##############ECHO OF PROBLEM################# ##############temp/mult2postode.ode################# diff ( y , x , 1 ) = sin ( x ) * cos ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.00000000001; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(2.0 - expt(cos(x),2)/2.0); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 9.999999999999999e-12 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 90000000000.00002 step_error = 1.111111111111111e-17 est_needed_step_err = 1.111111111111111e-17 opt_iter = 1 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 9.999999999999999e-12 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 90000000000.00002 step_error = 1.672203728377433e-17 est_needed_step_err = 1.672203728377433e-17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.077147734516545e-306 estimated_step_error = 4.077147734516545e-306 Double H and LOOP opt_iter = 2 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 2e-11 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 45000000000.00001 step_error = 2.36485319172222e-17 est_needed_step_err = 2.36485319172222e-17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.736127528235584e-298 estimated_step_error = 2.736127528235584e-298 Double H and LOOP opt_iter = 3 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 4e-11 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 22500000000 step_error = 3.344407456754866e-17 est_needed_step_err = 3.344407456754866e-17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.836184101789904e-290 estimated_step_error = 1.836184101789904e-290 Double H and LOOP opt_iter = 4 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 8e-11 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 11250000000 step_error = 4.729706383444441e-17 est_needed_step_err = 4.729706383444441e-17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.232242291659438e-282 estimated_step_error = 1.232242291659438e-282 Double H and LOOP opt_iter = 5 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 1.6e-10 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 5625000000.000001 step_error = 6.688814913509732e-17 est_needed_step_err = 6.688814913509732e-17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.269438036597189e-275 estimated_step_error = 8.269438036597189e-275 Double H and LOOP opt_iter = 6 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 3.2e-10 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 2812500000 step_error = 9.459412766888882e-17 est_needed_step_err = 9.459412766888882e-17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.549525925537611e-267 estimated_step_error = 5.549525925537611e-267 Double H and LOOP opt_iter = 7 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 6.4e-10 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 1406250000 step_error = 1.337762982701946e-16 est_needed_step_err = 1.337762982701946e-16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.724223806004829e-259 estimated_step_error = 3.724223806004829e-259 Double H and LOOP opt_iter = 8 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 1.28e-09 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 703125000.0000001 step_error = 1.891882553377776e-16 est_needed_step_err = 1.891882553377776e-16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.499284289015396e-251 estimated_step_error = 2.499284289015396e-251 Double H and LOOP opt_iter = 9 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 2.56e-09 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 351562500.0000001 step_error = 2.675525965403893e-16 est_needed_step_err = 2.675525965403893e-16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.677241294472591e-243 estimated_step_error = 1.677241294472591e-243 Double H and LOOP opt_iter = 10 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 5.12e-09 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 175781250 step_error = 3.783765106755553e-16 est_needed_step_err = 3.783765106755553e-16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.125577579237817e-235 estimated_step_error = 1.125577579237817e-235 Double H and LOOP opt_iter = 11 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 1.024e-08 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 87890625.00000001 step_error = 5.351051930807785e-16 est_needed_step_err = 5.351051930807785e-16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.553623268361628e-228 estimated_step_error = 7.553623268361628e-228 Double H and LOOP opt_iter = 12 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 2.048e-08 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 43945312.50000001 step_error = 7.567530213511105e-16 est_needed_step_err = 7.567530213511105e-16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.069150765847445e-220 estimated_step_error = 5.069150765847445e-220 Double H and LOOP opt_iter = 13 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 4.096e-08 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 21972656.25 step_error = 1.070210386161557e-15 est_needed_step_err = 1.070210386161557e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.401849492884454e-212 estimated_step_error = 3.401849492884454e-212 Double H and LOOP opt_iter = 14 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 8.192e-08 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 10986328.125 step_error = 1.513506042702221e-15 est_needed_step_err = 1.513506042702221e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.282942548962471e-204 estimated_step_error = 2.282942548962471e-204 Double H and LOOP opt_iter = 15 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 1.6384e-07 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 5493164.062500001 step_error = 2.140420772323114e-15 est_needed_step_err = 2.140420772323114e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.532056809439086e-196 estimated_step_error = 1.532056809439086e-196 Double H and LOOP opt_iter = 16 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 min_size = 1.504983355539689 glob_desired_digits_correct = 10 estimated_h = 3.2768e-07 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-10 range = 0.9 estimated_steps = 2746582.03125 step_error = 3.027012085404442e-15 est_needed_step_err = 3.027012085404442e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.028145919384519e-188 estimated_step_error = 1.028145919384519e-188 Double H and LOOP opt_iter = 17 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.504983355539689 y[1] (numeric) = 1.504983355539689 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 3.2768e-07 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] = 0.1100001382398525 y[1] (analytic) = 1.506025652751373 y[1] (numeric) = 1.506025652751392 absolute error = 1.887379141862766e-14 relative error = 1.253218455087199e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 3.2768e-07 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] = 0.120000276479705 y[1] (analytic) = 1.507165539147006 y[1] (numeric) = 1.507165539147032 absolute error = 2.620126338115369e-14 relative error = 1.738446288785407e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 3.2768e-07 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] = 0.1300000870395576 y[1] (analytic) = 1.508402516654464 y[1] (numeric) = 1.508402516654522 absolute error = 5.773159728050814e-14 relative error = 3.827333662141652e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 3.2768e-07 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] = 0.1400002252794101 y[1] (analytic) = 1.509736171550951 y[1] (numeric) = 1.509736171551012 absolute error = 6.150635556423367e-14 relative error = 4.073980389636439e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 3.2768e-07 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] = 0.1500000358392626 y[1] (analytic) = 1.511165883014212 y[1] (numeric) = 1.511165883014276 absolute error = 6.328271240363392e-14 relative error = 4.187674769192679e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 3.2768e-07 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] = 0.1600001740791151 y[1] (analytic) = 1.512691172859138 y[1] (numeric) = 1.51269117285923 absolute error = 9.14823772291129e-14 relative error = 6.047657239659964e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 3.2768e-07 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] = 0.1700003123189676 y[1] (analytic) = 1.514311385695132 y[1] (numeric) = 1.514311385695213 absolute error = 8.149037000748649e-14 relative error = 5.381348299780434e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 3.2768e-07 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] = 0.1800001228788202 y[1] (analytic) = 1.516025815724044 y[1] (numeric) = 1.516025815724172 absolute error = 1.27453603226968e-13 relative error = 8.407086601364827e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 3.2768e-07 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] = 0.1900002611186727 y[1] (analytic) = 1.517833889533035 y[1] (numeric) = 1.517833889533186 absolute error = 1.509903313490213e-13 relative error = 9.947750698561214e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 3.2768e-07 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] = 0.2000000716785252 y[1] (analytic) = 1.519734765455747 y[1] (numeric) = 1.519734765455937 absolute error = 1.898481372109018e-13 relative error = 1.249218886915237e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 3.2768e-07 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] = 0.2100002099183777 y[1] (analytic) = 1.521727807720149 y[1] (numeric) = 1.521727807720367 absolute error = 2.171596236166806e-13 relative error = 1.427059573433365e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 3.2768e-07 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] = 0.2200000204782303 y[1] (analytic) = 1.523812088556252 y[1] (numeric) = 1.523812088556487 absolute error = 2.349231920106831e-13 relative error = 1.541680852743877e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 3.2768e-07 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] = 0.2300001587180828 y[1] (analytic) = 1.525986910849926 y[1] (numeric) = 1.525986910850199 absolute error = 2.724487302430134e-13 relative error = 1.785393624977216e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 3.2768e-07 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] = 0.2400002969579353 y[1] (analytic) = 1.528251337869713 y[1] (numeric) = 1.528251337870014 absolute error = 3.010924842783425e-13 relative error = 1.970176480905598e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 3.2768e-07 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] = 0.2500001075177878 y[1] (analytic) = 1.530604385300799 y[1] (numeric) = 1.530604385301126 absolute error = 3.277378368693462e-13 relative error = 2.141231529301664e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 3.2768e-07 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] = 0.2600002457584874 y[1] (analytic) = 1.533045266136869 y[1] (numeric) = 1.533045266137012 absolute error = 1.427746809667951e-13 relative error = 9.313141896101605e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 3.2768e-07 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] = 0.2700000563191869 y[1] (analytic) = 1.535572844136906 y[1] (numeric) = 1.535572844136849 absolute error = 5.684341886080801e-14 relative error = 3.70177286462485e-12 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 14 h = 3.2768e-07 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] = 0.2800001945598865 y[1] (analytic) = 1.538186273920425 y[1] (numeric) = 1.538186273920176 absolute error = 2.489120021209601e-13 relative error = 1.618217548428319e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 3.2768e-07 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] = 0.290000005120586 y[1] (analytic) = 1.540884338924305 y[1] (numeric) = 1.540884338923888 absolute error = 4.172218126541338e-13 relative error = 2.707677676478932e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 3.2768e-07 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] = 0.3000001433612856 y[1] (analytic) = 1.543666136746524 y[1] (numeric) = 1.543666136745927 absolute error = 5.977440764581843e-13 relative error = 3.872236763047786e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 3.2768e-07 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] = 0.3100002816019852 y[1] (analytic) = 1.546530467644726 y[1] (numeric) = 1.546530467643926 absolute error = 8.004708007547379e-13 relative error = 5.17591355295966e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 3.2768e-07 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] = 0.3200000921626847 y[1] (analytic) = 1.549476088048498 y[1] (numeric) = 1.549476088047496 absolute error = 1.001421168211891e-12 relative error = 6.462966262829784e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 3.2768e-07 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] = 0.3300002304033843 y[1] (analytic) = 1.552502012757778 y[1] (numeric) = 1.552502012756551 absolute error = 1.227462576025573e-12 relative error = 7.906350947946127e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 3.2768e-07 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] = 0.3400000409640838 y[1] (analytic) = 1.555606833191234 y[1] (numeric) = 1.555606833189786 absolute error = 1.448174913321054e-12 relative error = 9.309388994841392e-11 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 13 h = 3.2768e-07 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] = 0.3500001792047834 y[1] (analytic) = 1.558789510902336 y[1] (numeric) = 1.558789510900681 absolute error = 1.654454351296408e-12 relative error = 1.061371236927746e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.3600003174454829 y[1] (analytic) = 1.562048672374157 y[1] (numeric) = 1.562048672372291 absolute error = 1.866284904394888e-12 relative error = 1.194767447008116e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.3700001280061825 y[1] (analytic) = 1.56538290347412 y[1] (numeric) = 1.56538290347202 absolute error = 2.100097873380946e-12 relative error = 1.341587332224027e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.380000266246882 y[1] (analytic) = 1.568791089026393 y[1] (numeric) = 1.568791089024063 absolute error = 2.329914039478354e-12 relative error = 1.485165268834056e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.3900000768075816 y[1] (analytic) = 1.572271642505529 y[1] (numeric) = 1.572271642502958 absolute error = 2.570610391217087e-12 relative error = 1.634965817433834e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.4000002150482811 y[1] (analytic) = 1.575823399796322 y[1] (numeric) = 1.575823399793498 absolute error = 2.824185330041473e-12 relative error = 1.792196594114863e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.4100000256089807 y[1] (analytic) = 1.579444707540047 y[1] (numeric) = 1.579444707536977 absolute error = 3.069988707693483e-12 relative error = 1.943713947717061e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.4200001638496803 y[1] (analytic) = 1.583134354544451 y[1] (numeric) = 1.583134354541119 absolute error = 3.331779296900095e-12 relative error = 2.104546141226794e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.4300003020903798 y[1] (analytic) = 1.586890747427491 y[1] (numeric) = 1.586890747423883 absolute error = 3.607558696216984e-12 relative error = 2.273350387898599e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.4400001126510794 y[1] (analytic) = 1.590712257362642 y[1] (numeric) = 1.59071225735877 absolute error = 3.872679954497471e-12 relative error = 2.434557184413899e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.4500002508917789 y[1] (analytic) = 1.594597606197494 y[1] (numeric) = 1.59459760619335 absolute error = 4.143796417110934e-12 relative error = 2.598647082502717e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.4600000614524785 y[1] (analytic) = 1.598544985284981 y[1] (numeric) = 1.59854498528057 absolute error = 4.410916076835747e-12 relative error = 2.759331840792325e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.470000199693178 y[1] (analytic) = 1.602553074374159 y[1] (numeric) = 1.602553074369479 absolute error = 4.679590048795035e-12 relative error = 2.920084285272451e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.4800000102538776 y[1] (analytic) = 1.606620007681831 y[1] (numeric) = 1.606620007676867 absolute error = 4.964251232308925e-12 relative error = 3.089872657238828e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.4900001484945771 y[1] (analytic) = 1.61074442497063 y[1] (numeric) = 1.610744424965382 absolute error = 5.248024237403115e-12 relative error = 3.258135900423065e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.5000002867352766 y[1] (analytic) = 1.614924544172695 y[1] (numeric) = 1.614924544167132 absolute error = 5.563549621001584e-12 relative error = 3.445083326696058e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.5100000972959762 y[1] (analytic) = 1.619158553640431 y[1] (numeric) = 1.619158553634576 absolute error = 5.854872142663226e-12 relative error = 3.61599679629857e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.5200002355366757 y[1] (analytic) = 1.623445037255732 y[1] (numeric) = 1.623445037249565 absolute error = 6.16706685718782e-12 relative error = 3.798753093367803e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.5300000460973753 y[1] (analytic) = 1.627781999641518 y[1] (numeric) = 1.62778199963503 absolute error = 6.488143355909415e-12 relative error = 3.985879778335356e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.5400001843380748 y[1] (analytic) = 1.632167990245775 y[1] (numeric) = 1.632167990238973 absolute error = 6.801892382668484e-12 relative error = 4.167397243003302e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.5500003225787744 y[1] (analytic) = 1.636601113385918 y[1] (numeric) = 1.636601113378789 absolute error = 7.12963021953783e-12 relative error = 4.356364028610208e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.5600001331394739 y[1] (analytic) = 1.641079448350276 y[1] (numeric) = 1.641079448342846 absolute error = 7.429168391581698e-12 relative error = 4.527001053513894e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.5700002713801735 y[1] (analytic) = 1.645601497302984 y[1] (numeric) = 1.645601497295258 absolute error = 7.725375894551689e-12 relative error = 4.694560564761879e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.580000081940873 y[1] (analytic) = 1.650165155210257 y[1] (numeric) = 1.650165155202217 absolute error = 8.040013099730459e-12 relative error = 4.872247528888123e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.5900002201815726 y[1] (analytic) = 1.654768895698892 y[1] (numeric) = 1.654768895690527 absolute error = 8.364864356735779e-12 relative error = 5.055004586125531e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.6000000307422722 y[1] (analytic) = 1.659410575707331 y[1] (numeric) = 1.659410575698641 absolute error = 8.69015970295095e-12 relative error = 5.236895455632932e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.6100001689829717 y[1] (analytic) = 1.664088642766893 y[1] (numeric) = 1.664088642757874 absolute error = 9.019451852054772e-12 relative error = 5.420054929921317e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.6200003072236713 y[1] (analytic) = 1.668801074173938 y[1] (numeric) = 1.668801074164586 absolute error = 9.351408536417694e-12 relative error = 5.60366881417947e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.6300001177843708 y[1] (analytic) = 1.673545828976111 y[1] (numeric) = 1.673545828966428 absolute error = 9.68314317617569e-12 relative error = 5.786004188543745e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.6400002560250704 y[1] (analytic) = 1.67832132023006 y[1] (numeric) = 1.67832132022004 absolute error = 1.001998484184696e-11 relative error = 5.970242242095484e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.6500000665857699 y[1] (analytic) = 1.683125324923485 y[1] (numeric) = 1.683125324913143 absolute error = 1.034283769740796e-11 relative error = 6.14501935432416e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.6600002048264695 y[1] (analytic) = 1.687956236296159 y[1] (numeric) = 1.68795623628549 absolute error = 1.06687991774379e-11 relative error = 6.320542528311154e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.670000015387169 y[1] (analytic) = 1.692811805537471 y[1] (numeric) = 1.692811805526445 absolute error = 1.10262909913672e-11 relative error = 6.513595282888718e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.6800001536278686 y[1] (analytic) = 1.697690408640775 y[1] (numeric) = 1.697690408629419 absolute error = 1.135580518507595e-11 relative error = 6.688972928914507e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.6900002918685681 y[1] (analytic) = 1.702589935461642 y[1] (numeric) = 1.702589935449952 absolute error = 1.168998231548812e-11 relative error = 6.865999893461423e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.7000001024292677 y[1] (analytic) = 1.707508264744388 y[1] (numeric) = 1.707508264732369 absolute error = 1.201860833077717e-11 relative error = 7.038682376495755e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.7100002406699673 y[1] (analytic) = 1.712443751491477 y[1] (numeric) = 1.712443751479102 absolute error = 1.237454583247199e-11 relative error = 7.226249517214339e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.7200000512306668 y[1] (analytic) = 1.717394098212 y[1] (numeric) = 1.717394098199283 absolute error = 1.271716065787132e-11 relative error = 7.404916944288623e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.7300001894713664 y[1] (analytic) = 1.722357649199783 y[1] (numeric) = 1.722357649186712 absolute error = 1.307087771351689e-11 relative error = 7.588945141323985e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.7400000000320659 y[1] (analytic) = 1.72733209389989 y[1] (numeric) = 1.72733209388648 absolute error = 1.340949573602757e-11 relative error = 7.763125448420422e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.7500001382727655 y[1] (analytic) = 1.73231576854627 y[1] (numeric) = 1.732315768532514 absolute error = 1.375588531971061e-11 relative error = 7.940749353828442e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.760000276513465 y[1] (analytic) = 1.737306516845008 y[1] (numeric) = 1.737306516830896 absolute error = 1.411226691061529e-11 relative error = 8.123072568819643e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.7700000870741646 y[1] (analytic) = 1.742302178745822 y[1] (numeric) = 1.742302178731364 absolute error = 1.445799036048356e-11 relative error = 8.298210572686649e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.7800002253148641 y[1] (analytic) = 1.7473010833863 y[1] (numeric) = 1.747301083371503 absolute error = 1.479683042759916e-11 relative error = 8.468391949327158e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.7900000358755637 y[1] (analytic) = 1.752300903754224 y[1] (numeric) = 1.752300903739062 absolute error = 1.516187175809591e-11 relative error = 8.65255032717971e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.8000001741162632 y[1] (analytic) = 1.757299967596332 y[1] (numeric) = 1.75729996758083 absolute error = 1.550248818205091e-11 relative error = 8.82176547425509e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.8100003123569628 y[1] (analytic) = 1.762296111468006 y[1] (numeric) = 1.762296111452132 absolute error = 1.587330267227571e-11 relative error = 9.007171138256178e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.8200001229176623 y[1] (analytic) = 1.767287173475237 y[1] (numeric) = 1.767287173459011 absolute error = 1.622635359410651e-11 relative error = 9.18150362750532e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.8300002611583619 y[1] (analytic) = 1.772271484294109 y[1] (numeric) = 1.772271484277532 absolute error = 1.657629589146836e-11 relative error = 9.353135813766512e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.8400000717190614 y[1] (analytic) = 1.77724672370589 y[1] (numeric) = 1.77724672368898 absolute error = 1.690980688806576e-11 relative error = 9.514608558571803e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.850000209959761 y[1] (analytic) = 1.782211227678732 y[1] (numeric) = 1.782211227661475 absolute error = 1.725686260556358e-11 relative error = 9.682838003461603e-10 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 12 h = 3.2768e-07 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] = 0.8600000205204605 y[1] (analytic) = 1.787162685214078 y[1] (numeric) = 1.787162685196469 absolute error = 1.760902534897468e-11 relative error = 9.853062339909677e-10 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 12 h = 3.2768e-07 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] = 0.8700001587611601 y[1] (analytic) = 1.792099440234227 y[1] (numeric) = 1.792099440216277 absolute error = 1.795008586213953e-11 relative error = 1.001623317274931e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 3.2768e-07 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] = 0.8800002970018597 y[1] (analytic) = 1.797019355574041 y[1] (numeric) = 1.797019355555739 absolute error = 1.830202656094571e-11 relative error = 1.018465744632967e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 3.2768e-07 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] = 0.8900001075625592 y[1] (analytic) = 1.80192030301086 y[1] (numeric) = 1.801920302992201 absolute error = 1.865863019645531e-11 relative error = 1.035485873891219e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 3.2768e-07 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] = 0.9000002458032588 y[1] (analytic) = 1.806800643360726 y[1] (numeric) = 1.806800643341739 absolute error = 1.898659007792958e-11 relative error = 1.050840342995103e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 3.2768e-07 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] = 0.9100000563639583 y[1] (analytic) = 1.811658104803621 y[1] (numeric) = 1.811658104784306 absolute error = 1.93149940486137e-11 relative error = 1.066150064264327e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 3.2768e-07 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] = 0.9200001946046579 y[1] (analytic) = 1.816491062700031 y[1] (numeric) = 1.816491062680358 absolute error = 1.967270790714792e-11 relative error = 1.083006039011633e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 3.2768e-07 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] = 0.9300000051653574 y[1] (analytic) = 1.821297267286679 y[1] (numeric) = 1.82129726726667 absolute error = 2.000888343900442e-11 relative error = 1.098606130827459e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 3.2768e-07 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] = 0.940000143406057 y[1] (analytic) = 1.826075111067553 y[1] (numeric) = 1.826075111047227 absolute error = 2.032662926865214e-11 relative error = 1.113132156802075e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 3.2768e-07 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] = 0.9500002816467565 y[1] (analytic) = 1.830822524977038 y[1] (numeric) = 1.830822524956365 absolute error = 2.067279680773026e-11 relative error = 1.129153510277548e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 3.2768e-07 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] = 0.9600000922074561 y[1] (analytic) = 1.835537456108882 y[1] (numeric) = 1.835537456087886 absolute error = 2.099653784171096e-11 relative error = 1.143890459539904e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 3.2768e-07 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] = 0.9700002304481556 y[1] (analytic) = 1.840218327494637 y[1] (numeric) = 1.840218327473309 absolute error = 2.132827248146896e-11 relative error = 1.159007720051691e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 3.2768e-07 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] = 0.9800000410088552 y[1] (analytic) = 1.844862960167971 y[1] (numeric) = 1.844862960146328 absolute error = 2.164335377585758e-11 relative error = 1.173168644129914e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 3.2768e-07 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] = 0.9900001792495547 y[1] (analytic) = 1.849469800672645 y[1] (numeric) = 1.849469800650671 absolute error = 2.19744222818008e-11 relative error = 1.188147125938947e-09 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 11 h = 3.2768e-07 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 ) * cos ( x ) ; Iterations = 2746583 Total Elapsed Time = 1 Minutes 4.0 Seconds Elapsed Time(since restart) = 1 Minutes 4.0 Seconds Time to Timeout = 8 Minutes 56.0 Seconds Percent Done = 100 %