##############ECHO OF PROBLEM################# ##############temp/arcsin_c_arccos_c_arctan_cpostode.ode################# diff ( y , x , 1 ) = arcsin ( 0.1 ) + arccos ( 0.1 ) + arctan ( 0.1 ) ; ! #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) $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((arcsin(0.1) + arccos(0.1) + arctan(0.1)) * 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 10000000.0 step_error 8.804123476816562e-21 est_needed_step_err 8.804123476816562e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 5000000.0 step_error 1.245091082572135e-20 est_needed_step_err 1.245091082572135e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 2500000.0 step_error 1.7608246953633124e-20 est_needed_step_err 1.7608246953633124e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 1250000.0 step_error 2.49018216514427e-20 est_needed_step_err 2.49018216514427e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 625000.0 step_error 3.521649390726625e-20 est_needed_step_err 3.521649390726625e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 312500.0 step_error 4.98036433028854e-20 est_needed_step_err 4.98036433028854e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 156250.0 step_error 7.04329878145325e-20 est_needed_step_err 7.04329878145325e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 78125.0 step_error 9.96072866057708e-20 est_needed_step_err 9.96072866057708e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 39062.5 step_error 1.40865975629065e-19 est_needed_step_err 1.40865975629065e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 19531.25 step_error 1.992145732115416e-19 est_needed_step_err 1.992145732115416e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 9765.625 step_error 2.8173195125813e-19 est_needed_step_err 2.8173195125813e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 4882.8125 step_error 3.984291464230832e-19 est_needed_step_err 3.984291464230832e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 2441.40625 step_error 5.6346390251626e-19 est_needed_step_err 5.6346390251626e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 1220.703125 step_error 7.968582928461664e-19 est_needed_step_err 7.968582928461664e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 0.016384 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 610.3515625 step_error 1.12692780503252e-18 est_needed_step_err 1.12692780503252e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 0.032768 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 305.17578125 step_error 1.5937165856923328e-18 est_needed_step_err 1.5937165856923328e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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 8.352324896430293 $glob_desired_digits_correct 16 estimated_h 0.065536 estimated_answer 8.352324896430293 desired_abs_gbl_error 8.352324896430293e-16 range 10.0 estimated_steps 152.587890625 step_error 2.25385561006504e-18 est_needed_step_err 2.25385561006504e-18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 0.0 estimated_step_error 0.0 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) -8.352324896430293 y[1] (numeric) -8.352324896430293 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) -8.185278398501687 y[1] (numeric) -8.185278398501687 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] -4.800000000000001 y[1] (closed_form) -8.018231900573083 y[1] (numeric) -8.018231900573081 absolute error 1.7763568394002505e-15 relative error 2.2153971865958254e-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] -4.700000000000001 y[1] (closed_form) -7.851185402644477 y[1] (numeric) -7.851185402644475 absolute error 1.7763568394002505e-15 relative error 2.262533296948928e-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] -4.600000000000001 y[1] (closed_form) -7.684138904715872 y[1] (numeric) -7.684138904715869 absolute error 2.6645352591003757e-15 relative error 3.4675782051065086e-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) -7.517092406787267 y[1] (numeric) -7.517092406787263 absolute error 3.552713678800501e-15 relative error 4.726180664737759e-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) -7.350045908858662 y[1] (numeric) -7.350045908858657 absolute error 4.440892098500626e-15 relative error 6.041992327079522e-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) -7.182999410930056 y[1] (numeric) -7.1829994109300515 absolute error 4.440892098500626e-15 relative error 6.182503776546487e-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) -7.015952913001451 y[1] (numeric) -7.0159529130014455 absolute error 5.329070518200751e-15 relative error 7.595647496899968e-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) -6.848906415072846 y[1] (numeric) -6.84890641507284 absolute error 6.217248937900877e-15 relative error 9.077725057270693e-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) -6.681859917144241 y[1] (numeric) -6.681859917144234 absolute error 7.105427357601002e-15 relative error 1.0633906495659953e-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] -3.9000000000000035 y[1] (closed_form) -6.514813419215635 y[1] (numeric) -6.514813419215628 absolute error 7.105427357601002e-15 relative error 1.0906570764779439e-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] -3.8000000000000034 y[1] (closed_form) -6.347766921287028 y[1] (numeric) -6.347766921287022 absolute error 6.217248937900877e-15 relative error 9.794387561792063e-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) -6.180720423358422 y[1] (numeric) -6.180720423358416 absolute error 6.217248937900877e-15 relative error 1.0059100739137794e-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] -3.600000000000003 y[1] (closed_form) -6.013673925429816 y[1] (numeric) -6.01367392542981 absolute error 6.217248937900877e-15 relative error 1.0338520204113845e-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] -3.500000000000003 y[1] (closed_form) -5.84662742750121 y[1] (numeric) -5.846627427501204 absolute error 6.217248937900877e-15 relative error 1.0633906495659954e-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] -3.400000000000003 y[1] (closed_form) -5.679580929572604 y[1] (numeric) -5.679580929572598 absolute error 6.217248937900877e-15 relative error 1.0946668451414659e-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] -3.300000000000003 y[1] (closed_form) -5.512534431643998 y[1] (numeric) -5.512534431643992 absolute error 6.217248937900877e-15 relative error 1.1278385677215103e-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] -3.200000000000003 y[1] (closed_form) -5.345487933715392 y[1] (numeric) -5.345487933715386 absolute error 6.217248937900877e-15 relative error 1.1630835229628074e-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] -3.1000000000000028 y[1] (closed_form) -5.1784414357867865 y[1] (numeric) -5.17844143578678 absolute error 6.217248937900877e-15 relative error 1.2006023462841883e-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] -3.0000000000000027 y[1] (closed_form) -5.011394937858181 y[1] (numeric) -5.011394937858174 absolute error 6.217248937900877e-15 relative error 1.240622424493661e-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] -2.9000000000000026 y[1] (closed_form) -4.844348439929575 y[1] (numeric) -4.844348439929568 absolute error 6.217248937900877e-15 relative error 1.2834025080968908e-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] -2.8000000000000025 y[1] (closed_form) -4.677301942000969 y[1] (numeric) -4.6773019420009625 absolute error 6.217248937900877e-15 relative error 1.329238311957494e-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] -2.7000000000000024 y[1] (closed_form) -4.510255444072362 y[1] (numeric) -4.510255444072357 absolute error 5.329070518200751e-15 relative error 1.1815451661844393e-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] -2.6000000000000023 y[1] (closed_form) -4.343208946143756 y[1] (numeric) -4.343208946143751 absolute error 5.329070518200751e-15 relative error 1.2269892110376872e-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] -2.500000000000002 y[1] (closed_form) -4.17616244821515 y[1] (numeric) -4.176162448215145 absolute error 5.329070518200751e-15 relative error 1.2760687794791945e-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] -2.400000000000002 y[1] (closed_form) -4.009115950286544 y[1] (numeric) -4.009115950286539 absolute error 5.329070518200751e-15 relative error 1.3292383119574944e-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] -2.300000000000002 y[1] (closed_form) -3.842069452357938 y[1] (numeric) -3.842069452357933 absolute error 5.329070518200751e-15 relative error 1.3870312820426027e-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] -2.200000000000002 y[1] (closed_form) -3.6750229544293322 y[1] (numeric) -3.675022954429327 absolute error 5.329070518200751e-15 relative error 1.4500781584990847e-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] -2.100000000000002 y[1] (closed_form) -3.5079764565007263 y[1] (numeric) -3.507976456500721 absolute error 5.329070518200751e-15 relative error 1.5191294993799934e-13% Desired digits 16 Estimated correct digits 12 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] -2.0000000000000018 y[1] (closed_form) -3.3409299585721204 y[1] (numeric) -3.340929958572115 absolute error 5.329070518200751e-15 relative error 1.595085974348993e-13% Desired digits 16 Estimated correct digits 12 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] -1.9000000000000017 y[1] (closed_form) -3.173883460643514 y[1] (numeric) -3.173883460643509 absolute error 4.884981308350689e-15 relative error 1.539118045424467e-13% Desired digits 16 Estimated correct digits 12 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] -1.8000000000000016 y[1] (closed_form) -3.006836962714908 y[1] (numeric) -3.006836962714903 absolute error 4.884981308350689e-15 relative error 1.624624603503604e-13% Desired digits 16 Estimated correct digits 12 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] -1.7000000000000015 y[1] (closed_form) -2.839790464786302 y[1] (numeric) -2.8397904647862973 absolute error 4.884981308350689e-15 relative error 1.720190756650875e-13% Desired digits 16 Estimated correct digits 12 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] -1.6000000000000014 y[1] (closed_form) -2.672743966857696 y[1] (numeric) -2.6727439668576913 absolute error 4.884981308350689e-15 relative error 1.8277026789415546e-13% Desired digits 16 Estimated correct digits 12 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] -1.5000000000000013 y[1] (closed_form) -2.5056974689290903 y[1] (numeric) -2.5056974689290854 absolute error 4.884981308350689e-15 relative error 1.9495495242043248e-13% Desired digits 16 Estimated correct digits 12 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] -1.4000000000000012 y[1] (closed_form) -2.3386509710004844 y[1] (numeric) -2.3386509710004795 absolute error 4.884981308350689e-15 relative error 2.0888030616474907e-13% Desired digits 16 Estimated correct digits 12 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] -1.3000000000000012 y[1] (closed_form) -2.171604473071878 y[1] (numeric) -2.1716044730718735 absolute error 4.440892098500626e-15 relative error 2.044982018396145e-13% Desired digits 16 Estimated correct digits 12 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] -1.200000000000001 y[1] (closed_form) -2.004557975143272 y[1] (numeric) -2.0045579751432676 absolute error 4.440892098500626e-15 relative error 2.2153971865958238e-13% Desired digits 16 Estimated correct digits 12 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] -1.100000000000001 y[1] (closed_form) -1.8375114772146661 y[1] (numeric) -1.8375114772146617 absolute error 4.440892098500626e-15 relative error 2.4167969308318076e-13% Desired digits 16 Estimated correct digits 12 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] -1.0000000000000009 y[1] (closed_form) -1.6704649792860602 y[1] (numeric) -1.6704649792860558 absolute error 4.440892098500626e-15 relative error 2.658476623914988e-13% Desired digits 16 Estimated correct digits 12 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] -0.9000000000000009 y[1] (closed_form) -1.5034184813574543 y[1] (numeric) -1.5034184813574498 absolute error 4.440892098500626e-15 relative error 2.953862915461098e-13% Desired digits 16 Estimated correct digits 12 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] -0.8000000000000009 y[1] (closed_form) -1.3363719834288486 y[1] (numeric) -1.336371983428844 absolute error 4.6629367034256575e-15 relative error 3.489250568888421e-13% Desired digits 16 Estimated correct digits 12 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] -0.700000000000001 y[1] (closed_form) -1.1693254855002426 y[1] (numeric) -1.169325485500238 absolute error 4.6629367034256575e-15 relative error 3.9877149358724805e-13% Desired digits 16 Estimated correct digits 12 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] -0.600000000000001 y[1] (closed_form) -1.002278987571637 y[1] (numeric) -1.002278987571632 absolute error 4.884981308350689e-15 relative error 4.873873810510808e-13% Desired digits 16 Estimated correct digits 12 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] -0.500000000000001 y[1] (closed_form) -0.835232489643031 y[1] (numeric) -0.8352324896430261 absolute error 4.884981308350689e-15 relative error 5.848648572612968e-13% Desired digits 16 Estimated correct digits 12 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] -0.400000000000001 y[1] (closed_form) -0.6681859917144252 y[1] (numeric) -0.6681859917144202 absolute error 4.9960036108132044e-15 relative error 7.476965504760893e-13% Desired digits 16 Estimated correct digits 12 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] -0.30000000000000104 y[1] (closed_form) -0.5011394937858193 y[1] (numeric) -0.5011394937858142 absolute error 5.10702591327572e-15 relative error 1.0190827058340763e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 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) -0.33409299585721347 y[1] (numeric) -0.33409299585720836 absolute error 5.10702591327572e-15 relative error 1.5286240587511118e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 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) -0.1670464979286076 y[1] (numeric) -0.1670464979286025 absolute error 5.10702591327572e-15 relative error 3.0572481175022078e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 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) -1.715494530695865e-15 y[1] (numeric) 3.3861802251067274e-15 absolute error 5.1016747558025925e-15 relative error 297.3879930548757% Desired digits 16 Estimated correct digits -2 Correct digits 1 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) 0.16704649792860415 y[1] (numeric) 0.16704649792860926 absolute error 5.10702591327572e-15 relative error 3.0572481175022708e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 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) 0.33409299585721003 y[1] (numeric) 0.33409299585721514 absolute error 5.10702591327572e-15 relative error 1.5286240587511275e-12% Desired digits 16 Estimated correct digits 11 Correct digits 14 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) 0.5011394937858159 y[1] (numeric) 0.501139493785821 absolute error 5.10702591327572e-15 relative error 1.0190827058340831e-12% Desired digits 16 Estimated correct digits 12 Correct digits 14 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) 0.6681859917144218 y[1] (numeric) 0.6681859917144268 absolute error 4.9960036108132044e-15 relative error 7.47696550476093e-13% Desired digits 16 Estimated correct digits 12 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) 0.8352324896430277 y[1] (numeric) 0.8352324896430328 absolute error 5.10702591327572e-15 relative error 6.11449623500449e-13% Desired digits 16 Estimated correct digits 12 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) 1.0022789875716336 y[1] (numeric) 1.0022789875716387 absolute error 5.10702591327572e-15 relative error 5.095413529170408e-13% Desired digits 16 Estimated correct digits 12 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) 1.1693254855002393 y[1] (numeric) 1.1693254855002446 absolute error 5.329070518200751e-15 relative error 4.557388498139991e-13% Desired digits 16 Estimated correct digits 12 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) 1.3363719834288452 y[1] (numeric) 1.3363719834288506 absolute error 5.329070518200751e-15 relative error 3.987714935872491e-13% Desired digits 16 Estimated correct digits 12 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) 1.503418481357451 y[1] (numeric) 1.5034184813574565 absolute error 5.551115123125783e-15 relative error 3.6923286443263805e-13% Desired digits 16 Estimated correct digits 12 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) 1.6704649792860569 y[1] (numeric) 1.6704649792860624 absolute error 5.551115123125783e-15 relative error 3.323095779893742e-13% Desired digits 16 Estimated correct digits 12 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) 1.8375114772146628 y[1] (numeric) 1.8375114772146683 absolute error 5.551115123125783e-15 relative error 3.020996163539765e-13% Desired digits 16 Estimated correct digits 12 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) 2.004557975143269 y[1] (numeric) 2.0045579751432743 absolute error 5.329070518200751e-15 relative error 2.658476623914993e-13% Desired digits 16 Estimated correct digits 12 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) 2.171604473071875 y[1] (numeric) 2.17160447307188 absolute error 5.329070518200751e-15 relative error 2.453978422075378e-13% Desired digits 16 Estimated correct digits 12 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) 2.338650971000481 y[1] (numeric) 2.338650971000486 absolute error 5.329070518200751e-15 relative error 2.278694249069993e-13% Desired digits 16 Estimated correct digits 12 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) 2.5056974689290867 y[1] (numeric) 2.505697468929092 absolute error 5.329070518200751e-15 relative error 2.1267812991319935e-13% Desired digits 16 Estimated correct digits 12 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) 2.6727439668576927 y[1] (numeric) 2.672743966857698 absolute error 5.329070518200751e-15 relative error 1.993857467936244e-13% Desired digits 16 Estimated correct digits 12 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) 2.839790464786299 y[1] (numeric) 2.839790464786304 absolute error 4.884981308350689e-15 relative error 1.7201907566508767e-13% Desired digits 16 Estimated correct digits 12 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) 3.006836962714905 y[1] (numeric) 3.00683696271491 absolute error 4.884981308350689e-15 relative error 1.6246246035036058e-13% Desired digits 16 Estimated correct digits 12 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) 3.173883460643511 y[1] (numeric) 3.173883460643516 absolute error 4.884981308350689e-15 relative error 1.5391180454244686e-13% Desired digits 16 Estimated correct digits 12 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) 3.340929958572117 y[1] (numeric) 3.3409299585721217 absolute error 4.884981308350689e-15 relative error 1.462162143153245e-13% Desired digits 16 Estimated correct digits 12 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) 3.5079764565007228 y[1] (numeric) 3.5079764565007276 absolute error 4.884981308350689e-15 relative error 1.392535374431662e-13% Desired digits 16 Estimated correct digits 12 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) 3.6750229544293287 y[1] (numeric) 3.6750229544293336 absolute error 4.884981308350689e-15 relative error 1.3292383119574956e-13% Desired digits 16 Estimated correct digits 12 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) 3.8420694523579346 y[1] (numeric) 3.8420694523579395 absolute error 4.884981308350689e-15 relative error 1.271445341872387e-13% Desired digits 16 Estimated correct digits 12 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) 4.0091159502865406 y[1] (numeric) 4.009115950286545 absolute error 4.440892098500626e-15 relative error 1.1076985932979129e-13% Desired digits 16 Estimated correct digits 12 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) 4.1761624482151465 y[1] (numeric) 4.176162448215151 absolute error 4.440892098500626e-15 relative error 1.0633906495659964e-13% Desired digits 16 Estimated correct digits 12 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) 4.343208946143752 y[1] (numeric) 4.343208946143757 absolute error 4.440892098500626e-15 relative error 1.0224910091980734e-13% Desired digits 16 Estimated correct digits 12 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) 4.510255444072358 y[1] (numeric) 4.510255444072363 absolute error 4.440892098500626e-15 relative error 9.84620971820367e-14% Desired digits 16 Estimated correct digits 12 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] 2.8000000000000003 y[1] (closed_form) 4.677301942000964 y[1] (numeric) 4.677301942000969 absolute error 4.440892098500626e-15 relative error 9.494559371124967e-14% Desired digits 16 Estimated correct digits 12 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) 4.84434843992957 y[1] (numeric) 4.844348439929575 absolute error 4.440892098500626e-15 relative error 9.167160772120658e-14% Desired digits 16 Estimated correct digits 12 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) 5.011394937858177 y[1] (numeric) 5.011394937858181 absolute error 3.552713678800501e-15 relative error 7.08927099710664e-14% Desired digits 16 Estimated correct digits 12 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) 5.178441435786783 y[1] (numeric) 5.1784414357867865 absolute error 3.552713678800501e-15 relative error 6.860584835909651e-14% Desired digits 16 Estimated correct digits 12 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) 5.345487933715389 y[1] (numeric) 5.345487933715392 absolute error 3.552713678800501e-15 relative error 6.646191559787476e-14% Desired digits 16 Estimated correct digits 12 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) 5.512534431643995 y[1] (numeric) 5.512534431643998 absolute error 3.552713678800501e-15 relative error 6.444791815551492e-14% Desired digits 16 Estimated correct digits 12 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) 5.679580929572601 y[1] (numeric) 5.679580929572604 absolute error 3.552713678800501e-15 relative error 6.255239115094095e-14% Desired digits 16 Estimated correct digits 12 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) 5.846627427501207 y[1] (numeric) 5.84662742750121 absolute error 3.552713678800501e-15 relative error 6.076517997519978e-14% Desired digits 16 Estimated correct digits 12 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) 6.013673925429813 y[1] (numeric) 6.013673925429816 absolute error 3.552713678800501e-15 relative error 5.9077258309222e-14% Desired digits 16 Estimated correct digits 12 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) 6.1807204233584185 y[1] (numeric) 6.180720423358422 absolute error 3.552713678800501e-15 relative error 5.7480575652216e-14% Desired digits 16 Estimated correct digits 12 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) 6.3477669212870245 y[1] (numeric) 6.347766921287028 absolute error 3.552713678800501e-15 relative error 5.5967928924526106e-14% Desired digits 16 Estimated correct digits 12 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) 6.51481341921563 y[1] (numeric) 6.514813419215634 absolute error 3.552713678800501e-15 relative error 5.4532853823897234e-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) 6.681859917144236 y[1] (numeric) 6.68185991714424 absolute error 3.552713678800501e-15 relative error 5.31695324782998e-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) 6.848906415072841 y[1] (numeric) 6.848906415072846 absolute error 4.440892098500626e-15 relative error 6.484089326621928e-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] 4.2 y[1] (closed_form) 7.015952913001446 y[1] (numeric) 7.015952913001452 absolute error 5.329070518200751e-15 relative error 7.595647496899973e-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] 4.3 y[1] (closed_form) 7.1829994109300515 y[1] (numeric) 7.182999410930058 absolute error 6.217248937900877e-15 relative error 8.655505287165087e-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] 4.3999999999999995 y[1] (closed_form) 7.350045908858657 y[1] (numeric) 7.350045908858664 absolute error 6.217248937900877e-15 relative error 8.458789257911335e-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] 4.499999999999999 y[1] (closed_form) 7.517092406787262 y[1] (numeric) 7.5170924067872695 absolute error 7.105427357601002e-15 relative error 9.452361329475525e-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] 4.599999999999999 y[1] (closed_form) 7.6841389047158675 y[1] (numeric) 7.6841389047158755 absolute error 7.993605777301127e-15 relative error 1.0402734615319532e-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) 7.8511854026444725 y[1] (numeric) 7.851185402644481 absolute error 8.881784197001252e-15 relative error 1.1312666484744646e-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) 8.018231900573078 y[1] (numeric) 8.018231900573086 absolute error 8.881784197001252e-15 relative error 1.1076985932979134e-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) 8.185278398501683 y[1] (numeric) 8.185278398501692 absolute error 8.881784197001252e-15 relative error 1.0850924995571396e-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) 8.35232489643029 y[1] (numeric) 8.352324896430298 absolute error 8.881784197001252e-15 relative error 1.0633906495659968e-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 , 1 ) = arcsin ( 0.1 ) + arccos ( 0.1 ) + arctan ( 0.1 ) ; 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%