|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 1 > ret := 1.0; > else > ret := -1.0; > fi;# end if 1; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 3 > # Begin Function number 4 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > array_const_2D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8_g, > array_tmp8_a1, > array_tmp8_a2, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 1 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (min_size < 1.0) then # if number 1 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g, array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 4 > # Begin Function number 5 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > array_const_2D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8_g, > array_tmp8_a1, > array_tmp8_a2, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms; > max_value3 := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > value3 := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > omniout_float(ALWAYS,"max_value3",32,max_value3,32,""); > max_value3; > end; test_suggested_h := proc() local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g, array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; max_value3 := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); value3 := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""); max_value3 end proc > # End Function number 5 > # Begin Function number 6 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > array_const_2D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8_g, > array_tmp8_a1, > array_tmp8_a2, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1 > ret := true; > else > ret := false; > fi;# end if 1; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g, array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 6 > # Begin Function number 7 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > array_const_2D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8_g, > array_tmp8_a1, > array_tmp8_a2, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 1 > if (iter >= 0) then # if number 2 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 4 > glob_good_digits := -trunc(log10(relerr)) + 2; > else > glob_good_digits := Digits; > fi;# end if 4; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 2; > #BOTTOM DISPLAY ALOT > fi;# end if 1; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g, array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 2 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 7 > # Begin Function number 8 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > array_const_2D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8_g, > array_tmp8_a1, > array_tmp8_a2, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1; > if ( not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g, array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 8 > # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > array_const_2D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8_g, > array_tmp8_a1, > array_tmp8_a2, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 1; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g, array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 9 > # Begin Function number 10 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > array_const_2D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8_g, > array_tmp8_a1, > array_tmp8_a2, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc,hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float * glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2; > if (m > 10) then # if number 1 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > glob_small_float * glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1; > n := n - 1; > od;# end do number 2; > m := n + cnt; > if (m <= 10) then # if number 1 > rad_c := glob_large_float; > ord_no := glob_large_float; > elif > (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2; > #BOTTOM RADII COMPLEX EQ = 1 > found_sing := 0; > #TOP WHICH RADII EQ = 1 > if (1 <> found_sing and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found_sing := 1; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found_sing := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing ) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 3; > fi;# end if 2; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if (array_pole[1] > array_poles[1,1]) then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2; > #BOTTOM WHICH RADIUS EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 2; > #BOTTOM ADJUST ALL SERIES > if (reached_interval()) then # if number 2 > display_pole(); > fi;# end if 2 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g, array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and ( omniabs(array_y_higher[1, m]) < glob_small_float*glob_small_float or omniabs(array_y_higher[1, m - 1]) < glob_small_float*glob_small_float or omniabs(array_y_higher[1, m - 2]) < glob_small_float*glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if glob_small_float*glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float elif glob_large_float <= omniabs(array_y_higher[1, m]) or glob_large_float <= omniabs(array_y_higher[1, m - 1]) or glob_large_float <= omniabs(array_y_higher[1, m - 2]) or glob_large_float <= omniabs(array_y_higher[1, m - 3]) or glob_large_float <= omniabs(array_y_higher[1, m - 4]) or glob_large_float <= omniabs(array_y_higher[1, m - 5]) or omniabs(array_y_higher[1, m]) <= glob_small_float or omniabs(array_y_higher[1, m - 1]) <= glob_small_float or omniabs(array_y_higher[1, m - 2]) <= glob_small_float or omniabs(array_y_higher[1, m - 3]) <= glob_small_float or omniabs(array_y_higher[1, m - 4]) <= glob_small_float or omniabs(array_y_higher[1, m - 5]) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found_sing := 0; if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found_sing := 1; array_type_pole[1] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and -1.0*glob_smallish_float < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1") end if end if; if 1 <> found_sing and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and -1.0*glob_smallish_float < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found_sing := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_pole() end if end proc > # End Function number 10 > # Begin Function number 11 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > array_const_2D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8_g, > array_tmp8_a1, > array_tmp8_a2, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 2 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 3; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 2; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g, array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 11 > # Begin Function number 12 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > array_const_2D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8_g, > array_tmp8_a1, > array_tmp8_a2, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_1D0[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > array_tmp4_a1[1] := sin(array_tmp3[1]); > array_tmp4_a2[1] := cos(array_tmp3[1]); > array_tmp4[1] := (array_tmp4_a1[1] / array_tmp4_a2[1]); > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp5[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp6[1] := array_tmp5[1] + array_const_1D0[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp7[1] := sqrt(array_tmp6[1]); > array_tmp8_a1[1] := sin(array_tmp7[1]); > array_tmp8_a2[1] := cos(array_tmp7[1]); > array_tmp8[1] := (array_tmp8_a1[1] / array_tmp8_a2[1]); > # emit pre mult FULL FULL $eq_no = 1 i = 1 > array_tmp9[1] := (array_tmp4[1] * (array_tmp8[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp10[1] := array_const_1D0[1] + array_tmp9[1]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp11[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp12[1] := array_tmp11[1] + array_const_1D0[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp13[1] := sqrt(array_tmp12[1]); > #emit pre div FULL - FULL $eq_no = 1 i = 1 > array_tmp14[1] := (array_tmp10[1] / (array_tmp13[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp15[1] := array_const_0D0[1] + array_tmp14[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp15[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0; > #emit pre tan $eq_no = 1 > array_tmp4_a1[2] := att(1,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[2] := -att(1,array_tmp4_a1,array_tmp3,1); > array_tmp4[2] := (array_tmp4_a1[2] - ats(2,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp5[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp6[2] := array_tmp5[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp7[2] := array_tmp6[2] / array_tmp7[1]/2.0; > #emit pre tan $eq_no = 1 > array_tmp8_a1[2] := att(1,array_tmp8_a2,array_tmp7,1); > array_tmp8_a2[2] := -att(1,array_tmp8_a1,array_tmp7,1); > array_tmp8[2] := (array_tmp8_a1[2] - ats(2,array_tmp8_a2,array_tmp8,2)) / array_tmp8_a2[1]; > # emit pre mult FULL FULL $eq_no = 1 i = 2 > array_tmp9[2] := ats(2,array_tmp4,array_tmp8,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp10[2] := array_tmp9[2]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp11[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp12[2] := array_tmp11[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp13[2] := array_tmp12[2] / array_tmp13[1]/2.0; > #emit pre div FULL - FULL $eq_no = 1 i = 2 > array_tmp14[2] := ((array_tmp10[2] - ats(2,array_tmp13,array_tmp14,2))/array_tmp13[1]); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp15[2] := array_tmp14[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp15[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0.0; > array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre tan $eq_no = 1 > array_tmp4_a1[3] := att(2,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[3] := -att(2,array_tmp4_a1,array_tmp3,1); > array_tmp4[3] := (array_tmp4_a1[3] - ats(3,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp7[3] := 0.0; > array_tmp7[3] := -ats(3,array_tmp7,array_tmp7,2) / array_tmp7[1] / 2.0; > #emit pre tan $eq_no = 1 > array_tmp8_a1[3] := att(2,array_tmp8_a2,array_tmp7,1); > array_tmp8_a2[3] := -att(2,array_tmp8_a1,array_tmp7,1); > array_tmp8[3] := (array_tmp8_a1[3] - ats(3,array_tmp8_a2,array_tmp8,2)) / array_tmp8_a2[1]; > # emit pre mult FULL FULL $eq_no = 1 i = 3 > array_tmp9[3] := ats(3,array_tmp4,array_tmp8,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp10[3] := array_tmp9[3]; > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp13[3] := 0.0; > array_tmp13[3] := -ats(3,array_tmp13,array_tmp13,2) / array_tmp13[1] / 2.0; > #emit pre div FULL - FULL $eq_no = 1 i = 3 > array_tmp14[3] := ((array_tmp10[3] - ats(3,array_tmp13,array_tmp14,2))/array_tmp13[1]); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp15[3] := array_tmp14[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp15[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0.0; > array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre tan $eq_no = 1 > array_tmp4_a1[4] := att(3,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[4] := -att(3,array_tmp4_a1,array_tmp3,1); > array_tmp4[4] := (array_tmp4_a1[4] - ats(4,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp7[4] := 0.0; > array_tmp7[4] := -ats(4,array_tmp7,array_tmp7,2) / array_tmp7[1] / 2.0; > #emit pre tan $eq_no = 1 > array_tmp8_a1[4] := att(3,array_tmp8_a2,array_tmp7,1); > array_tmp8_a2[4] := -att(3,array_tmp8_a1,array_tmp7,1); > array_tmp8[4] := (array_tmp8_a1[4] - ats(4,array_tmp8_a2,array_tmp8,2)) / array_tmp8_a2[1]; > # emit pre mult FULL FULL $eq_no = 1 i = 4 > array_tmp9[4] := ats(4,array_tmp4,array_tmp8,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp10[4] := array_tmp9[4]; > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp13[4] := 0.0; > array_tmp13[4] := -ats(4,array_tmp13,array_tmp13,2) / array_tmp13[1] / 2.0; > #emit pre div FULL - FULL $eq_no = 1 i = 4 > array_tmp14[4] := ((array_tmp10[4] - ats(4,array_tmp13,array_tmp14,2))/array_tmp13[1]); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp15[4] := array_tmp14[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp15[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0.0; > array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre tan $eq_no = 1 > array_tmp4_a1[5] := att(4,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[5] := -att(4,array_tmp4_a1,array_tmp3,1); > array_tmp4[5] := (array_tmp4_a1[5] - ats(5,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp7[5] := 0.0; > array_tmp7[5] := -ats(5,array_tmp7,array_tmp7,2) / array_tmp7[1] / 2.0; > #emit pre tan $eq_no = 1 > array_tmp8_a1[5] := att(4,array_tmp8_a2,array_tmp7,1); > array_tmp8_a2[5] := -att(4,array_tmp8_a1,array_tmp7,1); > array_tmp8[5] := (array_tmp8_a1[5] - ats(5,array_tmp8_a2,array_tmp8,2)) / array_tmp8_a2[1]; > # emit pre mult FULL FULL $eq_no = 1 i = 5 > array_tmp9[5] := ats(5,array_tmp4,array_tmp8,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp10[5] := array_tmp9[5]; > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp13[5] := 0.0; > array_tmp13[5] := -ats(5,array_tmp13,array_tmp13,2) / array_tmp13[1] / 2.0; > #emit pre div FULL - FULL $eq_no = 1 i = 5 > array_tmp14[5] := ((array_tmp10[5] - ats(5,array_tmp13,array_tmp14,2))/array_tmp13[1]); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp15[5] := array_tmp14[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp15[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0.0; > array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0; > array_tmp4_a1[kkk] := att(kkk-1 ,array_tmp4_a2,array_tmp3,1); > array_tmp4_a2[kkk] := -att(kkk-1,array_tmp4_a1,array_tmp3,1); > array_tmp4[kkk] := (array_tmp4_a1[kkk] - ats(kkk ,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1]; > #emit sqrt LINEAR $eq_no = 1 > array_tmp7[kkk] := 0.0; > array_tmp7[kkk] := -ats(kkk,array_tmp7,array_tmp7,2) /array_tmp7[1] / 2.0; > array_tmp8_a1[kkk] := att(kkk-1 ,array_tmp8_a2,array_tmp7,1); > array_tmp8_a2[kkk] := -att(kkk-1,array_tmp8_a1,array_tmp7,1); > array_tmp8[kkk] := (array_tmp8_a1[kkk] - ats(kkk ,array_tmp8_a2,array_tmp8,2)) / array_tmp8_a2[1]; > #emit mult FULL FULL $eq_no = 1 > array_tmp9[kkk] := ats(kkk,array_tmp4,array_tmp8,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp10[kkk] := array_tmp9[kkk]; > #emit sqrt LINEAR $eq_no = 1 > array_tmp13[kkk] := 0.0; > array_tmp13[kkk] := -ats(kkk,array_tmp13,array_tmp13,2) /array_tmp13[1] / 2.0; > #emit div FULL FULL $eq_no = 1 > array_tmp14[kkk] := ((array_tmp10[kkk] - ats(kkk,array_tmp13,array_tmp14,2))/array_tmp13[1]); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp15[kkk] := array_tmp14[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp15[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 2 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g, array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := array_const_2D0[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_1D0[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4_a1[1] := sin(array_tmp3[1]); array_tmp4_a2[1] := cos(array_tmp3[1]); array_tmp4[1] := array_tmp4_a1[1]/array_tmp4_a2[1]; array_tmp5[1] := array_const_2D0[1]*array_x[1]; array_tmp6[1] := array_tmp5[1] + array_const_1D0[1]; array_tmp7[1] := sqrt(array_tmp6[1]); array_tmp8_a1[1] := sin(array_tmp7[1]); array_tmp8_a2[1] := cos(array_tmp7[1]); array_tmp8[1] := array_tmp8_a1[1]/array_tmp8_a2[1]; array_tmp9[1] := array_tmp4[1]*array_tmp8[1]; array_tmp10[1] := array_const_1D0[1] + array_tmp9[1]; array_tmp11[1] := array_const_2D0[1]*array_x[1]; array_tmp12[1] := array_tmp11[1] + array_const_1D0[1]; array_tmp13[1] := sqrt(array_tmp12[1]); array_tmp14[1] := array_tmp10[1]/array_tmp13[1]; array_tmp15[1] := array_const_0D0[1] + array_tmp14[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp15[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_2D0[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0); array_tmp4_a1[2] := att(1, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[2] := -att(1, array_tmp4_a1, array_tmp3, 1); array_tmp4[2] := ( array_tmp4_a1[2] - ats(2, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp5[2] := array_const_2D0[1]*array_x[2]; array_tmp6[2] := array_tmp5[2]; array_tmp7[2] := array_tmp6[2]/(array_tmp7[1]*2.0); array_tmp8_a1[2] := att(1, array_tmp8_a2, array_tmp7, 1); array_tmp8_a2[2] := -att(1, array_tmp8_a1, array_tmp7, 1); array_tmp8[2] := ( array_tmp8_a1[2] - ats(2, array_tmp8_a2, array_tmp8, 2))/ array_tmp8_a2[1]; array_tmp9[2] := ats(2, array_tmp4, array_tmp8, 1); array_tmp10[2] := array_tmp9[2]; array_tmp11[2] := array_const_2D0[1]*array_x[2]; array_tmp12[2] := array_tmp11[2]; array_tmp13[2] := array_tmp12[2]/(array_tmp13[1]*2.0); array_tmp14[2] := (array_tmp10[2] - ats(2, array_tmp13, array_tmp14, 2) )/array_tmp13[1]; array_tmp15[2] := array_tmp14[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp15[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp3[3] := 0.; array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4_a1[3] := att(2, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[3] := -att(2, array_tmp4_a1, array_tmp3, 1); array_tmp4[3] := ( array_tmp4_a1[3] - ats(3, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp7[3] := 0.; array_tmp7[3] := -ats(3, array_tmp7, array_tmp7, 2)/(array_tmp7[1]*2.0) ; array_tmp8_a1[3] := att(2, array_tmp8_a2, array_tmp7, 1); array_tmp8_a2[3] := -att(2, array_tmp8_a1, array_tmp7, 1); array_tmp8[3] := ( array_tmp8_a1[3] - ats(3, array_tmp8_a2, array_tmp8, 2))/ array_tmp8_a2[1]; array_tmp9[3] := ats(3, array_tmp4, array_tmp8, 1); array_tmp10[3] := array_tmp9[3]; array_tmp13[3] := 0.; array_tmp13[3] := -ats(3, array_tmp13, array_tmp13, 2)/(array_tmp13[1]*2.0); array_tmp14[3] := (array_tmp10[3] - ats(3, array_tmp13, array_tmp14, 2) )/array_tmp13[1]; array_tmp15[3] := array_tmp14[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp15[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp3[4] := 0.; array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4_a1[4] := att(3, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[4] := -att(3, array_tmp4_a1, array_tmp3, 1); array_tmp4[4] := ( array_tmp4_a1[4] - ats(4, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp7[4] := 0.; array_tmp7[4] := -ats(4, array_tmp7, array_tmp7, 2)/(array_tmp7[1]*2.0) ; array_tmp8_a1[4] := att(3, array_tmp8_a2, array_tmp7, 1); array_tmp8_a2[4] := -att(3, array_tmp8_a1, array_tmp7, 1); array_tmp8[4] := ( array_tmp8_a1[4] - ats(4, array_tmp8_a2, array_tmp8, 2))/ array_tmp8_a2[1]; array_tmp9[4] := ats(4, array_tmp4, array_tmp8, 1); array_tmp10[4] := array_tmp9[4]; array_tmp13[4] := 0.; array_tmp13[4] := -ats(4, array_tmp13, array_tmp13, 2)/(array_tmp13[1]*2.0); array_tmp14[4] := (array_tmp10[4] - ats(4, array_tmp13, array_tmp14, 2) )/array_tmp13[1]; array_tmp15[4] := array_tmp14[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp15[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp3[5] := 0.; array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4_a1[5] := att(4, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[5] := -att(4, array_tmp4_a1, array_tmp3, 1); array_tmp4[5] := ( array_tmp4_a1[5] - ats(5, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp7[5] := 0.; array_tmp7[5] := -ats(5, array_tmp7, array_tmp7, 2)/(array_tmp7[1]*2.0) ; array_tmp8_a1[5] := att(4, array_tmp8_a2, array_tmp7, 1); array_tmp8_a2[5] := -att(4, array_tmp8_a1, array_tmp7, 1); array_tmp8[5] := ( array_tmp8_a1[5] - ats(5, array_tmp8_a2, array_tmp8, 2))/ array_tmp8_a2[1]; array_tmp9[5] := ats(5, array_tmp4, array_tmp8, 1); array_tmp10[5] := array_tmp9[5]; array_tmp13[5] := 0.; array_tmp13[5] := -ats(5, array_tmp13, array_tmp13, 2)/(array_tmp13[1]*2.0); array_tmp14[5] := (array_tmp10[5] - ats(5, array_tmp13, array_tmp14, 2) )/array_tmp13[1]; array_tmp15[5] := array_tmp14[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp15[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp3[kkk] := 0.; array_tmp3[kkk] := -ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0); array_tmp4_a1[kkk] := att(kkk - 1, array_tmp4_a2, array_tmp3, 1); array_tmp4_a2[kkk] := -att(kkk - 1, array_tmp4_a1, array_tmp3, 1); array_tmp4[kkk] := ( array_tmp4_a1[kkk] - ats(kkk, array_tmp4_a2, array_tmp4, 2))/ array_tmp4_a2[1]; array_tmp7[kkk] := 0.; array_tmp7[kkk] := -ats(kkk, array_tmp7, array_tmp7, 2)/(array_tmp7[1]*2.0); array_tmp8_a1[kkk] := att(kkk - 1, array_tmp8_a2, array_tmp7, 1); array_tmp8_a2[kkk] := -att(kkk - 1, array_tmp8_a1, array_tmp7, 1); array_tmp8[kkk] := ( array_tmp8_a1[kkk] - ats(kkk, array_tmp8_a2, array_tmp8, 2))/ array_tmp8_a2[1]; array_tmp9[kkk] := ats(kkk, array_tmp4, array_tmp8, 1); array_tmp10[kkk] := array_tmp9[kkk]; array_tmp13[kkk] := 0.; array_tmp13[kkk] := -ats(kkk, array_tmp13, array_tmp13, 2)/(array_tmp13[1]*2.0); array_tmp14[kkk] := ( array_tmp10[kkk] - ats(kkk, array_tmp13, array_tmp14, 2))/ array_tmp13[1]; array_tmp15[kkk] := array_tmp14[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp15[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 12 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, "\n") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 6 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # End Function number 16 > # Begin Function number 17 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 20 > # Begin Function number 21 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 21 > # Begin Function number 22 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 8 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 24 > # Begin Function number 25 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc > # End Function number 25 > # Begin Function number 26 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 8 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 8; > if (glob_max_iter < 2) then # if number 8 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 8; > if (errflag) then # if number 8 > quit; > fi;# end if 8 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 26 > # Begin Function number 27 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 8 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 9 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 9 > fi;# end if 8; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 27 > # Begin Function number 28 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 8 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 8; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 28 > # Begin Function number 29 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 29 > # Begin Function number 30 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 8 > if (array_fact_1[nnn] = 0) then # if number 9 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 9; > else > ret := factorial_2(nnn); > fi;# end if 8; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 8 > if (array_fact_2[mmm,nnn] = 0) then # if number 9 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 9; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 8; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 31 > # Begin Function number 32 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 33 > # Begin Function number 34 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 34 > # Begin Function number 35 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 35 > # Begin Function number 36 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 36 > # Begin Function number 37 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 37 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(tan(sqrt(2.0*x + 1.0))); > end; exact_soln_y := proc(x) return tan(sqrt(2.0*x + 1.0)) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > array_const_2D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8_g, > array_tmp8_a1, > array_tmp8_a2, > array_tmp8, > array_tmp9, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_value3 := 0.0; > glob_ratio_of_radius := 0.01; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.1e-200; > glob_smallish_float := 0.1e-100; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/tan_sqrt_newpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 1.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.001;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(tan(sqrt(2.0*x + 1.0)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4_g:= Array(0..(max_terms + 1),[]); > array_tmp4_a1:= Array(0..(max_terms + 1),[]); > array_tmp4_a2:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_tmp6:= Array(0..(max_terms + 1),[]); > array_tmp7:= Array(0..(max_terms + 1),[]); > array_tmp8_g:= Array(0..(max_terms + 1),[]); > array_tmp8_a1:= Array(0..(max_terms + 1),[]); > array_tmp8_a2:= Array(0..(max_terms + 1),[]); > array_tmp8:= Array(0..(max_terms + 1),[]); > array_tmp9:= Array(0..(max_terms + 1),[]); > array_tmp10:= Array(0..(max_terms + 1),[]); > array_tmp11:= Array(0..(max_terms + 1),[]); > array_tmp12:= Array(0..(max_terms + 1),[]); > array_tmp13:= Array(0..(max_terms + 1),[]); > array_tmp14:= Array(0..(max_terms + 1),[]); > array_tmp15:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4_a1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4_a2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp8_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp8_a1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp8_a2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4_a1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4_a2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4_a2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp7 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp8_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp8_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp8_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp8_a1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp8_a2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp8_a2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp8 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp9 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp9[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp10 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp11 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp12 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp13 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp14 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp15 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D0[1] := 0.0; > array_const_1D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1D0[1] := 1.0; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_2D0[1] := 2.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3; > iiif := iiif + 1; > od;# end do number 2; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 1.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.001; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > if (glob_display_interval < glob_h) then # if number 2 > glob_h := glob_display_interval; > fi;# end if 2; > if (glob_max_h < glob_h) then # if number 2 > glob_h := glob_max_h; > fi;# end if 2; > found_h := -1.0; > best_h := 0.0; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 3 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 4; > r_order := r_order + 1; > od;# end do number 3 > ; > atomall(); > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > value3 := test_suggested_h(); > omniout_float(ALWAYS,"value3",32,value3,32,""); > if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2 > best_h := glob_h; > found_h := 1.0; > fi;# end if 2; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > glob_h := glob_h * 0.5; > od;# end do number 2; > if (found_h > 0.0) then # if number 2 > glob_h := best_h ; > else > omniout_str(ALWAYS,"No increment to obtain desired accuracy found"); > fi;# end if 2; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2; > #BEGIN SOLUTION CODE > if (found_h > 0.0) then # if number 2 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > if (reached_interval()) then # if number 3 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 3; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 3 > #left paren 0004C > check_for_pole(); > fi;# end if 3;#was right paren 0004C > if (reached_interval()) then # if number 3 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 3; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 2;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 3 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 3; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 3; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 3 > logstart(html_log_file); > logitem_str(html_log_file,"2013-01-28T20:26:18-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"tan_sqrt_new") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 4 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 4; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 4 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 4; > log_revs(html_log_file," 165 ") > ; > logitem_str(html_log_file,"tan_sqrt_new diffeq.mxt") > ; > logitem_str(html_log_file,"tan_sqrt_new maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 3; > if (glob_html_log) then # if number 3 > fclose(html_log_file); > fi;# end if 3 > ; > ;; > fi;# end if 2 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_const_2D0, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8_g, array_tmp8_a1, array_tmp8_a2, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_value3 := 0.; glob_ratio_of_radius := 0.01; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.1*10^(-200); glob_smallish_float := 0.1*10^(-100); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/tan_sqrt_newpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 \ * x + 1.0 ) ) * tan( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 *\ x + 1.0 ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 1.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.001;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(tan(sqrt(2.0*x + 1.0)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4_g := Array(0 .. max_terms + 1, []); array_tmp4_a1 := Array(0 .. max_terms + 1, []); array_tmp4_a2 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_tmp6 := Array(0 .. max_terms + 1, []); array_tmp7 := Array(0 .. max_terms + 1, []); array_tmp8_g := Array(0 .. max_terms + 1, []); array_tmp8_a1 := Array(0 .. max_terms + 1, []); array_tmp8_a2 := Array(0 .. max_terms + 1, []); array_tmp8 := Array(0 .. max_terms + 1, []); array_tmp9 := Array(0 .. max_terms + 1, []); array_tmp10 := Array(0 .. max_terms + 1, []); array_tmp11 := Array(0 .. max_terms + 1, []); array_tmp12 := Array(0 .. max_terms + 1, []); array_tmp13 := Array(0 .. max_terms + 1, []); array_tmp14 := Array(0 .. max_terms + 1, []); array_tmp15 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_a2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp7[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8_a2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp9[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp10[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp11[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp12[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp13[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp14[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp15[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_g[term] := 0.; term := term + 1 end do; array_tmp4_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_a1[term] := 0.; term := term + 1 end do; array_tmp4_a2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_a2[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp7 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1 end do; array_tmp8_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8_g[term] := 0.; term := term + 1 end do; array_tmp8_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8_a1[term] := 0.; term := term + 1 end do; array_tmp8_a2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8_a2[term] := 0.; term := term + 1 end do; array_tmp8 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1 end do; array_tmp9 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1 end do; array_tmp10 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10[term] := 0.; term := term + 1 end do; array_tmp11 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp11[term] := 0.; term := term + 1 end do; array_tmp12 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp12[term] := 0.; term := term + 1 end do; array_tmp13 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp13[term] := 0.; term := term + 1 end do; array_tmp14 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp14[term] := 0.; term := term + 1 end do; array_tmp15 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp15[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1D0[term] := 0.; term := term + 1 end do; array_const_1D0[1] := 1.0; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 1.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_desired_digits_correct := 10; glob_display_interval := 0.001; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_max_h < glob_h then glob_h := glob_max_h end if; found_h := -1.0; best_h := 0.; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; while opt_iter <= 20 and found_h < 0. do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); value3 := test_suggested_h(); omniout_float(ALWAYS, "value3", 32, value3, 32, ""); if value3 < est_needed_step_err and found_h < 0. then best_h := glob_h; found_h := 1.0 end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1; glob_h := glob_h*0.5 end do; if 0. < found_h then glob_h := best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found") end if; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; if 0. < found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.\ 0 * x + 1.0 ) ) * tan( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt (\ 2.0 * x + 1.0 ) ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-01-28T20:26:18-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "tan_sqrt_new"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ( 1.0 + ( ta\ n ( sqrt ( 2.0 * x + 1.0 ) ) * tan( sqrt ( 2.0 * x + 1.0\ ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 165 "); logitem_str(html_log_file, "tan_sqrt_new diffeq.mxt"); logitem_str(html_log_file, "tan_sqrt_new maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/tan_sqrt_newpostode.ode################# diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 1.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.001; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(tan(sqrt(2.0*x + 1.0))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 memory used=3.8MB, alloc=2.8MB, time=0.14 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 0.9 estimated_steps = 900 step_error = 1.1111111111111111111111111111111e-13 est_needed_step_err = 1.1111111111111111111111111111111e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 3.4987749660157723633064599663529e-73 max_value3 = 3.4987749660157723633064599663529e-73 value3 = 3.4987749660157723633064599663529e-73 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.9428178495783909218790748349977 y[1] (numeric) = 1.9428178495783909218790748349977 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4448 Order of pole = 453.1 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.8MB, time=0.27 x[1] = 0.101 y[1] (analytic) = 1.9471823134389631452589090373945 y[1] (numeric) = 1.9471823134389631452589090373943 absolute error = 2e-31 relative error = 1.0271251881226028252481634083653e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4552 Order of pole = 464.8 TOP MAIN SOLVE Loop x[1] = 0.102 y[1] (analytic) = 1.9515586654531525990372423182078 y[1] (numeric) = 1.9515586654531525990372423182076 absolute error = 2e-31 relative error = 1.0248218695160769385728838035371e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4651 Order of pole = 476 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=3.9MB, time=0.41 x[1] = 0.103 y[1] (analytic) = 1.9559469661196914130190304516191 y[1] (numeric) = 1.955946966119691413019030451619 absolute error = 1e-31 relative error = 5.1126130581334300445712919600595e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4746 Order of pole = 486.7 TOP MAIN SOLVE Loop x[1] = 0.104 y[1] (analytic) = 1.9603472763054889150974699653473 y[1] (numeric) = 1.9603472763054889150974699653473 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4836 Order of pole = 497 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=3.9MB, time=0.55 x[1] = 0.105 y[1] (analytic) = 1.9647596572486519509309227817794 y[1] (numeric) = 1.9647596572486519509309227817793 absolute error = 1e-31 relative error = 5.0896810523906440718957179535094e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4922 Order of pole = 506.8 TOP MAIN SOLVE Loop x[1] = 0.106 y[1] (analytic) = 1.9691841705615333921812335989365 y[1] (numeric) = 1.9691841705615333921812335989364 absolute error = 1e-31 relative error = 5.0782451684792874219661564738432e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5002 Order of pole = 516.2 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.0MB, time=0.69 x[1] = 0.107 y[1] (analytic) = 1.9736208782338091543332063137118 y[1] (numeric) = 1.9736208782338091543332063137119 absolute error = 1e-31 relative error = 5.0668292529155789246900421979762e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5079 Order of pole = 525.1 TOP MAIN SOLVE Loop x[1] = 0.108 y[1] (analytic) = 1.9780698426355840491535941771793 y[1] (numeric) = 1.9780698426355840491535941771794 absolute error = 1e-31 relative error = 5.0554332230635399788172241745388e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.515 Order of pole = 533.6 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.0MB, time=0.83 x[1] = 0.109 y[1] (analytic) = 1.9825311265205268009455416770191 y[1] (numeric) = 1.9825311265205268009455416770191 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5217 Order of pole = 541.6 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 1.9870047930290345599119289346476 y[1] (numeric) = 1.9870047930290345599119289346477 absolute error = 1e-31 relative error = 5.0327004922598985175365330559882e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.528 Order of pole = 549.1 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.0MB, time=0.97 x[1] = 0.111 y[1] (analytic) = 1.9914909056914272501594629392249 y[1] (numeric) = 1.9914909056914272501594629392251 absolute error = 2e-31 relative error = 1.0042727256671144430267123738657e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5338 Order of pole = 556.2 TOP MAIN SOLVE Loop x[1] = 0.112 y[1] (analytic) = 1.9959895284311720941556024764486 y[1] (numeric) = 1.9959895284311720941556024764487 absolute error = 1e-31 relative error = 5.0100463241707988733449398242353e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5393 Order of pole = 562.9 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.0MB, time=1.11 x[1] = 0.113 y[1] (analytic) = 2.0005007255681386597934807361787 y[1] (numeric) = 2.0005007255681386597934807361788 absolute error = 1e-31 relative error = 4.9987484994088256213459742082526e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5443 Order of pole = 569.2 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.1MB, time=1.26 x[1] = 0.114 y[1] (analytic) = 2.005024561821884780626904551494 y[1] (numeric) = 2.005024561821884780626904551494 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5489 Order of pole = 575.1 TOP MAIN SOLVE Loop x[1] = 0.115 y[1] (analytic) = 2.0095611023149737043092832872775 y[1] (numeric) = 2.0095611023149737043092832872774 absolute error = 1e-31 relative error = 4.9762109688927609416393647038157e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5532 Order of pole = 580.7 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.1MB, time=1.40 x[1] = 0.116 y[1] (analytic) = 2.0141104125763228288080131628091 y[1] (numeric) = 2.014110412576322828808013162809 absolute error = 1e-31 relative error = 4.9649711046419901075525954473591e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5571 Order of pole = 585.8 TOP MAIN SOLVE Loop x[1] = 0.117 y[1] (analytic) = 2.0186725585445843905704725676912 y[1] (numeric) = 2.0186725585445843905704725676913 absolute error = 1e-31 relative error = 4.9537504027942826257293594163954e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5607 Order of pole = 590.7 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.1MB, time=1.54 x[1] = 0.118 y[1] (analytic) = 2.0232476065715584734904480868393 y[1] (numeric) = 2.0232476065715584734904480868395 absolute error = 2e-31 relative error = 9.8850975703811551784773542574503e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5639 Order of pole = 595.2 TOP MAIN SOLVE Loop x[1] = 0.119 y[1] (analytic) = 2.0278356234256387122656062962976 y[1] (numeric) = 2.0278356234256387122656062962978 absolute error = 2e-31 relative error = 9.8627323482037672556905314713268e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5669 Order of pole = 599.4 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.1MB, time=1.68 x[1] = 0.12 y[1] (analytic) = 2.0324366762952910685486695477345 y[1] (numeric) = 2.0324366762952910685486695477346 absolute error = 1e-31 relative error = 4.9202024922261873946791059336725e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5696 Order of pole = 603.3 TOP MAIN SOLVE Loop x[1] = 0.121 y[1] (analytic) = 2.0370508327925660631783817438778 y[1] (numeric) = 2.0370508327925660631783817438777 absolute error = 1e-31 relative error = 4.9090576626853892344939641546108e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.572 Order of pole = 606.9 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.1MB, time=1.82 x[1] = 0.122 y[1] (analytic) = 2.0416781609566448527323199296143 y[1] (numeric) = 2.0416781609566448527323199296143 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5742 Order of pole = 610.3 TOP MAIN SOLVE Loop x[1] = 0.123 y[1] (analytic) = 2.046318729257419543673297787348 y[1] (numeric) = 2.0463187292574195436732977873478 absolute error = 2e-31 relative error = 9.7736485103949179856384599147401e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5761 Order of pole = 613.4 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.1MB, time=1.97 x[1] = 0.124 y[1] (analytic) = 2.0509726065991081424657176381415 y[1] (numeric) = 2.0509726065991081424657176381416 absolute error = 1e-31 relative error = 4.8757355255864919856037157100032e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5779 Order of pole = 616.3 TOP MAIN SOLVE Loop x[1] = 0.125 y[1] (analytic) = 2.0556398623239045452189799437286 y[1] (numeric) = 2.0556398623239045452189799437289 absolute error = 3e-31 relative error = 1.4593996034930430995591513885137e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5794 Order of pole = 619 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.1MB, time=2.11 x[1] = 0.126 y[1] (analytic) = 2.0603205662156639756731974626111 y[1] (numeric) = 2.0603205662156639756731974626113 absolute error = 2e-31 relative error = 9.7072272771296992298483427853059e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5807 Order of pole = 621.5 TOP MAIN SOLVE Loop x[1] = 0.127 y[1] (analytic) = 2.0650147885036242856792517104042 y[1] (numeric) = 2.0650147885036242856792517104041 absolute error = 1e-31 relative error = 4.8425803319531283373432733569089e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5819 Order of pole = 623.8 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.1MB, time=2.25 x[1] = 0.128 y[1] (analytic) = 2.0697225998661635377419619219803 y[1] (numeric) = 2.0697225998661635377419619219804 absolute error = 1e-31 relative error = 4.8315653511473661319473822051105e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5829 Order of pole = 625.9 TOP MAIN SOLVE Loop x[1] = 0.129 y[1] (analytic) = 2.0744440714345942946931246168256 y[1] (numeric) = 2.0744440714345942946931246168255 absolute error = 1e-31 relative error = 4.8205686225536269854254842543502e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5837 Order of pole = 627.9 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.1MB, time=2.39 x[1] = 0.13 y[1] (analytic) = 2.0791792747969950471417624964508 y[1] (numeric) = 2.0791792747969950471417624964507 absolute error = 1e-31 relative error = 4.8095900729754872176820038075493e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5844 Order of pole = 629.7 TOP MAIN SOLVE Loop x[1] = 0.131 y[1] (analytic) = 2.0839282820020792150134566588438 y[1] (numeric) = 2.083928282002079215013456658844 absolute error = 2e-31 relative error = 9.5972592592224559263696334524886e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5849 Order of pole = 631.4 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.1MB, time=2.53 x[1] = 0.132 y[1] (analytic) = 2.0886911655631021652405129300577 y[1] (numeric) = 2.0886911655631021652405129300576 absolute error = 1e-31 relative error = 4.7876872200510519035469375296999e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5854 Order of pole = 633 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.1MB, time=2.68 x[1] = 0.133 y[1] (analytic) = 2.093467998461806693501343940472 y[1] (numeric) = 2.093467998461806693501343940472 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5857 Order of pole = 634.4 TOP MAIN SOLVE Loop x[1] = 0.134 y[1] (analytic) = 2.0982588541524074238322718979919 y[1] (numeric) = 2.098258854152407423832271897992 absolute error = 1e-31 relative error = 4.7658562146468360056640812687606e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5859 Order of pole = 635.7 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.1MB, time=2.82 x[1] = 0.135 y[1] (analytic) = 2.1030638065656145859494378687282 y[1] (numeric) = 2.1030638065656145859494378687282 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.586 Order of pole = 637 TOP MAIN SOLVE Loop x[1] = 0.136 y[1] (analytic) = 2.1078829301126976362241338863224 y[1] (numeric) = 2.1078829301126976362241338863224 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5861 Order of pole = 638.1 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.1MB, time=2.96 x[1] = 0.137 y[1] (analytic) = 2.1127162996895891944531741177715 y[1] (numeric) = 2.1127162996895891944531741177718 absolute error = 3e-31 relative error = 1.4199729516172024363925245534089e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.586 Order of pole = 639.1 TOP MAIN SOLVE Loop x[1] = 0.138 y[1] (analytic) = 2.11756399068102977485843853979 y[1] (numeric) = 2.1175639906810297748584385397902 absolute error = 2e-31 relative error = 9.4448149326376672153582244912831e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5859 Order of pole = 640.1 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.1MB, time=3.11 x[1] = 0.139 y[1] (analytic) = 2.1224260789647537961380337951145 y[1] (numeric) = 2.1224260789647537961380337951149 absolute error = 4e-31 relative error = 1.8846357193043264781558234935294e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5857 Order of pole = 640.9 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 2.1273026409157173618772270978666 y[1] (numeric) = 2.1273026409157173618772270978665 absolute error = 1e-31 relative error = 4.7007885985114963547586745296864e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5854 Order of pole = 641.8 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.1MB, time=3.25 x[1] = 0.141 y[1] (analytic) = 2.1321937534103683092120561535622 y[1] (numeric) = 2.1321937534103683092120561535624 absolute error = 2e-31 relative error = 9.3800105961340094552248299524403e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5851 Order of pole = 642.5 TOP MAIN SOLVE Loop x[1] = 0.142 y[1] (analytic) = 2.1370994938309590303239674873612 y[1] (numeric) = 2.1370994938309590303239674873615 absolute error = 3e-31 relative error = 1.4037717984866524637434834571815e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5847 Order of pole = 643.2 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.1MB, time=3.40 x[1] = 0.143 y[1] (analytic) = 2.1420199400699025781316849087745 y[1] (numeric) = 2.1420199400699025781316849087747 absolute error = 2e-31 relative error = 9.3369812418026887925379495594303e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5843 Order of pole = 643.8 TOP MAIN SOLVE Loop x[1] = 0.144 y[1] (analytic) = 2.1469551705341725744384884300015 y[1] (numeric) = 2.1469551705341725744384884300018 absolute error = 3e-31 relative error = 1.3973277323967532344195762093864e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5838 Order of pole = 644.4 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.1MB, time=3.54 x[1] = 0.145 y[1] (analytic) = 2.151905264149747445790953564179 y[1] (numeric) = 2.1519052641497474457909535641789 absolute error = 1e-31 relative error = 4.6470447219948419264636087309521e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5833 Order of pole = 644.9 TOP MAIN SOLVE Loop x[1] = 0.146 y[1] (analytic) = 2.1568703003660995194107564035924 y[1] (numeric) = 2.1568703003660995194107564035928 absolute error = 4e-31 relative error = 1.8545389582864830484442174102611e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5828 Order of pole = 645.4 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.1MB, time=3.69 x[1] = 0.147 y[1] (analytic) = 2.1618503591607295187762198142381 y[1] (numeric) = 2.1618503591607295187762198142384 absolute error = 3e-31 relative error = 1.3877001186912195654505322586318e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5822 Order of pole = 645.9 TOP MAIN SOLVE Loop x[1] = 0.148 y[1] (analytic) = 2.1668455210437470057567235231665 y[1] (numeric) = 2.1668455210437470057567235231664 absolute error = 1e-31 relative error = 4.6150036552596992485492711020265e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5816 Order of pole = 646.3 TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.1MB, time=3.83 x[1] = 0.149 y[1] (analytic) = 2.1718558670624973236428240086909 y[1] (numeric) = 2.171855867062497323642824008691 absolute error = 1e-31 relative error = 4.6043571084324814468119388741371e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5809 Order of pole = 646.7 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 2.176881478806235602969862990075 y[1] (numeric) = 2.1768814788062356029698629900749 absolute error = 1e-31 relative error = 4.5937273560174843176473979165987e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5802 Order of pole = 647 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.1MB, time=3.97 x[1] = 0.151 y[1] (analytic) = 2.1819224384108483997049566188606 y[1] (numeric) = 2.1819224384108483997049566188609 absolute error = 3e-31 relative error = 1.3749342997659344127619768016058e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5795 Order of pole = 647.3 TOP MAIN SOLVE Loop x[1] = 0.152 y[1] (analytic) = 2.186978828563623543158559224946 y[1] (numeric) = 2.1869788285636235431585592249461 absolute error = 1e-31 relative error = 4.5725179729187671948268771610723e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5788 Order of pole = 647.6 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.1MB, time=4.12 x[1] = 0.153 y[1] (analytic) = 2.1920507325080687788943318240068 y[1] (numeric) = 2.192050732508068778894331824007 absolute error = 2e-31 relative error = 9.1238764246649941339668202196039e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.578 Order of pole = 647.9 TOP MAIN SOLVE Loop x[1] = 0.154 y[1] (analytic) = 2.1971382340487797999469016248096 y[1] (numeric) = 2.1971382340487797999469016248096 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5772 Order of pole = 648.2 memory used=114.4MB, alloc=4.1MB, time=4.26 TOP MAIN SOLVE Loop x[1] = 0.155 y[1] (analytic) = 2.2022414175563582678183992853004 y[1] (numeric) = 2.2022414175563582678183992853007 absolute error = 3e-31 relative error = 1.3622484692567662309595186348627e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5764 Order of pole = 648.4 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.1MB, time=4.40 x[1] = 0.156 y[1] (analytic) = 2.2073603679723804330135710030591 y[1] (numeric) = 2.2073603679723804330135710030593 absolute error = 2e-31 relative error = 9.0605957641485795361733415509169e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5756 Order of pole = 648.6 TOP MAIN SOLVE Loop x[1] = 0.157 y[1] (analytic) = 2.2124951708144169732919894267429 y[1] (numeric) = 2.2124951708144169732919894267431 absolute error = 2e-31 relative error = 9.0395677531074667117335887385003e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5748 Order of pole = 648.8 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.1MB, time=4.55 x[1] = 0.158 y[1] (analytic) = 2.2176459121811046763666798301391 y[1] (numeric) = 2.2176459121811046763666798301394 absolute error = 3e-31 relative error = 1.3527858453514034919043508152556e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.574 Order of pole = 649 TOP MAIN SOLVE Loop x[1] = 0.159 y[1] (analytic) = 2.2228126787572706024636281212005 y[1] (numeric) = 2.2228126787572706024636281212009 absolute error = 4e-31 relative error = 1.7995218572517404901235260435920e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5731 Order of pole = 649.1 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.1MB, time=4.69 x[1] = 0.16 y[1] (analytic) = 2.2279955578191093709784812200598 y[1] (numeric) = 2.2279955578191093709784812200599 absolute error = 1e-31 relative error = 4.4883392899528835225000812439799e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5722 Order of pole = 649.3 TOP MAIN SOLVE Loop x[1] = 0.161 y[1] (analytic) = 2.2331946372394142244276692419634 y[1] (numeric) = 2.2331946372394142244276692419636 absolute error = 2e-31 relative error = 8.9557800589756023415685689117333e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5714 Order of pole = 649.4 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.1MB, time=4.84 x[1] = 0.162 y[1] (analytic) = 2.2384100054928625319935997695935 y[1] (numeric) = 2.238410005492862531993599769594 absolute error = 5e-31 relative error = 2.2337283999492662047027404897761e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5705 Order of pole = 649.6 TOP MAIN SOLVE Loop x[1] = 0.163 y[1] (analytic) = 2.2436417516613564042099711610368 y[1] (numeric) = 2.2436417516613564042099711610368 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5696 Order of pole = 649.7 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.1MB, time=4.98 x[1] = 0.164 y[1] (analytic) = 2.2488899654394190997261460277223 y[1] (numeric) = 2.2488899654394190997261460277228 absolute error = 5e-31 relative error = 2.2233190937925818551116674399081e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5687 Order of pole = 649.8 TOP MAIN SOLVE Loop x[1] = 0.165 y[1] (analytic) = 2.254154737139647914631488298539 y[1] (numeric) = 2.2541547371396479146314882985392 absolute error = 2e-31 relative error = 8.8725053655271639535841858785806e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5678 Order of pole = 649.9 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.1MB, time=5.13 x[1] = 0.166 y[1] (analytic) = 2.2594361576982242545142181155843 y[1] (numeric) = 2.2594361576982242545142181155845 absolute error = 2e-31 relative error = 8.8517659292373103033970451897652e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5668 Order of pole = 650 TOP MAIN SOLVE Loop x[1] = 0.167 y[1] (analytic) = 2.2647343186804815992773495784526 y[1] (numeric) = 2.2647343186804815992773495784528 absolute error = 2e-31 relative error = 8.8310579457517751827364178123512e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5659 Order of pole = 650.1 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.1MB, time=5.28 x[1] = 0.168 y[1] (analytic) = 2.2700493122865320807393704827587 y[1] (numeric) = 2.2700493122865320807393704827589 absolute error = 2e-31 relative error = 8.8103812951335319342164842565638e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.565 Order of pole = 650.1 TOP MAIN SOLVE Loop x[1] = 0.169 y[1] (analytic) = 2.2753812313569524032122772249263 y[1] (numeric) = 2.2753812313569524032122772249264 absolute error = 1e-31 relative error = 4.3948679290267211186877141281923e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.564 Order of pole = 650.2 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.1MB, time=5.42 x[1] = 0.17 y[1] (analytic) = 2.2807301693785298475772227636794 y[1] (numeric) = 2.2807301693785298475772227636795 absolute error = 1e-31 relative error = 4.3845607578931065056743457642494e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5631 Order of pole = 650.3 TOP MAIN SOLVE Loop x[1] = 0.171 y[1] (analytic) = 2.286096220490069109871257144247 y[1] (numeric) = 2.2860962204900691098712571442473 absolute error = 3e-31 relative error = 1.3122807225309579289746794944913e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5621 Order of pole = 650.3 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.1MB, time=5.56 x[1] = 0.172 y[1] (analytic) = 2.2914794794882607360603814020854 y[1] (numeric) = 2.2914794794882607360603814020855 absolute error = 1e-31 relative error = 4.3639928218921805376642009250822e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5612 Order of pole = 650.4 TOP MAIN SOLVE Loop x[1] = 0.173 y[1] (analytic) = 2.2968800418336119255073972701783 y[1] (numeric) = 2.2968800418336119255073972701785 absolute error = 2e-31 relative error = 8.7074638795824488898744203864243e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5602 Order of pole = 650.4 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.1MB, time=5.71 x[1] = 0.174 y[1] (analytic) = 2.3022980036564404866508766602483 y[1] (numeric) = 2.3022980036564404866508766602484 absolute error = 1e-31 relative error = 4.3434863706254796647648224112767e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5593 Order of pole = 650.5 TOP MAIN SOLVE Loop x[1] = 0.175 y[1] (analytic) = 2.3077334617629327395971163243918 y[1] (numeric) = 2.3077334617629327395971163243922 absolute error = 4e-31 relative error = 1.7333024226048637400121974573499e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5583 Order of pole = 650.5 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.1MB, time=5.85 x[1] = 0.176 y[1] (analytic) = 2.3131865136412661716933659856682 y[1] (numeric) = 2.3131865136412661716933659856682 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5573 Order of pole = 650.6 TOP MAIN SOLVE Loop x[1] = 0.177 y[1] (analytic) = 2.318657257467797663701167041657 y[1] (numeric) = 2.318657257467797663701167041657 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5564 Order of pole = 650.6 memory used=160.2MB, alloc=4.1MB, time=6.00 TOP MAIN SOLVE Loop x[1] = 0.178 y[1] (analytic) = 2.3241457921133181159266224715189 y[1] (numeric) = 2.3241457921133181159266224715194 absolute error = 5e-31 relative error = 2.1513280349997146652036316867001e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5554 Order of pole = 650.6 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.1MB, time=6.14 x[1] = 0.179 y[1] (analytic) = 2.3296522171493743155932112715882 y[1] (numeric) = 2.3296522171493743155932112715887 absolute error = 5e-31 relative error = 2.1462431015210226143440045452467e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5544 Order of pole = 650.7 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 2.335176632854658898865804166096 y[1] (numeric) = 2.3351766328546588988658041660963 absolute error = 3e-31 relative error = 1.2846993918111545372903125014830e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5534 Order of pole = 650.7 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.1MB, time=6.28 x[1] = 0.181 y[1] (analytic) = 2.3407191402214692732553416051369 y[1] (numeric) = 2.3407191402214692732553416051369 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5525 Order of pole = 650.7 TOP MAIN SOLVE Loop x[1] = 0.182 y[1] (analytic) = 2.3462798409622363786557803364655 y[1] (numeric) = 2.3462798409622363786557803364659 absolute error = 4e-31 relative error = 1.7048264789930402942119862983096e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5515 Order of pole = 650.7 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.1MB, time=6.43 x[1] = 0.183 y[1] (analytic) = 2.3518588375161241779920528597323 y[1] (numeric) = 2.3518588375161241779920528597328 absolute error = 5e-31 relative error = 2.1259779372135553834375024448540e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5505 Order of pole = 650.8 TOP MAIN SOLVE Loop x[1] = 0.184 y[1] (analytic) = 2.3574562330557007813936397149081 y[1] (numeric) = 2.3574562330557007813936397149081 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5495 Order of pole = 650.8 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.1MB, time=6.57 x[1] = 0.185 y[1] (analytic) = 2.3630721314936821209567274281254 y[1] (numeric) = 2.3630721314936821209567274281254 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5485 Order of pole = 650.8 TOP MAIN SOLVE Loop x[1] = 0.186 y[1] (analytic) = 2.3687066374897491065226910151747 y[1] (numeric) = 2.3687066374897491065226910151747 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5475 Order of pole = 650.8 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.1MB, time=6.71 x[1] = 0.187 y[1] (analytic) = 2.3743598564574392064857532481346 y[1] (numeric) = 2.374359856457439206485753248135 absolute error = 4e-31 relative error = 1.6846646009118545178790468446345e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5466 Order of pole = 650.8 TOP MAIN SOLVE Loop x[1] = 0.188 y[1] (analytic) = 2.3800318945711134114521672076296 y[1] (numeric) = 2.3800318945711134114521672076297 absolute error = 1e-31 relative error = 4.2016243659633898900659435203751e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5456 Order of pole = 650.8 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.1MB, time=6.86 x[1] = 0.189 y[1] (analytic) = 2.3857228587729995526112592725165 y[1] (numeric) = 2.3857228587729995526112592725167 absolute error = 2e-31 relative error = 8.3832034079122645167843026370257e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5446 Order of pole = 650.9 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 2.3914328567803129609493552564749 y[1] (numeric) = 2.3914328567803129609493552564749 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5436 Order of pole = 650.9 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.1MB, time=7.00 x[1] = 0.191 y[1] (analytic) = 2.3971619970924554679452766596989 y[1] (numeric) = 2.3971619970924554679452766596991 absolute error = 2e-31 relative error = 8.3431991764670986547343831994714e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5426 Order of pole = 650.9 TOP MAIN SOLVE Loop x[1] = 0.192 y[1] (analytic) = 2.4029103889982937631351077789197 y[1] (numeric) = 2.4029103889982937631351077789201 absolute error = 4e-31 relative error = 1.6646480111426411931018044681702e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5416 Order of pole = 650.9 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.1MB, time=7.15 x[1] = 0.193 y[1] (analytic) = 2.4086781425835181389287574987174 y[1] (numeric) = 2.4086781425835181389287574987176 absolute error = 2e-31 relative error = 8.3033094569240576928630266639280e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5406 Order of pole = 650.9 TOP MAIN SOLVE Loop x[1] = 0.194 y[1] (analytic) = 2.414465368738082668306022710872 y[1] (numeric) = 2.4144653687380826683060227108719 absolute error = 1e-31 relative error = 4.1417036373673429835665183249307e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5396 Order of pole = 650.9 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.1MB, time=7.29 x[1] = 0.195 y[1] (analytic) = 2.4202721791637278765200471915971 y[1] (numeric) = 2.4202721791637278765200471915977 absolute error = 6e-31 relative error = 2.4790600212878407701387699355146e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5386 Order of pole = 650.9 TOP MAIN SOLVE Loop x[1] = 0.196 y[1] (analytic) = 2.4260986863815869836959991743947 y[1] (numeric) = 2.4260986863815869836959991743949 absolute error = 2e-31 relative error = 8.2436877412555162895309457519277e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5376 Order of pole = 650.9 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.1MB, time=7.43 x[1] = 0.197 y[1] (analytic) = 2.4319450037398768112372987290248 y[1] (numeric) = 2.431945003739876811237298729025 absolute error = 2e-31 relative error = 8.2238701817860760043966396635905e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5366 Order of pole = 650.9 TOP MAIN SOLVE Loop x[1] = 0.198 y[1] (analytic) = 2.4378112454216744612457476855009 y[1] (numeric) = 2.437811245421674461245747685501 absolute error = 1e-31 relative error = 4.1020403112753195794429279045385e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5356 Order of pole = 650.9 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.1MB, time=7.58 x[1] = 0.199 y[1] (analytic) = 2.4436975264527808947304870962139 y[1] (numeric) = 2.443697526452780894730487096214 absolute error = 1e-31 relative error = 4.0921594803575327469165147352882e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5347 Order of pole = 650.9 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 2.4496039627096725512289708424385 y[1] (numeric) = 2.4496039627096725512289708424389 absolute error = 4e-31 relative error = 1.6329170187883471480649362065879e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5337 Order of pole = 650.9 memory used=206.0MB, alloc=4.1MB, time=7.72 TOP MAIN SOLVE Loop x[1] = 0.201 y[1] (analytic) = 2.4555306709275421695963458982059 y[1] (numeric) = 2.4555306709275421695963458982064 absolute error = 5e-31 relative error = 2.0362197300965987664781702428213e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5327 Order of pole = 650.9 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.1MB, time=7.86 x[1] = 0.202 y[1] (analytic) = 2.4614777687084299871431254975241 y[1] (numeric) = 2.4614777687084299871431254975242 absolute error = 1e-31 relative error = 4.0626001693475105212737731509149e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5317 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.203 y[1] (analytic) = 2.4674453745294465120202975955366 y[1] (numeric) = 2.4674453745294465120202975955371 absolute error = 5e-31 relative error = 2.0263873120001789776843581327567e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5307 Order of pole = 651 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.1MB, time=8.01 x[1] = 0.204 y[1] (analytic) = 2.4734336077510880817716077236633 y[1] (numeric) = 2.4734336077510880817716077236636 absolute error = 3e-31 relative error = 1.2128888321880934375246561765099e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5297 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.205 y[1] (analytic) = 2.4794425886256464393003889110952 y[1] (numeric) = 2.4794425886256464393003889110955 absolute error = 3e-31 relative error = 1.2099493707829299754029690180239e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5287 Order of pole = 651 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.1MB, time=8.15 x[1] = 0.206 y[1] (analytic) = 2.4854724383057135761387968636844 y[1] (numeric) = 2.4854724383057135761387968636849 absolute error = 5e-31 relative error = 2.0116899801183790323308446129536e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5277 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.207 y[1] (analytic) = 2.4915232788527831118665826305112 y[1] (numeric) = 2.4915232788527831118665826305116 absolute error = 4e-31 relative error = 1.6054435589467147036927098897874e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5267 Order of pole = 651 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.2MB, time=8.29 x[1] = 0.208 y[1] (analytic) = 2.4975952332459494978106583862192 y[1] (numeric) = 2.4975952332459494978106583862195 absolute error = 3e-31 relative error = 1.2011553994283974647216284378360e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5257 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.209 y[1] (analytic) = 2.503688425390706352771872656246 y[1] (numeric) = 2.5036884253907063527718726562465 absolute error = 5e-31 relative error = 1.9970536067081663602103918025333e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5247 Order of pole = 651 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.2MB, time=8.44 x[1] = 0.21 y[1] (analytic) = 2.5098029801278452584779272717105 y[1] (numeric) = 2.5098029801278452584779272717104 absolute error = 1e-31 relative error = 3.9843764945607867423838577300295e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5237 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.211 y[1] (analytic) = 2.5159390232424563627576905211968 y[1] (numeric) = 2.5159390232424563627576905211968 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5227 Order of pole = 651 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.2MB, time=8.58 x[1] = 0.212 y[1] (analytic) = 2.5220966814730321590788763877959 y[1] (numeric) = 2.5220966814730321590788763877959 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5217 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.213 y[1] (analytic) = 2.5282760825206758320948946357208 y[1] (numeric) = 2.528276082520675832094894635721 absolute error = 2e-31 relative error = 7.9105284973704778307202488193832e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5207 Order of pole = 651 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.2MB, time=8.72 x[1] = 0.214 y[1] (analytic) = 2.5344773550584155802144994639242 y[1] (numeric) = 2.5344773550584155802144994639246 absolute error = 4e-31 relative error = 1.5782346573413383315775468727510e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5197 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.215 y[1] (analytic) = 2.5407006287406263479466897984269 y[1] (numeric) = 2.5407006287406263479466897984268 absolute error = 1e-31 relative error = 3.9359221967669590065556415289691e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5187 Order of pole = 651 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.2MB, time=8.87 x[1] = 0.216 y[1] (analytic) = 2.5469460342125604228903054533026 y[1] (numeric) = 2.5469460342125604228903054533027 absolute error = 1e-31 relative error = 3.9262708615228673531026277699363e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5177 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.217 y[1] (analytic) = 2.5532137031199883747402362954294 y[1] (numeric) = 2.5532137031199883747402362954295 absolute error = 1e-31 relative error = 3.9166325904408831308149832888091e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5167 Order of pole = 651 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.2MB, time=9.01 x[1] = 0.218 y[1] (analytic) = 2.5595037681189518365775882323619 y[1] (numeric) = 2.5595037681189518365775882323622 absolute error = 3e-31 relative error = 1.1721022009687372691291678867458e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5157 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.219 y[1] (analytic) = 2.5658163628856296520071620660586 y[1] (numeric) = 2.5658163628856296520071620660583 absolute error = 3e-31 relative error = 1.1692185159447920819687575587241e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5147 Order of pole = 651 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.2MB, time=9.16 x[1] = 0.22 y[1] (analytic) = 2.5721516221263189354099942360334 y[1] (numeric) = 2.5721516221263189354099942360335 absolute error = 1e-31 relative error = 3.8877956936820491163419150497190e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5137 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.221 y[1] (analytic) = 2.5785096815875326166994447160583 y[1] (numeric) = 2.5785096815875326166994447160584 absolute error = 1e-31 relative error = 3.8782092118588503347367027004295e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5127 Order of pole = 651 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.2MB, time=9.30 x[1] = 0.222 y[1] (analytic) = 2.5848906780662150665145305370406 y[1] (numeric) = 2.584890678066215066514530537041 absolute error = 4e-31 relative error = 1.5474542246376329016988423129288e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5117 Order of pole = 651 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.2MB, time=9.44 x[1] = 0.223 y[1] (analytic) = 2.5912947494200774227622025221421 y[1] (numeric) = 2.5912947494200774227622025221425 absolute error = 4e-31 relative error = 1.5436298788067956443854586233892e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5107 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.224 y[1] (analytic) = 2.5977220345780542648395361287419 y[1] (numeric) = 2.5977220345780542648395361287422 absolute error = 3e-31 relative error = 1.1548579717411094739750416166488e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5097 Order of pole = 651 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.2MB, time=9.59 x[1] = 0.225 y[1] (analytic) = 2.6041726735508833077360266696581 y[1] (numeric) = 2.604172673550883307736026669658 absolute error = 1e-31 relative error = 3.8399911425092405835784090408977e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5087 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.226 y[1] (analytic) = 2.6106468074418098145442044295684 y[1] (numeric) = 2.6106468074418098145442044295684 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5077 Order of pole = 651 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.2MB, time=9.73 x[1] = 0.227 y[1] (analytic) = 2.6171445784574174527026684708135 y[1] (numeric) = 2.6171445784574174527026684708137 absolute error = 2e-31 relative error = 7.6419163712339831153582267463491e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5067 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.228 y[1] (analytic) = 2.6236661299185873465686283414691 y[1] (numeric) = 2.623666129918587346568628341469 absolute error = 1e-31 relative error = 3.8114605688454350395409312542813e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5057 Order of pole = 651 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.2MB, time=9.88 x[1] = 0.229 y[1] (analytic) = 2.6302116062715871066765911823711 y[1] (numeric) = 2.6302116062715871066765911823713 absolute error = 2e-31 relative error = 7.6039509339519145010332055558615e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5047 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 2.6367811530992916442955950248698 y[1] (numeric) = 2.6367811530992916442955950248699 absolute error = 1e-31 relative error = 3.7925028356054227900714333063382e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5037 Order of pole = 651 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.2MB, time=10.02 x[1] = 0.231 y[1] (analytic) = 2.6433749171325376086592358723193 y[1] (numeric) = 2.6433749171325376086592358723192 absolute error = 1e-31 relative error = 3.7830426305352600031094686637551e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5027 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.232 y[1] (analytic) = 2.6499930462616133135207513639784 y[1] (numeric) = 2.6499930462616133135207513639782 absolute error = 2e-31 relative error = 7.5471896155404306358730959361945e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5017 Order of pole = 651 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.2MB, time=10.17 x[1] = 0.233 y[1] (analytic) = 2.6566356895478860494899139175538 y[1] (numeric) = 2.6566356895478860494899139175539 absolute error = 1e-31 relative error = 3.7641593235171168471747426059099e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.5007 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.234 y[1] (analytic) = 2.6633029972355687089499846338337 y[1] (numeric) = 2.6633029972355687089499846338337 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4997 Order of pole = 651 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.2MB, time=10.31 x[1] = 0.235 y[1] (analytic) = 2.6699951207636276812422516911714 y[1] (numeric) = 2.6699951207636276812422516911718 absolute error = 4e-31 relative error = 1.4981300785508500861668024183498e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4987 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.236 y[1] (analytic) = 2.6767122127778340072537271984501 y[1] (numeric) = 2.6767122127778340072537271984506 absolute error = 5e-31 relative error = 1.8679632334516485826537091557033e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4977 Order of pole = 651 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.2MB, time=10.46 x[1] = 0.237 y[1] (analytic) = 2.6834544271429598145616519727365 y[1] (numeric) = 2.6834544271429598145616519727372 absolute error = 7e-31 relative error = 2.6085779319355954102740831374885e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4967 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.238 y[1] (analytic) = 2.6902219189551220868880555427891 y[1] (numeric) = 2.6902219189551220868880555427892 absolute error = 1e-31 relative error = 3.7171654611616517085513842154616e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4957 Order of pole = 651 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.2MB, time=10.60 x[1] = 0.239 y[1] (analytic) = 2.6970148445542758548104916074388 y[1] (numeric) = 2.6970148445542758548104916074391 absolute error = 3e-31 relative error = 1.1123409298460117338044969134403e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4947 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 2.7038333615368589284732318434022 y[1] (numeric) = 2.7038333615368589284732318434026 absolute error = 4e-31 relative error = 1.4793811101311361630216449016794e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4937 Order of pole = 651 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.2MB, time=10.75 x[1] = 0.241 y[1] (analytic) = 2.71067762876859032745893627205 y[1] (numeric) = 2.7106776287685903274589362720499 absolute error = 1e-31 relative error = 3.6891144464651118298003259550330e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4927 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.242 y[1] (analytic) = 2.7175478063974245980266840847934 y[1] (numeric) = 2.7175478063974245980266840847936 absolute error = 2e-31 relative error = 7.3595761417398680383038893154597e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4917 Order of pole = 651 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.2MB, time=10.89 x[1] = 0.243 y[1] (analytic) = 2.7244440558666642436110841515543 y[1] (numeric) = 2.7244440558666642436110841515546 absolute error = 3e-31 relative error = 1.1011420820111791689499188534734e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4907 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.244 y[1] (analytic) = 2.7313665399282325308221170882981 y[1] (numeric) = 2.7313665399282325308221170882981 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4897 Order of pole = 651 memory used=293.7MB, alloc=4.2MB, time=11.04 TOP MAIN SOLVE Loop x[1] = 0.245 y[1] (analytic) = 2.7383154226561089701998139444076 y[1] (numeric) = 2.7383154226561089701998139444079 absolute error = 3e-31 relative error = 1.0955640738750477605504752279674e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4887 Order of pole = 651 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.2MB, time=11.18 x[1] = 0.246 y[1] (analytic) = 2.7452908694599298086755762805264 y[1] (numeric) = 2.7452908694599298086755762805266 absolute error = 2e-31 relative error = 7.2852025344529414934524503395250e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4877 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.247 y[1] (analytic) = 2.7522930470987559090869248846299 y[1] (numeric) = 2.7522930470987559090869248846301 absolute error = 2e-31 relative error = 7.2666680683157550369964471406151e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4867 Order of pole = 651 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.2MB, time=11.33 x[1] = 0.248 y[1] (analytic) = 2.7593221236950104311990837759133 y[1] (numeric) = 2.7593221236950104311990837759132 absolute error = 1e-31 relative error = 3.6240785061401211527735150978638e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4857 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.249 y[1] (analytic) = 2.7663782687485887685197424155707 y[1] (numeric) = 2.766378268748588768519742415571 absolute error = 3e-31 relative error = 1.0844503927357314737194890947656e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4847 Order of pole = 651 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.2MB, time=11.47 x[1] = 0.25 y[1] (analytic) = 2.7734616531511432357676059913693 y[1] (numeric) = 2.77346165315114323576760599137 absolute error = 7e-31 relative error = 2.5239216817895287157915908044759e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4837 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.251 y[1] (analytic) = 2.7805724492005450431862972468585 y[1] (numeric) = 2.7805724492005450431862972468584 absolute error = 1e-31 relative error = 3.5963817460951773486463583810664e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4827 Order of pole = 651 TOP MAIN SOLVE Loop memory used=309.0MB, alloc=4.2MB, time=11.61 x[1] = 0.252 y[1] (analytic) = 2.7877108306155261359985202548313 y[1] (numeric) = 2.7877108306155261359985202548313 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4817 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.253 y[1] (analytic) = 2.794876972550503520187202901911 y[1] (numeric) = 2.7948769725505035201872029019112 absolute error = 2e-31 relative error = 7.1559500458972704682794089135663e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4807 Order of pole = 651 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.2MB, time=11.76 x[1] = 0.254 y[1] (analytic) = 2.8020710516105887394870352068442 y[1] (numeric) = 2.8020710516105887394870352068445 absolute error = 3e-31 relative error = 1.0706366629338840807040598950907e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4797 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.255 y[1] (analytic) = 2.8092932458667852129882271613147 y[1] (numeric) = 2.8092932458667852129882271613149 absolute error = 2e-31 relative error = 7.1192283074845602938062734842584e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4787 Order of pole = 651 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.2MB, time=11.90 x[1] = 0.256 y[1] (analytic) = 2.8165437348713761881116219395349 y[1] (numeric) = 2.8165437348713761881116219395355 absolute error = 6e-31 relative error = 2.1302704892221400249895539580787e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4777 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.257 y[1] (analytic) = 2.8238226996735061099281143568698 y[1] (numeric) = 2.8238226996735061099281143568701 absolute error = 3e-31 relative error = 1.0623896466116175525093423524475e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4767 Order of pole = 651 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.2MB, time=12.05 x[1] = 0.258 y[1] (analytic) = 2.831130322834958254883643569957 y[1] (numeric) = 2.831130322834958254883643569957 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4757 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.259 y[1] (analytic) = 2.838466788446131524972273605545 y[1] (numeric) = 2.8384667884461315249722736055454 absolute error = 4e-31 relative error = 1.4092114856801721827597658244523e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4747 Order of pole = 651 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.2MB, time=12.19 x[1] = 0.26 y[1] (analytic) = 2.8458322821422193472928935578192 y[1] (numeric) = 2.84583228214221934729289355782 absolute error = 8e-31 relative error = 2.8111284175812168087898212345447e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4737 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.261 y[1] (analytic) = 2.8532269911195936737491480098215 y[1] (numeric) = 2.8532269911195936737491480098218 absolute error = 3e-31 relative error = 1.0514410558070647038139385729370e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4727 Order of pole = 651 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.2MB, time=12.34 x[1] = 0.262 y[1] (analytic) = 2.8606511041523971264270840076125 y[1] (numeric) = 2.8606511041523971264270840076128 absolute error = 3e-31 relative error = 1.0487123003729221146482146077993e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4717 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.263 y[1] (analytic) = 2.8681048116093463859308715950835 y[1] (numeric) = 2.8681048116093463859308715950835 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4707 Order of pole = 651 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.2MB, time=12.48 x[1] = 0.264 y[1] (analytic) = 2.8755883054707499726944913907685 y[1] (numeric) = 2.8755883054707499726944913907684 absolute error = 1e-31 relative error = 3.4775492656494663891574580282355e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4697 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.265 y[1] (analytic) = 2.883101779345743625037640993462 y[1] (numeric) = 2.8831017793457436250376409934626 absolute error = 6e-31 relative error = 2.0810919832880709806052284185322e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4687 Order of pole = 651 TOP MAIN SOLVE Loop memory used=335.7MB, alloc=4.2MB, time=12.63 x[1] = 0.266 y[1] (analytic) = 2.8906454284897465325189457757622 y[1] (numeric) = 2.8906454284897465325189457757622 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4677 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.267 memory used=339.5MB, alloc=4.2MB, time=12.77 y[1] (analytic) = 2.8982194498221417389810328901005 y[1] (numeric) = 2.8982194498221417389810328901006 absolute error = 1e-31 relative error = 3.4503943449188021762868703230924e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4667 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.268 y[1] (analytic) = 2.9058240419441840866028276392316 y[1] (numeric) = 2.9058240419441840866028276392316 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4657 Order of pole = 651 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.2MB, time=12.92 x[1] = 0.269 y[1] (analytic) = 2.9134594051571391302977833830103 y[1] (numeric) = 2.9134594051571391302977833830104 absolute error = 1e-31 relative error = 3.4323457475669355256885882734157e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4647 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 2.9211257414806565109464354563209 y[1] (numeric) = 2.9211257414806565109464354563217 absolute error = 8e-31 relative error = 2.7386701936168520244822713553698e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4637 Order of pole = 651 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.2MB, time=13.06 x[1] = 0.271 y[1] (analytic) = 2.9288232546713813362520169983787 y[1] (numeric) = 2.9288232546713813362520169983788 absolute error = 1e-31 relative error = 3.4143405492462931256238851453777e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4627 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.272 y[1] (analytic) = 2.9365521502418071794838109203687 y[1] (numeric) = 2.9365521502418071794838109203695 absolute error = 8e-31 relative error = 2.7242833059652111874361640051319e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4617 Order of pole = 651 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.2MB, time=13.20 x[1] = 0.273 y[1] (analytic) = 2.9443126354793743690499532908705 y[1] (numeric) = 2.9443126354793743690499532908711 absolute error = 6e-31 relative error = 2.0378270730149952070699596670211e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4607 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.274 y[1] (analytic) = 2.9521049194658173057456755989767 y[1] (numeric) = 2.9521049194658173057456755989771 absolute error = 4e-31 relative error = 1.3549653921933774168918175439682e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4597 Order of pole = 651 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.2MB, time=13.35 x[1] = 0.275 y[1] (analytic) = 2.9599292130967646096812296171178 y[1] (numeric) = 2.9599292130967646096812296171184 absolute error = 6e-31 relative error = 2.0270755035126749938625015383258e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4587 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.276 y[1] (analytic) = 2.967785729101595965333374860279 y[1] (numeric) = 2.9677857291015959653333748602791 absolute error = 1e-31 relative error = 3.3695154949839273994909568078897e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4577 Order of pole = 651 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.2MB, time=13.49 x[1] = 0.277 y[1] (analytic) = 2.9756746820635596009133807288213 y[1] (numeric) = 2.9756746820635596009133807288216 absolute error = 3e-31 relative error = 1.0081747235620432035249741036762e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4567 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.278 y[1] (analytic) = 2.9835962884401544073317363797562 y[1] (numeric) = 2.983596288440154407331736379757 absolute error = 8e-31 relative error = 2.6813279098769952964112441202382e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4557 Order of pole = 651 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.2MB, time=13.63 x[1] = 0.279 y[1] (analytic) = 2.9915507665837807724945993684961 y[1] (numeric) = 2.9915507665837807724945993684963 absolute error = 2e-31 relative error = 6.6854957714253063469650500103871e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4547 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 2.999538336762664278519590818674 y[1] (numeric) = 2.999538336762664278519590818674 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4537 Order of pole = 651 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.2MB, time=13.78 x[1] = 0.281 y[1] (analytic) = 3.0075592211820564827397344097138 y[1] (numeric) = 3.0075592211820564827397344097141 absolute error = 3e-31 relative error = 9.9748659273978136550407547478493e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4527 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.282 y[1] (analytic) = 3.0156136440057170781057647953618 y[1] (numeric) = 3.0156136440057170781057647953617 absolute error = 1e-31 relative error = 3.3160746635688857966129526383489e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4517 Order of pole = 651 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.2MB, time=13.92 x[1] = 0.283 y[1] (analytic) = 3.0237018313776818048310960518308 y[1] (numeric) = 3.0237018313776818048310960518313 absolute error = 5e-31 relative error = 1.6536021998312784487959163458449e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4507 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.284 y[1] (analytic) = 3.0318240114443205628836327647012 y[1] (numeric) = 3.0318240114443205628836327647018 absolute error = 6e-31 relative error = 1.9790066894884442663568640095026e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4497 Order of pole = 651 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.2MB, time=14.07 x[1] = 0.285 y[1] (analytic) = 3.0399804143766902542483294492922 y[1] (numeric) = 3.0399804143766902542483294492925 absolute error = 3e-31 relative error = 9.8684846317179719879051909317887e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4487 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.286 y[1] (analytic) = 3.048171272393186964798797706486 y[1] (numeric) = 3.0481712723931869647987977064862 absolute error = 2e-31 relative error = 6.5613110986042315813936118251864e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4477 Order of pole = 651 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.2MB, time=14.21 x[1] = 0.287 y[1] (analytic) = 3.0563968197825021781610223319826 y[1] (numeric) = 3.056396819782502178161022331983 absolute error = 4e-31 relative error = 1.3087305856720025156150077733306e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4467 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.288 y[1] (analytic) = 3.0646572929268877981639560485021 y[1] (numeric) = 3.0646572929268877981639560485024 absolute error = 3e-31 relative error = 9.7890227625904065508822093133657e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4457 Order of pole = 651 memory used=381.4MB, alloc=4.2MB, time=14.35 TOP MAIN SOLVE Loop x[1] = 0.289 y[1] (analytic) = 3.0729529303257348423879009579087 y[1] (numeric) = 3.072952930325734842387900957909 absolute error = 3e-31 relative error = 9.7625966554651984588437527903100e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4447 Order of pole = 651 TOP MAIN SOLVE Loop memory used=385.3MB, alloc=4.2MB, time=14.50 x[1] = 0.29 y[1] (analytic) = 3.0812839726194707569805658384607 y[1] (numeric) = 3.0812839726194707569805658384608 absolute error = 1e-31 relative error = 3.2454003230019623148206872010073e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4437 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.291 y[1] (analytic) = 3.0896506626137803923518791398973 y[1] (numeric) = 3.0896506626137803923518791398973 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4427 Order of pole = 651 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.2MB, time=14.64 x[1] = 0.292 y[1] (analytic) = 3.0980532453041557706223854588106 y[1] (numeric) = 3.0980532453041557706223854588113 absolute error = 7e-31 relative error = 2.2594834387078989901257431554895e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4417 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.293 y[1] (analytic) = 3.1064919679007798688277130115536 y[1] (numeric) = 3.1064919679007798688277130115542 absolute error = 6e-31 relative error = 1.9314390836988114946369878604303e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4407 Order of pole = 651 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.2MB, time=14.78 x[1] = 0.294 y[1] (analytic) = 3.1149670798537497369155603494966 y[1] (numeric) = 3.1149670798537497369155603494969 absolute error = 3e-31 relative error = 9.6309204017040605907445147260787e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4397 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.295 y[1] (analytic) = 3.1234788328786443665553643536315 y[1] (numeric) = 3.1234788328786443665553643536322 absolute error = 7e-31 relative error = 2.2410909036155357247510677236630e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4387 Order of pole = 651 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.2MB, time=14.93 x[1] = 0.296 y[1] (analytic) = 3.1320274809824428257588224980514 y[1] (numeric) = 3.1320274809824428257588224980516 absolute error = 2e-31 relative error = 6.3856400116024760366159569456686e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4377 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.297 y[1] (analytic) = 3.1406132804897982753274166118098 y[1] (numeric) = 3.1406132804897982753274166118108 absolute error = 1.0e-30 relative error = 3.1840914836991447360878012475333e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4367 Order of pole = 651 TOP MAIN SOLVE Loop memory used=400.5MB, alloc=4.2MB, time=15.07 x[1] = 0.298 y[1] (analytic) = 3.1492364900696735862478419570344 y[1] (numeric) = 3.1492364900696735862478419570353 absolute error = 9e-31 relative error = 2.8578355510547524324702073294698e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4357 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.299 y[1] (analytic) = 3.157897370762344382395788199401 y[1] (numeric) = 3.1578973707623443823957881994011 absolute error = 1e-31 relative error = 3.1666640254321854257337501965670e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4347 Order of pole = 651 TOP MAIN SOLVE Loop memory used=404.3MB, alloc=4.2MB, time=15.22 x[1] = 0.3 y[1] (analytic) = 3.1665961860067754403320691383761 y[1] (numeric) = 3.1665961860067754403320691383764 absolute error = 3e-31 relative error = 9.4738950714872774716437601580795e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4337 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.301 y[1] (analytic) = 3.1753332016683764876331285589502 y[1] (numeric) = 3.1753332016683764876331285589511 absolute error = 9e-31 relative error = 2.8343482174630492561283896213686e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4327 Order of pole = 651 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.2MB, time=15.36 x[1] = 0.302 y[1] (analytic) = 3.1841086860671435531422190236687 y[1] (numeric) = 3.1841086860671435531422190236687 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4317 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.303 y[1] (analytic) = 3.192922910006192136811139525112 y[1] (numeric) = 3.1929229100061921368111395251127 absolute error = 7e-31 relative error = 2.1923485775566140047114580396506e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4307 Order of pole = 651 TOP MAIN SOLVE Loop memory used=412.0MB, alloc=4.2MB, time=15.51 x[1] = 0.304 y[1] (analytic) = 3.2017761468006885834797661842998 y[1] (numeric) = 3.2017761468006885834797661843007 absolute error = 9e-31 relative error = 2.8109397994588321833678904641266e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4297 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.305 y[1] (analytic) = 3.210668672307186164067554003459 y[1] (numeric) = 3.21066867230718616406755400346 absolute error = 1.0e-30 relative error = 3.1146159945597877812063845195071e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4287 Order of pole = 651 TOP MAIN SOLVE Loop memory used=415.8MB, alloc=4.2MB, time=15.65 x[1] = 0.306 y[1] (analytic) = 3.2196007649533724892849995221133 y[1] (numeric) = 3.2196007649533724892849995221142 absolute error = 9e-31 relative error = 2.7953776437030823916561711533726e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4277 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.307 y[1] (analytic) = 3.2285727057682350051724829949692 y[1] (numeric) = 3.2285727057682350051724829949692 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4267 Order of pole = 651 TOP MAIN SOLVE Loop memory used=419.6MB, alloc=4.2MB, time=15.80 x[1] = 0.308 y[1] (analytic) = 3.2375847784126514465992213916189 y[1] (numeric) = 3.2375847784126514465992213916192 absolute error = 3e-31 relative error = 9.2661666190278532808905923182402e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4257 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.309 y[1] (analytic) = 3.2466372692104122543680880589222 y[1] (numeric) = 3.2466372692104122543680880589225 absolute error = 3e-31 relative error = 9.2403300745993257794695489140280e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4247 Order of pole = 651 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.2MB, time=15.94 x[1] = 0.31 y[1] (analytic) = 3.2557304671796820938362244080823 y[1] (numeric) = 3.2557304671796820938362244080831 absolute error = 8e-31 relative error = 2.4572058653645557155774974356036e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4237 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.311 y[1] (analytic) = 3.2648646640649077480417673537492 y[1] (numeric) = 3.2648646640649077480417673537497 absolute error = 5e-31 relative error = 1.5314570478320434821559662869587e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4227 Order of pole = 651 memory used=427.2MB, alloc=4.2MB, time=16.09 TOP MAIN SOLVE Loop x[1] = 0.312 y[1] (analytic) = 3.2740401543691797962904250219158 y[1] (numeric) = 3.2740401543691797962904250219167 absolute error = 9e-31 relative error = 2.7488972571058951864639646440099e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4217 Order of pole = 651 TOP MAIN SOLVE Loop memory used=431.0MB, alloc=4.2MB, time=16.23 x[1] = 0.313 y[1] (analytic) = 3.2832572353870556300705801788258 y[1] (numeric) = 3.2832572353870556300705801788265 absolute error = 7e-31 relative error = 2.1320291095543070141662658008593e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4207 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.314 y[1] (analytic) = 3.292516207237851502102409702984 y[1] (numeric) = 3.2925162072378515021024097029843 absolute error = 3e-31 relative error = 9.1115724606159239488073241895054e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4197 Order of pole = 651 TOP MAIN SOLVE Loop memory used=434.8MB, alloc=4.2MB, time=16.38 x[1] = 0.315 y[1] (analytic) = 3.3018173728994114513573505574781 y[1] (numeric) = 3.3018173728994114513573505574785 absolute error = 4e-31 relative error = 1.2114540412898416243691554046533e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4187 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.316 y[1] (analytic) = 3.3111610382423610970831900701775 y[1] (numeric) = 3.3111610382423610970831900701787 absolute error = 1.2e-30 relative error = 3.6241064271431118447375724313264e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4177 Order of pole = 651 TOP MAIN SOLVE Loop memory used=438.7MB, alloc=4.2MB, time=16.52 x[1] = 0.317 y[1] (analytic) = 3.3205475120648544483131381978868 y[1] (numeric) = 3.3205475120648544483131381978879 absolute error = 1.1e-30 relative error = 3.3127067027448563230708102728400e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4167 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.318 y[1] (analytic) = 3.3299771061278220321024909375461 y[1] (numeric) = 3.3299771061278220321024909375463 absolute error = 2e-31 relative error = 6.0060472978015407501397195822308e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4157 Order of pole = 651 TOP MAIN SOLVE Loop memory used=442.5MB, alloc=4.2MB, time=16.67 x[1] = 0.319 y[1] (analytic) = 3.339450135190728803904026265396 y[1] (numeric) = 3.3394501351907288039040262653968 absolute error = 8e-31 relative error = 2.3956039695568292473571217457960e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4147 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 3.3489669170478504671453261014048 y[1] (numeric) = 3.348966917047850467145326101405 absolute error = 2e-31 relative error = 5.9719909140309484415775660848239e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4137 Order of pole = 651 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.2MB, time=16.81 x[1] = 0.321 y[1] (analytic) = 3.3585277725650769962922209694433 y[1] (numeric) = 3.358527772565076996292220969444 absolute error = 7e-31 relative error = 2.0842465729124362908636638707605e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4127 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.322 y[1] (analytic) = 3.3681330257172523285591952932284 y[1] (numeric) = 3.3681330257172523285591952932295 absolute error = 1.1e-30 relative error = 3.2659042609095056641984202432709e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4117 Order of pole = 651 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.2MB, time=16.96 x[1] = 0.323 y[1] (analytic) = 3.3777830036260593640488794673363 y[1] (numeric) = 3.3777830036260593640488794673372 absolute error = 9e-31 relative error = 2.6644695619400284727302327879288e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4107 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.324 y[1] (analytic) = 3.3874780365984595925600886040926 y[1] (numeric) = 3.3874780365984595925600886040937 absolute error = 1.1e-30 relative error = 3.2472535264156765082098272001159e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4097 Order of pole = 651 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.2MB, time=17.11 x[1] = 0.325 y[1] (analytic) = 3.3972184581656968476911057791988 y[1] (numeric) = 3.3972184581656968476911057791993 absolute error = 5e-31 relative error = 1.4717923093764518377876743608700e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4087 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.326 y[1] (analytic) = 3.4070046051228748752784406512474 y[1] (numeric) = 3.4070046051228748752784406512477 absolute error = 3e-31 relative error = 8.8053887437930360403279365377805e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4077 Order of pole = 651 TOP MAIN SOLVE Loop memory used=457.7MB, alloc=4.2MB, time=17.25 x[1] = 0.327 y[1] (analytic) = 3.4168368175691185937501205730192 y[1] (numeric) = 3.4168368175691185937501205730197 absolute error = 5e-31 relative error = 1.4633417593402105382864328961272e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4067 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.328 y[1] (analytic) = 3.4267154389483291187383730097989 y[1] (numeric) = 3.4267154389483291187383730097996 absolute error = 7e-31 relative error = 2.0427724813205745311747884955922e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4057 Order of pole = 651 TOP MAIN SOLVE Loop memory used=461.5MB, alloc=4.2MB, time=17.40 x[1] = 0.329 y[1] (analytic) = 3.4366408160905428233937812910488 y[1] (numeric) = 3.4366408160905428233937812910491 absolute error = 3e-31 relative error = 8.7294546056539679220629503454104e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4047 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 3.4466132992539049093789324540805 y[1] (numeric) = 3.4466132992539049093789324540813 absolute error = 8e-31 relative error = 2.3211191118341519700182766165610e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4037 Order of pole = 651 TOP MAIN SOLVE Loop memory used=465.4MB, alloc=4.2MB, time=17.54 x[1] = 0.331 y[1] (analytic) = 3.4566332421672681716044489536479 y[1] (numeric) = 3.4566332421672681716044489536485 absolute error = 6e-31 relative error = 1.7357930621063144506488516475795e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4027 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.332 y[1] (analytic) = 3.4667010020734278525173463758255 y[1] (numeric) = 3.4667010020734278525173463758261 absolute error = 6e-31 relative error = 1.7307520886316444405296498105660e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4017 Order of pole = 651 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.2MB, time=17.69 x[1] = 0.333 y[1] (analytic) = 3.4768169397730036992772367696892 y[1] (numeric) = 3.4768169397730036992772367696897 absolute error = 5e-31 relative error = 1.4380969969406680060601771538519e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.4007 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.334 y[1] (analytic) = 3.4869814196689805595795535832816 y[1] (numeric) = 3.4869814196689805595795535832825 absolute error = 9e-31 relative error = 2.5810289522145979084313696554997e-29 % Correct digits = 30 h = 0.001 memory used=473.0MB, alloc=4.2MB, time=17.83 Real estimate of pole used for equation 1 Radius of convergence = 0.3997 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.335 y[1] (analytic) = 3.4971948098119190793295596480164 y[1] (numeric) = 3.4971948098119190793295596480168 absolute error = 4e-31 relative error = 1.1437738580582881627524731455443e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3987 Order of pole = 651 TOP MAIN SOLVE Loop memory used=476.8MB, alloc=4.2MB, time=17.97 x[1] = 0.336 y[1] (analytic) = 3.5074574819458482979626623082224 y[1] (numeric) = 3.507457481945848297962662308223 absolute error = 6e-31 relative error = 1.7106408362422550138434130770750e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3977 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.337 y[1] (analytic) = 3.5177698115548521750752484592502 y[1] (numeric) = 3.5177698115548521750752484592505 absolute error = 3e-31 relative error = 8.5281304937744115077357218060584e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3967 Order of pole = 651 TOP MAIN SOLVE Loop memory used=480.6MB, alloc=4.2MB, time=18.12 x[1] = 0.338 y[1] (analytic) = 3.5281321779103623253092226287058 y[1] (numeric) = 3.528132177910362325309222628707 absolute error = 1.2e-30 relative error = 3.4012331156786038721848299906516e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3957 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.339 y[1] (analytic) = 3.5385449641191694872597555314787 y[1] (numeric) = 3.5385449641191694872597555314791 absolute error = 4e-31 relative error = 1.1304081311838573665818652714567e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3947 Order of pole = 651 TOP MAIN SOLVE Loop memory used=484.4MB, alloc=4.2MB, time=18.26 x[1] = 0.34 y[1] (analytic) = 3.5490085571721665066903307802814 y[1] (numeric) = 3.549008557172166506690330780282 absolute error = 6e-31 relative error = 1.6906129989105385709590749169242e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3937 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.341 y[1] (analytic) = 3.5595233479938358746868625094126 y[1] (numeric) = 3.5595233479938358746868625094138 absolute error = 1.2e-30 relative error = 3.3712378953106899898461048053910e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3927 Order of pole = 651 TOP MAIN SOLVE Loop memory used=488.3MB, alloc=4.2MB, time=18.41 x[1] = 0.342 y[1] (analytic) = 3.5700897314924951277123631933895 y[1] (numeric) = 3.5700897314924951277123631933902 absolute error = 7e-31 relative error = 1.9607350309017618220044487780815e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3917 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.343 y[1] (analytic) = 3.580708106611313688988478228021 y[1] (numeric) = 3.5807081066113136889884782280221 absolute error = 1.1e-30 relative error = 3.0720180680714870038524054034286e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3907 Order of pole = 651 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.2MB, time=18.55 x[1] = 0.344 y[1] (analytic) = 3.5913788763801150093876029985426 y[1] (numeric) = 3.5913788763801150093876029985433 absolute error = 7e-31 relative error = 1.9491120934184369909716983841017e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3897 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.345 y[1] (analytic) = 3.6021024479679781512311455150765 y[1] (numeric) = 3.6021024479679781512311455150772 absolute error = 7e-31 relative error = 1.9433095257878763041072322382069e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3887 Order of pole = 651 TOP MAIN SOLVE Loop memory used=495.9MB, alloc=4.2MB, time=18.69 x[1] = 0.346 y[1] (analytic) = 3.6128792327366532502222726923092 y[1] (numeric) = 3.6128792327366532502222726923103 absolute error = 1.1e-30 relative error = 3.0446630765645086054227152317833e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3877 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.347 y[1] (analytic) = 3.62370964629480558936639607708 y[1] (numeric) = 3.6237096462948055893663960770801 absolute error = 1e-31 relative error = 2.7596029969522711621984662682764e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3867 Order of pole = 651 TOP MAIN SOLVE Loop memory used=499.7MB, alloc=4.2MB, time=18.84 x[1] = 0.348 y[1] (analytic) = 3.6345941085531033243258113575595 y[1] (numeric) = 3.6345941085531033243258113575603 absolute error = 8e-31 relative error = 2.2010710855371749987748470273325e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3857 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.349 y[1] (analytic) = 3.6455330437801642123974386924357 y[1] (numeric) = 3.6455330437801642123974386924364 absolute error = 7e-31 relative error = 1.9201581540847828562776040803292e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3847 Order of pole = 651 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.2MB, time=18.98 x[1] = 0.35 y[1] (analytic) = 3.656526880659377017380843924038 y[1] (numeric) = 3.6565268806593770173808439240392 absolute error = 1.2e-30 relative error = 3.2818027575490036288465925664917e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3837 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.351 y[1] (analytic) = 3.6675760523466135902093358315811 y[1] (numeric) = 3.6675760523466135902093358315812 absolute error = 1e-31 relative error = 2.7265964924167643683565101384225e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3827 Order of pole = 651 TOP MAIN SOLVE Loop memory used=507.3MB, alloc=4.2MB, time=19.12 x[1] = 0.352 y[1] (analytic) = 3.6786809965288479605471374553849 y[1] (numeric) = 3.6786809965288479605471374553863 absolute error = 1.4e-30 relative error = 3.8057118878234357860842847668617e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3817 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.353 y[1] (analytic) = 3.6898421554836991178133239865616 y[1] (numeric) = 3.6898421554836991178133239865618 absolute error = 2e-31 relative error = 5.4202860602795114454826707549981e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3807 Order of pole = 651 memory used=511.1MB, alloc=4.2MB, time=19.27 TOP MAIN SOLVE Loop x[1] = 0.354 y[1] (analytic) = 3.7010599761399145114871877469629 y[1] (numeric) = 3.7010599761399145114871877469637 absolute error = 8e-31 relative error = 2.1615429232637673899270424130171e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3797 Order of pole = 651 TOP MAIN SOLVE Loop memory used=515.0MB, alloc=4.2MB, time=19.41 x[1] = 0.355 y[1] (analytic) = 3.712334910138811660294778794681 y[1] (numeric) = 3.7123349101388116602947787946815 absolute error = 5e-31 relative error = 1.3468612399017199542221684636202e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3787 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.356 y[1] (analytic) = 3.7236674138966956281936812031326 y[1] (numeric) = 3.7236674138966956281936812031328 absolute error = 2e-31 relative error = 5.3710489624718274689096958322585e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3777 Order of pole = 651 TOP MAIN SOLVE Loop memory used=518.8MB, alloc=4.2MB, time=19.55 x[1] = 0.357 y[1] (analytic) = 3.735057948668270502190180032619 y[1] (numeric) = 3.7350579486682705021901800326203 absolute error = 1.3e-30 relative error = 3.4805350221233197083653760138517e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3767 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.358 y[1] (analytic) = 3.7465069806110633931740750506632 y[1] (numeric) = 3.7465069806110633931740750506647 absolute error = 1.5e-30 relative error = 4.0037293611430740084272421258315e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3757 Order of pole = 651 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.2MB, time=19.70 x[1] = 0.359 y[1] (analytic) = 3.7580149808508798763826029989864 y[1] (numeric) = 3.7580149808508798763826029989877 absolute error = 1.3e-30 relative error = 3.4592730647009220177013800108974e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3747 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 3.7695824255483101930544361145925 y[1] (numeric) = 3.7695824255483101930544361145933 absolute error = 8e-31 relative error = 2.1222509808460676264380467178322e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3737 Order of pole = 651 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.2MB, time=19.84 x[1] = 0.361 y[1] (analytic) = 3.7812097959663059495630514799015 y[1] (numeric) = 3.7812097959663059495630514799023 absolute error = 8e-31 relative error = 2.1157249747248056013470375640626e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3727 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.362 y[1] (analytic) = 3.7928975785388474750889962093614 y[1] (numeric) = 3.7928975785388474750889962093616 absolute error = 2e-31 relative error = 5.2730134642087216436564818991038e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3717 Order of pole = 651 TOP MAIN SOLVE Loop memory used=530.2MB, alloc=4.2MB, time=19.99 x[1] = 0.363 y[1] (analytic) = 3.8046462649407224339735966860758 y[1] (numeric) = 3.8046462649407224339735966860774 absolute error = 1.6e-30 relative error = 4.2053843868318951198625644841677e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3707 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.364 y[1] (analytic) = 3.816456352158436734571425244237 y[1] (numeric) = 3.8164563521584367345714252442382 absolute error = 1.2e-30 relative error = 3.1442780665402539498381265969042e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3697 Order of pole = 651 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.2MB, time=20.13 x[1] = 0.365 y[1] (analytic) = 3.8283283425622792329726163739788 y[1] (numeric) = 3.8283283425622792329726163739798 absolute error = 1.0e-30 relative error = 2.6121061479557039934492669956238e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3687 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.366 y[1] (analytic) = 3.8402627439795621976947821485225 y[1] (numeric) = 3.8402627439795621976947821485226 absolute error = 1e-31 relative error = 2.6039884941927868782431867118922e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3677 Order of pole = 651 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.2MB, time=20.28 x[1] = 0.367 y[1] (analytic) = 3.8522600697690599806525537331091 y[1] (numeric) = 3.8522600697690599806525537331101 absolute error = 1.0e-30 relative error = 2.5958787358298714981297134698933e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3667 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.368 y[1] (analytic) = 3.8643208388966688307145795030017 y[1] (numeric) = 3.8643208388966688307145795030026 absolute error = 9e-31 relative error = 2.3289991631672222563078010813395e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3657 Order of pole = 651 TOP MAIN SOLVE Loop memory used=541.7MB, alloc=4.2MB, time=20.42 x[1] = 0.369 y[1] (analytic) = 3.8764455760123112892765154300739 y[1] (numeric) = 3.8764455760123112892765154300741 absolute error = 2e-31 relative error = 5.1593656115698505443102492367535e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3647 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 3.8886348115281091228473053242345 y[1] (numeric) = 3.8886348115281091228473053242358 absolute error = 1.3e-30 relative error = 3.3430755599524697302364495876976e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3637 Order of pole = 651 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.2MB, time=20.56 x[1] = 0.371 y[1] (analytic) = 3.9008890816978492760081265250395 y[1] (numeric) = 3.9008890816978492760081265250408 absolute error = 1.3e-30 relative error = 3.3325736076406951599411935629015e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3627 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.372 y[1] (analytic) = 3.9132089286977678696124691918051 y[1] (numeric) = 3.9132089286977678696124691918061 absolute error = 1.0e-30 relative error = 2.5554475066905732147379028509772e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3617 Order of pole = 651 TOP MAIN SOLVE Loop memory used=549.3MB, alloc=4.2MB, time=20.71 x[1] = 0.373 y[1] (analytic) = 3.9255949007086778241164093686376 y[1] (numeric) = 3.9255949007086778241164093686384 absolute error = 8e-31 relative error = 2.0379076808347646923516995876993e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3607 Order of pole = 651 TOP MAIN SOLVE Loop memory used=553.1MB, alloc=4.2MB, time=20.85 x[1] = 0.374 y[1] (analytic) = 3.9380475519994662568358587531706 y[1] (numeric) = 3.9380475519994662568358587531711 absolute error = 5e-31 relative error = 1.2696647092190007346207121232688e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3597 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.375 y[1] (analytic) = 3.9505674430119883851095780318076 y[1] (numeric) = 3.9505674430119883851095780318088 absolute error = 1.2e-30 relative error = 3.0375383215457701074402865325328e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3587 Order of pole = 651 TOP MAIN SOLVE Loop memory used=556.9MB, alloc=4.2MB, time=21.00 x[1] = 0.376 y[1] (analytic) = 3.9631551404473852652020818667935 y[1] (numeric) = 3.963155140447385265202081866794 absolute error = 5e-31 relative error = 1.2616210627160988015907511958627e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3577 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.377 y[1] (analytic) = 3.9758112173538533097206044139591 y[1] (numeric) = 3.9758112173538533097206044139605 absolute error = 1.4e-30 relative error = 3.5212939535187136829410104770864e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3567 Order of pole = 651 TOP MAIN SOLVE Loop memory used=560.7MB, alloc=4.2MB, time=21.14 x[1] = 0.378 y[1] (analytic) = 3.9885362532158941547691182367095 y[1] (numeric) = 3.9885362532158941547691182367104 absolute error = 9e-31 relative error = 2.2564668912670509924397069787165e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3557 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.379 y[1] (analytic) = 4.0013308340450740924572420032894 y[1] (numeric) = 4.0013308340450740924572420032906 absolute error = 1.2e-30 relative error = 2.9990022064406041305774776233213e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3547 Order of pole = 651 TOP MAIN SOLVE Loop memory used=564.5MB, alloc=4.2MB, time=21.29 x[1] = 0.38 y[1] (analytic) = 4.0141955524723229451735666706111 y[1] (numeric) = 4.0141955524723229451735666706114 absolute error = 3e-31 relative error = 7.4734774646250480208842644337092e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3537 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.381 y[1] (analytic) = 4.027131007841802935686369790984 y[1] (numeric) = 4.0271310078418029356863697909841 absolute error = 1e-31 relative error = 2.4831573595513951068635848622250e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3527 Order of pole = 651 TOP MAIN SOLVE Loop memory used=568.4MB, alloc=4.2MB, time=21.43 x[1] = 0.382 y[1] (analytic) = 4.0401378063063788021293072585666 y[1] (numeric) = 4.040137806306378802129307258568 absolute error = 1.4e-30 relative error = 3.4652283340798320021215845929592e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3517 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.383 y[1] (analytic) = 4.053216560924721119759943207241 y[1] (numeric) = 4.0532165609247211197599432072414 absolute error = 4e-31 relative error = 9.8687053599904861064045006901245e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3507 Order of pole = 651 TOP MAIN SOLVE Loop memory used=572.2MB, alloc=4.2MB, time=21.58 x[1] = 0.384 y[1] (analytic) = 4.0663678917600755225549277095736 y[1] (numeric) = 4.0663678917600755225549277095745 absolute error = 9e-31 relative error = 2.2132773619025564090538709664335e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3497 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.385 y[1] (analytic) = 4.0795924259807312677533733598711 y[1] (numeric) = 4.0795924259807312677533733598727 absolute error = 1.6e-30 relative error = 3.9219604140120960223342340430747e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3487 Order of pole = 651 TOP MAIN SOLVE Loop memory used=576.0MB, alloc=4.2MB, time=21.72 x[1] = 0.386 y[1] (analytic) = 4.0928907979622233559222751040214 y[1] (numeric) = 4.0928907979622233559222751040221 absolute error = 7e-31 relative error = 1.7102826206565721174740372122498e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3477 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.387 y[1] (analytic) = 4.1062636493913032085546426509912 y[1] (numeric) = 4.1062636493913032085546426509927 absolute error = 1.5e-30 relative error = 3.6529558939118637771628615885263e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3467 Order of pole = 651 TOP MAIN SOLVE Loop memory used=579.8MB, alloc=4.2MB, time=21.87 x[1] = 0.388 y[1] (analytic) = 4.1197116293717137152001695658256 y[1] (numeric) = 4.1197116293717137152001695658261 absolute error = 5e-31 relative error = 1.2136771817600584649354099718362e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3457 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.389 y[1] (analytic) = 4.1332353945318052932659843605638 y[1] (numeric) = 4.1332353945318052932659843605637 absolute error = 1e-31 relative error = 2.4194121663696717592108392183595e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3447 Order of pole = 651 TOP MAIN SOLVE Loop memory used=583.6MB, alloc=4.2MB, time=22.01 x[1] = 0.39 y[1] (analytic) = 4.1468356091340304565266355508052 y[1] (numeric) = 4.1468356091340304565266355508067 absolute error = 1.5e-30 relative error = 3.6172159723332748327117814291507e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3437 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.391 y[1] (analytic) = 4.1605129451863552636830242250216 y[1] (numeric) = 4.1605129451863552636830242250228 absolute error = 1.2e-30 relative error = 2.8842597434731699927386539105006e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3427 Order of pole = 651 TOP MAIN SOLVE Loop memory used=587.4MB, alloc=4.2MB, time=22.16 x[1] = 0.392 y[1] (analytic) = 4.174268082555626916665027793117 y[1] (numeric) = 4.1742680825556269166650277931173 absolute error = 3e-31 relative error = 7.1868886728599840814641749766558e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3417 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.393 y[1] (analytic) = 4.1881017090829377004587350435689 y[1] (numeric) = 4.1881017090829377004587350435701 absolute error = 1.2e-30 relative error = 2.8652599276600715263057409544925e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3407 Order of pole = 651 TOP MAIN SOLVE Loop memory used=591.3MB, alloc=4.2MB, time=22.30 x[1] = 0.394 y[1] (analytic) = 4.2020145207010264027551250694686 y[1] (numeric) = 4.2020145207010264027551250694694 absolute error = 8e-31 relative error = 1.9038487279347506335761022000556e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3397 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.395 y[1] (analytic) = 4.2160072215537593233839487947538 y[1] (numeric) = 4.216007221553759323383948794755 absolute error = 1.2e-30 relative error = 2.8462949348501217006635283442802e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3387 Order of pole = 651 TOP MAIN SOLVE Loop memory used=595.1MB, alloc=4.2MB, time=22.44 x[1] = 0.396 y[1] (analytic) = 4.2300805241177339810592838720153 y[1] (numeric) = 4.2300805241177339810592838720159 absolute error = 6e-31 relative error = 1.4184127147913850503103339163939e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3377 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.397 y[1] (analytic) = 4.2442351493260496491908354570254 y[1] (numeric) = 4.244235149326049649190835457026 absolute error = 6e-31 relative error = 1.4136822746385180059887414356122e-29 % Correct digits = 30 h = 0.001 memory used=598.9MB, alloc=4.2MB, time=22.59 Real estimate of pole used for equation 1 Radius of convergence = 0.3367 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.398 y[1] (analytic) = 4.2584718266942899042018520775158 y[1] (numeric) = 4.2584718266942899042018520775173 absolute error = 1.5e-30 relative error = 3.5223903340095597834393123436229e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3357 Order of pole = 651 TOP MAIN SOLVE Loop memory used=602.7MB, alloc=4.2MB, time=22.74 x[1] = 0.399 y[1] (analytic) = 4.2727912944487634497609277954874 y[1] (numeric) = 4.272791294448763449760927795488 absolute error = 6e-31 relative error = 1.4042342783733052094551118861376e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3347 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 4.2871942996570505894284231569851 y[1] (numeric) = 4.287194299657050589428423156985 absolute error = 1e-31 relative error = 2.3325278261356008621104496679246e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3337 Order of pole = 651 TOP MAIN SOLVE Loop memory used=606.5MB, alloc=4.2MB, time=22.88 x[1] = 0.401 y[1] (analytic) = 4.3016815983609038593142312532121 y[1] (numeric) = 4.3016815983609038593142312532127 absolute error = 6e-31 relative error = 1.3948033723105440496966833142190e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3327 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.402 y[1] (analytic) = 4.3162539557115525023466476391175 y[1] (numeric) = 4.3162539557115525023466476391174 absolute error = 1e-31 relative error = 2.3168238251522107692378847497812e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3317 Order of pole = 651 TOP MAIN SOLVE Loop memory used=610.3MB, alloc=4.2MB, time=23.03 x[1] = 0.403 y[1] (analytic) = 4.3309121461074616675967662650088 y[1] (numeric) = 4.330912146107461667596766265009 absolute error = 2e-31 relative error = 4.6179648363395237982700300583117e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3307 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.404 y[1] (analytic) = 4.3456569533345984527548917478896 y[1] (numeric) = 4.34565695333459845275489174789 absolute error = 4e-31 relative error = 9.2045921777848527978534638804223e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3297 Order of pole = 651 TOP MAIN SOLVE Loop memory used=614.1MB, alloc=4.2MB, time=23.17 x[1] = 0.405 y[1] (analytic) = 4.3604891707092581763130247472204 y[1] (numeric) = 4.3604891707092581763130247472217 absolute error = 1.3e-30 relative error = 2.9813168869504328161765189875398e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3287 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.406 y[1] (analytic) = 4.3754096012235055693021386603878 y[1] (numeric) = 4.3754096012235055693021386603873 absolute error = 5e-31 relative error = 1.1427501550030513305618025987954e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3277 Order of pole = 651 TOP MAIN SOLVE Loop memory used=618.0MB, alloc=4.2MB, time=23.32 x[1] = 0.407 y[1] (analytic) = 4.390419057693286915631052905481 y[1] (numeric) = 4.3904190576932869156310529054813 absolute error = 3e-31 relative error = 6.8330607183000682775803737588267e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3267 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.408 y[1] (analytic) = 4.4055183629092705462775648683032 y[1] (numeric) = 4.4055183629092705462775648683035 absolute error = 3e-31 relative error = 6.8096413472191070377973809381155e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3257 Order of pole = 651 TOP MAIN SOLVE Loop memory used=621.8MB, alloc=4.2MB, time=23.46 x[1] = 0.409 y[1] (analytic) = 4.4207083497904745069318178352082 y[1] (numeric) = 4.4207083497904745069318178352094 absolute error = 1.2e-30 relative error = 2.7144971010287879189146707415277e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3247 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 4.4359898615407416723650735259643 y[1] (numeric) = 4.4359898615407416723650735259637 absolute error = 6e-31 relative error = 1.3525729740770945887429634570147e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3237 Order of pole = 651 TOP MAIN SOLVE Loop memory used=625.6MB, alloc=4.2MB, time=23.61 x[1] = 0.411 y[1] (analytic) = 4.4513637518081240750127119076597 y[1] (numeric) = 4.4513637518081240750127119076598 absolute error = 1e-31 relative error = 2.2465025456385236238340759852241e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3227 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.412 y[1] (analytic) = 4.4668308848472397512786520323279 y[1] (numeric) = 4.4668308848472397512786520323276 absolute error = 3e-31 relative error = 6.7161709886462298763927122692896e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3217 Order of pole = 651 TOP MAIN SOLVE Loop memory used=629.4MB, alloc=4.2MB, time=23.75 x[1] = 0.413 y[1] (analytic) = 4.4823921356846669881929565284983 y[1] (numeric) = 4.4823921356846669881929565284978 absolute error = 5e-31 relative error = 1.1154758103813847907584015524888e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3207 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.414 y[1] (analytic) = 4.4980483902874424766334790495758 y[1] (numeric) = 4.4980483902874424766334790495759 absolute error = 1e-31 relative error = 2.2231863982594819962944930429947e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3197 Order of pole = 651 TOP MAIN SOLVE Loop memory used=633.2MB, alloc=4.2MB, time=23.90 x[1] = 0.415 y[1] (analytic) = 4.5138005457347315467509062253173 y[1] (numeric) = 4.5138005457347315467509062253182 absolute error = 9e-31 relative error = 1.9938851769833861057038115799768e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3187 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.416 y[1] (analytic) = 4.5296495103927403779575968896033 y[1] (numeric) = 4.5296495103927403779575968896047 absolute error = 1.4e-30 relative error = 3.0907468597468016703419919586672e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3177 Order of pole = 651 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.2MB, time=24.04 x[1] = 0.417 y[1] (analytic) = 4.5455962040929418413475205615705 y[1] (numeric) = 4.5455962040929418413475205615705 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3167 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.418 y[1] (analytic) = 4.5616415583136884482526642209161 y[1] (numeric) = 4.5616415583136884482526642209158 absolute error = 3e-31 relative error = 6.5765798597928774106831846468857e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3157 Order of pole = 651 TOP MAIN SOLVE Loop memory used=640.8MB, alloc=4.2MB, time=24.19 x[1] = 0.419 y[1] (analytic) = 4.5777865163652877464098461293724 y[1] (numeric) = 4.5777865163652877464098461293728 absolute error = 4e-31 relative error = 8.7378473978641452697138112294506e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3147 Order of pole = 651 TOP MAIN SOLVE Loop memory used=644.7MB, alloc=4.2MB, time=24.33 x[1] = 0.42 y[1] (analytic) = 4.5940320335786174265663637352369 y[1] (numeric) = 4.5940320335786174265663637352371 absolute error = 2e-31 relative error = 4.3534742147674101673440072904150e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3137 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.421 y[1] (analytic) = 4.610379077497359379006958756356 y[1] (numeric) = 4.6103790774973593790069587563557 absolute error = 3e-31 relative error = 6.5070571195383841344514195302332e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3127 Order of pole = 651 TOP MAIN SOLVE Loop memory used=648.5MB, alloc=4.2MB, time=24.47 x[1] = 0.422 y[1] (analytic) = 4.6268286280739339732123307351219 y[1] (numeric) = 4.6268286280739339732123307351224 absolute error = 5e-31 relative error = 1.0806538132105857995314291739123e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3117 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.423 y[1] (analytic) = 4.6433816778692179264978059251744 y[1] (numeric) = 4.6433816778692179264978059251745 absolute error = 1e-31 relative error = 2.1536028467487209320461176232337e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3107 Order of pole = 651 TOP MAIN SOLVE Loop memory used=652.3MB, alloc=4.2MB, time=24.62 x[1] = 0.424 y[1] (analytic) = 4.6600392322561312809319511331586 y[1] (numeric) = 4.660039232256131280931951133158 absolute error = 6e-31 relative error = 1.2875428083241982481338048676161e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3097 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.425 y[1] (analytic) = 4.6768023096271812240688727596621 y[1] (numeric) = 4.6768023096271812240688727596633 absolute error = 1.2e-30 relative error = 2.5658557290946512537402800554999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3087 Order of pole = 651 TOP MAIN SOLVE Loop memory used=656.1MB, alloc=4.2MB, time=24.76 x[1] = 0.426 y[1] (analytic) = 4.6936719416060527700850446322195 y[1] (numeric) = 4.69367194160605277008504463222 absolute error = 5e-31 relative error = 1.0652640538591049708999390106690e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3077 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.427 y[1] (analytic) = 4.7106491732633386659053288080635 y[1] (numeric) = 4.7106491732633386659053288080642 absolute error = 7e-31 relative error = 1.4859947626179717887621765240954e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3067 Order of pole = 651 TOP MAIN SOLVE Loop memory used=659.9MB, alloc=4.2MB, time=24.91 x[1] = 0.428 y[1] (analytic) = 4.7277350633365033040230080909884 y[1] (numeric) = 4.7277350633365033040230080909884 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3057 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.429 y[1] (analytic) = 4.7449306844541779122338016982065 y[1] (numeric) = 4.7449306844541779122338016982079 absolute error = 1.4e-30 relative error = 2.9505172848716666773434453165414e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3047 Order of pole = 651 TOP MAIN SOLVE Loop memory used=663.7MB, alloc=4.2MB, time=25.05 x[1] = 0.43 y[1] (analytic) = 4.7622371233648868527648212392127 y[1] (numeric) = 4.762237123364886852764821239212 absolute error = 7e-31 relative error = 1.4698974071778184660561924016609e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3037 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.431 y[1] (analytic) = 4.7796554811703075017225061115617 y[1] (numeric) = 4.779655481170307501722506111563 absolute error = 1.3e-30 relative error = 2.7198613061577663982088499982160e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3027 Order of pole = 651 TOP MAIN SOLVE Loop memory used=667.5MB, alloc=4.2MB, time=25.19 x[1] = 0.432 y[1] (analytic) = 4.797186873563168896933844904337 y[1] (numeric) = 4.7971868735631688969338449043361 absolute error = 9e-31 relative error = 1.8760995219090017512662350047070e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3017 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.433 y[1] (analytic) = 4.8148324310698971407301026654177 y[1] (numeric) = 4.8148324310698971407301026654173 absolute error = 4e-31 relative error = 8.3076619119456367610818358819892e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.3007 Order of pole = 651 TOP MAIN SOLVE Loop memory used=671.4MB, alloc=4.2MB, time=25.34 x[1] = 0.434 y[1] (analytic) = 4.8325932992981184267353626106778 y[1] (numeric) = 4.8325932992981184267353626106785 absolute error = 7e-31 relative error = 1.4484976422527990931938163564621e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2997 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.435 y[1] (analytic) = 4.8504706391891335290869136419764 y[1] (numeric) = 4.8504706391891335290869136419773 absolute error = 9e-31 relative error = 1.8554900481790267402136630583364e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2987 Order of pole = 651 TOP MAIN SOLVE Loop memory used=675.2MB, alloc=4.2MB, time=25.48 x[1] = 0.436 y[1] (analytic) = 4.8684656272754806516482874737115 y[1] (numeric) = 4.8684656272754806516482874737119 absolute error = 4e-31 relative error = 8.2161409902743906393333574442438e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2977 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.437 y[1] (analytic) = 4.886579455943706686704148307505 y[1] (numeric) = 4.8865794559437066867041483075054 absolute error = 4e-31 relative error = 8.1856849685206058641593229759259e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2967 Order of pole = 651 TOP MAIN SOLVE Loop memory used=679.0MB, alloc=4.2MB, time=25.62 x[1] = 0.438 y[1] (analytic) = 4.9048133337024701804873917568064 y[1] (numeric) = 4.9048133337024701804873917568076 absolute error = 1.2e-30 relative error = 2.4465762881421675325748015765646e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2957 Order of pole = 651 TOP MAIN SOLVE Loop memory used=682.8MB, alloc=4.2MB, time=25.77 x[1] = 0.439 y[1] (analytic) = 4.9231684854561026499379798669934 y[1] (numeric) = 4.9231684854561026499379798669947 absolute error = 1.3e-30 relative error = 2.6405758889634317155979767182941e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2947 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 4.9416461527837583447074070527968 y[1] (numeric) = 4.9416461527837583447074070527962 absolute error = 6e-31 relative error = 1.2141703016554601528623621000509e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2937 Order of pole = 651 TOP MAIN SOLVE Loop memory used=686.6MB, alloc=4.2MB, time=25.91 x[1] = 0.441 y[1] (analytic) = 4.9602475942242861041063571324483 y[1] (numeric) = 4.9602475942242861041063571324497 absolute error = 1.4e-30 relative error = 2.8224397540763095188919958217227e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2927 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.442 y[1] (analytic) = 4.978974085566960624082313190325 y[1] (numeric) = 4.9789740855669606240823131903252 absolute error = 2e-31 relative error = 4.0168917645054544481174746500744e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2917 Order of pole = 651 TOP MAIN SOLVE Loop memory used=690.4MB, alloc=4.2MB, time=26.06 x[1] = 0.443 y[1] (analytic) = 4.9978269201482142281824524797358 y[1] (numeric) = 4.997826920148214228182452479735 absolute error = 8e-31 relative error = 1.6006956879096473641110988662678e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2907 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.444 y[1] (analytic) = 5.0168074091545141327222240641277 y[1] (numeric) = 5.016807409154514132722224064127 absolute error = 7e-31 relative error = 1.3953096918224561912994773778745e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2897 Order of pole = 651 TOP MAIN SOLVE Loop memory used=694.3MB, alloc=4.2MB, time=26.20 x[1] = 0.445 y[1] (analytic) = 5.0359168819315342141079428808447 y[1] (numeric) = 5.0359168819315342141079428808449 absolute error = 2e-31 relative error = 3.9714714259400101656254523380216e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2887 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.446 y[1] (analytic) = 5.0551566862997744296743905024794 y[1] (numeric) = 5.0551566862997744296743905024804 absolute error = 1.0e-30 relative error = 1.9781780507618063577937694796978e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2877 Order of pole = 651 TOP MAIN SOLVE Loop memory used=698.1MB, alloc=4.2MB, time=26.34 x[1] = 0.447 y[1] (analytic) = 5.0745281888767853168796222546312 y[1] (numeric) = 5.0745281888767853168796222546317 absolute error = 5e-31 relative error = 9.8531327719488308536103560885658e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2867 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.448 y[1] (analytic) = 5.0940327754061594038015603709419 y[1] (numeric) = 5.0940327754061594038015603709408 absolute error = 1.1e-30 relative error = 2.1593893257043175814463582652701e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2857 Order of pole = 651 TOP MAIN SOLVE Loop memory used=701.9MB, alloc=4.2MB, time=26.49 x[1] = 0.449 y[1] (analytic) = 5.1136718510934559113330212686105 y[1] (numeric) = 5.1136718510934559113330212686095 absolute error = 1.0e-30 relative error = 1.9555419845451563453644744676426e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2847 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 5.1334468409492298191854396837764 y[1] (numeric) = 5.133446840949229819185439683777 absolute error = 6e-31 relative error = 1.1688053243560101098268245322167e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2837 Order of pole = 651 TOP MAIN SOLVE Loop memory used=705.7MB, alloc=4.2MB, time=26.63 x[1] = 0.451 y[1] (analytic) = 5.1533591901393412088896936959504 y[1] (numeric) = 5.1533591901393412088896936959491 absolute error = 1.3e-30 relative error = 2.5226264113075522271660896972651e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2827 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.452 y[1] (analytic) = 5.1734103643427257927273469978856 y[1] (numeric) = 5.1734103643427257927273469978868 absolute error = 1.2e-30 relative error = 2.3195530906863566425988917779815e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2817 Order of pole = 651 TOP MAIN SOLVE Loop memory used=709.5MB, alloc=4.2MB, time=26.77 x[1] = 0.453 y[1] (analytic) = 5.1936018501168126934473351333489 y[1] (numeric) = 5.1936018501168126934473351333489 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2807 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.454 y[1] (analytic) = 5.2139351552707808614483549309271 y[1] (numeric) = 5.2139351552707808614483549309277 absolute error = 6e-31 relative error = 1.1507622978269271539630677063359e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2797 Order of pole = 651 TOP MAIN SOLVE Loop memory used=713.3MB, alloc=4.2MB, time=26.92 x[1] = 0.455 y[1] (analytic) = 5.2344118092468510097887225282589 y[1] (numeric) = 5.2344118092468510097887225282602 absolute error = 1.3e-30 relative error = 2.4835646245935117185854457573134e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2787 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.456 y[1] (analytic) = 5.2550333635098156191117912466715 memory used=717.1MB, alloc=4.2MB, time=27.06 y[1] (numeric) = 5.2550333635098156191117912466712 absolute error = 3e-31 relative error = 5.7088124707857460344373555228280e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2777 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.457 y[1] (analytic) = 5.2758013919450154207807326802417 y[1] (numeric) = 5.2758013919450154207807326802425 absolute error = 8e-31 relative error = 1.5163573087141291441104549875782e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2767 Order of pole = 651 TOP MAIN SOLVE Loop memory used=721.0MB, alloc=4.2MB, time=27.20 x[1] = 0.458 y[1] (analytic) = 5.2967174912649768138928779041183 y[1] (numeric) = 5.296717491264976813892877904119 absolute error = 7e-31 relative error = 1.3215732218197350972057084184407e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2757 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.459 y[1] (analytic) = 5.3177832814249309173501294606991 y[1] (numeric) = 5.3177832814249309173501294606995 absolute error = 4e-31 relative error = 7.5219312038759442768070997905690e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2747 Order of pole = 651 TOP MAIN SOLVE Loop memory used=724.8MB, alloc=4.2MB, time=27.35 x[1] = 0.46 y[1] (analytic) = 5.3390004060474414090371186967038 y[1] (numeric) = 5.3390004060474414090371186967037 absolute error = 1e-31 relative error = 1.8730097845044332773708351796032e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2737 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.461 y[1] (analytic) = 5.360370532856374967933725835238 y[1] (numeric) = 5.3603705328563749679337258352377 absolute error = 3e-31 relative error = 5.5966280345948271186296536938343e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2727 Order of pole = 651 TOP MAIN SOLVE Loop memory used=728.6MB, alloc=4.2MB, time=27.49 x[1] = 0.462 y[1] (analytic) = 5.3818953541204550194991258974216 y[1] (numeric) = 5.3818953541204550194991258974219 absolute error = 3e-31 relative error = 5.5742443927363947558055853593481e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2717 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.463 y[1] (analytic) = 5.403576587106646598064907379662 y[1] (numeric) = 5.4035765871066465980649073796619 absolute error = 1e-31 relative error = 1.8506261249004551250731303976904e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2707 Order of pole = 651 TOP MAIN SOLVE Loop memory used=732.4MB, alloc=4.2MB, time=27.64 x[1] = 0.464 y[1] (analytic) = 5.4254159745436274907518460240942 y[1] (numeric) = 5.425415974543627490751846024094 absolute error = 2e-31 relative error = 3.6863532849538509899472849452339e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2697 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.465 y[1] (analytic) = 5.4474152850956084244128478538782 y[1] (numeric) = 5.4474152850956084244128478538769 absolute error = 1.3e-30 relative error = 2.3864528991517552343866560537821e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2687 Order of pole = 651 TOP MAIN SOLVE Loop memory used=736.2MB, alloc=4.2MB, time=27.78 x[1] = 0.466 y[1] (analytic) = 5.4695763138467729095006538502565 y[1] (numeric) = 5.4695763138467729095006538502576 absolute error = 1.1e-30 relative error = 2.0111246957378422612789039414517e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2677 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.467 y[1] (analytic) = 5.491900882796615472139711557682 y[1] (numeric) = 5.4919008827966154721397115576834 absolute error = 1.4e-30 relative error = 2.5492084250564340623675404258415e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2667 Order of pole = 651 TOP MAIN SOLVE Loop memory used=740.0MB, alloc=4.2MB, time=27.92 x[1] = 0.468 y[1] (analytic) = 5.5143908413664653980202255097914 y[1] (numeric) = 5.5143908413664653980202255097913 absolute error = 1e-31 relative error = 1.8134369303286455450469831783080e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2657 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.469 y[1] (analytic) = 5.5370480669174917894163020247657 y[1] (numeric) = 5.5370480669174917894163020247666 absolute error = 9e-31 relative error = 1.6254148223442016344063352739994e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2647 Order of pole = 651 TOP MAIN SOLVE Loop memory used=743.8MB, alloc=4.2MB, time=28.07 x[1] = 0.47 y[1] (analytic) = 5.5598744652804947104801121061443 y[1] (numeric) = 5.5598744652804947104801121061453 absolute error = 1.0e-30 relative error = 1.7986017602459485962496084235948e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2637 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.471 y[1] (analytic) = 5.5828719712977964772540135853044 y[1] (numeric) = 5.5828719712977964772540135853031 absolute error = 1.3e-30 relative error = 2.3285506217650223503093715007663e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2627 Order of pole = 651 TOP MAIN SOLVE Loop memory used=747.7MB, alloc=4.2MB, time=28.21 x[1] = 0.472 y[1] (analytic) = 5.6060425493775567493203784224942 y[1] (numeric) = 5.6060425493775567493203784224931 absolute error = 1.1e-30 relative error = 1.9621684821534825004873915353345e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2617 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.473 y[1] (analytic) = 5.6293881940608450119179272118659 y[1] (numeric) = 5.6293881940608450119179272118672 absolute error = 1.3e-30 relative error = 2.3093095647081768886114851711636e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2607 Order of pole = 651 TOP MAIN SOLVE Loop memory used=751.5MB, alloc=4.2MB, time=28.36 x[1] = 0.474 y[1] (analytic) = 5.6529109306018143134557343650818 y[1] (numeric) = 5.6529109306018143134557343650809 absolute error = 9e-31 relative error = 1.5921000897570928784349379601733e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2597 Order of pole = 651 TOP MAIN SOLVE Loop memory used=755.3MB, alloc=4.2MB, time=28.51 x[1] = 0.475 y[1] (analytic) = 5.6766128155613307569564332628322 y[1] (numeric) = 5.6766128155613307569564332628336 absolute error = 1.4e-30 relative error = 2.4662594499349543388079490423163e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2587 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.476 y[1] (analytic) = 5.700495937414424248931133718096 y[1] (numeric) = 5.7004959374144242489311337180945 absolute error = 1.5e-30 relative error = 2.6313500026461828792069918703002e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2577 Order of pole = 651 TOP MAIN SOLVE Loop memory used=759.1MB, alloc=4.2MB, time=28.65 x[1] = 0.477 y[1] (analytic) = 5.724562417171937399997239319719 y[1] (numeric) = 5.7245624171719373999972393197191 absolute error = 1e-31 relative error = 1.7468584096494531604443436413904e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2567 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.478 y[1] (analytic) = 5.748814409016761263286154671349 y[1] (numeric) = 5.7488144090167612632861546713492 absolute error = 2e-31 relative error = 3.4789781991624019272522399389175e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2557 Order of pole = 651 TOP MAIN SOLVE Loop memory used=762.9MB, alloc=4.2MB, time=28.80 x[1] = 0.479 y[1] (analytic) = 5.7732541009550588050919193465264 y[1] (numeric) = 5.773254100955058805091919346528 absolute error = 1.6e-30 relative error = 2.7714006208999443545317528612085e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2547 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 5.7978837154828896437077202436037 y[1] (numeric) = 5.7978837154828896437077202436038 absolute error = 1e-31 relative error = 1.7247672583179995277211384573911e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2537 Order of pole = 651 TOP MAIN SOLVE Loop memory used=766.7MB, alloc=4.2MB, time=28.94 x[1] = 0.481 y[1] (analytic) = 5.8227055102686626841235574112853 y[1] (numeric) = 5.8227055102686626841235574112849 absolute error = 4e-31 relative error = 6.8696587745091678240528806917442e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2527 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.482 y[1] (analytic) = 5.8477217788518568361026117246748 y[1] (numeric) = 5.8477217788518568361026117246736 absolute error = 1.2e-30 relative error = 2.0520812127891766793710481529084e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2517 Order of pole = 651 TOP MAIN SOLVE Loop memory used=770.5MB, alloc=4.2MB, time=29.09 x[1] = 0.483 y[1] (analytic) = 5.8729348513584640497884799295123 y[1] (numeric) = 5.8729348513584640497884799295136 absolute error = 1.3e-30 relative error = 2.2135440506364513790898276652178e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2507 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.484 y[1] (analytic) = 5.8983470952336234559153680559059 y[1] (numeric) = 5.8983470952336234559153680559074 absolute error = 1.5e-30 relative error = 2.5430853352325268025440413286996e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2497 Order of pole = 651 TOP MAIN SOLVE Loop memory used=774.4MB, alloc=4.2MB, time=29.23 x[1] = 0.485 y[1] (analytic) = 5.9239609159919304772557928462547 y[1] (numeric) = 5.9239609159919304772557928462549 absolute error = 2e-31 relative error = 3.3761195057869695899828771534936e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2487 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.486 y[1] (analytic) = 5.9497787579859204054065904689257 y[1] (numeric) = 5.9497787579859204054065904689253 absolute error = 4e-31 relative error = 6.7229390582483665952165704825726e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2477 Order of pole = 651 TOP MAIN SOLVE Loop memory used=778.2MB, alloc=4.2MB, time=29.38 x[1] = 0.487 y[1] (analytic) = 5.9758031051932421345933371751559 y[1] (numeric) = 5.9758031051932421345933371751577 absolute error = 1.8e-30 relative error = 3.0121474357743127481776568358778e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2467 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.488 y[1] (analytic) = 6.002036482023054535069220032638 y[1] (numeric) = 6.0020364820230545350692200326397 absolute error = 1.7e-30 relative error = 2.8323719875607882019341086974668e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2457 Order of pole = 651 TOP MAIN SOLVE Loop memory used=782.0MB, alloc=4.2MB, time=29.52 x[1] = 0.489 y[1] (analytic) = 6.0284814541421953571435976959717 y[1] (numeric) = 6.0284814541421953571435976959703 absolute error = 1.4e-30 relative error = 2.3223095412163108174652372696237e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2447 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 6.0551406293216906082390309989501 y[1] (numeric) = 6.0551406293216906082390309989515 absolute error = 1.4e-30 relative error = 2.3120850294055530449332805690916e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2437 Order of pole = 651 TOP MAIN SOLVE Loop memory used=785.8MB, alloc=4.2MB, time=29.67 x[1] = 0.491 y[1] (analytic) = 6.0820166583041910661330525886638 y[1] (numeric) = 6.0820166583041910661330525886626 absolute error = 1.2e-30 relative error = 1.9730297817608874374072606450489e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2427 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.492 y[1] (analytic) = 6.1091122356929420093875604981361 y[1] (numeric) = 6.1091122356929420093875604981371 absolute error = 1.0e-30 relative error = 1.6368990475529745910494076628605e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2417 Order of pole = 651 TOP MAIN SOLVE Loop memory used=789.6MB, alloc=4.2MB, time=29.82 x[1] = 0.493 y[1] (analytic) = 6.1364301008629123898653069373943 y[1] (numeric) = 6.1364301008629123898653069373943 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2407 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.494 y[1] (analytic) = 6.1639730388947305724693854177991 y[1] (numeric) = 6.1639730388947305724693854178001 absolute error = 1.0e-30 relative error = 1.6223302627866639794413843858050e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2397 Order of pole = 651 memory used=793.4MB, alloc=4.2MB, time=29.96 TOP MAIN SOLVE Loop x[1] = 0.495 y[1] (analytic) = 6.1917438815320954555036149066208 y[1] (numeric) = 6.191743881532095455503614906622 absolute error = 1.2e-30 relative error = 1.9380646599081711277247682352659e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2387 Order of pole = 651 TOP MAIN SOLVE Loop memory used=797.3MB, alloc=4.2MB, time=30.10 x[1] = 0.496 y[1] (analytic) = 6.2197455081633542944913082074536 y[1] (numeric) = 6.2197455081633542944913082074543 absolute error = 7e-31 relative error = 1.1254479770615324088788173213143e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2377 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.497 y[1] (analytic) = 6.2479808468279619175997707382535 y[1] (numeric) = 6.2479808468279619175997707382549 absolute error = 1.4e-30 relative error = 2.2407238983627265019147536575826e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2367 Order of pole = 651 TOP MAIN SOLVE Loop memory used=801.1MB, alloc=4.2MB, time=30.25 x[1] = 0.498 y[1] (analytic) = 6.2764528752485602783097688620986 y[1] (numeric) = 6.2764528752485602783097688620995 absolute error = 9e-31 relative error = 1.4339309445772874898449515837412e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2357 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.499 y[1] (analytic) = 6.3051646218894424786567656321692 y[1] (numeric) = 6.3051646218894424786567656321677 absolute error = 1.5e-30 relative error = 2.3790021196155561023851403327103e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2347 Order of pole = 651 TOP MAIN SOLVE Loop memory used=804.9MB, alloc=4.2MB, time=30.40 x[1] = 0.5 y[1] (analytic) = 6.3341191670421915540568332642278 y[1] (numeric) = 6.3341191670421915540568332642276 absolute error = 2e-31 relative error = 3.1575029570116674824638062185873e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2337 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.501 y[1] (analytic) = 6.3633196439393114800992272472331 y[1] (numeric) = 6.3633196439393114800992272472346 absolute error = 1.5e-30 relative error = 2.3572601785432262078043143664602e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2327 Order of pole = 651 TOP MAIN SOLVE Loop memory used=808.7MB, alloc=4.2MB, time=30.54 x[1] = 0.502 y[1] (analytic) = 6.3927692398966960864030285269123 y[1] (numeric) = 6.3927692398966960864030285269132 absolute error = 9e-31 relative error = 1.4078405871170528036093869098901e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2317 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.503 y[1] (analytic) = 6.4224711974858108884423169062379 y[1] (numeric) = 6.422471197485810888442316906238 absolute error = 1e-31 relative error = 1.5570330628986978677421263159208e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2307 Order of pole = 651 TOP MAIN SOLVE Loop memory used=812.5MB, alloc=4.2MB, time=30.69 x[1] = 0.504 y[1] (analytic) = 6.4524288157364933230789902991232 y[1] (numeric) = 6.4524288157364933230789902991225 absolute error = 7e-31 relative error = 1.0848628012645507644258898760476e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2297 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.505 y[1] (analytic) = 6.4826454513713085476461659480604 y[1] (numeric) = 6.4826454513713085476461659480585 absolute error = 1.9e-30 relative error = 2.9309022285000683975000761454990e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2287 Order of pole = 651 TOP MAIN SOLVE Loop memory used=816.3MB, alloc=4.2MB, time=30.83 x[1] = 0.506 y[1] (analytic) = 6.5131245200724308884667897467052 y[1] (numeric) = 6.5131245200724308884667897467031 absolute error = 2.1e-30 relative error = 3.2242589459607727659254188800156e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2277 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.507 y[1] (analytic) = 6.5438694977820552578959359049392 y[1] (numeric) = 6.5438694977820552578959359049404 absolute error = 1.2e-30 relative error = 1.8337774009807525875469424062519e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2267 Order of pole = 651 TOP MAIN SOLVE Loop memory used=820.1MB, alloc=4.2MB, time=30.97 x[1] = 0.508 y[1] (analytic) = 6.574883922037378457257073357651 y[1] (numeric) = 6.5748839220373784572570733576504 absolute error = 6e-31 relative error = 9.1256363931985015187517156489527e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2257 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.509 y[1] (analytic) = 6.6061713933412273071532906441384 y[1] (numeric) = 6.6061713933412273071532906441366 absolute error = 1.8e-30 relative error = 2.7247249470613681130057318439949e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2247 Order of pole = 651 TOP MAIN SOLVE Loop memory used=824.0MB, alloc=4.2MB, time=31.12 x[1] = 0.51 y[1] (analytic) = 6.6377355765694490603123912881818 y[1] (numeric) = 6.6377355765694490603123912881821 absolute error = 3e-31 relative error = 4.5196136022496944191655473249644e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2237 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.511 y[1] (analytic) = 6.6695802024162196222564492844704 y[1] (numeric) = 6.6695802024162196222564492844685 absolute error = 1.9e-30 relative error = 2.8487550075665605238117320799281e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2227 Order of pole = 651 TOP MAIN SOLVE Loop memory used=827.8MB, alloc=4.2MB, time=31.27 x[1] = 0.512 y[1] (analytic) = 6.7017090688784668018770764525868 y[1] (numeric) = 6.7017090688784668018770764525859 absolute error = 9e-31 relative error = 1.3429410181045285116987668391758e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2217 Order of pole = 651 TOP MAIN SOLVE Loop memory used=831.6MB, alloc=4.2MB, time=31.41 x[1] = 0.513 y[1] (analytic) = 6.7341260427806492111516465192235 y[1] (numeric) = 6.7341260427806492111516465192228 absolute error = 7e-31 relative error = 1.0394815831379310441063332658017e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2207 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.514 y[1] (analytic) = 6.76683506134117660814763143496 y[1] (numeric) = 6.7668350613411766081476314349593 absolute error = 7e-31 relative error = 1.0344570152139352498213325083991e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2197 Order of pole = 651 TOP MAIN SOLVE Loop memory used=835.4MB, alloc=4.2MB, time=31.56 x[1] = 0.515 y[1] (analytic) = 6.7998401337818045114193422737278 y[1] (numeric) = 6.7998401337818045114193422737255 absolute error = 2.3e-30 relative error = 3.3824324612773361861920921764307e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2187 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.516 y[1] (analytic) = 6.833145342981384892298333816744 y[1] (numeric) = 6.8331453429813848922983338167435 absolute error = 5e-31 relative error = 7.3172744746834827939395823672047e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2177 Order of pole = 651 TOP MAIN SOLVE Loop memory used=839.2MB, alloc=4.2MB, time=31.70 x[1] = 0.517 y[1] (analytic) = 6.866754847175405764144872760369 y[1] (numeric) = 6.8667548471754057641448727603676 absolute error = 1.4e-30 relative error = 2.0388087694376926093647557042550e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2167 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.518 y[1] (analytic) = 6.9006728817028056286684222708353 y[1] (numeric) = 6.9006728817028056286684222708333 absolute error = 2.0e-30 relative error = 2.8982680881787882671028875276242e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2157 Order of pole = 651 TOP MAIN SOLVE Loop memory used=843.0MB, alloc=4.2MB, time=31.85 x[1] = 0.519 y[1] (analytic) = 6.934903760801604108076946821595 y[1] (numeric) = 6.9349037608016041080769468215958 absolute error = 8e-31 relative error = 1.1535848623046041572408569764561e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2147 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 6.9694518794549477923178392103793 y[1] (numeric) = 6.969451879454947792317839210377 absolute error = 2.3e-30 relative error = 3.3001160489824252202319819647444e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2137 Order of pole = 651 TOP MAIN SOLVE Loop memory used=846.8MB, alloc=4.2MB, time=31.99 x[1] = 0.521 y[1] (analytic) = 7.0043217152892304726581220703007 y[1] (numeric) = 7.0043217152892304726581220703013 absolute error = 6e-31 relative error = 8.5661399402929069051496965635281e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2127 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.522 y[1] (analytic) = 7.0395178305260096316454166517755 y[1] (numeric) = 7.0395178305260096316454166517771 absolute error = 1.6e-30 relative error = 2.2728829424393178475228528088757e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2117 Order of pole = 651 TOP MAIN SOLVE Loop memory used=850.7MB, alloc=4.2MB, time=32.14 x[1] = 0.523 y[1] (analytic) = 7.0750448739895064364419997466559 y[1] (numeric) = 7.075044873989506436441999746656 absolute error = 1e-31 relative error = 1.4134185970697818923660456922962e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2107 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.524 y[1] (analytic) = 7.1109075831715446653454833804513 y[1] (numeric) = 7.1109075831715446653454833804522 absolute error = 9e-31 relative error = 1.2656612246373618168817128195049e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2097 Order of pole = 651 TOP MAIN SOLVE Loop memory used=854.5MB, alloc=4.2MB, time=32.28 x[1] = 0.525 y[1] (analytic) = 7.147110786355855120446051713375 y[1] (numeric) = 7.1471107863558551204460517133736 absolute error = 1.4e-30 relative error = 1.9588334948895164741528228903176e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2087 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.526 y[1] (analytic) = 7.183659404803746284386888278794 y[1] (numeric) = 7.1836594048037462843868882787964 absolute error = 2.4e-30 relative error = 3.3409156319342045847337906770962e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2077 Order of pole = 651 TOP MAIN SOLVE Loop memory used=858.3MB, alloc=4.2MB, time=32.43 x[1] = 0.527 y[1] (analytic) = 7.2205584550032194151902191935583 y[1] (numeric) = 7.2205584550032194151902191935572 absolute error = 1.1e-30 relative error = 1.5234278717566445424155856876864e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2067 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.528 y[1] (analytic) = 7.2578130509836870971582555118863 y[1] (numeric) = 7.2578130509836870971582555118888 absolute error = 2.5e-30 relative error = 3.4445637858654442812501997798365e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2057 Order of pole = 651 TOP MAIN SOLVE Loop memory used=862.1MB, alloc=4.2MB, time=32.57 x[1] = 0.529 y[1] (analytic) = 7.2954284066985386434687932134004 y[1] (numeric) = 7.2954284066985386434687932134029 absolute error = 2.5e-30 relative error = 3.4268035550928611625650699003283e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2047 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 7.3334098384778838517096913829561 y[1] (numeric) = 7.3334098384778838517096913829574 absolute error = 1.3e-30 relative error = 1.7727087789079941369527837975262e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2037 Order of pole = 651 TOP MAIN SOLVE Loop memory used=865.9MB, alloc=4.2MB, time=32.71 x[1] = 0.531 y[1] (analytic) = 7.3717627675538986311522074816167 y[1] (numeric) = 7.3717627675538986311522074816171 absolute error = 4e-31 relative error = 5.4261105872880410847899242242393e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2027 Order of pole = 651 TOP MAIN SOLVE Loop memory used=869.7MB, alloc=4.2MB, time=32.86 x[1] = 0.532 y[1] (analytic) = 7.410492722661292143997700756504 y[1] (numeric) = 7.4104927226612921439977007565036 absolute error = 4e-31 relative error = 5.3977517416190114946606974891946e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2017 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.533 y[1] (analytic) = 7.4496053427155155367228757823826 y[1] (numeric) = 7.4496053427155155367228757823844 absolute error = 1.8e-30 relative error = 2.4162353805226781696614223041298e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.2007 Order of pole = 651 TOP MAIN SOLVE Loop memory used=873.5MB, alloc=4.3MB, time=33.00 x[1] = 0.534 y[1] (analytic) = 7.4891063795714372978415093284686 y[1] (numeric) = 7.489106379571437297841509328468 absolute error = 6e-31 relative error = 8.0116367639891221174357900046342e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1997 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.535 y[1] (analytic) = 7.5290017008653199926906323501524 y[1] (numeric) = 7.5290017008653199926906323501527 absolute error = 3e-31 relative error = 3.9845920072713030299080479657682e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1987 Order of pole = 651 TOP MAIN SOLVE Loop memory used=877.4MB, alloc=4.3MB, time=33.15 x[1] = 0.536 y[1] (analytic) = 7.5692972929430478347060265257454 y[1] (numeric) = 7.5692972929430478347060265257447 absolute error = 7e-31 relative error = 9.2478862027604452216406648632704e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1977 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.537 y[1] (analytic) = 7.6099992638776745099929207844257 y[1] (numeric) = 7.6099992638776745099929207844277 absolute error = 2.0e-30 relative error = 2.6281211477816886957323577631943e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1967 Order of pole = 651 TOP MAIN SOLVE Loop memory used=881.2MB, alloc=4.3MB, time=33.29 x[1] = 0.538 y[1] (analytic) = 7.6511138465794861460124818994577 y[1] (numeric) = 7.6511138465794861460124818994598 absolute error = 2.1e-30 relative error = 2.7446984087667547820117956729806e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1957 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.539 y[1] (analytic) = 7.6926474020019055892345374840675 y[1] (numeric) = 7.6926474020019055892345374840658 absolute error = 1.7e-30 relative error = 2.2099024057148367442834592719179e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1947 Order of pole = 651 TOP MAIN SOLVE Loop memory used=885.0MB, alloc=4.3MB, time=33.44 x[1] = 0.54 y[1] (analytic) = 7.7346064224467015300839918803707 y[1] (numeric) = 7.7346064224467015300839918803704 absolute error = 3e-31 relative error = 3.8786718239387864953153367454391e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1937 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.541 y[1] (analytic) = 7.7769975349721098029572327557455 y[1] (numeric) = 7.7769975349721098029572327557457 absolute error = 2e-31 relative error = 2.5716865551342527003584719043260e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1927 Order of pole = 651 TOP MAIN SOLVE Loop memory used=888.8MB, alloc=4.3MB, time=33.58 x[1] = 0.542 y[1] (analytic) = 7.8198275049076247291926669557181 y[1] (numeric) = 7.8198275049076247291926669557204 absolute error = 2.3e-30 relative error = 2.9412413490662666434519672900880e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1917 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.543 y[1] (analytic) = 7.8631032394793760156390020138793 y[1] (numeric) = 7.8631032394793760156390020138793 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1907 Order of pole = 651 TOP MAIN SOLVE Loop memory used=892.6MB, alloc=4.3MB, time=33.73 x[1] = 0.544 y[1] (analytic) = 7.9068317915501718453952998512964 y[1] (numeric) = 7.9068317915501718453952998512982 absolute error = 1.8e-30 relative error = 2.2765123218172084944560935414955e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1897 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.545 y[1] (analytic) = 7.9510203634784617967494765082943 y[1] (numeric) = 7.9510203634784617967494765082914 absolute error = 2.9e-30 relative error = 3.6473306159805758304204406893434e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1887 Order of pole = 651 TOP MAIN SOLVE Loop memory used=896.4MB, alloc=4.3MB, time=33.88 x[1] = 0.546 y[1] (analytic) = 7.9956763111006545208958765913945 y[1] (numeric) = 7.9956763111006545208958765913974 absolute error = 2.9e-30 relative error = 3.6269602309611217646557141101457e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1877 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.547 y[1] (analytic) = 8.0408071478414151429675917915699 y[1] (numeric) = 8.0408071478414151429675917915712 absolute error = 1.3e-30 relative error = 1.6167531145787893682650698488207e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1867 Order of pole = 651 TOP MAIN SOLVE Loop memory used=900.3MB, alloc=4.3MB, time=34.02 x[1] = 0.548 y[1] (analytic) = 8.0864205489567665948932617910286 y[1] (numeric) = 8.0864205489567665948932617910289 absolute error = 3e-31 relative error = 3.7099232989892315105834261384630e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1857 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.549 y[1] (analytic) = 8.1325243559150280412271916082989 y[1] (numeric) = 8.1325243559150280412271916083013 absolute error = 2.4e-30 relative error = 2.9511132029434480146073848646420e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1847 Order of pole = 651 TOP MAIN SOLVE Loop memory used=904.1MB, alloc=4.3MB, time=34.16 x[1] = 0.55 y[1] (analytic) = 8.1791265809208427489106928230822 y[1] (numeric) = 8.1791265809208427489106928230802 absolute error = 2.0e-30 relative error = 2.4452488663830301440461501096276e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1837 Order of pole = 651 TOP MAIN SOLVE Loop memory used=907.9MB, alloc=4.3MB, time=34.31 x[1] = 0.551 y[1] (analytic) = 8.2262354115877777392266837053387 y[1] (numeric) = 8.2262354115877777392266837053369 absolute error = 1.8e-30 relative error = 2.1881211878090113989658608734785e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1827 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.552 y[1] (analytic) = 8.273859215765218939255455120509 y[1] (numeric) = 8.2738592157652189392554551205109 absolute error = 1.9e-30 relative error = 2.2963890857360641686595636123826e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1817 Order of pole = 651 TOP MAIN SOLVE Loop memory used=911.7MB, alloc=4.3MB, time=34.45 x[1] = 0.553 y[1] (analytic) = 8.3220065465255389513481024309871 y[1] (numeric) = 8.3220065465255389513481024309851 absolute error = 2.0e-30 relative error = 2.4032665545486810549683168862518e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1807 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.554 y[1] (analytic) = 8.370686147317780651516340687654 y[1] (numeric) = 8.3706861473177806515163406876545 absolute error = 5e-31 relative error = 5.9732259841114103062446047726850e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1797 Order of pole = 651 TOP MAIN SOLVE Loop memory used=915.5MB, alloc=4.3MB, time=34.60 x[1] = 0.555 y[1] (analytic) = 8.4199069572943793213854576055721 y[1] (numeric) = 8.4199069572943793213854576055736 absolute error = 1.5e-30 relative error = 1.7814923699370714418079233310667e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1787 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.556 y[1] (analytic) = 8.4696781168177396676254521380664 y[1] (numeric) = 8.4696781168177396676254521380683 absolute error = 1.9e-30 relative error = 2.2432965855305436020377496965557e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1777 Order of pole = 651 TOP MAIN SOLVE Loop memory used=919.3MB, alloc=4.3MB, time=34.74 x[1] = 0.557 y[1] (analytic) = 8.5200089731537926886661732708628 y[1] (numeric) = 8.5200089731537926886661732708625 absolute error = 3e-31 relative error = 3.5211230521621279305058243713892e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1767 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.558 y[1] (analytic) = 8.5709090863599817622719532859011 y[1] (numeric) = 8.5709090863599817622719532858969 absolute error = 4.2e-30 relative error = 4.9002969902971133269791045795067e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1757 Order of pole = 651 TOP MAIN SOLVE Loop memory used=923.1MB, alloc=4.3MB, time=34.89 x[1] = 0.559 y[1] (analytic) = 8.6223882353754684540555251002698 y[1] (numeric) = 8.622388235375468454055525100266 absolute error = 3.8e-30 relative error = 4.4071316394796111957379750940466e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1747 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 8.6744564243217073484077643415089 y[1] (numeric) = 8.6744564243217073484077643415089 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1737 Order of pole = 651 TOP MAIN SOLVE Loop memory used=927.0MB, alloc=4.3MB, time=35.03 x[1] = 0.561 y[1] (analytic) = 8.7271238890219167030505871829267 y[1] (numeric) = 8.7271238890219167030505871829267 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1727 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.562 y[1] (analytic) = 8.7804011037483690154935586594324 y[1] (numeric) = 8.7804011037483690154935586594307 absolute error = 1.7e-30 relative error = 1.9361302290327795434690428777345e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1717 Order of pole = 651 TOP MAIN SOLVE Loop memory used=930.8MB, alloc=4.3MB, time=35.18 x[1] = 0.563 y[1] (analytic) = 8.8342987882068438232748789202442 y[1] (numeric) = 8.834298788206843823274878920241 absolute error = 3.2e-30 relative error = 3.6222456096592191544583110856919e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1707 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.564 y[1] (analytic) = 8.8888279147680254743172794060475 y[1] (numeric) = 8.8888279147680254743172794060475 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1697 Order of pole = 651 TOP MAIN SOLVE Loop memory used=934.6MB, alloc=4.3MB, time=35.32 x[1] = 0.565 y[1] (analytic) = 8.9439997159560925138349888889776 y[1] (numeric) = 8.943999715956092513834988888978 absolute error = 4e-31 relative error = 4.4722720561629729621776009378662e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1687 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.566 y[1] (analytic) = 8.9998256922052341410375427026899 y[1] (numeric) = 8.999825692205234141037542702686 absolute error = 3.9e-30 relative error = 4.3334172609340615250101375884975e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1677 Order of pole = 651 TOP MAIN SOLVE Loop memory used=938.4MB, alloc=4.3MB, time=35.47 x[1] = 0.567 y[1] (analytic) = 9.056317619895344385888416751627 y[1] (numeric) = 9.0563176198953443858884167516284 absolute error = 1.4e-30 relative error = 1.5458821772377043958627152624576e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1667 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.568 y[1] (analytic) = 9.113487559678687836035506049083 y[1] (numeric) = 9.1134875596786878360355060490845 absolute error = 1.5e-30 relative error = 1.6459121606052701517068351673142e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1657 Order of pole = 651 TOP MAIN SOLVE Loop memory used=942.2MB, alloc=4.3MB, time=35.61 x[1] = 0.569 y[1] (analytic) = 9.1713478651099036057498970786337 y[1] (numeric) = 9.171347865109903605749897078636 absolute error = 2.3e-30 relative error = 2.5078102301078057094473401100861e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1647 Order of pole = 651 TOP MAIN SOLVE Loop memory used=946.0MB, alloc=4.3MB, time=35.76 x[1] = 0.57 y[1] (analytic) = 9.2299111915923185954694509029655 y[1] (numeric) = 9.2299111915923185954694509029692 absolute error = 3.7e-30 relative error = 4.0087059595658864575504144405037e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1637 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.571 y[1] (analytic) = 9.2891905056541788781117301202957 y[1] (numeric) = 9.2891905056541788781117301202919 absolute error = 3.8e-30 relative error = 4.0907762605223802087677574976645e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1627 Order of pole = 651 TOP MAIN SOLVE Loop memory used=949.8MB, alloc=4.3MB, time=35.90 x[1] = 0.572 y[1] (analytic) = 9.3491990945690813341484809923905 y[1] (numeric) = 9.349199094569081334148480992387 absolute error = 3.5e-30 relative error = 3.7436361816630243351166654444438e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1617 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.573 y[1] (analytic) = 9.4099505763355986504906147117629 y[1] (numeric) = 9.4099505763355986504906147117582 absolute error = 4.7e-30 relative error = 4.9947127371951226649895459022810e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1607 Order of pole = 651 TOP MAIN SOLVE Loop memory used=953.7MB, alloc=4.3MB, time=36.05 x[1] = 0.574 y[1] (analytic) = 9.4714589100318418596392176754245 y[1] (numeric) = 9.4714589100318418596392176754255 absolute error = 1.0e-30 relative error = 1.0558035562407757150218787524367e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1597 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.575 y[1] (analytic) = 9.5337384065614982500915574564859 y[1] (numeric) = 9.5337384065614982500915574564832 absolute error = 2.7e-30 relative error = 2.8320474979067524338939979909944e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1587 Order of pole = 651 TOP MAIN SOLVE Loop memory used=957.5MB, alloc=4.3MB, time=36.19 x[1] = 0.576 y[1] (analytic) = 9.5968037398087214275377220600897 y[1] (numeric) = 9.5968037398087214275377220600892 absolute error = 5e-31 relative error = 5.2100679930124917161361929541998e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1577 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.577 y[1] (analytic) = 9.6606699582201374394255163890915 y[1] (numeric) = 9.6606699582201374394255163890961 absolute error = 4.6e-30 relative error = 4.7615745283647955438922378980943e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1567 Order of pole = 651 TOP MAIN SOLVE Loop memory used=961.3MB, alloc=4.3MB, time=36.34 x[1] = 0.578 y[1] (analytic) = 9.7253524968331692876986548090793 y[1] (numeric) = 9.7253524968331692876986548090804 absolute error = 1.1e-30 relative error = 1.1310644013758770680926849050611e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1557 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.579 y[1] (analytic) = 9.7908671897708751606645337033704 y[1] (numeric) = 9.7908671897708751606645337033687 absolute error = 1.7e-30 relative error = 1.7363119803893318058114677538772e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1547 Order of pole = 651 TOP MAIN SOLVE Loop memory used=965.1MB, alloc=4.3MB, time=36.48 x[1] = 0.58 y[1] (analytic) = 9.857230283224546866989658656071 y[1] (numeric) = 9.8572302832245468669896586560743 absolute error = 3.3e-30 relative error = 3.3477963943036617001331586758999e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1537 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.581 y[1] (analytic) = 9.9244584489464280605907968461996 y[1] (numeric) = 9.9244584489464280605907968462025 absolute error = 2.9e-30 relative error = 2.9220737987047157176821214704355e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1527 Order of pole = 651 TOP MAIN SOLVE Loop memory used=968.9MB, alloc=4.3MB, time=36.63 x[1] = 0.582 y[1] (analytic) = 9.9925687982760909886369417656105 y[1] (numeric) = 9.9925687982760909886369417656124 absolute error = 1.9e-30 relative error = 1.9014129783402505037226693206382e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1517 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.583 y[1] (analytic) = 10.061578896725260058047395338774 y[1] (numeric) = 10.061578896725260058047395338775 absolute error = 1e-30 relative error = 9.9387979785704387524529001254387e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1507 Order of pole = 651 TOP MAIN SOLVE Loop memory used=972.7MB, alloc=4.3MB, time=36.77 x[1] = 0.584 y[1] (analytic) = 10.131506779147195202803730820983 y[1] (numeric) = 10.131506779147195202803730820987 absolute error = 4e-30 relative error = 3.9480800706098862842522912641220e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1497 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.585 y[1] (analytic) = 10.202370965518152897104528055904 y[1] (numeric) = 10.202370965518152897104528055905 absolute error = 1e-30 relative error = 9.8016432001912851616679072530615e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1487 Order of pole = 651 TOP MAIN SOLVE Loop memory used=976.5MB, alloc=4.3MB, time=36.92 x[1] = 0.586 y[1] (analytic) = 10.274190477359933126146976234129 y[1] (numeric) = 10.274190477359933126146976234133 absolute error = 4e-30 relative error = 3.8932507712547726088870858896366e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1477 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.587 y[1] (analytic) = 10.346984854834102532409996468839 y[1] (numeric) = 10.346984854834102532409996468839 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1467 Order of pole = 651 memory used=980.4MB, alloc=4.3MB, time=37.06 TOP MAIN SOLVE Loop x[1] = 0.588 y[1] (analytic) = 10.420774174540163576579536113019 y[1] (numeric) = 10.420774174540163576579536113025 absolute error = 6e-30 relative error = 5.7577296077090753950467458263808e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1457 Order of pole = 651 TOP MAIN SOLVE Loop memory used=984.2MB, alloc=4.3MB, time=37.20 x[1] = 0.589 y[1] (analytic) = 10.495579068051723641621690422757 y[1] (numeric) = 10.495579068051723641621690422762 absolute error = 5e-30 relative error = 4.7639105642297270907718911371433e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1447 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 10.571420741226613835820152828377 y[1] (numeric) = 10.571420741226613835820152828382 absolute error = 5e-30 relative error = 4.7297332330184451419952841920575e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1437 Order of pole = 651 TOP MAIN SOLVE Loop memory used=988.0MB, alloc=4.3MB, time=37.35 x[1] = 0.591 y[1] (analytic) = 10.648320994328922646090500821819 y[1] (numeric) = 10.648320994328922646090500821823 absolute error = 4e-30 relative error = 3.7564607623402017614004246741572e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1427 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.592 y[1] (analytic) = 10.726302243003052994653977428163 y[1] (numeric) = 10.726302243003052994653977428162 absolute error = 1e-30 relative error = 9.3228773285063525601192946673800e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1417 Order of pole = 651 TOP MAIN SOLVE Loop memory used=991.8MB, alloc=4.3MB, time=37.49 x[1] = 0.593 y[1] (analytic) = 10.805387540142191757978371095598 y[1] (numeric) = 10.805387540142191757978371095604 absolute error = 6e-30 relative error = 5.5527855689672412858476354458816e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1407 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.594 y[1] (analytic) = 10.885600598696008230911831827523 y[1] (numeric) = 10.885600598696008230911831827518 absolute error = 5e-30 relative error = 4.5932238232210656395991560458058e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1397 Order of pole = 651 TOP MAIN SOLVE Loop memory used=995.6MB, alloc=4.3MB, time=37.64 x[1] = 0.595 y[1] (analytic) = 10.966965815464982953620713018149 y[1] (numeric) = 10.966965815464982953620713018147 absolute error = 2e-30 relative error = 1.8236584609206270150524512421468e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1387 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.596 y[1] (analytic) = 11.049508295931522202932250131254 y[1] (numeric) = 11.049508295931522202932250131251 absolute error = 3e-30 relative error = 2.7150529414097216081541781115405e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1377 Order of pole = 651 TOP MAIN SOLVE Loop memory used=999.4MB, alloc=4.3MB, time=37.78 x[1] = 0.597 y[1] (analytic) = 11.133253880180948642057148553536 y[1] (numeric) = 11.133253880180948642057148553538 absolute error = 2e-30 relative error = 1.7964200057993234444579393255812e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1367 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.598 y[1] (analytic) = 11.218229169968588484343382146445 y[1] (numeric) = 11.218229169968588484343382146442 absolute error = 3e-30 relative error = 2.6742188580271266884386657441475e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1357 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1003.3MB, alloc=4.3MB, time=37.92 x[1] = 0.599 y[1] (analytic) = 11.304461556992514509695668423944 y[1] (numeric) = 11.304461556992514509695668423939 absolute error = 5e-30 relative error = 4.4230324237842077139741810064062e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1347 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 11.391979252435068017605863802322 y[1] (numeric) = 11.391979252435068017605863802328 absolute error = 6e-30 relative error = 5.2668635248062648180867584058138e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1337 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1007.1MB, alloc=4.3MB, time=38.07 x[1] = 0.601 y[1] (analytic) = 11.48081131784008824593599998256 y[1] (numeric) = 11.480811317840088245935999982561 absolute error = 1e-30 relative error = 8.7101858249869080457521935504504e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1327 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.602 y[1] (analytic) = 11.570987697396843281908389850472 y[1] (numeric) = 11.570987697396843281908389850479 absolute error = 7e-30 relative error = 6.0496132076735412365368873386049e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1317 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1010.9MB, alloc=4.3MB, time=38.21 x[1] = 0.603 y[1] (analytic) = 11.66253925170600193797435752277 y[1] (numeric) = 11.662539251706001937974357522772 absolute error = 2e-30 relative error = 1.7148924062205741542580610244756e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1307 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.604 y[1] (analytic) = 11.755497793107633044604267409088 y[1] (numeric) = 11.755497793107633044604267409087 absolute error = 1e-30 relative error = 8.5066580556572439564118587035858e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1297 Order of pole = 651 memory used=1014.7MB, alloc=4.3MB, time=38.36 TOP MAIN SOLVE Loop x[1] = 0.605 y[1] (analytic) = 11.849896122656190553615986765695 y[1] (numeric) = 11.849896122656190553615986765701 absolute error = 6e-30 relative error = 5.0633355245438907704043459604940e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1287 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1018.5MB, alloc=4.3MB, time=38.50 x[1] = 0.606 y[1] (analytic) = 11.945768068832765196641366254518 y[1] (numeric) = 11.945768068832765196641366254513 absolute error = 5e-30 relative error = 4.1855826860102062724415865182716e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1277 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.607 y[1] (analytic) = 12.043148528090583860223249980422 y[1] (numeric) = 12.043148528090583860223249980427 absolute error = 5e-30 relative error = 4.1517382172423805488123920228864e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1267 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1022.3MB, alloc=4.3MB, time=38.65 x[1] = 0.608 y[1] (analytic) = 12.142073507335846398549817066383 y[1] (numeric) = 12.142073507335846398549817066383 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1257 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.609 y[1] (analytic) = 12.242580168452539036785934425677 y[1] (numeric) = 12.242580168452539036785934425671 absolute error = 6e-30 relative error = 4.9009276781876278507989301234716e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1247 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1026.1MB, alloc=4.3MB, time=38.79 x[1] = 0.61 y[1] (analytic) = 12.344706874986889462649987803789 y[1] (numeric) = 12.344706874986889462649987803788 absolute error = 1e-30 relative error = 8.1006378695489441271441809473277e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1237 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.611 y[1] (analytic) = 12.448493241114669996729031881813 y[1] (numeric) = 12.44849324111466999672903188181 absolute error = 3e-30 relative error = 2.4099302155634799617323534565553e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1227 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1030.0MB, alloc=4.3MB, time=38.94 x[1] = 0.612 y[1] (analytic) = 12.553980183022654218614706928959 y[1] (numeric) = 12.553980183022654218614706928958 absolute error = 1e-30 relative error = 7.9656012310131544142102975764276e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1217 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.613 y[1] (analytic) = 12.661209972844235311016508324242 y[1] (numeric) = 12.661209972844235311016508324245 absolute error = 3e-30 relative error = 2.3694417882922725116406087546026e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1207 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1033.8MB, alloc=4.3MB, time=39.09 x[1] = 0.614 y[1] (analytic) = 12.770226295298571618337010477889 y[1] (numeric) = 12.770226295298571618337010477883 absolute error = 6e-30 relative error = 4.6984288776534310025989771468586e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1197 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.615 y[1] (analytic) = 12.881074307192691625826186183482 y[1] (numeric) = 12.881074307192691625826186183475 absolute error = 7e-30 relative error = 5.4343293370268460360938554869822e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1187 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1037.6MB, alloc=4.3MB, time=39.23 x[1] = 0.616 y[1] (analytic) = 12.993800699956827028362943944915 y[1] (numeric) = 12.993800699956827028362943944908 absolute error = 7e-30 relative error = 5.3871843670984256944840112952920e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1177 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.617 y[1] (analytic) = 13.10845376539491473383892362987 y[1] (numeric) = 13.108453765394914733838923629873 absolute error = 3e-30 relative error = 2.2885994440623637016493076100408e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1167 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1041.4MB, alloc=4.3MB, time=39.38 x[1] = 0.618 y[1] (analytic) = 13.22508346484478876572716944166 y[1] (numeric) = 13.225083464844788765727169441664 absolute error = 4e-30 relative error = 3.0245555807892547772908197759915e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1157 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.619 y[1] (analytic) = 13.343741501956150250450732643373 y[1] (numeric) = 13.343741501956150250450732643379 absolute error = 6e-30 relative error = 4.4964899830534179632827004234014e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1147 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1045.2MB, alloc=4.3MB, time=39.52 x[1] = 0.62 y[1] (analytic) = 13.464481399309044813511741427646 y[1] (numeric) = 13.464481399309044813511741427648 absolute error = 2e-30 relative error = 1.4853895524729483911082276810027e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1137 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.621 y[1] (analytic) = 13.587358579111387053447290614568 y[1] (numeric) = 13.587358579111387053447290614571 absolute error = 3e-30 relative error = 2.2079346640722864714178420578326e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1127 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1049.0MB, alloc=4.3MB, time=39.66 x[1] = 0.622 y[1] (analytic) = 13.712430448231155987866213509321 y[1] (numeric) = 13.712430448231155987866213509312 absolute error = 9e-30 relative error = 6.5633878939097634129078604671829e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1117 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1052.8MB, alloc=4.3MB, time=39.80 x[1] = 0.623 y[1] (analytic) = 13.839756487837358545503341065429 y[1] (numeric) = 13.839756487837358545503341065436 absolute error = 7e-30 relative error = 5.0578924608621063901570504682990e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1107 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.624 y[1] (analytic) = 13.969398347943846925671353214794 y[1] (numeric) = 13.969398347943846925671353214794 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1097 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1056.7MB, alloc=4.3MB, time=39.95 x[1] = 0.625 y[1] (analytic) = 14.101419947171719387646083651988 y[1] (numeric) = 14.101419947171719387646083651986 absolute error = 2e-30 relative error = 1.4182968860530489757796178586960e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1087 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.626 y[1] (analytic) = 14.235887578069486433615570305264 y[1] (numeric) = 14.235887578069486433615570305271 absolute error = 7e-30 relative error = 4.9171503790066193761432203532908e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1077 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1060.5MB, alloc=4.3MB, time=40.09 x[1] = 0.627 y[1] (analytic) = 14.372870018355614917880000170341 y[1] (numeric) = 14.372870018355614917880000170339 absolute error = 2e-30 relative error = 1.3915105316097598132868914311196e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1067 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.628 y[1] (analytic) = 14.512438648475658500321819042864 y[1] (numeric) = 14.51243864847565850032181904286 absolute error = 4e-30 relative error = 2.7562562687699269491302302832628e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1057 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1064.3MB, alloc=4.3MB, time=40.24 x[1] = 0.629 y[1] (analytic) = 14.654667575896150874173607154267 y[1] (numeric) = 14.654667575896150874173607154261 absolute error = 6e-30 relative error = 4.0942586851091316208342288728752e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1047 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 14.799633766590007084538576890428 y[1] (numeric) = 14.799633766590007084538576890434 absolute error = 6e-30 relative error = 4.0541543761339060284600235190310e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1037 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1068.1MB, alloc=4.3MB, time=40.38 x[1] = 0.631 y[1] (analytic) = 14.947417184203601263308138137697 y[1] (numeric) = 14.947417184203601263308138137689 absolute error = 8e-30 relative error = 5.3520952157904463993529775369376e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1027 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.632 y[1] (analytic) = 15.098100937434246877927700626396 y[1] (numeric) = 15.098100937434246877927700626395 absolute error = 1e-30 relative error = 6.6233495467009296453957910193547e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1017 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1071.9MB, alloc=4.3MB, time=40.53 x[1] = 0.633 y[1] (analytic) = 15.251771436188809421366539559023 y[1] (numeric) = 15.251771436188809421366539559024 absolute error = 1e-30 relative error = 6.5566154343700623257696756702524e-30 % Correct digits = 31 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.1007 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.634 y[1] (analytic) = 15.408518557139976999480931077028 y[1] (numeric) = 15.408518557139976999480931077034 absolute error = 6e-30 relative error = 3.8939499457718657158029549795063e-29 % Correct digits = 30 h = 0.001 Real estimate of pole used for equation 1 Radius of convergence = 0.0997 Order of pole = 651 memory used=1075.7MB, alloc=4.3MB, time=40.67 TOP MAIN SOLVE Loop x[1] = 0.63598404094770977956435079636215 y[1] (analytic) = 15.728990118799854947817392823411 y[1] (numeric) = 15.728990118799854947817392823411 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.00098703544634808129080768261232708 Real estimate of pole used for equation 1 Radius of convergence = 0.09772 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1079.5MB, alloc=4.3MB, time=40.82 x[1] = 0.63696120603959438004225040214836 y[1] (analytic) = 15.891648827152134399189249659825 y[1] (numeric) = 15.891648827152134399189249659825 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.00097716509188460047789960578620866 Real estimate of pole used for equation 1 Radius of convergence = 0.09674 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.63792859948056013451537101187671 y[1] (analytic) = 16.055944679442236565441354631468 y[1] (numeric) = 16.055944679442236565441354631475 absolute error = 7e-30 relative error = 4.3597559282591967949146711125605e-29 % Correct digits = 30 h = 0.00096739344096575447312060972835137 Real estimate of pole used for equation 1 Radius of convergence = 0.09577 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1083.4MB, alloc=4.3MB, time=40.96 x[1] = 0.63888631898711623144376041550778 y[1] (analytic) = 16.221894276021271625041972240427 y[1] (numeric) = 16.221894276021271625041972240408 absolute error = 1.9e-29 relative error = 1.1712565546728561029946788161143e-28 % Correct digits = 29 h = 0.00095771950655609692838940363107071 Real estimate of pole used for equation 1 Radius of convergence = 0.09481 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1087.2MB, alloc=4.3MB, time=41.10 x[1] = 0.63983446129860676740286592510254 y[1] (analytic) = 16.389514384179317292884723366272 y[1] (numeric) = 16.38951438417931729288472336628 absolute error = 8e-30 relative error = 4.8811696383892518553546019012769e-29 % Correct digits = 30 h = 0.00094814231149053595910550959476189 Real estimate of pole used for equation 1 Radius of convergence = 0.09387 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.64077312218698239800238037960136 y[1] (analytic) = 16.558821939841522565969359105102 y[1] (numeric) = 16.558821939841522565969359105113 absolute error = 1.1e-29 relative error = 6.6429846519053011304944850641160e-29 % Correct digits = 30 h = 0.00093866088837563059951445449881521 Real estimate of pole used for equation 1 Radius of convergence = 0.09293 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1091.0MB, alloc=4.3MB, time=41.25 x[1] = 0.64170239646647427229589968955519 y[1] (analytic) = 16.729834049281185775586990610531 y[1] (numeric) = 16.729834049281185775586990610511 absolute error = 2.0e-29 relative error = 1.1954691206790135619301368657787e-28 % Correct digits = 29 h = 0.00092927427949187429351930995382707 Real estimate of pole used for equation 1 Radius of convergence = 0.092 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.64262237800317122784648380640948 y[1] (analytic) = 16.902567990849981549228436942517 y[1] (numeric) = 16.902567990849981549228436942497 absolute error = 2.0e-29 relative error = 1.1832521549877379017231591658147e-28 % Correct digits = 29 h = 0.00091998153669695555058411685428972 Real estimate of pole used for equation 1 Radius of convergence = 0.09108 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1094.8MB, alloc=4.3MB, time=41.39 x[1] = 0.64353315972450121384156208209523 y[1] (analytic) = 17.07704121672551297283879401745 y[1] (numeric) = 17.077041216725512972838794017435 absolute error = 1.5e-29 relative error = 8.7837230171399789517988964847239e-29 % Correct digits = 30 h = 0.00091078172132998599507827568574773 Real estimate of pole used for equation 1 Radius of convergence = 0.09017 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.64443483362861789997668957502412 y[1] (analytic) = 17.253271354676366950659849340898 y[1] (numeric) = 17.253271354676366950659849340898 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.00090167390411668613512749292889205 Real estimate of pole used for equation 1 Radius of convergence = 0.08927 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1098.6MB, alloc=4.3MB, time=41.54 x[1] = 0.64532749079369341925046579302372 y[1] (analytic) = 17.431276209844852485858446273719 y[1] (numeric) = 17.431276209844852485858446273733 absolute error = 1.4e-29 relative error = 8.0315404514633684148231320895527e-29 % Correct digits = 30 h = 0.00089265716507551927377621799960491 Real estimate of pole used for equation 1 Radius of convergence = 0.08837 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.64621122138711818333150424884333 y[1] (analytic) = 17.611073766547603350560999653583 y[1] (numeric) = 17.611073766547603350560999653585 absolute error = 2e-30 relative error = 1.1356490958541201507592796000089e-29 % Correct digits = 30 h = 0.00088373059342476408103845581961149 Real estimate of pole used for equation 1 Radius of convergence = 0.08749 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1102.4MB, alloc=4.3MB, time=41.68 x[1] = 0.64708611467460869977173232010474 y[1] (analytic) = 17.792682190094228378933465317426 y[1] (numeric) = 17.792682190094228378933465317419 absolute error = 7e-30 relative error = 3.9342016707841442400407804557491e-29 % Correct digits = 30 h = 0.00087489328749051644022807126140759 Real estimate of pole used for equation 1 Radius of convergence = 0.08661 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1106.3MB, alloc=4.3MB, time=41.82 x[1] = 0.64880974194029376621062564329685 y[1] (analytic) = 18.161405214962128645093135915313 y[1] (numeric) = 18.161405214962128645093135915293 absolute error = 2.0e-29 relative error = 1.1012363725865859611294716771527e-28 % Correct digits = 29 h = 0.00085748291106945516306753264330899 Real estimate of pole used for equation 1 Radius of convergence = 0.08489 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.64965865002225252682206250061373 y[1] (analytic) = 18.348557068491729241941004222328 y[1] (numeric) = 18.348557068491729241941004222326 absolute error = 2e-30 relative error = 1.0900039673606890936922278341566e-29 % Correct digits = 30 h = 0.00084890808195876061143685731687591 Real estimate of pole used for equation 1 Radius of convergence = 0.08404 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1110.1MB, alloc=4.3MB, time=41.97 x[1] = 0.65049906902339169982738498935744 y[1] (analytic) = 18.537594297048474347234677238966 y[1] (numeric) = 18.537594297048474347234677238943 absolute error = 2.3e-29 relative error = 1.2407219422027173526157131614879e-28 % Correct digits = 29 h = 0.00084041900113917300532248874371049 Real estimate of pole used for equation 1 Radius of convergence = 0.0832 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1113.9MB, alloc=4.3MB, time=42.11 x[1] = 0.65133108383451948110265425321372 y[1] (analytic) = 18.72853599883132221581477238297 y[1] (numeric) = 18.728535998831322215814772382986 absolute error = 1.6e-29 relative error = 8.5431130340344886760320915246547e-29 % Correct digits = 30 h = 0.00083201481112778127526926385627669 Real estimate of pole used for equation 1 Radius of convergence = 0.08237 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.65215477849753598456517082443143 y[1] (analytic) = 18.921401464333596485222240240005 y[1] (numeric) = 18.921401464333596485222240240004 absolute error = 1e-30 relative error = 5.2850207839254234874446924813159e-30 % Correct digits = 31 h = 0.00082369466301650346251657121771312 Real estimate of pole used for equation 1 Radius of convergence = 0.08155 Order of pole = 651 memory used=1117.7MB, alloc=4.3MB, time=42.26 TOP MAIN SOLVE Loop x[1] = 0.65377753935314479803667472138744 y[1] (analytic) = 19.312981821662724944777678750087 y[1] (numeric) = 19.312981821662724944777678750095 absolute error = 8e-30 relative error = 4.1422914772418352865331915944518e-29 % Correct digits = 30 h = 0.00080730313922247504361249145048065 Real estimate of pole used for equation 1 Radius of convergence = 0.07992 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1121.5MB, alloc=4.3MB, time=42.40 x[1] = 0.65457676946097504832985108792341 y[1] (analytic) = 19.511736273598550236967445654688 y[1] (numeric) = 19.511736273598550236967445654689 absolute error = 1e-30 relative error = 5.1251205222218287153115523046780e-30 % Correct digits = 31 h = 0.00079923010783025029317636653596952 Real estimate of pole used for equation 1 Radius of convergence = 0.07912 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.65536800726772699612009569079402 y[1] (analytic) = 19.712493613470976627693838064381 y[1] (numeric) = 19.712493613470976627693838064399 absolute error = 1.8e-29 relative error = 9.1312648480450461452884305619338e-29 % Correct digits = 30 h = 0.00079123780675194779024460287060905 Real estimate of pole used for equation 1 Radius of convergence = 0.07833 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1125.3MB, alloc=4.3MB, time=42.55 x[1] = 0.65615133269641142443243784763593 y[1] (analytic) = 19.915274122893755038852343700327 y[1] (numeric) = 19.915274122893755038852343700333 absolute error = 6e-30 relative error = 3.0127629491690773691933663893140e-29 % Correct digits = 30 h = 0.00078332542868442831234215684190529 Real estimate of pole used for equation 1 Radius of convergence = 0.07755 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1129.1MB, alloc=4.3MB, time=42.69 x[1] = 0.65769456212346261665058313083016 y[1] (analytic) = 20.326986800384588955364926421691 y[1] (numeric) = 20.326986800384588955364926421702 absolute error = 1.1e-29 relative error = 5.4115251355365069259155013045716e-29 % Correct digits = 30 h = 0.00076773725265360818892654792074835 Real estimate of pole used for equation 1 Radius of convergence = 0.07601 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.6584546220035896887576204132717 y[1] (analytic) = 20.535960561452523038753264632629 y[1] (numeric) = 20.535960561452523038753264632617 absolute error = 1.2e-29 relative error = 5.8434081834598300859166255398197e-29 % Correct digits = 30 h = 0.00076005988012707210703728244154163 Real estimate of pole used for equation 1 Radius of convergence = 0.07525 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1133.0MB, alloc=4.3MB, time=42.83 x[1] = 0.65920708128491549014358732288883 y[1] (analytic) = 20.747040682274773641757002714727 y[1] (numeric) = 20.747040682274773641757002714739 absolute error = 1.2e-29 relative error = 5.7839574249508246544141425418159e-29 % Correct digits = 30 h = 0.00075245928132580138596690961713367 Real estimate of pole used for equation 1 Radius of convergence = 0.07449 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1136.8MB, alloc=4.3MB, time=42.97 x[1] = 0.66068950131505545145408073152553 y[1] (analytic) = 21.175605514036759571745888012407 y[1] (numeric) = 21.175605514036759571745888012394 absolute error = 1.3e-29 relative error = 6.1391396772019752811200705585923e-29 % Correct digits = 30 h = 0.00073748534162741793838616811574981 Real estimate of pole used for equation 1 Radius of convergence = 0.07301 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1140.6MB, alloc=4.3MB, time=43.12 x[1] = 0.66141961180326659521308303796013 y[1] (analytic) = 21.393133519725313020133977059841 y[1] (numeric) = 21.393133519725313020133977059823 absolute error = 1.8e-29 relative error = 8.4139146719218528399144321800644e-29 % Correct digits = 30 h = 0.00073011048821114375900230643459955 Real estimate of pole used for equation 1 Radius of convergence = 0.07228 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.66214242118659562753449532133037 y[1] (analytic) = 21.612854479041658165856884308757 y[1] (numeric) = 21.612854479041658165856884308747 absolute error = 1.0e-29 relative error = 4.6268761073171362478464836146800e-29 % Correct digits = 30 h = 0.00072280938332903232141228337024283 Real estimate of pole used for equation 1 Radius of convergence = 0.07156 Order of pole = 651 memory used=1144.4MB, alloc=4.3MB, time=43.26 TOP MAIN SOLVE Loop x[1] = 0.66356642795269215411090966079809 y[1] (analytic) = 22.058964268576213399064234906859 y[1] (numeric) = 22.058964268576213399064234906841 absolute error = 1.8e-29 relative error = 8.1599479381004511930605183533830e-29 % Correct digits = 30 h = 0.00070842547660078457821617893117291 Real estimate of pole used for equation 1 Radius of convergence = 0.07013 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1148.2MB, alloc=4.3MB, time=43.41 x[1] = 0.66426776917452693084334367793996 y[1] (analytic) = 22.285398165314475985929088471267 y[1] (numeric) = 22.285398165314475985929088471287 absolute error = 2.0e-29 relative error = 8.9744862764572346414706311840647e-29 % Correct digits = 30 h = 0.00070134122183477673243401714186952 Real estimate of pole used for equation 1 Radius of convergence = 0.06943 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1152.0MB, alloc=4.3MB, time=43.55 x[1] = 0.66564948151566362448391193511115 y[1] (analytic) = 22.745138337517136189797101049996 y[1] (numeric) = 22.745138337517136189797101049999 absolute error = 3e-30 relative error = 1.3189631803872689018594761374206e-29 % Correct digits = 30 h = 0.00068738453152026467545858020074497 Real estimate of pole used for equation 1 Radius of convergence = 0.06805 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.66632999220186868651261592950989 y[1] (analytic) = 22.978491055998233320578817722804 y[1] (numeric) = 22.978491055998233320578817722805 absolute error = 1e-30 relative error = 4.3518958558375970153108053901074e-30 % Correct digits = 31 h = 0.00068051068620506202870399439873618 Real estimate of pole used for equation 1 Radius of convergence = 0.06737 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1155.8MB, alloc=4.3MB, time=43.69 x[1] = 0.66700369778121169792103288396463 y[1] (analytic) = 23.214196881934149855376487002558 y[1] (numeric) = 23.214196881934149855376487002534 absolute error = 2.4e-29 relative error = 1.0338501100021849629138799987333e-28 % Correct digits = 29 h = 0.00067370557934301140841695445474482 Real estimate of pole used for equation 1 Radius of convergence = 0.0667 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1159.7MB, alloc=4.3MB, time=43.84 x[1] = 0.66833096514307536469675512593593 y[1] (analytic) = 23.692763339638770620915882947249 y[1] (numeric) = 23.692763339638770620915882947241 absolute error = 8e-30 relative error = 3.3765584390976199278744185823308e-29 % Correct digits = 30 h = 0.00066029883831408548138945706109737 Real estimate of pole used for equation 1 Radius of convergence = 0.06537 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1163.5MB, alloc=4.3MB, time=43.98 x[1] = 0.669631819884437944503640495292 y[1] (analytic) = 24.181031092635539111424430361958 y[1] (numeric) = 24.181031092635539111424430361971 absolute error = 1.3e-29 relative error = 5.3761148357148503663316858938115e-29 % Correct digits = 30 h = 0.00064715889143163518030980686557834 Real estimate of pole used for equation 1 Radius of convergence = 0.06407 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.67027250718695526333214720408893 y[1] (analytic) = 24.428864456204060663846302712121 y[1] (numeric) = 24.428864456204060663846302712132 absolute error = 1.1e-29 relative error = 4.5028699634077310370276771248257e-29 % Correct digits = 30 h = 0.00064068730251731882850670879692573 Real estimate of pole used for equation 1 Radius of convergence = 0.06343 Order of pole = 651 memory used=1167.3MB, alloc=4.3MB, time=44.13 TOP MAIN SOLVE Loop memory used=1171.1MB, alloc=4.3MB, time=44.27 x[1] = 0.67153472524164463315618827108975 y[1] (analytic) = 24.932055338191596782755898194175 y[1] (numeric) = 24.932055338191596782755898194184 absolute error = 9e-30 relative error = 3.6098106946736784065669431529874e-29 % Correct digits = 30 h = 0.0006279376251972241838194252918607 Real estimate of pole used for equation 1 Radius of convergence = 0.06217 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.6721563834905898850981695021287 y[1] (analytic) = 25.187463687774077661890954528111 y[1] (numeric) = 25.187463687774077661890954528077 absolute error = 3.4e-29 relative error = 1.3498778766082550060546219516247e-28 % Correct digits = 29 h = 0.00062165824894525194198123103894641 Real estimate of pole used for equation 1 Radius of convergence = 0.06154 Order of pole = 651 memory used=1174.9MB, alloc=4.3MB, time=44.41 TOP MAIN SOLVE Loop x[1] = 0.67338111240683692594906672539853 y[1] (analytic) = 25.706035210041725234581493471247 y[1] (numeric) = 25.706035210041725234581493471198 absolute error = 4.9e-29 relative error = 1.9061671548967144174510136987174e-28 % Correct digits = 29 h = 0.00060928724979124142833580454126716 Real estimate of pole used for equation 1 Radius of convergence = 0.06032 Order of pole = 651 memory used=1178.7MB, alloc=4.3MB, time=44.56 TOP MAIN SOLVE Loop x[1] = 0.67458146921765065068703109392529 y[1] (analytic) = 26.235121552230589216573516093872 y[1] (numeric) = 26.235121552230589216573516093876 absolute error = 4e-30 relative error = 1.5246737058322902747510736080565e-29 % Correct digits = 30 h = 0.00059716243352039572391192203090187 Real estimate of pole used for equation 1 Radius of convergence = 0.05912 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1182.5MB, alloc=4.3MB, time=44.70 x[1] = 0.67517266002683584245370389673588 y[1] (analytic) = 26.503674422297653985929980858926 y[1] (numeric) = 26.503674422297653985929980858885 absolute error = 4.1e-29 relative error = 1.5469553144490231764513440996012e-28 % Correct digits = 29 h = 0.00059119080918519176667280281059403 Real estimate of pole used for equation 1 Radius of convergence = 0.05853 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1186.4MB, alloc=4.3MB, time=44.84 x[1] = 0.67633736504001158875322598555303 y[1] (analytic) = 27.048935204148030035685199510879 y[1] (numeric) = 27.048935204148030035685199510847 absolute error = 3.2e-29 relative error = 1.1830410239251381067048714882840e-28 % Correct digits = 29 h = 0.00057942611208240645051601403466207 Real estimate of pole used for equation 1 Radius of convergence = 0.05736 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1190.2MB, alloc=4.3MB, time=44.99 x[1] = 0.67747889242342513770138758480272 y[1] (analytic) = 27.605253438567085069823131847904 y[1] (numeric) = 27.605253438567085069823131847885 absolute error = 1.9e-29 relative error = 6.8827478951724629491261079320935e-29 % Correct digits = 30 h = 0.00056789553245196656215074535536949 Real estimate of pole used for equation 1 Radius of convergence = 0.05622 Order of pole = 651 TOP MAIN SOLVE Loop x[1] = 0.67804110900055258459791682270454 y[1] (analytic) = 27.887629171328436511596661370924 y[1] (numeric) = 27.887629171328436511596661370897 absolute error = 2.7e-29 relative error = 9.6817122151634828267692946340123e-29 % Correct digits = 30 h = 0.00056221657712744689652923790181524 Real estimate of pole used for equation 1 Radius of convergence = 0.05566 Order of pole = 651 memory used=1194.0MB, alloc=4.3MB, time=45.13 TOP MAIN SOLVE Loop x[1] = 0.67914873187915136772876907429491 y[1] (analytic) = 28.460956492273009279672589518717 y[1] (numeric) = 28.460956492273009279672589518679 absolute error = 3.8e-29 relative error = 1.3351624359608851428728159560524e-28 % Correct digits = 29 h = 0.00055102846724261070328830606756858 Real estimate of pole used for equation 1 Radius of convergence = 0.05455 Order of pole = 651 memory used=1197.8MB, alloc=4.3MB, time=45.28 TOP MAIN SOLVE Loop memory used=1201.6MB, alloc=4.3MB, time=45.42 x[1] = 0.68023431306246603507531736607864 y[1] (analytic) = 29.04591182358243237956716750321 y[1] (numeric) = 29.045911823582432379567167503158 absolute error = 5.2e-29 relative error = 1.7902691544281663323260823428020e-28 % Correct digits = 29 h = 0.00054006300074448275029286877682932 Real estimate of pole used for equation 1 Radius of convergence = 0.05347 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1205.4MB, alloc=4.3MB, time=45.57 x[1] = 0.68129829118023274054166934685587 y[1] (analytic) = 29.642731527849135317486574385353 y[1] (numeric) = 29.642731527849135317486574385348 absolute error = 5e-30 relative error = 1.6867541357659754070141353231472e-29 % Correct digits = 30 h = 0.00052931574702966754356204068816781 Real estimate of pole used for equation 1 Radius of convergence = 0.0524 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1209.3MB, alloc=4.3MB, time=45.71 x[1] = 0.68234109613345588856924092321562 y[1] (analytic) = 30.251656761012976242023515231718 y[1] (numeric) = 30.251656761012976242023515231702 absolute error = 1.6e-29 relative error = 5.2889665271556651948186950157803e-29 % Correct digits = 30 h = 0.00051878236366377715944515607847431 Real estimate of pole used for equation 1 Radius of convergence = 0.05136 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1213.1MB, alloc=4.3MB, time=45.86 x[1] = 0.68336314926810989595106382520582 y[1] (analytic) = 30.872933569820081768537549734145 y[1] (numeric) = 30.872933569820081768537549734094 absolute error = 5.1e-29 relative error = 1.6519324243892127404429090993110e-28 % Correct digits = 29 h = 0.00050845859462686799397219747251419 Real estimate of pole used for equation 1 Radius of convergence = 0.05034 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1216.9MB, alloc=4.3MB, time=46.01 x[1] = 0.68436486354538428858598845144642 y[1] (analytic) = 31.506812991256951436528138257379 y[1] (numeric) = 31.506812991256951436528138257347 absolute error = 3.2e-29 relative error = 1.0156533448457610269131035995355e-28 % Correct digits = 29 h = 0.00049834026859379332089215074281166 Real estimate of pole used for equation 1 Radius of convergence = 0.04934 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1220.7MB, alloc=4.3MB, time=46.15 x[1] = 0.68534664370854092080747807762483 y[1] (analytic) = 32.153551154000043458214630245371 y[1] (numeric) = 32.153551154000043458214630245305 absolute error = 6.6e-29 relative error = 2.0526504112684707035976641547096e-28 % Correct digits = 29 h = 0.00048842329724877683380639694302875 Real estimate of pole used for equation 1 Radius of convergence = 0.04835 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1224.5MB, alloc=4.3MB, time=46.29 x[1] = 0.68630888644645073604776006024229 y[1] (analytic) = 32.813409381921870795822309770229 y[1] (numeric) = 32.813409381921870795822309770209 absolute error = 2.0e-29 relative error = 6.0950691734638049536626080803317e-29 % Correct digits = 30 h = 0.00047870367363352617481364964386343 Real estimate of pole used for equation 1 Radius of convergence = 0.04739 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1228.3MB, alloc=4.3MB, time=46.44 x[1] = 0.68725198055387614596476043140566 y[1] (analytic) = 33.486654299695465666235954352649 y[1] (numeric) = 33.486654299695465666235954352671 absolute error = 2.2e-29 relative error = 6.5697814428120017954335361453711e-29 % Correct digits = 30 h = 0.00046917747052821900393485801595102 Real estimate of pole used for equation 1 Radius of convergence = 0.04645 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1232.1MB, alloc=4.3MB, time=46.58 x[1] = 0.68817630708856379022441249518288 y[1] (analytic) = 34.173557940539916643793280037163 y[1] (numeric) = 34.173557940539916643793280037073 absolute error = 9.0e-29 relative error = 2.6336151522939161466173732777826e-28 % Correct digits = 29 h = 0.0004598408388647074457565543414286 Real estimate of pole used for equation 1 Radius of convergence = 0.04552 Order of pole = 651 memory used=1236.0MB, alloc=4.3MB, time=46.72 TOP MAIN SOLVE Loop x[1] = 0.68908223952521115036329748289093 y[1] (analytic) = 34.874397856150545951357907861324 y[1] (numeric) = 34.874397856150545951357907861272 absolute error = 5.2e-29 relative error = 1.4910651709167541985189335838187e-28 % Correct digits = 29 h = 0.00045069000617129976758599891003462 Real estimate of pole used for equation 1 Radius of convergence = 0.04462 Order of pole = 651 memory used=1239.8MB, alloc=4.3MB, time=46.87 TOP MAIN SOLVE Loop memory used=1243.6MB, alloc=4.3MB, time=47.01 x[1] = 0.69040744796866723402860758650001 y[1] (analytic) = 35.952409273842674684112757977284 y[1] (numeric) = 35.952409273842674684112757977278 absolute error = 6e-30 relative error = 1.6688728575320611474380512686748e-29 % Correct digits = 30 h = 0.00043730406229800599318892715641073 Real estimate of pole used for equation 1 Radius of convergence = 0.04329 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1247.4MB, alloc=4.3MB, time=47.15 x[1] = 0.69126898070180053563578909189085 y[1] (analytic) = 36.689341398265589409673768879239 y[1] (numeric) = 36.689341398265589409673768879223 absolute error = 1.6e-29 relative error = 4.3609395508953905545125289045715e-29 % Correct digits = 30 h = 0.00042860171145827567392446750599605 Real estimate of pole used for equation 1 Radius of convergence = 0.04243 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1251.2MB, alloc=4.3MB, time=47.30 x[1] = 0.69211336893354448454098768532442 y[1] (analytic) = 37.441226326336746294522009555031 y[1] (numeric) = 37.441226326336746294522009554989 absolute error = 4.2e-29 relative error = 1.1217581292324429220574839277111e-28 % Correct digits = 29 h = 0.00042007253740025598801337060262549 Real estimate of pole used for equation 1 Radius of convergence = 0.04159 Order of pole = 651 memory used=1255.0MB, alloc=4.3MB, time=47.44 TOP MAIN SOLVE Loop x[1] = 0.69334854980244365984788621223102 y[1] (analytic) = 38.597756483163226199480611810685 y[1] (numeric) = 38.597756483163226199480611810682 absolute error = 3e-30 relative error = 7.7724724785717367016519369027580e-30 % Correct digits = 31 h = 0.00040759596296693098491338548235812 Real estimate of pole used for equation 1 Radius of convergence = 0.04035 Order of pole = 651 memory used=1258.8MB, alloc=4.3MB, time=47.58 TOP MAIN SOLVE Loop x[1] = 0.69415155460908481058126407296982 y[1] (analytic) = 39.388366090208518825015433370925 y[1] (numeric) = 39.388366090208518825015433370954 absolute error = 2.9e-29 relative error = 7.3625800911830806904715778152003e-29 % Correct digits = 30 h = 0.0003994848033038890583136091112592 Real estimate of pole used for equation 1 Radius of convergence = 0.03955 Order of pole = 651 memory used=1262.7MB, alloc=4.3MB, time=47.73 TOP MAIN SOLVE Loop memory used=1266.5MB, alloc=4.3MB, time=47.87 x[1] = 0.69532619932523476266444035088696 y[1] (analytic) = 40.604463413125774025482355351933 y[1] (numeric) = 40.604463413125774025482355351847 absolute error = 8.6e-29 relative error = 2.1179937566223247408607028299610e-28 % Correct digits = 29 h = 0.00038761970516096024939263660704455 Real estimate of pole used for equation 1 Radius of convergence = 0.03837 Order of pole = 651 memory used=1270.3MB, alloc=4.3MB, time=48.02 TOP MAIN SOLVE Loop x[1] = 0.6960898489063723704517687842665 y[1] (analytic) = 41.435794628051269113657434877196 y[1] (numeric) = 41.435794628051269113657434877095 absolute error = 1.01e-28 relative error = 2.4375060477692603941968797640538e-28 % Correct digits = 29 h = 0.00037990607302825714042972313856663 Real estimate of pole used for equation 1 Radius of convergence = 0.03761 Order of pole = 651 memory used=1274.1MB, alloc=4.3MB, time=48.16 TOP MAIN SOLVE Loop memory used=1277.9MB, alloc=4.3MB, time=48.30 x[1] = 0.69720692434359858471923120175342 y[1] (analytic) = 42.714530742492370287480681955595 y[1] (numeric) = 42.714530742492370287480681955608 absolute error = 1.3e-29 relative error = 3.0434608022200776897832439594060e-29 % Correct digits = 30 h = 0.00036862248275324487510181993162734 Real estimate of pole used for equation 1 Radius of convergence = 0.03649 Order of pole = 651 memory used=1281.7MB, alloc=4.3MB, time=48.45 TOP MAIN SOLVE Loop x[1] = 0.69829082152326374319673571797856 y[1] (analytic) = 44.032389990970916245440552984853 y[1] (numeric) = 44.032389990970916245440552984742 absolute error = 1.11e-28 relative error = 2.5208715680152987498997382163555e-28 % Correct digits = 29 h = 0.00035767402639299074906642077784022 Real estimate of pole used for equation 1 Radius of convergence = 0.03541 Order of pole = 651 memory used=1285.5MB, alloc=4.3MB, time=48.59 TOP MAIN SOLVE Loop memory used=1289.4MB, alloc=4.3MB, time=48.73 x[1] = 0.6993425258727956668022998725673 y[1] (analytic) = 45.390570523900458120295589938597 y[1] (numeric) = 45.390570523900458120295589938585 absolute error = 1.2e-29 relative error = 2.6437209009482235814845476926436e-29 % Correct digits = 30 h = 0.00034705075013509253082839901431554 Real estimate of pole used for equation 1 Radius of convergence = 0.03436 Order of pole = 651 TOP MAIN SOLVE Loop memory used=1293.2MB, alloc=4.3MB, time=48.88 x[1] = 0.7000262505556368125972849014654 y[1] (analytic) = 46.319033165470321622177929298065 y[1] (numeric) = 46.31903316547032162217792929796 absolute error = 1.05e-28 relative error = 2.2668866948258079896904938218700e-28 % Correct digits = 29 h = 0.00034014444020740418946491387393033 Real estimate of pole used for equation 1 Radius of convergence = 0.03367 Order of pole = 651 memory used=1297.0MB, alloc=4.3MB, time=49.02 TOP MAIN SOLVE Loop x[1] = 0.70102641092747822366858334475539 y[1] (analytic) = 47.747178465624295534739815903375 y[1] (numeric) = 47.747178465624295534739815903231 absolute error = 1.44e-28 relative error = 3.0158850140992765037599818087992e-28 % Correct digits = 29 h = 0.00033004181018880407763361646696204 Real estimate of pole used for equation 1 Radius of convergence = 0.03267 Order of pole = 651 memory used=1300.8MB, alloc=4.3MB, time=49.17 memory used=1304.6MB, alloc=4.3MB, time=49.31 TOP MAIN SOLVE Loop memory used=1308.4MB, alloc=4.3MB, time=49.45 x[1] = 0.70231390238211611553329973520126 y[1] (analytic) = 49.719577962274192407516441864202 y[1] (numeric) = 49.719577962274192407516441864057 absolute error = 1.45e-28 relative error = 2.9163562110286192149179155277656e-28 % Correct digits = 29 h = 0.00031703684600054254364658222003374 Real estimate of pole used for equation 1 Radius of convergence = 0.03139 Order of pole = 651 memory used=1312.3MB, alloc=4.3MB, time=49.59 TOP MAIN SOLVE Loop x[1] = 0.70324611720705926482809560191446 y[1] (analytic) = 51.251775328937145950664890007971 y[1] (numeric) = 51.251775328937145950664890007984 absolute error = 1.3e-29 relative error = 2.5364975001480778293102060290622e-29 % Correct digits = 30 h = 0.00030762053463748042955773508151561 Real estimate of pole used for equation 1 Radius of convergence = 0.03045 Order of pole = 651 memory used=1316.1MB, alloc=4.3MB, time=49.74 TOP MAIN SOLVE Loop memory used=1319.9MB, alloc=4.3MB, time=49.88 x[1] = 0.70415064431948677764568673659041 y[1] (analytic) = 52.830857565646458492636720683295 y[1] (numeric) = 52.830857565646458492636720683373 absolute error = 7.8e-29 relative error = 1.4764098785085765490815269465965e-28 % Correct digits = 29 h = 0.00029848389713821262331944079185863 Real estimate of pole used for equation 1 Radius of convergence = 0.02955 Order of pole = 651 memory used=1323.7MB, alloc=4.3MB, time=50.03 TOP MAIN SOLVE Loop x[1] = 0.70502830607214808090508259697535 y[1] (analytic) = 54.458260309291993537803720079419 y[1] (numeric) = 54.458260309291993537803720079349 absolute error = 7.0e-29 relative error = 1.2853881046225081493886407205266e-28 % Correct digits = 29 h = 0.00028961862690931057019423008090165 Real estimate of pole used for equation 1 Radius of convergence = 0.02867 Order of pole = 651 memory used=1327.5MB, alloc=4.3MB, time=50.17 memory used=1331.3MB, alloc=4.3MB, time=50.31 TOP MAIN SOLVE Loop x[1] = 0.70615810689052435316195054325173 y[1] (analytic) = 56.705859638050944804207267580481 y[1] (numeric) = 56.705859638050944804207267580411 absolute error = 7.0e-29 relative error = 1.2344403285093376698552631634139e-28 % Correct digits = 29 h = 0.00027820649743076236557940234073418 Real estimate of pole used for equation 1 Radius of convergence = 0.02754 Order of pole = 651 memory used=1335.1MB, alloc=4.3MB, time=50.46 memory used=1339.0MB, alloc=4.3MB, time=50.60 TOP MAIN SOLVE Loop memory used=1342.8MB, alloc=4.3MB, time=50.74 x[1] = 0.70724338904875133497057158754172 y[1] (analytic) = 59.045630613043562779190517666138 y[1] (numeric) = 59.045630613043562779190517666014 absolute error = 1.24e-28 relative error = 2.1000707200950377473265657310814e-28 % Correct digits = 29 h = 0.00026724405138806557963373522669842 Real estimate of pole used for equation 1 Radius of convergence = 0.02646 Order of pole = 651 memory used=1346.6MB, alloc=4.3MB, time=51.01 TOP MAIN SOLVE Loop x[1] = 0.70802919319020875161286104296856 y[1] (analytic) = 60.86321579194807274059916035016 y[1] (numeric) = 60.863215791948072740599160350088 absolute error = 7.2e-29 relative error = 1.1829805419109200811034587964870e-28 % Correct digits = 29 h = 0.00025930663581778864385303365672538 Real estimate of pole used for equation 1 Radius of convergence = 0.02567 Order of pole = 651 memory used=1350.4MB, alloc=4.3MB, time=51.35 memory used=1354.2MB, alloc=4.3MB, time=51.69 TOP MAIN SOLVE Loop x[1] = 0.70904074708259383238176639443682 y[1] (analytic) = 63.373480518373232619207424297974 y[1] (numeric) = 63.373480518373232619207424297917 absolute error = 5.7e-29 relative error = 8.9942984879100282591397746507285e-29 % Correct digits = 30 h = 0.00024908891973309085830853515704809 Real estimate of pole used for equation 1 Radius of convergence = 0.02466 Order of pole = 651 memory used=1358.0MB, alloc=4.3MB, time=52.04 memory used=1361.8MB, alloc=4.3MB, time=52.38 TOP MAIN SOLVE Loop x[1] = 0.71001244171551891035190460712488 y[1] (analytic) = 65.986694257988248770756249784241 y[1] (numeric) = 65.986694257988248770756249784059 absolute error = 1.82e-28 relative error = 2.7581318028818720073410127967006e-28 % Correct digits = 29 h = 0.00023927382243081734345865422080584 Real estimate of pole used for equation 1 Radius of convergence = 0.02369 Order of pole = 651 memory used=1365.7MB, alloc=4.3MB, time=52.72 memory used=1369.5MB, alloc=4.3MB, time=53.06 TOP MAIN SOLVE Loop memory used=1373.3MB, alloc=4.3MB, time=53.40 x[1] = 0.71117339472717840160371180439758 y[1] (analytic) = 69.404434762661596486567349373348 y[1] (numeric) = 69.404434762661596486567349373455 absolute error = 1.07e-28 relative error = 1.5416882273575431108472140857312e-28 % Correct digits = 29 h = 0.00022754702433324672475353101602987 Real estimate of pole used for equation 1 Radius of convergence = 0.02253 Order of pole = 651 memory used=1377.1MB, alloc=4.3MB, time=53.74 memory used=1380.9MB, alloc=4.3MB, time=54.09 TOP MAIN SOLVE Loop x[1] = 0.71206105453364274565407417237099 y[1] (analytic) = 72.264992086666593422651591003856 y[1] (numeric) = 72.264992086666593422651591004014 absolute error = 1.58e-28 relative error = 2.1863975271804136427713748286388e-28 % Correct digits = 29 h = 0.00021858076366188971414381012740955 Real estimate of pole used for equation 1 Radius of convergence = 0.02164 Order of pole = 651 memory used=1384.7MB, alloc=4.3MB, time=54.43 memory used=1388.5MB, alloc=4.3MB, time=54.77 TOP MAIN SOLVE Loop memory used=1392.4MB, alloc=4.3MB, time=55.11 x[1] = 0.71312160513331176736210142082926 y[1] (analytic) = 76.006231181486969851825802482818 y[1] (numeric) = 76.006231181486969851825802482654 absolute error = 1.64e-28 relative error = 2.1577178272186964479637644685466e-28 % Correct digits = 29 h = 0.00020786813134200060598191872883826 Real estimate of pole used for equation 1 Radius of convergence = 0.02058 Order of pole = 651 memory used=1396.2MB, alloc=4.3MB, time=55.45 memory used=1400.0MB, alloc=4.3MB, time=55.79 TOP MAIN SOLVE Loop x[1] = 0.71413017820101248523970243707113 y[1] (analytic) = 79.940247727623239390493291153298 y[1] (numeric) = 79.94024772762323939049329115308 absolute error = 2.18e-28 relative error = 2.7270368330954071928990641500919e-28 % Correct digits = 29 h = 0.00019768052459754891024857513043761 Real estimate of pole used for equation 1 Radius of convergence = 0.01957 Order of pole = 651 memory used=1403.8MB, alloc=4.3MB, time=56.14 memory used=1407.6MB, alloc=4.3MB, time=56.48 TOP MAIN SOLVE Loop memory used=1411.4MB, alloc=4.3MB, time=56.82 x[1] = 0.71508932115299298701238804959928 y[1] (analytic) = 84.076978139538848759552965083849 y[1] (numeric) = 84.076978139538848759552965083908 absolute error = 5.9e-29 relative error = 7.0173787528472187418290835562578e-29 % Correct digits = 30 h = 0.00018799221195128121557498308470137 Real estimate of pole used for equation 1 Radius of convergence = 0.01861 Order of pole = 651 memory used=1415.3MB, alloc=4.3MB, time=57.16 memory used=1419.1MB, alloc=4.3MB, time=57.50 TOP MAIN SOLVE Loop memory used=1422.9MB, alloc=4.3MB, time=57.85 x[1] = 0.71600145655675815769702137871443 y[1] (analytic) = 88.426870836660207056425327247633 y[1] (numeric) = 88.42687083666020705642532724715 absolute error = 4.83e-28 relative error = 5.4621405849833238154482696836240e-28 % Correct digits = 29 h = 0.00017877872302436029956858582090934 Real estimate of pole used for equation 1 Radius of convergence = 0.0177 Order of pole = 651 memory used=1426.7MB, alloc=4.3MB, time=58.19 memory used=1430.5MB, alloc=4.3MB, time=58.53 TOP MAIN SOLVE Loop memory used=1434.3MB, alloc=4.3MB, time=58.87 x[1] = 0.71703720486876304874768313082737 y[1] (analytic) = 93.943625257907266119247519158296 y[1] (numeric) = 93.943625257907266119247519158582 absolute error = 2.86e-28 relative error = 3.0443790008617672019457981719069e-28 % Correct digits = 29 h = 0.0001683166188626947334002852945152 Real estimate of pole used for equation 1 Radius of convergence = 0.01666 Order of pole = 651 memory used=1438.1MB, alloc=4.3MB, time=59.21 memory used=1442.0MB, alloc=4.3MB, time=59.55 TOP MAIN SOLVE Loop memory used=1445.8MB, alloc=4.3MB, time=59.89 x[1] = 0.71801234134429124713590288506658 y[1] (analytic) = 99.803251133152410291137001536891 y[1] (numeric) = 99.803251133152410291137001536603 absolute error = 2.88e-28 relative error = 2.8856775378566083033848152321648e-28 % Correct digits = 29 h = 0.00015846675547352101230715646381824 Real estimate of pole used for equation 1 Radius of convergence = 0.01569 Order of pole = 651 memory used=1449.6MB, alloc=4.3MB, time=60.24 memory used=1453.4MB, alloc=4.3MB, time=60.58 memory used=1457.2MB, alloc=4.3MB, time=60.92 TOP MAIN SOLVE Loop x[1] = 0.71907811435053001920902717656913 y[1] (analytic) = 107.10134078723099384925838345374 y[1] (numeric) = 107.10134078723099384925838345304 absolute error = 7.0e-28 relative error = 6.5358658897709757873256047809240e-28 % Correct digits = 29 h = 0.00014770137157211927419478988298539 Real estimate of pole used for equation 1 memory used=1461.0MB, alloc=4.3MB, time=61.26 Radius of convergence = 0.01462 Order of pole = 651 memory used=1464.8MB, alloc=4.3MB, time=61.60 memory used=1468.7MB, alloc=4.3MB, time=61.95 memory used=1472.5MB, alloc=4.3MB, time=62.29 TOP MAIN SOLVE Loop x[1] = 0.72007148443837983892514618258517 y[1] (analytic) = 114.93131808515891752028753572216 y[1] (numeric) = 114.93131808515891752028753572194 absolute error = 2.2e-28 relative error = 1.9141866957184806064860247738448e-28 % Correct digits = 29 h = 0.00013766733028070695382995143837758 Real estimate of pole used for equation 1 Radius of convergence = 0.01363 Order of pole = 651 memory used=1476.3MB, alloc=4.3MB, time=62.63 memory used=1480.1MB, alloc=4.3MB, time=62.97 memory used=1483.9MB, alloc=4.3MB, time=63.31 memory used=1487.7MB, alloc=4.3MB, time=63.66 TOP MAIN SOLVE Loop x[1] = 0.72112440207352455684867293722092 y[1] (analytic) = 124.58101670108705551467698977843 y[1] (numeric) = 124.58101670108705551467698977893 absolute error = 5.0e-28 relative error = 4.0134525567380215019974505434878e-28 % Correct digits = 29 h = 0.0001270317986125784899559438157937 Real estimate of pole used for equation 1 Radius of convergence = 0.01258 Order of pole = 651 memory used=1491.5MB, alloc=4.3MB, time=64.00 memory used=1495.4MB, alloc=4.3MB, time=64.34 memory used=1499.2MB, alloc=4.3MB, time=64.68 memory used=1503.0MB, alloc=4.3MB, time=65.02 TOP MAIN SOLVE Loop x[1] = 0.72209597623502393785445683903642 y[1] (analytic) = 135.03857335968232143077975241778 y[1] (numeric) = 135.03857335968232143077975241858 absolute error = 8.0e-28 relative error = 5.9242332031245475972473328464447e-28 % Correct digits = 29 h = 0.00011721791819339282323085389846578 Real estimate of pole used for equation 1 Radius of convergence = 0.0116 Order of pole = 651 memory used=1506.8MB, alloc=4.3MB, time=65.36 memory used=1510.6MB, alloc=4.3MB, time=65.70 memory used=1514.4MB, alloc=4.3MB, time=66.04 memory used=1518.3MB, alloc=4.3MB, time=66.38 memory used=1522.1MB, alloc=4.3MB, time=66.72 TOP MAIN SOLVE Loop x[1] = 0.72309957172777453767897591727688 y[1] (analytic) = 147.85340470543282550548391845842 y[1] (numeric) = 147.85340470543282550548391845891 absolute error = 4.9e-28 relative error = 3.3140934493610285362657883198686e-28 % Correct digits = 29 h = 0.00010708058998379080480136825967384 Real estimate of pole used for equation 1 Radius of convergence = 0.0106 Order of pole = 651 memory used=1525.9MB, alloc=4.3MB, time=67.06 memory used=1529.7MB, alloc=4.3MB, time=67.41 memory used=1533.5MB, alloc=4.3MB, time=67.75 memory used=1537.3MB, alloc=4.3MB, time=68.09 TOP MAIN SOLVE Loop memory used=1541.1MB, alloc=4.3MB, time=68.43 x[1] = 0.724016373519899053914615516812 y[1] (analytic) = 161.88136647015435964890556171992 y[1] (numeric) = 161.88136647015435964890556171877 absolute error = 1.15e-27 relative error = 7.1039677084269143804855279934937e-28 % Correct digits = 29 h = 9.7819965820916903431271294672412e-05 Real estimate of pole used for equation 1 Radius of convergence = 0.009684 Order of pole = 651 memory used=1545.0MB, alloc=4.3MB, time=68.77 memory used=1548.8MB, alloc=4.3MB, time=69.11 memory used=1552.6MB, alloc=4.3MB, time=69.45 memory used=1556.4MB, alloc=4.3MB, time=69.79 memory used=1560.2MB, alloc=4.3MB, time=70.13 TOP MAIN SOLVE Loop memory used=1564.0MB, alloc=4.3MB, time=70.47 x[1] = 0.72502993635062486932360651636545 y[1] (analytic) = 180.84250726717189023441490061784 y[1] (numeric) = 180.84250726717189023441490061876 absolute error = 9.2e-28 relative error = 5.0872995177003190498093376631000e-28 % Correct digits = 29 h = 8.7581957429747050815200592112105e-05 Real estimate of pole used for equation 1 Radius of convergence = 0.008671 Order of pole = 651 memory used=1567.8MB, alloc=4.3MB, time=70.82 memory used=1571.7MB, alloc=4.3MB, time=71.16 memory used=1575.5MB, alloc=4.3MB, time=71.50 memory used=1579.3MB, alloc=4.3MB, time=71.84 memory used=1583.1MB, alloc=4.3MB, time=72.18 TOP MAIN SOLVE Loop memory used=1586.9MB, alloc=4.3MB, time=72.52 x[1] = 0.72601504924816945765245204060369 y[1] (analytic) = 204.06393842541884066288036163794 y[1] (numeric) = 204.06393842541884066288036163959 absolute error = 1.65e-27 relative error = 8.0857010441511250059801707003114e-28 % Correct digits = 29 h = 7.7631322101013835372316508897741e-05 Real estimate of pole used for equation 1 Radius of convergence = 0.007686 Order of pole = 651 memory used=1590.7MB, alloc=4.3MB, time=72.86 memory used=1594.5MB, alloc=4.3MB, time=73.20 memory used=1598.4MB, alloc=4.3MB, time=73.54 memory used=1602.2MB, alloc=4.3MB, time=73.88 memory used=1606.0MB, alloc=4.3MB, time=74.22 memory used=1609.8MB, alloc=4.3MB, time=74.57 memory used=1613.6MB, alloc=4.3MB, time=74.91 TOP MAIN SOLVE Loop x[1] = 0.72702380342068724165258456674943 y[1] (analytic) = 234.9435680392472667585912058318 y[1] (numeric) = 234.94356803924726675859120583259 absolute error = 7.9e-28 relative error = 3.3625095872725942820873141556731e-28 % Correct digits = 29 h = 6.7441886014975613148755638737462e-05 Real estimate of pole used for equation 1 Radius of convergence = 0.006677 Order of pole = 651 memory used=1617.4MB, alloc=4.3MB, time=75.25 memory used=1621.3MB, alloc=4.3MB, time=75.60 memory used=1625.1MB, alloc=4.3MB, time=75.94 memory used=1628.9MB, alloc=4.3MB, time=76.28 memory used=1632.7MB, alloc=4.3MB, time=76.62 memory used=1636.5MB, alloc=4.3MB, time=76.96 memory used=1640.3MB, alloc=4.3MB, time=77.30 memory used=1644.1MB, alloc=4.3MB, time=77.64 TOP MAIN SOLVE Loop x[1] = 0.72801558225963999312802343662525 y[1] (analytic) = 275.98709855720088046895860183653 y[1] (numeric) = 275.98709855720088046895860184009 memory used=1648.0MB, alloc=4.3MB, time=77.98 absolute error = 3.56e-27 relative error = 1.2899153687295122064491377375509e-27 % Correct digits = 28 h = 5.7423917944745800265534730900924e-05 Real estimate of pole used for equation 1 Radius of convergence = 0.005685 Order of pole = 651 memory used=1651.8MB, alloc=4.3MB, time=78.33 memory used=1655.6MB, alloc=4.3MB, time=78.67 memory used=1659.4MB, alloc=4.3MB, time=79.01 memory used=1663.2MB, alloc=4.3MB, time=79.35 memory used=1667.0MB, alloc=4.3MB, time=79.69 memory used=1670.8MB, alloc=4.3MB, time=80.03 memory used=1674.7MB, alloc=4.3MB, time=80.37 memory used=1678.5MB, alloc=4.3MB, time=80.71 memory used=1682.3MB, alloc=4.3MB, time=81.06 TOP MAIN SOLVE Loop x[1] = 0.72900380804906765642803060342851 y[1] (analytic) = 334.12420078129053094549674894363 y[1] (numeric) = 334.12420078129053094549674894473 absolute error = 1.10e-27 relative error = 3.2921889447931157077209371370087e-28 % Correct digits = 29 h = 4.7441839263658292184654258141803e-05 Real estimate of pole used for equation 1 Radius of convergence = 0.004697 Order of pole = 651 memory used=1686.1MB, alloc=4.3MB, time=81.40 memory used=1689.9MB, alloc=4.3MB, time=81.74 memory used=1693.7MB, alloc=4.3MB, time=82.08 memory used=1697.5MB, alloc=4.3MB, time=82.42 memory used=1701.4MB, alloc=4.3MB, time=82.77 memory used=1705.2MB, alloc=4.3MB, time=83.11 memory used=1709.0MB, alloc=4.3MB, time=83.45 memory used=1712.8MB, alloc=4.3MB, time=83.79 memory used=1716.6MB, alloc=4.3MB, time=84.13 memory used=1720.4MB, alloc=4.3MB, time=84.47 memory used=1724.3MB, alloc=4.3MB, time=84.82 memory used=1728.1MB, alloc=4.3MB, time=85.16 TOP MAIN SOLVE Loop memory used=1731.9MB, alloc=4.3MB, time=85.50 x[1] = 0.73001042254532437644041802140417 y[1] (analytic) = 425.35601076430910645399222613627 y[1] (numeric) = 425.35601076430910645399222613567 absolute error = 6.0e-28 relative error = 1.4105830993709915882948368247653e-28 % Correct digits = 29 h = 3.7274016069145968827205591720240e-05 Real estimate of pole used for equation 1 Radius of convergence = 0.00369 Order of pole = 651 memory used=1735.7MB, alloc=4.3MB, time=85.84 memory used=1739.5MB, alloc=4.3MB, time=86.18 memory used=1743.3MB, alloc=4.3MB, time=86.53 memory used=1747.1MB, alloc=4.3MB, time=86.88 memory used=1751.0MB, alloc=4.3MB, time=87.21 memory used=1754.8MB, alloc=4.3MB, time=87.56 memory used=1758.6MB, alloc=4.3MB, time=87.90 memory used=1762.4MB, alloc=4.3MB, time=88.24 memory used=1766.2MB, alloc=4.3MB, time=88.58 memory used=1770.0MB, alloc=4.3MB, time=88.92 memory used=1773.8MB, alloc=4.3MB, time=89.26 memory used=1777.7MB, alloc=4.3MB, time=89.60 memory used=1781.5MB, alloc=4.3MB, time=89.94 memory used=1785.3MB, alloc=4.3MB, time=90.28 memory used=1789.1MB, alloc=4.3MB, time=90.63 memory used=1792.9MB, alloc=4.3MB, time=90.97 TOP MAIN SOLVE Loop x[1] = 0.73102528019563134726402260584809 y[1] (analytic) = 586.8352783318154121124073855816 y[1] (numeric) = 586.83527833181541211240738557045 absolute error = 1.115e-26 relative error = 1.9000221035953864087101008611862e-27 % Correct digits = 28 h = 2.7022928692307879699886556933462e-05 Real estimate of pole used for equation 1 Radius of convergence = 0.002675 Order of pole = 651 memory used=1796.7MB, alloc=4.3MB, time=91.32 memory used=1800.5MB, alloc=4.3MB, time=91.66 memory used=1804.4MB, alloc=4.3MB, time=92.00 memory used=1808.2MB, alloc=4.3MB, time=92.34 memory used=1812.0MB, alloc=4.3MB, time=92.69 memory used=1815.8MB, alloc=4.3MB, time=93.04 memory used=1819.6MB, alloc=4.3MB, time=93.38 memory used=1823.4MB, alloc=4.3MB, time=93.72 memory used=1827.3MB, alloc=4.3MB, time=94.07 memory used=1831.1MB, alloc=4.3MB, time=94.41 memory used=1834.9MB, alloc=4.3MB, time=94.76 memory used=1838.7MB, alloc=4.3MB, time=95.10 memory used=1842.5MB, alloc=4.3MB, time=95.44 memory used=1846.3MB, alloc=4.3MB, time=95.78 memory used=1850.1MB, alloc=4.3MB, time=96.12 memory used=1854.0MB, alloc=4.3MB, time=96.46 memory used=1857.8MB, alloc=4.3MB, time=96.81 memory used=1861.6MB, alloc=4.3MB, time=97.15 memory used=1865.4MB, alloc=4.3MB, time=97.49 memory used=1869.2MB, alloc=4.3MB, time=97.83 memory used=1873.0MB, alloc=4.3MB, time=98.18 memory used=1876.8MB, alloc=4.3MB, time=98.52 memory used=1880.7MB, alloc=4.3MB, time=98.86 TOP MAIN SOLVE Loop memory used=1884.5MB, alloc=4.3MB, time=99.20 x[1] = 0.73201560190777102589744390196282 y[1] (analytic) = 931.93320644904181261031665731227 y[1] (numeric) = 931.9332064490418126103166573143 absolute error = 2.03e-27 relative error = 2.1782676976764649425796497828111e-28 % Correct digits = 29 h = 1.7019679074735368251186596178802e-05 Real estimate of pole used for equation 1 Radius of convergence = 0.001685 Order of pole = 651 memory used=1888.3MB, alloc=4.3MB, time=99.55 memory used=1892.1MB, alloc=4.3MB, time=99.89 memory used=1895.9MB, alloc=4.3MB, time=100.23 memory used=1899.7MB, alloc=4.3MB, time=100.57 memory used=1903.6MB, alloc=4.3MB, time=100.91 memory used=1907.4MB, alloc=4.3MB, time=101.26 memory used=1911.2MB, alloc=4.3MB, time=101.60 memory used=1915.0MB, alloc=4.3MB, time=101.95 memory used=1918.8MB, alloc=4.3MB, time=102.29 memory used=1922.6MB, alloc=4.3MB, time=102.64 memory used=1926.4MB, alloc=4.3MB, time=102.98 memory used=1930.3MB, alloc=4.3MB, time=103.32 memory used=1934.1MB, alloc=4.3MB, time=103.67 memory used=1937.9MB, alloc=4.3MB, time=104.01 memory used=1941.7MB, alloc=4.3MB, time=104.36 memory used=1945.5MB, alloc=4.3MB, time=104.70 memory used=1949.3MB, alloc=4.3MB, time=105.04 memory used=1953.1MB, alloc=4.3MB, time=105.38 memory used=1957.0MB, alloc=4.3MB, time=105.72 memory used=1960.8MB, alloc=4.3MB, time=106.06 memory used=1964.6MB, alloc=4.3MB, time=106.40 memory used=1968.4MB, alloc=4.3MB, time=106.74 memory used=1972.2MB, alloc=4.3MB, time=107.08 memory used=1976.0MB, alloc=4.3MB, time=107.43 memory used=1979.8MB, alloc=4.3MB, time=107.77 memory used=1983.7MB, alloc=4.3MB, time=108.11 memory used=1987.5MB, alloc=4.3MB, time=108.45 memory used=1991.3MB, alloc=4.3MB, time=108.79 memory used=1995.1MB, alloc=4.3MB, time=109.13 memory used=1998.9MB, alloc=4.3MB, time=109.47 memory used=2002.7MB, alloc=4.3MB, time=109.82 memory used=2006.6MB, alloc=4.3MB, time=110.17 memory used=2010.4MB, alloc=4.3MB, time=110.51 memory used=2014.2MB, alloc=4.3MB, time=110.86 memory used=2018.0MB, alloc=4.3MB, time=111.20 memory used=2021.8MB, alloc=4.3MB, time=111.54 memory used=2025.6MB, alloc=4.3MB, time=111.88 memory used=2029.4MB, alloc=4.3MB, time=112.22 memory used=2033.3MB, alloc=4.3MB, time=112.56 memory used=2037.1MB, alloc=4.3MB, time=112.90 memory used=2040.9MB, alloc=4.3MB, time=113.24 memory used=2044.7MB, alloc=4.3MB, time=113.59 memory used=2048.5MB, alloc=4.3MB, time=113.93 memory used=2052.3MB, alloc=4.3MB, time=114.27 memory used=2056.1MB, alloc=4.3MB, time=114.61 TOP MAIN SOLVE Loop x[1] = 0.73300475131937491429788585665302 y[1] (analytic) = 2257.2253290094868897274872306031 y[1] (numeric) = 2257.2253290094868897274872307969 absolute error = 1.938e-25 relative error = 8.5857622413373812625642429413143e-27 % Correct digits = 28 h = 7.0282708767162934992476599137214e-06 Real estimate of pole used for equation 1 Radius of convergence = 0.0006958 Order of pole = 651 memory used=2060.0MB, alloc=4.3MB, time=114.96 memory used=2063.8MB, alloc=4.3MB, time=115.30 memory used=2067.6MB, alloc=4.3MB, time=115.64 memory used=2071.4MB, alloc=4.3MB, time=115.99 memory used=2075.2MB, alloc=4.3MB, time=116.34 memory used=2079.0MB, alloc=4.3MB, time=116.68 memory used=2082.8MB, alloc=4.3MB, time=117.02 memory used=2086.7MB, alloc=4.3MB, time=117.37 memory used=2090.5MB, alloc=4.3MB, time=117.71 memory used=2094.3MB, alloc=4.3MB, time=118.05 memory used=2098.1MB, alloc=4.3MB, time=118.39 memory used=2101.9MB, alloc=4.3MB, time=118.74 memory used=2105.7MB, alloc=4.3MB, time=119.08 memory used=2109.6MB, alloc=4.3MB, time=119.42 memory used=2113.4MB, alloc=4.3MB, time=119.77 memory used=2117.2MB, alloc=4.3MB, time=120.11 memory used=2121.0MB, alloc=4.3MB, time=120.46 memory used=2124.8MB, alloc=4.3MB, time=120.80 memory used=2128.6MB, alloc=4.3MB, time=121.15 memory used=2132.4MB, alloc=4.3MB, time=121.49 memory used=2136.3MB, alloc=4.3MB, time=121.84 memory used=2140.1MB, alloc=4.3MB, time=122.18 memory used=2143.9MB, alloc=4.3MB, time=122.53 memory used=2147.7MB, alloc=4.3MB, time=122.87 memory used=2151.5MB, alloc=4.3MB, time=123.21 memory used=2155.3MB, alloc=4.3MB, time=123.56 memory used=2159.1MB, alloc=4.3MB, time=123.90 memory used=2163.0MB, alloc=4.3MB, time=124.24 memory used=2166.8MB, alloc=4.3MB, time=124.59 memory used=2170.6MB, alloc=4.3MB, time=124.93 memory used=2174.4MB, alloc=4.3MB, time=125.27 memory used=2178.2MB, alloc=4.3MB, time=125.61 memory used=2182.0MB, alloc=4.3MB, time=125.96 memory used=2185.8MB, alloc=4.3MB, time=126.30 memory used=2189.7MB, alloc=4.3MB, time=126.64 memory used=2193.5MB, alloc=4.3MB, time=126.99 memory used=2197.3MB, alloc=4.3MB, time=127.33 memory used=2201.1MB, alloc=4.3MB, time=127.69 memory used=2204.9MB, alloc=4.3MB, time=128.03 memory used=2208.7MB, alloc=4.3MB, time=128.37 memory used=2212.6MB, alloc=4.3MB, time=128.71 memory used=2216.4MB, alloc=4.3MB, time=129.05 memory used=2220.2MB, alloc=4.3MB, time=129.39 memory used=2224.0MB, alloc=4.3MB, time=129.74 memory used=2227.8MB, alloc=4.3MB, time=130.08 memory used=2231.6MB, alloc=4.3MB, time=130.42 memory used=2235.4MB, alloc=4.3MB, time=130.77 memory used=2239.3MB, alloc=4.3MB, time=131.11 memory used=2243.1MB, alloc=4.3MB, time=131.45 memory used=2246.9MB, alloc=4.3MB, time=131.80 memory used=2250.7MB, alloc=4.3MB, time=132.14 memory used=2254.5MB, alloc=4.3MB, time=132.48 memory used=2258.3MB, alloc=4.3MB, time=132.82 memory used=2262.1MB, alloc=4.3MB, time=133.17 memory used=2266.0MB, alloc=4.3MB, time=133.51 memory used=2269.8MB, alloc=4.3MB, time=133.86 memory used=2273.6MB, alloc=4.3MB, time=134.20 memory used=2277.4MB, alloc=4.3MB, time=134.54 memory used=2281.2MB, alloc=4.3MB, time=134.89 memory used=2285.0MB, alloc=4.3MB, time=135.23 memory used=2288.8MB, alloc=4.3MB, time=135.57 memory used=2292.7MB, alloc=4.3MB, time=135.91 memory used=2296.5MB, alloc=4.3MB, time=136.26 memory used=2300.3MB, alloc=4.3MB, time=136.59 memory used=2304.1MB, alloc=4.3MB, time=136.94 memory used=2307.9MB, alloc=4.3MB, time=137.28 memory used=2311.7MB, alloc=4.3MB, time=137.62 memory used=2315.6MB, alloc=4.3MB, time=137.96 memory used=2319.4MB, alloc=4.3MB, time=138.31 memory used=2323.2MB, alloc=4.3MB, time=138.65 memory used=2327.0MB, alloc=4.3MB, time=138.99 memory used=2330.8MB, alloc=4.3MB, time=139.35 memory used=2334.6MB, alloc=4.3MB, time=139.69 memory used=2338.4MB, alloc=4.3MB, time=140.03 memory used=2342.3MB, alloc=4.3MB, time=140.37 memory used=2346.1MB, alloc=4.3MB, time=140.72 memory used=2349.9MB, alloc=4.3MB, time=141.06 memory used=2353.7MB, alloc=4.3MB, time=141.40 memory used=2357.5MB, alloc=4.3MB, time=141.74 memory used=2361.3MB, alloc=4.3MB, time=142.08 memory used=2365.1MB, alloc=4.3MB, time=142.43 memory used=2369.0MB, alloc=4.3MB, time=142.77 memory used=2372.8MB, alloc=4.3MB, time=143.11 memory used=2376.6MB, alloc=4.3MB, time=143.46 memory used=2380.4MB, alloc=4.3MB, time=143.80 memory used=2384.2MB, alloc=4.3MB, time=144.14 memory used=2388.0MB, alloc=4.3MB, time=144.48 memory used=2391.8MB, alloc=4.3MB, time=144.83 memory used=2395.7MB, alloc=4.3MB, time=145.18 memory used=2399.5MB, alloc=4.3MB, time=145.52 memory used=2403.3MB, alloc=4.3MB, time=145.86 memory used=2407.1MB, alloc=4.3MB, time=146.20 memory used=2410.9MB, alloc=4.3MB, time=146.54 memory used=2414.7MB, alloc=4.3MB, time=146.88 memory used=2418.6MB, alloc=4.3MB, time=147.23 memory used=2422.4MB, alloc=4.3MB, time=147.57 memory used=2426.2MB, alloc=4.3MB, time=147.91 memory used=2430.0MB, alloc=4.3MB, time=148.26 memory used=2433.8MB, alloc=4.3MB, time=148.60 memory used=2437.6MB, alloc=4.3MB, time=148.94 memory used=2441.4MB, alloc=4.3MB, time=149.28 memory used=2445.3MB, alloc=4.3MB, time=149.62 memory used=2449.1MB, alloc=4.3MB, time=149.97 memory used=2452.9MB, alloc=4.3MB, time=150.31 memory used=2456.7MB, alloc=4.3MB, time=150.65 memory used=2460.5MB, alloc=4.3MB, time=150.99 memory used=2464.3MB, alloc=4.3MB, time=151.33 memory used=2468.1MB, alloc=4.3MB, time=151.67 memory used=2472.0MB, alloc=4.3MB, time=152.02 memory used=2475.8MB, alloc=4.3MB, time=152.36 memory used=2479.6MB, alloc=4.3MB, time=152.70 memory used=2483.4MB, alloc=4.3MB, time=153.05 memory used=2487.2MB, alloc=4.3MB, time=153.39 memory used=2491.0MB, alloc=4.3MB, time=153.73 memory used=2494.8MB, alloc=4.3MB, time=154.08 memory used=2498.7MB, alloc=4.3MB, time=154.42 memory used=2502.5MB, alloc=4.3MB, time=154.76 memory used=2506.3MB, alloc=4.3MB, time=155.11 memory used=2510.1MB, alloc=4.3MB, time=155.45 memory used=2513.9MB, alloc=4.3MB, time=155.80 memory used=2517.7MB, alloc=4.3MB, time=156.14 memory used=2521.6MB, alloc=4.3MB, time=156.48 memory used=2525.4MB, alloc=4.3MB, time=156.83 memory used=2529.2MB, alloc=4.3MB, time=157.17 memory used=2533.0MB, alloc=4.3MB, time=157.52 memory used=2536.8MB, alloc=4.3MB, time=157.86 memory used=2540.6MB, alloc=4.3MB, time=158.20 memory used=2544.4MB, alloc=4.3MB, time=158.55 memory used=2548.3MB, alloc=4.3MB, time=158.90 memory used=2552.1MB, alloc=4.3MB, time=159.24 memory used=2555.9MB, alloc=4.3MB, time=159.59 memory used=2559.7MB, alloc=4.3MB, time=159.93 memory used=2563.5MB, alloc=4.3MB, time=160.28 memory used=2567.3MB, alloc=4.3MB, time=160.62 memory used=2571.1MB, alloc=4.3MB, time=160.97 memory used=2575.0MB, alloc=4.3MB, time=161.31 memory used=2578.8MB, alloc=4.3MB, time=161.66 memory used=2582.6MB, alloc=4.3MB, time=162.00 memory used=2586.4MB, alloc=4.3MB, time=162.34 memory used=2590.2MB, alloc=4.3MB, time=162.69 memory used=2594.0MB, alloc=4.3MB, time=163.04 memory used=2597.8MB, alloc=4.3MB, time=163.38 memory used=2601.7MB, alloc=4.3MB, time=163.72 memory used=2605.5MB, alloc=4.3MB, time=164.07 memory used=2609.3MB, alloc=4.3MB, time=164.41 memory used=2613.1MB, alloc=4.3MB, time=164.75 memory used=2616.9MB, alloc=4.3MB, time=165.10 memory used=2620.7MB, alloc=4.3MB, time=165.44 memory used=2624.6MB, alloc=4.3MB, time=165.78 memory used=2628.4MB, alloc=4.3MB, time=166.13 memory used=2632.2MB, alloc=4.3MB, time=166.47 memory used=2636.0MB, alloc=4.3MB, time=166.82 memory used=2639.8MB, alloc=4.3MB, time=167.16 memory used=2643.6MB, alloc=4.3MB, time=167.50 memory used=2647.4MB, alloc=4.3MB, time=167.85 memory used=2651.3MB, alloc=4.3MB, time=168.19 memory used=2655.1MB, alloc=4.3MB, time=168.54 memory used=2658.9MB, alloc=4.3MB, time=168.89 memory used=2662.7MB, alloc=4.3MB, time=169.23 memory used=2666.5MB, alloc=4.3MB, time=169.58 memory used=2670.3MB, alloc=4.3MB, time=169.92 memory used=2674.1MB, alloc=4.3MB, time=170.27 memory used=2678.0MB, alloc=4.3MB, time=170.61 memory used=2681.8MB, alloc=4.3MB, time=170.95 memory used=2685.6MB, alloc=4.3MB, time=171.30 memory used=2689.4MB, alloc=4.3MB, time=171.64 memory used=2693.2MB, alloc=4.3MB, time=171.99 memory used=2697.0MB, alloc=4.3MB, time=172.33 memory used=2700.8MB, alloc=4.3MB, time=172.67 memory used=2704.7MB, alloc=4.3MB, time=173.02 memory used=2708.5MB, alloc=4.3MB, time=173.36 memory used=2712.3MB, alloc=4.3MB, time=173.70 memory used=2716.1MB, alloc=4.3MB, time=174.05 memory used=2719.9MB, alloc=4.3MB, time=174.40 memory used=2723.7MB, alloc=4.3MB, time=174.75 memory used=2727.6MB, alloc=4.3MB, time=175.09 memory used=2731.4MB, alloc=4.3MB, time=175.44 memory used=2735.2MB, alloc=4.3MB, time=175.78 memory used=2739.0MB, alloc=4.3MB, time=176.12 memory used=2742.8MB, alloc=4.3MB, time=176.47 memory used=2746.6MB, alloc=4.3MB, time=176.81 memory used=2750.4MB, alloc=4.3MB, time=177.15 memory used=2754.3MB, alloc=4.3MB, time=177.50 memory used=2758.1MB, alloc=4.3MB, time=177.84 memory used=2761.9MB, alloc=4.3MB, time=178.19 memory used=2765.7MB, alloc=4.3MB, time=178.53 memory used=2769.5MB, alloc=4.3MB, time=178.87 memory used=2773.3MB, alloc=4.3MB, time=179.21 memory used=2777.1MB, alloc=4.3MB, time=179.56 memory used=2781.0MB, alloc=4.3MB, time=179.90 memory used=2784.8MB, alloc=4.3MB, time=180.25 Finished! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = ( 1.0 + ( tan ( sqrt ( 2.0 * x + 1.0 ) ) * tan( sqrt ( 2.0 * x + 1.0 ) ) ) ) / sqrt ( 2.0 * x + 1.0 ) ; Iterations = 1404 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 3 Minutes 0 Seconds Expected Time Remaining = 1 Minutes 15 Seconds Optimized Time Remaining = 1 Minutes 15 Seconds Expected Total Time = 4 Minutes 15 Seconds Time to Timeout Unknown Percent Done = 70.41 % > quit memory used=2784.9MB, alloc=4.3MB, time=180.26