951582504428e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.839999999999798 y[1] (closed_form) = 14.24336061627666 y[1] (numeric) = 14.24336061627833 absolute error = 1.669775429036235e-12 relative error = 1.172318439461606e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.849999999999797 y[1] (closed_form) = 14.29351329450298 y[1] (numeric) = 14.29351329450466 absolute error = 1.682209926912037e-12 relative error = 1.176904440673088e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.859999999999796 y[1] (closed_form) = 14.3436659727293 y[1] (numeric) = 14.343665972731 absolute error = 1.694644424787839e-12 relative error = 1.181458371946027e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.869999999999795 y[1] (closed_form) = 14.39381865095563 y[1] (numeric) = 14.39381865095734 absolute error = 1.70530256582424e-12 relative error = 1.184746457612916e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.879999999999794 y[1] (closed_form) = 14.44397132918195 y[1] (numeric) = 14.44397132918367 absolute error = 1.717737063700042e-12 relative error = 1.189241535137641e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.889999999999793 y[1] (closed_form) = 14.49412400740828 y[1] (numeric) = 14.49412400741001 absolute error = 1.730171561575844e-12 relative error = 1.193705504859427e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.899999999999792 y[1] (closed_form) = 14.5442766856346 y[1] (numeric) = 14.54427668563634 absolute error = 1.740829702612245e-12 relative error = 1.196917344354199e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.909999999999791 y[1] (closed_form) = 14.59442936386093 y[1] (numeric) = 14.59442936386268 absolute error = 1.753264200488047e-12 relative error = 1.201324256520451e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.919999999999789 y[1] (closed_form) = 14.64458204208725 y[1] (numeric) = 14.64458204208902 absolute error = 1.765698698363849e-12 relative error = 1.205700984356798e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.929999999999788 y[1] (closed_form) = 14.69473472031357 y[1] (numeric) = 14.69473472031535 absolute error = 1.778133196239651e-12 relative error = 1.210047836917812e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.939999999999787 y[1] (closed_form) = 14.7448873985399 y[1] (numeric) = 14.74488739854169 absolute error = 1.788791337276052e-12 relative error = 1.213160391752592e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.949999999999786 y[1] (closed_form) = 14.79504007676622 y[1] (numeric) = 14.79504007676803 absolute error = 1.801225835151854e-12 relative error = 1.217452487999986e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.959999999999785 y[1] (closed_form) = 14.84519275499255 y[1] (numeric) = 14.84519275499436 absolute error = 1.813660333027656e-12 relative error = 1.221715583597059e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.969999999999784 y[1] (closed_form) = 14.89534543321887 y[1] (numeric) = 14.8953454332207 absolute error = 1.824318474064057e-12 relative error = 1.224757413141659e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.979999999999783 y[1] (closed_form) = 14.9454981114452 y[1] (numeric) = 14.94549811144703 absolute error = 1.836752971939859e-12 relative error = 1.22896738418727e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.989999999999782 y[1] (closed_form) = 14.99565078967152 y[1] (numeric) = 14.99565078967337 absolute error = 1.849187469815661e-12 relative error = 1.233149194891439e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 2.999999999999781 y[1] (closed_form) = 15.04580346789785 y[1] (numeric) = 15.04580346789971 absolute error = 1.859845610852062e-12 relative error = 1.236122494102945e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.00999999999978 y[1] (closed_form) = 15.09595614612417 y[1] (numeric) = 15.09595614612604 absolute error = 1.872280108727864e-12 relative error = 1.24025274756019e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.019999999999778 y[1] (closed_form) = 15.14610882435049 y[1] (numeric) = 15.14610882435238 absolute error = 1.884714606603666e-12 relative error = 1.244355648345533e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.029999999999777 y[1] (closed_form) = 15.19626150257682 y[1] (numeric) = 15.19626150257871 absolute error = 1.895372747640067e-12 relative error = 1.247262523956086e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.039999999999776 y[1] (closed_form) = 15.24641418080314 y[1] (numeric) = 15.24641418080505 absolute error = 1.907807245515869e-12 relative error = 1.251315373498118e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.049999999999775 y[1] (closed_form) = 15.29656685902947 y[1] (numeric) = 15.29656685903139 absolute error = 1.920241743391671e-12 relative error = 1.255341646977579e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.059999999999774 y[1] (closed_form) = 15.34671953725579 y[1] (numeric) = 15.34671953725772 absolute error = 1.932676241267473e-12 relative error = 1.259341604944103e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.069999999999773 y[1] (closed_form) = 15.39687221548212 y[1] (numeric) = 15.39687221548406 absolute error = 1.943334382303874e-12 relative error = 1.262161791762992e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.079999999999772 y[1] (closed_form) = 15.44702489370844 y[1] (numeric) = 15.4470248937104 absolute error = 1.955768880179676e-12 relative error = 1.266113632649261e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.089999999999771 y[1] (closed_form) = 15.49717757193476 y[1] (numeric) = 15.49717757193673 absolute error = 1.968203378055478e-12 relative error = 1.270039895277366e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.09999999999977 y[1] (closed_form) = 15.54733025016109 y[1] (numeric) = 15.54733025016307 absolute error = 1.978861519091879e-12 relative error = 1.272798279351772e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.109999999999769 y[1] (closed_form) = 15.59748292838741 y[1] (numeric) = 15.5974829283894 absolute error = 1.991296016967681e-12 relative error = 1.276677798661682e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.119999999999767 y[1] (closed_form) = 15.64763560661374 y[1] (numeric) = 15.64763560661574 absolute error = 2.003730514843483e-12 relative error = 1.280532449258067e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.129999999999766 y[1] (closed_form) = 15.69778828484006 y[1] (numeric) = 15.69778828484208 absolute error = 2.014388655879884e-12 relative error = 1.283230872609777e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.139999999999765 y[1] (closed_form) = 15.74794096306639 y[1] (numeric) = 15.74794096306841 absolute error = 2.026823153755686e-12 relative error = 1.28704010162928e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.149999999999764 y[1] (closed_form) = 15.79809364129271 y[1] (numeric) = 15.79809364129475 absolute error = 2.039257651631488e-12 relative error = 1.290825145067707e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.159999999999763 y[1] (closed_form) = 15.84824631951903 y[1] (numeric) = 15.84824631952108 absolute error = 2.049915792667889e-12 relative error = 1.293465378654021e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.169999999999762 y[1] (closed_form) = 15.89839899774536 y[1] (numeric) = 15.89839899774742 absolute error = 2.062350290543691e-12 relative error = 1.29720627267951e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.179999999999761 y[1] (closed_form) = 15.94855167597168 y[1] (numeric) = 15.94855167597376 absolute error = 2.074784788419493e-12 relative error = 1.300923639069617e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.18999999999976 y[1] (closed_form) = 15.99870435419801 y[1] (numeric) = 15.99870435420009 absolute error = 2.085442929455894e-12 relative error = 1.30350738615198e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.199999999999759 y[1] (closed_form) = 16.04885703242433 y[1] (numeric) = 16.04885703242641 absolute error = 2.081890215777094e-12 relative error = 1.297220239155314e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.209999999999757 y[1] (closed_form) = 16.09900971065066 y[1] (numeric) = 16.09900971065273 absolute error = 2.074784788419493e-12 relative error = 1.2887654742185e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.219999999999756 y[1] (closed_form) = 16.14916238887698 y[1] (numeric) = 16.14916238887905 absolute error = 2.067679361061892e-12 relative error = 1.280363223349616e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.229999999999755 y[1] (closed_form) = 16.1993150671033 y[1] (numeric) = 16.19931506710537 absolute error = 2.064126647383091e-12 relative error = 1.274206124661905e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.239999999999754 y[1] (closed_form) = 16.24946774532963 y[1] (numeric) = 16.24946774533169 absolute error = 2.05702122002549e-12 relative error = 1.265900675803189e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.249999999999753 y[1] (closed_form) = 16.29962042355595 y[1] (numeric) = 16.299620423558 absolute error = 2.049915792667889e-12 relative error = 1.257646337398988e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.259999999999752 y[1] (closed_form) = 16.34977310178228 y[1] (numeric) = 16.34977310178432 absolute error = 2.046363078989089e-12 relative error = 1.251615582827884e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.269999999999751 y[1] (closed_form) = 16.3999257800086 y[1] (numeric) = 16.39992578001064 absolute error = 2.039257651631488e-12 relative error = 1.24345541497348e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.27999999999975 y[1] (closed_form) = 16.45007845823493 y[1] (numeric) = 16.45007845823696 absolute error = 2.032152224273887e-12 relative error = 1.23534500424014e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.289999999999749 y[1] (closed_form) = 16.50023113646125 y[1] (numeric) = 16.50023113646328 absolute error = 2.028599510595086e-12 relative error = 1.229437026559225e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.299999999999748 y[1] (closed_form) = 16.55038381468757 y[1] (numeric) = 16.5503838146896 absolute error = 2.021494083237485e-12 relative error = 1.221418249795221e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.309999999999746 y[1] (closed_form) = 16.6005364929139 y[1] (numeric) = 16.60053649291591 absolute error = 2.014388655879884e-12 relative error = 1.213447924854564e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.319999999999745 y[1] (closed_form) = 16.65068917114022 y[1] (numeric) = 16.65068917114223 absolute error = 2.010835942201084e-12 relative error = 1.20765928757253e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.329999999999744 y[1] (closed_form) = 16.70084184936655 y[1] (numeric) = 16.70084184936855 absolute error = 2.003730514843483e-12 relative error = 1.199778150656209e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.339999999999743 y[1] (closed_form) = 16.75099452759287 y[1] (numeric) = 16.75099452759487 absolute error = 1.996625087485882e-12 relative error = 1.191944206176514e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.349999999999742 y[1] (closed_form) = 16.80114720581919 y[1] (numeric) = 16.80114720582119 absolute error = 1.993072373807081e-12 relative error = 1.186271597642313e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.359999999999741 y[1] (closed_form) = 16.85129988404552 y[1] (numeric) = 16.85129988404751 absolute error = 1.98596694644948e-12 relative error = 1.178524481858966e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.36999999999974 y[1] (closed_form) = 16.90145256227185 y[1] (numeric) = 16.90145256227382 absolute error = 1.978861519091879e-12 relative error = 1.170823343023889e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.379999999999739 y[1] (closed_form) = 16.95160524049817 y[1] (numeric) = 16.95160524050014 absolute error = 1.975308805413079e-12 relative error = 1.165263570846951e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.389999999999738 y[1] (closed_form) = 17.00175791872449 y[1] (numeric) = 17.00175791872646 absolute error = 1.968203378055478e-12 relative error = 1.157646984190877e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.399999999999737 y[1] (closed_form) = 17.05191059695082 y[1] (numeric) = 17.05191059695278 absolute error = 1.961097950697877e-12 relative error = 1.150075200985721e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.409999999999735 y[1] (closed_form) = 17.10206327517714 y[1] (numeric) = 17.1020632751791 absolute error = 1.957545237019076e-12 relative error = 1.144625186751801e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.419999999999734 y[1] (closed_form) = 17.15221595340347 y[1] (numeric) = 17.15221595340542 absolute error = 1.950439809661475e-12 relative error = 1.137135758411702e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.429999999999733 y[1] (closed_form) = 17.20236863162979 y[1] (numeric) = 17.20236863163174 absolute error = 1.946887095982675e-12 relative error = 1.131755247008808e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.439999999999732 y[1] (closed_form) = 17.25252130985611 y[1] (numeric) = 17.25252130985805 absolute error = 1.939781668625074e-12 relative error = 1.124346774472265e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.449999999999731 y[1] (closed_form) = 17.30267398808244 y[1] (numeric) = 17.30267398808437 absolute error = 1.932676241267473e-12 relative error = 1.1169812496026e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.45999999999973 y[1] (closed_form) = 17.35282666630876 y[1] (numeric) = 17.35282666631069 absolute error = 1.929123527588672e-12 relative error = 1.111705640058139e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.469999999999729 y[1] (closed_form) = 17.40297934453509 y[1] (numeric) = 17.40297934453701 absolute error = 1.922018100231071e-12 relative error = 1.104418997563556e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.479999999999728 y[1] (closed_form) = 17.45313202276141 y[1] (numeric) = 17.45313202276333 absolute error = 1.91491267287347e-12 relative error = 1.097174232324689e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.489999999999727 y[1] (closed_form) = 17.50328470098773 y[1] (numeric) = 17.50328470098965 absolute error = 1.911359959194669e-12 relative error = 1.092000725490575e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.499999999999726 y[1] (closed_form) = 17.55343737921406 y[1] (numeric) = 17.55343737921596 absolute error = 1.904254531837068e-12 relative error = 1.084832839687568e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.509999999999724 y[1] (closed_form) = 17.60359005744039 y[1] (numeric) = 17.60359005744228 absolute error = 1.897149104479467e-12 relative error = 1.077705796538708e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.519999999999723 y[1] (closed_form) = 17.65374273566671 y[1] (numeric) = 17.6537427356686 absolute error = 1.893596390800667e-12 relative error = 1.072631690148596e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.529999999999722 y[1] (closed_form) = 17.70389541389303 y[1] (numeric) = 17.70389541389492 absolute error = 1.886490963443066e-12 relative error = 1.065579591010605e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.539999999999721 y[1] (closed_form) = 17.75404809211936 y[1] (numeric) = 17.75404809212124 absolute error = 1.879385536085465e-12 relative error = 1.058567334240625e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.54999999999972 y[1] (closed_form) = 17.80420077034568 y[1] (numeric) = 17.80420077034756 absolute error = 1.875832822406664e-12 relative error = 1.053590018784226e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.559999999999719 y[1] (closed_form) = 17.85435344857201 y[1] (numeric) = 17.85435344857387 absolute error = 1.868727395049063e-12 relative error = 1.046650835288872e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.569999999999718 y[1] (closed_form) = 17.90450612679833 y[1] (numeric) = 17.90450612680019 absolute error = 1.861621967691462e-12 relative error = 1.039750526771082e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.579999999999717 y[1] (closed_form) = 17.95465880502465 y[1] (numeric) = 17.95465880502651 absolute error = 1.858069254012662e-12 relative error = 1.034867481576802e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.589999999999716 y[1] (closed_form) = 18.00481148325098 y[1] (numeric) = 18.00481148325283 absolute error = 1.850963826655061e-12 relative error = 1.028038437601485e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.599999999999715 y[1] (closed_form) = 18.0549641614773 y[1] (numeric) = 18.05496416147915 absolute error = 1.84385839929746e-12 relative error = 1.021247332759364e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.609999999999713 y[1] (closed_form) = 18.10511683970363 y[1] (numeric) = 18.10511683970547 absolute error = 1.840305685618659e-12 relative error = 1.016456122273102e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.619999999999712 y[1] (closed_form) = 18.15526951792995 y[1] (numeric) = 18.15526951793179 absolute error = 1.833200258261058e-12 relative error = 1.009734532693447e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.629999999999711 y[1] (closed_form) = 18.20542219615628 y[1] (numeric) = 18.2054221961581 absolute error = 1.826094830903457e-12 relative error = 1.003049976665195e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.63999999999971 y[1] (closed_form) = 18.2555748743826 y[1] (numeric) = 18.25557487438442 absolute error = 1.822542117224657e-12 relative error = 9.983482469139691e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.649999999999709 y[1] (closed_form) = 18.30572755260892 y[1] (numeric) = 18.30572755261074 absolute error = 1.815436689867056e-12 relative error = 9.917315138934867e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.659999999999708 y[1] (closed_form) = 18.35588023083525 y[1] (numeric) = 18.35588023083706 absolute error = 1.808331262509455e-12 relative error = 9.851509378840451e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.669999999999707 y[1] (closed_form) = 18.40603290906157 y[1] (numeric) = 18.40603290906338 absolute error = 1.804778548830654e-12 relative error = 9.805364131138407e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.679999999999706 y[1] (closed_form) = 18.4561855872879 y[1] (numeric) = 18.4561855872897 absolute error = 1.797673121473053e-12 relative error = 9.740220225739603e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.689999999999705 y[1] (closed_form) = 18.50633826551422 y[1] (numeric) = 18.50633826551601 absolute error = 1.790567694115452e-12 relative error = 9.675429403838897e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.699999999999704 y[1] (closed_form) = 18.55649094374055 y[1] (numeric) = 18.55649094374233 absolute error = 1.787014980436652e-12 relative error = 9.630134198618224e-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) = 18.60664362196687 y[1] (numeric) = 18.60664362196865 absolute error = 1.779909553079051e-12 relative error = 9.565989381221353e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.719999999999701 y[1] (closed_form) = 18.65679630019319 y[1] (numeric) = 18.65679630019497 absolute error = 1.77635683940025e-12 relative error = 9.521231892218581e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.7299999999997 y[1] (closed_form) = 18.70694897841952 y[1] (numeric) = 18.70694897842129 absolute error = 1.769251412042649e-12 relative error = 9.457722978149305e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.739999999999699 y[1] (closed_form) = 18.75710165664584 y[1] (numeric) = 18.75710165664761 absolute error = 1.762145984685048e-12 relative error = 9.394553683941362e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.749999999999698 y[1] (closed_form) = 18.80725433487217 y[1] (numeric) = 18.80725433487392 absolute error = 1.758593271006248e-12 relative error = 9.350611416710025e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.759999999999697 y[1] (closed_form) = 18.85740701309849 y[1] (numeric) = 18.85740701310024 absolute error = 1.751487843648647e-12 relative error = 9.288063000560209e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.769999999999696 y[1] (closed_form) = 18.90755969132482 y[1] (numeric) = 18.90755969132656 absolute error = 1.744382416291046e-12 relative error = 9.225846406246731e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.779999999999695 y[1] (closed_form) = 18.95771236955114 y[1] (numeric) = 18.95771236955288 absolute error = 1.740829702612245e-12 relative error = 9.182699202717479e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.789999999999694 y[1] (closed_form) = 19.00786504777746 y[1] (numeric) = 19.0078650477792 absolute error = 1.733724275254644e-12 relative error = 9.12108893290656e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.799999999999693 y[1] (closed_form) = 19.05801772600379 y[1] (numeric) = 19.05801772600552 absolute error = 1.726618847897043e-12 relative error = 9.059802927673592e-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) = 19.10817040423011 y[1] (numeric) = 19.10817040423183 absolute error = 1.723066134218243e-12 relative error = 9.017431275559461e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.81999999999969 y[1] (closed_form) = 19.15832308245644 y[1] (numeric) = 19.15832308245815 absolute error = 1.715960706860642e-12 relative error = 8.956737494587784e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.829999999999689 y[1] (closed_form) = 19.20847576068276 y[1] (numeric) = 19.20847576068447 absolute error = 1.708855279503041e-12 relative error = 8.896360652420137e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.839999999999688 y[1] (closed_form) = 19.25862843890908 y[1] (numeric) = 19.25862843891079 absolute error = 1.70530256582424e-12 relative error = 8.854745659763289e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.849999999999687 y[1] (closed_form) = 19.30878111713541 y[1] (numeric) = 19.30878111713711 absolute error = 1.698197138466639e-12 relative error = 8.794947377385666e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.859999999999686 y[1] (closed_form) = 19.35893379536174 y[1] (numeric) = 19.35893379536343 absolute error = 1.691091711109038e-12 relative error = 8.735458930668031e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.869999999999685 y[1] (closed_form) = 19.40908647358806 y[1] (numeric) = 19.40908647358975 absolute error = 1.687538997430238e-12 relative error = 8.694582301576357e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.879999999999684 y[1] (closed_form) = 19.45923915181438 y[1] (numeric) = 19.45923915181606 absolute error = 1.680433570072637e-12 relative error = 8.635659169212446e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.889999999999683 y[1] (closed_form) = 19.50939183004071 y[1] (numeric) = 19.50939183004238 absolute error = 1.673328142715036e-12 relative error = 8.577038983544493e-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) = 19.55954450826703 y[1] (numeric) = 19.5595445082687 absolute error = 1.669775429036235e-12 relative error = 8.53688299505384e-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) = 19.60969718649336 y[1] (numeric) = 19.60969718649502 absolute error = 1.662670001678634e-12 relative error = 8.47881528136925e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.919999999999679 y[1] (closed_form) = 19.65984986471968 y[1] (numeric) = 19.65984986472134 absolute error = 1.655564574321033e-12 relative error = 8.421043831529988e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.929999999999678 y[1] (closed_form) = 19.710002542946 y[1] (numeric) = 19.71000254294766 absolute error = 1.652011860642233e-12 relative error = 8.381591311531667e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.939999999999677 y[1] (closed_form) = 19.76015522117233 y[1] (numeric) = 19.76015522117397 absolute error = 1.644906433284632e-12 relative error = 8.324359879127726e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.949999999999676 y[1] (closed_form) = 19.81030789939865 y[1] (numeric) = 19.81030789940029 absolute error = 1.637801005927031e-12 relative error = 8.267418226128361e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.959999999999675 y[1] (closed_form) = 19.86046057762498 y[1] (numeric) = 19.86046057762661 absolute error = 1.63424829224823e-12 relative error = 8.228652532305285e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.969999999999674 y[1] (closed_form) = 19.9106132558513 y[1] (numeric) = 19.91061325585293 absolute error = 1.627142864890629e-12 relative error = 8.172238815459123e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.979999999999673 y[1] (closed_form) = 19.96076593407763 y[1] (numeric) = 19.96076593407925 absolute error = 1.620037437533028e-12 relative error = 8.116108584627261e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 3.989999999999672 y[1] (closed_form) = 20.01091861230395 y[1] (numeric) = 20.01091861230557 absolute error = 1.616484723854228e-12 relative error = 8.078013584345465e-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) = 20.06107129053028 y[1] (numeric) = 20.06107129053188 absolute error = 1.609379296496627e-12 relative error = 8.022399567745547e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.009999999999674 y[1] (closed_form) = 20.11122396875662 y[1] (numeric) = 20.1112239687582 absolute error = 1.580957587066223e-12 relative error = 7.861070959789852e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.019999999999677 y[1] (closed_form) = 20.16137664698297 y[1] (numeric) = 20.16137664698452 absolute error = 1.552535877635819e-12 relative error = 7.700544981724483e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.029999999999681 y[1] (closed_form) = 20.21152932520932 y[1] (numeric) = 20.21152932521084 absolute error = 1.524114168205415e-12 relative error = 7.540815658637106e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.039999999999684 y[1] (closed_form) = 20.26168200343566 y[1] (numeric) = 20.26168200343716 absolute error = 1.495692458775011e-12 relative error = 7.381877074772936e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.049999999999687 y[1] (closed_form) = 20.31183468166201 y[1] (numeric) = 20.31183468166348 absolute error = 1.470823463023407e-12 relative error = 7.241214228428616e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.059999999999691 y[1] (closed_form) = 20.36198735988835 y[1] (numeric) = 20.3619873598898 absolute error = 1.442401753593003e-12 relative error = 7.083796527810595e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.069999999999694 y[1] (closed_form) = 20.4121400381147 y[1] (numeric) = 20.41214003811611 absolute error = 1.413980044162599e-12 relative error = 6.927152378546963e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.079999999999697 y[1] (closed_form) = 20.46229271634105 y[1] (numeric) = 20.46229271634243 absolute error = 1.385558334732195e-12 relative error = 6.771276092760113e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.089999999999701 y[1] (closed_form) = 20.51244539456739 y[1] (numeric) = 20.51244539456875 absolute error = 1.357136625301791e-12 relative error = 6.616162038199606e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.099999999999704 y[1] (closed_form) = 20.56259807279374 y[1] (numeric) = 20.56259807279507 absolute error = 1.328714915871387e-12 relative error = 6.461804637563785e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.109999999999707 y[1] (closed_form) = 20.61275075102009 y[1] (numeric) = 20.61275075102139 absolute error = 1.300293206440983e-12 relative error = 6.308198367831301e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.119999999999711 y[1] (closed_form) = 20.66290342924643 y[1] (numeric) = 20.66290342924771 absolute error = 1.271871497010579e-12 relative error = 6.155337759602373e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.129999999999714 y[1] (closed_form) = 20.71305610747278 y[1] (numeric) = 20.71305610747402 absolute error = 1.243449787580175e-12 relative error = 6.003217396449614e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.139999999999717 y[1] (closed_form) = 20.76320878569913 y[1] (numeric) = 20.76320878570034 absolute error = 1.215028078149771e-12 relative error = 5.85183191427827e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.149999999999721 y[1] (closed_form) = 20.81336146392547 y[1] (numeric) = 20.81336146392666 absolute error = 1.186606368719367e-12 relative error = 5.701176000695705e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.159999999999724 y[1] (closed_form) = 20.86351414215182 y[1] (numeric) = 20.86351414215298 absolute error = 1.158184659288963e-12 relative error = 5.551244394389978e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.169999999999727 y[1] (closed_form) = 20.91366682037817 y[1] (numeric) = 20.9136668203793 absolute error = 1.129762949858559e-12 relative error = 5.402031884517373e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.179999999999731 y[1] (closed_form) = 20.96381949860451 y[1] (numeric) = 20.96381949860562 absolute error = 1.104893954106956e-12 relative error = 5.270480191744184e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.189999999999734 y[1] (closed_form) = 21.01397217683086 y[1] (numeric) = 21.01397217683193 absolute error = 1.076472244676552e-12 relative error = 5.122649995051511e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.199999999999737 y[1] (closed_form) = 21.06412485505721 y[1] (numeric) = 21.06412485505825 absolute error = 1.048050535246148e-12 relative error = 4.975523751676422e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.209999999999741 y[1] (closed_form) = 21.11427753328355 y[1] (numeric) = 21.11427753328457 absolute error = 1.019628825815744e-12 relative error = 4.829096445324491e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.219999999999744 y[1] (closed_form) = 21.1644302115099 y[1] (numeric) = 21.16443021151089 absolute error = 9.912071163853398e-13 relative error = 4.683363107249112e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.229999999999747 y[1] (closed_form) = 21.21458288973625 y[1] (numeric) = 21.21458288973721 absolute error = 9.627854069549358e-13 relative error = 4.538318815689455e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.239999999999751 y[1] (closed_form) = 21.26473556796259 y[1] (numeric) = 21.26473556796353 absolute error = 9.343636975245317e-13 relative error = 4.3939586953164e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.249999999999754 y[1] (closed_form) = 21.31488824618894 y[1] (numeric) = 21.31488824618985 absolute error = 9.059419880941277e-13 relative error = 4.250277916686279e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.259999999999757 y[1] (closed_form) = 21.36504092441529 y[1] (numeric) = 21.36504092441616 absolute error = 8.775202786637237e-13 relative error = 4.107271695702307e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.269999999999761 y[1] (closed_form) = 21.41519360264163 y[1] (numeric) = 21.41519360264248 absolute error = 8.490985692333197e-13 relative error = 3.964935293083601e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.279999999999764 y[1] (closed_form) = 21.46534628086798 y[1] (numeric) = 21.4653462808688 absolute error = 8.206768598029157e-13 relative error = 3.823264013841619e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.289999999999767 y[1] (closed_form) = 21.51549895909433 y[1] (numeric) = 21.51549895909512 absolute error = 7.922551503725117e-13 relative error = 3.682253206763934e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.299999999999771 y[1] (closed_form) = 21.56565163732067 y[1] (numeric) = 21.56565163732144 absolute error = 7.638334409421077e-13 relative error = 3.541898263905216e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.309999999999774 y[1] (closed_form) = 21.61580431554702 y[1] (numeric) = 21.61580431554776 absolute error = 7.389644451905042e-13 relative error = 3.41863034288763e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.319999999999777 y[1] (closed_form) = 21.66595699377336 y[1] (numeric) = 21.66595699377407 absolute error = 7.105427357601002e-13 relative error = 3.279535429541861e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.329999999999781 y[1] (closed_form) = 21.71610967199971 y[1] (numeric) = 21.71610967200039 absolute error = 6.821210263296962e-13 relative error = 3.141082986927481e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.339999999999784 y[1] (closed_form) = 21.76626235022606 y[1] (numeric) = 21.76626235022671 absolute error = 6.536993168992922e-13 relative error = 3.003268574002569e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.349999999999787 y[1] (closed_form) = 21.8164150284524 y[1] (numeric) = 21.81641502845303 absolute error = 6.252776074688882e-13 relative error = 2.866087790562369e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.359999999999791 y[1] (closed_form) = 21.86656770667875 y[1] (numeric) = 21.86656770667935 absolute error = 5.968558980384842e-13 relative error = 2.729536276770978e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.369999999999794 y[1] (closed_form) = 21.9167203849051 y[1] (numeric) = 21.91672038490567 absolute error = 5.684341886080801e-13 relative error = 2.593609712699456e-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) = 21.96687306313144 y[1] (numeric) = 21.96687306313198 absolute error = 5.400124791776761e-13 relative error = 2.45830381787027e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.389999999999801 y[1] (closed_form) = 22.01702574135779 y[1] (numeric) = 22.0170257413583 absolute error = 5.115907697472721e-13 relative error = 2.323614350807959e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.399999999999804 y[1] (closed_form) = 22.06717841958414 y[1] (numeric) = 22.06717841958462 absolute error = 4.831690603168681e-13 relative error = 2.189537108595932e-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) = 22.11733109781049 y[1] (numeric) = 22.11733109781094 absolute error = 4.547473508864641e-13 relative error = 2.056067926439289e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.419999999999811 y[1] (closed_form) = 22.16748377603683 y[1] (numeric) = 22.16748377603726 absolute error = 4.263256414560601e-13 relative error = 1.923202677233581e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.429999999999814 y[1] (closed_form) = 22.21763645426318 y[1] (numeric) = 22.21763645426358 absolute error = 3.979039320256561e-13 relative error = 1.790937271139412e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.439999999999817 y[1] (closed_form) = 22.26778913248953 y[1] (numeric) = 22.2677891324899 absolute error = 3.694822225952521e-13 relative error = 1.659267655162783e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.449999999999821 y[1] (closed_form) = 22.31794181071587 y[1] (numeric) = 22.31794181071621 absolute error = 3.446132268436486e-13 relative error = 1.544108456623827e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.459999999999824 y[1] (closed_form) = 22.36809448894222 y[1] (numeric) = 22.36809448894253 absolute error = 3.161915174132446e-13 relative error = 1.413582715190852e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.469999999999827 y[1] (closed_form) = 22.41824716716856 y[1] (numeric) = 22.41824716716885 absolute error = 2.877698079828406e-13 relative error = 1.283640981549523e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.479999999999831 y[1] (closed_form) = 22.46839984539491 y[1] (numeric) = 22.46839984539517 absolute error = 2.593480985524366e-13 relative error = 1.154279344933378e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.489999999999834 y[1] (closed_form) = 22.51855252362126 y[1] (numeric) = 22.51855252362149 absolute error = 2.309263891220326e-13 relative error = 1.025493929415747e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.499999999999837 y[1] (closed_form) = 22.5687052018476 y[1] (numeric) = 22.56870520184781 absolute error = 2.025046796916286e-13 relative error = 8.972808935226393e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.509999999999841 y[1] (closed_form) = 22.61885788007395 y[1] (numeric) = 22.61885788007412 absolute error = 1.740829702612245e-13 relative error = 7.696364298507869e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.519999999999844 y[1] (closed_form) = 22.6690105583003 y[1] (numeric) = 22.66901055830044 absolute error = 1.456612608308205e-13 relative error = 6.425567646907571e-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) = 22.71916323652664 y[1] (numeric) = 22.71916323652676 absolute error = 1.172395514004165e-13 relative error = 5.160381576550545e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.539999999999851 y[1] (closed_form) = 22.76931591475299 y[1] (numeric) = 22.76931591475308 absolute error = 8.881784197001252e-14 relative error = 3.900769013111391e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.549999999999854 y[1] (closed_form) = 22.81946859297934 y[1] (numeric) = 22.8194685929794 absolute error = 6.039613253960852e-14 relative error = 2.646693208192852e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.559999999999858 y[1] (closed_form) = 22.86962127120568 y[1] (numeric) = 22.86962127120572 absolute error = 3.197442310920451e-14 relative error = 1.398117735752028e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.569999999999861 y[1] (closed_form) = 22.91977394943203 y[1] (numeric) = 22.91977394943203 absolute error = 3.552713678800501e-15 relative error = 1.550064885735289e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.579999999999864 y[1] (closed_form) = 22.96992662765837 y[1] (numeric) = 22.96992662765835 absolute error = 2.131628207280301e-14 relative error = 9.280082787524365e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.589999999999868 y[1] (closed_form) = 23.02007930588472 y[1] (numeric) = 23.02007930588467 absolute error = 4.973799150320701e-14 relative error = 2.160635106521648e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.599999999999871 y[1] (closed_form) = 23.07023198411107 y[1] (numeric) = 23.07023198411099 absolute error = 7.815970093361102e-14 relative error = 3.387902687213599e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.609999999999874 y[1] (closed_form) = 23.12038466233741 y[1] (numeric) = 23.12038466233731 absolute error = 1.06581410364015e-13 relative error = 4.609845896622721e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.619999999999878 y[1] (closed_form) = 23.17053734056376 y[1] (numeric) = 23.17053734056363 absolute error = 1.35003119794419e-13 relative error = 5.826499308588511e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.629999999999881 y[1] (closed_form) = 23.22069001879011 y[1] (numeric) = 23.22069001878994 absolute error = 1.63424829224823e-13 relative error = 7.03789719825639e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.639999999999884 y[1] (closed_form) = 23.27084269701646 y[1] (numeric) = 23.27084269701626 absolute error = 1.918465386552271e-13 relative error = 8.24407354529639e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.649999999999888 y[1] (closed_form) = 23.3209953752428 y[1] (numeric) = 23.32099537524258 absolute error = 2.202682480856311e-13 relative error = 9.445062037080302e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.659999999999891 y[1] (closed_form) = 23.37114805346915 y[1] (numeric) = 23.3711480534689 absolute error = 2.486899575160351e-13 relative error = 1.064089607181793e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.669999999999894 y[1] (closed_form) = 23.4213007316955 y[1] (numeric) = 23.42130073169522 absolute error = 2.771116669464391e-13 relative error = 1.183160876165303e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.679999999999898 y[1] (closed_form) = 23.47145340992184 y[1] (numeric) = 23.47145340992154 absolute error = 3.055333763768431e-13 relative error = 1.301723293571962e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.689999999999901 y[1] (closed_form) = 23.52160608814819 y[1] (numeric) = 23.52160608814786 absolute error = 3.339550858072471e-13 relative error = 1.419780114315904e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.699999999999904 y[1] (closed_form) = 23.57175876637454 y[1] (numeric) = 23.57175876637417 absolute error = 3.623767952376511e-13 relative error = 1.537334565609873e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.709999999999908 y[1] (closed_form) = 23.62191144460088 y[1] (numeric) = 23.62191144460049 absolute error = 3.872457909892546e-13 relative error = 1.639349939556924e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.719999999999911 y[1] (closed_form) = 23.67206412282723 y[1] (numeric) = 23.67206412282681 absolute error = 4.156675004196586e-13 relative error = 1.755941088461424e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.729999999999914 y[1] (closed_form) = 23.72221680105357 y[1] (numeric) = 23.72221680105313 absolute error = 4.440892098500626e-13 relative error = 1.872039251535461e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.739999999999918 y[1] (closed_form) = 23.77236947927992 y[1] (numeric) = 23.77236947927945 absolute error = 4.725109192804666e-13 relative error = 1.987647548942518e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.749999999999921 y[1] (closed_form) = 23.82252215750627 y[1] (numeric) = 23.82252215750577 absolute error = 5.009326287108706e-13 relative error = 2.10276907457102e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.759999999999924 y[1] (closed_form) = 23.87267483573261 y[1] (numeric) = 23.87267483573208 absolute error = 5.293543381412746e-13 relative error = 2.217406896310326e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.769999999999928 y[1] (closed_form) = 23.92282751395896 y[1] (numeric) = 23.9228275139584 absolute error = 5.577760475716786e-13 relative error = 2.331564056323261e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.779999999999931 y[1] (closed_form) = 23.97298019218531 y[1] (numeric) = 23.97298019218472 absolute error = 5.861977570020827e-13 relative error = 2.445243571315222e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.789999999999934 y[1] (closed_form) = 24.02313287041165 y[1] (numeric) = 24.02313287041104 absolute error = 6.146194664324867e-13 relative error = 2.558448432799909e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.799999999999938 y[1] (closed_form) = 24.073285548638 y[1] (numeric) = 24.07328554863736 absolute error = 6.430411758628907e-13 relative error = 2.671181607361743e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.809999999999941 y[1] (closed_form) = 24.12343822686435 y[1] (numeric) = 24.12343822686368 absolute error = 6.714628852932947e-13 relative error = 2.783446036915004e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.819999999999944 y[1] (closed_form) = 24.17359090509069 y[1] (numeric) = 24.17359090508999 absolute error = 6.998845947236987e-13 relative error = 2.895244638959744e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.829999999999948 y[1] (closed_form) = 24.22374358331704 y[1] (numeric) = 24.22374358331631 absolute error = 7.283063041541027e-13 relative error = 3.006580306834527e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.839999999999951 y[1] (closed_form) = 24.27389626154338 y[1] (numeric) = 24.27389626154263 absolute error = 7.531752999057062e-13 relative error = 3.10281996672675e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.849999999999954 y[1] (closed_form) = 24.32404893976973 y[1] (numeric) = 24.32404893976895 absolute error = 7.815970093361102e-13 relative error = 3.213268528078818e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.859999999999958 y[1] (closed_form) = 24.37420161799608 y[1] (numeric) = 24.37420161799527 absolute error = 8.100187187665142e-13 relative error = 3.323262568602277e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.869999999999961 y[1] (closed_form) = 24.42435429622243 y[1] (numeric) = 24.42435429622159 absolute error = 8.384404281969182e-13 relative error = 3.432804888220095e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.879999999999964 y[1] (closed_form) = 24.47450697444877 y[1] (numeric) = 24.47450697444791 absolute error = 8.668621376273222e-13 relative error = 3.541898263905053e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.889999999999968 y[1] (closed_form) = 24.52465965267512 y[1] (numeric) = 24.52465965267422 absolute error = 8.952838470577262e-13 relative error = 3.650545449914408e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.899999999999971 y[1] (closed_form) = 24.57481233090147 y[1] (numeric) = 24.57481233090054 absolute error = 9.237055564881302e-13 relative error = 3.758749178021684e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.909999999999974 y[1] (closed_form) = 24.62496500912781 y[1] (numeric) = 24.62496500912686 absolute error = 9.521272659185342e-13 relative error = 3.86651215774563e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.919999999999978 y[1] (closed_form) = 24.67511768735416 y[1] (numeric) = 24.67511768735318 absolute error = 9.805489753489383e-13 relative error = 3.97383707657639e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.929999999999981 y[1] (closed_form) = 24.72527036558051 y[1] (numeric) = 24.7252703655795 absolute error = 1.008970684779342e-12 relative error = 4.080726600198911e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.939999999999984 y[1] (closed_form) = 24.77542304380685 y[1] (numeric) = 24.77542304380582 absolute error = 1.037392394209746e-12 relative error = 4.187183372713648e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.949999999999988 y[1] (closed_form) = 24.8255757220332 y[1] (numeric) = 24.82557572203213 absolute error = 1.06581410364015e-12 relative error = 4.293210016854589e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.959999999999991 y[1] (closed_form) = 24.87572840025955 y[1] (numeric) = 24.87572840025845 absolute error = 1.094235813070554e-12 relative error = 4.398809134204638e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.969999999999994 y[1] (closed_form) = 24.92588107848589 y[1] (numeric) = 24.92588107848477 absolute error = 1.119104808822158e-12 relative error = 4.489730193682435e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.979999999999998 y[1] (closed_form) = 24.97603375671224 y[1] (numeric) = 24.97603375671109 absolute error = 1.147526518252562e-12 relative error = 4.594510599362749e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = 4.990000000000001 y[1] (closed_form) = 25.02618643493858 y[1] (numeric) = 25.02618643493741 absolute error = 1.175948227682966e-12 relative error = 4.69887104349725e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = sinh ( 0.1 ) * cosh ( 0.05 ) / tanh ( 0.02 ) ; Iterations = 4900 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %