##############ECHO OF PROBLEM################# ##############temp/sing3postode.ode################# diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=16; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-2.0); x_end=c(-0.7); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.001); glob_min_h=c(0.001); glob_type_given_pole=1; array_given_rad_poles[1][1]=c(0.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(2.0); array_given_ord_poles[1][2]=c(0.0); /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(1.0)/c(x)/c(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (closed_form) = 0.25 y[1] (numeric) = 0.25 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.990000000000001 y[1] (closed_form) = 0.2525188757859647 y[1] (numeric) = 0.252518875785965 absolute error = 3.33066907387547e-16 relative error = 1.318978259945426e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.980000000000002 y[1] (closed_form) = 0.2550760126517697 y[1] (numeric) = 0.2550760126517703 absolute error = 6.106226635438361e-16 relative error = 2.39388509015726e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.970000000000003 y[1] (closed_form) = 0.2576721894405928 y[1] (numeric) = 0.2576721894405938 absolute error = 9.992007221626409e-16 relative error = 3.877798082641006e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.960000000000004 y[1] (closed_form) = 0.2603082049146178 y[1] (numeric) = 0.260308204914619 absolute error = 1.27675647831893e-15 relative error = 4.904787687110023e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.950000000000006 y[1] (closed_form) = 0.2629848783694922 y[1] (numeric) = 0.2629848783694939 absolute error = 1.609823385706477e-15 relative error = 6.121353424148914e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.940000000000007 y[1] (closed_form) = 0.2657030502710153 y[1] (numeric) = 0.2657030502710171 absolute error = 1.77635683940025e-15 relative error = 6.685496600766827e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.930000000000008 y[1] (closed_form) = 0.2684635829149755 y[1] (numeric) = 0.2684635829149776 absolute error = 2.164934898019055e-15 relative error = 8.064166001631243e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.920000000000009 y[1] (closed_form) = 0.2712673611111086 y[1] (numeric) = 0.2712673611111111 absolute error = 2.498001805406602e-15 relative error = 9.208633855450983e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.91000000000001 y[1] (closed_form) = 0.2741152928921876 y[1] (numeric) = 0.2741152928921904 absolute error = 2.775557561562891e-15 relative error = 1.012551154033769e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.900000000000011 y[1] (closed_form) = 0.2770083102493043 y[1] (numeric) = 0.2770083102493073 absolute error = 3.05311331771918e-15 relative error = 1.102173907696637e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.890000000000012 y[1] (closed_form) = 0.2799473698944563 y[1] (numeric) = 0.2799473698944596 absolute error = 3.33066907387547e-15 relative error = 1.189748299879072e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.880000000000013 y[1] (closed_form) = 0.2829334540516031 y[1] (numeric) = 0.2829334540516068 absolute error = 3.719247132494274e-15 relative error = 1.314530706508795e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.870000000000014 y[1] (closed_form) = 0.2859675712774128 y[1] (numeric) = 0.2859675712774168 absolute error = 3.996802888650564e-15 relative error = 1.397642002132237e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.860000000000015 y[1] (closed_form) = 0.2890507573129794 y[1] (numeric) = 0.2890507573129838 absolute error = 4.440892098500626e-15 relative error = 1.536371030397302e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.850000000000017 y[1] (closed_form) = 0.2921840759678545 y[1] (numeric) = 0.2921840759678593 absolute error = 4.773959005888173e-15 relative error = 1.633887469765257e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.840000000000018 y[1] (closed_form) = 0.2953686200378015 y[1] (numeric) = 0.2953686200378067 absolute error = 5.218048215738236e-15 relative error = 1.766622403920371e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.830000000000019 y[1] (closed_form) = 0.2986055122577502 y[1] (numeric) = 0.2986055122577558 absolute error = 5.606626274357041e-15 relative error = 1.877603073019468e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.82000000000002 y[1] (closed_form) = 0.3018959062915041 y[1] (numeric) = 0.3018959062915101 absolute error = 5.995204332975845e-15 relative error = 1.985851483254962e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.810000000000021 y[1] (closed_form) = 0.3052409877598293 y[1] (numeric) = 0.3052409877598357 absolute error = 6.38378239159465e-15 relative error = 2.091390949310372e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.800000000000022 y[1] (closed_form) = 0.3086419753086345 y[1] (numeric) = 0.3086419753086412 absolute error = 6.716849298982197e-15 relative error = 2.176259172870285e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.790000000000023 y[1] (closed_form) = 0.3121001217190394 y[1] (numeric) = 0.3121001217190466 absolute error = 7.16093850883226e-15 relative error = 2.294436307615004e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.780000000000024 y[1] (closed_form) = 0.3156167150612211 y[1] (numeric) = 0.3156167150612286 absolute error = 7.494005416219807e-15 relative error = 2.374400676075148e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.770000000000025 y[1] (closed_form) = 0.3191930798940187 y[1] (numeric) = 0.3191930798940267 absolute error = 7.938094626069869e-15 relative error = 2.486925665401501e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.760000000000026 y[1] (closed_form) = 0.322830578512387 y[1] (numeric) = 0.3228305785123953 absolute error = 8.326672684688674e-15 relative error = 2.579270130809241e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.750000000000028 y[1] (closed_form) = 0.3265306122448877 y[1] (numeric) = 0.3265306122448964 absolute error = 8.715250743307479e-15 relative error = 2.669045540137999e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.740000000000029 y[1] (closed_form) = 0.3302946228035299 y[1] (numeric) = 0.330294622803539 absolute error = 9.103828801926284e-15 relative error = 2.756275208071292e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.73000000000003 y[1] (closed_form) = 0.3341240936883844 y[1] (numeric) = 0.334124093688394 absolute error = 9.603429163007604e-15 relative error = 2.874210314196645e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.720000000000031 y[1] (closed_form) = 0.3380205516495282 y[1] (numeric) = 0.3380205516495381 absolute error = 9.880984919163893e-15 relative error = 2.923190578485551e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.710000000000032 y[1] (closed_form) = 0.3419855682090088 y[1] (numeric) = 0.3419855682090192 absolute error = 1.038058528024521e-14 relative error = 3.035386941796616e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.700000000000033 y[1] (closed_form) = 0.3460207612456613 y[1] (numeric) = 0.3460207612456721 absolute error = 1.082467449009528e-14 relative error = 3.128330927637656e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.690000000000034 y[1] (closed_form) = 0.3501277966457615 y[1] (numeric) = 0.3501277966457729 absolute error = 1.13242748511766e-14 relative error = 3.234326140244679e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.680000000000035 y[1] (closed_form) = 0.3543083900226609 y[1] (numeric) = 0.3543083900226725 absolute error = 1.160183060733289e-14 relative error = 3.274500670613771e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.670000000000036 y[1] (closed_form) = 0.3585643085087154 y[1] (numeric) = 0.3585643085087276 absolute error = 1.215694211964546e-14 relative error = 3.390449587748072e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.660000000000037 y[1] (closed_form) = 0.3628973726230058 y[1] (numeric) = 0.3628973726230184 absolute error = 1.260103132949553e-14 relative error = 3.472340193155944e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.650000000000039 y[1] (closed_form) = 0.3673094582185319 y[1] (numeric) = 0.367309458218545 absolute error = 1.310063169057685e-14 relative error = 3.566646977759713e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.64000000000004 y[1] (closed_form) = 0.371802498512772 y[1] (numeric) = 0.3718024985127855 absolute error = 1.348920974919565e-14 relative error = 3.628057854143838e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.630000000000041 y[1] (closed_form) = 0.3763784862057097 y[1] (numeric) = 0.3763784862057236 absolute error = 1.393329895904571e-14 relative error = 3.701938200429041e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.620000000000042 y[1] (closed_form) = 0.3810394756896618 y[1] (numeric) = 0.3810394756896763 absolute error = 1.448841047135829e-14 relative error = 3.802338444103466e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.610000000000043 y[1] (closed_form) = 0.3857875853554827 y[1] (numeric) = 0.3857875853554977 absolute error = 1.504352198367087e-14 relative error = 3.899431333387534e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.600000000000044 y[1] (closed_form) = 0.3906249999999785 y[1] (numeric) = 0.3906249999999941 absolute error = 1.554312234475219e-14 relative error = 3.97903932025678e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.590000000000045 y[1] (closed_form) = 0.3955539733396397 y[1] (numeric) = 0.3955539733396559 absolute error = 1.615374500829603e-14 relative error = 4.083828275547551e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.580000000000046 y[1] (closed_form) = 0.4005768306360926 y[1] (numeric) = 0.4005768306361092 absolute error = 1.665334536937735e-14 relative error = 4.157341138011604e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.570000000000047 y[1] (closed_form) = 0.4056959714389791 y[1] (numeric) = 0.4056959714389963 absolute error = 1.720845688168993e-14 relative error = 4.241712536768006e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.560000000000048 y[1] (closed_form) = 0.4109138724523084 y[1] (numeric) = 0.4109138724523263 absolute error = 1.787459069646502e-14 relative error = 4.349960391891998e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.55000000000005 y[1] (closed_form) = 0.4162330905306705 y[1] (numeric) = 0.416233090530689 absolute error = 1.84297022087776e-14 relative error = 4.427735955659102e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.540000000000051 y[1] (closed_form) = 0.4216562658120823 y[1] (numeric) = 0.4216562658121012 absolute error = 1.898481372109018e-14 relative error = 4.502438422094042e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.530000000000052 y[1] (closed_form) = 0.4271861249946313 y[1] (numeric) = 0.427186124994651 absolute error = 1.970645868709653e-14 relative error = 4.613084914062739e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.520000000000053 y[1] (closed_form) = 0.4328254847645128 y[1] (numeric) = 0.4328254847645332 absolute error = 2.042810365310288e-14 relative error = 4.719709068013218e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.510000000000054 y[1] (closed_form) = 0.4385772553835044 y[1] (numeric) = 0.4385772553835254 absolute error = 2.098321516541546e-14 relative error = 4.784382889866721e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.500000000000055 y[1] (closed_form) = 0.4444444444444118 y[1] (numeric) = 0.4444444444444333 absolute error = 2.148281552649678e-14 relative error = 4.83363349346213e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.490000000000056 y[1] (closed_form) = 0.4504301608035335 y[1] (numeric) = 0.4504301608035555 absolute error = 2.203792703880936e-14 relative error = 4.892640181886434e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.480000000000057 y[1] (closed_form) = 0.4565376186997456 y[1] (numeric) = 0.4565376186997683 absolute error = 2.270406085358445e-14 relative error = 4.973097489369523e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.470000000000058 y[1] (closed_form) = 0.4627701420703969 y[1] (numeric) = 0.4627701420704203 absolute error = 2.348121697082206e-14 relative error = 5.074056175225343e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.460000000000059 y[1] (closed_form) = 0.4691311690748351 y[1] (numeric) = 0.4691311690748593 absolute error = 2.420286193682841e-14 relative error = 5.159082050454765e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.450000000000061 y[1] (closed_form) = 0.4756242568370589 y[1] (numeric) = 0.4756242568370838 absolute error = 2.486899575160351e-14 relative error = 5.228706356775074e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.440000000000062 y[1] (closed_form) = 0.4822530864197118 y[1] (numeric) = 0.4822530864197374 absolute error = 2.559064071760986e-14 relative error = 5.306475259204035e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.430000000000063 y[1] (closed_form) = 0.4890214680424042 y[1] (numeric) = 0.4890214680424304 absolute error = 2.625677453238495e-14 relative error = 5.36924782412787e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.420000000000064 y[1] (closed_form) = 0.4959333465581779 y[1] (numeric) = 0.495933346558205 absolute error = 2.703393064962256e-14 relative error = 5.451121776190384e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.410000000000065 y[1] (closed_form) = 0.5029928072028106 y[1] (numeric) = 0.5029928072028385 absolute error = 2.786659791809143e-14 relative error = 5.540158332096268e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.400000000000066 y[1] (closed_form) = 0.5102040816326049 y[1] (numeric) = 0.5102040816326334 absolute error = 2.853273173286652e-14 relative error = 5.592415419642367e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.390000000000067 y[1] (closed_form) = 0.5175715542673274 y[1] (numeric) = 0.5175715542673567 absolute error = 2.930988785010413e-14 relative error = 5.662963431519167e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.380000000000068 y[1] (closed_form) = 0.5250997689560497 y[1] (numeric) = 0.5250997689560799 absolute error = 3.019806626980426e-14 relative error = 5.750919740422092e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.370000000000069 y[1] (closed_form) = 0.5327934359848147 y[1] (numeric) = 0.5327934359848456 absolute error = 3.097522238704187e-14 relative error = 5.813739489824477e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.36000000000007 y[1] (closed_form) = 0.5406574394463107 y[1] (numeric) = 0.5406574394463424 absolute error = 3.164135620181696e-14 relative error = 5.852385243088672e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.350000000000072 y[1] (closed_form) = 0.5486968449930831 y[1] (numeric) = 0.5486968449931154 absolute error = 3.230749001659206e-14 relative error = 5.888040055524527e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.340000000000073 y[1] (closed_form) = 0.5569169079972663 y[1] (numeric) = 0.5569169079972995 absolute error = 3.319566843629218e-14 relative error = 5.960614224421271e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.330000000000074 y[1] (closed_form) = 0.5653230821413812 y[1] (numeric) = 0.565323082141415 absolute error = 3.386180225106727e-14 relative error = 5.989814200191954e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.320000000000075 y[1] (closed_form) = 0.5739210284664179 y[1] (numeric) = 0.5739210284664528 absolute error = 3.486100297322992e-14 relative error = 6.07418115805627e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.310000000000076 y[1] (closed_form) = 0.582716624905241 y[1] (numeric) = 0.5827166249052769 absolute error = 3.586020369539256e-14 relative error = 6.15396955616703e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.300000000000077 y[1] (closed_form) = 0.5917159763312908 y[1] (numeric) = 0.5917159763313278 absolute error = 3.697042672001771e-14 relative error = 6.248002115683734e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.290000000000078 y[1] (closed_form) = 0.6009254251546654 y[1] (numeric) = 0.6009254251547036 absolute error = 3.819167204710538e-14 relative error = 6.355476145359578e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.280000000000079 y[1] (closed_form) = 0.6103515624999244 y[1] (numeric) = 0.6103515624999637 absolute error = 3.930189507173054e-14 relative error = 6.439222488553129e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.27000000000008 y[1] (closed_form) = 0.6200012400024015 y[1] (numeric) = 0.6200012400024418 absolute error = 4.030109579389318e-14 relative error = 6.500163740597854e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.260000000000081 y[1] (closed_form) = 0.6298815822624532 y[1] (numeric) = 0.6298815822624945 absolute error = 4.130029651605582e-14 relative error = 6.556835074889871e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.250000000000083 y[1] (closed_form) = 0.6399999999999154 y[1] (numeric) = 0.6399999999999578 absolute error = 4.241051954068098e-14 relative error = 6.626643678232279e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.240000000000084 y[1] (closed_form) = 0.6503642039541265 y[1] (numeric) = 0.6503642039541701 absolute error = 4.352074256530614e-14 relative error = 6.691749376842375e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.230000000000085 y[1] (closed_form) = 0.6609822195782021 y[1] (numeric) = 0.660982219578247 absolute error = 4.485301019485632e-14 relative error = 6.78581191238075e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.220000000000086 y[1] (closed_form) = 0.671862402579857 y[1] (numeric) = 0.671862402579903 absolute error = 4.6074255521944e-14 relative error = 6.85769219188711e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.210000000000087 y[1] (closed_form) = 0.6830134553649725 y[1] (numeric) = 0.6830134553650197 absolute error = 4.718447854656915e-14 relative error = 6.908279504004183e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.200000000000088 y[1] (closed_form) = 0.6944444444443425 y[1] (numeric) = 0.6944444444443908 absolute error = 4.829470157119431e-14 relative error = 6.954437026253002e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.190000000000089 y[1] (closed_form) = 0.706164818868618 y[1] (numeric) = 0.7061648188686674 absolute error = 4.940492459581947e-14 relative error = 6.996231372015044e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.18000000000009 y[1] (closed_form) = 0.7181844297614528 y[1] (numeric) = 0.7181844297615034 absolute error = 5.062616992290714e-14 relative error = 7.049187900066669e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.170000000000091 y[1] (closed_form) = 0.7305135510262574 y[1] (numeric) = 0.7305135510263094 absolute error = 5.206945985491984e-14 relative error = 7.127788359541091e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.160000000000093 y[1] (closed_form) = 0.7431629013078481 y[1] (numeric) = 0.7431629013079017 absolute error = 5.362377208939506e-14 relative error = 7.215614772350151e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.150000000000094 y[1] (closed_form) = 0.7561436672966633 y[1] (numeric) = 0.756143667296718 absolute error = 5.473399511402022e-14 relative error = 7.238570853830352e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.140000000000095 y[1] (closed_form) = 0.7694675284701707 y[1] (numeric) = 0.7694675284702267 absolute error = 5.595524044110789e-14 relative error = 7.271943047727589e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.130000000000096 y[1] (closed_form) = 0.7831466833736631 y[1] (numeric) = 0.7831466833737206 absolute error = 5.750955267558311e-14 relative error = 7.343394781146453e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.120000000000097 y[1] (closed_form) = 0.7971938775508824 y[1] (numeric) = 0.7971938775509417 absolute error = 5.928590951498336e-14 relative error = 7.436824489560799e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.110000000000098 y[1] (closed_form) = 0.8116224332439115 y[1] (numeric) = 0.8116224332439725 absolute error = 6.106226635438361e-14 relative error = 7.523481837524934e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.100000000000099 y[1] (closed_form) = 0.8264462809915866 y[1] (numeric) = 0.8264462809916493 absolute error = 6.272760089132134e-14 relative error = 7.590039707851251e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.0900000000001 y[1] (closed_form) = 0.8416799932664053 y[1] (numeric) = 0.8416799932664697 absolute error = 6.439293542825908e-14 relative error = 7.650524658232867e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.080000000000101 y[1] (closed_form) = 0.8573388203016225 y[1] (numeric) = 0.8573388203016885 absolute error = 6.605826996519681e-14 relative error = 7.705036608742001e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.070000000000102 y[1] (closed_form) = 0.8734387282730444 y[1] (numeric) = 0.8734387282731123 absolute error = 6.794564910705958e-14 relative error = 7.779097366268741e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.060000000000104 y[1] (closed_form) = 0.8899964400140661 y[1] (numeric) = 0.8899964400141358 absolute error = 6.972200594645983e-14 relative error = 7.833964588145757e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.050000000000105 y[1] (closed_form) = 0.9070294784578692 y[1] (numeric) = 0.9070294784579408 absolute error = 7.16093850883226e-14 relative error = 7.89493470598914e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.040000000000106 y[1] (closed_form) = 0.9245562130175634 y[1] (numeric) = 0.9245562130176371 absolute error = 7.371880883511039e-14 relative error = 7.973426363607163e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.030000000000107 y[1] (closed_form) = 0.9425959091335588 y[1] (numeric) = 0.9425959091336342 absolute error = 7.538414337204813e-14 relative error = 7.997503770342245e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.020000000000108 y[1] (closed_form) = 0.9611687812377819 y[1] (numeric) = 0.9611687812378596 absolute error = 7.771561172376096e-14 relative error = 8.085532243741801e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.010000000000109 y[1] (closed_form) = 0.9802960494067092 y[1] (numeric) = 0.9802960494067892 absolute error = 7.993605777301127e-14 relative error = 8.15427725342664e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -1.00000000000011 y[1] (closed_form) = 0.9999999999997797 y[1] (numeric) = 0.9999999999998618 absolute error = 8.204548151979907e-14 relative error = 8.204548151981715e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9900000000001101 y[1] (closed_form) = 1.020304050606854 y[1] (numeric) = 1.020304050606936 absolute error = 8.215650382226158e-14 relative error = 8.052158939621649e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9800000000001101 y[1] (closed_form) = 1.041232819658242 y[1] (numeric) = 1.041232819658323 absolute error = 8.171241461241152e-14 relative error = 7.847660299377765e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9700000000001101 y[1] (closed_form) = 1.062812201083827 y[1] (numeric) = 1.062812201083909 absolute error = 8.193445921733655e-14 relative error = 7.709213267760947e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9600000000001101 y[1] (closed_form) = 1.085069444444196 y[1] (numeric) = 1.085069444444277 absolute error = 8.149037000748649e-14 relative error = 7.510152499891676e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9500000000001101 y[1] (closed_form) = 1.108033240996973 y[1] (numeric) = 1.108033240997055 absolute error = 8.149037000748649e-14 relative error = 7.35450589317736e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9400000000001101 y[1] (closed_form) = 1.131733816206163 y[1] (numeric) = 1.131733816206244 absolute error = 8.104628079763643e-14 relative error = 7.161249371280832e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9300000000001101 y[1] (closed_form) = 1.156203029251663 y[1] (numeric) = 1.156203029251744 absolute error = 8.104628079763643e-14 relative error = 7.009692826189233e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9200000000001101 y[1] (closed_form) = 1.181474480150946 y[1] (numeric) = 1.181474480151027 absolute error = 8.104628079763643e-14 relative error = 6.859757206713588e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9100000000001101 y[1] (closed_form) = 1.207583625165751 y[1] (numeric) = 1.207583625165832 absolute error = 8.126832540256146e-14 relative error = 6.729830026587743e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.90000000000011 y[1] (closed_form) = 1.234567901234266 y[1] (numeric) = 1.234567901234347 absolute error = 8.104628079763643e-14 relative error = 6.564748744610156e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.89000000000011 y[1] (closed_form) = 1.262466860244606 y[1] (numeric) = 1.262466860244687 absolute error = 8.104628079763643e-14 relative error = 6.419675901982369e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.88000000000011 y[1] (closed_form) = 1.291322314049264 y[1] (numeric) = 1.291322314049345 absolute error = 8.060219158778636e-14 relative error = 6.241833716559736e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.87000000000011 y[1] (closed_form) = 1.321178491213829 y[1] (numeric) = 1.32117849121391 absolute error = 8.08242361927114e-14 relative error = 6.117586437427872e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.86000000000011 y[1] (closed_form) = 1.352082206597815 y[1] (numeric) = 1.352082206597896 absolute error = 8.060219158778636e-14 relative error = 5.961338089834205e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.85000000000011 y[1] (closed_form) = 1.384083044982341 y[1] (numeric) = 1.384083044982421 absolute error = 8.060219158778636e-14 relative error = 5.823508342219072e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.84000000000011 y[1] (closed_form) = 1.417233560090332 y[1] (numeric) = 1.417233560090412 absolute error = 8.038014698286133e-14 relative error = 5.671623171112181e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.83000000000011 y[1] (closed_form) = 1.451589490491704 y[1] (numeric) = 1.451589490491785 absolute error = 8.038014698286133e-14 relative error = 5.537388325650785e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.82000000000011 y[1] (closed_form) = 1.487209994050761 y[1] (numeric) = 1.487209994050841 absolute error = 7.993605777301127e-14 relative error = 5.374900524658719e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.81000000000011 y[1] (closed_form) = 1.524157902758312 y[1] (numeric) = 1.524157902758392 absolute error = 8.01581023779363e-14 relative error = 5.259173097017829e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.80000000000011 y[1] (closed_form) = 1.56249999999957 y[1] (numeric) = 1.56249999999965 absolute error = 7.993605777301127e-14 relative error = 5.115907697474129e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7900000000001099 y[1] (closed_form) = 1.602307322544018 y[1] (numeric) = 1.602307322544098 absolute error = 7.993605777301127e-14 relative error = 4.988809365615022e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7800000000001099 y[1] (closed_form) = 1.643655489808873 y[1] (numeric) = 1.643655489808952 absolute error = 7.926992395823618e-14 relative error = 4.822782173620449e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7700000000001099 y[1] (closed_form) = 1.686625063247958 y[1] (numeric) = 1.686625063248038 absolute error = 7.926992395823618e-14 relative error = 4.699913791485165e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7600000000001099 y[1] (closed_form) = 1.731301939057671 y[1] (numeric) = 1.73130193905775 absolute error = 7.904787935331115e-14 relative error = 4.565805511448572e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7500000000001099 y[1] (closed_form) = 1.777777777777257 y[1] (numeric) = 1.777777777777336 absolute error = 7.926992395823618e-14 relative error = 4.458933222652092e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7400000000001099 y[1] (closed_form) = 1.826150474798581 y[1] (numeric) = 1.82615047479866 absolute error = 7.904787935331115e-14 relative error = 4.328661873388605e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7300000000001099 y[1] (closed_form) = 1.876524676298928 y[1] (numeric) = 1.876524676299007 absolute error = 7.860379014346108e-14 relative error = 4.188795976746302e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7200000000001099 y[1] (closed_form) = 1.929012345678424 y[1] (numeric) = 1.929012345678502 absolute error = 7.838174553853605e-14 relative error = 4.063309688718949e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7100000000001099 y[1] (closed_form) = 1.983733386232276 y[1] (numeric) = 1.983733386232355 absolute error = 7.815970093361102e-14 relative error = 3.940030524064551e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.7000000000001099 y[1] (closed_form) = 2.040816326529971 y[1] (numeric) = 2.04081632653005 absolute error = 7.815970093361102e-14 relative error = 3.829825345748143e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 Finished! diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; Iterations = 1301 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %