##############ECHO OF PROBLEM################# ##############temp/diffpostode.ode################# diff ( y , x , 2 ) = diff ( y , x , 1 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-5.0 x_end=5.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $array_y_init[1 + 1] = exact_soln_yp(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 #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(1.0 + exp(x)) end def exact_soln_yp (x) return(exp(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 10.0 estimated_steps 10000000.0 step_error 1.0540925533894597e-21 est_needed_step_err 1.0540925533894597e-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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 10000000.0 step_error 1.0611949731463284e-21 est_needed_step_err 1.0611949731463284e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6707388510135153e-185 estimated_step_error 1.6707388510135153e-185 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 5000000.0 step_error 1.5007563233456902e-21 est_needed_step_err 1.5007563233456902e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.121213884085043e-177 estimated_step_error 1.121213884085043e-177 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 2500000.0 step_error 2.122389946292657e-21 est_needed_step_err 2.122389946292657e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.524339284876733e-170 estimated_step_error 7.524339284876733e-170 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 1250000.0 step_error 3.0015126466913805e-21 est_needed_step_err 3.0015126466913805e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.049498991623487e-162 estimated_step_error 5.049498991623487e-162 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 625000.0 step_error 4.244779892585314e-21 est_needed_step_err 4.244779892585314e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.388661912994031e-154 estimated_step_error 3.388661912994031e-154 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 312500.0 step_error 6.003025293382761e-21 est_needed_step_err 6.003025293382761e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.2740931884165298e-146 estimated_step_error 2.2740931884165298e-146 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 156250.0 step_error 8.489559785170627e-21 est_needed_step_err 8.489559785170627e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.5261190094150118e-138 estimated_step_error 1.5261190094150118e-138 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 78125.0 step_error 1.2006050586765522e-20 est_needed_step_err 1.2006050586765522e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0241623443297896e-130 estimated_step_error 1.0241623443297896e-130 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 39062.5 step_error 1.6979119570341255e-20 est_needed_step_err 1.6979119570341255e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.873053439671608e-123 estimated_step_error 6.873053439671608e-123 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 19531.25 step_error 2.4012101173531044e-20 est_needed_step_err 2.4012101173531044e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.612449951998501e-115 estimated_step_error 4.612449951998501e-115 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 9765.625 step_error 3.395823914068251e-20 est_needed_step_err 3.395823914068251e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.095392114506209e-107 estimated_step_error 3.095392114506209e-107 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 4882.8125 step_error 4.802420234706209e-20 est_needed_step_err 4.802420234706209e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.0773218772354828e-99 estimated_step_error 2.0773218772354828e-99 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 2441.40625 step_error 6.791647828136502e-20 est_needed_step_err 6.791647828136502e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3941199885180905e-91 estimated_step_error 1.3941199885180905e-91 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 1220.703125 step_error 9.604840469412418e-20 est_needed_step_err 9.604840469412418e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.356490626122473e-84 estimated_step_error 9.356490626122473e-84 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 0.016384 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 610.3515625 step_error 1.3583295656273004e-19 est_needed_step_err 1.3583295656273004e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.279987395861075e-76 estimated_step_error 6.279987395861075e-76 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 0.032768 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 305.17578125 step_error 1.9209680938824835e-19 est_needed_step_err 1.9209680938824835e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.215707624202583e-68 estimated_step_error 4.215707624202583e-68 Double H and LOOP opt_iter 17 NO POLE (given) for Equation 1 NO 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 1.0067379469990854 $glob_desired_digits_correct 16 estimated_h 0.065536 estimated_answer 1.0067379469990854 desired_abs_gbl_error 1.0067379469990853e-16 range 10.0 estimated_steps 152.587890625 step_error 2.716659131254601e-19 est_needed_step_err 2.716659131254601e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.8308322181905846e-60 estimated_step_error 2.8308322181905846e-60 Double H and LOOP opt_iter 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] -5.0 y[1] (closed_form) 1.0067379469990854 y[1] (numeric) 1.0067379469990854 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -4.9 y[1] (closed_form) 1.0074465830709243 y[1] (numeric) 1.0074465830709243 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -4.800000000000001 y[1] (closed_form) 1.00822974704902 y[1] (numeric) 1.00822974704902 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -4.700000000000001 y[1] (closed_form) 1.0090952771016959 y[1] (numeric) 1.0090952771016959 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -4.600000000000001 y[1] (closed_form) 1.0100518357446335 y[1] (numeric) 1.0100518357446338 absolute error 2.220446049250313e-16 relative error 2.1983486101120235e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -4.500000000000002 y[1] (closed_form) 1.0111089965382423 y[1] (numeric) 1.0111089965382425 absolute error 2.220446049250313e-16 relative error 2.1960501358928727e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -4.400000000000002 y[1] (closed_form) 1.0122773399030685 y[1] (numeric) 1.0122773399030687 absolute error 2.220446049250313e-16 relative error 2.1935155137058922e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -4.3000000000000025 y[1] (closed_form) 1.013568559012201 y[1] (numeric) 1.0135685590122012 absolute error 2.220446049250313e-16 relative error 2.190721120448236e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -4.200000000000003 y[1] (closed_form) 1.0149955768204777 y[1] (numeric) 1.014995576820478 absolute error 2.220446049250313e-16 relative error 2.187641108945486e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -4.100000000000003 y[1] (closed_form) 1.0165726754017612 y[1] (numeric) 1.0165726754017614 absolute error 2.220446049250313e-16 relative error 2.1842472289280915e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -4.0000000000000036 y[1] (closed_form) 1.0183156388887342 y[1] (numeric) 1.0183156388887344 absolute error 2.220446049250313e-16 relative error 2.180508640399e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -3.9000000000000035 y[1] (closed_form) 1.0202419114458043 y[1] (numeric) 1.0202419114458046 absolute error 2.220446049250313e-16 relative error 2.1763917207671624e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -3.8000000000000034 y[1] (closed_form) 1.0223707718561654 y[1] (numeric) 1.0223707718561659 absolute error 4.440892098500626e-16 relative error 4.3437197352952136e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -3.7000000000000033 y[1] (closed_form) 1.0247235264703394 y[1] (numeric) 1.0247235264703396 absolute error 2.220446049250313e-16 relative error 2.166873299863272e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -3.600000000000003 y[1] (closed_form) 1.0273237224472924 y[1] (numeric) 1.0273237224472929 absolute error 4.440892098500626e-16 relative error 4.322777719881251e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -3.500000000000003 y[1] (closed_form) 1.0301973834223184 y[1] (numeric) 1.0301973834223188 absolute error 4.440892098500626e-16 relative error 4.3107196445675014e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -3.400000000000003 y[1] (closed_form) 1.033373269960326 y[1] (numeric) 1.0333732699603264 absolute error 4.440892098500626e-16 relative error 4.2974714245038715e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -3.300000000000003 y[1] (closed_form) 1.03688316740124 y[1] (numeric) 1.0368831674012404 absolute error 4.440892098500626e-16 relative error 4.282924285125506e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -3.200000000000003 y[1] (closed_form) 1.0407622039783662 y[1] (numeric) 1.0407622039783666 absolute error 4.440892098500626e-16 relative error 4.26696134960041e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -3.1000000000000028 y[1] (closed_form) 1.0450492023935576 y[1] (numeric) 1.0450492023935583 absolute error 6.661338147750939e-16 relative error 6.374186145967059e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -3.0000000000000027 y[1] (closed_form) 1.0497870683678638 y[1] (numeric) 1.0497870683678643 absolute error 4.440892098500626e-16 relative error 4.230278913041877e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -2.9000000000000026 y[1] (closed_form) 1.0550232200564071 y[1] (numeric) 1.0550232200564076 absolute error 4.440892098500626e-16 relative error 4.2092837523170275e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -2.8000000000000025 y[1] (closed_form) 1.0608100626252177 y[1] (numeric) 1.0608100626252184 absolute error 6.661338147750939e-16 relative error 6.279482428047421e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -2.7000000000000024 y[1] (closed_form) 1.0672055127397495 y[1] (numeric) 1.0672055127397502 absolute error 6.661338147750939e-16 relative error 6.241851328756567e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -2.6000000000000023 y[1] (closed_form) 1.0742735782143338 y[1] (numeric) 1.0742735782143342 absolute error 4.440892098500626e-16 relative error 4.1338558338950425e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -2.500000000000002 y[1] (closed_form) 1.0820849986238987 y[1] (numeric) 1.0820849986238992 absolute error 4.440892098500626e-16 relative error 4.1040141062376476e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -2.400000000000002 y[1] (closed_form) 1.0907179532894122 y[1] (numeric) 1.090717953289413 absolute error 6.661338147750939e-16 relative error 6.107296691744665e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -2.300000000000002 y[1] (closed_form) 1.1002588437228036 y[1] (numeric) 1.1002588437228042 absolute error 6.661338147750939e-16 relative error 6.054337291406657e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -2.200000000000002 y[1] (closed_form) 1.1108031583623337 y[1] (numeric) 1.1108031583623343 absolute error 6.661338147750939e-16 relative error 5.996866409321166e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -2.100000000000002 y[1] (closed_form) 1.1224564282529816 y[1] (numeric) 1.1224564282529823 absolute error 6.661338147750939e-16 relative error 5.934607330922241e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -2.0000000000000018 y[1] (closed_form) 1.1353352832366124 y[1] (numeric) 1.135335283236613 absolute error 6.661338147750939e-16 relative error 5.867287175961629e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -1.9000000000000017 y[1] (closed_form) 1.1495686192226349 y[1] (numeric) 1.1495686192226353 absolute error 4.440892098500626e-16 relative error 3.8630944027540184e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -1.8000000000000016 y[1] (closed_form) 1.1652988882215862 y[1] (numeric) 1.165298888221587 absolute error 6.661338147750939e-16 relative error 5.716420237830227e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -1.7000000000000015 y[1] (closed_form) 1.1826835240527345 y[1] (numeric) 1.182683524052735 absolute error 4.440892098500626e-16 relative error 3.754928523298353e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -1.6000000000000014 y[1] (closed_form) 1.2018965179946552 y[1] (numeric) 1.2018965179946557 absolute error 4.440892098500626e-16 relative error 3.6949038723484966e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -1.5000000000000013 y[1] (closed_form) 1.2231301601484295 y[1] (numeric) 1.2231301601484301 absolute error 6.661338147750939e-16 relative error 5.446140046896212e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -1.4000000000000012 y[1] (closed_form) 1.2465969639416061 y[1] (numeric) 1.2465969639416068 absolute error 6.661338147750939e-16 relative error 5.34361813836647e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -1.3000000000000012 y[1] (closed_form) 1.2725317930340123 y[1] (numeric) 1.272531793034013 absolute error 6.661338147750939e-16 relative error 5.234712550378609e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -1.200000000000001 y[1] (closed_form) 1.3011942119122017 y[1] (numeric) 1.3011942119122024 absolute error 6.661338147750939e-16 relative error 5.119403457814039e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -1.100000000000001 y[1] (closed_form) 1.3328710836980793 y[1] (numeric) 1.33287108369808 absolute error 6.661338147750939e-16 relative error 4.997736262136406e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -1.0000000000000009 y[1] (closed_form) 1.367879441171442 y[1] (numeric) 1.3678794411714428 absolute error 8.881784197001252e-16 relative error 6.493104530758177e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.9000000000000009 y[1] (closed_form) 1.4065696597405988 y[1] (numeric) 1.4065696597405997 absolute error 8.881784197001252e-16 relative error 6.314500057280663e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.8000000000000009 y[1] (closed_form) 1.4493289641172211 y[1] (numeric) 1.4493289641172222 absolute error 1.1102230246251565e-15 relative error 7.660255553516711e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.700000000000001 y[1] (closed_form) 1.496585303791409 y[1] (numeric) 1.49658530379141 absolute error 1.1102230246251565e-15 relative error 7.418374494340867e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.600000000000001 y[1] (closed_form) 1.548811636094026 y[1] (numeric) 1.548811636094027 absolute error 8.881784197001252e-16 relative error 5.734579977330473e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.500000000000001 y[1] (closed_form) 1.6065306597126328 y[1] (numeric) 1.606530659712634 absolute error 1.3322676295501878e-15 relative error 8.292824176716904e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.400000000000001 y[1] (closed_form) 1.6703200460356387 y[1] (numeric) 1.67032004603564 absolute error 1.3322676295501878e-15 relative error 7.976121897789653e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.30000000000000104 y[1] (closed_form) 1.740818220681717 y[1] (numeric) 1.7408182206817187 absolute error 1.5543122344752192e-15 relative error 8.928630318830988e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.20000000000000104 y[1] (closed_form) 1.818730753077981 y[1] (numeric) 1.8187307530779826 absolute error 1.5543122344752192e-15 relative error 8.546137089531996e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -0.10000000000000103 y[1] (closed_form) 1.9048374180359586 y[1] (numeric) 1.9048374180359604 absolute error 1.7763568394002505e-15 relative error 9.325503702210019e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] -1.0269562977782698e-15 y[1] (closed_form) 1.9999999999999991 y[1] (numeric) 2.000000000000001 absolute error 1.7763568394002505e-15 relative error 8.881784197001256e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.09999999999999898 y[1] (closed_form) 2.105170918075647 y[1] (numeric) 2.1051709180756486 absolute error 1.7763568394002505e-15 relative error 8.438064691792494e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.19999999999999898 y[1] (closed_form) 2.2214027581601687 y[1] (numeric) 2.221402758160171 absolute error 2.220446049250313e-15 relative error 9.995693221743148e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.299999999999999 y[1] (closed_form) 2.349858807576002 y[1] (numeric) 2.3498588075760045 absolute error 2.6645352591003757e-15 relative error 1.1339129187293506e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.399999999999999 y[1] (closed_form) 2.4918246976412686 y[1] (numeric) 2.4918246976412717 absolute error 3.1086244689504383e-15 relative error 1.2475293594661875e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.499999999999999 y[1] (closed_form) 2.6487212707001264 y[1] (numeric) 2.6487212707001295 absolute error 3.1086244689504383e-15 relative error 1.173632161049829e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.599999999999999 y[1] (closed_form) 2.8221188003905073 y[1] (numeric) 2.8221188003905104 absolute error 3.1086244689504383e-15 relative error 1.101521476884774e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.699999999999999 y[1] (closed_form) 3.0137527074704744 y[1] (numeric) 3.013752707470478 absolute error 3.552713678800501e-15 relative error 1.1788338406114255e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.7999999999999989 y[1] (closed_form) 3.225540928492465 y[1] (numeric) 3.225540928492469 absolute error 3.9968028886505635e-15 relative error 1.2391108893845494e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.8999999999999989 y[1] (closed_form) 3.459603111156947 y[1] (numeric) 3.4596031111569516 absolute error 4.440892098500626e-15 relative error 1.283642069860297e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 0.9999999999999989 y[1] (closed_form) 3.7182818284590424 y[1] (numeric) 3.7182818284590473 absolute error 4.884981308350689e-15 relative error 1.3137738164336936e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.099999999999999 y[1] (closed_form) 4.00416602394643 y[1] (numeric) 4.004166023946436 absolute error 5.329070518200751e-15 relative error 1.3308815084916286e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.199999999999999 y[1] (closed_form) 4.320116922736545 y[1] (numeric) 4.320116922736551 absolute error 6.217248937900877e-15 relative error 1.439139043941109e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.2999999999999992 y[1] (closed_form) 4.669296667619241 y[1] (numeric) 4.669296667619248 absolute error 7.105427357601002e-15 relative error 1.5217339705304875e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.3999999999999992 y[1] (closed_form) 5.055199966844672 y[1] (numeric) 5.055199966844679 absolute error 7.105427357601002e-15 relative error 1.4055680100101024e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.4999999999999993 y[1] (closed_form) 5.481689070338062 y[1] (numeric) 5.48168907033807 absolute error 7.993605777301127e-15 relative error 1.4582377210256752e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.5999999999999994 y[1] (closed_form) 5.953032424395112 y[1] (numeric) 5.95303242439512 absolute error 7.993605777301127e-15 relative error 1.3427788070738348e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.6999999999999995 y[1] (closed_form) 6.473947391727197 y[1] (numeric) 6.473947391727206 absolute error 8.881784197001252e-15 relative error 1.3719271504045485e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.7999999999999996 y[1] (closed_form) 7.049647464412944 y[1] (numeric) 7.049647464412953 absolute error 8.881784197001252e-15 relative error 1.259890546560952e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.8999999999999997 y[1] (closed_form) 7.685894442279268 y[1] (numeric) 7.6858944422792765 absolute error 8.881784197001252e-15 relative error 1.1555953914932173e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 1.9999999999999998 y[1] (closed_form) 8.389056098930649 y[1] (numeric) 8.389056098930658 absolute error 8.881784197001252e-15 relative error 1.0587346290524165e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.0999999999999996 y[1] (closed_form) 9.166169912567646 y[1] (numeric) 9.166169912567659 absolute error 1.2434497875801753e-14 relative error 1.3565641914135733e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.1999999999999997 y[1] (closed_form) 10.025013499434118 y[1] (numeric) 10.025013499434131 absolute error 1.2434497875801753e-14 relative error 1.240347245068911e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.3 y[1] (closed_form) 10.974182454814718 y[1] (numeric) 10.974182454814732 absolute error 1.4210854715202004e-14 relative error 1.294935160201137e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.4 y[1] (closed_form) 12.023176380641601 y[1] (numeric) 12.023176380641615 absolute error 1.4210854715202004e-14 relative error 1.181955106146722e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.5 y[1] (closed_form) 13.182493960703473 y[1] (numeric) 13.18249396070349 absolute error 1.5987211554602254e-14 relative error 1.2127607721467228e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.6 y[1] (closed_form) 14.463738035001692 y[1] (numeric) 14.463738035001708 absolute error 1.5987211554602254e-14 relative error 1.1053305525801017e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.7 y[1] (closed_form) 15.879731724872837 y[1] (numeric) 15.879731724872853 absolute error 1.5987211554602254e-14 relative error 1.0067683655864959e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.8000000000000003 y[1] (closed_form) 17.444646771097055 y[1] (numeric) 17.44464677109707 absolute error 1.4210854715202004e-14 relative error 8.146255353675077e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 2.9000000000000004 y[1] (closed_form) 19.174145369443067 y[1] (numeric) 19.17414536944308 absolute error 1.4210854715202004e-14 relative error 7.411467077875175e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.0000000000000004 y[1] (closed_form) 21.085536923187675 y[1] (numeric) 21.085536923187693 absolute error 1.7763568394002505e-14 relative error 8.424527418349961e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.1000000000000005 y[1] (closed_form) 23.197951281441647 y[1] (numeric) 23.19795128144166 absolute error 1.4210854715202004e-14 relative error 6.125909371389482e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.2000000000000006 y[1] (closed_form) 25.532530197109363 y[1] (numeric) 25.53253019710938 absolute error 1.7763568394002505e-14 relative error 6.957229956008663e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.3000000000000007 y[1] (closed_form) 28.112638920657908 y[1] (numeric) 28.112638920657922 absolute error 1.4210854715202004e-14 relative error 5.0549700280038433e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.400000000000001 y[1] (closed_form) 30.964100047397036 y[1] (numeric) 30.964100047397054 absolute error 1.7763568394002505e-14 relative error 5.736826959870187e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.500000000000001 y[1] (closed_form) 34.11545195869234 y[1] (numeric) 34.11545195869236 absolute error 2.1316282072803006e-14 relative error 6.248277788790012e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.600000000000001 y[1] (closed_form) 37.598234443678024 y[1] (numeric) 37.59823444367804 absolute error 1.4210854715202004e-14 relative error 3.7796601158200116e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.700000000000001 y[1] (closed_form) 41.447304360067434 y[1] (numeric) 41.44730436006745 absolute error 1.4210854715202004e-14 relative error 3.4286559607706375e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.800000000000001 y[1] (closed_form) 45.70118449330087 y[1] (numeric) 45.701184493300886 absolute error 1.4210854715202004e-14 relative error 3.10951562257322e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 3.9000000000000012 y[1] (closed_form) 50.40244910553024 y[1] (numeric) 50.402449105530245 absolute error 7.105427357601002e-15 relative error 1.4097385114608216e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.000000000000001 y[1] (closed_form) 55.598150033144286 y[1] (numeric) 55.59815003314432 absolute error 3.552713678800501e-14 relative error 6.389985416210046e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.1000000000000005 y[1] (closed_form) 61.340287597362 y[1] (numeric) 61.340287597362064 absolute error 6.394884621840902e-14 relative error 1.0425260252799858e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.2 y[1] (closed_form) 67.68633104092515 y[1] (numeric) 67.68633104092524 absolute error 8.526512829121202e-14 relative error 1.2597097077053594e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.3 y[1] (closed_form) 74.69979369959579 y[1] (numeric) 74.6997936995959 absolute error 1.1368683772161603e-13 relative error 1.5219163546663344e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.3999999999999995 y[1] (closed_form) 82.45086866496807 y[1] (numeric) 82.45086866496824 absolute error 1.7053025658242404e-13 relative error 2.0682651298115355e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.499999999999999 y[1] (closed_form) 91.01713130052174 y[1] (numeric) 91.01713130052195 absolute error 2.1316282072803006e-13 relative error 2.342007682314287e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.599999999999999 y[1] (closed_form) 100.48431564193369 y[1] (numeric) 100.48431564193396 absolute error 2.7000623958883807e-13 relative error 2.6870485992160173e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.699999999999998 y[1] (closed_form) 110.94717245212333 y[1] (numeric) 110.94717245212367 absolute error 3.410605131648481e-13 relative error 3.074080263848318e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.799999999999998 y[1] (closed_form) 122.51041751873464 y[1] (numeric) 122.51041751873507 absolute error 4.263256414560601e-13 relative error 3.479913382801631e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.899999999999998 y[1] (closed_form) 135.28977968493518 y[1] (numeric) 135.2897796849357 absolute error 5.115907697472721e-13 relative error 3.7814443259400095e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 TOP MAIN SOLVE Loop x[1] 4.999999999999997 y[1] (closed_form) 149.4131591025762 y[1] (numeric) 149.41315910257686 absolute error 6.536993168992922e-13 relative error 4.375112077313818e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.1 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 Finished! diff ( y , x , 2 ) = diff ( y , x , 1 ) ; Iterations 101 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 101.99999999999996%