##############ECHO OF PROBLEM################# ##############temp/sub_sin_cospostode.ode################# diff ( y , x , 1 ) = m1 * sin ( x ) - cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=5.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # 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=16 $glob_max_minutes=3.0 $glob_subiter_method=3 $glob_max_iter=100000000 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(cos(x) - sin(x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 4900000.000000001 step_error 1.129384878631564e-21 est_needed_step_err 1.129384878631564e-21 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 0.8951707486311977 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 4900000.000000001 step_error 1.129384878631564e-21 est_needed_step_err 1.129384878631564e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.406416108484866e-258 estimated_step_error 2.406416108484866e-258 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 0.8951707486311977 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 2450000.0000000005 step_error 1.5971914124998497e-21 est_needed_step_err 1.5971914124998497e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6536765305101633e-247 estimated_step_error 1.6536765305101633e-247 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 0.8951707486311977 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 1225000.0000000002 step_error 2.258769757263128e-21 est_needed_step_err 2.258769757263128e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1363978211085625e-236 estimated_step_error 1.1363978211085625e-236 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 0.8951707486311977 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 612500.0000000001 step_error 3.1943828249996993e-21 est_needed_step_err 3.1943828249996993e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.809265846774536e-226 estimated_step_error 7.809265846774536e-226 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 0.8951707486311977 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 306250.00000000006 step_error 4.517539514526256e-21 est_needed_step_err 4.517539514526256e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.366485917261428e-215 estimated_step_error 5.366485917261428e-215 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 0.8951707486311977 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 153125.00000000003 step_error 6.388765649999399e-21 est_needed_step_err 6.388765649999399e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.6878200662339585e-204 estimated_step_error 3.6878200662339585e-204 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 0.8951707486311977 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 76562.50000000001 step_error 9.035079029052512e-21 est_needed_step_err 9.035079029052512e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.534249312149395e-193 estimated_step_error 2.534249312149395e-193 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 0.8951707486311977 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 4.9 estimated_steps 38281.25000000001 step_error 1.2777531299998797e-20 est_needed_step_err 1.2777531299998797e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.741521024354856e-182 estimated_step_error 1.741521024354856e-182 Double H and LOOP opt_iter 9 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4900332889205668 Order of pole (three term test) 32.599334665397926 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] (closed_form) 0.8951707486311977 y[1] (numeric) 0.8951707486311977 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.000128 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] 0.2000959999999943 y[1] (closed_form) 0.7812840847984535 y[1] (numeric) 0.7812840847984452 absolute error 8.215650382226158e-15 relative error 1.0515573710100003e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.000128 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] 0.3000639999999968 y[1] (closed_form) 0.659736226284491 y[1] (numeric) 0.6597362262844849 absolute error 6.106226635438361e-15 relative error 9.2555575882614e-13% Desired digits 16 Estimated correct digits 12 Correct digits 15 h 0.000128 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] 0.40003200000001005 y[1] (closed_form) 0.5316007160832656 y[1] (numeric) 0.5316007160832749 absolute error 9.2148511043888e-15 relative error 1.7334158562242154e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 h 0.000128 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] 0.5000000000000233 y[1] (closed_form) 0.3981570232861381 y[1] (numeric) 0.39815702328616526 absolute error 2.7144952952085077e-14 relative error 6.817650164261245e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 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] 0.6000960000000366 y[1] (closed_form) 0.26055970241704574 y[1] (numeric) 0.2605597024170916 absolute error 4.5852210917018965e-14 relative error 1.7597583391321577e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 0.7000640000000499 y[1] (closed_form) 0.1205343199677803 y[1] (numeric) 0.12053431996784497 absolute error 6.467049118441537e-14 relative error 5.3653176291783336e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 0.8000320000000631 y[1] (closed_form) -0.02069463155147433 y[1] (numeric) -0.02069463155139091 absolute error 8.34193825127727e-14 relative error 4.0309672730959893e-10% Desired digits 16 Estimated correct digits 10 Correct digits 12 h 0.000128 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] 0.9000000000000764 y[1] (closed_form) -0.16171694135692638 y[1] (numeric) -0.16171694135682405 absolute error 1.023348072948238e-13 relative error 6.328020208406e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 1.0000960000000896 y[1] (closed_form) -0.3013013277877965 y[1] (numeric) -0.3013013277876758 absolute error 1.2068124277675452e-13 relative error 4.0053339181349076e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 1.1000640000000161 y[1] (closed_form) -0.4376973051624083 y[1] (numeric) -0.43769730516238786 absolute error 2.042810365310288e-14 relative error 4.667176016887515e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 h 0.000128 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] 1.2000319999999427 y[1] (closed_form) -0.5697227518976888 y[1] (numeric) -0.5697227518977664 absolute error 7.760458942129844e-14 relative error 1.3621465732727965e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 1.2999999999998693 y[1] (closed_form) -0.6960593567924447 y[1] (numeric) -0.6960593567926142 absolute error 1.695310558602614e-13 relative error 2.4355833192371442e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 1.4000959999997957 y[1] (closed_form) -0.8155935033498665 y[1] (numeric) -0.8155935033501241 absolute error 2.5768276401549883e-13 relative error 3.159450914666742e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 1.5000639999997223 y[1] (closed_form) -0.9268261498980577 y[1] (numeric) -0.9268261498983978 absolute error 3.4017233474514796e-13 relative error 3.670292802836474e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 1.6000319999996488 y[1] (closed_form) -1.0288041767862997 y[1] (numeric) -1.0288041767867138 absolute error 4.141131881851834e-13 relative error 4.025189608762658e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 1.6999999999995754 y[1] (closed_form) -1.1205093047476269 y[1] (numeric) -1.120509304748109 absolute error 4.82058837292243e-13 relative error 4.3021404217684514e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 1.8000959999995019 y[1] (closed_form) -1.201121398007837 y[1] (numeric) -1.2011213980083768 absolute error 5.397904345727511e-13 relative error 4.49405393549761e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 1.9000639999994284 y[1] (closed_form) -1.269629524623748 y[1] (numeric) -1.2696295246243419 absolute error 5.939693181744587e-13 relative error 4.678288482228549e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 2.000031999999355 y[1] (closed_form) -1.325460043512765 y[1] (numeric) -1.3254600435134023 absolute error 6.372680161348399e-13 relative error 4.807900617252387e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 2.099999999999455 y[1] (closed_form) -1.368055471248536 y[1] (numeric) -1.368055471249131 absolute error 5.950795411990839e-13 relative error 4.349820264641705e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 2.2000959999995553 y[1] (closed_form) -1.3970186341849513 y[1] (numeric) -1.3970186341855175 absolute error 5.662137425588298e-13 relative error 4.053014961315604e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 2.3000639999996553 y[1] (closed_form) -1.4119863140329936 y[1] (numeric) -1.4119863140335436 absolute error 5.500044863993026e-13 relative error 3.8952536645227763e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 2.4000319999997553 y[1] (closed_form) -1.4128549135919095 y[1] (numeric) -1.4128549135924588 absolute error 5.493383525845275e-13 relative error 3.8881441208138014e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 2.4999999999998552 y[1] (closed_form) -1.3996157596509196 y[1] (numeric) -1.3996157596514813 absolute error 5.617728504603292e-13 relative error 4.013764825000555e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 2.6000959999999553 y[1] (closed_form) -1.3723573456778748 y[1] (numeric) -1.3723573456784663 absolute error 5.915268275202834e-13 relative error 4.310297382698813e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 2.7000640000000553 y[1] (closed_form) -1.3314215112193177 y[1] (numeric) -1.331421511219948 absolute error 6.301625887772389e-13 relative error 4.733005914859638e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 2.8000320000001553 y[1] (closed_form) -1.277191058676444 y[1] (numeric) -1.2771910586771293 absolute error 6.854516954035716e-13 relative error 5.3668688858024645e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 2.9000000000002553 y[1] (closed_form) -1.210207494363386 y[1] (numeric) -1.2102074943641377 absolute error 7.51620987671231e-13 relative error 6.210678674293051e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 3.0000960000003554 y[1] (closed_form) -1.1310310076890697 y[1] (numeric) -1.1310310076899033 absolute error 8.335554468885675e-13 relative error 7.36987263144707e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 3.1000640000004553 y[1] (closed_form) -1.040654527087568 y[1] (numeric) -1.0406545270884904 absolute error 9.2237328885858e-13 relative error 8.86339572691798e-11% Desired digits 16 Estimated correct digits 11 Correct digits 13 h 0.000128 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] 3.2000320000005553 y[1] (closed_form) -0.9398868184799377 y[1] (numeric) -0.9398868184809592 absolute error 1.0215162049576065e-12 relative error 1.0868502301263109e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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] 3.3000000000006553 y[1] (closed_form) -0.829734075764866 y[1] (numeric) -0.8297340757659983 absolute error 1.1323164628151972e-12 relative error 1.3646739309475805e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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] 3.4000960000007554 y[1] (closed_form) -0.7111397427021316 y[1] (numeric) -0.7111397427033816 absolute error 1.2500001034254637e-12 relative error 1.757741873173638e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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] 3.5000640000008554 y[1] (closed_form) -0.5855910750461137 y[1] (numeric) -0.5855910750474905 absolute error 1.3767875728376566e-12 relative error 2.3511075074517456e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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] 3.6000320000009554 y[1] (closed_form) -0.4541951158819445 y[1] (numeric) -0.4541951158834514 absolute error 1.506905711323725e-12 relative error 3.317749704106029e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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] 3.7000000000010553 y[1] (closed_form) -0.3182638908004608 y[1] (numeric) -0.31826389080210316 absolute error 1.642352920327994e-12 relative error 5.160349533204463e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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] 3.8000960000011554 y[1] (closed_form) -0.17897514888707122 y[1] (numeric) -0.17897514888885202 absolute error 1.780797731498751e-12 relative error 9.949972063565032e-10% Desired digits 16 Estimated correct digits 10 Correct digits 12 h 0.000128 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] 3.9000640000012554 y[1] (closed_form) -0.03807566823463249 y[1] (numeric) -0.038075668236553936 absolute error 1.9214491109309506e-12 relative error 5.046396294584945e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.000128 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] 4.000032000001355 y[1] (closed_form) 0.1032040086691205 y[1] (numeric) 0.10320400866705762 absolute error 2.0628776464803877e-12 relative error 1.998834806014292e-09% Desired digits 16 Estimated correct digits 10 Correct digits 11 h 0.000128 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] 4.100000000001455 y[1] (closed_form) 0.243453164533169 y[1] (numeric) 0.24345316453096624 absolute error 2.2027657475831575e-12 relative error 9.048006222498882e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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] 4.2000960000015555 y[1] (closed_form) 0.3814456856307071 y[1] (numeric) 0.381445685628366 absolute error 2.3410717808758363e-12 relative error 6.137365997481283e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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] 4.3000640000016555 y[1] (closed_form) 0.5154510493830963 y[1] (numeric) 0.5154510493806216 absolute error 2.474687121889474e-12 relative error 4.80101286989567e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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] 4.400032000001755 y[1] (closed_form) 0.6443094895016372 y[1] (numeric) 0.6443094894990327 absolute error 2.6045832157706172e-12 relative error 4.0424411842594766e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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] 4.500000000001855 y[1] (closed_form) 0.7667343182365222 y[1] (numeric) 0.7667343182337955 absolute error 2.7267077484793845e-12 relative error 3.5562615153978927e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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] 4.6000960000019555 y[1] (closed_form) 0.8816446336172146 y[1] (numeric) 0.8816446336143724 absolute error 2.8421709430404007e-12 relative error 3.223714901297059e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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] 4.7000640000020555 y[1] (closed_form) 0.9875993800437214 y[1] (numeric) 0.9875993800407715 absolute error 2.949862576429041e-12 relative error 2.986902013140642e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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] 4.8000320000021555 y[1] (closed_form) 1.0836926690224178 y[1] (numeric) 1.083692669019375 absolute error 3.042677221287704e-12 relative error 2.807693830791026e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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] 4.900000000002255 y[1] (closed_form) 1.1689649820487031 y[1] (numeric) 1.1689649820455783 absolute error 3.1248337251099656e-12 relative error 2.673162817617897e-10% Desired digits 16 Estimated correct digits 11 Correct digits 12 h 0.000128 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 ) = m1 * sin ( x ) - cos ( x ) ; Iterations 38282 Total Elapsed Time 13 Seconds Elapsed Time(since restart) 13 Seconds Time to Timeout 2 Minutes 47.0 Seconds Percent Done 100.00457142861951%