##############ECHO OF PROBLEM################# ##############temp/lin_arccos_m0d5_0d5postode.ode################# diff ( y , x , 1 ) = arccos ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ max_terms=30; Digits=32; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-0.5); x_end=c(0.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_display_interval=0.0001; glob_type_given_pole=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=true; 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(x) *arccos(c(x)) - sqrt(glob__1 - c(x) * c(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -0.5 y[1] (closed_form) = -1.913222954981036 y[1] (numeric) = -1.913222954981036 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.49 y[1] (closed_form) = -1.892336611955132 y[1] (numeric) = -1.892336613214119 absolute error = 1.25898669267599e-09 relative error = 6.653080031967593e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.48 y[1] (closed_form) = -1.871564986794205 y[1] (numeric) = -1.8715649892631 absolute error = 2.468895088370004e-09 relative error = 1.319160758932001e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.47 y[1] (closed_form) = -1.85090735416453 y[1] (numeric) = -1.850907357796412 absolute error = 3.631882128374286e-09 relative error = 1.962217136477725e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.46 y[1] (closed_form) = -1.830363016861295 y[1] (numeric) = -1.830363021611254 absolute error = 4.749958648631036e-09 relative error = 2.595091031054737e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.45 y[1] (closed_form) = -1.809931304603575 y[1] (numeric) = -1.809931310428576 absolute error = 5.825001148096476e-09 relative error = 3.218354825556384e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4399999999999999 y[1] (closed_form) = -1.789611572909663 y[1] (numeric) = -1.789611579768426 absolute error = 6.858763779149513e-09 relative error = 3.832543264121892e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4299999999999999 y[1] (closed_form) = -1.769403202046341 y[1] (numeric) = -1.769403209899227 absolute error = 7.852885675063703e-09 relative error = 4.438155003891553e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4199999999999999 y[1] (closed_form) = -1.749305596046283 y[1] (numeric) = -1.749305604855184 absolute error = 8.80890160814829e-09 relative error = 5.035656221564631e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4099999999999999 y[1] (closed_form) = -1.729318181788363 y[1] (numeric) = -1.729318191516612 absolute error = 9.728249095175556e-09 relative error = 5.625482457551653e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3999999999999999 y[1] (closed_form) = -1.709440408136122 y[1] (numeric) = -1.709440418748397 absolute error = 1.061227550280819e-08 relative error = 6.208040626803259e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3899999999999999 y[1] (closed_form) = -1.689671745130089 y[1] (numeric) = -1.689671756592334 absolute error = 1.146224581916044e-08 relative error = 6.783711600905038e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3799999999999999 y[1] (closed_form) = -1.670011683230054 y[1] (numeric) = -1.670011695509401 absolute error = 1.227934731673486e-08 relative error = 7.352851144720587e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3699999999999999 y[1] (closed_form) = -1.650459732603735 y[1] (numeric) = -1.650459745668429 absolute error = 1.306469465944815e-08 relative error = 7.915791219478909e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3599999999999999 y[1] (closed_form) = -1.631015422458601 y[1] (numeric) = -1.631015436277936 absolute error = 1.381933523170176e-08 relative error = 8.472841544852114e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3499999999999999 y[1] (closed_form) = -1.611678300413902 y[1] (numeric) = -1.611678314958157 absolute error = 1.454425468949694e-08 relative error = 9.024291439403116e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3399999999999999 y[1] (closed_form) = -1.592447931910199 y[1] (numeric) = -1.592447947150579 absolute error = 1.524038006905926e-08 relative error = 9.570410286996239e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3299999999999998 y[1] (closed_form) = -1.57332389965394 y[1] (numeric) = -1.573323915562523 absolute error = 1.590858289546304e-08 relative error = 1.011144806162431e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3199999999999998 y[1] (closed_form) = -1.554305803094809 y[1] (numeric) = -1.554305819644493 absolute error = 1.654968428965731e-08 relative error = 1.064763720028897e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3099999999999998 y[1] (closed_form) = -1.535393257933789 y[1] (numeric) = -1.535393275098246 absolute error = 1.716445696686719e-08 relative error = 1.11791926128201e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2999999999999998 y[1] (closed_form) = -1.516585895660034 y[1] (numeric) = -1.516585913413662 absolute error = 1.775362856726304e-08 relative error = 1.17063125920319e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2899999999999998 y[1] (closed_form) = -1.497883363114811 y[1] (numeric) = -1.497883381432695 absolute error = 1.831788476458485e-08 relative error = 1.222917966489278e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2799999999999998 y[1] (closed_form) = -1.479285322080902 y[1] (numeric) = -1.479285340938773 absolute error = 1.885787015432072e-08 relative error = 1.274796002693616e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2699999999999998 y[1] (closed_form) = -1.460791448896002 y[1] (numeric) = -1.460791468270194 absolute error = 1.937419225050974e-08 relative error = 1.326280508087027e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2599999999999998 y[1] (closed_form) = -1.442401434088739 y[1] (numeric) = -1.442401453956162 absolute error = 1.986742281800957e-08 relative error = 1.377385126531099e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2499999999999998 y[1] (closed_form) = -1.424114982036098 y[1] (numeric) = -1.424115002374197 absolute error = 2.033809920476415e-08 relative error = 1.428121988835915e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2399999999999998 y[1] (closed_form) = -1.405931810641054 y[1] (numeric) = -1.405931831427782 absolute error = 2.07867281165619e-08 relative error = 1.478501870377619e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2299999999999998 y[1] (closed_form) = -1.387851651029399 y[1] (numeric) = -1.387851672243183 absolute error = 2.121378472885738e-08 relative error = 1.528534026898528e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2199999999999998 y[1] (closed_form) = -1.369874247264748 y[1] (numeric) = -1.369874268884463 absolute error = 2.161971579539568e-08 relative error = 1.578226310813869e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2099999999999997 y[1] (closed_form) = -1.351999356080843 y[1] (numeric) = -1.351999378085784 absolute error = 2.200494098048011e-08 relative error = 1.627585167219882e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1999999999999997 y[1] (closed_form) = -1.334226746630316 y[1] (numeric) = -1.334226769000169 absolute error = 2.236985285897219e-08 relative error = 1.67661553146561e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1899999999999997 y[1] (closed_form) = -1.316556200249146 y[1] (numeric) = -1.316556222963966 absolute error = 2.27148204690053e-08 relative error = 1.725320990072945e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1799999999999997 y[1] (closed_form) = -1.298987510236095 y[1] (numeric) = -1.298987533276282 absolute error = 2.304018731358326e-08 relative error = 1.773703529250689e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1699999999999997 y[1] (closed_form) = -1.28152048164649 y[1] (numeric) = -1.281520504992765 absolute error = 2.33462751353386e-08 relative error = 1.821763715031963e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1599999999999997 y[1] (closed_form) = -1.264154931099734 y[1] (numeric) = -1.264154954733116 absolute error = 2.363338214017574e-08 relative error = 1.869500451152471e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1499999999999997 y[1] (closed_form) = -1.246890686599996 y[1] (numeric) = -1.246890710501784 absolute error = 2.390178743816307e-08 relative error = 1.916911217240552e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1399999999999997 y[1] (closed_form) = -1.22972758736959 y[1] (numeric) = -1.229727611521338 absolute error = 2.41517486010423e-08 relative error = 1.963991769323752e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1299999999999997 y[1] (closed_form) = -1.212665483694555 y[1] (numeric) = -1.212665508078058 absolute error = 2.438350366062991e-08 relative error = 2.010736183101556e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1199999999999997 y[1] (closed_form) = -1.19570423678203 y[1] (numeric) = -1.195704261379303 absolute error = 2.459727288517399e-08 relative error = 2.057136884567043e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1099999999999997 y[1] (closed_form) = -1.178843718629031 y[1] (numeric) = -1.178843743422286 absolute error = 2.479325522664055e-08 relative error = 2.103184233400722e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.09999999999999964 y[1] (closed_form) = -1.162083811902265 y[1] (numeric) = -1.162083836873899 absolute error = 2.497163409387326e-08 relative error = 2.148866875014473e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.08999999999999964 y[1] (closed_form) = -1.145424409828681 y[1] (numeric) = -1.145424434961256 absolute error = 2.51325755762366e-08 relative error = 2.194171466975778e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.07999999999999963 y[1] (closed_form) = -1.128865416096453 y[1] (numeric) = -1.12886544137268 absolute error = 2.527622711134825e-08 relative error = 2.239082423018316e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.06999999999999962 y[1] (closed_form) = -1.112406744766147 y[1] (numeric) = -1.112406770168868 absolute error = 2.540272125983734e-08 relative error = 2.283582096149333e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.05999999999999961 y[1] (closed_form) = -1.096048320191832 y[1] (numeric) = -1.096048345704006 absolute error = 2.551217348489843e-08 relative error = 2.327650434283156e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.0499999999999996 y[1] (closed_form) = -1.079790076951942 y[1] (numeric) = -1.079790102556626 absolute error = 2.560468415069295e-08 relative error = 2.371264998375471e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.03999999999999959 y[1] (closed_form) = -1.063631959789699 y[1] (numeric) = -1.063631985470034 absolute error = 2.568033563576932e-08 relative error = 2.414400526366925e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.02999999999999958 y[1] (closed_form) = -1.047573923562962 y[1] (numeric) = -1.04757394930216 absolute error = 2.573919766213351e-08 relative error = 2.457029244732484e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.01999999999999957 y[1] (closed_form) = -1.031615933203364 y[1] (numeric) = -1.031615958984687 absolute error = 2.578132307640146e-08 relative error = 2.499120287561432e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.009999999999999565 y[1] (closed_form) = -1.015757963684627 y[1] (numeric) = -1.015757989491377 absolute error = 2.580674962615603e-08 relative error = 2.540639655193342e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.371503159461554e-16 y[1] (closed_form) = -0.9999999999999993 y[1] (numeric) = -1.000000025815499 absolute error = 2.581549995994692e-08 relative error = 2.581549995994694e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.01000000000000044 y[1] (closed_form) = -0.9843420371487295 y[1] (numeric) = -0.9843420629563122 absolute error = 2.580758273751371e-08 relative error = 2.621810484927437e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.02000000000000045 y[1] (closed_form) = -0.9687840801315682 y[1] (numeric) = -0.9687841059145587 absolute error = 2.578299040933985e-08 relative error = 2.661376351873817e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03000000000000046 y[1] (closed_form) = -0.9533261439552685 y[1] (numeric) = -0.9533261696969696 absolute error = 2.574170110403173e-08 relative error = 2.70019880051035e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.04000000000000047 y[1] (closed_form) = -0.9379682536461067 y[1] (numeric) = -0.9379682793297839 absolute error = 2.568367718502884e-08 relative error = 2.738224570521471e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.05000000000000047 y[1] (closed_form) = -0.922710444272452 y[1] (numeric) = -0.9227104698813184 absolute error = 2.560886647184901e-08 relative error = 2.775395751810456e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.06000000000000048 y[1] (closed_form) = -0.9075527609764447 y[1] (numeric) = -0.9075527864936458 absolute error = 2.551720112986544e-08 relative error = 2.811649330713428e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.07000000000000049 y[1] (closed_form) = -0.8924952590148613 y[1] (numeric) = -0.8924952844234594 absolute error = 2.540859811439589e-08 relative error = 2.846916872414759e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.0800000000000005 y[1] (closed_form) = -0.8775380038092693 y[1] (numeric) = -0.8775380290922279 absolute error = 2.528295861559116e-08 relative error = 2.881124065948299e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09000000000000051 y[1] (closed_form) = -0.8626810710055991 y[1] (numeric) = -0.8626810961457668 absolute error = 2.51401677253682e-08 relative error = 2.914190257595792e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1000000000000005 y[1] (closed_form) = -0.8479245465432854 y[1] (numeric) = -0.8479245715233797 absolute error = 2.498009432638781e-08 relative error = 2.946027972444434e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1100000000000005 y[1] (closed_form) = -0.8332685267341536 y[1] (numeric) = -0.8332685515367444 absolute error = 2.480259075898772e-08 relative error = 2.976542370584548e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1200000000000005 y[1] (closed_form) = -0.8187131183512547 y[1] (numeric) = -0.8187131429587473 absolute error = 2.460749259913797e-08 relative error = 3.005630671790524e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1300000000000005 y[1] (closed_form) = -0.8042584387278811 y[1] (numeric) = -0.804258463122499 absolute error = 2.439461799230713e-08 relative error = 3.033181477199395e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1400000000000005 y[1] (closed_form) = -0.7899046158670185 y[1] (numeric) = -0.7899046400307856 absolute error = 2.416376709835077e-08 relative error = 3.059074046785767e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1500000000000005 y[1] (closed_form) = -0.7756517885615271 y[1] (numeric) = -0.7756518124762485 absolute error = 2.391472142537765e-08 relative error = 3.083177500270879e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1600000000000006 y[1] (closed_form) = -0.7615001065253668 y[1] (numeric) = -0.7615001301726109 absolute error = 2.36472440517943e-08 relative error = 3.105350064846849e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1700000000000006 y[1] (closed_form) = -0.747449730536225 y[1] (numeric) = -0.7474497538973033 absolute error = 2.336107829403744e-08 relative error = 3.125438051503217e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1800000000000006 y[1] (closed_form) = -0.7335008325899314 y[1] (numeric) = -0.7335008556458781 absolute error = 2.305594670737321e-08 relative error = 3.143274783474281e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1900000000000006 y[1] (closed_form) = -0.7196535960670845 y[1] (numeric) = -0.7196536187986355 absolute error = 2.273155108589719e-08 relative error = 3.158679566130899e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000000006 y[1] (closed_form) = -0.7059082159123573 y[1] (numeric) = -0.7059082382999291 absolute error = 2.238757179640061e-08 relative error = 3.171456471499711e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2100000000000006 y[1] (closed_form) = -0.6922648988269857 y[1] (numeric) = -0.6922649208506512 absolute error = 2.202366544690193e-08 relative error = 3.181392770920513e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2200000000000006 y[1] (closed_form) = -0.6787238634749926 y[1] (numeric) = -0.6787238851144575 absolute error = 2.163946488664692e-08 relative error = 3.188257559687854e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2300000000000006 y[1] (closed_form) = -0.6652853407037458 y[1] (numeric) = -0.6652853619383242 absolute error = 2.123457842895249e-08 relative error = 3.191800138943439e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2400000000000006 y[1] (closed_form) = -0.6519495737795029 y[1] (numeric) = -0.6519495945880911 absolute error = 2.080858818587217e-08 relative error = 3.191748107946441e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2500000000000006 y[1] (closed_form) = -0.6387168186386489 y[1] (numeric) = -0.6387168389996977 absolute error = 2.036104873592848e-08 relative error = 3.187805321820975e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2600000000000006 y[1] (closed_form) = -0.6255873441553929 y[1] (numeric) = -0.625587364046879 absolute error = 1.989148612491221e-08 relative error = 3.179649702115978e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2700000000000006 y[1] (closed_form) = -0.6125614324267571 y[1] (numeric) = -0.612561451826153 absolute error = 1.939939586748096e-08 relative error = 3.166930668590617e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2800000000000006 y[1] (closed_form) = -0.5996393790757599 y[1] (numeric) = -0.5996393979600017 absolute error = 1.888424172591385e-08 relative error = 3.149266439942726e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2900000000000006 y[1] (closed_form) = -0.5868214935737702 y[1] (numeric) = -0.5868215119192237 absolute error = 1.834545348966543e-08 relative error = 3.126240891065657e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000007 y[1] (closed_form) = -0.5741080995830951 y[1] (numeric) = -0.5741081173655213 absolute error = 1.778242619820958e-08 relative error = 3.097400334731872e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3100000000000007 y[1] (closed_form) = -0.5614995353209522 y[1] (numeric) = -0.5614995525154682 absolute error = 1.719451603321431e-08 relative error = 3.062249378957358e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3200000000000007 y[1] (closed_form) = -0.5489961539460748 y[1] (numeric) = -0.5489961705271151 absolute error = 1.65810403185418e-08 relative error = 3.020247081761973e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3300000000000007 y[1] (closed_form) = -0.5365983239693082 y[1] (numeric) = -0.5365983399105814 absolute error = 1.594127319037852e-08 relative error = 2.970801897489773e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3400000000000007 y[1] (closed_form) = -0.5243064296896691 y[1] (numeric) = -0.5243064449641137 absolute error = 1.527444459803462e-08 relative error = 2.91326669540852e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500000000000007 y[1] (closed_form) = -0.5121208716574737 y[1] (numeric) = -0.5121208862372096 absolute error = 1.457973597407403e-08 relative error = 2.846932585834057e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3600000000000007 y[1] (closed_form) = -0.5000420671662749 y[1] (numeric) = -0.5000420810225528 absolute error = 1.385627790284616e-08 relative error = 2.771022442445556e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3700000000000007 y[1] (closed_form) = -0.4880704507755106 y[1] (numeric) = -0.4880704638786569 absolute error = 1.310314623470532e-08 relative error = 2.684683371813498e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3800000000000007 y[1] (closed_form) = -0.4762064748659317 y[1] (numeric) = -0.4762064871852907 absolute error = 1.231935897738623e-08 relative error = 2.58697846997031e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3900000000000007 y[1] (closed_form) = -0.4644506102300686 y[1] (numeric) = -0.46445062173394 absolute error = 1.150387141102271e-08 relative error = 2.476877230352695e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000007 y[1] (closed_form) = -0.4528033467002037 y[1] (numeric) = -0.4528033573557756 absolute error = 1.065557192481137e-08 relative error = 2.353244957764482e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4100000000000008 y[1] (closed_form) = -0.4412651938165469 y[1] (numeric) = -0.4412652035898242 absolute error = 9.773277243052547e-09 relative error = 2.21483075937227e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4200000000000008 y[1] (closed_form) = -0.4298366815385689 y[1] (numeric) = -0.429836690394296 absolute error = 8.855727151590997e-09 relative error = 2.060253936423614e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4300000000000008 y[1] (closed_form) = -0.4185183610027289 y[1] (numeric) = -0.4185183689043072 absolute error = 7.901578280566923e-09 relative error = 1.887988441328002e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4400000000000008 y[1] (closed_form) = -0.4073108053301528 y[1] (numeric) = -0.4073108122395501 absolute error = 6.909397276544382e-09 relative error = 1.696345195395406e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4500000000000008 y[1] (closed_form) = -0.3962146104881666 y[1] (numeric) = -0.3962146163658215 absolute error = 5.877654862818105e-09 relative error = 1.483452327912993e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4600000000000008 y[1] (closed_form) = -0.3852303962099893 y[1] (numeric) = -0.385230401014706 absolute error = 4.80471668007354e-09 relative error = 1.247231975291608e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4700000000000008 y[1] (closed_form) = -0.3743588069773265 y[1] (numeric) = -0.3743588106661619 absolute error = 3.688835403803381e-09 relative error = 9.853742813179763e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4800000000000008 y[1] (closed_form) = -0.3636005130711034 y[1] (numeric) = -0.3636005155992439 absolute error = 2.528140474744589e-09 relative error = 6.953071802322242e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900000000000008 y[1] (closed_form) = -0.3529562116961324 y[1] (numeric) = -0.3529562130167607 absolute error = 1.320628273404623e-09 relative error = 3.741620715664242e-07 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arccos ( x ) ; Iterations = 1000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.1 %