##############ECHO OF PROBLEM################# ##############temp/sinpostode.ode################# diff ( y , x , 1 ) = sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK # ELIMINATED in preodein.rb # Digits:=16; ELIMINATED in preodein.rb max_terms=40 # ELIMINATED in preodein.rb ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK # ELIMINATED in preodein.rb x_start=c(0.0) x_end=c(1.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=false # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=3 # ELIMINATED in preodein.rb #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 def exact_soln_y (x) x = c(x) return(c(2.0) - cos(c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (closed_form) 1.0 y[1] (numeric) 1.0 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 NO POLE (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 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] 0.00999999400000118 y[1] (closed_form) 1.0000499995233358 y[1] (numeric) 1.000049999523335 absolute error 8.881784197001252e-16 relative error 8.881340134227958e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.019999987333335884 y[1] (closed_form) 1.000199993080106 y[1] (numeric) 1.0001999930801049 absolute error 1.1102230246251565e-15 relative error 1.1100010320998261e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.029999980666670686 y[1] (closed_form) 1.0004499656710997 y[1] (numeric) 1.0004499656710988 absolute error 8.881784197001252e-16 relative error 8.877789496492581e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.039999974000005184 y[1] (closed_form) 1.0007998922993 y[1] (numeric) 1.0007998922992989 absolute error 1.1102230246251565e-15 relative error 1.1093356755609366e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.04999996733333964 y[1] (closed_form) 1.0012497379723817 y[1] (numeric) 1.0012497379723813 absolute error 4.440892098500626e-16 relative error 4.435349074341653e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.059999960666674096 y[1] (closed_form) 1.0017994577062128 y[1] (numeric) 1.0017994577062117 absolute error 1.1102230246251565e-15 relative error 1.1082288137460142e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.06999995400000855 y[1] (closed_form) 1.0024489965293513 y[1] (numeric) 1.0024489965293502 absolute error 1.1102230246251565e-15 relative error 1.1075107346797066e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.07999994733334301 y[1] (closed_form) 1.0031982894885423 y[1] (numeric) 1.0031982894885414 absolute error 8.881784197001252e-16 relative error 8.853468242583853e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.08999994066667746 y[1] (closed_form) 1.0040472616552145 y[1] (numeric) 1.0040472616552145 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.09999993400001192 y[1] (closed_form) 1.004995828132972 y[1] (numeric) 1.0049958281329732 absolute error 1.1102230246251565e-15 relative error 1.1047041127401195e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.10999992733334638 y[1] (closed_form) 1.0060438940660839 y[1] (numeric) 1.0060438940660843 absolute error 4.440892098500626e-16 relative error 4.414213062366559e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.11999992066668083 y[1] (closed_form) 1.0071913546489701 y[1] (numeric) 1.0071913546489717 absolute error 1.5543122344752192e-15 relative error 1.5432144321939036e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.1299999140000153 y[1] (closed_form) 1.0084380951366814 y[1] (numeric) 1.0084380951366825 absolute error 1.1102230246251565e-15 relative error 1.100933245163333e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.13999990733334974 y[1] (closed_form) 1.009783990856374 y[1] (numeric) 1.0097839908563744 absolute error 4.440892098500626e-16 relative error 4.397863442788799e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.1499999006666842 y[1] (closed_form) 1.0112289072197775 y[1] (numeric) 1.0112289072197775 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.15999989400001866 y[1] (closed_form) 1.0127726997366517 y[1] (numeric) 1.0127726997366524 absolute error 6.661338147750939e-16 relative error 6.577327913245556e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.1699998873333531 y[1] (closed_form) 1.0144152140292375 y[1] (numeric) 1.014415214029238 absolute error 4.440892098500626e-16 relative error 4.377785385198916e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.17999988066668757 y[1] (closed_form) 1.0161562858476936 y[1] (numeric) 1.0161562858476951 absolute error 1.5543122344752192e-15 relative error 1.529599586326022e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.18999987400002202 y[1] (closed_form) 1.017995741086521 y[1] (numeric) 1.0179957410865232 absolute error 2.220446049250313e-15 relative error 2.1811938494756373e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.19999986733335648 y[1] (closed_form) 1.0199333958019738 y[1] (numeric) 1.0199333958019752 absolute error 1.3322676295501878e-15 relative error 1.3062300293664033e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.20999986066669094 y[1] (closed_form) 1.0219690562304535 y[1] (numeric) 1.0219690562304553 absolute error 1.7763568394002505e-15 relative error 1.7381708659089604e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.2199998540000254 y[1] (closed_form) 1.0241025188078856 y[1] (numeric) 1.0241025188078867 absolute error 1.1102230246251565e-15 relative error 1.084093637341621e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.22999984733335985 y[1] (closed_form) 1.026333570190074 y[1] (numeric) 1.026333570190074 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.2399998406666943 y[1] (closed_form) 1.0286619872740375 y[1] (numeric) 1.0286619872740377 absolute error 2.220446049250313e-16 relative error 2.1585769443415645e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.24999983400002876 y[1] (closed_form) 1.0310875372203183 y[1] (numeric) 1.0310875372203185 absolute error 2.220446049250313e-16 relative error 2.1534990668555214e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.25999982733336596 y[1] (closed_form) 1.0336099774762677 y[1] (numeric) 1.033609977476267 absolute error 6.661338147750939e-16 relative error 6.444730887772305e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.2699998206667032 y[1] (closed_form) 1.0362290558002971 y[1] (numeric) 1.036229055800295 absolute error 2.220446049250313e-15 relative error 2.1428139240270824e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.2799998140000404 y[1] (closed_form) 1.0389445102871062 y[1] (numeric) 1.0389445102871038 absolute error 2.4424906541753444e-15 relative error 2.3509346553074103e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.28999980733337766 y[1] (closed_form) 1.0417560693938712 y[1] (numeric) 1.0417560693938674 absolute error 3.774758283725532e-15 relative error 3.623456963319459e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.2999998006667149 y[1] (closed_form) 1.0446634519673994 y[1] (numeric) 1.044663451967395 absolute error 4.440892098500626e-15 relative error 4.2510265771595236e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.3099997940000521 y[1] (closed_form) 1.0476663672722437 y[1] (numeric) 1.0476663672722384 absolute error 5.329070518200751e-15 relative error 5.086610284222242e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.31999978733338935 y[1] (closed_form) 1.0507645150197762 y[1] (numeric) 1.0507645150197713 absolute error 4.884981308350689e-15 relative error 4.648978185429824e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.3299997806667266 y[1] (closed_form) 1.0539575853982175 y[1] (numeric) 1.0539575853982126 absolute error 4.884981308350689e-15 relative error 4.634893639012042e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.3399997740000638 y[1] (closed_form) 1.0572452591036163 y[1] (numeric) 1.057245259103611 absolute error 5.329070518200751e-15 relative error 5.040524393288834e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.34999976733340105 y[1] (closed_form) 1.06062720737178 y[1] (numeric) 1.0606272073717744 absolute error 5.551115123125783e-15 relative error 5.233804191089319e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.3599997606667383 y[1] (closed_form) 1.0641030920111507 y[1] (numeric) 1.0641030920111443 absolute error 6.439293542825908e-15 relative error 6.051381291126284e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.3699997540000755 y[1] (closed_form) 1.0676725654366248 y[1] (numeric) 1.0676725654366175 absolute error 7.327471962526033e-15 relative error 6.863032918270652e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.37999974733341274 y[1] (closed_form) 1.0713352707043102 y[1] (numeric) 1.0713352707043016 absolute error 8.659739592076221e-15 relative error 8.083127503478152e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.38999974066674997 y[1] (closed_form) 1.0750908415472207 y[1] (numeric) 1.0750908415472105 absolute error 1.021405182655144e-14 relative error 9.500640719673374e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.3999997340000872 y[1] (closed_form) 1.0789389024119025 y[1] (numeric) 1.0789389024118914 absolute error 1.1102230246251565e-14 relative error 1.0289952676127632e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.40999972733342444 y[1] (closed_form) 1.0828790684959886 y[1] (numeric) 1.0828790684959761 absolute error 1.2434497875801753e-14 relative error 1.1482813028302445e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.41999972066676167 y[1] (closed_form) 1.0869109457866797 y[1] (numeric) 1.0869109457866655 absolute error 1.4210854715202004e-14 relative error 1.307453455160168e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.4299997140000989 y[1] (closed_form) 1.0910341311001437 y[1] (numeric) 1.091034131100128 absolute error 1.5765166949677223e-14 relative error 1.4449746804694759e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.43999970733343613 y[1] (closed_form) 1.0952482121218357 y[1] (numeric) 1.0952482121218183 absolute error 1.7319479184152442e-14 relative error 1.581329144614556e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.44999970066677336 y[1] (closed_form) 1.0995527674477266 y[1] (numeric) 1.0995527674477095 absolute error 1.709743457922741e-14 relative error 1.5549444360832127e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.4599996940001106 y[1] (closed_form) 1.103947366626445 y[1] (numeric) 1.103947366626427 absolute error 1.7985612998927536e-14 relative error 1.6292092850304818e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.4699996873334478 y[1] (closed_form) 1.1084315702023213 y[1] (numeric) 1.1084315702023024 absolute error 1.887379141862766e-14 relative error 1.7027475512252542e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.47999968066678506 y[1] (closed_form) 1.1130049297593323 y[1] (numeric) 1.1130049297593125 absolute error 1.9761969838327786e-14 relative error 1.77555097106362e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.4899996740001223 y[1] (closed_form) 1.1176669879659435 y[1] (numeric) 1.1176669879659227 absolute error 2.0872192862952943e-14 relative error 1.867478693357358e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.4999996673334595 y[1] (closed_form) 1.1224172786208406 y[1] (numeric) 1.1224172786208186 absolute error 2.19824158875781e-14 relative error 1.9584887284155836e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.5099996606667913 y[1] (closed_form) 1.1272553266995473 y[1] (numeric) 1.1272553266995269 absolute error 2.042810365310288e-14 relative error 1.8121984584374184e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.5199996540001229 y[1] (closed_form) 1.1321806484019354 y[1] (numeric) 1.1321806484019166 absolute error 1.887379141862766e-14 relative error 1.6670300314060197e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.5299996473334546 y[1] (closed_form) 1.1371927512005957 y[1] (numeric) 1.137192751200578 absolute error 1.7763568394002505e-14 relative error 1.5620543109555129e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.5399996406667863 y[1] (closed_form) 1.142291133890093 y[1] (numeric) 1.142291133890076 absolute error 1.687538997430238e-14 relative error 1.4773282811740764e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.549999634000118 y[1] (closed_form) 1.1474752866370872 y[1] (numeric) 1.1474752866370712 absolute error 1.5987211554602254e-14 relative error 1.3932510565396204e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.5599996273334497 y[1] (closed_form) 1.1527446910313146 y[1] (numeric) 1.1527446910313004 absolute error 1.4210854715202004e-14 relative error 1.2327842258365225e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.5699996206667813 y[1] (closed_form) 1.1580988201374298 y[1] (numeric) 1.1580988201374187 absolute error 1.1102230246251565e-14 relative error 9.58660008386338e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.579999614000113 y[1] (closed_form) 1.1635371385476976 y[1] (numeric) 1.163537138547689 absolute error 8.659739592076221e-15 relative error 7.442598353916855e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.5899996073334447 y[1] (closed_form) 1.1690591024355341 y[1] (numeric) 1.1690591024355275 absolute error 6.661338147750939e-15 relative error 5.698033686982278e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.5999996006667764 y[1] (closed_form) 1.1746641596098883 y[1] (numeric) 1.1746641596098841 absolute error 4.218847493575595e-15 relative error 3.591535043494214e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.6099995940001081 y[1] (closed_form) 1.1803517495704612 y[1] (numeric) 1.180351749570459 absolute error 2.220446049250313e-15 relative error 1.8811731757574384e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.6199995873334397 y[1] (closed_form) 1.1861213035637541 y[1] (numeric) 1.186121303563754 absolute error 2.220446049250313e-16 relative error 1.8720227371170928e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 9.999993333334665e-05 NO POLE (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] 0.6299995806667714 y[1] (closed_form) 1.1919722446399457 y[1] (numeric) 1.1919722446399474 absolute error 1.7763568394002505e-15 relative error 1.490266948234879e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.6399995740001031 y[1] (closed_form) 1.1979039877105837 y[1] (numeric) 1.1979039877105853 absolute error 1.5543122344752192e-15 relative error 1.2975265550670698e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.6499995673334348 y[1] (closed_form) 1.203915939607095 y[1] (numeric) 1.2039159396070989 absolute error 3.774758283725532e-15 relative error 3.135400204899228e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.6599995606667665 y[1] (closed_form) 1.2100074991401022 y[1] (numeric) 1.2100074991401075 absolute error 5.329070518200751e-15 relative error 4.404163215507244e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.6699995540000981 y[1] (closed_form) 1.2161780571595395 y[1] (numeric) 1.216178057159546 absolute error 6.439293542825908e-15 relative error 5.294696368610106e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.6799995473334298 y[1] (closed_form) 1.22242699661557 y[1] (numeric) 1.2224269966155787 absolute error 8.659739592076221e-15 relative error 7.08405460289384e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.6899995406667615 y[1] (closed_form) 1.2287536926202893 y[1] (numeric) 1.2287536926202993 absolute error 9.992007221626409e-15 relative error 8.13182274172351e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.6999995340000932 y[1] (closed_form) 1.2351575125102126 y[1] (numeric) 1.235157512510224 absolute error 1.1546319456101628e-14 relative error 9.348054267699045e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 9.999993333334665e-05 NO POLE (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] 0.7099995273334249 y[1] (closed_form) 1.2416378159095405 y[1] (numeric) 1.241637815909555 absolute error 1.4432899320127035e-14 relative error 1.1624081624442522e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.7199995206667565 y[1] (closed_form) 1.248193954794198 y[1] (numeric) 1.2481939547942136 absolute error 1.554312234475219e-14 relative error 1.2452489683235918e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.7299995140000882 y[1] (closed_form) 1.2548252735566339 y[1] (numeric) 1.2548252735566527 absolute error 1.887379141862766e-14 relative error 1.5040971692522921e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.7399995073334199 y[1] (closed_form) 1.2615311090713823 y[1] (numeric) 1.2615311090714036 absolute error 2.1316282072803006e-14 relative error 1.6897151342144863e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.7499995006667516 y[1] (closed_form) 1.2683107907613742 y[1] (numeric) 1.2683107907613977 absolute error 2.353672812205332e-14 relative error 1.8557539913323677e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.7599994940000833 y[1] (closed_form) 1.2751636406649938 y[1] (numeric) 1.2751636406650193 absolute error 2.55351295663786e-14 relative error 2.002498248229703e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.769999487333415 y[1] (closed_form) 1.2820889735038754 y[1] (numeric) 1.2820889735039034 absolute error 2.7977620220553945e-14 relative error 2.182190222266144e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.7799994806667466 y[1] (closed_form) 1.2890860967514297 y[1] (numeric) 1.2890860967514597 absolute error 2.9976021664879227e-14 relative error 2.3253700230279815e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.7899994740000783 y[1] (closed_form) 1.2961543107020956 y[1] (numeric) 1.2961543107021265 absolute error 3.086420008457935e-14 relative error 2.3812133964096416e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.79999946733341 y[1] (closed_form) 1.3032929085413105 y[1] (numeric) 1.3032929085413436 absolute error 3.3084646133829665e-14 relative error 2.5385426343537096e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.8099994606667417 y[1] (closed_form) 1.3105011764161916 y[1] (numeric) 1.3105011764162255 absolute error 3.397282455352979e-14 relative error 2.5923536098177934e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.8199994540000733 y[1] (closed_form) 1.3177783935069187 y[1] (numeric) 1.3177783935069558 absolute error 3.708144902248023e-14 relative error 2.8139366379955403e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.829999447333405 y[1] (closed_form) 1.325123832098818 y[1] (numeric) 1.3251238320988565 absolute error 3.863576125695545e-14 relative error 2.915634020087134e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.8399994406667367 y[1] (closed_form) 1.33253675765513 y[1] (numeric) 1.3325367576551719 absolute error 4.196643033083092e-14 relative error 3.1493638047688384e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.8499994340000684 y[1] (closed_form) 1.3400164288904657 y[1] (numeric) 1.3400164288905096 absolute error 4.39648317751562e-14 relative error 3.2809173699130765e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.8599994273334001 y[1] (closed_form) 1.3475620978449312 y[1] (numeric) 1.3475620978449776 absolute error 4.6407322429331543e-14 relative error 3.443798434487566e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.8699994206667317 y[1] (closed_form) 1.3551730099589259 y[1] (numeric) 1.3551730099589745 absolute error 4.8627768478581856e-14 relative error 3.5883070369041456e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.8799994140000634 y[1] (closed_form) 1.362848404148595 y[1] (numeric) 1.3628484041486466 absolute error 5.1514348342607263e-14 relative error 3.779903046134433e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.8899994073333951 y[1] (closed_form) 1.3705875128819391 y[1] (numeric) 1.3705875128819938 absolute error 5.46229728115577e-14 relative error 3.985369215622123e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.8999994006667268 y[1] (closed_form) 1.3783895622555664 y[1] (numeric) 1.378389562255624 absolute error 5.750955267558311e-14 relative error 4.17222781210529e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.9099993940000585 y[1] (closed_form) 1.3862537720720811 y[1] (numeric) 1.3862537720721404 absolute error 5.928590951498336e-14 relative error 4.276699599263609e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.9199993873333902 y[1] (closed_form) 1.3941793559181035 y[1] (numeric) 1.3941793559181646 absolute error 6.106226635438361e-14 relative error 4.379799922813554e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.9299993806667218 y[1] (closed_form) 1.4021655212429107 y[1] (numeric) 1.4021655212429738 absolute error 6.306066779870889e-14 relative error 4.4973768676618516e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.9399993740000535 y[1] (closed_form) 1.4102114694376897 y[1] (numeric) 1.4102114694377548 absolute error 6.505906924303417e-14 relative error 4.613426472057836e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.9499993673333852 y[1] (closed_form) 1.418316395915399 y[1] (numeric) 1.418316395915466 absolute error 6.705747068735946e-14 relative error 4.727962736698093e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.9599993606667169 y[1] (closed_form) 1.4264794901912257 y[1] (numeric) 1.4264794901912947 absolute error 6.905587213168474e-14 relative error 4.841000000808109e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.9699993540000486 y[1] (closed_form) 1.434699935963633 y[1] (numeric) 1.4346999359637038 absolute error 7.083222897108499e-14 relative error 4.9370761924171756e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.9799993473333802 y[1] (closed_form) 1.4429769111959898 y[1] (numeric) 1.4429769111960626 absolute error 7.283063041541027e-14 relative error 5.04724849374379e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.9899993406667119 y[1] (closed_form) 1.4513095881987743 y[1] (numeric) 1.4513095881988498 absolute error 7.549516567451064e-14 relative error 5.201865011324563e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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] 0.9999993340000436 y[1] (closed_form) 1.459697133712341 y[1] (numeric) 1.4596971337124187 absolute error 7.771561172376096e-14 relative error 5.324091548094811e-12% Desired digits 8 Estimated correct digits 12 Correct digits 14 h 9.999993333334665e-05 NO POLE (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 ) = sin ( x ) ; Iterations 9992 Total Elapsed Time 2 Seconds Elapsed Time(since restart) 2 Seconds Time to Timeout 2 Minutes 58.0 Seconds Percent Done 100.01993338667103%