|\^/| 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_2, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1[1]) < min_size) then # if number 1 > min_size := omniabs(array_y1[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (omniabs(array_y2[1]) < min_size) then # if number 1 > min_size := omniabs(array_y2[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_2, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y1[1]) < min_size then min_size := omniabs(array_y1[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if omniabs(array_y2[1]) < min_size then min_size := omniabs(array_y2[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_2, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[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; > value3 := omniabs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[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_2, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1[no_terms - 3] + array_y1[no_terms - 2]*hn_div_ho + array_y1[no_terms - 1]*hn_div_ho_2 + array_y1[no_terms]*hn_div_ho_3); if max_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; value3 := omniabs(array_y2[no_terms - 3] + array_y2[no_terms - 2]*hn_div_ho + array_y2[no_terms - 1]*hn_div_ho_2 + array_y2[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_2, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_2, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_2, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1(ind_var); > omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y1[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y1[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," "); > ; > analytic_val_y := exact_soln_y2(ind_var); > omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y2[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y2[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[2] := relerr; > else > array_last_rel_error[2] := 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_2, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1(ind_var); omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y1[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y1[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, " "); analytic_val_y := exact_soln_y2(ind_var); omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y2[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[2] := relerr else array_last_rel_error[2] := 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_2, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y2_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_2, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_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_2, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_2, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_2, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_y1_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y1_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y1_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_y1_higher[1,m]/array_y1_higher[1,m-1]; > rm1 := array_y1_higher[1,m-1]/array_y1_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 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 2 - 1; > while ((m >= 10) and ((omniabs(array_y2_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y2_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y2_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_y2_higher[1,m]/array_y2_higher[1,m-1]; > rm1 := array_y2_higher[1,m-1]/array_y2_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[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1; > #BOTTOM RADII REAL EQ = 2 > #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_y1_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_y1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y1_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y1_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-5]) <= (glob_small_float)))) then # if number 2 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]); > rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]); > rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]); > rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]); > rm4 := (array_y1_higher[1,m-4])/(array_y1_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 > #TOP RADII COMPLEX EQ = 2 > #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 - 2 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y2_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2; > n := n - 1; > od;# end do number 2; > m := n + cnt; > if (m <= 10) then # if number 2 > rad_c := glob_large_float; > ord_no := glob_large_float; > elif > (((omniabs(array_y2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y2_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y2_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-5]) <= (glob_small_float)))) then # if number 3 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]); > rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]); > rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]); > rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]); > rm4 := (array_y2_higher[1,m-4])/(array_y2_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 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > 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 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3; > #BOTTOM RADII COMPLEX EQ = 2 > 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 3 > 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 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > 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 3 > 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 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Real estimate of pole used for equation 1"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > 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 3 > 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 4 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 4; > fi;# end if 3; > 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 3 > 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 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Real estimate of pole used for equation 1"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > 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 3 > 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 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (1 <> found_sing ) then # if number 3 > 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 4 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 4; > fi;# end if 3; > #BOTTOM WHICH RADII EQ = 1 > #TOP WHICH RADII EQ = 2 > if (2 <> found_sing and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found_sing := 2; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 2"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > -1.0 * glob_smallish_float) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0)))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found_sing := 2; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Real estimate of pole used for equation 2"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float)))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found_sing := 2; > array_type_pole[2] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE for equation 2"); > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > -1.0 * glob_smallish_float))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found_sing := 2; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Real estimate of pole used for equation 2"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found_sing := 2; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 2"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing ) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE for equation 2"); > fi;# end if 4; > fi;# end if 3; > #BOTTOM WHICH RADII EQ = 2 > 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 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if (array_pole[1] > array_poles[2,1]) then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3; > #BOTTOM WHICH RADIUS EQ = 2 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 3 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 2 > array_y1[term] := array_y1[term]* ratio; > array_y1_higher[1,term] := array_y1_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > array_y2[term] := array_y2[term]* ratio; > array_y2_higher[1,term] := array_y2_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 3; > #BOTTOM ADJUST ALL SERIES > if (reached_interval()) then # if number 3 > display_pole(); > fi;# end if 3 > 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_2, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1_higher[1, m]) < glob_small_float*glob_small_float or omniabs(array_y1_higher[1, m - 1]) < glob_small_float*glob_small_float or omniabs(array_y1_higher[1, m - 2]) < glob_small_float*glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_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; m := n - 3; while 10 <= m and ( omniabs(array_y2_higher[1, m]) < glob_small_float*glob_small_float or omniabs(array_y2_higher[1, m - 1]) < glob_small_float*glob_small_float or omniabs(array_y2_higher[1, m - 2]) < glob_small_float*glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_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[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 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_y1_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_y1_higher[1, m]) or glob_large_float <= omniabs(array_y1_higher[1, m - 1]) or glob_large_float <= omniabs(array_y1_higher[1, m - 2]) or glob_large_float <= omniabs(array_y1_higher[1, m - 3]) or glob_large_float <= omniabs(array_y1_higher[1, m - 4]) or glob_large_float <= omniabs(array_y1_higher[1, m - 5]) or omniabs(array_y1_higher[1, m]) <= glob_small_float or omniabs(array_y1_higher[1, m - 1]) <= glob_small_float or omniabs(array_y1_higher[1, m - 2]) <= glob_small_float or omniabs(array_y1_higher[1, m - 3]) <= glob_small_float or omniabs(array_y1_higher[1, m - 4]) <= glob_small_float or omniabs(array_y1_higher[1, m - 5]) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3]; rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4]; rm4 := array_y1_higher[1, m - 4]/array_y1_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; n := glob_max_terms - 3; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y2_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_y2_higher[1, m]) or glob_large_float <= omniabs(array_y2_higher[1, m - 1]) or glob_large_float <= omniabs(array_y2_higher[1, m - 2]) or glob_large_float <= omniabs(array_y2_higher[1, m - 3]) or glob_large_float <= omniabs(array_y2_higher[1, m - 4]) or glob_large_float <= omniabs(array_y2_higher[1, m - 5]) or omniabs(array_y2_higher[1, m]) <= glob_small_float or omniabs(array_y2_higher[1, m - 1]) <= glob_small_float or omniabs(array_y2_higher[1, m - 2]) <= glob_small_float or omniabs(array_y2_higher[1, m - 3]) <= glob_small_float or omniabs(array_y2_higher[1, m - 4]) <= glob_small_float or omniabs(array_y2_higher[1, m - 5]) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3]; rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4]; rm4 := array_y2_higher[1, m - 4]/array_y2_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[2, 1] := rad_c; array_complex_pole[2, 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; if 2 <> found_sing and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found_sing := 2; array_type_pole[2] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 2") end if end if end if; if 2 <> found_sing and array_real_pole[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and -1.0*glob_smallish_float < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found_sing := 2; array_type_pole[2] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 2") end if end if end if; if 2 <> found_sing and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found_sing := 2; array_type_pole[2] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 2") end if end if; if 2 <> found_sing and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and -1.0*glob_smallish_float < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found_sing := 2; array_type_pole[2] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 2") end if end if end if; if 2 <> found_sing and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 2; found_sing := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 2") end if end if end if; if 2 <> found_sing then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 2") 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_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 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_y1[term] := array_y1[term]*ratio; array_y1_higher[1, term] := array_y1_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; array_y2[term] := array_y2[term]*ratio; array_y2_higher[1, term] := array_y2_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_2, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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 3 > 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_y1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y1[iii]); > fi;# end if 4; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y2[iii]); > fi;# end if 4; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 3; > 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_2, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1[iii]) then array_norms[iii] := omniabs(array_y1[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y2[iii]) then array_norms[iii] := omniabs(array_y2[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_2, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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 FULL FULL $eq_no = 1 i = 1 > array_tmp1[1] := (array_m1[1] * (array_y2[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y1_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #emit pre diff $eq_no = 2 i = 1 order_d = 1 > array_tmp4[1] := array_y1_higher[2,1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[2,3]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * expt(glob_h , (2)) * factorial_3(0,2); > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y2_higher[3,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > # emit pre mult FULL FULL $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y1_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #emit pre diff $eq_no = 2 i = 2 order_d = 1 > array_tmp4[2] := array_y1_higher[2,2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[2,4]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * expt(glob_h , (2)) * factorial_3(1,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y2_higher[2,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[3,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > # emit pre mult FULL FULL $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y1_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y1_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #emit pre diff $eq_no = 2 i = 3 order_d = 1 > array_tmp4[3] := array_y1_higher[2,3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[2,5]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * expt(glob_h , (2)) * factorial_3(2,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y2_higher[2,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > # emit pre mult FULL FULL $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y1_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y1_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #emit pre diff $eq_no = 2 i = 4 order_d = 1 > array_tmp4[4] := array_y1_higher[2,4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[2,6]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * expt(glob_h , (2)) * factorial_3(3,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y2_higher[2,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y2_higher[3,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > # emit pre mult FULL FULL $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y1_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y1_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #emit pre diff $eq_no = 2 i = 5 order_d = 1 > array_tmp4[5] := array_y1_higher[2,5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[2,7]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * expt(glob_h , (2)) * factorial_3(4,6); > array_y2[7] := temporary; > array_y2_higher[1,7] := temporary; > temporary := temporary / glob_h * (6.0); > array_y2_higher[2,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y2_higher[3,5] := 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 mult FULL FULL $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_m1,array_y2,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp2[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y1[kkk + order_d] := temporary; > array_y1_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_y1_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; > #emit diff $eq_no = 2 > array_tmp4[kkk] := array_y1_higher[2,kkk]; > #emit assign $eq_no = 2 > order_d := 2; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y2_set_initial[2,kkk + order_d]) then # if number 2 > temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y2[kkk + order_d] := temporary; > array_y2_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_y2_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_2, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := array_m1[1]*array_y2[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y1_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y1[2] := temporary; array_y1_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp4[1] := array_y1_higher[2, 1]; if not array_y2_set_initial[2, 3] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*expt(glob_h, 2)*factorial_3(0, 2); array_y2[3] := temporary; array_y2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 2] := temporary; temporary := temporary*1.0/glob_h; array_y2_higher[3, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := ats(2, array_m1, array_y2, 1); array_tmp2[2] := array_tmp1[2]; if not array_y1_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y1[3] := temporary; array_y1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp4[2] := array_y1_higher[2, 2]; if not array_y2_set_initial[2, 4] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*expt(glob_h, 2)*factorial_3(1, 3); array_y2[4] := temporary; array_y2_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[2, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[3, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := ats(3, array_m1, array_y2, 1); array_tmp2[3] := array_tmp1[3]; if not array_y1_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y1[4] := temporary; array_y1_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp4[3] := array_y1_higher[2, 3]; if not array_y2_set_initial[2, 5] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*expt(glob_h, 2)*factorial_3(2, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[2, 4] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := ats(4, array_m1, array_y2, 1); array_tmp2[4] := array_tmp1[4]; if not array_y1_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y1[5] := temporary; array_y1_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp4[4] := array_y1_higher[2, 4]; if not array_y2_set_initial[2, 6] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*expt(glob_h, 2)*factorial_3(3, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[2, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[3, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := ats(5, array_m1, array_y2, 1); array_tmp2[5] := array_tmp1[5]; if not array_y1_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; array_tmp4[5] := array_y1_higher[2, 5]; if not array_y2_set_initial[2, 7] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*expt(glob_h, 2)*factorial_3(4, 6); array_y2[7] := temporary; array_y2_higher[1, 7] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[2, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[3, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := ats(kkk, array_m1, array_y2, 1); array_tmp2[kkk] := array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y1[kkk + order_d] := temporary; array_y1_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_y1_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; array_tmp4[kkk] := array_y1_higher[2, kkk]; order_d := 2; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[2, kkk + order_d] then temporary := array_tmp4[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y2[kkk + order_d] := temporary; array_y2_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_y2_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_y1 := proc(x) > return( - cos(x)); > end; exact_soln_y1 := proc(x) return -cos(x) end proc > exact_soln_y2 := proc(x) > return( - sin(x)); > end; exact_soln_y2 := proc(x) return -sin(x) end proc > exact_soln_y2p := proc(x) > return( - cos(x)); > end; exact_soln_y2p := proc(x) return -cos(x) 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_2, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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 := 2; > 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/mtest5postode.ode#################"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 ;"); > omniout_str(ALWAYS,"diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;"); > 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 := 0.5;"); > omniout_str(ALWAYS,"x_end := 5.0;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);"); > omniout_str(ALWAYS,"glob_max_iter := 20;"); > 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_y1 := proc(x)"); > omniout_str(ALWAYS,"return( - cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return( - sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"return( - cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > 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_y1_init:= Array(0..(max_terms + 1),[]); > array_y2_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_y1:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_y2:= 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:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(2+ 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_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y2_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_y1[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_y2[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[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_y1_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_y1_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_y1_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 <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_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 <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_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 <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_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 <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_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 <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_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 <=2) 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 <=2) 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 <=2) 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_y1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y1[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_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_y2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y2[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 := 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_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_2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_2[1] := 2; > 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 := 0.5; > x_end := 5.0; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > array_y2_init[1 + 1] := exact_soln_y2p(x_start); > glob_max_iter := 20; > #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_y1_set_initial[1,1] := true; > array_y1_set_initial[1,2] := false; > array_y1_set_initial[1,3] := false; > array_y1_set_initial[1,4] := false; > array_y1_set_initial[1,5] := false; > array_y1_set_initial[1,6] := false; > array_y1_set_initial[1,7] := false; > array_y1_set_initial[1,8] := false; > array_y1_set_initial[1,9] := false; > array_y1_set_initial[1,10] := false; > array_y1_set_initial[1,11] := false; > array_y1_set_initial[1,12] := false; > array_y1_set_initial[1,13] := false; > array_y1_set_initial[1,14] := false; > array_y1_set_initial[1,15] := false; > array_y1_set_initial[1,16] := false; > array_y1_set_initial[1,17] := false; > array_y1_set_initial[1,18] := false; > array_y1_set_initial[1,19] := false; > array_y1_set_initial[1,20] := false; > array_y1_set_initial[1,21] := false; > array_y1_set_initial[1,22] := false; > array_y1_set_initial[1,23] := false; > array_y1_set_initial[1,24] := false; > array_y1_set_initial[1,25] := false; > array_y1_set_initial[1,26] := false; > array_y1_set_initial[1,27] := false; > array_y1_set_initial[1,28] := false; > array_y1_set_initial[1,29] := false; > array_y1_set_initial[1,30] := false; > array_y2_set_initial[2,1] := true; > array_y2_set_initial[2,2] := true; > array_y2_set_initial[2,3] := false; > array_y2_set_initial[2,4] := false; > array_y2_set_initial[2,5] := false; > array_y2_set_initial[2,6] := false; > array_y2_set_initial[2,7] := false; > array_y2_set_initial[2,8] := false; > array_y2_set_initial[2,9] := false; > array_y2_set_initial[2,10] := false; > array_y2_set_initial[2,11] := false; > array_y2_set_initial[2,12] := false; > array_y2_set_initial[2,13] := false; > array_y2_set_initial[2,14] := false; > array_y2_set_initial[2,15] := false; > array_y2_set_initial[2,16] := false; > array_y2_set_initial[2,17] := false; > array_y2_set_initial[2,18] := false; > array_y2_set_initial[2,19] := false; > array_y2_set_initial[2,20] := false; > array_y2_set_initial[2,21] := false; > array_y2_set_initial[2,22] := false; > array_y2_set_initial[2,23] := false; > array_y2_set_initial[2,24] := false; > array_y2_set_initial[2,25] := false; > array_y2_set_initial[2,26] := false; > array_y2_set_initial[2,27] := false; > array_y2_set_initial[2,28] := false; > array_y2_set_initial[2,29] := false; > array_y2_set_initial[2,30] := 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 3 > glob_h := glob_display_interval; > fi;# end if 3; > if (glob_max_h < glob_h) then # if number 3 > glob_h := glob_max_h; > fi;# end if 3; > 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_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 3 > array_y1[term_no] := array_y1_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_y1_higher[r_order,term_no] := array_y1_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 > ; > order_diff := 2; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 3 > array_y2[term_no] := array_y2_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_y2_higher[r_order,term_no] := array_y2_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 > ; > if (glob_subiter_method = 1 ) then # if number 3 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 4 > subiter := 1; > while (subiter <= 3) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > else > subiter := 1; > while (subiter <= 3 + glob_max_terms) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > fi;# end if 4; > 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 4 > best_h := glob_h; > found_h := 1.0; > fi;# end if 4; > 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 4 > glob_h := best_h ; > else > omniout_str(ALWAYS,"No increment to obtain desired accuracy found"); > fi;# end if 4; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 4 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 4; > #BEGIN SOLUTION CODE > if (found_h > 0.0) then # if number 4 > 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_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_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_y1_higher[r_order,term_no] := array_y1_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 > ; > order_diff := 2; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_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_y2_higher[r_order,term_no] := array_y2_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 5 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 5; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > if (glob_subiter_method = 1 ) then # if number 5 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 6 > subiter := 1; > while (subiter <= 3) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > else > subiter := 1; > while (subiter <= 3 + glob_max_terms) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > fi;# end if 6; > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y1; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[2,iii] := array_y1_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_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y1_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_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_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_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y1_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_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_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_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y1_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_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y1_higher[ord,term_no] := array_y1_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 > #Jump Series array_y2; > order_diff := 3; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #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_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y2_higher[ord,term_no] := array_y2_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 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * y2 ;"); > omniout_str(INFO,"diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-01-28T16:57:26-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest5") > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * y2 ;") > ; > 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 7 > 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 7; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 165 ") > ; > logitem_str(html_log_file,"mtest5 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest5 maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 7 > 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 7; > logditto(html_log_file) > ; > if (glob_percent_done < 100.0) then # if number 7 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 7; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #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_2, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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 := 2; 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/mtest5postode.ode#################"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 ;"); omniout_str(ALWAYS, "diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;"); 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 := 0.5;"); omniout_str(ALWAYS, "x_end := 5.0;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);") ; omniout_str(ALWAYS, "glob_max_iter := 20;"); 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_y1 := proc(x)"); omniout_str(ALWAYS, "return( - cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return( - sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "return( - cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); 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_y1_init := Array(0 .. max_terms + 1, []); array_y2_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_y1 := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_y2 := 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 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y2_higher := Array(0 .. 4, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []); array_y2_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []); array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); array_complex_pole := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2_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_y1[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_y2[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[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_y1_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_y1_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_y1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y2_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 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 <= 2 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 <= 2 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_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[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 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[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_2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2[term] := 0.; term := term + 1 end do; array_const_2[1] := 2; 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 := 0.5; x_end := 5.0; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); array_y2_init[2] := exact_soln_y2p(x_start); glob_max_iter := 20; 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_y1_set_initial[1, 1] := true; array_y1_set_initial[1, 2] := false; array_y1_set_initial[1, 3] := false; array_y1_set_initial[1, 4] := false; array_y1_set_initial[1, 5] := false; array_y1_set_initial[1, 6] := false; array_y1_set_initial[1, 7] := false; array_y1_set_initial[1, 8] := false; array_y1_set_initial[1, 9] := false; array_y1_set_initial[1, 10] := false; array_y1_set_initial[1, 11] := false; array_y1_set_initial[1, 12] := false; array_y1_set_initial[1, 13] := false; array_y1_set_initial[1, 14] := false; array_y1_set_initial[1, 15] := false; array_y1_set_initial[1, 16] := false; array_y1_set_initial[1, 17] := false; array_y1_set_initial[1, 18] := false; array_y1_set_initial[1, 19] := false; array_y1_set_initial[1, 20] := false; array_y1_set_initial[1, 21] := false; array_y1_set_initial[1, 22] := false; array_y1_set_initial[1, 23] := false; array_y1_set_initial[1, 24] := false; array_y1_set_initial[1, 25] := false; array_y1_set_initial[1, 26] := false; array_y1_set_initial[1, 27] := false; array_y1_set_initial[1, 28] := false; array_y1_set_initial[1, 29] := false; array_y1_set_initial[1, 30] := false; array_y2_set_initial[2, 1] := true; array_y2_set_initial[2, 2] := true; array_y2_set_initial[2, 3] := false; array_y2_set_initial[2, 4] := false; array_y2_set_initial[2, 5] := false; array_y2_set_initial[2, 6] := false; array_y2_set_initial[2, 7] := false; array_y2_set_initial[2, 8] := false; array_y2_set_initial[2, 9] := false; array_y2_set_initial[2, 10] := false; array_y2_set_initial[2, 11] := false; array_y2_set_initial[2, 12] := false; array_y2_set_initial[2, 13] := false; array_y2_set_initial[2, 14] := false; array_y2_set_initial[2, 15] := false; array_y2_set_initial[2, 16] := false; array_y2_set_initial[2, 17] := false; array_y2_set_initial[2, 18] := false; array_y2_set_initial[2, 19] := false; array_y2_set_initial[2, 20] := false; array_y2_set_initial[2, 21] := false; array_y2_set_initial[2, 22] := false; array_y2_set_initial[2, 23] := false; array_y2_set_initial[2, 24] := false; array_y2_set_initial[2, 25] := false; array_y2_set_initial[2, 26] := false; array_y2_set_initial[2, 27] := false; array_y2_set_initial[2, 28] := false; array_y2_set_initial[2, 29] := false; array_y2_set_initial[2, 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_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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; order_diff := 2; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 3 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 3 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; 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_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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; order_diff := 2; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 3 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 3 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; 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_y1_higher_work[2, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_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_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 3; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_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 := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_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 := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_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_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_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 ( y1 , x , 1 ) = m1 * y2 ;"); omniout_str(INFO, "diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;"); 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, "2013-01-28T16:57:26-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest5"); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 ;"); 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, "mtest5 diffeq.mxt"); logitem_str(html_log_file, "mtest5 maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_good_digits(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 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; logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); 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/mtest5postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 2 ) = diff ( y1, x , 1) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.5; x_end := 5.0; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); array_y2_init[1 + 1] := exact_soln_y2p(x_start); glob_max_iter := 20; #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_y1 := proc(x) return( - cos(x)); end; exact_soln_y2 := proc(x) return( - sin(x)); end; exact_soln_y2p := proc(x) return( - cos(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 memory used=3.8MB, alloc=3.1MB, time=0.18 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 4.5 estimated_steps = 4500 step_error = 2.2222222222222222222222222222222e-14 est_needed_step_err = 2.2222222222222222222222222222222e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 2.1760284259377227129349898378789e-105 max_value3 = 2.1760284259377227129349898378789e-105 value3 = 2.1760284259377227129349898378789e-105 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.5 y1[1] (analytic) = -0.87758256189037271611628158260383 y1[1] (numeric) = -0.87758256189037271611628158260383 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.47942553860420300027328793521557 y2[1] (numeric) = -0.47942553860420300027328793521557 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 memory used=7.6MB, alloc=4.3MB, time=0.41 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.501 y1[1] (analytic) = -0.87710269764042838630733124421144 y1[1] (numeric) = -0.87710269764042838630733124421144 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.4803028813070802939494724420977 y2[1] (numeric) = -0.4803028813070802939494724420977 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.3MB, time=0.63 x[1] = 0.502 y1[1] (analytic) = -0.87662195628785950795902823784783 y1[1] (numeric) = -0.87662195628785950795902823784783 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.48117974370711630578413774821874 y2[1] (numeric) = -0.48117974370711630578413774821874 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.3MB, time=0.86 x[1] = 0.503 y1[1] (analytic) = -0.87614033831340739357847286646878 y1[1] (numeric) = -0.87614033831340739357847286646878 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.48205612492744870881313625285219 y2[1] (numeric) = -0.48205612492744870881313625285219 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=1.09 x[1] = 0.504 y1[1] (analytic) = -0.87565784419868997748294964411447 y1[1] (numeric) = -0.87565784419868997748294964411447 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.48293202409169635573583085364091 y2[1] (numeric) = -0.48293202409169635573583085364091 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.4MB, time=1.31 x[1] = 0.505 y1[1] (analytic) = -0.87517447442620133418203311345153 y1[1] (numeric) = -0.87517447442620133418203311345152 absolute error = 1e-32 relative error = 1.1426293033233620870529366873743e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.48380744032396015529616921547434 y2[1] (numeric) = -0.48380744032396015529616921547434 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.506 y1[1] (analytic) = -0.87469022947931119588355354403665 y1[1] (numeric) = -0.87469022947931119588355354403665 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.48468237274882394818170203495237 y2[1] (numeric) = -0.48468237274882394818170203495237 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.4MB, time=1.54 x[1] = 0.507 y1[1] (analytic) = -0.87420510984226446912390500529606 y1[1] (numeric) = -0.87420510984226446912390500529606 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.48555682049135538243966940149045 y2[1] (numeric) = -0.48555682049135538243966940149045 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.4MB, time=1.77 x[1] = 0.508 y1[1] (analytic) = -0.87371911600018075052317918387225 y1[1] (numeric) = -0.87371911600018075052317918387225 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.48643078267710678840927983905261 y2[1] (numeric) = -0.48643078267710678840927983905261 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.4MB, time=2.00 x[1] = 0.509 y1[1] (analytic) = -0.87323224843905384166560919016402 y1[1] (numeric) = -0.87323224843905384166560919016402 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.48730425843211605316930709630622 y2[1] (numeric) = -0.48730425843211605316930709630621 absolute error = 1e-32 relative error = 2.0521060152797844996304253934296e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.4MB, time=2.22 x[1] = 0.51 y1[1] (analytic) = -0.87274450764575126310580847357551 y1[1] (numeric) = -0.8727445076457512631058084735755 absolute error = 1e-32 relative error = 1.1458107054692597333792993299734e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.48817724688290749450013023767457 y2[1] (numeric) = -0.48817724688290749450013023767457 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.4MB, time=2.45 x[1] = 0.511 y1[1] (analytic) = -0.87225589410801376750129084019472 y1[1] (numeric) = -0.87225589410801376750129084019471 absolute error = 1e-32 relative error = 1.1464525568183404445720642484331e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.48904974715649273435934307332011 y2[1] (numeric) = -0.4890497471564927343593430733201 absolute error = 1e-32 relative error = 2.0447817544418574498910821923363e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.512 y1[1] (analytic) = -0.87176640831445485187175844034113 y1[1] (numeric) = -0.87176640831445485187175844034112 absolute error = 1e-32 relative error = 1.1470962754041906265274784616296e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.48992175838037157187005945252148 y2[1] (numeric) = -0.48992175838037157187005945252147 absolute error = 1e-32 relative error = 2.0411422495418289100182919394413e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.4MB, time=2.68 x[1] = 0.513 y1[1] (analytic) = -0.87127605075456026898564546665356 y1[1] (numeric) = -0.87127605075456026898564546665356 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.49079327968253285582104143221207 y2[1] (numeric) = -0.49079327968253285582104143221207 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.4MB, time=2.91 x[1] = 0.514 y1[1] (analytic) = -0.87078482191868753787440617613407 y1[1] (numeric) = -0.87078482191868753787440617613407 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.49166431019145535667777782062445 y2[1] (numeric) = -0.49166431019145535667777782062444 absolute error = 1e-32 relative error = 2.0339080532621890090270796231821e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.4MB, time=3.14 x[1] = 0.515 y1[1] (analytic) = -0.87029272229806545347503672181887 y1[1] (numeric) = -0.87029272229806545347503672181887 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.4925348490361086381036410850348 y2[1] (numeric) = -0.4925348490361086381036410850348 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.4MB, time=3.37 x[1] = 0.516 y1[1] (analytic) = -0.86979975238479359540132115151374 y1[1] (numeric) = -0.86979975238479359540132115151374 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.49340489534595392799025110252325 y2[1] (numeric) = -0.49340489534595392799025110252324 absolute error = 1e-32 relative error = 2.0267330329157835904226077575619e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.517 y1[1] (analytic) = -0.86930591267184183584429280230693 y1[1] (numeric) = -0.86930591267184183584429280230693 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.49427444825094498899617472345866 y2[1] (numeric) = -0.49427444825094498899617472345865 absolute error = 1e-32 relative error = 2.0231675004415689598105062421035e-30 % Correct digits = 31 h = 0.001 memory used=61.0MB, alloc=4.4MB, time=3.60 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.518 y1[1] (analytic) = -0.86881120365304984660240319035711 y1[1] (numeric) = -0.86881120365304984660240319035712 absolute error = 1e-32 relative error = 1.1509980485925443354659107778665e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.49514350688152898859309060908113 y2[1] (numeric) = -0.49514350688152898859309060908113 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.4MB, time=3.83 x[1] = 0.519 y1[1] (analytic) = -0.8683156258231266052418913657465 y1[1] (numeric) = -0.8683156258231266052418913657465 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.49601207036864736861854929708972 y2[1] (numeric) = -0.49601207036864736861854929708972 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.4MB, time=4.06 x[1] = 0.52 y1[1] (analytic) = -0.86781917967764990038784757198851 y1[1] (numeric) = -0.86781917967764990038784757198852 absolute error = 1e-32 relative error = 1.1523137808171610842144187861275e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.49688013784373671433445894254775 y2[1] (numeric) = -0.49688013784373671433445894254775 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.4MB, time=4.29 x[1] = 0.521 y1[1] (analytic) = -0.86732186571306583614646591908526 y1[1] (numeric) = -0.86732186571306583614646591908527 absolute error = 1e-32 relative error = 1.1529745063879523774566849261671e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.49774770843872962299042767569256 y2[1] (numeric) = -0.49774770843872962299042767569256 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.4MB, time=4.52 x[1] = 0.522 y1[1] (analytic) = -0.8668236844266883356589816478407 y1[1] (numeric) = -0.86682368442668833565898164784071 absolute error = 1e-32 relative error = 1.1536371443996637347321571338613e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.49861478128605557189109401337953 y2[1] (numeric) = -0.49861478128605557189109401337952 absolute error = 1e-32 relative error = 2.0055562681490171362466380754140e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.523 y1[1] (analytic) = -0.86632463631669864378778943145095 y1[1] (numeric) = -0.86632463631669864378778943145095 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.49948135551864178596657725690241 y2[1] (numeric) = -0.4994813555186417859665772569024 absolute error = 1e-32 relative error = 2.0020767320967152978577767922169e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.4MB, time=4.75 x[1] = 0.524 y1[1] (analytic) = -0.86582472188214482893524002821195 y1[1] (numeric) = -0.86582472188214482893524002821195 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.50034743026991410484518030581186 y2[1] (numeric) = -0.50034743026991410484518030581186 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.4MB, time=4.98 x[1] = 0.525 y1[1] (analytic) = -0.86532394162294128399561346650638 y1[1] (numeric) = -0.86532394162294128399561346650638 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.5012130046737978494274778151016 y2[1] (numeric) = -0.50121300467379784942747781510159 absolute error = 1e-32 relative error = 1.9951597238599692612900207493465e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.4MB, time=5.21 x[1] = 0.526 y1[1] (analytic) = -0.86482229603986822644076781005499 y1[1] (numeric) = -0.86482229603986822644076781005498 absolute error = 1e-32 relative error = 1.1563069136620641590525037439531e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.50207807786471868796092312174618 y2[1] (numeric) = -0.50207807786471868796092312174617 absolute error = 1e-32 relative error = 1.9917220928125102843723291241161e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.4MB, time=5.44 x[1] = 0.527 y1[1] (analytic) = -0.86431978563457119753996341774188 y1[1] (numeric) = -0.86431978563457119753996341774188 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.50294264897760350161410786605581 y2[1] (numeric) = -0.5029426489776035016141078660558 absolute error = 1e-32 relative error = 1.9882982722440206478591663980072e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.4MB, time=5.67 x[1] = 0.528 y1[1] (analytic) = -0.86381641090956056071436347814793 y1[1] (numeric) = -0.86381641090956056071436347814793 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.50380671714788124954980873366049 y2[1] (numeric) = -0.50380671714788124954980873366048 absolute error = 1e-32 relative error = 1.9848881842249678761233363914590e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.529 y1[1] (analytic) = -0.86331217236821099902671246424977 y1[1] (numeric) = -0.86331217236821099902671246424977 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.50467028151148383349595624514904 y2[1] (numeric) = -0.50467028151148383349595624514903 absolute error = 1e-32 relative error = 1.9814917514164044919160219830145e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.4MB, time=5.90 x[1] = 0.53 y1[1] (analytic) = -0.8628070705147610118066950185642 y1[1] (numeric) = -0.8628070705147610118066950185642 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.50553334120484696181366102246608 y2[1] (numeric) = -0.50553334120484696181366102246607 absolute error = 1e-32 relative error = 1.9781088970643983742702067676338e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.4MB, time=6.13 x[1] = 0.531 y1[1] (analytic) = -0.86230110585431241041247864333708 y1[1] (numeric) = -0.86230110585431241041247864333707 absolute error = 1e-32 relative error = 1.1596877160551294805208445428365e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.50639589536491101306143346411287 y2[1] (numeric) = -0.50639589536491101306143346411286 absolute error = 1e-32 relative error = 1.9747395449945260557524332352078e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.4MB, time=6.36 x[1] = 0.532 y1[1] (analytic) = -0.86179427889282981312894443419202 y1[1] (numeric) = -0.86179427889282981312894443419201 absolute error = 1e-32 relative error = 1.1603697361332298209198435369779e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.50725794312912189905473326500416 y2[1] (numeric) = -0.50725794312912189905473326500415 absolute error = 1e-32 relative error = 1.9713836196064281309263285504649e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.4MB, time=6.58 x[1] = 0.533 y1[1] (analytic) = -0.86128659013714013920311095896611 y1[1] (numeric) = -0.8612865901371401392031109589661 absolute error = 1e-32 relative error = 1.1610537206213473393701607787774e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.50811948363543192741998572150358 y2[1] (numeric) = -0.50811948363543192741998572150357 absolute error = 1e-32 relative error = 1.9680410458684259603211899768436e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.534 y1[1] (analytic) = -0.86077804009493210201725724626652 y1[1] (numeric) = -0.86077804009493210201725724626651 absolute error = 1e-32 relative error = 1.1617396743645012257930441125052e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.508980516022300663642202267693 y2[1] (numeric) = -0.50898051602230066364220226769299 absolute error = 1e-32 relative error = 1.9647117493121988664192910490892e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=114.4MB, alloc=4.4MB, time=6.82 TOP MAIN SOLVE Loop x[1] = 0.535 y1[1] (analytic) = -0.86026862927475570140025171058284 y1[1] (numeric) = -0.86026862927475570140025171058283 absolute error = 1e-32 relative error = 1.1624276022282063116156899598612e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.50984103942869579260534319532731 y2[1] (numeric) = -0.5098410394286957926053431953273 absolute error = 1e-32 relative error = 1.9613956560275210301903624993301e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.4MB, time=7.05 x[1] = 0.536 y1[1] (analytic) = -0.85975835818602171507759470258392 y1[1] (numeric) = -0.85975835818602171507759470258391 absolute error = 1e-32 relative error = 1.1631175090985680026627953047615e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.51070105299409397962456101718358 y2[1] (numeric) = -0.51070105299409397962456101718356 absolute error = 2e-32 relative error = 3.9161853853141146170295081118490e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.4MB, time=7.27 x[1] = 0.537 y1[1] (analytic) = -0.85924722733900118926068323451424 y1[1] (numeric) = -0.85924722733900118926068323451423 absolute error = 1e-32 relative error = 1.1638093998823777750371627040419e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.51156055585848173096946344163303 y2[1] (numeric) = -0.51156055585848173096946344163301 absolute error = 2e-32 relative error = 3.9096055727824344089037027513106e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.4MB, time=7.51 x[1] = 0.538 y1[1] (analytic) = -0.85873523724482492837580729138267 y1[1] (numeric) = -0.85873523724482492837580729138265 absolute error = 2e-32 relative error = 2.3290065590144184755312534114755e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.51241954716235625387753543524462 y2[1] (numeric) = -0.51241954716235625387753543524459 absolute error = 3e-32 relative error = 5.8545775948891987011932596138791e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.4MB, time=7.73 x[1] = 0.539 y1[1] (analytic) = -0.85822238841548298393338799890475 y1[1] (numeric) = -0.85822238841548298393338799890473 absolute error = 2e-32 relative error = 2.3303983058430295320320004853246e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.51327802604672631605686036006966 y2[1] (numeric) = -0.51327802604672631605686036006964 absolute error = 2e-32 relative error = 3.8965237132865878841458912457051e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.54 y1[1] (analytic) = -0.8577086813638241425379687789178 y1[1] (numeric) = -0.85770868136382414253796877891778 absolute error = 2e-32 relative error = 2.3317940501894454174408521413526e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.51413599165311310467728068295824 y2[1] (numeric) = -0.51413599165311310467728068295822 absolute error = 2e-32 relative error = 3.8900213804704756779805487539004e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.4MB, time=7.96 x[1] = 0.541 y1[1] (analytic) = -0.85719411660355541303947148223492 y1[1] (numeric) = -0.85719411660355541303947148223491 absolute error = 1e-32 relative error = 1.1665969010173351744704636303864e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.514993443123551084849139265818 y2[1] (numeric) = -0.51499344312355108484913926581797 absolute error = 3e-32 relative error = 5.8253168852098875737381175155704e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.4MB, time=8.19 x[1] = 0.542 y1[1] (analytic) = -0.85667869464924151282623034763916 y1[1] (numeric) = -0.85667869464924151282623034763915 absolute error = 1e-32 relative error = 1.1672987857010263995794483466827e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.51585037960058885758874275814576 y2[1] (numeric) = -0.51585037960058885758874275814573 absolute error = 3e-32 relative error = 5.8156398030041798894677144667936e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.4MB, time=8.42 x[1] = 0.543 y1[1] (analytic) = -0.85616241601630435326031749394093 y1[1] (numeric) = -0.85616241601630435326031749394091 absolute error = 2e-32 relative error = 2.3360053683574834044762617763151e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.51670680022729001726968912644003 y2[1] (numeric) = -0.51670680022729001726968912644001 absolute error = 2e-32 relative error = 3.8706670768030070695183949482276e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.4MB, time=8.66 x[1] = 0.544 y1[1] (analytic) = -0.85564528122102252425567450973039 y1[1] (numeric) = -0.85564528122102252425567450973037 absolute error = 2e-32 relative error = 2.3374172030095940534406817217967e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.51756270414723400855920186923829 y2[1] (numeric) = -0.51756270414723400855920186923826 absolute error = 3e-32 relative error = 5.7963991144666655176298499935634e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.4MB, time=8.88 x[1] = 0.545 y1[1] (analytic) = -0.85512729078053077799956556265031 y1[1] (numeric) = -0.85512729078053077799956556265029 absolute error = 2e-32 relative error = 2.3388330855099581632528508177254e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.5184180905045169828386139815162 y2[1] (numeric) = -0.51841809050451698283861398151618 absolute error = 2e-32 relative error = 3.8578900633147831417946008540503e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.546 y1[1] (analytic) = -0.85460844521281951181786830669308 y1[1] (numeric) = -0.85460844521281951181786830669306 absolute error = 2e-32 relative error = 2.3402530260532921523669817287396e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.51927295844375265410714524803636 y2[1] (numeric) = -0.51927295844375265410714524803633 absolute error = 3e-32 relative error = 5.7773083524143463773839641211561e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.4MB, time=9.11 x[1] = 0.547 y1[1] (analytic) = -0.8540887450367342501847197221881 y1[1] (numeric) = -0.85408874503673425018471972218808 absolute error = 2e-32 relative error = 2.3416770348776581173060551874706e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.52012730711007315436811696194029 y2[1] (numeric) = -0.52012730711007315436811696194027 absolute error = 2e-32 relative error = 3.8452124559896358907255885699583e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.4MB, time=9.35 x[1] = 0.548 y1[1] (analytic) = -0.8535681907719751258770348787904 y1[1] (numeric) = -0.85356819077197512587703487879038 absolute error = 2e-32 relative error = 2.3431051222646677218566543997354e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.52098113564912988849674868244063 y2[1] (numeric) = -0.5209811356491298884967486824406 absolute error = 3e-32 relative error = 5.7583658883580738349895190725948e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.4MB, time=9.57 x[1] = 0.549 y1[1] (analytic) = -0.85304678293909636027441746690851 y1[1] (numeric) = -0.85304678293909636027441746690849 absolute error = 2e-32 relative error = 2.3445372985396873068724199794709e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.52183444320709438858868216388758 y2[1] (numeric) = -0.52183444320709438858868216388756 absolute error = 2e-32 relative error = 3.8326331771210494350205585667746e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.4MB, time=9.81 x[1] = 0.55 y1[1] (analytic) = -0.85252452205950574280498179761777 y1[1] (numeric) = -0.85252452205950574280498179761775 absolute error = 2e-32 relative error = 2.3459735740720442289799436665089e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.52268722893065916778837810775729 y2[1] (numeric) = -0.52268722893065916778837810775727 absolute error = 2e-32 relative error = 3.8263800783724990896847033647784e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.551 y1[1] (analytic) = -0.8520014086554641095376068251937 y1[1] (numeric) = -0.85200140865546410953760682519368 absolute error = 2e-32 relative error = 2.3474139592752344365462720082990e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.52353949196703857359653190923621 y2[1] (numeric) = -0.52353949196703857359653190923619 absolute error = 2e-32 relative error = 3.8201511646917318540415083513243e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=167.8MB, alloc=4.4MB, time=10.04 TOP MAIN SOLVE Loop x[1] = 0.552 y1[1] (analytic) = -0.85147744325008482092114359996793 y1[1] (numeric) = -0.85147744325008482092114359996791 absolute error = 2e-32 relative error = 2.3488584646071312913331202108982e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.52439123146396964065565509105708 y2[1] (numeric) = -0.52439123146396964065565509105706 absolute error = 2e-32 relative error = 3.8139463057315020262987421233741e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.4MB, time=10.27 x[1] = 0.553 y1[1] (analytic) = -0.85095262636733323867109841225574 y1[1] (numeric) = -0.85095262636733323867109841225571 absolute error = 3e-32 relative error = 3.5254606508552934664941107265041e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.52524244656971294301296963907598 y2[1] (numeric) = -0.52524244656971294301296963907595 absolute error = 3e-32 relative error = 5.7116480581350429842175618003783e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.4MB, time=10.49 x[1] = 0.554 y1[1] (analytic) = -0.85042695853202620180431474062843 y1[1] (numeric) = -0.8504269585320262018043147406284 absolute error = 3e-32 relative error = 3.5276398165675307614812312251812e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.52609313643305344585976297676717 y2[1] (numeric) = -0.52609313643305344585976297676715 absolute error = 2e-32 relative error = 3.8016082353024663942648632049072e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.4MB, time=10.73 x[1] = 0.555 y1[1] (analytic) = -0.84990044026983150182217796980501 y1[1] (numeric) = -0.84990044026983150182217796980499 absolute error = 2e-32 relative error = 2.3532168066238769978228150001394e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.52694330020330135674635183935189 y2[1] (numeric) = -0.52694330020330135674635183935186 absolute error = 3e-32 relative error = 5.6932121517487028401436579231192e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.4MB, time=10.96 x[1] = 0.556 y1[1] (analytic) = -0.84937307210726735704286769491463 y1[1] (numeric) = -0.84937307210726735704286769491461 absolute error = 2e-32 relative error = 2.3546778979442615590717287485309e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.52779293703029297627180383266784 y2[1] (numeric) = -0.52779293703029297627180383266781 absolute error = 3e-32 relative error = 5.6840472645957619002502663340334e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.557 y1[1] (analytic) = -0.8488448545717018860831832798337 y1[1] (numeric) = -0.84884485457170188608318327983368 absolute error = 2e-32 relative error = 2.3561431623557778088376158167628e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.52864204606439154824756598712908 y2[1] (numeric) = -0.52864204606439154824756598712905 absolute error = 3e-32 relative error = 5.6749175029384311890480677232296e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.4MB, time=11.19 x[1] = 0.558 y1[1] (analytic) = -0.84831578819135258049046918772829 y1[1] (numeric) = -0.84831578819135258049046918772827 absolute error = 2e-32 relative error = 2.3576126105870196808918781168057e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.52949062645648810933415014321829 y2[1] (numeric) = -0.52949062645648810933415014321826 absolute error = 3e-32 relative error = 5.6658226795758596058277856398849e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.4MB, time=11.42 x[1] = 0.559 y1[1] (analytic) = -0.8477858734952857765251674518325 y1[1] (numeric) = -0.84778587349528577652516745183248 absolute error = 2e-32 relative error = 2.3590862534124558750329209926701e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.53033867735800233815002553189701 y2[1] (numeric) = -0.53033867735800233815002553189699 absolute error = 2e-32 relative error = 3.7711750724337808507517443596380e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.4MB, time=11.65 x[1] = 0.56 y1[1] (analytic) = -0.84725511101341612609452550386632 y1[1] (numeric) = -0.8472551110134161260945255038663 absolute error = 2e-32 relative error = 2.3605641016526489556437951570644e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.53118619792088340385186944111203 y2[1] (numeric) = -0.53118619792088340385186944111201 absolute error = 2e-32 relative error = 3.7651580704246507747019089774180e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.4MB, time=11.88 x[1] = 0.561 y1[1] (analytic) = -0.84672350127650606683798842634102 y1[1] (numeric) = -0.846723501276506066837988426341 absolute error = 2e-32 relative error = 2.3620461661744757748271664945235e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.53203318729761081418532738821783 y2[1] (numeric) = -0.53203318729761081418532738821781 absolute error = 2e-32 relative error = 3.7591639915523392788238661871071e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.4MB, time=12.12 x[1] = 0.562 y1[1] (analytic) = -0.84619104481616529136480554331576 y1[1] (numeric) = -0.84619104481616529136480554331574 absolute error = 2e-32 relative error = 2.3635324578913492292349669059997e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.53287964464119526300543474762577 y2[1] (numeric) = -0.53287964464119526300543474762575 absolute error = 2e-32 relative error = 3.7531927145512629307401755112782e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.563 y1[1] (analytic) = -0.8456577421648502156443821119545 y1[1] (numeric) = -0.84565774216485021564438211195448 absolute error = 2e-32 relative error = 2.3650229877634413597827332550146e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.53372556910517947726585231332886 y2[1] (numeric) = -0.53372556910517947726585231332884 absolute error = 2e-32 relative error = 3.7472441190200254812486498088424e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.4MB, time=12.35 x[1] = 0.564 y1[1] (analytic) = -0.84512359385586344654990772448725 y1[1] (numeric) = -0.84512359385586344654990772448723 absolute error = 2e-32 relative error = 2.3665177667979078035119436567398e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.53457095984363906347606880713726 y2[1] (numeric) = -0.53457095984363906347606880713724 absolute error = 2e-32 relative error = 3.7413180854137605972258889664189e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.4MB, time=12.58 x[1] = 0.565 y1[1] (analytic) = -0.84458860042335324855579387690292 y1[1] (numeric) = -0.8445886004233532485557938769029 absolute error = 2e-32 relative error = 2.3680168060491136069376172799120e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.53541581601118335362572387549242 y2[1] (numeric) = -0.5354158160111833536257238754924 absolute error = 2e-32 relative error = 3.7354144950365559219179872206392e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.4MB, time=12.81 x[1] = 0.566 y1[1] (analytic) = -0.84405276240231300958945400689171 y1[1] (numeric) = -0.84405276240231300958945400689168 absolute error = 3e-32 relative error = 3.5542801749282906154395930435315e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.53626013676295625057520565060748 y2[1] (numeric) = -0.53626013676295625057520565060746 absolute error = 2e-32 relative error = 3.7295332300339574568296008078323e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.4MB, time=13.04 x[1] = 0.567 y1[1] (analytic) = -0.84351608032858070603796014921248 y1[1] (numeric) = -0.84351608032858070603796014921245 absolute error = 3e-32 relative error = 3.5565415644849225182384108008157e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.5371039212546370729116774854067 y2[1] (numeric) = -0.53710392125463707291167748540668 absolute error = 2e-32 relative error = 3.7236741733855532736136783489260e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.568 y1[1] (analytic) = -0.84297855473883836691011120178398 y1[1] (numeric) = -0.84297855473883836691011120178395 absolute error = 3e-32 relative error = 3.5588093945396089860596781913816e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.53794716864244139926968900630767 y2[1] (numeric) = -0.53794716864244139926968900630765 absolute error = 2e-32 relative error = 3.7178372088976355783304131620300e-30 % Correct digits = 31 h = 0.001 memory used=221.2MB, alloc=4.4MB, time=13.27 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.569 y1[1] (analytic) = -0.84244018617061153715444864038683 y1[1] (numeric) = -0.84244018617061153715444864038681 absolute error = 2e-32 relative error = 2.3740557879737217245277370140947e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.53878987808312191211552716330558 y2[1] (numeric) = -0.53878987808312191211552716330556 absolute error = 2e-32 relative error = 3.7120222211959401641893263807249e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.4MB, time=13.50 x[1] = 0.57 y1[1] (analytic) = -0.84190097516226874013375636391601 y1[1] (numeric) = -0.84190097516226874013375636391599 absolute error = 2e-32 relative error = 2.3755762957924098227706054253769e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.53963204873396924099446349307883 y2[1] (numeric) = -0.53963204873396924099446349307881 absolute error = 2e-32 relative error = 3.7062290957184623024167079069551e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.4MB, time=13.73 x[1] = 0.571 y1[1] (analytic) = -0.84136092225302093925658219563904 y1[1] (numeric) = -0.84136092225302093925658219563902 absolute error = 2e-32 relative error = 2.3771011311582446410393861337951e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.54047367975281280524005434793895 y2[1] (numeric) = -0.54047367975281280524005434793893 absolute error = 2e-32 relative error = 3.7004577187083481342057297473535e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.4MB, time=13.96 x[1] = 0.572 y1[1] (analytic) = -0.84082002798292099876631940889362 y1[1] (numeric) = -0.8408200279829209987663194088936 absolute error = 2e-32 relative error = 2.3786303054624962262690821802296e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.54131477029802165614465138139488 y2[1] (numeric) = -0.54131477029802165614465138139486 absolute error = 2e-32 relative error = 3.6947079772068606398121309802951e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.4MB, time=14.20 x[1] = 0.573 y1[1] (analytic) = -0.84027829289286314368838748809822 y1[1] (numeric) = -0.8402782928928631436883874880982 absolute error = 2e-32 relative error = 2.3801638301455007005261241437895e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.54215531952850531859028011989125 y2[1] (numeric) = -0.54215531952850531859028011989122 absolute error = 3e-32 relative error = 5.5334696385696289106371675858671e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.574 y1[1] (analytic) = -0.83973571752458241893605217784984 y1[1] (numeric) = -0.83973571752458241893605217784982 absolute error = 2e-32 relative error = 2.3817017166968987604358298317404e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.54299532660371463213904498991224 y2[1] (numeric) = -0.54299532660371463213904498991221 absolute error = 3e-32 relative error = 5.5249094292655685517068268018154e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.4MB, time=14.43 x[1] = 0.575 y1[1] (analytic) = -0.83919230242065414757542571424383 y1[1] (numeric) = -0.83919230242065414757542571424381 absolute error = 2e-32 relative error = 2.3832439766558756356842211053178e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.54383479068364259158221971011618 y2[1] (numeric) = -0.54383479068364259158221971011615 absolute error = 3e-32 relative error = 5.5163811719893221237755998510549e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.4MB, time=14.66 x[1] = 0.576 y1[1] (analytic) = -0.83864804812449338825018897337042 y1[1] (numeric) = -0.8386480481244933882501889733704 absolute error = 2e-32 relative error = 2.3847906216114025167901209542059e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.54467371092882518694718249948034 y2[1] (numeric) = -0.54467371092882518694718249948031 absolute error = 3e-32 relative error = 5.5078847019881645508323074605453e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.4MB, time=14.89 x[1] = 0.577 y1[1] (analytic) = -0.83810295518035439176657811222054 y1[1] (numeric) = -0.83810295518035439176657811222051 absolute error = 3e-32 relative error = 3.5795124948037191936386963691827e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.54551208650034224296135609459091 y2[1] (numeric) = -0.54551208650034224296135609459088 absolute error = 3e-32 relative error = 5.4994198556554216003843940170005e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.4MB, time=15.12 x[1] = 0.578 y1[1] (analytic) = -0.83755702413333005683917911696904 y1[1] (numeric) = -0.83755702413333005683917911696901 absolute error = 3e-32 relative error = 3.5818456696775696949712668691394e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.54634991655981825797231311220796 y2[1] (numeric) = -0.54634991655981825797231311220793 absolute error = 3e-32 relative error = 5.4909864705205619900262581166744e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.4MB, time=15.36 x[1] = 0.579 y1[1] (analytic) = -0.83701025552935138499807451279544 y1[1] (numeric) = -0.83701025552935138499807451279541 absolute error = 3e-32 relative error = 3.5841854746483440097217423145760e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.54718720026942324232320783707006 y2[1] (numeric) = -0.54718720026942324232320783707003 absolute error = 3e-32 relative error = 5.4825843852393921835492712020519e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.58 y1[1] (analytic) = -0.83646264991518693465788732805002 y1[1] (numeric) = -0.83646264991518693465788732804999 absolute error = 3e-32 relative error = 3.5865319274018807255892525647368e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.54802393679187355618269605957646 y2[1] (numeric) = -0.54802393679187355618269605957643 absolute error = 3e-32 relative error = 5.4742134395843526372782926957189e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.4MB, time=15.58 x[1] = 0.581 y1[1] (analytic) = -0.83591420783844227434926824367577 y1[1] (numeric) = -0.83591420783844227434926824367574 absolute error = 3e-32 relative error = 3.5888850457005416823891358172835e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.54886012529043274682850513349703 y2[1] (numeric) = -0.548860125290432746828505133497 absolute error = 3e-32 relative error = 5.4658734744349142743842118543434e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.4MB, time=15.82 x[1] = 0.582 y1[1] (analytic) = -0.83536492984755943511337269635362 y1[1] (numeric) = -0.83536492984755943511337269635358 absolute error = 4e-32 relative error = 4.7883264631781168870812644142852e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.54969576492891238538381697020945 y2[1] (numeric) = -0.54969576492891238538381697020942 absolute error = 3e-32 relative error = 5.4575643317680739817228813941505e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.4MB, time=16.06 x[1] = 0.583 y1[1] (analytic) = -0.83481481649181636205987554084799 y1[1] (numeric) = -0.83481481649181636205987554084796 absolute error = 3e-32 relative error = 3.5936113503675564126609267307189e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.55053085487167290300562723315059 y2[1] (numeric) = -0.55053085487167290300562723315056 absolute error = 3e-32 relative error = 5.4492858546489479402922821487880e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.4MB, time=16.29 x[1] = 0.584 y1[1] (analytic) = -0.8342638683213263650890717134926 y1[1] (numeric) = -0.83426386832132636508907171349257 absolute error = 3e-32 relative error = 3.5959845726466429544028572054019e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.55136539428362442652424454419241 y2[1] (numeric) = -0.55136539428362442652424454419238 absolute error = 3e-32 relative error = 5.4410378872214616166863127194491e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.585 y1[1] (analytic) = -0.83371208588703756877861217466974 y1[1] (numeric) = -0.83371208588703756877861217466971 absolute error = 3e-32 relative error = 3.5983645322930822979440874741124e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.5521993823302276135330940625129 y2[1] (numeric) = -0.55219938233022761353309406251287 absolute error = 3e-32 relative error = 5.4328202746991352589595908659091e-30 % Correct digits = 31 h = 0.001 memory used=274.6MB, alloc=4.4MB, time=16.52 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.586 y1[1] (analytic) = -0.83315946974073236143542524350155 y1[1] (numeric) = -0.83315946974073236143542524350152 absolute error = 3e-32 relative error = 3.6007512474575344777474133830513e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.55303281817749448692799034622804 y2[1] (numeric) = -0.55303281817749448692799034622801 absolute error = 3e-32 relative error = 5.4246328633559637561073600681857e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.4MB, time=16.75 x[1] = 0.587 y1[1] (analytic) = -0.83260602043502684331337427278583 y1[1] (numeric) = -0.83260602043502684331337427278581 absolute error = 2e-32 relative error = 2.4020964909129813236565264157596e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.55386570099198926889504495758147 y2[1] (numeric) = -0.55386570099198926889504495758143 absolute error = 4e-32 relative error = 7.2219673340231863145496145846669e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.4MB, time=16.98 x[1] = 0.588 y1[1] (analytic) = -0.83205173852337027399720344647288 y1[1] (numeric) = -0.83205173852337027399720344647286 absolute error = 2e-32 relative error = 2.4036966782250463983901800337751e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.55469802994082921434637482385373 y2[1] (numeric) = -0.55469802994082921434637482385369 absolute error = 4e-32 relative error = 7.2111307127351583882919602243041e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.4MB, time=17.21 x[1] = 0.589 y1[1] (analytic) = -0.83149662456004451895332431569136 y1[1] (numeric) = -0.83149662456004451895332431569134 absolute error = 2e-32 relative error = 2.4053014058333977447781917331944e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.55552980419168544380277791835226 y2[1] (numeric) = -0.55552980419168544380277791835222 absolute error = 4e-32 relative error = 7.2003337531460343196997596657173e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.4MB, time=17.45 x[1] = 0.59 y1[1] (analytic) = -0.83094067910016349524799652249068 y1[1] (numeric) = -0.83094067910016349524799652249066 absolute error = 2e-32 relative error = 2.4069106860502076983229003419316e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.55636102291278377572254337887577 y2[1] (numeric) = -0.55636102291278377572254337887573 absolute error = 4e-32 relative error = 7.1895762558245344501566017081622e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.591 y1[1] (analytic) = -0.83038390269967261643345699307291 y1[1] (numeric) = -0.83038390269967261643345699307289 absolute error = 2e-32 relative error = 2.4085245312412394761023154415858e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.55719168527290555827556373491228 y2[1] (numeric) = -0.55719168527290555827556373491223 absolute error = 5e-32 relative error = 8.9735725283679748010228757203611e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.4MB, time=17.68 x[1] = 0.592 y1[1] (analytic) = -0.82982629591534823660255271433876 y1[1] (numeric) = -0.82982629591534823660255271433874 absolute error = 2e-32 relative error = 2.4101429538261135690514595166700e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.55802179044138850056191746952789 y2[1] (numeric) = -0.55802179044138850056191746952785 absolute error = 4e-32 relative error = 7.1681788570228561908649519147573e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.4MB, time=17.91 x[1] = 0.593 y1[1] (analytic) = -0.82926785930479709361243303906856 y1[1] (numeric) = -0.82926785930479709361243303906855 absolute error = 1e-32 relative error = 1.2058829831392878950376086568880e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.55885133758812750327409069743309 y2[1] (numeric) = -0.55885133758812750327409069743305 absolute error = 4e-32 relative error = 7.1575385634094934895251985247763e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.4MB, time=18.15 x[1] = 0.594 y1[1] (analytic) = -0.82870859342645575147785829599953 y1[1] (numeric) = -0.82870859342645575147785829599952 absolute error = 1e-32 relative error = 1.2066967905633834948956206931193e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.55968032588357548880200729707396 y2[1] (numeric) = -0.55968032588357548880200729707392 absolute error = 4e-32 relative error = 7.1469369477748600380631603297717e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.4MB, time=18.38 x[1] = 0.595 y1[1] (analytic) = -0.82814849883959004193468231144419 y1[1] (numeric) = -0.82814849883959004193468231144418 absolute error = 1e-32 relative error = 1.2075129054767472258992223861655e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.56050875449874423078003739178746 y2[1] (numeric) = -0.56050875449874423078003739178742 absolute error = 4e-32 relative error = 7.1363738173494694962556102663044e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.4MB, time=18.61 x[1] = 0.596 y1[1] (analytic) = -0.827587576104294505174067278921 y1[1] (numeric) = -0.82758757610429450517406727892099 absolute error = 1e-32 relative error = 1.2083313341982524897322440439095e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.56133662260520518307515463308144 y2[1] (numeric) = -0.5613366226052051830751546330814 absolute error = 4e-32 relative error = 7.1258489806627996259472027206356e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.597 y1[1] (analytic) = -0.82702582578149182974799024253562 y1[1] (numeric) = -0.8270258257814918297479902425356 absolute error = 2e-32 relative error = 2.4183041661487596863244481959077e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.56216392937509030821541329795109 y2[1] (numeric) = -0.56216392937509030821541329795105 absolute error = 4e-32 relative error = 7.1153622475324214220595220028005e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.4MB, time=18.84 x[1] = 0.598 y1[1] (analytic) = -0.82646324843293229164660128855966 y1[1] (numeric) = -0.82646324843293229164660128855964 absolute error = 2e-32 relative error = 2.4199503169587105022825483422406e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.56299067398109290525791677182386 y2[1] (numeric) = -0.56299067398109290525791677182382 absolute error = 4e-32 relative error = 7.1049134290532373389499680819147e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.4MB, time=19.08 x[1] = 0.599 y1[1] (analytic) = -0.82589984462119319254799436780206 y1[1] (numeric) = -0.82589984462119319254799436780204 absolute error = 2e-32 relative error = 2.4216011336305784079094446077796e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.56381685559646843709544954923328 y2[1] (numeric) = -0.56381685559646843709544954923324 absolute error = 4e-32 relative error = 7.0945023375868273372735047024986e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.4MB, time=19.31 x[1] = 0.6 y1[1] (analytic) = -0.82533561490967829724095249895538 y1[1] (numeric) = -0.82533561490967829724095249895536 absolute error = 2e-32 relative error = 2.4232566290246334092291102427448e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.56464247339503535720094544565866 y2[1] (numeric) = -0.56464247339503535720094544565862 absolute error = 4e-32 relative error = 7.0841287867509014934984484284217e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.4MB, time=19.54 x[1] = 0.601 y1[1] (analytic) = -0.82477055986261727022122993012494 y1[1] (numeric) = -0.82477055986261727022122993012492 absolute error = 2e-32 relative error = 2.4249168160574762654918475127050e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.56546752655117593580896527613138 y2[1] (numeric) = -0.56546752655117593580896527613134 absolute error = 4e-32 relative error = 7.0737925914088579309710831840230e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.602 y1[1] (analytic) = -0.82420468004506511146193466221171 y1[1] (numeric) = -0.82420468004506511146193466221169 absolute error = 2e-32 relative error = 2.4265817077023219825333958349069e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.56629201423983708553335781919889 y2[1] (numeric) = -0.56629201423983708553335781919884 absolute error = 5e-32 relative error = 8.8293669595743060598964648073446e-30 % Correct digits = 31 h = 0.001 memory used=328.0MB, alloc=4.4MB, time=19.77 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.603 y1[1] (analytic) = -0.82363797602290159135857556371942 y1[1] (numeric) = -0.8236379760229015913585755637194 absolute error = 2e-32 relative error = 2.4282513169892850844245050410015e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.56711593563653118642027844865423 y2[1] (numeric) = -0.56711593563653118642027844865419 absolute error = 4e-32 relative error = 7.0532315328265254340155556140589e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.4MB, time=20.00 x[1] = 0.604 y1[1] (analytic) = -0.82307044836283068484933913189164 y1[1] (numeric) = -0.82307044836283068484933913189162 absolute error = 2e-32 relative error = 2.4299256570056666762207135152888e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.56793928991733691043574038008136 y2[1] (numeric) = -0.56793928991733691043574038008132 absolute error = 4e-32 relative error = 7.0430063054489444831840588872918e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=335.6MB, alloc=4.4MB, time=20.23 x[1] = 0.605 y1[1] (analytic) = -0.82250209763238000471116177985496 y1[1] (numeric) = -0.82250209763238000471116177985493 absolute error = 3e-32 relative error = 3.6474071113443649660926341738015e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.5687620762589000453868740447335 y2[1] (numeric) = -0.56876207625890004538687404473345 absolute error = 5e-32 relative error = 8.7910221315881194074810671352648e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.4MB, time=20.46 x[1] = 0.606 y1[1] (analytic) = -0.8219329243999002340321643536487 y1[1] (numeric) = -0.82193292439990023403216435364867 absolute error = 3e-32 relative error = 3.6499328727953365084660545419897e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.56958429383843431827607066955397 y2[1] (numeric) = -0.56958429383843431827607066955392 absolute error = 5e-32 relative error = 8.7783319415374841507365155309403e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.4MB, time=20.70 x[1] = 0.607 y1[1] (analytic) = -0.82136292923456455786101640665948 y1[1] (numeric) = -0.82136292923456455786101640665945 absolute error = 3e-32 relative error = 3.6524657897523166362969124684516e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.57040594183372221808718670926455 y2[1] (numeric) = -0.5704059418337222180871867092645 absolute error = 5e-32 relative error = 8.7656870893142606956800596542302e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.608 y1[1] (analytic) = -0.82079211270636809403379858204876 y1[1] (numeric) = -0.82079211270636809403379858204873 absolute error = 3e-32 relative error = 3.6550058821937368488167044509387e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.57122701942311581800298634438536 y2[1] (numeric) = -0.57122701942311581800298634438531 absolute error = 5e-32 relative error = 8.7530873540427370508232419105997e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.4MB, time=20.92 x[1] = 0.609 y1[1] (analytic) = -0.82022047538612732317893227626382 y1[1] (numeric) = -0.8202204753861273231789322762638 absolute error = 2e-32 relative error = 2.4383687801240016472493456831857e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.57204752578553759705299982781237 y2[1] (numeric) = -0.57204752578553759705299982781232 absolute error = 5e-32 relative error = 8.7405325163044505614784223866337e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.4MB, time=21.16 x[1] = 0.61 y1[1] (analytic) = -0.81964801784547951790074657865482 y1[1] (numeric) = -0.8196480178454795179007465786548 absolute error = 2e-32 relative error = 2.4400717825892931863375557676783e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.57286746010048126119097603216272 y2[1] (numeric) = -0.57286746010048126119097603216267 absolute error = 5e-32 relative error = 8.7280223581262536813531656245745e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.4MB, time=21.39 x[1] = 0.611 y1[1] (analytic) = -0.81907474065688217114225330358349 y1[1] (numeric) = -0.81907474065688217114225330358347 absolute error = 2e-32 relative error = 2.4417796090208306374770077400077e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.57368682154801256380110812050361 y2[1] (numeric) = -0.57368682154801256380110812050356 absolute error = 5e-32 relative error = 8.7155566629684969670460733338302e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.4MB, time=21.62 x[1] = 0.612 y1[1] (analytic) = -0.81850064439361242372770175220081 y1[1] (numeric) = -0.81850064439361242372770175220079 absolute error = 2e-32 relative error = 2.4434922729739612569868767081837e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.57450560930877012563221183430752 y2[1] (numeric) = -0.57450560930877012563221183430747 absolute error = 5e-32 relative error = 8.7031352157133279547320636939141e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.4MB, time=21.86 x[1] = 0.613 y1[1] (analytic) = -0.81792572962976649108548566129119 y1[1] (numeric) = -0.81792572962976649108548566129117 absolute error = 2e-32 relative error = 2.4452097880638852134740988806275e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.57532382256396625415903646452381 y2[1] (numeric) = -0.57532382256396625415903646452376 absolute error = 5e-32 relative error = 8.6907578026531045958224026827403e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.614 y1[1] (analytic) = -0.81734999694025908915197561622843 y1[1] (numeric) = -0.81734999694025908915197561622842 absolute error = 1e-32 relative error = 1.2234660839829806450085651131168e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.57614146049538776236988914452402 y2[1] (numeric) = -0.57614146049538776236988914452396 absolute error = 6e-32 relative error = 1.0414109053774706334750747998139e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.4MB, time=22.09 x[1] = 0.615 y1[1] (analytic) = -0.8167734469008228594568510241632 y1[1] (numeric) = -0.81677344690082285945685102416319 absolute error = 1e-32 relative error = 1.2243297132080072627997464947452e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.5769585222853967869797536773647 y2[1] (numeric) = -0.57695852228539678697975367736464 absolute error = 6e-32 relative error = 1.0399361077523100979228794339272e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.4MB, time=22.32 x[1] = 0.616 y1[1] (analytic) = -0.81619608008800779339050656206213 y1[1] (numeric) = -0.81619608008800779339050656206212 absolute error = 1e-32 relative error = 1.2251957886053229049734029448165e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.57777500711693160606808568431733 y2[1] (numeric) = -0.57777500711693160606808568431727 absolute error = 6e-32 relative error = 1.0384665182974424543904630415705e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.4MB, time=22.55 x[1] = 0.617 y1[1] (analytic) = -0.8156178970791806556541088321442 y1[1] (numeric) = -0.81561789707918065565410883214418 absolute error = 2e-32 relative error = 2.4521286342075434460399442495470e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.57859091417350745614046643693812 y2[1] (numeric) = -0.57859091417350745614046643693806 absolute error = 6e-32 relative error = 1.0370021120312172782049123324137e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.4MB, time=22.78 x[1] = 0.618 y1[1] (analytic) = -0.81503889845252440689287977460952 y1[1] (numeric) = -0.81503889845252440689287977460951 absolute error = 1e-32 relative error = 1.2269353056628983473485246712077e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.57940624263921734861329831109204 y2[1] (numeric) = -0.57940624263921734861329831109198 absolute error = 6e-32 relative error = 1.0355428641344582477117162190391e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.619 y1[1] (analytic) = -0.81445908478703762551318420432926 y1[1] (numeric) = -0.81445908478703762551318420432925 absolute error = 1e-32 relative error = 1.2278087612731056578691568555630e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.58022099169873288572072537830366 y2[1] (numeric) = -0.5802209916987328857207253783036 absolute error = 6e-32 relative error = 1.0340887499491520182810680171622e-29 % Correct digits = 30 h = 0.001 memory used=381.4MB, alloc=4.4MB, time=23.02 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.62 y1[1] (analytic) = -0.8138784566625339286839996543607 y1[1] (numeric) = -0.81387845666253392868399965436068 absolute error = 2e-32 relative error = 2.4573693819116271203698230429704e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.58103516053730507584296322758221 y2[1] (numeric) = -0.58103516053730507584296322758216 absolute error = 5e-32 relative error = 8.6053312081429149013201760950189e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=385.2MB, alloc=4.4MB, time=23.25 x[1] = 0.621 y1[1] (analytic) = -0.81329701465964139252334752476951 y1[1] (numeric) = -0.81329701465964139252334752476949 absolute error = 2e-32 relative error = 2.4591262035272375495462474440990e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.58184874834076514825522268945897 y2[1] (numeric) = -0.58184874834076514825522268945892 absolute error = 5e-32 relative error = 8.5932985406573451091992570751501e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.4MB, time=23.48 x[1] = 0.622 y1[1] (analytic) = -0.81271475935980197147026535027979 y1[1] (numeric) = -0.81271475935980197147026535027977 absolute error = 2e-32 relative error = 2.4608880015609112931968578684299e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.58266175429552536729641271338109 y2[1] (numeric) = -0.58266175429552536729641271338104 absolute error = 5e-32 relative error = 8.5813080456006827383768811709840e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.4MB, time=23.71 x[1] = 0.623 y1[1] (analytic) = -0.81213169134527091684290081473111 y1[1] (numeric) = -0.81213169134527091684290081473108 absolute error = 3e-32 relative error = 3.6939821853652739479878140548276e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.58347417758857984595680822982696 y2[1] (numeric) = -0.58347417758857984595680822982691 absolute error = 5e-32 relative error = 8.5693595227544195021825208909339e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.4MB, time=23.95 x[1] = 0.624 y1[1] (analytic) = -0.81154781119911619458330895420011 y1[1] (numeric) = -0.81154781119911619458330895420009 absolute error = 2e-32 relative error = 2.4644265838692438501198942640811e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.58428601740750535888386940954296 y2[1] (numeric) = -0.58428601740750535888386940954291 absolute error = 5e-32 relative error = 8.5574527731900045393854490759187e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.625 y1[1] (analytic) = -0.81096311950521790218953480394108 y1[1] (numeric) = -0.81096311950521790218953480394106 absolute error = 2e-32 relative error = 2.4662033967959397343420378504374e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.58509727294046215480539931415008 y2[1] (numeric) = -0.58509727294046215480539931415003 absolute error = 5e-32 relative error = 8.5455875992585353778969911590453e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=400.5MB, alloc=4.4MB, time=24.18 x[1] = 0.626 y1[1] (analytic) = -0.81037761684826768483556455701403 y1[1] (numeric) = -0.81037761684826768483556455701401 absolute error = 2e-32 relative error = 2.4679852434454308413846998497794e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.58590794337619476836922751503053 y2[1] (numeric) = -0.58590794337619476836922751503048 absolute error = 5e-32 relative error = 8.5337638045805477366913305414256e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=404.3MB, alloc=4.5MB, time=24.41 x[1] = 0.627 y1[1] (analytic) = -0.80979130381376815067972911460066 y1[1] (numeric) = -0.80979130381376815067972911460065 absolute error = 1e-32 relative error = 1.2348860691519294412650345483321e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.5867180279040328313986078408783 y2[1] (numeric) = -0.58671802790403283139860784087825 absolute error = 5e-32 relative error = 8.5219811940359030625626809229602e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.5MB, time=24.64 x[1] = 0.628 y1[1] (analytic) = -0.80920418098803228536214471955587 y1[1] (numeric) = -0.80920418098803228536214471955586 absolute error = 1e-32 relative error = 1.2357820479610071205311551907818e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.58752752571389188356251899858354 y2[1] (numeric) = -0.58752752571389188356251899858349 absolute error = 5e-32 relative error = 8.5102395737537727123927179024710e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.5MB, time=24.87 x[1] = 0.629 y1[1] (analytic) = -0.80861624895818286569177617570531 y1[1] (numeric) = -0.8086162489581828656917761757053 absolute error = 1e-32 relative error = 1.2366805654578361525135769551621e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.5883364359962741824600573972178 y2[1] (numeric) = -0.58833643599627418246005739721775 absolute error = 5e-32 relative error = 8.4985387511027177054571211487724e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=415.8MB, alloc=4.5MB, time=25.10 x[1] = 0.63 y1[1] (analytic) = -0.80802750831215187252370896577706 y1[1] (numeric) = -0.80802750831215187252370896577704 absolute error = 2e-32 relative error = 2.4751632579659319645638230364282e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.58914475794226951311811209079462 y2[1] (numeric) = -0.58914475794226951311811209079457 absolute error = 5e-32 relative error = 8.4868785346808629839571103195541e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.631 y1[1] (analytic) = -0.8074379596386799028272173906462 y1[1] (numeric) = -0.80743795963867990282721739064619 absolute error = 1e-32 relative error = 1.2384852459097781449353441408811e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.58995249074355599690151234219815 y2[1] (numeric) = -0.5899524907435559969015123421981 absolute error = 5e-32 relative error = 8.4752587343061651334240993931167e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=419.6MB, alloc=4.5MB, time=25.33 x[1] = 0.632 y1[1] (analytic) = -0.80684760352731558094521666177536 y1[1] (numeric) = -0.80684760352731558094521666177535 absolute error = 1e-32 relative error = 1.2393914236446577030015644544833e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.59075963359240089983483889819962 y2[1] (numeric) = -0.59075963359240089983483889819957 absolute error = 5e-32 relative error = 8.4636791610067725279161273090641e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.5MB, time=25.56 x[1] = 0.633 y1[1] (analytic) = -0.80625644056841496904568768734982 y1[1] (numeric) = -0.80625644056841496904568768734981 absolute error = 1e-32 relative error = 1.2403001696271657904202456594462e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.59156618568166144033509065381761 y2[1] (numeric) = -0.59156618568166144033509065381756 absolute error = 5e-32 relative error = 8.4521396270114768780065763580424e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=427.2MB, alloc=4.5MB, time=25.80 x[1] = 0.634 y1[1] (analytic) = -0.80566447135314097676566410063355 y1[1] (numeric) = -0.80566447135314097676566410063353 absolute error = 2e-32 relative error = 2.4824229826604265426987703591118e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.59237214620478559635439897342298 y2[1] (numeric) = -0.59237214620478559635439897342293 absolute error = 5e-32 relative error = 8.4406399457402551724618396414472e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=431.0MB, alloc=4.5MB, time=26.03 x[1] = 0.635 y1[1] (analytic) = -0.80507169647346277004837188650966 y1[1] (numeric) = -0.80507169647346277004837188650964 absolute error = 2e-32 relative error = 2.4842507925204710442067194476401e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.59317751435581291193198252594122 y2[1] (numeric) = -0.59317751435581291193198252594117 absolute error = 5e-32 relative error = 8.4291799317949010172179696104589e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.636 y1[1] (analytic) = -0.80447811652215517917411276901668 y1[1] (numeric) = -0.80447811652215517917411276901666 absolute error = 2e-32 relative error = 2.4860837839147366892055326110141e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.59398228932937530315453608226469 y2[1] (numeric) = -0.59398228932937530315453608226465 absolute error = 4e-32 relative error = 6.7342075207597955102398440640729e-30 % Correct digits = 31 h = 0.001 memory used=434.8MB, alloc=4.5MB, time=26.26 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.637 y1[1] (analytic) = -0.80388373209279810598548332894764 y1[1] (numeric) = -0.80388373209279810598548332894763 absolute error = 1e-32 relative error = 1.2439609859956250197880253239322e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.59478647032069786352424731455312 y2[1] (numeric) = -0.59478647032069786352424731455308 absolute error = 4e-32 relative error = 6.7251025361139670589459667686985e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.5MB, time=26.49 x[1] = 0.638 y1[1] (analytic) = -0.80328854377977593030752262624373 y1[1] (numeric) = -0.80328854377977593030752262624372 absolute error = 1e-32 relative error = 1.2448826859830745095213196848991e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.59559005652559966873363622947259 y2[1] (numeric) = -0.59559005652559966873363622947254 absolute error = 5e-32 relative error = 8.3950360574649551052771238268397e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=442.5MB, alloc=4.5MB, time=26.72 x[1] = 0.639 y1[1] (analytic) = -0.80269255217827691556338190698517 y1[1] (numeric) = -0.80269255217827691556338190698516 absolute error = 1e-32 relative error = 1.2458069995620208155747425630590e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.59639304714049458084641246060074 y2[1] (numeric) = -0.5963930471404945808464124606007 absolute error = 4e-32 relative error = 6.7069863057234883729869341059897e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.5MB, time=26.95 x[1] = 0.64 y1[1] (analytic) = -0.80209575788429261358611077926032 y1[1] (numeric) = -0.80209575788429261358611077926031 absolute error = 1e-32 relative error = 1.2467339344091835043765333244264e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.59719544136239205188354623920793 y2[1] (numeric) = -0.59719544136239205188354623920788 absolute error = 5e-32 relative error = 8.3724684645840824055940683082232e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.5MB, time=27.18 x[1] = 0.641 y1[1] (analytic) = -0.80149816149461726862715504607705 y1[1] (numeric) = -0.80149816149461726862715504607704 absolute error = 1e-32 relative error = 1.2476634982358794062620039495917e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.59799723838889792681374945741014 y2[1] (numeric) = -0.5979972383888979268137494574101 absolute error = 4e-32 relative error = 6.6889941010039649408048908019081e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.642 y1[1] (analytic) = -0.80089976360684722056216218676894 y1[1] (numeric) = -0.80089976360684722056216218676893 absolute error = 1e-32 relative error = 1.2485956987882054980512047377118e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.59879843741821524594756383327983 y2[1] (numeric) = -0.59879843741821524594756383327979 absolute error = 4e-32 relative error = 6.6800441518291800285747473205491e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.5MB, time=27.42 x[1] = 0.643 y1[1] (analytic) = -0.80030056481938030729469128104118 y1[1] (numeric) = -0.80030056481938030729469128104117 absolute error = 1e-32 relative error = 1.2495305438472229778515559294847e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.59959903764914504673425378389305 y2[1] (numeric) = -0.59959903764914504673425378389301 absolute error = 4e-32 relative error = 6.6711247831264818907427986319169e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=457.7MB, alloc=4.5MB, time=27.65 x[1] = 0.644 y1[1] (analytic) = -0.79970056573141526635842497189628 y1[1] (numeric) = -0.79970056573141526635842497189627 absolute error = 1e-32 relative error = 1.2504680412291425410605890579101e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.6003990382810871649607022094871 y2[1] (numeric) = -0.60039903828108716496070220948706 absolute error = 4e-32 relative error = 6.6622358547605317969976852498846e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=461.5MB, alloc=4.5MB, time=27.89 x[1] = 0.645 y1[1] (analytic) = -0.79909976694295113571848186517791 y1[1] (numeric) = -0.7990997669429511357184818651779 absolute error = 1e-32 relative error = 1.2514081987855108666216063064170e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.60119843851404103535150798989947 y2[1] (numeric) = -0.60119843851404103535150798989943 absolute error = 4e-32 relative error = 6.6533772274702601296629479864980e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=465.4MB, alloc=4.5MB, time=28.12 x[1] = 0.646 y1[1] (analytic) = -0.79849816905478665377242856437044 y1[1] (numeric) = -0.79849816905478665377242856437043 absolute error = 1e-32 relative error = 1.2523510244033983226634860075774e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.6019972375486064915694845932574 y2[1] (numeric) = -0.60199723754860649156948459325737 absolute error = 3e-32 relative error = 4.9834115721465812331592057121551e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.5MB, time=28.35 x[1] = 0.647 y1[1] (analytic) = -0.79789577266851965855159133959223 y1[1] (numeric) = -0.79789577266851965855159133959222 absolute error = 1e-32 relative error = 1.2532965260055879007350458310562e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.60279543458598456561575979648616 y2[1] (numeric) = -0.60279543458598456561575979648613 absolute error = 3e-32 relative error = 4.9768127425525000690439786175868e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.648 y1[1] (analytic) = -0.79729257838654648612326822942085 y1[1] (numeric) = -0.79729257838654648612326822942083 absolute error = 2e-32 relative error = 2.5084894231015307758486609261628e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.60359302882797828662867711760275 y2[1] (numeric) = -0.60359302882797828662867711760272 absolute error = 3e-32 relative error = 4.9702363293115311463091204428679e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.5MB, time=28.58 x[1] = 0.649 y1[1] (analytic) = -0.79668858681206136819444317328799 y1[1] (numeric) = -0.79668858681206136819444317328797 absolute error = 2e-32 relative error = 2.5103911780674215724678520934294e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.60439001947699347908070016096041 y2[1] (numeric) = -0.60439001947699347908070016096038 absolute error = 3e-32 relative error = 4.9636822305504617272620533144429e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=476.8MB, alloc=4.5MB, time=28.81 x[1] = 0.65 y1[1] (analytic) = -0.79608379854905582891760457067991 y1[1] (numeric) = -0.79608379854905582891760457067989 absolute error = 2e-32 relative error = 2.5122983329709819773298556155496e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.60518640573603956037252167860594 y2[1] (numeric) = -0.60518640573603956037252167860591 absolute error = 3e-32 relative error = 4.9571503450269033048518397165628e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=480.6MB, alloc=4.5MB, time=29.04 x[1] = 0.651 y1[1] (analytic) = -0.79547821420231808089927146127429 y1[1] (numeric) = -0.79547821420231808089927146127428 absolute error = 1e-32 relative error = 1.2571054519736537215445087119633e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.60598218680873033782357975370724 y2[1] (numeric) = -0.60598218680873033782357975370721 absolute error = 3e-32 relative error = 4.9506405721244531397209601525967e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=484.4MB, alloc=4.5MB, time=29.28 x[1] = 0.652 y1[1] (analytic) = -0.7948718343774324204118313174373 y1[1] (numeric) = -0.79487183437743242041183131743729 absolute error = 1e-32 relative error = 1.2580644536024227627151643637900e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.60677736189928480505818411560141 y2[1] (numeric) = -0.60677736189928480505818411560138 absolute error = 3e-32 relative error = 4.9441528118479003411920111061232e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.653 y1[1] (analytic) = -0.7942646596807786218092942371924 y1[1] (numeric) = -0.79426465968077862180929423719239 absolute error = 1e-32 relative error = 1.2590261795128944452876514505279e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.60757193021252793778645620040338 y2[1] (numeric) = -0.60757193021252793778645620040335 absolute error = 3e-32 relative error = 4.9376869648184760147363344846620e-30 % Correct digits = 31 h = 0.001 memory used=488.2MB, alloc=4.5MB, time=29.51 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.654 y1[1] (analytic) = -0.79365669071953133114756912185648 y1[1] (numeric) = -0.79365669071953133114756912185647 absolute error = 1e-32 relative error = 1.2599906378832354567444027432598e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.60836589095389148897928717630129 y2[1] (numeric) = -0.60836589095389148897928717630126 absolute error = 3e-32 relative error = 4.9312429322691470043121536297316e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.5MB, time=29.74 x[1] = 0.655 y1[1] (analytic) = -0.7930479281016594590098682180164 y1[1] (numeric) = -0.79304792810165945900986821801639 absolute error = 1e-32 relative error = 1.2609578369288819432657999874737e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.60915924332941478343651875864697 y2[1] (numeric) = -0.60915924332941478343651875864694 absolute error = 3e-32 relative error = 4.9248206160399527637201034133141e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=495.9MB, alloc=4.5MB, time=29.98 x[1] = 0.656 y1[1] (analytic) = -0.79243837243592557253784719839097 y1[1] (numeric) = -0.79243837243592557253784719839096 absolute error = 1e-32 relative error = 1.2619277849027399292381260511423e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.60995198654574551174755224672681 y2[1] (numeric) = -0.60995198654574551174755224672678 absolute error = 3e-32 relative error = 4.9184199185733848968053262605786e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=499.7MB, alloc=4.5MB, time=30.21 x[1] = 0.657 y1[1] (analytic) = -0.79182802433188528666908875038748 y1[1] (numeric) = -0.79182802433188528666908875038747 absolute error = 1e-32 relative error = 1.2629004900953870619893086618886e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.61074411981014052364359182167023 y2[1] (numeric) = -0.6107441198101405236435918216702 absolute error = 3e-32 relative error = 4.9120407429098089119387650074190e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.5MB, time=30.44 x[1] = 0.658 y1[1] (analytic) = -0.79121688439988665458153843481859 y1[1] (numeric) = -0.79121688439988665458153843481858 absolute error = 1e-32 relative error = 1.2638759608352756918867192807970e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.61153564233046662074072875331851 y2[1] (numeric) = -0.61153564233046662074072875331848 absolute error = 3e-32 relative error = 4.9056829926829277417371000759070e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.659 y1[1] (analytic) = -0.79060495325106955734550237029284 y1[1] (numeric) = -0.79060495325106955734550237029283 absolute error = 1e-32 relative error = 1.2648542054889372980203115652805e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.61232655331520134867307377303585 y2[1] (numeric) = -0.61232655331520134867307377303582 absolute error = 3e-32 relative error = 4.8993465721152865844321155455050e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=507.3MB, alloc=4.5MB, time=30.66 x[1] = 0.66 y1[1] (analytic) = -0.78999223149736509278381709123024 y1[1] (numeric) = -0.78999223149736509278381709123023 absolute error = 1e-32 relative error = 1.2658352324611882697842840177057e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.6131168519734337886151454793963 y2[1] (numeric) = -0.61311685197343378861514547939627 absolute error = 3e-32 relative error = 4.8930313860138186286772799436418e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=511.1MB, alloc=4.5MB, time=30.90 x[1] = 0.661 y1[1] (analytic) = -0.7893787197514949635408027192822 y1[1] (numeric) = -0.78937871975149496354080271928219 absolute error = 1e-32 relative error = 1.2668190501953370547612404662198e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.61390653751486534819272325442414 y2[1] (numeric) = -0.61390653751486534819272325442411 absolute error = 3e-32 relative error = 4.8867373397654312288831175751684e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=514.9MB, alloc=4.5MB, time=31.13 x[1] = 0.662 y1[1] (analytic) = -0.78876441862697086436061137915158 y1[1] (numeric) = -0.78876441862697086436061137915157 absolute error = 1e-32 relative error = 1.2678056671733926834045097624308e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.61469560914981055178137377960066 y2[1] (numeric) = -0.61469560914981055178137377960063 absolute error = 3e-32 relative error = 4.8804643393326321034046308687363e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=518.8MB, alloc=4.5MB, time=31.36 x[1] = 0.663 y1[1] (analytic) = -0.78814932873809386857558358041344 y1[1] (numeric) = -0.78814932873809386857558358041343 absolute error = 1e-32 relative error = 1.2687950919162746811068824087803e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.61548406608919783019186085317667 y2[1] (numeric) = -0.61548406608919783019186085317665 absolute error = 2e-32 relative error = 3.2494748608327967553764674021859e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.5MB, time=31.59 x[1] = 0.664 y1[1] (analytic) = -0.78753345069995381380522607692892 y1[1] (numeric) = -0.78753345069995381380522607692891 absolute error = 1e-32 relative error = 1.2697873329840243783375367682794e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.61627190754457030974164882344686 y2[1] (numeric) = -0.61627190754457030974164882344683 absolute error = 3e-32 relative error = 4.8679811026158653425881135366565e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.665 y1[1] (analytic) = -0.78691678512842868686642550482327 y1[1] (numeric) = -0.78691678512842868686642550482325 absolute error = 2e-32 relative error = 2.5415647979520352592467424081221e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.61705913272808660071171056654808 y2[1] (numeric) = -0.61705913272808660071171056654806 absolute error = 2e-32 relative error = 3.2411804540640684350284501643617e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.5MB, time=31.82 x[1] = 0.666 y1[1] (analytic) = -0.78629933264018400789551288876302 y1[1] (numeric) = -0.786299332640184007895512888763 absolute error = 2e-32 relative error = 2.5435605970623579044926824251895e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.61784574085252158518785155203961 y2[1] (numeric) = -0.61784574085252158518785155203959 absolute error = 2e-32 relative error = 3.2370539566079093295585695954522e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=530.2MB, alloc=4.5MB, time=32.05 x[1] = 0.667 y1[1] (analytic) = -0.78568109385267221368279489441666 y1[1] (numeric) = -0.78568109385267221368279489441664 absolute error = 2e-32 relative error = 2.5455620806563941912494654879701e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.61863173113126720428576215500663 y2[1] (numeric) = -0.61863173113126720428576215500661 absolute error = 2e-32 relative error = 3.2329411818929489238123236978107e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.5MB, time=32.28 x[1] = 0.668 y1[1] (analytic) = -0.78506206938413204022016849251592 y1[1] (numeric) = -0.7850620693841320402201684925159 absolute error = 2e-32 relative error = 2.5475692661714841048871899274620e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.61941710277833324475901098970051 y2[1] (numeric) = -0.61941710277833324475901098970049 absolute error = 2e-32 relative error = 3.2288420694701530460082385710247e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.5MB, time=32.52 x[1] = 0.669 y1[1] (analytic) = -0.78444225985358790446243648685181 y1[1] (numeric) = -0.78444225985358790446243648685179 absolute error = 2e-32 relative error = 2.5495821711253670453956366982708e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.62020185500834812498919265678791 y2[1] (numeric) = -0.62020185500834812498919265678789 absolute error = 2e-32 relative error = 3.2247565592545338794312769272015e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.67 y1[1] (analytic) = -0.78382166588084928530294214483812 y1[1] (numeric) = -0.7838216658808492853029421448381 absolute error = 2e-32 relative error = 2.5516008131166216838211760134168e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.62098598703655968035744391412659 y2[1] (numeric) = -0.62098598703655968035744391412657 absolute error = 2e-32 relative error = 3.2206845915224376887618799982969e-30 % Correct digits = 31 h = 0.001 memory used=541.6MB, alloc=4.5MB, time=32.75 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.671 y1[1] (analytic) = -0.78320028808651010376414195495638 y1[1] (numeric) = -0.78320028808651010376414195495636 absolute error = 2e-32 relative error = 2.5536252098251087697803567052295e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.62176949807883594799654289961709 y2[1] (numeric) = -0.62176949807883594799654289961707 absolute error = 2e-32 relative error = 3.2166261069088568116144724793270e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.5MB, time=32.98 x[1] = 0.672 y1[1] (analytic) = -0.78257812709194810240373632045772 y1[1] (numeric) = -0.7825781270919481024037363204577 absolute error = 2e-32 relative error = 2.5556553790124169129785897163702e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.62255238735166595092280665409653 y2[1] (numeric) = -0.62255238735166595092280665409651 absolute error = 2e-32 relative error = 3.2125810464047656625553711551400e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=549.3MB, alloc=4.5MB, time=33.21 x[1] = 0.673 y1[1] (analytic) = -0.78195518351932422393697878313928 y1[1] (numeric) = -0.78195518351932422393697878313926 absolute error = 2e-32 relative error = 2.5576913385223113618668452074445e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.62333465407216048154700281244236 y2[1] (numeric) = -0.62333465407216048154700281244233 absolute error = 3e-32 relative error = 4.8128240270317207498115542760429e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=553.1MB, alloc=4.5MB, time=33.45 x[1] = 0.674 y1[1] (analytic) = -0.78133145799158198907578515483418 y1[1] (numeric) = -0.78133145799158198907578515483416 absolute error = 2e-32 relative error = 2.5597331062811858027758424407214e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.62411629745805288456349195203955 y2[1] (numeric) = -0.62411629745805288456349195203952 absolute error = 3e-32 relative error = 4.8067964451795640625227283102779e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=556.9MB, alloc=4.5MB, time=33.68 x[1] = 0.675 y1[1] (analytic) = -0.78070695113244687358526471745402 y1[1] (numeric) = -0.78070695113244687358526471745399 absolute error = 3e-32 relative error = 3.8426710504477758046137686537196e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.6248973167276998392168177095343 y2[1] (numeric) = -0.62489731672769983921681770953427 absolute error = 3e-32 relative error = 4.8007887371154380312415782600538e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.676 y1[1] (analytic) = -0.78008166356642568455829643500084 y1[1] (numeric) = -0.78008166356642568455829643500082 absolute error = 2e-32 relative error = 2.5638341386673237221209119136759e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.62567771110008214094496239934914 y2[1] (numeric) = -0.62567771110008214094496239934911 absolute error = 3e-32 relative error = 4.7948008164224441565376270226373e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=560.7MB, alloc=4.5MB, time=33.91 x[1] = 0.677 y1[1] (analytic) = -0.77945559591880593590877390292041 y1[1] (numeric) = -0.77945559591880593590877390292038 absolute error = 3e-32 relative error = 3.8488401593469385709239300843407e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.62645747979480548239848649076909 y2[1] (numeric) = -0.62645747979480548239848649076905 absolute error = 4e-32 relative error = 6.3851101295976058788145017336848e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=564.5MB, alloc=4.5MB, time=34.14 x[1] = 0.678 y1[1] (analytic) = -0.77882874881565522308414354149961 y1[1] (numeric) = -0.77882874881565522308414354149959 absolute error = 2e-32 relative error = 2.5679586212519098459266475389892e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.62723662203210123383477092452439 y2[1] (numeric) = -0.62723662203210123383477092452435 absolute error = 4e-32 relative error = 6.3771786587347648471167305400629e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=568.3MB, alloc=4.5MB, time=34.37 x[1] = 0.679 y1[1] (analytic) = -0.77820112288382059699786132071801 y1[1] (numeric) = -0.77820112288382059699786132071799 absolute error = 2e-32 relative error = 2.5700297020755963577360541986633e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.6280151370328272228865818746926 y2[1] (numeric) = -0.62801513703282722288658187469257 absolute error = 3e-32 relative error = 4.7769549220963854507430250033235e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=572.2MB, alloc=4.5MB, time=34.60 x[1] = 0.68 y1[1] (analytic) = -0.77757271875092793718239408404432 y1[1] (numeric) = -0.7775727187509279371823940840443 absolute error = 2e-32 relative error = 2.5721067004675094853378319286034e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.62879302401846851370417818742025 y2[1] (numeric) = -0.62879302401846851370417818742021 absolute error = 4e-32 relative error = 6.3613937292703083689638677092411e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=576.0MB, alloc=4.5MB, time=34.83 x[1] = 0.681 y1[1] (analytic) = -0.77694353704538132416339231812446 y1[1] (numeric) = -0.77694353704538132416339231812444 absolute error = 2e-32 relative error = 2.5741896349453510747441876060520e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.62957028221113818547018235442143 y2[1] (numeric) = -0.62957028221113818547018235442139 absolute error = 4e-32 relative error = 6.3535400463176962398430732546072e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.682 y1[1] (analytic) = -0.77631357839636241105566199413604 y1[1] (numeric) = -0.77631357839636241105566199413602 absolute error = 2e-32 relative error = 2.5762785241131774106771820040629e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.63034691083357811028643650644746 y2[1] (numeric) = -0.63034691083357811028643650644743 absolute error = 3e-32 relative error = 4.7592840520670831773595059183183e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=579.8MB, alloc=4.5MB, time=35.06 x[1] = 0.683 y1[1] (analytic) = -0.77568284343382979438156388478507 y1[1] (numeric) = -0.77568284343382979438156388478505 absolute error = 2e-32 relative error = 2.5783733866618792854047699958201e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.63112290910915973043206553993625 y2[1] (numeric) = -0.63112290910915973043206553993621 absolute error = 4e-32 relative error = 6.3379096880607062339239482629150e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=583.6MB, alloc=4.5MB, time=35.30 x[1] = 0.684 y1[1] (analytic) = -0.77505133278851838411246953849312 y1[1] (numeric) = -0.77505133278851838411246953849311 absolute error = 1e-32 relative error = 1.2902371206848326666390019169482e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.63189827626188483499197011884303 y2[1] (numeric) = -0.63189827626188483499197011884299 absolute error = 4e-32 relative error = 6.3301327923582342835763722953799e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=587.4MB, alloc=4.5MB, time=35.53 x[1] = 0.685 y1[1] (analytic) = -0.77441904709193877293390386926657 y1[1] (numeric) = -0.77441904709193877293390386926656 absolute error = 1e-32 relative error = 1.2912905535512743283615987235738e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.63267301151638633585497292322433 y2[1] (numeric) = -0.6326730115163863358549729232243 absolute error = 3e-32 relative error = 4.7417859548167236825337217708106e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=591.2MB, alloc=4.5MB, time=35.76 x[1] = 0.686 y1[1] (analytic) = -0.77378598697637660473500509705261 y1[1] (numeric) = -0.7737859869763766047350050970526 absolute error = 1e-32 relative error = 1.2923470014074183848379492153398e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.63344711409792904308084214649343 y2[1] (numeric) = -0.6334471140979290430808421464934 absolute error = 3e-32 relative error = 4.7359912662514852143706603987940e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.687 y1[1] (analytic) = -0.77315215307489194232293354906961 y1[1] (numeric) = -0.7731521530748919423229335490696 absolute error = 1e-32 relative error = 1.2934064737748124423394677949525e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.63422058323241043963541687438845 y2[1] (numeric) = -0.63422058323241043963541687438842 absolute error = 3e-32 relative error = 4.7302154476128828954295380686367e-30 % Correct digits = 31 h = 0.001 memory used=595.1MB, alloc=4.5MB, time=35.99 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.688 y1[1] (analytic) = -0.77251754602131863436286160765029 y1[1] (numeric) = -0.77251754602131863436286160765028 absolute error = 1e-32 relative error = 1.2944689802196462850523152078977e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.63499341814636145549305961059239 y2[1] (numeric) = -0.63499341814636145549305961059235 absolute error = 4e-32 relative error = 6.2992778912206433599374653797513e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=598.9MB, alloc=4.5MB, time=36.22 x[1] = 0.689 y1[1] (analytic) = -0.77188216645026368154417786455494 y1[1] (numeric) = -0.77188216645026368154417786455492 absolute error = 2e-32 relative error = 2.5910690607060038042015079280260e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.63576561806694724110566184661687 y2[1] (numeric) = -0.63576561806694724110566184661683 absolute error = 4e-32 relative error = 6.2916267981934074072475285758132e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=602.7MB, alloc=4.5MB, time=36.45 x[1] = 0.69 y1[1] (analytic) = -0.77124601499710660197353931549777 y1[1] (numeric) = -0.77124601499710660197353931549775 absolute error = 2e-32 relative error = 2.5932062676622104529085434785654e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.63653718222196794023742920700872 y2[1] (numeric) = -0.63653718222196794023742920700868 absolute error = 4e-32 relative error = 6.2840005450068953592940889430377e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=606.5MB, alloc=4.5MB, time=36.68 x[1] = 0.691 y1[1] (analytic) = -0.77060909229799879579540620178138 y1[1] (numeric) = -0.77060909229799879579540620178136 absolute error = 2e-32 relative error = 2.5953496007111591986251652576661e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.63730810983985946216467333515846 y2[1] (numeric) = -0.63730810983985946216467333515842 absolute error = 4e-32 relative error = 6.2763990262184266189986808481808e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=610.3MB, alloc=4.5MB, time=36.92 x[1] = 0.692 y1[1] (analytic) = -0.76997139898986290904069487845139 y1[1] (numeric) = -0.76997139898986290904069487845137 absolute error = 2e-32 relative error = 2.5974990793474019473729256336214e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.63807840014969425323983831998321 y2[1] (numeric) = -0.63807840014969425323983831998317 absolute error = 4e-32 relative error = 6.2688221370000823590148252012874e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.693 y1[1] (analytic) = -0.7693329357103921967041848602655 y1[1] (numeric) = -0.76933293571039219670418486026548 absolute error = 2e-32 relative error = 2.5996547231573097420349866874457e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.63884805238118206781899009952198 y2[1] (numeric) = -0.63884805238118206781899009952194 absolute error = 4e-32 relative error = 6.2612697731342792616109227924369e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=614.1MB, alloc=4.5MB, time=37.15 x[1] = 0.694 y1[1] (analytic) = -0.76869370309804988505131696801677 y1[1] (numeric) = -0.76869370309804988505131696801675 absolute error = 2e-32 relative error = 2.6018165518195902096123653330163e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.63961706576467073855199791401804 y2[1] (numeric) = -0.639617065764670738551997914018 absolute error = 4e-32 relative error = 6.2537418310093815513951812380843e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=617.9MB, alloc=4.5MB, time=37.38 x[1] = 0.695 y1[1] (analytic) = -0.76805370179206853315502026835991 y1[1] (numeric) = -0.76805370179206853315502026835989 absolute error = 2e-32 relative error = 2.6039845851058085706912805650885e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.64038543953114694603463751837122 y2[1] (numeric) = -0.64038543953114694603463751837119 absolute error = 3e-32 relative error = 4.6846786557115132014505074700963e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=621.8MB, alloc=4.5MB, time=37.61 x[1] = 0.696 y1[1] (analytic) = -0.76741293243244939366320627026033 y1[1] (numeric) = -0.76741293243244939366320627026031 absolute error = 2e-32 relative error = 2.6061588428809122395739693435567e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.64115317291223698782184650192101 y2[1] (numeric) = -0.64115317291223698782184650192098 absolute error = 3e-32 relative error = 4.6790691004045755513109322114436e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=625.6MB, alloc=4.5MB, time=37.85 x[1] = 0.697 y1[1] (analytic) = -0.76677139565996177279756961051859 y1[1] (numeric) = -0.76677139565996177279756961051857 absolute error = 2e-32 relative error = 2.6083393451037590437860184677693e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.64192026514020754680136270236923 y2[1] (numeric) = -0.64192026514020754680136270236919 absolute error = 4e-32 relative error = 6.2313035079618871695442394547337e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=629.4MB, alloc=4.5MB, time=38.08 x[1] = 0.698 y1[1] (analytic) = -0.76612909211614238958433522951618 y1[1] (numeric) = -0.76612909211614238958433522951616 absolute error = 2e-32 relative error = 2.6105261118276490919366279638628e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.64268671544796645892697734026787 y2[1] (numeric) = -0.64268671544796645892697734026783 absolute error = 4e-32 relative error = 6.2238722286517374128651882137163e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.699 y1[1] (analytic) = -0.76548602244329473431759280638201 y1[1] (numeric) = -0.765486022443294734317592806382 absolute error = 1e-32 relative error = 1.3063595816004301595871539146873e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.64345252306906348031063514088304 y2[1] (numeric) = -0.64345252306906348031063514088301 absolute error = 3e-32 relative error = 4.6623486464719355464444562915859e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=633.2MB, alloc=4.5MB, time=38.31 x[1] = 0.7 y1[1] (analytic) = -0.76484218728448842625585999019186 y1[1] (numeric) = -0.76484218728448842625585999019185 absolute error = 1e-32 relative error = 1.3074592597335938698746728353053e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.64421768723769105367261435139872 y2[1] (numeric) = -0.64421768723769105367261435139869 absolute error = 3e-32 relative error = 4.6568109808713117359699209228648e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.5MB, time=38.54 x[1] = 0.701 y1[1] (analytic) = -0.76419758728355857055251673058384 y1[1] (numeric) = -0.76419758728355857055251673058382 absolute error = 2e-32 relative error = 2.6171242009664864364659994419761e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.64498220718868507414902020334415 y2[1] (numeric) = -0.64498220718868507414902020334412 absolute error = 3e-32 relative error = 4.6512911000696346246566817930041e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=640.8MB, alloc=4.5MB, time=38.77 x[1] = 0.702 y1[1] (analytic) = -0.76355222308510511442075377730208 y1[1] (numeric) = -0.76355222308510511442075377730206 absolute error = 2e-32 relative error = 2.6193362281352183170817991655533e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.64574608215752565445582601281535 y2[1] (numeric) = -0.64574608215752565445582601281532 absolute error = 3e-32 relative error = 4.6457889298787399508483892036349e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=644.6MB, alloc=4.5MB, time=39.00 x[1] = 0.703 y1[1] (analytic) = -0.7629060953344922025336791836665 y1[1] (numeric) = -0.76290609533449220253367918366648 absolute error = 2e-32 relative error = 2.6215546215070026679886165922185e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.64650931138033788940869675451334 y2[1] (numeric) = -0.64650931138033788940869675451331 absolute error = 3e-32 relative error = 4.6403043965365510715860237738692e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.704 y1[1] (analytic) = -0.7622592046778475316602274138083 y1[1] (numeric) = -0.76225920467784753166022741380828 absolute error = 2e-32 relative error = 2.6237794017131705357903150925233e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.64727189409389261979783058983915 y2[1] (numeric) = -0.64727189409389261979783058983912 absolute error = 3e-32 relative error = 4.6348374267040598114858362881597e-30 % Correct digits = 31 h = 0.001 memory used=648.5MB, alloc=4.5MB, time=39.24 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.705 y1[1] (analytic) = -0.76161155176206170453751641770848 y1[1] (numeric) = -0.76161155176206170453751641770846 absolute error = 2e-32 relative error = 2.6260105894833229676748568835030e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.64803382953560719561705447426787 y2[1] (numeric) = -0.64803382953560719561705447426784 absolute error = 3e-32 relative error = 4.6293879474623330258832951971515e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=652.3MB, alloc=4.5MB, time=39.47 x[1] = 0.706 y1[1] (analytic) = -0.76096313723478758298029880162827 y1[1] (numeric) = -0.76096313723478758298029880162826 absolute error = 1e-32 relative error = 1.3141241028229465708823773382326e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.64879511694354623864641061496962 y2[1] (numeric) = -0.6487951169435462386464106149696 absolute error = 2e-32 relative error = 3.0826372575396964155586104413016e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=656.1MB, alloc=4.5MB, time=39.70 x[1] = 0.707 y1[1] (analytic) = -0.76031396174443964022815398442661 y1[1] (numeric) = -0.7603139617444396402281539844266 absolute error = 1e-32 relative error = 1.3152461355643562094593720346897e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.64955575555642240438747119615466 y2[1] (numeric) = -0.64955575555642240438747119615463 absolute error = 3e-32 relative error = 4.6185411711580327954783808449991e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=659.9MB, alloc=4.5MB, time=39.93 x[1] = 0.708 y1[1] (analytic) = -0.7596640259401933125310689925183 y1[1] (numeric) = -0.75966402594019331253106899251829 absolute error = 1e-32 relative error = 1.3163714034797901738747780195774e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.6503157446135971433506194368912 y2[1] (numeric) = -0.65031574461359714335061943689117 absolute error = 3e-32 relative error = 4.6131437303313822050152357663582e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=663.7MB, alloc=4.5MB, time=40.17 x[1] = 0.709 y1[1] (analytic) = -0.75901333047198434997405630783822 y1[1] (numeric) = -0.75901333047198434997405630783821 absolute error = 1e-32 relative error = 1.3174999171334193274588603440274e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.65107508335508146169353569417858 y2[1] (numeric) = -0.65107508335508146169353569417855 absolute error = 3e-32 relative error = 4.6077634925615308855601536333626e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.71 y1[1] (analytic) = -0.75836187599050816654145794413955 y1[1] (numeric) = -0.75836187599050816654145794413955 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.65183377102153668121012797285284 y2[1] (numeric) = -0.6518337710215366812101279728528 absolute error = 4e-32 relative error = 6.1365338493145354795558043626039e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=667.5MB, alloc=4.5MB, time=40.40 x[1] = 0.711 y1[1] (analytic) = -0.7577096631472191894215856872678 y1[1] (numeric) = -0.7577096631472191894215856872678 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.6525918068542751986691468534576 y2[1] (numeric) = -0.65259180685427519866914685345756 absolute error = 4e-32 relative error = 6.1294057908594099789995805609435e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=671.3MB, alloc=4.5MB, time=40.63 x[1] = 0.712 y1[1] (analytic) = -0.7570566925943302075523481947161 y1[1] (numeric) = -0.7570566925943302075523481947161 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.65334919009526124450172549952873 y2[1] (numeric) = -0.65334919009526124450172549952869 absolute error = 4e-32 relative error = 6.1223003879698420469895983060776e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=675.2MB, alloc=4.5MB, time=40.86 x[1] = 0.713 y1[1] (analytic) = -0.75640296498481171940851640878051 y1[1] (numeric) = -0.75640296498481171940851640878051 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.65410591998711164083708605681577 y2[1] (numeric) = -0.65410591998711164083708605681573 absolute error = 4e-32 relative error = 6.1152175477617067280401723422698e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=679.0MB, alloc=4.5MB, time=41.09 x[1] = 0.714 y1[1] (analytic) = -0.75574848097239128003127949599547 y1[1] (numeric) = -0.75574848097239128003127949599547 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.65486199577309655888565440879708 y2[1] (numeric) = -0.65486199577309655888565440879704 absolute error = 4e-32 relative error = 6.1081571778765458891089446868709e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=682.8MB, alloc=4.5MB, time=41.32 x[1] = 0.715 y1[1] (analytic) = -0.75509324121155284730074428323906 y1[1] (numeric) = -0.75509324121155284730074428323906 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.655617416697140275668825905437 y2[1] (numeric) = -0.65561741669714027566882590543696 absolute error = 4e-32 relative error = 6.1011191864779017530712343467792e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.716 y1[1] (analytic) = -0.75443724635753612745203191795418 y1[1] (numeric) = -0.75443724635753612745203191795417 absolute error = 1e-32 relative error = 1.3254912914600308276402197034088e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.65637218200382193009462533548235 y2[1] (numeric) = -0.65637218200382193009462533548231 absolute error = 4e-32 relative error = 6.0941034822476811829624987571222e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=686.6MB, alloc=4.5MB, time=41.55 x[1] = 0.717 y1[1] (analytic) = -0.75378049706633591983562623633442 y1[1] (numeric) = -0.75378049706633591983562623633442 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.65712629093837627837850506670131 y2[1] (numeric) = -0.65712629093837627837850506670127 absolute error = 4e-32 relative error = 6.0871099743825504168433514124405e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=690.4MB, alloc=4.5MB, time=41.79 x[1] = 0.718 y1[1] (analytic) = -0.75312299399470146092262907907173 y1[1] (numeric) = -0.75312299399470146092262907907173 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.6578797427466944488085259333295 y2[1] (numeric) = -0.65787974274669444880852593332946 absolute error = 4e-32 relative error = 6.0801385725903599564860647859773e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=694.2MB, alloc=4.5MB, time=42.02 x[1] = 0.719 y1[1] (analytic) = -0.75246473780013576755557854935575 y1[1] (numeric) = -0.75246473780013576755557854935575 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.65863253667532469585416610560527 y2[1] (numeric) = -0.65863253667532469585416610560523 absolute error = 4e-32 relative error = 6.0731891870865993163841089404334e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=698.1MB, alloc=4.5MB, time=42.25 x[1] = 0.72 y1[1] (analytic) = -0.75180572914089497944548696225195 y1[1] (numeric) = -0.75180572914089497944548696225195 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.65938467197147315361800383264817 y2[1] (numeric) = -0.65938467197147315361800383264812 absolute error = 5e-32 relative error = 7.5828271607386016785595195780243e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.721 y1[1] (analytic) = -0.75114596867598770091575598836582 y1[1] (numeric) = -0.75114596867598770091575598836582 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.6601361478830045886295206070606 y2[1] (numeric) = -0.66013614788300458862952060706055 absolute error = 5e-32 relative error = 7.5741951354043197702103600884167e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=701.9MB, alloc=4.5MB, time=42.48 TOP MAIN SOLVE Loop x[1] = 0.722 y1[1] (analytic) = -0.75048545706517434189362724782304 y1[1] (numeric) = -0.75048545706517434189362724782305 absolute error = 1e-32 relative error = 1.3324708568112294397396837168672e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.66088696365844315198027195751232 y2[1] (numeric) = -0.66088696365844315198027195751227 absolute error = 5e-32 relative error = 7.5655902975021900650222003751604e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=705.7MB, alloc=4.5MB, time=42.71 x[1] = 0.723 y1[1] (analytic) = -0.74982419496896645814982736306022 y1[1] (numeric) = -0.74982419496896645814982736306023 absolute error = 1e-32 relative error = 1.3336459488899097972801320625457e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.66163711854697313079967373419959 y2[1] (numeric) = -0.66163711854697313079967373419954 absolute error = 5e-32 relative error = 7.5570125372961877767303828918517e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=709.5MB, alloc=4.5MB, time=42.95 x[1] = 0.724 y1[1] (analytic) = -0.74916218304862609078706723072606 y1[1] (numeric) = -0.74916218304862609078706723072606 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.66238661179843969907065241145532 y2[1] (numeric) = -0.66238661179843969907065241145528 absolute error = 4e-32 relative error = 6.0387693965305811114546479759501e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=713.3MB, alloc=4.5MB, time=43.18 x[1] = 0.725 y1[1] (analytic) = -0.7484994219661651049780560241387 y1[1] (numeric) = -0.7484994219661651049780560241387 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.66313544266334966778440859192254 y2[1] (numeric) = -0.6631354426633496677844085919225 absolute error = 4e-32 relative error = 6.0319502512711540529109587678310e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=717.1MB, alloc=4.5MB, time=43.41 x[1] = 0.726 y1[1] (analytic) = -0.74783591238434452795369118823017 y1[1] (numeric) = -0.74783591238434452795369118823017 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.66388361039287223443354355759009 y2[1] (numeric) = -0.66388361039287223443354355759005 absolute error = 4e-32 relative error = 6.0251525077308127421385312918569e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.727 y1[1] (analytic) = -0.7471716549666738862420864387327 y1[1] (numeric) = -0.7471716549666738862420864387327 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.66463111423883973184279937462657 y2[1] (numeric) = -0.66463111423883973184279937462653 absolute error = 4e-32 relative error = 6.0183760800620186898274963941289e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=720.9MB, alloc=4.5MB, time=43.64 x[1] = 0.728 y1[1] (analytic) = -0.74650665037741054215910052652369 y1[1] (numeric) = -0.74650665037741054215910052652369 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.66537795345374837633666372133474 y2[1] (numeric) = -0.6653779534537483763366637213347 absolute error = 4e-32 relative error = 6.0116208828942620304029637217291e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=724.8MB, alloc=4.5MB, time=43.88 x[1] = 0.729 y1[1] (analytic) = -0.74584089928155902955103027654531 y1[1] (numeric) = -0.74584089928155902955103027654531 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.66612412729075901524309127168396 y2[1] (numeric) = -0.66612412729075901524309127168392 absolute error = 4e-32 relative error = 6.0048868313307994296325045775305e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=728.6MB, alloc=4.5MB, time=44.11 x[1] = 0.73 y1[1] (analytic) = -0.74517440234487038879013215855033 y1[1] (numeric) = -0.74517440234487038879013215855033 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.66686963500369787373259413076153 y2[1] (numeric) = -0.66686963500369787373259413076149 absolute error = 4e-32 relative error = 5.9981738409454188306385170619870e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=732.4MB, alloc=4.5MB, time=44.34 x[1] = 0.731 y1[1] (analytic) = -0.74450716023384150102363739409716 y1[1] (numeric) = -0.74450716023384150102363739409715 absolute error = 1e-32 relative error = 1.3431704265757645787032644145165e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.66761447584705730099195448311474 y2[1] (numeric) = -0.6676144758470573009919544831147 absolute error = 4e-32 relative error = 5.9914818277792307813861922611489e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=736.2MB, alloc=4.5MB, time=44.57 x[1] = 0.732 y1[1] (analytic) = -0.74383917361571442167692635072351 y1[1] (numeric) = -0.7438391736157144216769263507235 absolute error = 1e-32 relative error = 1.3443766280002679046520701249114e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.66835864907599651573181328033319 y2[1] (numeric) = -0.66835864907599651573181328033316 absolute error = 3e-32 relative error = 4.4886080312531145671445171086879e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.733 y1[1] (analytic) = -0.74317044315847571321152872006884 y1[1] (numeric) = -0.74317044315847571321152872006883 absolute error = 1e-32 relative error = 1.3455863445672007765209508248948e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.66910215394634235102738946034485 y2[1] (numeric) = -0.66910215394634235102738946034481 absolute error = 4e-32 relative error = 5.9781603995864195532435384423453e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=740.0MB, alloc=4.5MB, time=44.80 x[1] = 0.734 y1[1] (analytic) = -0.74250096953085577713861672188964 y1[1] (numeric) = -0.74250096953085577713861672188963 absolute error = 1e-32 relative error = 1.3467995881969598587254286818316e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.66984498971458999849158485776852 y2[1] (numeric) = -0.66984498971458999849158485776848 absolute error = 4e-32 relative error = 5.9715308189501195195086868107639e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=743.8MB, alloc=4.5MB, time=45.04 x[1] = 0.735 y1[1] (analytic) = -0.74183075340232818528865932041883 y1[1] (numeric) = -0.74183075340232818528865932041882 absolute error = 1e-32 relative error = 1.3480163708684304434182711974633e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.67058715563790375177973063228011 y2[1] (numeric) = -0.67058715563790375177973063228008 absolute error = 3e-32 relative error = 4.4736914132305672678675986236346e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=747.6MB, alloc=4.5MB, time=45.27 x[1] = 0.736 y1[1] (analytic) = -0.74115979544310901033790618335927 y1[1] (numeric) = -0.74115979544310901033790618335926 absolute error = 1e-32 relative error = 1.3492367046193338902099365869454e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.67132865097411774942523171030799 y2[1] (numeric) = -0.67132865097411774942523171030796 absolute error = 3e-32 relative error = 4.4687501354916272011796261628125e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=751.5MB, alloc=4.5MB, time=45.51 x[1] = 0.737 y1[1] (analytic) = -0.74048809632415615559237085697158 y1[1] (numeric) = -0.74048809632415615559237085697158 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.67206947498173671700536640447498 y2[1] (numeric) = -0.67206947498173671700536640447495 absolute error = 3e-32 relative error = 4.4638242200801101477933105770503e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.738 y1[1] (analytic) = -0.73981565671716868402998337321739 y1[1] (numeric) = -0.73981565671716868402998337321739 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.67280962691993670863649904504927 y2[1] (numeric) = -0.67280962691993670863649904504923 absolute error = 4e-32 relative error = 5.9452181418860609322306790613549e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=755.3MB, alloc=4.5MB, time=45.74 TOP MAIN SOLVE Loop x[1] = 0.739 y1[1] (analytic) = -0.73914247729458614660158324674932 y1[1] (numeric) = -0.73914247729458614660158324674931 absolute error = 1e-32 relative error = 1.3529191336157626424229708466991e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.67354910604856584779796412825327 y2[1] (numeric) = -0.67354910604856584779796412825323 absolute error = 4e-32 relative error = 5.9386909789938648330639182476479e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=759.1MB, alloc=4.5MB, time=45.97 x[1] = 0.74 y1[1] (analytic) = -0.73846855872958790979142456069883 y1[1] (numeric) = -0.73846855872958790979142456069883 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.67428791162814506748388115760817 y2[1] (numeric) = -0.67428791162814506748388115760814 absolute error = 3e-32 relative error = 4.4491380436528334605194900702897e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=762.9MB, alloc=4.5MB, time=46.20 x[1] = 0.741 y1[1] (analytic) = -0.73779390169609248243786558070087 y1[1] (numeric) = -0.73779390169609248243786558070087 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.67502604291986884968216002656091 y2[1] (numeric) = -0.67502604291986884968216002656088 absolute error = 3e-32 relative error = 4.4442729750444972177418708385651e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=766.7MB, alloc=4.5MB, time=46.43 x[1] = 0.742 y1[1] (analytic) = -0.73711850686875684181491607640942 y1[1] (numeric) = -0.73711850686875684181491607640942 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.67576349918560596417995746344981 y2[1] (numeric) = -0.67576349918560596417995746344977 absolute error = 4e-32 relative error = 5.9192306255377600567081402798996e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=770.5MB, alloc=4.5MB, time=46.67 x[1] = 0.743 y1[1] (analytic) = -0.73644237492297575897531626890064 y1[1] (numeric) = -0.73644237492297575897531626890064 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.67650027968790020669484573341403 y2[1] (numeric) = -0.676500279687900206694845733414 absolute error = 3e-32 relative error = 4.4345879670353336555976767611827e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.744 y1[1] (analytic) = -0.73576550653488112335582206082836 y1[1] (numeric) = -0.73576550653488112335582206082836 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.67723638368997113633095546613973 y2[1] (numeric) = -0.6772363836899711363309554661397 absolute error = 3e-32 relative error = 4.4297679100675074059160819995172e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=774.3MB, alloc=4.5MB, time=46.90 x[1] = 0.745 y1[1] (analytic) = -0.73508790238134126664537194399042 y1[1] (numeric) = -0.73508790238134126664537194399042 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.67797181045571481235935515336133 y2[1] (numeric) = -0.6779718104557148123593551533613 absolute error = 3e-32 relative error = 4.4249627399456017725405899014717e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=778.2MB, alloc=4.5MB, time=47.13 x[1] = 0.746 y1[1] (analytic) = -0.73440956313996028591681171608261 y1[1] (numeric) = -0.7344095631399602859168117160826 absolute error = 1e-32 relative error = 1.3616380425719276074383377393056e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.67870655924970453032193053580006 y2[1] (numeric) = -0.67870655924970453032193053580003 absolute error = 3e-32 relative error = 4.4201723986820391509508608207422e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=782.0MB, alloc=4.5MB, time=47.36 x[1] = 0.747 y1[1] (analytic) = -0.73373048948907736602285387485905 y1[1] (numeric) = -0.73373048948907736602285387485905 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.67944062933719155745802777572154 y2[1] (numeric) = -0.6794406293371915574580277757215 absolute error = 4e-32 relative error = 5.8871957714717223493520794075237e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=785.8MB, alloc=4.5MB, time=47.60 x[1] = 0.748 y1[1] (analytic) = -0.73305068210776610125694929368327 y1[1] (numeric) = -0.73305068210776610125694929368327 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.68017401998410586745312498853057 y2[1] (numeric) = -0.68017401998410586745312498853053 absolute error = 4e-32 relative error = 5.8808479631337153645093166053926e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.749 y1[1] (analytic) = -0.73237014167583381627974951754159 y1[1] (numeric) = -0.73237014167583381627974951754159 absolute error = 0 relative error = 0 % memory used=789.6MB, alloc=4.5MB, time=47.83 Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.6809067304570568745087973847929 y2[1] (numeric) = -0.68090673045705687450879738479286 absolute error = 4e-32 relative error = 5.8745196971617689664704517534208e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.75 y1[1] (analytic) = -0.73168886887382088631183875300008 y1[1] (numeric) = -0.73168886887382088631183875300009 absolute error = 1e-32 relative error = 1.3667011246722261352150686601568e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.68163876002333416673324195277989 y2[1] (numeric) = -0.68163876002333416673324195277986 absolute error = 3e-32 relative error = 4.4011581734250303509177349886343e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=793.4MB, alloc=4.5MB, time=48.06 x[1] = 0.751 y1[1] (analytic) = -0.73100686438300005659341535931644 y1[1] (numeric) = -0.73100686438300005659341535931645 absolute error = 1e-32 relative error = 1.3679762102426237054576128479217e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.68237010795090823885162829107258 y2[1] (numeric) = -0.68237010795090823885162829107254 absolute error = 4e-32 relative error = 5.8619214901010465271766385039930e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=797.2MB, alloc=4.5MB, time=48.29 x[1] = 0.752 y1[1] (analytic) = -0.73032412888537576111160338096846 y1[1] (numeric) = -0.73032412888537576111160338096847 absolute error = 1e-32 relative error = 1.3692550477911839849634210873016e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.6831007735084312242355428809353 y2[1] (numeric) = -0.68310077350843122423554288093527 absolute error = 3e-32 relative error = 4.3917385491922185146052724187920e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=801.1MB, alloc=4.5MB, time=48.52 x[1] = 0.753 y1[1] (analytic) = -0.72964066306368344059607539423096 y1[1] (numeric) = -0.72964066306368344059607539423097 absolute error = 1e-32 relative error = 1.3705376504115142044315224651556e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.68383075596523762625079476907575 y2[1] (numeric) = -0.68383075596523762625079476907572 absolute error = 3e-32 relative error = 4.3870504124451873675217155085914e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=804.9MB, alloc=4.5MB, time=48.75 x[1] = 0.754 y1[1] (analytic) = -0.72895646760138885978366867212136 y1[1] (numeric) = -0.72895646760138885978366867212136 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.68456005459134504892285131304652 y2[1] (numeric) = -0.68456005459134504892285131304649 absolute error = 3e-32 relative error = 4.3823766518057789922395183867584e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.755 y1[1] (analytic) = -0.72827154318268742395267740304088 y1[1] (numeric) = -0.72827154318268742395267740304088 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.68528866865745492691917332391348 y2[1] (numeric) = -0.68528866865745492691917332391345 absolute error = 3e-32 relative error = 4.3777172120433315705772683994324e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=808.7MB, alloc=4.5MB, time=48.98 x[1] = 0.756 y1[1] (analytic) = -0.72758589049250349472750442876228 y1[1] (numeric) = -0.72758589049250349472750442876228 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.68601659743495325484771962391653 y2[1] (numeric) = -0.6860165974349532548477196239165 absolute error = 3e-32 relative error = 4.3730720382234689334945504599883e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=812.5MB, alloc=4.5MB, time=49.21 x[1] = 0.757 y1[1] (analytic) = -0.72689951021648970515435669705521 y1[1] (numeric) = -0.7268995102164897051543566970552 absolute error = 1e-32 relative error = 1.3757059757849799883937507515178e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.68674384019591131587089172067901 y2[1] (numeric) = -0.68674384019591131587089172067898 absolute error = 3e-32 relative error = 4.3684410757061511619149786726501e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=816.3MB, alloc=4.5MB, time=49.45 x[1] = 0.758 y1[1] (analytic) = -0.72621240304102627404866935319676 y1[1] (numeric) = -0.72621240304102627404866935319675 absolute error = 1e-32 relative error = 1.3770076024761952581711971469885e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.68747039621308640963418998408183 y2[1] (numeric) = -0.6874703962130864096341899840818 absolute error = 3e-32 relative error = 4.3638242701437406389795012336708e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=820.1MB, alloc=4.5MB, time=49.68 x[1] = 0.759 y1[1] (analytic) = -0.72552456965322031961494412288604 y1[1] (numeric) = -0.72552456965322031961494412288603 absolute error = 1e-32 relative error = 1.3783130741912309976470940107383e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.68819626475992257950885339720676 y2[1] (numeric) = -0.68819626475992257950885339720673 absolute error = 3e-32 relative error = 4.3592215674790834112849349931250e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=823.9MB, alloc=4.5MB, time=49.91 x[1] = 0.76 y1[1] (analytic) = -0.72483601074090517233968836666701 y1[1] (numeric) = -0.724836010740905172339688366667 absolute error = 1e-32 relative error = 1.3796224044909559951870120177153e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.68892144511055133914775563876973 y2[1] (numeric) = -0.68892144511055133914775563876969 absolute error = 4e-32 relative error = 5.8061772185914742908830794190411e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.761 y1[1] (analytic) = -0.72414672699263968715814191286342 y1[1] (numeric) = -0.72414672699263968715814191286341 absolute error = 1e-32 relative error = 1.3809356070046341838703295024502e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.68964593653979239835383094120862 y2[1] (numeric) = -0.68964593653979239835383094120859 absolute error = 3e-32 relative error = 4.3500582560554255495314897565865e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=827.8MB, alloc=4.5MB, time=50.13 x[1] = 0.762 y1[1] (analytic) = -0.72345671909770755489547950224168 y1[1] (numeric) = -0.72345671909770755489547950224167 absolute error = 1e-32 relative error = 1.3822526954303446988676251224651e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.69036973832315438826030385606026 y2[1] (numeric) = -0.69036973832315438826030385606023 absolute error = 3e-32 relative error = 4.3454975406174790943329321234601e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=831.6MB, alloc=4.5MB, time=50.37 x[1] = 0.763 y1[1] (analytic) = -0.72276598774611661298317740314174 y1[1] (numeric) = -0.72276598774611661298317740314173 absolute error = 1e-32 relative error = 1.3835736835354050624796556890293e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.69109284973683558582199774645707 y2[1] (numeric) = -0.69109284973683558582199774645705 absolute error = 2e-32 relative error = 2.8939671431437746286563639618862e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=835.4MB, alloc=4.5MB, time=50.60 x[1] = 0.764 y1[1] (analytic) = -0.72207453362859815545123348065203 y1[1] (numeric) = -0.72207453362859815545123348065202 absolute error = 1e-32 relative error = 1.3848985851567975239523010317893e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.69181527005772463761699751549553 y2[1] (numeric) = -0.69181527005772463761699751549551 absolute error = 2e-32 relative error = 2.8909451504779899391611313797591e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=839.2MB, alloc=4.5MB, time=50.84 x[1] = 0.765 y1[1] (analytic) = -0.72138235743660624219693072755086 y1[1] (numeric) = -0.72138235743660624219693072755086 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.69253699856340128295794276887376 y2[1] (numeric) = -0.69253699856340128295794276887374 absolute error = 2e-32 relative error = 2.8879323475118295561677584315777e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.766 y1[1] (analytic) = -0.72068945986231700753083498819317 y1[1] (numeric) = -0.72068945986231700753083498819317 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.69325803453213707631222830056559 y2[1] (numeric) = -0.69325803453213707631222830056557 absolute error = 2e-32 relative error = 2.8849286995278045006601901813843e-30 % Correct digits = 31 h = 0.001 memory used=843.0MB, alloc=4.5MB, time=51.07 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.767 y1[1] (analytic) = -0.71999584159862796800071832928725 y1[1] (numeric) = -0.71999584159862796800071832928725 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.69397837724289610903038948139061 y2[1] (numeric) = -0.69397837724289610903038948139059 absolute error = 2e-32 relative error = 2.8819341719922051737663522332970e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=846.8MB, alloc=4.5MB, time=51.30 x[1] = 0.768 y1[1] (analytic) = -0.71930150333915732949410023358049 y1[1] (numeric) = -0.71930150333915732949410023358049 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.69469802597533573038195082215509 y2[1] (numeric) = -0.69469802597533573038195082215507 absolute error = 2e-32 relative error = 2.8789487305539100059382089727785e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=850.6MB, alloc=4.5MB, time=51.54 x[1] = 0.769 y1[1] (analytic) = -0.71860644577824329362009951385514 y1[1] (numeric) = -0.71860644577824329362009951385514 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.69541698000980726789801667557526 y2[1] (numeric) = -0.69541698000980726789801667557524 absolute error = 2e-32 relative error = 2.8759723410432034155739238993246e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=854.5MB, alloc=4.5MB, time=51.77 x[1] = 0.77 y1[1] (analytic) = -0.71791066961094336337129056532434 y1[1] (numeric) = -0.71791066961094336337129056532434 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.69613523862735674701988373445221 y2[1] (numeric) = -0.69613523862735674701988373445219 absolute error = 2e-32 relative error = 2.8730049694706029924906087380248e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=858.3MB, alloc=4.5MB, time=52.00 x[1] = 0.771 y1[1] (analytic) = -0.71721417553303364806625829451439 y1[1] (numeric) = -0.71721417553303364806625829451439 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.69685280110972561005295567754602 y2[1] (numeric) = -0.696852801109725610052955677546 absolute error = 2e-32 relative error = 2.8700465820256958225340192452756e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.772 y1[1] (analytic) = -0.71651696424100816757354678202036 y1[1] (numeric) = -0.71651696424100816757354678202036 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.69756966673935143442524100929425 y2[1] (numeric) = -0.69756966673935143442524100929423 absolute error = 2e-32 relative error = 2.8670971450759838704791931171554e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=862.1MB, alloc=4.5MB, time=52.23 x[1] = 0.773 y1[1] (analytic) = -0.71581903643207815581769745512838 y1[1] (numeric) = -0.71581903643207815581769745512838 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.69828583479936865024971583493689 y2[1] (numeric) = -0.69828583479936865024971583493687 absolute error = 2e-32 relative error = 2.8641566251657383392335615596497e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=865.9MB, alloc=4.5MB, time=52.46 x[1] = 0.774 y1[1] (analytic) = -0.71512039280417136356807326420846 y1[1] (numeric) = -0.71512039280417136356807326420846 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.69900130457360925718983400874474 y2[1] (numeric) = -0.69900130457360925718983400874472 absolute error = 2e-32 relative error = 2.8612249890148629242016313985396e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=869.7MB, alloc=4.5MB, time=52.70 x[1] = 0.775 y1[1] (analytic) = -0.71442103405593136051116607399548 y1[1] (numeric) = -0.71442103405593136051116607399548 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.69971607534660354062746778990087 y2[1] (numeric) = -0.69971607534660354062746778990085 absolute error = 2e-32 relative error = 2.8583022035177658825080577514550e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=873.5MB, alloc=4.5MB, time=52.93 x[1] = 0.776 y1[1] (analytic) = -0.71372096088671683660708519739286 y1[1] (numeric) = -0.71372096088671683660708519739286 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.70043014640358078713256283815412 y2[1] (numeric) = -0.7004301464035807871325628381541 absolute error = 2e-32 relative error = 2.8553882357422408376039350897018e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=877.3MB, alloc=4.5MB, time=53.16 x[1] = 0.777 y1[1] (analytic) = -0.71302017399660090273092571525215 y1[1] (numeric) = -0.71302017399660090273092571525215 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.70114351703046999923379207964931 y2[1] (numeric) = -0.70114351703046999923379207964929 absolute error = 2e-32 relative error = 2.8524830529283562405995520217707e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.778 y1[1] (analytic) = -0.71231867408637039059971594070188 y1[1] (numeric) = -0.71231867408637039059971594070188 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.70185618651390060948949367233982 y2[1] (numeric) = -0.7018561865139006094894936723398 absolute error = 2e-32 relative error = 2.8495866224873534104758056048059e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=881.2MB, alloc=4.5MB, time=53.39 x[1] = 0.779 y1[1] (analytic) = -0.71161646185752515198564410101998 y1[1] (numeric) = -0.71161646185752515198564410101998 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.70256815414120319385817900010418 y2[1] (numeric) = -0.70256815414120319385817900010415 absolute error = 3e-32 relative error = 4.2700483680008296141891139474849e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=885.0MB, alloc=4.5MB, time=53.62 x[1] = 0.78 y1[1] (analytic) = -0.71091353801227735721626502376456 y1[1] (numeric) = -0.71091353801227735721626502376456 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.70327941920041018436789732511792 y2[1] (numeric) = -0.70327941920041018436789732511789 absolute error = 3e-32 relative error = 4.2657298338274055159561119486760e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=888.8MB, alloc=4.5MB, time=53.86 x[1] = 0.781 y1[1] (analytic) = -0.71020990325355079296238832689801 y1[1] (numeric) = -0.710209903253550792962388326898 absolute error = 1e-32 relative error = 1.4080344351985074368036091125514e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7039899809802565810837444291757 y2[1] (numeric) = -0.70398998098025658108374442917567 absolute error = 3e-32 relative error = 4.2614242830881070235016775996123e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=892.6MB, alloc=4.5MB, time=54.09 x[1] = 0.782 y1[1] (analytic) = -0.70950555828498015931435032495762 y1[1] (numeric) = -0.70950555828498015931435032495761 absolute error = 1e-32 relative error = 1.4094322282931852368071629590089e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.70469983877018066337280327651411 y2[1] (numeric) = -0.70469983877018066337280327651408 absolute error = 3e-32 relative error = 4.2571316679105572718228417434928e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.783 y1[1] (analytic) = -0.70880050381091036614737257494236 y1[1] (numeric) = -0.70880050381091036614737257494235 absolute error = 1e-32 relative error = 1.4108342116342148149836444679748e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.70540899186032470046580543325401 y2[1] (numeric) = -0.70540899186032470046580543325398 absolute error = 3e-32 relative error = 4.2528519406710630202567808887299e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=896.4MB, alloc=4.5MB, time=54.32 TOP MAIN SOLVE Loop x[1] = 0.784 y1[1] (analytic) = -0.7080947405363958287767106964985 y1[1] (numeric) = -0.70809474053639582877671069649849 absolute error = 1e-32 relative error = 1.4122404005465146371753847564895e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.70611743954153566131480268186001 y2[1] (numeric) = -0.70611743954153566131480268185998 absolute error = 3e-32 relative error = 4.2485850539930365367080167815956e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=900.2MB, alloc=4.5MB, time=54.55 x[1] = 0.785 y1[1] (analytic) = -0.70738826916719976290329781119664 y1[1] (numeric) = -0.70738826916719976290329781119663 absolute error = 1e-32 relative error = 1.4136508104344007995802845111018e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.70682518110536592374613897300473 y2[1] (numeric) = -0.7068251811053659237461389730047 absolute error = 3e-32 relative error = 4.2443309607454295656123777820601e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=904.0MB, alloc=4.5MB, time=54.78 x[1] = 0.786 y1[1] (analytic) = -0.70668109040979347885058765519795 y1[1] (numeric) = -0.70668109040979347885058765519794 absolute error = 1e-32 relative error = 1.4150654567820902122398256828700e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.707532215844073982908013561925 y2[1] (numeric) = -0.70753221584407398290801356192497 absolute error = 3e-32 relative error = 4.2400896140411792720835472155990e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=907.9MB, alloc=4.5MB, time=55.02 x[1] = 0.787 y1[1] (analytic) = -0.70597320497135567509330312840764 y1[1] (numeric) = -0.70597320497135567509330312840763 absolute error = 1e-32 relative error = 1.4164843551542076417677780378816e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.70823854305062515901192688176582 y2[1] (numeric) = -0.70823854305062515901192688176579 absolute error = 3e-32 relative error = 4.2358609672356660557815476056666e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=911.7MB, alloc=4.5MB, time=55.25 x[1] = 0.788 y1[1] (analytic) = -0.70526461355977173107879675130834 y1[1] (numeric) = -0.70526461355977173107879675130833 absolute error = 1e-32 relative error = 1.4179075211962966478091299447353e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.70894416201869230436730141252522 y2[1] (numeric) = -0.70894416201869230436730141252519 absolute error = 3e-32 relative error = 4.2316449739251831291235447502941e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.789 y1[1] (analytic) = -0.70455531688363299934173020805386 y1[1] (numeric) = -0.70455531688363299934173020805385 absolute error = 1e-32 relative error = 1.4193349706353344480717719138876e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.70964907204265650970857051103813 y2[1] (numeric) = -0.7096490720426565097085705110381 absolute error = 3e-32 relative error = 4.2274415879454177555260602801835e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=915.5MB, alloc=4.5MB, time=55.48 x[1] = 0.79 y1[1] (analytic) = -0.70384531565223609691278086108495 y1[1] (numeric) = -0.70384531565223609691278086108494 absolute error = 1e-32 relative error = 1.4207667192802507471305291751001e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7103532724176078098140288749692 y2[1] (numeric) = -0.71035327241760780981402887496917 absolute error = 3e-32 relative error = 4.2232507633699440444242117090390e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=919.3MB, alloc=4.5MB, time=55.71 x[1] = 0.791 y1[1] (analytic) = -0.70313461057558219602208382850135 y1[1] (numeric) = -0.70313461057558219602208382850134 absolute error = 1e-32 relative error = 1.4222027830224505645643281652602e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.71105676243934588841573902202295 y2[1] (numeric) = -0.71105676243934588841573902202292 absolute error = 3e-32 relative error = 4.2190724545087272008581089734547e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=923.1MB, alloc=4.5MB, time=55.95 x[1] = 0.792 y1[1] (analytic) = -0.7024232023643763140981189206891 y1[1] (numeric) = -0.70242320236437631409811892068908 absolute error = 2e-32 relative error = 2.8472863556726821967052882267401e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.71175954140438078239978887452354 y2[1] (numeric) = -0.71175954140438078239978887452351 absolute error = 3e-32 relative error = 4.2149066159066391284491778355392e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=926.9MB, alloc=4.5MB, time=56.18 x[1] = 0.793 y1[1] (analytic) = -0.70171109173002660306275243725682 y1[1] (numeric) = -0.7017110917300266030627524372568 absolute error = 2e-32 relative error = 2.8501758395597253196539332292484e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7124616086099335852961962491652 y2[1] (numeric) = -0.71246160860993358529619624916517 absolute error = 3e-32 relative error = 4.2107532023419852856101029573463e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=930.8MB, alloc=4.5MB, time=56.41 x[1] = 0.794 y1[1] (analytic) = -0.70099827938464363792314452918013 y1[1] (numeric) = -0.70099827938464363792314452918011 absolute error = 2e-32 relative error = 2.8530740499900474336937832064312e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.71316296335393715005775676208747 y2[1] (numeric) = -0.71316296335393715005775676208744 absolute error = 3e-32 relative error = 4.2066121688250426958414345493380e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.795 y1[1] (analytic) = -0.70028476604103970466123353418745 y1[1] (numeric) = -0.70028476604103970466123353418743 absolute error = 2e-32 relative error = 2.8559810194168801644973133149726e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.71386360493503679112713237048599 y2[1] (numeric) = -0.71386360493503679112713237048596 absolute error = 3e-32 relative error = 4.2024834705966090139658278005648e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=934.6MB, alloc=4.5MB, time=56.64 x[1] = 0.796 y1[1] (analytic) = -0.69957055241272808742150939584346 y1[1] (numeric) = -0.69957055241272808742150939584344 absolute error = 2e-32 relative error = 2.8588967804637565699930761569864e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.71456353265259098579147848372865 y2[1] (numeric) = -0.71456353265259098579147848372862 absolute error = 3e-32 relative error = 4.1983670631265625511375273596097e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=938.4MB, alloc=4.5MB, time=56.88 x[1] = 0.797 y1[1] (analytic) = -0.69885563921392235499778897849759 y1[1] (numeric) = -0.69885563921392235499778897849756 absolute error = 3e-32 relative error = 4.2927320488884094855637383409709e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.71526274580667207482390828940861 y2[1] (numeric) = -0.71526274580667207482390828940858 absolute error = 3e-32 relative error = 4.1942629021124331624402115150825e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=942.2MB, alloc=4.5MB, time=57.11 x[1] = 0.798 y1[1] (analytic) = -0.6981400271595356466197067912625 y1[1] (numeric) = -0.69814002715953564661970679126247 absolute error = 3e-32 relative error = 4.2971322131547891233630398959572e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.71596124369806696241109365292809 y2[1] (numeric) = -0.71596124369806696241109365292806 absolute error = 3e-32 relative error = 4.1901709434779839018508120336935e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=946.0MB, alloc=4.5MB, time=57.34 x[1] = 0.799 y1[1] (analytic) = -0.69742371696517995703963533447258 y1[1] (numeric) = -0.69742371696517995703963533447255 absolute error = 3e-32 relative error = 4.3015457132063376710915856945082e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.71665902562827781536630266307047 y2[1] (numeric) = -0.71665902562827781536630266307044 absolute error = 3e-32 relative error = 4.1860911433718033503005635417634e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.8 y1[1] (analytic) = -0.69670670934716542092074998164232 y1[1] (numeric) = -0.6967067093471654209207499816423 absolute error = 2e-32 relative error = 2.8706483993444796009939048163257e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.71735609089952276162717461058139 y2[1] (numeric) = -0.71735609089952276162717461058135 absolute error = 4e-32 relative error = 5.5760312775545446980099289044278e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=949.8MB, alloc=4.5MB, time=57.57 TOP MAIN SOLVE Loop x[1] = 0.801 y1[1] (analytic) = -0.69598900502249959652695400880021 y1[1] (numeric) = -0.69598900502249959652695400880018 absolute error = 3e-32 relative error = 4.3104129208233935368230483610303e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.71805243881473658803753390204202 y2[1] (numeric) = -0.71805243881473658803753390204198 absolute error = 4e-32 relative error = 5.5706237926058110229153412476437e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=953.6MB, alloc=4.5MB, time=57.81 x[1] = 0.802 y1[1] (analytic) = -0.69527060470888674871538008121325 y1[1] (numeric) = -0.69527060470888674871538008121322 absolute error = 3e-32 relative error = 4.3148667291293220750741653556910e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.71874806867757143741254512727889 y2[1] (numeric) = -0.71874806867757143741254512727885 absolute error = 4e-32 relative error = 5.5652323454025027308885043082506e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=957.5MB, alloc=4.5MB, time=58.04 x[1] = 0.803 y1[1] (analytic) = -0.69455150912472713123218520494112 y1[1] (numeric) = -0.69455150912472713123218520494109 absolute error = 3e-32 relative error = 4.3193340747046909835864437723527e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.71944297979239750488651221521307 y2[1] (numeric) = -0.71944297979239750488651221521303 absolute error = 4e-32 relative error = 5.5598568786566520678025228052317e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=961.3MB, alloc=4.5MB, time=58.27 x[1] = 0.804 y1[1] (analytic) = -0.69383171898911626831235684736494 y1[1] (numeric) = -0.69383171898911626831235684736491 absolute error = 3e-32 relative error = 4.3238150085886448820891731017386e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.72013717146430373354262533040782 y2[1] (numeric) = -0.72013717146430373354262533040778 absolute error = 4e-32 relative error = 5.5544973353708833191652246812700e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=965.1MB, alloc=4.5MB, time=58.50 x[1] = 0.805 y1[1] (analytic) = -0.69311123502184423558424862682483 y1[1] (numeric) = -0.6931112350218442355842486268248 absolute error = 3e-32 relative error = 4.3283095820910353383713982112350e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.72083064299909850932395988062557 y2[1] (numeric) = -0.72083064299909850932395988062554 absolute error = 3e-32 relative error = 4.1618652441274640466588992444147e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.806 y1[1] (analytic) = -0.69239005794339494027956466677061 y1[1] (numeric) = -0.69239005794339494027956466677057 absolute error = 4e-32 relative error = 5.7770904623922438681724548067820e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.72152339370331035522503272445332 y2[1] (numeric) = -0.72152339370331035522503272445328 absolute error = 4e-32 relative error = 5.5438257926322978033756973773288e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=968.9MB, alloc=4.5MB, time=58.73 x[1] = 0.807 y1[1] (analytic) = -0.69166818847494540074951240438124 y1[1] (numeric) = -0.6916681884749454007495124043812 absolute error = 4e-32 relative error = 5.7831198060728706611012706920107e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.72221542288418862476322138749789 y2[1] (numeric) = -0.72221542288418862476322138749785 absolute error = 4e-32 relative error = 5.5385136806216098851166476406452e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=972.7MB, alloc=4.5MB, time=58.97 x[1] = 0.808 y1[1] (analytic) = -0.69094562733836502528784433744029 y1[1] (numeric) = -0.69094562733836502528784433744026 absolute error = 3e-32 relative error = 4.3418756575050458107199648211203e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.72290672984970419472935281578983 y2[1] (numeric) = -0.7229067298497041947293528157898 absolute error = 3e-32 relative error = 4.1499129502138049104280312701175e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=976.5MB, alloc=4.5MB, time=59.20 x[1] = 0.809 y1[1] (analytic) = -0.69022237525621489026150988636545 y1[1] (numeric) = -0.69022237525621489026150988636542 absolute error = 3e-32 relative error = 4.3464253080558003015573550820762e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7235973139085501572167689158648 y2[1] (numeric) = -0.72359731390855015721676891586477 absolute error = 3e-32 relative error = 4.1459523720387202717141442537959e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=980.3MB, alloc=4.5MB, time=59.43 x[1] = 0.81 y1[1] (analytic) = -0.6894984329517470175496392406801 y1[1] (numeric) = -0.68949843295174701754963924068007 absolute error = 3e-32 relative error = 4.3509888588970124447695049767235e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.72428717437014251092817685251454 y2[1] (numeric) = -0.72428717437014251092817685251451 absolute error = 3e-32 relative error = 4.1420034844726774493234715007737e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=984.2MB, alloc=4.5MB, time=59.66 x[1] = 0.811 y1[1] (analytic) = -0.68877380114890365129158175088298 y1[1] (numeric) = -0.68877380114890365129158175088295 absolute error = 3e-32 relative error = 4.3555663630002678703896653204879e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.72497631054462085175959279741491 y2[1] (numeric) = -0.72497631054462085175959279741488 absolute error = 3e-32 relative error = 4.1380662462561333022404053466002e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.812 y1[1] (analytic) = -0.68804848057231653394472211761713 y1[1] (numeric) = -0.6880484805723165339447221176171 absolute error = 3e-32 relative error = 4.3601578736204890072829344729829e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.72566472174284906266068854474458 y2[1] (numeric) = -0.72566472174284906266068854474455 absolute error = 3e-32 relative error = 4.1341406163370005116268811233381e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=988.0MB, alloc=4.5MB, time=59.89 x[1] = 0.813 y1[1] (analytic) = -0.68732247194730618165279832026176 y1[1] (numeric) = -0.68732247194730618165279832026172 absolute error = 4e-32 relative error = 5.8196845923970624995799340911329e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.72635240727641600277085113350541 y2[1] (numeric) = -0.72635240727641600277085113350538 absolute error = 3e-32 relative error = 4.1302265538693799433384386721789e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=991.8MB, alloc=4.5MB, time=60.13 x[1] = 0.814 y1[1] (analytic) = -0.68659577599988115892544591656855 y1[1] (numeric) = -0.68659577599988115892544591656851 absolute error = 4e-32 relative error = 5.8258441718125168739482062350494e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.72703936645763619583026634054226 y2[1] (numeric) = -0.72703936645763619583026634054224 absolute error = 2e-32 relative error = 2.7508826788082015846372233398686e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=995.6MB, alloc=4.5MB, time=60.36 x[1] = 0.815 y1[1] (analytic) = -0.68586839345673735262969403373784 y1[1] (numeric) = -0.6858683934567373526296940337378 absolute error = 4e-32 relative error = 5.8320226418952322505760044525357e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.72772559859955051786533763323611 y2[1] (numeric) = -0.72772559859955051786533763323609 absolute error = 2e-32 relative error = 2.7482886459523196806330552986665e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=999.4MB, alloc=4.5MB, time=60.59 x[1] = 0.816 y1[1] (analytic) = -0.68514032504525724529413905937801 y1[1] (numeric) = -0.68514032504525724529413905937797 absolute error = 4e-32 relative error = 5.8382200751879233527468306152115e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7284111030159268841477528965088 y2[1] (numeric) = -0.72841110301592688414775289650878 absolute error = 2e-32 relative error = 2.7457022438553761562553917464141e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.817 y1[1] (analytic) = -0.68441157149350918772652272811398 y1[1] (numeric) = -0.68441157149350918772652272811394 absolute error = 4e-32 relative error = 5.8444365446236981696844419841882e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.72909587902126093542651197513003 y2[1] (numeric) = -0.72909587902126093542651197513001 memory used=1003.2MB, alloc=4.5MB, time=60.83 absolute error = 2e-32 relative error = 2.7431234458282799175597780612408e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.818 y1[1] (analytic) = -0.683682133530246670945441986206 y1[1] (numeric) = -0.68368213353024667094544198620596 absolute error = 4e-32 relative error = 5.8506721235286407341372463919404e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.72977992593077672343222879935612 y2[1] (numeric) = -0.7297799259307767234322287993561 absolute error = 2e-32 relative error = 2.7405522253152658033531871348204e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1007.0MB, alloc=4.5MB, time=61.05 x[1] = 0.819 y1[1] (analytic) = -0.68295201188490759742691870240827 y1[1] (numeric) = -0.68295201188490759742691870240823 absolute error = 4e-32 relative error = 5.8569268856244145407999594543371e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.73046324306042739565302258965564 y2[1] (numeric) = -0.73046324306042739565302258965562 absolute error = 2e-32 relative error = 2.7379885558930861661982361065214e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1010.9MB, alloc=4.5MB, time=61.29 x[1] = 0.82 y1[1] (analytic) = -0.68222120728761355166655797843693 y1[1] (numeric) = -0.68222120728761355166655797843689 absolute error = 4e-32 relative error = 5.8632009050308867979377978218422e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.73114582972689587938131336468772 y2[1] (numeric) = -0.7311458297268958793813133646877 absolute error = 2e-32 relative error = 2.7354324112702083839988580904326e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1014.7MB, alloc=4.5MB, time=61.52 x[1] = 0.821 y1[1] (analytic) = -0.6814897204691690700580244968283 y1[1] (numeric) = -0.68148972046916907005802449682825 absolute error = 5e-32 relative error = 7.3368678203359671332890085986235e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.73182768524759556503083770579453 y2[1] (numeric) = -0.7318276852475955650308377057945 absolute error = 3e-32 relative error = 4.0993256479290273774701589600126e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1018.5MB, alloc=4.5MB, time=61.75 x[1] = 0.822 y1[1] (analytic) = -0.68075755216106091008856702765017 y1[1] (numeric) = -0.68075755216106091008856702765012 absolute error = 5e-32 relative error = 7.3447587678278837051706462364695e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7325088089406709887232014610491 y2[1] (numeric) = -0.73250880894067098872320146104907 absolute error = 3e-32 relative error = 4.0955138878650438040499117202837e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.823 y1[1] (analytic) = -0.68002470309545731885232189848084 y1[1] (numeric) = -0.68002470309545731885232189848079 absolute error = 5e-32 relative error = 7.3526740679274021124503991072678e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.73318920012499851414328680236277 y2[1] (numeric) = -0.73318920012499851414328680236274 absolute error = 3e-32 relative error = 4.0917132978616459673259867464692e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1022.3MB, alloc=4.5MB, time=61.98 x[1] = 0.824 y1[1] (analytic) = -0.67929117400520730088212691429132 y1[1] (numeric) = -0.67929117400520730088212691429127 absolute error = 5e-32 relative error = 7.3606138153087074692163561297901e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.73386885812018701366283178030184 y2[1] (numeric) = -0.73386885812018701366283178030181 absolute error = 3e-32 relative error = 4.0879238392599630405331180786430e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1026.1MB, alloc=4.5MB, time=62.21 x[1] = 0.825 y1[1] (analytic) = -0.67855696562383988530057789535586 y1[1] (numeric) = -0.67855696562383988530057789535581 absolute error = 5e-32 relative error = 7.3685781051605403240512002099803e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.73454778224657854873150125309078 y2[1] (numeric) = -0.73454778224657854873150125309075 absolute error = 3e-32 relative error = 4.0841454735928088832118416370059e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1029.9MB, alloc=4.5MB, time=62.45 x[1] = 0.826 y1[1] (analytic) = -0.67782207868556339229106068207321 y1[1] (numeric) = -0.67782207868556339229106068207316 absolute error = 5e-32 relative error = 7.3765670331896384190426241532792e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.73522597182524904953476879878772 y2[1] (numeric) = -0.73522597182524904953476879878769 absolute error = 3e-32 relative error = 4.0803781625835301179608567696876e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1033.8MB, alloc=4.5MB, time=62.68 x[1] = 0.827 y1[1] (analytic) = -0.67708651392526469888949213560539 y1[1] (numeric) = -0.67708651392526469888949213560534 absolute error = 5e-32 relative error = 7.3845806956242062470946196971304e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.73590342617800899391792995280695 y2[1] (numeric) = -0.73590342617800899391792995280692 absolute error = 3e-32 relative error = 4.0766218681448625878087716819283e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1037.6MB, alloc=4.5MB, time=62.92 x[1] = 0.828 y1[1] (analytic) = -0.67635027207850850409750434253192 y1[1] (numeric) = -0.67635027207850850409750434253187 absolute error = 5e-32 relative error = 7.3926191892174126694104967062694e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.73658014462740408557556784683173 y2[1] (numeric) = -0.7365801446274040855755678468317 absolute error = 3e-32 relative error = 4.0728765523777961234225687479352e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.829 y1[1] (analytic) = -0.67561335388153659331780691027389 y1[1] (numeric) = -0.67561335388153659331780691027384 absolute error = 5e-32 relative error = 7.4006826112509168578430024168150e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.73725612649671593150579305970836 y2[1] (numeric) = -0.73725612649671593150579305970833 absolute error = 3e-32 relative error = 4.0691421775704475500534314376207e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1041.4MB, alloc=4.5MB, time=63.14 x[1] = 0.83 y1[1] (analytic) = -0.67487576007126710211246291786445 y1[1] (numeric) = -0.6748757600712671021124629178644 absolute error = 5e-32 relative error = 7.4087710595384228296657374923848e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.73793137110996271872858022613808 y2[1] (numeric) = -0.73793137110996271872858022613805 absolute error = 3e-32 relative error = 4.0654187061969418647964719051794e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1045.2MB, alloc=4.5MB, time=63.37 x[1] = 0.831 y1[1] (analytic) = -0.67413749138529377928481476372833 y1[1] (numeric) = -0.67413749138529377928481476372828 absolute error = 5e-32 relative error = 7.4168846324292628452136704024338e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.73860587779189989026752468488655 y2[1] (numeric) = -0.73860587779189989026752468488652 absolute error = 3e-32 relative error = 4.0617061009163015154094763396948e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1049.0MB, alloc=4.5MB, time=63.60 x[1] = 0.832 y1[1] (analytic) = -0.67339854856188524928579682848309 y1[1] (numeric) = -0.67339854856188524928579682848304 absolute error = 5e-32 relative error = 7.4250234288120099417694049918137e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.73927964586802082039434318481062 y2[1] (numeric) = -0.73927964586802082039434318481059 absolute error = 3e-32 relative error = 4.0580043245713437125971319456021e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1052.8MB, alloc=4.5MB, time=63.83 x[1] = 0.833 y1[1] (analytic) = -0.67265893233998427394537254638808 y1[1] (numeric) = -0.67265893233998427394537254638803 absolute error = 5e-32 relative error = 7.4331875481181198800364358416256e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.73995267466455748913544340425803 y2[1] (numeric) = -0.73995267466455748913544340425799 absolute error = 4e-32 relative error = 5.4057511202501142777618689561073e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1056.6MB, alloc=4.5MB, time=64.07 x[1] = 0.834 y1[1] (analytic) = -0.67191864345920701352983415394244 y1[1] (numeric) = -0.67191864345920701352983415394239 absolute error = 5e-32 relative error = 7.4413770903256027825414170179311e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.74062496350848115603988777732654 y2[1] (numeric) = -0.7406249635084811560398877773265 absolute error = 4e-32 relative error = 5.4008441479628772977944755526449e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.835 y1[1] (analytic) = -0.67117768265984228712570405827083 y1[1] (numeric) = -0.67117768265984228712570405827078 absolute error = 5e-32 relative error = 7.4495921559627247463449642089756e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.74129651172750303320807785907504 y2[1] (numeric) = -0.741296511727503033208077859075 absolute error = 4e-32 relative error = 5.3959514670836336104825925111761e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1060.5MB, alloc=4.5MB, time=64.30 x[1] = 0.836 y1[1] (analytic) = -0.67043605068285083235097744133388 y1[1] (numeric) = -0.67043605068285083235097744133383 absolute error = 5e-32 relative error = 7.4578328461117397155152075728460e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7419673186500749575804862010582 y2[1] (numeric) = -0.74196731865007495758048620105816 absolute error = 4e-32 relative error = 5.3910730290352201595712683412684e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1064.3MB, alloc=4.5MB, time=64.53 x[1] = 0.837 y1[1] (analytic) = -0.6696937482698645643944463886591 y1[1] (numeric) = -0.66969374826986456439444638865905 absolute error = 5e-32 relative error = 7.4660992624126519019307198534167e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.74263738360539006248576344850885 y2[1] (numeric) = -0.74263738360539006248576344850881 absolute error = 4e-32 relative error = 5.3862087854783398734425139628837e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1068.1MB, alloc=4.5MB, time=64.76 x[1] = 0.838 y1[1] (analytic) = -0.66895077616318583438384650320632 y1[1] (numeric) = -0.66895077616318583438384650320627 absolute error = 5e-32 relative error = 7.4743915070670090461300760810225e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.74330670592338344844754911111696 y2[1] (numeric) = -0.74330670592338344844754911111693 absolute error = 3e-32 relative error = 4.0360190162326153680952507056752e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1071.9MB, alloc=4.5MB, time=64.99 x[1] = 0.839 y1[1] (analytic) = -0.6682071351057866870835676361593 y1[1] (numeric) = -0.66820713510578668708356763615925 absolute error = 5e-32 relative error = 7.4827096828417268131146797988324e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.74397528493473285324931520065042 y2[1] (numeric) = -0.74397528493473285324931520065039 absolute error = 3e-32 relative error = 4.0323920172471626144757758623807e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.84 y1[1] (analytic) = -0.66746282584130811792267103687086 y1[1] (numeric) = -0.66746282584130811792267103687081 absolute error = 5e-32 relative error = 7.4910538930729446212401464520246e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.74464311997085932125657267062965 y2[1] (numeric) = -0.74464311997085932125657267062961 absolute error = 4e-32 relative error = 5.3717007419024230098649252988190e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1075.7MB, alloc=4.5MB, time=65.22 TOP MAIN SOLVE Loop x[1] = 0.841 y1[1] (analytic) = -0.66671784911405932935395589388254 y1[1] (numeric) = -0.66671784911405932935395589388249 absolute error = 5e-32 relative error = 7.4994242416699132056000055417991e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.74531021036392787199577133590554 y2[1] (numeric) = -0.74531021036392787199577133590551 absolute error = 3e-32 relative error = 4.0251695982202210723742011368869e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1079.5MB, alloc=4.5MB, time=65.45 x[1] = 0.842 y1[1] (analytic) = -0.66597220566901698654481890789019 y1[1] (numeric) = -0.66597220566901698654481890789014 absolute error = 5e-32 relative error = 7.5078208331189142206143157004533e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.74597655544684816798922469329651 y2[1] (numeric) = -0.74597655544684816798922469329648 absolute error = 3e-32 relative error = 4.0215741072492110395383514726858e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1083.3MB, alloc=4.5MB, time=65.68 x[1] = 0.843 y1[1] (analytic) = -0.66522589625182447240065120573399 y1[1] (numeric) = -0.66522589625182447240065120573394 absolute error = 5e-32 relative error = 7.5162437724872121898855355647377e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.74664215455327518184539180841532 y2[1] (numeric) = -0.74664215455327518184539180841529 absolute error = 3e-32 relative error = 4.0179890483078007120459325011389e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1087.2MB, alloc=4.5MB, time=65.92 x[1] = 0.844 y1[1] (analytic) = -0.6644789216087911419215175719538 y1[1] (numeric) = -0.66447892160879114192151757195375 absolute error = 5e-32 relative error = 7.5246931654270391147752211835215e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.74730700701760986260384917845964 y2[1] (numeric) = -0.74730700701760986260384917845961 absolute error = 3e-32 relative error = 4.0144143863611688498743921254230e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1091.0MB, alloc=4.5MB, time=66.15 x[1] = 0.845 y1[1] (analytic) = -0.66373128248689157589286364116858 y1[1] (numeric) = -0.66373128248689157589286364116853 absolute error = 5e-32 relative error = 7.5331691181796120565883991956886e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7479711121749998013342862260498 y2[1] (numeric) = -0.74797111217499980133428622604977 absolute error = 3e-32 relative error = 4.0108500865446552589227277715939e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.846 y1[1] (analytic) = -0.66298297963376483391099736051039 y1[1] (numeric) = -0.66298297963376483391099736051034 absolute error = 5e-32 relative error = 7.5416717375791840107283743319058e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.74863446936133989598885882517379 y2[1] (numeric) = -0.74863446936133989598885882517376 absolute error = 3e-32 relative error = 4.0072961141627637758579732143581e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1094.8MB, alloc=4.5MB, time=66.38 x[1] = 0.847 y1[1] (analytic) = -0.66223401379771370674409169656935 y1[1] (numeric) = -0.6622340137977137067440916965693 absolute error = 5e-32 relative error = 7.5502011310571283947038589234993e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.74929707791327301550723600694142 y2[1] (numeric) = -0.74929707791327301550723600694139 absolute error = 3e-32 relative error = 4.0037524346881723397246014676591e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1098.6MB, alloc=4.5MB, time=66.61 x[1] = 0.848 y1[1] (analytic) = -0.66148438572770396802945622578448 y1[1] (numeric) = -0.66148438572770396802945622578443 absolute error = 5e-32 relative error = 7.5587574066460574754332590008922e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.74995893716819066317367574015619 y2[1] (numeric) = -0.74995893716819066317367574015616 absolute error = 3e-32 relative error = 4.0002190137607500918888740713362e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1102.4MB, alloc=4.5MB, time=66.84 x[1] = 0.849 y1[1] (analytic) = -0.66073409617336362530782591094651 y1[1] (numeric) = -0.66073409617336362530782591094646 absolute error = 5e-32 relative error = 7.5673406729839750648983233033213e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.75062004646423363922546642968444 y2[1] (numeric) = -0.75062004646423363922546642968441 absolute error = 3e-32 relative error = 3.9966958171865814464409784983454e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1106.2MB, alloc=4.5MB, time=67.08 x[1] = 0.85 y1[1] (analytic) = -0.65998314588498217039541602946147 y1[1] (numeric) = -0.65998314588498217039541602946142 absolute error = 5e-32 relative error = 7.5759510393184638168517744357460e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.75128040514029270271207152423547 y2[1] (numeric) = -0.75128040514029270271207152423544 absolute error = 3e-32 relative error = 3.9931828109369970737227756632712e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1110.0MB, alloc=4.5MB, time=67.31 x[1] = 0.851 y1[1] (analytic) = -0.65923153561350982909449288125765 y1[1] (numeric) = -0.65923153561350982909449288125761 absolute error = 4e-32 relative error = 6.0676708924087259687852970013575e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.75194001253600923260431537446319 y2[1] (numeric) = -0.75194001253600923260431537446316 absolute error = 3e-32 relative error = 3.9896799611476117401881971574061e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.852 y1[1] (analytic) = -0.65847926611055681024321056570271 y1[1] (numeric) = -0.65847926611055681024321056570267 absolute error = 4e-32 relative error = 6.0746028096325986517433869137239e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7525988679917758881529492322585 y2[1] (numeric) = -0.75259886799177588815294923225848 absolute error = 2e-32 relative error = 2.6574581560782459655579030061111e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1113.9MB, alloc=4.5MB, time=67.53 x[1] = 0.853 y1[1] (analytic) = -0.65772633812839255410546477763153 y1[1] (numeric) = -0.65772633812839255410546477763148 absolute error = 5e-32 relative error = 7.6019458400097804163495903364328e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.75325697084873726849593703272151 y2[1] (numeric) = -0.75325697084873726849593703272149 absolute error = 2e-32 relative error = 2.6551363975383948806595448262732e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1117.7MB, alloc=4.5MB, time=67.77 x[1] = 0.854 y1[1] (analytic) = -0.65697275241994498010151523256845 y1[1] (numeric) = -0.65697275241994498010151523256841 absolute error = 4e-32 relative error = 6.0885325689171829024328336293729e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.75391432044879057151380135158264 y2[1] (numeric) = -0.75391432044879057151380135158262 absolute error = 2e-32 relative error = 2.6528213428940291164632324384628e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1121.5MB, alloc=4.5MB, time=68.00 x[1] = 0.855 y1[1] (analytic) = -0.6562185097387997338801289904588 y1[1] (numeric) = -0.65621850973879973388012899045876 absolute error = 4e-32 relative error = 6.0955305902482912472473049950523e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.75457091613458625193237068278176 y2[1] (numeric) = -0.75457091613458625193237068278173 absolute error = 3e-32 relative error = 3.9757694550009877275792232881475e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1125.3MB, alloc=4.5MB, time=68.23 x[1] = 0.856 y1[1] (analytic) = -0.65546361083919943373299760570348 y1[1] (numeric) = -0.65546361083919943373299760570344 absolute error = 4e-32 relative error = 6.1025508263971249329321214018583e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.75522675724952867867226993351268 y2[1] (numeric) = -0.75522675724952867867226993351265 absolute error = 3e-32 relative error = 3.9723168852302633874516517467777e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.857 y1[1] (analytic) = -0.65470805647604291635218168901687 y1[1] (numeric) = -0.65470805647604291635218168901684 absolute error = 3e-32 relative error = 4.5821950262036771339675404016878e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.75588184313777679144449678729755 y2[1] (numeric) = -0.75588184313777679144449678729752 absolute error = 3e-32 relative error = 3.9688742721303615664958712158781e-30 % Correct digits = 31 h = 0.001 memory used=1129.1MB, alloc=4.5MB, time=68.47 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.858 y1[1] (analytic) = -0.65395184740488448193133712360054 y1[1] (numeric) = -0.65395184740488448193133712360051 absolute error = 3e-32 relative error = 4.5874937304712513145863021174410e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.75653617314424475659142733956925 y2[1] (numeric) = -0.75653617314424475659142733956922 absolute error = 3e-32 relative error = 3.9654415829605094693711849629261e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1132.9MB, alloc=4.5MB, time=68.70 x[1] = 0.859 y1[1] (analytic) = -0.65319498438193313861147783434356 y1[1] (numeric) = -0.65319498438193313861147783434353 absolute error = 3e-32 relative error = 4.5928093015574258120943913848476e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.75718974661460262217259516481102 y2[1] (numeric) = -0.75718974661460262217259516481098 absolute error = 4e-32 relative error = 5.2826917135156817360596192225247e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1136.8MB, alloc=4.5MB, time=68.93 x[1] = 0.86 y1[1] (analytic) = -0.65243746816405184627203066422386 y1[1] (numeric) = -0.65243746816405184627203066422383 absolute error = 3e-32 relative error = 4.5981418088111186570356829178024e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.75784256289527697229458872952865 y2[1] (numeric) = -0.75784256289527697229458872952861 absolute error = 4e-32 relative error = 5.2781411283081271322218975196752e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1140.6MB, alloc=4.5MB, time=69.16 x[1] = 0.861 y1[1] (analytic) = -0.65167929950875675966793856679259 y1[1] (numeric) = -0.65167929950875675966793856679256 absolute error = 3e-32 relative error = 4.6034913219760609150053489384393e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.75849462133345158068441282121256 y2[1] (numeric) = -0.75849462133345158068441282121253 absolute error = 3e-32 relative error = 3.9552027339705173682836438315414e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1144.4MB, alloc=4.5MB, time=69.39 x[1] = 0.862 y1[1] (analytic) = -0.6509204791742164709135689775753 y1[1] (numeric) = -0.65092047917421647091356897757527 absolute error = 3e-32 relative error = 4.6088579111935745991021006683427e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.75914592127706806350566041998264 y2[1] (numeric) = -0.7591459212770680635056604199826 absolute error = 4e-32 relative error = 5.2690792216482269995625956418811e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.863 y1[1] (analytic) = -0.65016100791925125131418488041842 y1[1] (numeric) = -0.65016100791925125131418488041839 absolute error = 3e-32 relative error = 4.6142416470053741505360447559271e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.75979646207482653141684219679836 y2[1] (numeric) = -0.75979646207482653141684219679832 absolute error = 4e-32 relative error = 5.2645678147499331880457188203681e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1148.2MB, alloc=4.5MB, time=69.62 x[1] = 0.864 y1[1] (analytic) = -0.64940088650333229254573673724674 y1[1] (numeric) = -0.64940088650333229254573673724671 absolute error = 3e-32 relative error = 4.6196426003563917207539329695010e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7604462430761862408712215799592 y2[1] (numeric) = -0.76044624307618624087122157995917 absolute error = 3e-32 relative error = 3.9450520366361272367905389852626e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1152.0MB, alloc=4.5MB, time=69.86 x[1] = 0.865 y1[1] (analytic) = -0.64864011568658094718373410137685 y1[1] (numeric) = -0.64864011568658094718373410137682 absolute error = 3e-32 relative error = 4.6250608425976264910888563623112e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.76109526363136624465750409011438 y2[1] (numeric) = -0.76109526363136624465750409011435 absolute error = 3e-32 relative error = 3.9416879112954764321447287042372e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1155.8MB, alloc=4.5MB, time=70.09 x[1] = 0.866 y1[1] (analytic) = -0.6478786962297679685819563854515 y1[1] (numeric) = -0.64787869622976796858195638545147 absolute error = 3e-32 relative error = 4.6304964454890182686204865298448e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.76174352309134604168073040314686 y2[1] (numeric) = -0.76174352309134604168073040314683 absolute error = 3e-32 relative error = 3.9383334535294090425778227291118e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1159.6MB, alloc=4.5MB, time=70.32 x[1] = 0.867 y1[1] (analytic) = -0.64711662889431275010176290522087 y1[1] (numeric) = -0.64711662889431275010176290522084 absolute error = 3e-32 relative error = 4.6359494812023455996452764812381e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.76239102080786622598272336009272 y2[1] (numeric) = -0.76239102080786622598272336009269 absolute error = 3e-32 relative error = 3.9349886319766142898694335027968e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1163.5MB, alloc=4.5MB, time=70.55 x[1] = 0.868 y1[1] (analytic) = -0.64635391444228256369276296979723 y1[1] (numeric) = -0.6463539144422825636927629697972 absolute error = 3e-32 relative error = 4.6414200223241486449040894982454e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.76303775613342913500143990370295 y2[1] (numeric) = -0.76303775613342913500143990370292 absolute error = 3e-32 relative error = 3.9316534154247052562028460328552e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.869 y1[1] (analytic) = -0.64559055363639179782560743764955 y1[1] (numeric) = -0.64559055363639179782560743764951 absolute error = 4e-32 relative error = 6.1958775224782360846640283464103e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.76368372842129949706857968234979 y2[1] (numeric) = -0.76368372842129949706857968234976 absolute error = 3e-32 relative error = 3.9283277728093710083539690745761e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1167.3MB, alloc=4.5MB, time=70.78 x[1] = 0.87 y1[1] (analytic) = -0.64482654724000119477766380548283 y1[1] (numeric) = -0.64482654724000119477766380548279 absolute error = 4e-32 relative error = 6.2032185509744842069896284561557e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.76432893702550507814480282372285 y2[1] (numeric) = -0.76432893702550507814480282372283 absolute error = 2e-32 relative error = 2.6166744488090230629376485463679e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1171.1MB, alloc=4.5MB, time=71.01 x[1] = 0.871 y1[1] (analytic) = -0.64406189601711708727233754426375 y1[1] (numeric) = -0.64406189601711708727233754426371 absolute error = 4e-32 relative error = 6.2105832137190940187504209894292e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.76497338130083732779191014315134 y2[1] (numeric) = -0.76497338130083732779191014315132 absolute error = 2e-32 relative error = 2.6144700572443445772483017081825e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1174.9MB, alloc=4.5MB, time=71.24 x[1] = 0.872 y1[1] (analytic) = -0.6432966007323906344728030430074 y1[1] (numeric) = -0.64329660073239063447280304300737 absolute error = 3e-32 relative error = 4.6634787073093684479341011354045e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.76561706060285202438133981442577 y2[1] (numeric) = -0.76561706060285202438133981442575 absolute error = 2e-32 relative error = 2.6122719867621373856870182017770e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1178.7MB, alloc=4.5MB, time=71.48 x[1] = 0.873 y1[1] (analytic) = -0.64253066215111705733090816653077 y1[1] (numeric) = -0.64253066215111705733090816653073 absolute error = 4e-32 relative error = 6.2253838386614432317100682230939e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7662599742878699195383352946765 y2[1] (numeric) = -0.76625997428786991953833529467648 absolute error = 2e-32 relative error = 2.6100802170421554838142622056340e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1182.5MB, alloc=4.5MB, time=71.71 x[1] = 0.874 y1[1] (analytic) = -0.64176408103923487329201707820441 y1[1] (numeric) = -0.64176408103923487329201707820438 absolute error = 3e-32 relative error = 4.6746150004873707987513805005772e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.76690212171297738182114005919467 y2[1] (numeric) = -0.76690212171297738182114005919464 absolute error = 3e-32 relative error = 3.9118420917901530582645563241526e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.875 y1[1] (analytic) = -0.64099685816332513035655662279603 y1[1] (numeric) = -0.640996858163325130356556622796 absolute error = 3e-32 relative error = 4.6802101473570781022249973936949e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.76754350223602703963457546705454 y2[1] (numeric) = -0.76754350223602703963457546705451 absolute error = 3e-32 relative error = 3.9085732486306307455793127483892e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1186.3MB, alloc=4.5MB, time=71.94 x[1] = 0.876 y1[1] (analytic) = -0.64022899429061064049903220779546 y1[1] (numeric) = -0.64022899429061064049903220779543 absolute error = 3e-32 relative error = 4.6858233956181151360571926398288e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.768184115215638423377358844013 y2[1] (numeric) = -0.76818411521563842337735884401297 absolute error = 3e-32 relative error = 3.9053137660336341330080894504577e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1190.2MB, alloc=4.5MB, time=72.17 x[1] = 0.877 y1[1] (analytic) = -0.63946049018895521244527976414145 y1[1] (numeric) = -0.63946049018895521244527976414142 absolute error = 3e-32 relative error = 4.6914548217256161635309229120491e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.76882396001119860682251963542151 y2[1] (numeric) = -0.76882396001119860682251963542148 absolute error = 3e-32 relative error = 3.9020636140896315507510330795693e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1194.0MB, alloc=4.5MB, time=72.40 x[1] = 0.878 y1[1] (analytic) = -0.63869134662686288380872100903435 y1[1] (numeric) = -0.63869134662686288380872100903432 absolute error = 3e-32 relative error = 4.6971045025801234607016199904206e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.76946303598286284773027224878795 y2[1] (numeric) = -0.76946303598286284773027224878792 absolute error = 3e-32 relative error = 3.8988227630297951302273112387974e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1197.8MB, alloc=4.5MB, time=72.63 x[1] = 0.879 y1[1] (analytic) = -0.63792156437347715258638987451539 y1[1] (numeric) = -0.63792156437347715258638987451536 absolute error = 3e-32 relative error = 4.7027725155307995069406731116684e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77010134249155522769270497316878 y2[1] (numeric) = -0.77010134249155522769270497316875 absolute error = 3e-32 relative error = 3.8955911832252095840809976470888e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.88 y1[1] (analytic) = -0.63715114419858020801549860572209 y1[1] (numeric) = -0.63715114419858020801549860572207 absolute error = 2e-32 relative error = 3.1389726255857780631344520842366e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77073887889896929120964513075599 y2[1] (numeric) = -0.77073887889896929120964513075597 absolute error = 2e-32 relative error = 2.5949125634573909376318057961271e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1201.6MB, alloc=4.5MB, time=72.86 TOP MAIN SOLVE Loop x[1] = 0.881 y1[1] (analytic) = -0.63638008687259216079131267218969 y1[1] (numeric) = -0.63638008687259216079131267218967 absolute error = 2e-32 relative error = 3.1427758995865850945198813310350e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77137564456756868399506138484697 y2[1] (numeric) = -0.77137564456756868399506138484695 absolute error = 2e-32 relative error = 2.5927704797073223003282575414298e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1205.4MB, alloc=4.5MB, time=73.09 x[1] = 0.882 y1[1] (analytic) = -0.63560839316657027264710427425938 y1[1] (numeric) = -0.63560839316657027264710427425936 absolute error = 2e-32 relative error = 3.1465915514993386617499877931419e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77201163886058779051336489784803 y2[1] (numeric) = -0.77201163886058779051336489784801 absolute error = 2e-32 relative error = 2.5906345180906865604125519784595e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1209.2MB, alloc=4.5MB, time=73.32 x[1] = 0.883 y1[1] (analytic) = -0.63483606385220818529695486457581 y1[1] (numeric) = -0.63483606385220818529695486457579 absolute error = 2e-32 relative error = 3.1504196341082573324015864697931e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77264686114203237074497180306374 y2[1] (numeric) = -0.77264686114203237074497180306373 absolute error = 1e-32 relative error = 1.2942523296113853923792647908356e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1213.0MB, alloc=4.5MB, time=73.56 x[1] = 0.884 y1[1] (analytic) = -0.63406309970183514874217774180693 y1[1] (numeric) = -0.63406309970183514874217774180691 absolute error = 2e-32 relative error = 3.1542602005076301136477207789292e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7732813107766801961804902247626 y2[1] (numeric) = -0.77328131077668019618049022476258 absolute error = 2e-32 relative error = 2.5863808838095533277085494640009e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1216.9MB, alloc=4.5MB, time=73.79 x[1] = 0.885 y1[1] (analytic) = -0.63328950148841524894213241009944 y1[1] (numeric) = -0.63328950148841524894213241009941 absolute error = 3e-32 relative error = 4.7371699561561086997758765857702e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77391498713008168504289585238488 y2[1] (numeric) = -0.77391498713008168504289585238487 absolute error = 1e-32 relative error = 1.2921315863235988036937656907822e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.886 y1[1] (analytic) = -0.63251526998554663485020303339089 y1[1] (numeric) = -0.63251526998554663485020303339086 absolute error = 3e-32 relative error = 4.7429684979282031493003170621054e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77454788956856053673706084677032 y2[1] (numeric) = -0.77454788956856053673706084677031 absolute error = 1e-32 relative error = 1.2910757533107746637076184641791e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1220.7MB, alloc=4.5MB, time=74.02 x[1] = 0.887 y1[1] (analytic) = -0.63174040596746074481571394853584 y1[1] (numeric) = -0.63174040596746074481571394853582 absolute error = 2e-32 relative error = 3.1658573380899347441790084706243e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77518001745921436552600162892925 y2[1] (numeric) = -0.77518001745921436552600162892925 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1224.5MB, alloc=4.5MB, time=74.25 x[1] = 0.888 y1[1] (analytic) = -0.6309649102090215323525558352659 y1[1] (numeric) = -0.63096491020902153235255583526588 absolute error = 2e-32 relative error = 3.1697483768748001170042920782364e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77581137016991533343321187516253 y2[1] (numeric) = -0.77581137016991533343321187516253 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1228.3MB, alloc=4.5MB, time=74.49 x[1] = 0.889 y1[1] (analytic) = -0.63018878348572469127529677429298 y1[1] (numeric) = -0.63018878348572469127529677429296 absolute error = 2e-32 relative error = 3.1736521696522782756043935363141e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77644194706931078237044781624973 y2[1] (numeric) = -0.77644194706931078237044781624973 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1232.1MB, alloc=4.5MB, time=74.72 x[1] = 0.89 y1[1] (analytic) = -0.62941202657369688020355305738025 y1[1] (numeric) = -0.62941202657369688020355305738023 absolute error = 2e-32 relative error = 3.1775687714251565781190693028830e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77707174752682386549033371297318 y2[1] (numeric) = -0.77707174752682386549033371297319 absolute error = 1e-32 relative error = 1.2868824573569776297419516230397e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1235.9MB, alloc=4.5MB, time=74.95 x[1] = 0.891 y1[1] (analytic) = -0.62863464024969494643539524494522 y1[1] (numeric) = -0.6286346402496949464353952449452 absolute error = 2e-32 relative error = 3.1814982375225074583823651874732e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77770077091265417776315615542491 y2[1] (numeric) = -0.77770077091265417776315615542492 absolute error = 1e-32 relative error = 1.2858415953818218490810269496703e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.892 y1[1] (analytic) = -0.6278566252911051491905655977243 y1[1] (numeric) = -0.62785662529110514919056559772428 absolute error = 2e-32 relative error = 3.1854406236020872313462107425496e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77832901659777838577721660935467 y2[1] (numeric) = -0.77832901659777838577721660935468 absolute error = 1e-32 relative error = 1.2848036995603567713274278652274e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1239.7MB, alloc=4.5MB, time=75.18 x[1] = 0.893 y1[1] (analytic) = -0.62707798247594238222428363921666 y1[1] (numeric) = -0.62707798247594238222428363921664 absolute error = 2e-32 relative error = 3.1893959856527561459363439688953e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77895648395395085676211240925914 y2[1] (numeric) = -0.77895648395395085676211240925915 absolute error = 1e-32 relative error = 1.2837687606424962392933258371052e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1243.6MB, alloc=4.5MB, time=75.42 x[1] = 0.894 y1[1] (analytic) = -0.62629871258284939581241723503701 y1[1] (numeric) = -0.626298712582849395812417235037 absolute error = 1e-32 relative error = 1.5966821899984599525329223983828e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.77958317235370428683431717498358 y2[1] (numeric) = -0.77958317235370428683431717498359 absolute error = 1e-32 relative error = 1.2827367694210445396527536769572e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1247.4MB, alloc=4.5MB, time=75.65 x[1] = 0.895 y1[1] (analytic) = -0.62551881639109601810879720394146 y1[1] (numeric) = -0.62551881639109601810879720394144 absolute error = 2e-32 relative error = 3.1973458632929928751327535273905e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.780209081170350328464432406308 y2[1] (numeric) = -0.78020908117035032846443240630801 absolute error = 1e-32 relative error = 1.2817077167314599219070075336885e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1251.2MB, alloc=4.5MB, time=75.88 x[1] = 0.896 y1[1] (analytic) = -0.62473829468057837587545410314681 y1[1] (numeric) = -0.62473829468057837587545410314679 absolute error = 2e-32 relative error = 3.2013404925378832099641408395249e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.78083420977798021716548278831839 y2[1] (numeric) = -0.7808342097779802171654827883184 absolute error = 1e-32 relative error = 1.2806815934516197097182666572943e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.897 y1[1] (analytic) = -0.62395714823181811458655645764182 y1[1] (numeric) = -0.6239571482318181145865564576418 absolute error = 2e-32 relative error = 3.2053483250695001168400939689699e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7814585575514653974016285193201 y2[1] (numeric) = -0.78145855755146539740162851932011 absolute error = 1e-32 relative error = 1.2796583905015869922116855079715e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1255.0MB, alloc=4.5MB, time=76.12 TOP MAIN SOLVE Loop x[1] = 0.898 y1[1] (analytic) = -0.62317537782596161790683032948689 y1[1] (numeric) = -0.62317537782596161790683032948687 absolute error = 2e-32 relative error = 3.2093694185692834949379125592495e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.78208212386645814771666875263308 y2[1] (numeric) = -0.78208212386645814771666875263309 absolute error = 1e-32 relative error = 1.2786380988433788829567750118323e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1258.8MB, alloc=4.5MB, time=76.35 x[1] = 0.899 y1[1] (analytic) = -0.62239298424477922654524074861785 y1[1] (numeric) = -0.62239298424477922654524074861783 absolute error = 2e-32 relative error = 3.2134038310647561792798993314101e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.78270490809939220508171102381767 y2[1] (numeric) = -0.78270490809939220508171102381768 absolute error = 1e-32 relative error = 1.2776207094807363344483455244582e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1262.6MB, alloc=4.5MB, time=76.58 x[1] = 0.9 y1[1] (analytic) = -0.62160996827066445648471615140713 y1[1] (numeric) = -0.62160996827066445648471615140711 absolute error = 2e-32 relative error = 3.2174516209320990260480257246128e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.78332690962748338846138231571355 y2[1] (numeric) = -0.78332690962748338846138231571356 absolute error = 1e-32 relative error = 1.2766062134588954960156456522320e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1266.5MB, alloc=4.5MB, time=76.81 x[1] = 0.901 y1[1] (analytic) = -0.62082633068663321658869759719283 y1[1] (numeric) = -0.62082633068663321658869759719281 absolute error = 2e-32 relative error = 3.2215128468987490779460004892798e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7839481278287302215979581951327 y2[1] (numeric) = -0.78394812782873022159795819513272 absolute error = 2e-32 relative error = 2.5511892037287212063912212891560e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1270.3MB, alloc=4.5MB, time=77.04 x[1] = 0.902 y1[1] (analytic) = -0.62004207227632302558529515616121 y1[1] (numeric) = -0.62004207227632302558529515616118 absolute error = 3e-32 relative error = 4.8383813520690315767166425714325e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.78456856208191455501278723712927 y2[1] (numeric) = -0.78456856208191455501278723712929 absolute error = 2e-32 relative error = 2.5491717316493567734246872110239e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.903 y1[1] (analytic) = -0.61925719382399222842983448436099 y1[1] (numeric) = -0.61925719382399222842983448436096 absolute error = 3e-32 relative error = 4.8445137657176285823575764732050e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.78518821176660218722438873547354 y2[1] (numeric) = -0.78518821176660218722438873547356 absolute error = 2e-32 relative error = 2.5471599930164279786202082633918e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1274.1MB, alloc=4.5MB, time=77.27 x[1] = 0.904 y1[1] (analytic) = -0.61847169611451921204657722323764 y1[1] (numeric) = -0.61847169611451921204657722323761 absolute error = 3e-32 relative error = 4.8506666009894581868691340193637e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.78580707626314348518260248128427 y2[1] (numeric) = -0.78580707626314348518260248128429 absolute error = 2e-32 relative error = 2.5451539702478567575823677474892e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1277.9MB, alloc=4.5MB, time=77.50 x[1] = 0.905 y1[1] (analytic) = -0.61768557993340162045039948190176 y1[1] (numeric) = -0.61768557993340162045039948190173 absolute error = 3e-32 relative error = 4.8568399481228907274745678328002e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7864251549526740039181701757212 y2[1] (numeric) = -0.78642515495267400391817017572122 absolute error = 2e-32 relative error = 2.5431536458423144914262370056121e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1281.7MB, alloc=4.5MB, time=77.74 x[1] = 0.906 y1[1] (analytic) = -0.61689884606675556924921328038782 y1[1] (numeric) = -0.61689884606675556924921328038779 absolute error = 3e-32 relative error = 4.8630338979031991962378405882140e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.78704244721711510540712882720798 y2[1] (numeric) = -0.787042447217115105407128827208 absolute error = 2e-32 relative error = 2.5411590023787827486034641399428e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1285.5MB, alloc=4.5MB, time=77.97 x[1] = 0.907 y1[1] (analytic) = -0.61611149530131485952791645141623 y1[1] (numeric) = -0.6161114953013148595279164514162 absolute error = 3e-32 relative error = 4.8692485416666719708925325259691e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.78765895243917457664939726884371 y2[1] (numeric) = -0.78765895243917457664939726884373 absolute error = 2e-32 relative error = 2.5391700225161169504750881157470e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1289.3MB, alloc=4.5MB, time=78.21 x[1] = 0.908 y1[1] (analytic) = -0.61532352842443019111465711664343 y1[1] (numeric) = -0.6153235284244301911146571166434 absolute error = 3e-32 relative error = 4.8754839713047627950977230847508e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.78827467000234724696093771746807 y2[1] (numeric) = -0.78827467000234724696093771746809 absolute error = 2e-32 relative error = 2.5371866889926129381462053823707e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.909 y1[1] (analytic) = -0.61453494622406837523019947106989 y1[1] (numeric) = -0.61453494622406837523019947106986 absolute error = 3e-32 relative error = 4.8817402792682784020691585523155e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.78888959929091560447887508226995 y2[1] (numeric) = -0.78888959929091560447887508226997 absolute error = 2e-32 relative error = 2.5352089846255764182757026200127e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1293.2MB, alloc=4.5MB, time=78.43 x[1] = 0.91 y1[1] (analytic) = -0.61374574948881154652117822617468 y1[1] (numeric) = -0.61374574948881154652117822617465 absolute error = 3e-32 relative error = 4.8880175585716041803035613176014e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.78950373968995041187895751787155 y2[1] (numeric) = -0.78950373968995041187895751787157 absolute error = 2e-32 relative error = 2.5332368923108952657703973971395e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1297.0MB, alloc=4.5MB, time=78.67 x[1] = 0.911 y1[1] (analytic) = -0.61295593900785637447802967845642 y1[1] (numeric) = -0.6129559390078563744780296784564 absolute error = 2e-32 relative error = 3.2628772685313121899656924756644e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.79011709058531132130474250447886 y2[1] (numeric) = -0.79011709058531132130474250447889 absolute error = 3e-32 relative error = 3.7969055925339219922006798535335e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1300.8MB, alloc=4.5MB, time=78.90 x[1] = 0.912 y1[1] (analytic) = -0.61216551557101327423838798538397 y1[1] (numeric) = -0.61216551557101327423838798538395 absolute error = 2e-32 relative error = 3.2670902707324964021807987395207e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.79072965136364748850789352596358 y2[1] (numeric) = -0.7907296513636474885078935259636 absolute error = 2e-32 relative error = 2.5293094758125150430985447359827e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1304.6MB, alloc=4.5MB, time=79.13 x[1] = 0.913 y1[1] (analytic) = -0.61137447996870561677673584529461 y1[1] (numeric) = -0.61137447996870561677673584529459 absolute error = 2e-32 relative error = 3.2713174421385299917641826006727e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.7913414214123981861989732056309 y2[1] (numeric) = -0.79134142141239818619897320563093 absolute error = 3e-32 relative error = 3.7910311767145392720434444925965e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.914 y1[1] (analytic) = -0.61058283299196893848109939152343 y1[1] (numeric) = -0.61058283299196893848109939152342 absolute error = 1e-32 relative error = 1.6377794231452837248401140761797e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.79195240011979341660811954893143 memory used=1308.4MB, alloc=4.5MB, time=79.36 y2[1] (numeric) = -0.79195240011979341660811954893145 absolute error = 2e-32 relative error = 2.5254043042201440264346922930085e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.915 y1[1] (analytic) = -0.60979057543245015011757772400305 y1[1] (numeric) = -0.60979057543245015011757772400304 absolute error = 1e-32 relative error = 1.6399072735599789376378595382856e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.79256258687485452325499273249163 y2[1] (numeric) = -0.79256258687485452325499273249165 absolute error = 2e-32 relative error = 2.5234600183263503037904764043960e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1312.2MB, alloc=4.5MB, time=79.60 x[1] = 0.916 y1[1] (analytic) = -0.60899770808240674518349811373816 y1[1] (numeric) = -0.60899770808240674518349811373815 absolute error = 1e-32 relative error = 1.6420423044756100103985192364699e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.79317198106739480192738066956736 y2[1] (numeric) = -0.79317198106739480192738066956738 absolute error = 2e-32 relative error = 2.5215212434868681717080471534475e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1316.0MB, alloc=4.5MB, time=79.83 x[1] = 0.917 y1[1] (analytic) = -0.60820423173470600764998852693391 y1[1] (numeric) = -0.6082042317347060076499885269339 absolute error = 1e-32 relative error = 1.6441845482525223253726253708369e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.79378058208802011086785237336563 y2[1] (numeric) = -0.79378058208802011086785237336565 absolute error = 2e-32 relative error = 2.5195879631359205863560289653529e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1319.9MB, alloc=4.5MB, time=80.06 x[1] = 0.918 y1[1] (analytic) = -0.60741014718282421909475972613934 y1[1] (numeric) = -0.60741014718282421909475972613933 absolute error = 1e-32 relative error = 1.6463340374506622544683300454830e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.79438838932812948016784893163212 y2[1] (numeric) = -0.79438838932812948016784893163214 absolute error = 2e-32 relative error = 2.5176601607829913538715809276631e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1323.7MB, alloc=4.5MB, time=80.30 x[1] = 0.919 y1[1] (analytic) = -0.60661545522084586522588981555792 y1[1] (numeric) = -0.60661545522084586522588981555791 absolute error = 1e-32 relative error = 1.6484908048311060948655700038510e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.79499540217991572036860269846429 y2[1] (numeric) = -0.79499540217991572036860269846431 absolute error = 2e-32 relative error = 2.5157378200124221823536117823140e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.92 y1[1] (analytic) = -0.60582015664346284179740470667438 y1[1] (numeric) = -0.60582015664346284179740470667437 absolute error = 1e-32 relative error = 1.6506548833576031067674696397598e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.79560162003636603026827610248162 y2[1] (numeric) = -0.79560162003636603026827610248164 absolute error = 2e-32 relative error = 2.5138209244830123802050892723598e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1327.5MB, alloc=4.5MB, time=80.53 x[1] = 0.921 y1[1] (analytic) = -0.60502425224597365991744858855121 y1[1] (numeric) = -0.6050242522459736599174485885512 absolute error = 1e-32 relative error = 1.6528263061981328051897789597990e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.79620704229126260393471226426473 y2[1] (numeric) = -0.79620704229126260393471226426475 absolute error = 2e-32 relative error = 2.5119094579276211807679157555656e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1331.3MB, alloc=4.5MB, time=80.76 x[1] = 0.922 y1[1] (analytic) = -0.60422774282428265074983909455821 y1[1] (numeric) = -0.60422774282428265074983909455821 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.79681166833918323692319041036348 y2[1] (numeric) = -0.7968116683391832369231904103635 absolute error = 2e-32 relative error = 2.5100034041527726733680757967780e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1335.1MB, alloc=4.5MB, time=80.99 x[1] = 0.923 y1[1] (analytic) = -0.60343062917489916960980246391359 y1[1] (numeric) = -0.60343062917489916960980246391359 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.79741549757550193169857986616904 y2[1] (numeric) = -0.79741549757550193169857986616905 absolute error = 1e-32 relative error = 1.2540513735191316605306485826162e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1338.9MB, alloc=4.5MB, time=81.22 x[1] = 0.924 y1[1] (analytic) = -0.60263291209493679945468460223509 y1[1] (numeric) = -0.60263291209493679945468460223508 absolute error = 1e-32 relative error = 1.6593849753802747855467377902422e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.79801852939638950226128720554643 y2[1] (numeric) = -0.79801852939638950226128720554645 absolute error = 2e-32 relative error = 2.5062074705367720455403226729897e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1342.7MB, alloc=4.5MB, time=81.45 x[1] = 0.925 y1[1] (analytic) = -0.60183459238211255377043455032378 y1[1] (numeric) = -0.60183459238211255377043455032378 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.79862076319881417797639193133085 y2[1] (numeric) = -0.79862076319881417797639193133087 absolute error = 2e-32 relative error = 2.5043175586734728598340847592780e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.926 y1[1] (analytic) = -0.60103567083474607885465747463065 y1[1] (numeric) = -0.60103567083474607885465747463064 absolute error = 1e-32 relative error = 1.6637947604859356311838218011391e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.79922219838054220660536685760223 y2[1] (numeric) = -0.79922219838054220660536685760225 absolute error = 2e-32 relative error = 2.5024329955456500295966255996805e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1346.6MB, alloc=4.5MB, time=81.68 x[1] = 0.927 y1[1] (analytic) = -0.60023614825175885549703489628633 y1[1] (numeric) = -0.60023614825175885549703489628632 absolute error = 1e-32 relative error = 1.6660109573750079912310589449888e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.79982283434013845653978016206811 y2[1] (numeric) = -0.79982283434013845653978016206813 absolute error = 2e-32 relative error = 2.5005537653223157439495305329115e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1350.4MB, alloc=4.5MB, time=81.92 x[1] = 0.928 y1[1] (analytic) = -0.59943602543267340005791047820747 y1[1] (numeric) = -0.59943602543267340005791047820747 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80042267047696701823637687490283 y2[1] (numeric) = -0.80042267047696701823637687490285 absolute error = 2e-32 relative error = 2.4986798522438302770059592752693e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1354.2MB, alloc=4.5MB, time=82.15 x[1] = 0.929 y1[1] (analytic) = -0.59863530317761246494584029162724 y1[1] (numeric) = -0.59863530317761246494584029162723 absolute error = 1e-32 relative error = 1.6704661330394415320713533092074e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.80102170619119180485293836901168 y2[1] (numeric) = -0.8010217061911918048529383690117 absolute error = 2e-32 relative error = 2.4968112406215246213670850501330e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1358.0MB, alloc=4.5MB, time=82.38 x[1] = 0.93 y1[1] (analytic) = -0.59783398228729823849490708443298 y1[1] (numeric) = -0.59783398228729823849490708443298 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80161994088377715208431921591065 y2[1] (numeric) = -0.80161994088377715208431921591068 absolute error = 3e-32 relative error = 3.7424218722559883625643552630592e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1361.8MB, alloc=4.5MB, time=82.62 x[1] = 0.931 y1[1] (analytic) = -0.59703206356305154424259867393038 y1[1] (numeric) = -0.59703206356305154424259867393038 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80221737395648841719806157123484 y2[1] (numeric) = -0.80221737395648841719806157123487 absolute error = 3e-32 relative error = 3.7396347890150748951134521020647e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.932 y1[1] (analytic) = -0.59622954780679103960905118608862 y1[1] (numeric) = -0.59622954780679103960905118608862 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80281400481189257726898805431102 y2[1] (numeric) = -0.80281400481189257726898805431105 absolute error = 3e-32 relative error = 3.7368555879925516169529941296977e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1365.6MB, alloc=4.5MB, time=82.84 x[1] = 0.933 y1[1] (analytic) = -0.59542643582103241397845846195686 y1[1] (numeric) = -0.59542643582103241397845846195686 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80340983285335882661217488725149 y2[1] (numeric) = -0.80340983285335882661217488725152 absolute error = 3e-32 relative error = 3.7340842460756520207707314715083e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1369.5MB, alloc=4.5MB, time=83.08 x[1] = 0.934 y1[1] (analytic) = -0.59462272840888758618344954977562 y1[1] (numeric) = -0.59462272840888758618344954977561 absolute error = 1e-32 relative error = 1.6817386087407643787212858819216e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.80400485748505917341370786064566 y2[1] (numeric) = -0.80400485748505917341370786064569 absolute error = 3e-32 relative error = 3.7313207402552900821472829274771e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1373.3MB, alloc=4.5MB, time=83.31 x[1] = 0.935 y1[1] (analytic) = -0.59381842637406390139323679833869 y1[1] (numeric) = -0.59381842637406390139323679833869 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80459907811196903555862449514329 y2[1] (numeric) = -0.80459907811196903555862449514332 absolute error = 3e-32 relative error = 3.7285650476255158815876423090094e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1377.1MB, alloc=4.5MB, time=83.55 x[1] = 0.936 y1[1] (analytic) = -0.59301353052086332740633766339073 y1[1] (numeric) = -0.59301353052086332740633766339073 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80519249413986783565544657103677 y2[1] (numeric) = -0.80519249413986783565544657103679 absolute error = 2e-32 relative error = 2.4838780969219831631360844125863e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.937 y1[1] (analytic) = -0.59220804165418165034867393427147 y1[1] (numeric) = -0.59220804165418165034867393427147 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80578510497533959525670800135952 y2[1] (numeric) = -0.80578510497533959525670800135955 absolute error = 3e-32 relative error = 3.7230770108263698743567914517663e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1380.9MB, alloc=4.5MB, time=83.77 TOP MAIN SOLVE Loop x[1] = 0.938 y1[1] (analytic) = -0.59140196057950766977785268264058 y1[1] (numeric) = -0.59140196057950766977785268264058 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80637691002577352827488382802226 y2[1] (numeric) = -0.80637691002577352827488382802228 absolute error = 2e-32 relative error = 2.4802297475706189658540454397675e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1384.7MB, alloc=4.5MB, time=84.01 x[1] = 0.939 y1[1] (analytic) = -0.59059528810292239319443382893499 y1[1] (numeric) = -0.59059528810292239319443382893499 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80696790869936463359312692510733 y2[1] (numeric) = -0.80696790869936463359312692510736 absolute error = 3e-32 relative error = 3.7176199544728711599539634486287e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1388.5MB, alloc=4.5MB, time=84.24 x[1] = 0.94 y1[1] (analytic) = -0.58978802503109822996098981522402 y1[1] (numeric) = -0.58978802503109822996098981522402 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80755810040511428687021979863415 y2[1] (numeric) = -0.80755810040511428687021979863417 absolute error = 2e-32 relative error = 2.4766019918525901111130853040033e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1392.3MB, alloc=4.5MB, time=84.48 x[1] = 0.941 y1[1] (analytic) = -0.58898017217129818462976346533545 y1[1] (numeric) = -0.58898017217129818462976346533545 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80814748455283083153914967789289 y2[1] (numeric) = -0.80814748455283083153914967789291 absolute error = 2e-32 relative error = 2.4747957993170669580083123578334e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1396.2MB, alloc=4.5MB, time=84.71 x[1] = 0.942 y1[1] (analytic) = -0.58817173033137504967973070452754 y1[1] (numeric) = -0.58817173033137504967973070452754 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80873606055313016899871589982091 y2[1] (numeric) = -0.80873606055313016899871589982093 absolute error = 2e-32 relative error = 2.4729947105760463034208478273959e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.943 y1[1] (analytic) = -0.58736270031977059766387540157688 y1[1] (numeric) = -0.58736270031977059766387540157688 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80932382781743634799757939486348 y2[1] (numeric) = -0.80932382781743634799757939486349 absolute error = 1e-32 relative error = 1.2355993554480834224770151017406e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1400.0MB, alloc=4.5MB, time=84.94 x[1] = 0.944 y1[1] (analytic) = -0.58655308294551477276748418593998 y1[1] (numeric) = -0.58655308294551477276748418593998 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.80991078575798215321016489031852 y2[1] (numeric) = -0.80991078575798215321016489031853 absolute error = 1e-32 relative error = 1.2347038928048309478368307209916e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1403.8MB, alloc=4.5MB, time=85.18 x[1] = 0.945 y1[1] (analytic) = -0.58574287901822488177826968162643 y1[1] (numeric) = -0.58574287901822488177826968162643 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.81049693378780969300382725531229 y2[1] (numeric) = -0.8104969337878096930038272553123 absolute error = 1e-32 relative error = 1.2338109600570095757940763411185e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1407.6MB, alloc=4.5MB, time=85.41 x[1] = 0.946 y1[1] (analytic) = -0.5849320893481047844691311875929 y1[1] (numeric) = -0.5849320893481047844691311875929 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.81108227132077098639669422028845 y2[1] (numeric) = -0.81108227132077098639669422028846 absolute error = 1e-32 relative error = 1.2329205499358213182400234005287e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1411.4MB, alloc=4.5MB, time=85.64 x[1] = 0.947 y1[1] (analytic) = -0.58412071474594408339436242182994 y1[1] (numeric) = -0.58412071474594408339436242182994 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.81166679777152854920559851321694 y2[1] (numeric) = -0.81166679777152854920559851321695 absolute error = 1e-32 relative error = 1.2320326552047584040276460495651e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1415.2MB, alloc=4.5MB, time=85.88 x[1] = 0.948 y1[1] (analytic) = -0.58330875602311731310011653286618 y1[1] (numeric) = -0.58330875602311731310011653286619 absolute error = 1e-32 relative error = 1.7143579445263267240080872279642e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.81225051255555597938351326463913 y2[1] (numeric) = -0.81225051255555597938351326463914 absolute error = 1e-32 relative error = 1.2311472686594364047560852535509e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.949 y1[1] (analytic) = -0.58249621399158312874993916815753 y1[1] (numeric) = -0.58249621399158312874993916815753 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.81283341508913854154590534416286 y2[1] (numeric) = -0.81283341508913854154590534416287 absolute error = 1e-32 relative error = 1.2302643831274284253830141955925e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1419.0MB, alloc=4.5MB, time=86.11 x[1] = 0.95 y1[1] (analytic) = -0.58168308946388349416618097376046 y1[1] (numeric) = -0.58168308946388349416618097376046 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.81341550478937375068542210210256 y2[1] (numeric) = -0.81341550478937375068542210210257 absolute error = 1e-32 relative error = 1.2293839914681003518494659282533e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1422.9MB, alloc=4.5MB, time=86.34 x[1] = 0.951 y1[1] (analytic) = -0.58086938325314286928810148380949 y1[1] (numeric) = -0.5808693832531428692881014838095 absolute error = 1e-32 relative error = 1.7215574255257313392573477860512e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.81399678107417195507432780162642 y2[1] (numeric) = -0.81399678107417195507432780162644 absolute error = 2e-32 relative error = 2.4570121731448942959350847585267e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1426.7MB, alloc=4.5MB, time=86.58 x[1] = 0.952 y1[1] (analytic) = -0.58005509617306739704747694162704 y1[1] (numeric) = -0.58005509617306739704747694162705 absolute error = 1e-32 relative error = 1.7239741648638774802004512419334e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.8145772433622569183541068390228 y2[1] (numeric) = -0.81457724336225691835410683902282 absolute error = 2e-32 relative error = 2.4552613227258603877733196519726e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1430.5MB, alloc=4.5MB, time=86.81 x[1] = 0.953 y1[1] (analytic) = -0.57924022903794408966252517679013 y1[1] (numeric) = -0.57924022903794408966252517679014 absolute error = 1e-32 relative error = 1.7263994278520550500580812701109e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.81515689107316640081165166253105 y2[1] (numeric) = -0.81515689107316640081165166253107 absolute error = 2e-32 relative error = 2.4535154175866313170372126936671e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.954 y1[1] (analytic) = -0.57842478266264001435096124416137 y1[1] (numeric) = -0.57842478266264001435096124416138 absolute error = 1e-32 relative error = 1.7288332553746044491713238218463e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.81573572362725273984145411359738 y2[1] (numeric) = -0.8157357236272527398414541135974 absolute error = 2e-32 relative error = 2.4517744436970277967313959806555e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1434.3MB, alloc=4.5MB, time=87.04 TOP MAIN SOLVE Loop x[1] = 0.955 y1[1] (analytic) = -0.57760875786260147846299811176052 y1[1] (numeric) = -0.57760875786260147846299811176053 absolute error = 1e-32 relative error = 1.7312756885827460392908796679797e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.81631374044568342959321972841275 y2[1] (numeric) = -0.81631374044568342959321972841277 absolute error = 2e-32 relative error = 2.4500383870888397505194577096881e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1438.1MB, alloc=4.5MB, time=87.27 x[1] = 0.956 y1[1] (analytic) = -0.57679215545385321403510726440825 y1[1] (numeric) = -0.57679215545385321403510726440825 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.81689094095044169980432535216677 y2[1] (numeric) = -0.81689094095044169980432535216679 absolute error = 2e-32 relative error = 2.4483072338555091711644445031611e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1441.9MB, alloc=4.5MB, time=87.50 x[1] = 0.957 y1[1] (analytic) = -0.57597497625299756176535466931334 y1[1] (numeric) = -0.57597497625299756176535466931334 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.81746732456432709381654123360831 y2[1] (numeric) = -0.81746732456432709381654123360833 absolute error = 2e-32 relative error = 2.4465809701518149871974237298207e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1445.7MB, alloc=4.5MB, time=87.73 x[1] = 0.958 y1[1] (analytic) = -0.57515722107721365441112812819955 y1[1] (numeric) = -0.57515722107721365441112812819955 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.81804289071095604577643958323874 y2[1] (numeric) = -0.81804289071095604577643958323877 absolute error = 3e-32 relative error = 3.6672893732903398848042584737585e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1449.6MB, alloc=4.5MB, time=87.97 x[1] = 0.959 y1[1] (analytic) = -0.5743388907442565996100726181766 y1[1] (numeric) = -0.5743388907442565996100726181766 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.81861763881476245701891239477757 y2[1] (numeric) = -0.8186176388147624570189123947776 absolute error = 3e-32 relative error = 3.6647145843858890088472668677770e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.96 y1[1] (analytic) = -0.57351998607245666212505080035186 y1[1] (numeric) = -0.57351998607245666212505080035186 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.81919156830099827163322214643043 y2[1] (numeric) = -0.81919156830099827163322214643046 absolute error = 3e-32 relative error = 3.6621470680197480524596705997817e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1453.4MB, alloc=4.5MB, time=88.20 x[1] = 0.961 y1[1] (analytic) = -0.57270050788071844551394645115419 y1[1] (numeric) = -0.57270050788071844551394645115419 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.81976467859573405121100981595691 y2[1] (numeric) = -0.81976467859573405121100981595694 absolute error = 3e-32 relative error = 3.6595868037874395066596877474082e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1457.2MB, alloc=4.5MB, time=88.43 x[1] = 0.962 y1[1] (analytic) = -0.57188045698852007322512914649815 y1[1] (numeric) = -0.57188045698852007322512914649816 absolute error = 1e-32 relative error = 1.7486171939952723324908895571614e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82033696912585954877568546157796 y2[1] (numeric) = -0.82033696912585954877568546157799 absolute error = 3e-32 relative error = 3.6570337713741721905469841385010e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1461.0MB, alloc=4.5MB, time=88.66 x[1] = 0.963 y1[1] (analytic) = -0.57105983421591236911939910325581 y1[1] (numeric) = -0.57105983421591236911939910325581 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.82090843931908428189262743938018 y2[1] (numeric) = -0.82090843931908428189262743938021 absolute error = 3e-32 relative error = 3.6544879505543861714547362760586e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1464.8MB, alloc=4.5MB, time=88.90 x[1] = 0.964 y1[1] (analytic) = -0.57023864038351803741923165602284 y1[1] (numeric) = -0.57023864038351803741923165602285 absolute error = 1e-32 relative error = 1.7536517681920729109942651787821e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.8214790886039381049596171470655 y2[1] (numeric) = -0.82147908860393810495961714706553 absolute error = 3e-32 relative error = 3.6519493211913005478128077887606e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1468.6MB, alloc=4.5MB, time=89.13 x[1] = 0.965 y1[1] (analytic) = -0.56941687631253084208614141986634 y1[1] (numeric) = -0.56941687631253084208614141986635 absolute error = 1e-32 relative error = 1.7561825818649231232703078243025e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82204891640977178067693700365927 y2[1] (numeric) = -0.8220489164097717806769370036593 absolute error = 3e-32 relative error = 3.6494178632364640740519771721586e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.966 y1[1] (analytic) = -0.56859454282471478562698676162152 y1[1] (numeric) = -0.56859454282471478562698676162153 absolute error = 1e-32 relative error = 1.7587224721364904931053489516757e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82261792216675755069656019512629 y2[1] (numeric) = -0.82261792216675755069656019512632 absolute error = 3e-32 relative error = 3.6468935567293086070506905343282e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1472.4MB, alloc=4.5MB, time=89.36 x[1] = 0.967 y1[1] (analytic) = -0.56777164074240328733003577336466 y1[1] (numeric) = -0.56777164074240328733003577336467 absolute error = 1e-32 relative error = 1.7612714835359269806823722839970e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82318610530588970544986153675268 y2[1] (numeric) = -0.82318610530588970544986153675271 absolute error = 3e-32 relative error = 3.6443763817967053537957539622650e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1476.3MB, alloc=4.5MB, time=89.60 x[1] = 0.968 y1[1] (analytic) = -0.56694817088849836093161551192762 y1[1] (numeric) = -0.56694817088849836093161551192763 absolute error = 1e-32 relative error = 1.7638296608891783482384250810092e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.8237534652589851531532796246302 y2[1] (numeric) = -0.82375346525898515315327962463022 absolute error = 2e-32 relative error = 2.4279108791016826000644949773663e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1480.1MB, alloc=4.5MB, time=89.83 x[1] = 0.969 y1[1] (analytic) = -0.56612413408646979171416683773636 y1[1] (numeric) = -0.56612413408646979171416683773637 absolute error = 1e-32 relative error = 1.7663970493214479619069825912346e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82432000145868398799136127062821 y2[1] (numeric) = -0.82432000145868398799136127062823 absolute error = 2e-32 relative error = 2.4262422317314626669071350227983e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1483.9MB, alloc=4.5MB, time=90.06 x[1] = 0.97 y1[1] (analytic) = -0.56529953116035431303652775484986 y1[1] (numeric) = -0.56529953116035431303652775484987 absolute error = 1e-32 relative error = 1.7689736942596852047933142508645e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82488571333845005747662003785634 y2[1] (numeric) = -0.82488571333845005747662003785637 absolute error = 3e-32 relative error = 3.6368674490172701085989792582711e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.971 y1[1] (analytic) = -0.56447436293475478229726872184762 y1[1] (numeric) = -0.56447436293475478229726872184763 absolute error = 1e-32 relative error = 1.7715596414350987884968047397766e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82545060033257152898564151680643 y2[1] (numeric) = -0.82545060033257152898564151680646 absolute error = 3e-32 relative error = 3.6343786033849986310017226878515e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1487.7MB, alloc=4.5MB, time=90.29 TOP MAIN SOLVE Loop x[1] = 0.972 y1[1] (analytic) = -0.5636486302348393563319039701617 y1[1] (numeric) = -0.56364863023483935633190397016171 absolute error = 1e-32 relative error = 1.7741549368856952541314499667518e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82601466187616145547086880611577 y2[1] (numeric) = -0.8260146618761614554708688061158 absolute error = 3e-32 relative error = 3.6318967912578878805778373082542e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1491.5MB, alloc=4.5MB, time=90.53 x[1] = 0.973 y1[1] (analytic) = -0.56282233388634066624480343257325 y1[1] (numeric) = -0.56282233388634066624480343257326 absolute error = 1e-32 relative error = 1.7767596269588429577907860359642e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82657789740515834034750248621335 y2[1] (numeric) = -0.82657789740515834034750248621338 absolute error = 3e-32 relative error = 3.6294219932782807145188488647307e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1495.3MB, alloc=4.5MB, time=90.76 x[1] = 0.974 y1[1] (analytic) = -0.56199547471555499167663044989289 y1[1] (numeric) = -0.56199547471555499167663044989291 absolute error = 2e-32 relative error = 3.5587475166277236787145725296284e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82714030635632670155495019899613 y2[1] (numeric) = -0.82714030635632670155495019899616 absolute error = 3e-32 relative error = 3.6269541901729298351043895843790e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1499.2MB, alloc=4.5MB, time=90.99 x[1] = 0.975 y1[1] (analytic) = -0.5611680535493414345081309883184 y1[1] (numeric) = -0.56116805354934143450813098831842 absolute error = 2e-32 relative error = 3.5639947558492785551395265421550e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82770188816725763479226177213277 y2[1] (numeric) = -0.8277018881672576347922617721328 absolute error = 3e-32 relative error = 3.6244933627525757351247613929321e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1503.0MB, alloc=4.5MB, time=91.22 x[1] = 0.976 y1[1] (analytic) = -0.56034007121512109200110066361155 y1[1] (numeric) = -0.56034007121512109200110066361157 absolute error = 2e-32 relative error = 3.5692610661645446766730882997937e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82826264227636937592698665260668 y2[1] (numeric) = -0.82826264227636937592698665260671 absolute error = 3e-32 relative error = 3.6220394919115272689523420388287e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.977 y1[1] (analytic) = -0.55951152854087622937735643105834 y1[1] (numeric) = -0.55951152854087622937735643105836 absolute error = 2e-32 relative error = 3.5745465427954734548363390886868e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82882256812290786257689124068781 y2[1] (numeric) = -0.82882256812290786257689124068784 absolute error = 3e-32 relative error = 3.6195925586272448305484660029140e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1506.8MB, alloc=4.5MB, time=91.45 x[1] = 0.978 y1[1] (analytic) = -0.55868242635514945183654036217185 y1[1] (numeric) = -0.55868242635514945183654036217186 absolute error = 1e-32 relative error = 1.7899256408045827628021436809745e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82938166514694729486397454266257 y2[1] (numeric) = -0.8293816651469472948639745426626 absolute error = 3e-32 relative error = 3.6171525439599261198458554028201e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1510.6MB, alloc=4.5MB, time=91.69 x[1] = 0.979 y1[1] (analytic) = -0.55785276548704287601358349026492 y1[1] (numeric) = -0.55785276548704287601358349026494 absolute error = 2e-32 relative error = 3.5851753791233173727097865209547e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.82993993278939069534022138835309 y2[1] (numeric) = -0.82993993278939069534022138835312 absolute error = 3e-32 relative error = 3.6147194290520944790987103453164e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1514.4MB, alloc=4.5MB, time=91.92 x[1] = 0.98 y1[1] (analytic) = -0.55702254676621730087665826735994 y1[1] (numeric) = -0.55702254676621730087665826735996 absolute error = 2e-32 relative error = 3.5905189325117232773273185710517e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.83049737049197046808453328771915 y2[1] (numeric) = -0.83049737049197046808453328771917 absolute error = 2e-32 relative error = 2.4081954634187931872954718154711e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1518.2MB, alloc=4.5MB, time=92.16 x[1] = 0.981 y1[1] (analytic) = -0.55619177102289137806644873441393 y1[1] (numeric) = -0.55619177102289137806644873441395 absolute error = 2e-32 relative error = 3.5958820396098332507492969073544e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.83105397769724895697027782965853 y2[1] (numeric) = -0.83105397769724895697027782965855 absolute error = 2e-32 relative error = 2.4065825489961079000402776799413e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1522.0MB, alloc=4.5MB, time=92.39 x[1] = 0.982 y1[1] (analytic) = -0.55536043908784078167756806551989 y1[1] (numeric) = -0.5553604390878407816775680655199 absolute error = 1e-32 relative error = 1.8006323994601838077945311914900e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.831609753848619003102898355503 y2[1] (numeric) = -0.83160975384861900310289835550302 absolute error = 2e-32 relative error = 2.4049741970247109336543535597737e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.983 y1[1] (analytic) = -0.55452855179239737748295370459744 y1[1] (numeric) = -0.55452855179239737748295370459745 absolute error = 1e-32 relative error = 1.8033336548094944550514342946892e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.8321646983903045014270264696466 y2[1] (numeric) = -0.83216469839030450142702646964662 absolute error = 2e-32 relative error = 2.4033703951497756471479053545288e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1525.9MB, alloc=4.5MB, time=92.62 x[1] = 0.984 y1[1] (analytic) = -0.55369610996844839160207087010861 y1[1] (numeric) = -0.55369610996844839160207087010862 absolute error = 1e-32 relative error = 1.8060448357800158997101014235917e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.83271881076736095650254078024015 y2[1] (numeric) = -0.83271881076736095650254078024018 absolute error = 3e-32 relative error = 3.6026566966050183390752146762248e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1529.7MB, alloc=4.5MB, time=92.85 x[1] = 0.985 y1[1] (analytic) = -0.55286311444843557861375575952576 y1[1] (numeric) = -0.55286311444843557861375575952577 absolute error = 1e-32 relative error = 1.8087659926411458434050701952102e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.83327209042567603744901609393959 y2[1] (numeric) = -0.83327209042567603744901609393962 absolute error = 3e-32 relative error = 3.6002645888061049015442314422047e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1533.5MB, alloc=4.5MB, time=93.08 x[1] = 0.986 y1[1] (analytic) = -0.55202956606535438911453034063932 y1[1] (numeric) = -0.55202956606535438911453034063933 absolute error = 1e-32 relative error = 1.8114971760074363637967484305947e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.83382453681197013205800812030509 y2[1] (numeric) = -0.83382453681197013205800812030512 absolute error = 3e-32 relative error = 3.5978792510354114950246673711137e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1537.3MB, alloc=4.5MB, time=93.32 x[1] = 0.987 y1[1] (analytic) = -0.55119546565275313672322117132106 y1[1] (numeric) = -0.55119546565275313672322117132107 absolute error = 1e-32 relative error = 1.8142384368415479789693951387736e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.83437614937379690007261957361258 y2[1] (numeric) = -0.83437614937379690007261957361261 absolute error = 3e-32 relative error = 3.5955006650795491485030722632390e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.988 y1[1] (analytic) = -0.55036081404473216453271524305467 y1[1] (numeric) = -0.55036081404473216453271524305467 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.83492692755954382563379439255752 y2[1] (numeric) = -0.83492692755954382563379439255755 absolute error = 3e-32 relative error = 3.5931288128038622451671307173857e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1541.1MB, alloc=4.5MB, time=93.55 TOP MAIN SOLVE Loop x[1] = 0.989 y1[1] (analytic) = -0.54952561207594301100968639640836 y1[1] (numeric) = -0.54952561207594301100968639640836 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.83547687081843276889278763160284 y2[1] (numeric) = -0.83547687081843276889278763160287 absolute error = 3e-32 relative error = 3.5907636761520415784667259836973e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1544.9MB, alloc=4.5MB, time=93.78 x[1] = 0.99 y1[1] (analytic) = -0.54868986058158757534312640865361 y1[1] (numeric) = -0.54868986058158757534312640865362 absolute error = 1e-32 relative error = 1.8225231990619311821271370478539e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.83602597860052051678925941154711 y2[1] (numeric) = -0.83602597860052051678925941154714 absolute error = 3e-32 relative error = 3.5884052371457397853012115026251e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1548.7MB, alloc=4.5MB, time=94.02 x[1] = 0.991 y1[1] (analytic) = -0.54785356039741728224251540492934 y1[1] (numeric) = -0.54785356039741728224251540492935 absolute error = 1e-32 relative error = 1.8253052864612071404476973904094e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.83657425035669933299444215126483 y2[1] (numeric) = -0.83657425035669933299444215126486 absolute error = 3e-32 relative error = 3.5860534778841891396445805323667e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1552.6MB, alloc=4.5MB, time=94.25 x[1] = 0.992 y1[1] (analytic) = -0.54701671235973224618646679471148 y1[1] (numeric) = -0.54701671235973224618646679471149 absolute error = 1e-32 relative error = 1.8280977114687755718969658900926e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.83712168553869750701883113749755 y2[1] (numeric) = -0.83712168553869750701883113749758 absolute error = 3e-32 relative error = 3.5837083805438216900551926880852e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1556.4MB, alloc=4.5MB, time=94.48 x[1] = 0.993 y1[1] (analytic) = -0.54617931730538043512268248487347 y1[1] (numeric) = -0.54617931730538043512268248487348 absolute error = 1e-32 relative error = 1.8309005271997123251325957699038e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.83766828359907990248384932505085 y2[1] (numeric) = -0.83766828359907990248384932505088 absolute error = 3e-32 relative error = 3.5813699273778917246504629643601e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.994 y1[1] (analytic) = -0.54534137607175683362005466931271 y1[1] (numeric) = -0.54534137607175683362005466931271 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.83821404399124850455693809577825 y2[1] (numeric) = -0.83821404399124850455693809577828 absolute error = 3e-32 relative error = 3.5790381007161005472594561855663e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1560.2MB, alloc=4.5MB, time=94.71 x[1] = 0.995 y1[1] (analytic) = -0.54450288949680260547375104297137 y1[1] (numeric) = -0.54450288949680260547375104297137 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.83875896616944296654952654130677 y2[1] (numeric) = -0.83875896616944296654952654130679 absolute error = 2e-32 relative error = 2.3844752553094823657317799928519e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1564.0MB, alloc=4.5MB, time=94.95 x[1] = 0.996 y1[1] (analytic) = -0.54366385841900425576412083509674 y1[1] (numeric) = -0.54366385841900425576412083509674 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.83930304958874115567733267158042 y2[1] (numeric) = -0.83930304958874115567733267158044 absolute error = 2e-32 relative error = 2.3829295044024930376256296153930e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1567.8MB, alloc=4.5MB, time=95.18 x[1] = 0.997 y1[1] (analytic) = -0.54282428367739279237025960276506 y1[1] (numeric) = -0.54282428367739279237025960276506 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.83984629370505969798245078896603 y2[1] (numeric) = -0.83984629370505969798245078896606 absolute error = 3e-32 relative error = 3.5720822041914624488844179205578e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1571.6MB, alloc=4.5MB, time=95.41 x[1] = 0.998 y1[1] (analytic) = -0.5419841661115428869390712710343 y1[1] (numeric) = -0.5419841661115428869390712710343 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.84038869797515452241668010587928 y2[1] (numeric) = -0.84038869797515452241668010587931 absolute error = 3e-32 relative error = 3.5697767083591750149702695812886e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1575.4MB, alloc=4.5MB, time=95.64 x[1] = 0.999 y1[1] (analytic) = -0.54114350656157203531066645059386 y1[1] (numeric) = -0.54114350656157203531066645059386 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.84093026185662140408555052264772 y2[1] (numeric) = -0.84093026185662140408555052264774 absolute error = 2e-32 relative error = 2.3783185012088433646364386320590e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1 y1[1] (analytic) = -0.54030230586813971740093660744298 y1[1] (numeric) = -0.54030230586813971740093660744298 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.8414709848078965066525023216303 y2[1] (numeric) = -0.84147098480789650665250232163032 absolute error = 2e-32 relative error = 2.3767902115562424325231989047491e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1579.3MB, alloc=4.5MB, time=95.87 x[1] = 1.001 y1[1] (analytic) = -0.53946056487244655654214420195355 y1[1] (numeric) = -0.53946056487244655654214420195355 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.84201086628825692390267737345894 y2[1] (numeric) = -0.84201086628825692390267737345896 absolute error = 2e-32 relative error = 2.3752662585179904968943505435918e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1583.1MB, alloc=4.5MB, time=96.11 x[1] = 1.002 y1[1] (analytic) = -0.53861828441623347828236945665729 y1[1] (numeric) = -0.5386182844162334782823694566573 absolute error = 1e-32 relative error = 1.8566024008706320205390925698140e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.84254990575782122046578029165595 y2[1] (numeric) = -0.84254990575782122046578029165597 absolute error = 2e-32 relative error = 2.3737466307127818514639863258414e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1586.9MB, alloc=4.5MB, time=96.34 x[1] = 1.003 y1[1] (analytic) = -0.53777546534178086864465495324034 y1[1] (numeric) = -0.53777546534178086864465495324034 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.84308810267754997169746881281128 y2[1] (numeric) = -0.8430881026775499716974688128113 absolute error = 2e-32 relative error = 2.3722313168080917104874862636194e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1590.7MB, alloc=4.5MB, time=96.58 x[1] = 1.004 y1[1] (analytic) = -0.53693210849190773184668979953043 y1[1] (numeric) = -0.53693210849190773184668979953043 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.84362545650924630271873352097427 y2[1] (numeric) = -0.84362545650924630271873352097429 absolute error = 2e-32 relative error = 2.3707203055199408890688378689127e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1594.5MB, alloc=4.5MB, time=96.81 x[1] = 1.005 y1[1] (analytic) = -0.53608821470997084748187564672253 y1[1] (numeric) = -0.53608821470997084748187564672253 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.84416196671555642661272787692495 y2[1] (numeric) = -0.84416196671555642661272787692497 absolute error = 2e-32 relative error = 2.3692135856126619104238053444078e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.006 y1[1] (analytic) = -0.53524378483986392716261737570645 y1[1] (numeric) = -0.53524378483986392716261737570645 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.84469763275997018177851035553985 y2[1] (numeric) = -0.84469763275997018177851035553988 absolute error = 3e-32 relative error = 3.5515667188479997953617774733114e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1598.3MB, alloc=4.5MB, time=97.04 x[1] = 1.007 y1[1] (analytic) = -0.53439881972601677062668180913559 y1[1] (numeric) = -0.53439881972601677062668180913559 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.8452324541068215684411613375549 y2[1] (numeric) = -0.84523245410682156844116133755492 absolute error = 2e-32 relative error = 2.3662129752382146683629673482805e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1602.2MB, alloc=4.5MB, time=97.27 x[1] = 1.008 y1[1] (analytic) = -0.53355332021339442130746834280773 y1[1] (numeric) = -0.53355332021339442130746834280774 absolute error = 1e-32 relative error = 1.8742269274981747455111938469080e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.84576643022128928431773824565316 y2[1] (numeric) = -0.84576643022128928431773824565318 absolute error = 2e-32 relative error = 2.3647190625391847380821096209414e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1606.0MB, alloc=4.5MB, time=97.50 x[1] = 1.009 y1[1] (analytic) = -0.53270728714749632136903592601697 y1[1] (numeric) = -0.53270728714749632136903592601697 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.84629956056939725943853325896709 y2[1] (numeric) = -0.84629956056939725943853325896711 absolute error = 2e-32 relative error = 2.3632293967568453634338106846320e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1609.8MB, alloc=4.5MB, time=97.74 x[1] = 1.01 y1[1] (analytic) = -0.53186072137435546620673135577918 y1[1] (numeric) = -0.53186072137435546620673135577918 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.84683184461801519012309878478201 y2[1] (numeric) = -0.84683184461801519012309878478203 absolute error = 2e-32 relative error = 2.3617439668936284749326841280005e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.011 y1[1] (analytic) = -0.53101362374053755841426438423256 y1[1] (numeric) = -0.53101362374053755841426438423256 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.84736328183485907211050671145982 y2[1] (numeric) = -0.84736328183485907211050671145985 absolute error = 3e-32 relative error = 3.5403941429983556614260704329027e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1613.6MB, alloc=4.5MB, time=97.97 TOP MAIN SOLVE Loop x[1] = 1.012 y1[1] (analytic) = -0.53016599509314016121807567206737 y1[1] (numeric) = -0.53016599509314016121807567206738 absolute error = 1e-32 relative error = 1.8862016976858707616427378880796e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.84789387168849173284330831236832 y2[1] (numeric) = -0.84789387168849173284330831236835 absolute error = 3e-32 relative error = 3.5381786567531318380090369736152e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1617.4MB, alloc=4.5MB, time=98.20 x[1] = 1.013 y1[1] (analytic) = -0.52931783627979185137984415354655 y1[1] (numeric) = -0.52931783627979185137984415354655 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.84842361364832336290466251690027 y2[1] (numeric) = -0.8484236136483233629046625169003 absolute error = 3e-32 relative error = 3.5359694753186323429604843081444e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1621.2MB, alloc=4.5MB, time=98.44 x[1] = 1.014 y1[1] (analytic) = -0.5284691481486513715679809105391 y1[1] (numeric) = -0.52846914814865137156798091053911 absolute error = 1e-32 relative error = 1.8922580504523856242970294573500e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.84895250718461204660810111149857 y2[1] (numeric) = -0.8489525071846120466081011114986 absolute error = 3e-32 relative error = 3.5337665824781222054550087132630e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1625.0MB, alloc=4.5MB, time=98.67 x[1] = 1.015 y1[1] (analytic) = -0.52761993154840678219895718400196 y1[1] (numeric) = -0.52761993154840678219895718400197 absolute error = 1e-32 relative error = 1.8953036839705788244452531881653e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.84948055176846429173940028096624 y2[1] (numeric) = -0.84948055176846429173940028096627 absolute error = 3e-32 relative error = 3.5315699620839401541036861534614e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1628.9MB, alloc=4.5MB, time=98.90 x[1] = 1.016 y1[1] (analytic) = -0.52677018732827461274931468151135 y1[1] (numeric) = -0.52677018732827461274931468151136 absolute error = 1e-32 relative error = 1.8983610387518310050932246766797e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.85000774687183555845002874823405 y2[1] (numeric) = -0.85000774687183555845002874823408 absolute error = 3e-32 relative error = 3.5293795980571703721223369535778e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.017 y1[1] (analytic) = -0.5259199163379990125392068687629 y1[1] (numeric) = -0.52591991633799901253920686876291 absolute error = 1e-32 relative error = 1.9014301777408225732819621264400e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.85053409196753078730164361918161 y2[1] (numeric) = -0.85053409196753078730164361918164 absolute error = 3e-32 relative error = 3.5271954743873162230474846227437e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1632.7MB, alloc=4.5MB, time=99.13 x[1] = 1.018 y1[1] (analytic) = -0.52506911942785090098832046142821 y1[1] (numeric) = -0.52506911942785090098832046142823 absolute error = 2e-32 relative error = 3.8090223286780389855501490734744e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.85105958652920492646110588806011 y2[1] (numeric) = -0.85105958652920492646110588806014 absolute error = 3e-32 relative error = 3.5250175751319759335607517338245e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1636.5MB, alloc=4.5MB, time=99.36 x[1] = 1.019 y1[1] (analytic) = -0.52421779744862711734502686137579 y1[1] (numeric) = -0.5242177974486271173450268613758 absolute error = 1e-32 relative error = 1.9076040624088103755200678229361e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.85158423003136345804548840854512 y2[1] (numeric) = -0.85158423003136345804548840854515 absolute error = 3e-32 relative error = 3.5228458844165202200883651412137e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1640.3MB, alloc=4.5MB, time=99.59 x[1] = 1.02 y1[1] (analytic) = -0.52336595125164956988961380803381 y1[1] (numeric) = -0.52336595125164956988961380803382 absolute error = 1e-32 relative error = 1.9107089362776886454378422779994e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.85210802194936292361654998545538 y2[1] (numeric) = -0.85210802194936292361654998545541 absolute error = 3e-32 relative error = 3.5206803864337718459474393016745e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1644.1MB, alloc=4.5MB, time=99.83 x[1] = 1.021 y1[1] (analytic) = -0.52251358168876438461244804159244 y1[1] (numeric) = -0.52251358168876438461244804159245 absolute error = 1e-32 relative error = 1.9138258507424803483872712697485e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.85263096175941144882415009270724 y2[1] (numeric) = -0.85263096175941144882415009270728 absolute error = 4e-32 relative error = 4.6913614205915827945530389245071e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1647.9MB, alloc=4.5MB, time=100.06 x[1] = 1.022 y1[1] (analytic) = -0.52166068961234105336792029981187 y1[1] (numeric) = -0.52166068961234105336792029981188 absolute error = 1e-32 relative error = 1.9169548710736181905169679860766e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.85315304893856926719807957413383 y2[1] (numeric) = -0.85315304893856926719807957413386 absolute error = 3e-32 relative error = 3.5163679057730391551971023544547e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.023 y1[1] (analytic) = -0.52080727587527158150502449442017 y1[1] (numeric) = -0.52080727587527158150502449442018 absolute error = 1e-32 relative error = 1.9200960630194623957189998385956e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.8536742829647492430877835353817 y2[1] (numeric) = -0.85367428296474924308778353538174 absolute error = 4e-32 relative error = 4.6856278557534711731784424453269e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1651.7MB, alloc=4.5MB, time=100.29 x[1] = 1.024 y1[1] (analytic) = -0.51995334133096963497542343645084 y1[1] (numeric) = -0.51995334133096963497542343645085 absolute error = 1e-32 relative error = 1.9232494928106689815419122894995e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.85419466331671739374945348720597 y2[1] (numeric) = -0.854194663316717393749453487206 absolute error = 3e-32 relative error = 3.5120800080293444460649672195146e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1655.6MB, alloc=4.5MB, time=100.53 x[1] = 1.025 y1[1] (analytic) = -0.51909888683336968691985400238309 y1[1] (numeric) = -0.51909888683336968691985400238309 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.85471418947409341057996665311494 y2[1] (numeric) = -0.85471418947409341057996665311497 absolute error = 3e-32 relative error = 3.5099452389411053648970081337228e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1659.4MB, alloc=4.5MB, time=100.76 x[1] = 1.026 y1[1] (analytic) = -0.51824391323692616373372515460867 y1[1] (numeric) = -0.51824391323692616373372515460867 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.85523286091735117949715120746866 y2[1] (numeric) = -0.85523286091735117949715120746869 absolute error = 3e-32 relative error = 3.5078165691412983509994923455031e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1663.2MB, alloc=4.5MB, time=101.00 x[1] = 1.027 y1[1] (analytic) = -0.51738842139661259061276275055613 y1[1] (numeric) = -0.51738842139661259061276275055613 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.85575067712781930046585706380934 y2[1] (numeric) = -0.85575067712781930046585706380937 absolute error = 3e-32 relative error = 3.5056939832860975316634274869564e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.028 memory used=1667.0MB, alloc=4.5MB, time=101.23 y1[1] (analytic) = -0.51653241216792073657955559475628 y1[1] (numeric) = -0.51653241216792073657955559475628 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.8562676375876816061693126873962 y2[1] (numeric) = -0.85626763758768160616931268739623 absolute error = 3e-32 relative error = 3.5035774660966334844507497909547e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.029 y1[1] (analytic) = -0.51567588640685975899185770723182 y1[1] (numeric) = -0.51567588640685975899185770723182 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.85678374177997767982524926063117 y2[1] (numeric) = -0.8567837417799776798252492606312 absolute error = 3e-32 relative error = 3.5014670023586895908609436516115e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1670.8MB, alloc=4.5MB, time=101.46 x[1] = 1.03 y1[1] (analytic) = -0.51481884496995534753350229983735 y1[1] (numeric) = -0.51481884496995534753350229983735 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.85729898918860337214627438529442 y2[1] (numeric) = -0.85729898918860337214627438529445 absolute error = 3e-32 relative error = 3.4993625769224001938371104637419e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1674.6MB, alloc=4.5MB, time=101.69 x[1] = 1.031 y1[1] (analytic) = -0.51396128871424886768878346956461 y1[1] (numeric) = -0.51396128871424886768878346956461 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.85781337929831131744397836125908 y2[1] (numeric) = -0.85781337929831131744397836125911 absolute error = 3e-32 relative error = 3.4972641747019505469790923285279e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1678.4MB, alloc=4.5MB, time=101.93 x[1] = 1.032 y1[1] (analytic) = -0.51310321849729650370116213435977 y1[1] (numeric) = -0.51310321849729650370116213435977 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.85832691159471144887625693762188 y2[1] (numeric) = -0.85832691159471144887625693762191 absolute error = 3e-32 relative error = 3.4951717806752785434257439455245e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1682.3MB, alloc=4.5MB, time=102.16 x[1] = 1.033 y1[1] (analytic) = -0.5122446351771684010171532526755 y1[1] (numeric) = -0.51224463517716840101715325267551 absolute error = 1e-32 relative error = 1.9521922365358364816741235847983e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.85883958556427151283733528896996 y2[1] (numeric) = -0.85883958556427151283733528896999 absolute error = 3e-32 relative error = 3.4930853798837782124621123836760e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.034 y1[1] (analytic) = -0.5113855396124478082162518827991 y1[1] (numeric) = -0.51138553961244780821625188279911 absolute error = 1e-32 relative error = 1.9554717967931736607540732673920e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.85935140069431758248997882680264 y2[1] (numeric) = -0.85935140069431758248997882680267 absolute error = 3e-32 relative error = 3.4910049574320049720001373885283e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1686.1MB, alloc=4.5MB, time=102.39 TOP MAIN SOLVE Loop x[1] = 1.035 y1[1] (analytic) = -0.51052593266223021842775615195905 y1[1] (numeric) = -0.51052593266223021842775615195906 absolute error = 1e-32 relative error = 1.9587643565632765003298562483878e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.85986235647303457043937731394017 y2[1] (numeric) = -0.8598623564730345704393773139402 absolute error = 3e-32 relative error = 3.4889304984873826251735323072176e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1689.9MB, alloc=4.5MB, time=102.62 x[1] = 1.036 y1[1] (analytic) = -0.50966581518612251023534571831565 y1[1] (numeric) = -0.50966581518612251023534571831566 absolute error = 1e-32 relative error = 1.9620699882231940718536594579440e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.86037245238946674054818960807816 y2[1] (numeric) = -0.86037245238946674054818960807818 absolute error = 2e-32 relative error = 2.3245746588532747262525035876635e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1693.7MB, alloc=4.5MB, time=102.86 x[1] = 1.037 y1[1] (analytic) = -0.50880518804424208807027482118548 y1[1] (numeric) = -0.50880518804424208807027482118549 absolute error = 1e-32 relative error = 1.9653887646936632595422637731244e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.8608816879335182188922372194854 y2[1] (numeric) = -0.86088168793351821889223721948542 absolute error = 2e-32 relative error = 2.3231996080679212307896271825989e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1697.5MB, alloc=4.5MB, time=103.09 x[1] = 1.038 y1[1] (analytic) = -0.50794405209721602209403952623517 y1[1] (numeric) = -0.50794405209721602209403952623518 absolute error = 1e-32 relative error = 1.9687207594442090231482373974635e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.86139006259595350385633572719432 y2[1] (numeric) = -0.86139006259595350385633572719434 absolute error = 2e-32 relative error = 2.3218285035383867337475572489904e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1701.3MB, alloc=4.5MB, time=103.32 x[1] = 1.039 y1[1] (analytic) = -0.50708240820618018757137928290543 y1[1] (numeric) = -0.50708240820618018757137928290544 absolute error = 1e-32 relative error = 1.9720660464983022101406280133472e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.86189757586839797536975395789502 y2[1] (numeric) = -0.86189757586839797536975395789504 absolute error = 2e-32 relative error = 2.3204613355420057589691291433484e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.04 y1[1] (analytic) = -0.50622025723277840373447342099217 y1[1] (numeric) = -0.50622025723277840373447342099218 absolute error = 1e-32 relative error = 1.9754247004385756762283379285025e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.86240422724333840328079169211617 y2[1] (numeric) = -0.86240422724333840328079169211618 absolute error = 1e-32 relative error = 1.1595490471985327900404013996952e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1705.1MB, alloc=4.5MB, time=103.56 x[1] = 1.041 y1[1] (analytic) = -0.50535760003916157213919372211638 y1[1] (numeric) = -0.50535760003916157213919372211639 absolute error = 1e-32 relative error = 1.9787967964120994846194103600250e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.86291001621412345486996752315744 y2[1] (numeric) = -0.86291001621412345486996752315745 absolute error = 1e-32 relative error = 1.1588693852313088500426408671509e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1709.0MB, alloc=4.5MB, time=103.79 x[1] = 1.042 y1[1] (analytic) = -0.5044944374879868145142747097584 y1[1] (numeric) = -0.5044944374879868145142747097584 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.86341494227496420150130935562797 y2[1] (numeric) = -0.86341494227496420150130935562798 absolute error = 1e-32 relative error = 1.1581916770691452202470919705679e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1712.8MB, alloc=4.5MB, time=104.03 x[1] = 1.043 y1[1] (analytic) = -0.50363077044241661010426380861447 y1[1] (numeric) = -0.50363077044241661010426380861447 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.86391900492093462441124089234244 y2[1] (numeric) = -0.86391900492093462441124089234245 absolute error = 1e-32 relative error = 1.1575159179320513163167013564945e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1716.6MB, alloc=4.5MB, time=104.26 x[1] = 1.044 y1[1] (analytic) = -0.50276659976611793250711403025355 y1[1] (numeric) = -0.50276659976611793250711403025355 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.86442220364797211963455832073057 y2[1] (numeric) = -0.86442220364797211963455832073058 absolute error = 1e-32 relative error = 1.1568421030601392019052771075551e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1720.4MB, alloc=4.5MB, time=104.49 x[1] = 1.045 y1[1] (analytic) = -0.50190192632326138600728234740967 y1[1] (numeric) = -0.50190192632326138600728234740967 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.86492453795287800206699227282532 y2[1] (numeric) = -0.86492453795287800206699227282533 absolute error = 1e-32 relative error = 1.1561702277135315255450899299057e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.046 y1[1] (analytic) = -0.50103675097852034140519742373961 y1[1] (numeric) = -0.50103675097852034140519742373961 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.86542600733331800866385099630989 y2[1] (numeric) = -0.8654260073333180086638509963099 absolute error = 1e-32 relative error = 1.1555002871722699977390799565373e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1724.2MB, alloc=4.5MB, time=104.72 x[1] = 1.047 y1[1] (analytic) = -0.50017107459707007134396086950605 y1[1] (numeric) = -0.50017107459707007134396086950605 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.8659266112878228007742415380223 y2[1] (numeric) = -0.86592661128782280077424153802231 absolute error = 1e-32 relative error = 1.1548322767362244046860524445955e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1728.0MB, alloc=4.5MB, time=104.96 x[1] = 1.048 y1[1] (analytic) = -0.49930489804458688513414669641293 y1[1] (numeric) = -0.49930489804458688513414669641294 absolute error = 1e-32 relative error = 2.0027842785365628186255353151317e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.86642634931578846561036660573817 y2[1] (numeric) = -0.86642634931578846561036660573818 absolute error = 1e-32 relative error = 1.1541661917250021550946638701774e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1731.9MB, alloc=4.5MB, time=105.20 x[1] = 1.049 y1[1] (analytic) = -0.49843822218724726307756414672153 y1[1] (numeric) = -0.49843822218724726307756414672153 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.86692522091747701685139563897667 y2[1] (numeric) = -0.86692522091747701685139563897668 absolute error = 1e-32 relative error = 1.1535020274778583565691835717951e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1735.7MB, alloc=4.5MB, time=105.43 x[1] = 1.05 y1[1] (analytic) = -0.4975710478917269902908495728121 y1[1] (numeric) = -0.4975710478917269902908495728121 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.86742322559401689438140948500027 y2[1] (numeric) = -0.86742322559401689438140948500028 absolute error = 1e-32 relative error = 1.1528397793536064180769674011258e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.051 y1[1] (analytic) = -0.49670337602520029002975354352727 y1[1] (numeric) = -0.49670337602520029002975354352727 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.8679203628474034631609189421053 y2[1] (numeric) = -0.86792036284740346316091894210531 absolute error = 1e-32 relative error = 1.1521794427305291750343010205972e-30 % Correct digits = 31 h = 0.001 memory used=1739.5MB, alloc=4.5MB, time=105.66 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.052 y1[1] (analytic) = -0.49583520745533895651498985293764 y1[1] (numeric) = -0.49583520745533895651498985293764 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.86841663218049951123145829872623 y2[1] (numeric) = -0.86841663218049951123145829872625 absolute error = 2e-32 relative error = 2.3030420260125810671475274650154e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1743.3MB, alloc=4.5MB, time=105.89 x[1] = 1.053 y1[1] (analytic) = -0.49496654305031148726051360560842 y1[1] (numeric) = -0.49496654305031148726051360560842 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.86891203309703574685275586380183 y2[1] (numeric) = -0.86891203309703574685275586380184 absolute error = 1e-32 relative error = 1.1508644855978476305825312015644e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1747.1MB, alloc=4.5MB, time=106.13 x[1] = 1.054 y1[1] (analytic) = -0.49409738367878221490509605001672 y1[1] (numeric) = -0.49409738367878221490509605001672 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.86940656510161129477198435127385 y2[1] (numeric) = -0.86940656510161129477198435127386 absolute error = 1e-32 relative error = 1.1502098559413635061270792871806e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1750.9MB, alloc=4.5MB, time=106.36 x[1] = 1.055 y1[1] (analytic) = -0.49322773020991043854806432847228 y1[1] (numeric) = -0.49322773020991043854806432847228 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.86990022769969419162459484950948 y2[1] (numeric) = -0.86990022769969419162459484950949 absolute error = 1e-32 relative error = 1.1495571194921202849055735564563e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1754.7MB, alloc=4.5MB, time=106.60 x[1] = 1.056 y1[1] (analytic) = -0.49235758351334955459007480772949 y1[1] (numeric) = -0.49235758351334955459007480772949 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.87039302039762188046623897485466 y2[1] (numeric) = -0.87039302039762188046623897485467 absolute error = 1e-32 relative error = 1.1489062717244328633948320042712e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.057 y1[1] (analytic) = -0.491486944459246187079789149445 y1[1] (numeric) = -0.491486944459246187079789149445 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.87088494270260170443528467743741 y2[1] (numeric) = -0.87088494270260170443528467743743 absolute error = 2e-32 relative error = 2.2965146162631261987682682845238e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1758.6MB, alloc=4.5MB, time=106.83 x[1] = 1.058 y1[1] (analytic) = -0.49061581391823931756732277373228 y1[1] (numeric) = -0.49061581391823931756732277373227 absolute error = 1e-32 relative error = 2.0382547232092463638793665372597e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87137599412271139954543203674655 y2[1] (numeric) = -0.87137599412271139954543203674657 absolute error = 2e-32 relative error = 2.2952204484512690012266399819514e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1762.4MB, alloc=4.5MB, time=107.06 x[1] = 1.059 y1[1] (analytic) = -0.48974419276145941446533586229225 y1[1] (numeric) = -0.48974419276145941446533586229224 absolute error = 1e-32 relative error = 2.0418823025984747103570218710808e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87186617416689958660793625441095 y2[1] (numeric) = -0.87186617416689958660793625441096 absolute error = 1e-32 relative error = 1.1469650155375474092575796551699e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1766.2MB, alloc=4.5MB, time=107.30 x[1] = 1.06 y1[1] (analytic) = -0.48887208186052756191863753995641 y1[1] (numeric) = -0.4888720818605275619186375399564 absolute error = 1e-32 relative error = 2.0455248665340933506028342705602e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87235548234498626228294592199742 y2[1] (numeric) = -0.87235548234498626228294592199743 absolute error = 1e-32 relative error = 1.1463216776168946790260800959306e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1770.0MB, alloc=4.5MB, time=107.53 x[1] = 1.061 y1[1] (analytic) = -0.4879994820875545881831743649656 y1[1] (numeric) = -0.48799948208755458818317436496559 absolute error = 1e-32 relative error = 2.0491825026580349318231635807999e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87284391816766328925946551252992 y2[1] (numeric) = -0.87284391816766328925946551252993 absolute error = 1e-32 relative error = 1.1456802060318778416661124290112e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1773.8MB, alloc=4.5MB, time=107.78 x[1] = 1.062 y1[1] (analytic) = -0.48712639431514019351527474892341 y1[1] (numeric) = -0.4871263943151401935152747489234 absolute error = 1e-32 relative error = 2.0528552993025928784284343581830e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87333148114649488556345191580828 y2[1] (numeric) = -0.8733314811464948855634519158083 absolute error = 2e-32 relative error = 2.2900811927384475193775450998145e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.063 y1[1] (analytic) = -0.486252819416372077572021417107 y1[1] (numeric) = -0.48625281941637207757202141710698 absolute error = 2e-32 relative error = 4.1130866909944342127028708367251e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87381817079391811299355570947089 y2[1] (numeric) = -0.8738181707939181129935557094709 absolute error = 1e-32 relative error = 1.1444028442341017621563120656434e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1777.6MB, alloc=4.5MB, time=108.33 x[1] = 1.064 y1[1] (analytic) = -0.48537875826482506632362450869026 y1[1] (numeric) = -0.48537875826482506632362450869024 absolute error = 2e-32 relative error = 4.1204934619507803958178644083571e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87430398662324336468401873010056 y2[1] (numeric) = -0.87430398662324336468401873010057 absolute error = 1e-32 relative error = 1.1437669452500412603952173338388e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1781.4MB, alloc=4.5MB, time=108.88 x[1] = 1.065 y1[1] (analytic) = -0.48450421173456023847866840443344 y1[1] (numeric) = -0.48450421173456023847866840443342 absolute error = 2e-32 relative error = 4.1279310923631703014655520740732e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87478892814865485179424038151686 y2[1] (numeric) = -0.87478892814865485179424038151687 absolute error = 1e-32 relative error = 1.1431328950588498405227937841821e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1785.3MB, alloc=4.5MB, time=109.44 x[1] = 1.066 y1[1] (analytic) = -0.48362918070012405142310585651952 y1[1] (numeric) = -0.4836291807001240514231058565195 absolute error = 2e-32 relative error = 4.1353997645566116638877475581844e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87527299488521108932452599072897 y2[1] (numeric) = -0.87527299488521108932452599072898 absolute error = 1e-32 relative error = 1.1425006893205318296985525191048e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1789.1MB, alloc=4.5MB, time=109.99 x[1] = 1.067 y1[1] (analytic) = -0.48275366603654746667387348147052 y1[1] (numeric) = -0.4827536660365474666738734814705 absolute error = 2e-32 relative error = 4.1428996623064225734096327309821e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87575618634884538105753139584126 y2[1] (numeric) = -0.87575618634884538105753139584127 absolute error = 1e-32 relative error = 1.1418703237132073330350183328108e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1792.9MB, alloc=4.5MB, time=110.54 x[1] = 1.068 y1[1] (analytic) = -0.48187766861934507484800316245521 y1[1] (numeric) = -0.4818776686193450748480031624552 absolute error = 1e-32 relative error = 2.0752154854263250685709251096491e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.8762385020563663036249188245075 y2[1] (numeric) = -0.8762385020563663036249188245075 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.069 y1[1] (analytic) = -0.48100118932451422014810439180406 y1[1] (numeric) = -0.48100118932451422014810439180404 absolute error = 2e-32 relative error = 4.1579938769146615553427362620064e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87671994152545818969873999631796 y2[1] (numeric) = -0.87671994152545818969873999631796 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1796.7MB, alloc=4.5MB, time=111.09 x[1] = 1.07 y1[1] (analytic) = -0.48012422902853412436509306817592 y1[1] (numeric) = -0.48012422902853412436509306817591 absolute error = 1e-32 relative error = 2.0827942843529550116983739353760e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87720050427468161030706325777682 y2[1] (numeric) = -0.87720050427468161030706325777682 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1800.5MB, alloc=4.5MB, time=111.65 x[1] = 1.071 y1[1] (analytic) = -0.47924678860836501039904274557493 y1[1] (numeric) = -0.47924678860836501039904274557492 absolute error = 1e-32 relative error = 2.0866076179744389539701174443959e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.8776801898234738562733624342827 y2[1] (numeric) = -0.8776801898234738562733624342827 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1804.3MB, alloc=4.5MB, time=112.19 x[1] = 1.072 y1[1] (analytic) = -0.47836886894144722529903481329303 y1[1] (numeric) = -0.47836886894144722529903481329302 absolute error = 1e-32 relative error = 2.0904370349450998424684155606768e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87815899769214941877918595976375 y2[1] (numeric) = -0.87815899769214941877918595976375 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1808.1MB, alloc=4.5MB, time=112.75 x[1] = 1.073 y1[1] (analytic) = -0.4774904709057003628228845668551 y1[1] (numeric) = -0.47749047090570036282288456685508 absolute error = 2e-32 relative error = 4.1885652633159671674858715056237e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87863692740190046904962572133815 y2[1] (numeric) = -0.87863692740190046904962572133815 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.074 y1[1] (analytic) = -0.47661159537952238551762061016733 y1[1] (numeric) = -0.47661159537952238551762061016732 absolute error = 1e-32 relative error = 2.0981445052836097959263380275013e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87911397847479733716110593357116 y2[1] (numeric) = -0.87911397847479733716110593357116 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1812.0MB, alloc=4.5MB, time=113.30 TOP MAIN SOLVE Loop x[1] = 1.075 y1[1] (analytic) = -0.47573224324178874632159550831645 y1[1] (numeric) = -0.47573224324178874632159550831644 absolute error = 1e-32 relative error = 2.1020227537778105858269424463489e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.87959015043378898997101323457973 y2[1] (numeric) = -0.87959015043378898997101323457973 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1815.8MB, alloc=4.5MB, time=113.84 x[1] = 1.076 y1[1] (analytic) = -0.47485241537185150968910608883573 y1[1] (numeric) = -0.47485241537185150968910608883572 absolute error = 1e-32 relative error = 2.1059174758896643861646078503781e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88006544280270350816869007439444 y2[1] (numeric) = -0.88006544280270350816869007439444 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1819.6MB, alloc=4.5MB, time=114.40 x[1] = 1.077 y1[1] (analytic) = -0.47397211264953847223840226674448 y1[1] (numeric) = -0.47397211264953847223840226674447 absolute error = 1e-32 relative error = 2.1098287711695262004991558179994e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88053985510624856244731434462506 y2[1] (numeric) = -0.88053985510624856244731434462507 absolute error = 1e-32 relative error = 1.1356669368240430418035995295460e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1823.4MB, alloc=4.5MB, time=114.94 x[1] = 1.078 y1[1] (analytic) = -0.47309133595515228292396374527868 y1[1] (numeric) = -0.47309133595515228292396374527868 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.88101338687001188879618907758993 y2[1] (numeric) = -0.88101338687001188879618907758994 absolute error = 1e-32 relative error = 1.1350565325150318683763382934322e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1827.2MB, alloc=4.5MB, time=115.51 x[1] = 1.079 y1[1] (analytic) = -0.47221008616946956273392441996298 y1[1] (numeric) = -0.47221008616946956273392441996298 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.88148603762046176291296692265885 y2[1] (numeric) = -0.88148603762046176291296692265886 absolute error = 1e-32 relative error = 1.1344479178586449293382062678394e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.08 y1[1] (analytic) = -0.47132836417374002391352478852603 y1[1] (numeric) = -0.47132836417374002391352478852604 absolute error = 1e-32 relative error = 2.1216631037112423847777714573716e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88195780688494747373533498762476 y2[1] (numeric) = -0.88195780688494747373533498762477 absolute error = 1e-32 relative error = 1.1338410887613485138577285970714e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1831.0MB, alloc=4.5MB, time=116.05 x[1] = 1.081 y1[1] (analytic) = -0.47044617084968558871547314313363 y1[1] (numeric) = -0.47044617084968558871547314313364 absolute error = 1e-32 relative error = 2.1256417034787909481364516517154e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88242869419169979609168651345866 y2[1] (numeric) = -0.88242869419169979609168651345868 absolute error = 2e-32 relative error = 2.2664720822932779245921466903336e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1834.9MB, alloc=4.5MB, time=116.61 x[1] = 1.082 y1[1] (analytic) = -0.46956350707949950767809679450479 y1[1] (numeric) = -0.4695635070794995076780967945048 absolute error = 1e-32 relative error = 2.1296373864732526504503418754339e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88289869906983146247030673181564 y2[1] (numeric) = -0.88289869906983146247030673181565 absolute error = 1e-32 relative error = 1.1326327709549684104386913394694e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1838.7MB, alloc=4.5MB, time=117.16 x[1] = 1.083 y1[1] (analytic) = -0.4686803737458454774321650496862 y1[1] (numeric) = -0.46868037374584547743216504968621 absolute error = 1e-32 relative error = 2.1336502572268512836260317172029e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88336782104933763390660113614524 y2[1] (numeric) = -0.88336782104933763390660113614526 absolute error = 2e-32 relative error = 2.2640625482873419167155203261433e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1842.5MB, alloc=4.5MB, time=117.71 x[1] = 1.084 y1[1] (analytic) = -0.46779677173185675803726613658852 y1[1] (numeric) = -0.46779677173185675803726613658853 absolute error = 1e-32 relative error = 2.1376804211321162310256981977454e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88383605966109636998789527921744 y2[1] (numeric) = -0.88383605966109636998789527921746 absolute error = 2e-32 relative error = 2.2628630933737785224160166241433e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1846.3MB, alloc=4.5MB, time=118.26 x[1] = 1.085 y1[1] (analytic) = -0.46691270192113528984862073883405 y1[1] (numeric) = -0.46691270192113528984862073883406 absolute error = 1e-32 relative error = 2.1417279844507351969979281919442e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88430341443686909797533609230331 y2[1] (numeric) = -0.88430341443686909797533609230333 absolute error = 2e-32 relative error = 2.2616671691510030785571177378448e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.086 y1[1] (analytic) = -0.46602816519775080991521527402859 y1[1] (numeric) = -0.4660281651977508099152152740286 absolute error = 1e-32 relative error = 2.1457930543225165062658366061409e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88476988490930108104242560414834 y2[1] (numeric) = -0.88476988490930108104242560414836 absolute error = 2e-32 relative error = 2.2604747676340980092866597389935e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1850.1MB, alloc=4.5MB, time=118.80 x[1] = 1.087 y1[1] (analytic) = -0.4651431624462399679101385172507 y1[1] (numeric) = -0.46514316244623996791013851725071 absolute error = 1e-32 relative error = 2.1498757387744625585154759090791e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88523547061192188562971882124367 y2[1] (numeric) = -0.88523547061192188562971882124368 absolute error = 1e-32 relative error = 1.1296429404356637017722623851799e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1853.9MB, alloc=4.5MB, time=119.35 x[1] = 1.088 y1[1] (analytic) = -0.46425769455160544159400563934789 y1[1] (numeric) = -0.4642576945516054415940056393479 absolute error = 1e-32 relative error = 2.1539761467299560497969214206770e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88570017107914584791521841473618 y2[1] (numeric) = -0.88570017107914584791521841473619 absolute error = 1e-32 relative error = 1.1290502504719967594852187132465e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1857.7MB, alloc=4.5MB, time=119.90 x[1] = 1.089 y1[1] (analytic) = -0.46337176239931505181235419654219 y1[1] (numeric) = -0.46337176239931505181235419654219 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.88616398584627253939999974362188 y2[1] (numeric) = -0.88616398584627253939999974362189 absolute error = 1e-32 relative error = 1.1284593099831470516498034646589e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1861.6MB, alloc=4.5MB, time=120.46 x[1] = 1.09 y1[1] (analytic) = -0.46248536687530087702789707387514 y1[1] (numeric) = -0.46248536687530087702789707387515 absolute error = 1e-32 relative error = 2.1622305733829374458118142722034e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88662691444948723160860062863605 y2[1] (numeric) = -0.88662691444948723160860062863606 absolute error = 1e-32 relative error = 1.1278701150425902640436112388449e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1865.4MB, alloc=4.5MB, time=121.02 x[1] = 1.091 y1[1] (analytic) = -0.46159850886595836738851785016573 y1[1] (numeric) = -0.46159850886595836738851785016574 absolute error = 1e-32 relative error = 2.1663848144933799112410381295956e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.8870889564258613599037111764894 y2[1] (numeric) = -0.88708895642586135990371117648942 absolute error = 2e-32 relative error = 2.2545653234802167296409948913241e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.092 y1[1] (analytic) = -0.4607111892581454583318945164118 y1[1] (numeric) = -0.46071118925814545833189451641181 absolute error = 1e-32 relative error = 2.1705572239524673462775085900449e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88755011131335298641469983979884 y2[1] (numeric) = -0.88755011131335298641469983979885 absolute error = 1e-32 relative error = 1.1266969461817194760394051265972e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1869.2MB, alloc=4.5MB, time=121.56 x[1] = 1.093 y1[1] (analytic) = -0.45982340893918168372763794293757 y1[1] (numeric) = -0.45982340893918168372763794293758 absolute error = 1e-32 relative error = 2.1747479153073403153466288103302e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88801037865080726207951278422546 y2[1] (numeric) = -0.88801037865080726207951278422547 absolute error = 1e-32 relative error = 1.1261129644896081437330617766330e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1873.0MB, alloc=4.5MB, time=122.11 x[1] = 1.094 y1[1] (analytic) = -0.4589351687968472885578319530748 y1[1] (numeric) = -0.45893516879684728855783195307481 absolute error = 1e-32 relative error = 2.1789570030590987967787589104096e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88846975797795688779948452095893 y2[1] (numeric) = -0.88846975797795688779948452095894 absolute error = 1e-32 relative error = 1.1255307128020560040124875971070e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1876.8MB, alloc=4.5MB, time=122.67 x[1] = 1.095 y1[1] (analytic) = -0.45804646971938234113686232276356 y1[1] (numeric) = -0.45804646971938234113686232276357 absolute error = 1e-32 relative error = 2.1831846026728252093463303787048e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88892824883542257470659864977599 y2[1] (numeric) = -0.888928248835422574706598649776 absolute error = 1e-32 relative error = 1.1249501872733728427217317259549e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1880.6MB, alloc=4.5MB, time=123.21 x[1] = 1.096 y1[1] (analytic) = -0.4571573125954858448714224861697 y1[1] (numeric) = -0.45715731259548584487142248616971 absolute error = 1e-32 relative error = 2.1874308305877341052999841934998e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88938585076471350354273844545073 y2[1] (numeric) = -0.88938585076471350354273844545075 absolute error = 2e-32 relative error = 2.2487427681476560923511543771197e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.097 y1[1] (analytic) = -0.45626769831431484956158418723923 y1[1] (numeric) = -0.45626769831431484956158418723924 absolute error = 1e-32 relative error = 2.1916958042274504012981731145216e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.88984256330822778315046790830432 y2[1] (numeric) = -0.88984256330822778315046790830434 absolute error = 2e-32 relative error = 2.2475885987791648810622599392695e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1884.4MB, alloc=4.5MB, time=123.76 TOP MAIN SOLVE Loop x[1] = 1.098 y1[1] (analytic) = -0.45537762776548356224382177604491 y1[1] (numeric) = -0.45537762776548356224382177604492 absolute error = 1e-32 relative error = 2.1959796420104180502898371273774e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.89029838600925290807488478815132 y2[1] (numeric) = -0.89029838600925290807488478815134 absolute error = 2e-32 relative error = 2.2464378588452410347244681799447e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1888.3MB, alloc=4.5MB, time=124.31 x[1] = 1.099 y1[1] (analytic) = -0.45448710183906245757687930682668 y1[1] (numeric) = -0.45448710183906245757687930682669 absolute error = 1e-32 relative error = 2.2002824633604410896789750704144e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.89075331841196621527608797982779 y2[1] (numeric) = -0.89075331841196621527608797982781 absolute error = 2e-32 relative error = 2.2452905407813660860470684673566e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1892.1MB, alloc=4.5MB, time=124.86 x[1] = 1.1 y1[1] (analytic) = -0.45359612142557738777137005178472 y1[1] (numeric) = -0.45359612142557738777137005178472 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.8912073600614353399518025778717 y2[1] (numeric) = -0.89120736006143533995180257787172 absolute error = 2e-32 relative error = 2.2441466370544000988174833006507e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1895.9MB, alloc=4.5MB, time=125.41 x[1] = 1.101 y1[1] (analytic) = -0.45270468741600869206399850095133 y1[1] (numeric) = -0.45270468741600869206399850095133 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.89166051050361867046970676776874 y2[1] (numeric) = -0.89166051050361867046970676776875 absolute error = 1e-32 relative error = 1.1215030700812242037252490776535e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1899.7MB, alloc=4.5MB, time=125.96 x[1] = 1.102 y1[1] (analytic) = -0.45181280070179030573729537384563 y1[1] (numeric) = -0.45181280070179030573729537384564 absolute error = 1e-32 relative error = 2.2133060383564238964713776856284e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.89211276928536580240900562147437 y2[1] (numeric) = -0.89211276928536580240900562147438 absolute error = 1e-32 relative error = 1.1209345213173645549246876060957e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.103 y1[1] (analytic) = -0.45092046217480886868575662310162 y1[1] (numeric) = -0.45092046217480886868575662310162 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.89256413595441799171079775567638 y2[1] (numeric) = -0.89256413595441799171079775567639 absolute error = 1e-32 relative error = 1.1203676685157206544463240355863e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1903.5MB, alloc=4.5MB, time=126.50 x[1] = 1.104 y1[1] (analytic) = -0.45002767272740283352927786385636 y1[1] (numeric) = -0.45002767272740283352927786385636 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.89301461005940860693678170246878 y2[1] (numeric) = -0.89301461005940860693678170246879 absolute error = 1e-32 relative error = 1.1198025079718170489473626439195e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1907.3MB, alloc=4.5MB, time=127.06 x[1] = 1.105 y1[1] (analytic) = -0.44913443325236157327477611538967 y1[1] (numeric) = -0.44913443325236157327477611538967 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.89346419114986358063584973376864 y2[1] (numeric) = -0.89346419114986358063584973376865 absolute error = 1e-32 relative error = 1.1192390359965381427112416677311e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1911.1MB, alloc=4.5MB, time=127.62 x[1] = 1.106 y1[1] (analytic) = -0.44824074464292448852689119331899 y1[1] (numeric) = -0.44824074464292448852689119331899 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.89391287877620185981811777291938 y2[1] (numeric) = -0.89391287877620185981811777291939 absolute error = 1e-32 relative error = 1.1186772489160634274419034526527e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1915.0MB, alloc=4.5MB, time=128.17 x[1] = 1.107 y1[1] (analytic) = -0.44734660779278011424865954157383 y1[1] (numeric) = -0.44734660779278011424865954157383 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.89436067248973585553594091948841 y2[1] (numeric) = -0.89436067248973585553594091948842 absolute error = 1e-32 relative error = 1.1181171430718030771687694065526e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1918.8MB, alloc=4.5MB, time=128.72 x[1] = 1.108 y1[1] (analytic) = -0.44645202359606522607305374340142 y1[1] (numeric) = -0.44645202359606522607305374340142 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.89480757184267189157146500628082 y2[1] (numeric) = -0.89480757184267189157146500628083 absolute error = 1e-32 relative error = 1.1175587148203339060037678248393e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.109 y1[1] (analytic) = -0.44555699294736394616628139978959 y1[1] (numeric) = -0.44555699294736394616628139978959 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.89525357638811065223026550105512 y2[1] (numeric) = -0.89525357638811065223026550105513 absolute error = 1e-32 relative error = 1.1170019605333356865082455731544e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1922.6MB, alloc=4.5MB, time=129.27 x[1] = 1.11 y1[1] (analytic) = -0.44466151674170684864373751193357 y1[1] (numeric) = -0.44466151674170684864373751193357 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.89569868568004762924062595933937 y2[1] (numeric) = -0.89569868568004762924062595933939 absolute error = 2e-32 relative error = 2.2328937531950556528878894438313e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1926.4MB, alloc=4.5MB, time=129.82 x[1] = 1.111 y1[1] (analytic) = -0.44376559587457006453950495171964 y1[1] (numeric) = -0.44376559587457006453950495171964 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.89614289927337356775800912910654 y2[1] (numeric) = -0.89614289927337356775800912910655 absolute error = 1e-32 relative error = 1.1158934594146064016984437285823e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1930.2MB, alloc=4.5MB, time=130.38 x[1] = 1.112 y1[1] (analytic) = -0.44286923124187438633029805065073 y1[1] (numeric) = -0.44286923124187438633029805065072 absolute error = 1e-32 relative error = 2.2580028808861795568128105831080e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.89658621672387491147427470287502 y2[1] (numeric) = -0.89658621672387491147427470287503 absolute error = 1e-32 relative error = 1.1153417054011815431915508448929e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1934.0MB, alloc=4.5MB, time=130.93 x[1] = 1.113 y1[1] (analytic) = -0.44197242373998437201474478319558 y1[1] (numeric) = -0.44197242373998437201474478319557 absolute error = 1e-32 relative error = 2.2625846009530842491806327722041e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.89702863758823424683119860805389 y2[1] (numeric) = -0.8970286375882342468311986080539 absolute error = 1e-32 relative error = 1.1147916109887151755850962636068e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.114 y1[1] (analytic) = -0.44107517426570744874890346520485 y1[1] (numeric) = -0.44107517426570744874890346520484 absolute error = 1e-32 relative error = 2.2671872241841284561300813030067e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.89747016142403074633784962205036 y2[1] (numeric) = -0.89747016142403074633784962205037 absolute error = 1e-32 relative error = 1.1142431726234591056344002768403e-30 % Correct digits = 31 h = 0.001 memory used=1937.8MB, alloc=4.5MB, time=131.48 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.115 y1[1] (analytic) = -0.44017748371629301603891033180253 y1[1] (numeric) = -0.44017748371629301603891033180252 absolute error = 1e-32 relative error = 2.2718108876385158652546828200257e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.89791078778974061099137999479996 y2[1] (numeric) = -0.89791078778974061099137999479997 absolute error = 1e-32 relative error = 1.1136963867663934580353985488203e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1941.7MB, alloc=4.5MB, time=132.03 x[1] = 1.116 y1[1] (analytic) = -0.4392793529894315484916548020305 y1[1] (numeric) = -0.43927935298943154849165480203049 absolute error = 1e-32 relative error = 2.2764557295823066193347475552686e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.89835051624473751180078765796561 y2[1] (numeric) = -0.89835051624473751180078765796562 absolute error = 1e-32 relative error = 1.1131512498931654566369836513436e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1945.5MB, alloc=4.5MB, time=132.59 x[1] = 1.117 y1[1] (analytic) = -0.4383807829832536981243796794962 y1[1] (numeric) = -0.43838078298325369812437967949619 absolute error = 1e-32 relative error = 2.2811218895017128425921012675214e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.89878934634929303041320849708013 y2[1] (numeric) = -0.89878934634929303041320849708014 absolute error = 1e-32 relative error = 1.1126077584940285489035754007702e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1949.3MB, alloc=4.5MB, time=133.14 x[1] = 1.118 y1[1] (analytic) = -0.4374817745963293962341039793483 y1[1] (numeric) = -0.43748177459632939623410397934829 absolute error = 1e-32 relative error = 2.2858095081165703513826187485612e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.89922727766457709884229806037674 y2[1] (numeric) = -0.89922727766457709884229806037675 absolute error = 1e-32 relative error = 1.1120659090737818715282623902331e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1953.1MB, alloc=4.5MB, time=133.69 x[1] = 1.119 y1[1] (analytic) = -0.43658232872766695482776651208281 y1[1] (numeric) = -0.4365823287276669548277665120828 absolute error = 1e-32 relative error = 2.2905187273939892790650123739292e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.8996643097526584382982629759624 y2[1] (numeric) = -0.89966430975265843829826297596241 absolute error = 1e-32 relative error = 1.1115256981517100551120645381755e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.12 y1[1] (analytic) = -0.43568244627671216761398879396113 y1[1] (numeric) = -0.43568244627671216761398879396112 absolute error = 1e-32 relative error = 2.2952496905621863932273286161367e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90010044217650499711910324733915 y2[1] (numeric) = -0.90010044217650499711910324733916 absolute error = 1e-32 relative error = 1.1109871222615233658399525717416e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1956.9MB, alloc=4.5MB, time=134.24 x[1] = 1.121 y1[1] (analytic) = -0.43478212814334741055735629220213 y1[1] (numeric) = -0.43478212814334741055735629220212 absolute error = 1e-32 relative error = 2.3000025421245019328649034567719e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90053567449998438780262749606768 y2[1] (numeric) = -0.90053567449998438780262749606769 absolute error = 1e-32 relative error = 1.1104501779512981820992262175856e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1960.7MB, alloc=4.5MB, time=134.79 x[1] = 1.122 y1[1] (analytic) = -0.43388137522789074199611745059221 y1[1] (numeric) = -0.43388137522789074199611745059221 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.9009700062878643231388041195943 y2[1] (numeric) = -0.90097000628786432313880411959432 absolute error = 2e-32 relative error = 2.2198297235668356080013991187421e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1964.6MB, alloc=4.5MB, time=135.34 x[1] = 1.123 y1[1] (analytic) = -0.43298018843109500232420037773924 y1[1] (numeric) = -0.43298018843109500232420037773924 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.90140343710581305144201223192652 y2[1] (numeric) = -0.90140343710581305144201223192654 absolute error = 2e-32 relative error = 2.2187623406690271875557412122106e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1968.4MB, alloc=4.5MB, time=135.89 x[1] = 1.124 y1[1] (analytic) = -0.43207856865414691323844751587859 y1[1] (numeric) = -0.43207856865414691323844751587858 absolute error = 1e-32 relative error = 2.3143938916360377767414927522348e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90183596652039979088275715494243 y2[1] (numeric) = -0.90183596652039979088275715494245 absolute error = 2e-32 relative error = 2.2176982003908128901077273072082e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1972.2MB, alloc=4.5MB, time=136.45 x[1] = 1.125 y1[1] (analytic) = -0.43117651679866617655196904292169 y1[1] (numeric) = -0.43117651679866617655196904292168 absolute error = 1e-32 relative error = 2.3192357678118648669611859199829e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90226759409909516291841612865483 y2[1] (numeric) = -0.90226759409909516291841612865485 absolute error = 2e-32 relative error = 2.2166372959420971579608571152352e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.126 y1[1] (analytic) = -0.43027403376670457257451619431852 y1[1] (numeric) = -0.43027403376670457257451619431851 absolute error = 1e-32 relative error = 2.3241002745292363306450010955897e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90269831941027162482258080972027 y2[1] (numeric) = -0.90269831941027162482258080972029 absolute error = 2e-32 relative error = 2.2155796205609313305353232122149e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1976.0MB, alloc=4.5MB, time=136.99 x[1] = 1.127 y1[1] (analytic) = -0.42937112046074505806077612428553 y1[1] (numeric) = -0.42937112046074505806077612428552 absolute error = 1e-32 relative error = 2.3289875642472891271496257296125e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90312814202320390131256402888671 y2[1] (numeric) = -0.90312814202320390131256402888673 absolute error = 2e-32 relative error = 2.2145251675133985322747586087895e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1979.8MB, alloc=4.5MB, time=137.54 x[1] = 1.128 y1[1] (analytic) = -0.42846777778370086372749035802905 y1[1] (numeric) = -0.42846777778370086372749035802904 absolute error = 1e-32 relative error = 2.3338977908038164687828261827171e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90355706150806941527463917990897 y2[1] (numeric) = -0.90355706150806941527463917990899 absolute error = 2e-32 relative error = 2.2134739300934992024944601699869e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1983.6MB, alloc=4.5MB, time=138.09 x[1] = 1.129 y1[1] (analytic) = -0.42756400663891459134029931777049 y1[1] (numeric) = -0.42756400663891459134029931777048 absolute error = 1e-32 relative error = 2.3388311094308688779195261286089e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90398507743594871758658151472839 y2[1] (numeric) = -0.90398507743594871758658151472841 absolute error = 2e-32 relative error = 2.2124259016230372632933414572569e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1987.4MB, alloc=4.5MB, time=138.65 x[1] = 1.13 y1[1] (analytic) = -0.42665980793015731037121583565354 y1[1] (numeric) = -0.42665980793015731037121583565353 absolute error = 1e-32 relative error = 2.3437876767705676070253513391040e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.9044121893788259160370815224114 y2[1] (numeric) = -0.90441218937882591603708152241142 absolute error = 2e-32 relative error = 2.2113810754515069216797302583732e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1991.3MB, alloc=4.5MB, time=139.21 x[1] = 1.131 y1[1] (analytic) = -0.42575518256162765422763099598465 y1[1] (numeric) = -0.42575518256162765422763099598464 absolute error = 1e-32 relative error = 2.3487676508911338016415950372979e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90483839690958910334160147246914 y2[1] (numeric) = -0.90483839690958910334160147246916 absolute error = 2e-32 relative error = 2.2103394449559801020887678769565e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.132 y1[1] (analytic) = -0.4248501314379509160537560777255 y1[1] (numeric) = -0.42485013143795091605375607772549 absolute error = 1e-32 relative error = 2.3537711913031368480097055133851e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90526369960203078425424710673748 y2[1] (numeric) = -0.90526369960203078425424710673751 absolute error = 3e-32 relative error = 3.3139515053114917582448866874099e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1995.1MB, alloc=4.5MB, time=139.75 x[1] = 1.133 y1[1] (analytic) = -0.42394465546417814410540479572036 y1[1] (numeric) = -0.42394465546417814410540479572035 absolute error = 1e-32 relative error = 2.3587984589759654099043837826155e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.9056880970308483017752273679812 y2[1] (numeric) = -0.90568809703084830177522736798122 absolute error = 2e-32 relative error = 2.2082657446384422913636858308029e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1998.9MB, alloc=4.5MB, time=140.30 x[1] = 1.134 y1[1] (analytic) = -0.42303875554578523669902046580051 y1[1] (numeric) = -0.4230387555457852366990204658005 absolute error = 1e-32 relative error = 2.3638496163545247234312066851836e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90611158877164426245347595779809 y2[1] (numeric) = -0.90611158877164426245347595779811 absolute error = 2e-32 relative error = 2.2072336617074593786667944577999e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2002.7MB, alloc=4.5MB, time=140.85 x[1] = 1.135 y1[1] (analytic) = -0.42213243258867203673585314466327 y1[1] (numeric) = -0.42213243258867203673585314466326 absolute error = 1e-32 relative error = 2.3689248273761637840570950105866e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90653417440092696078400942123703 y2[1] (numeric) = -0.90653417440092696078400942123705 absolute error = 2e-32 relative error = 2.2062047482343153623055420151386e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2006.5MB, alloc=4.5MB, time=141.41 x[1] = 1.136 y1[1] (analytic) = -0.42122568749916142580219222027303 y1[1] (numeric) = -0.42122568749916142580219222027302 absolute error = 1e-32 relative error = 2.3740242574878361270104142736642e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90695585349611080269959736080713 y2[1] (numeric) = -0.90695585349611080269959736080715 absolute error = 2e-32 relative error = 2.2051789977323040411965157182720e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.137 y1[1] (analytic) = -0.42031852118399841784656035247612 y1[1] (numeric) = -0.42031852118399841784656035247611 absolute error = 1e-32 relative error = 2.3791480736634979704432880580161e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90737662563551672815632128824315 y2[1] (numeric) = -0.90737662563551672815632128824317 absolute error = 2e-32 relative error = 2.2041564037416345543938966711839e-30 % Correct digits = 31 h = 0.001 memory used=2010.3MB, alloc=4.5MB, time=141.97 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.138 y1[1] (analytic) = -0.41941093455034925243477508656013 y1[1] (numeric) = -0.41941093455034925243477508656012 absolute error = 1e-32 relative error = 2.3842964444217475604238752740276e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90779649039837263281259952850347 y2[1] (numeric) = -0.90779649039837263281259952850349 absolute error = 2e-32 relative error = 2.2031369598293231216018980448835e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2014.1MB, alloc=4.5MB, time=142.51 x[1] = 1.139 y1[1] (analytic) = -0.41850292850580048758378488462047 y1[1] (numeric) = -0.41850292850580048758378488462046 absolute error = 1e-32 relative error = 2.3894695398437096279537847502768e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90821544736481378880125649701092 y2[1] (numeric) = -0.90821544736481378880125649701094 absolute error = 2e-32 relative error = 2.2021206595890853844702156356720e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2018.0MB, alloc=4.5MB, time=143.06 x[1] = 1.14 y1[1] (analytic) = -0.41759450395835809217518674082258 y1[1] (numeric) = -0.41759450395835809217518674082257 absolute error = 1e-32 relative error = 2.3946675315911689408191841299543e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.9086334961158832645942155781022 y2[1] (numeric) = -0.90863349611588326459421557810222 absolute error = 2e-32 relative error = 2.2011074966412293450894451099310e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2021.8MB, alloc=4.5MB, time=143.61 x[1] = 1.141 y1[1] (analytic) = -0.41668566181644653794933296696646 y1[1] (numeric) = -0.41668566181644653794933296696645 absolute error = 1e-32 relative error = 2.3998905929249570072180786984330e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90905063623353234395939574002804 y2[1] (numeric) = -0.90905063623353234395939574002805 absolute error = 1e-32 relative error = 1.1000487323162744490644837338538e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2025.6MB, alloc=4.5MB, time=144.17 x[1] = 1.142 y1[1] (analytic) = -0.41577640298890789108093515417116 y1[1] (numeric) = -0.41577640298890789108093515417115 absolute error = 1e-32 relative error = 2.4051388987235960637961500687675e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.90946686730062094400939292964235 y2[1] (numeric) = -0.90946686730062094400939292964236 absolute error = 1e-32 relative error = 1.0995452786181089765425760282659e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.143 y1[1] (analytic) = -0.4148667283850009033370737349995 y1[1] (numeric) = -0.41486672838500090333707373499949 absolute error = 1e-32 relative error = 2.4104126255022045580058269462117e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.9098821889009180323415281981339 y2[1] (numeric) = -0.90988218890091803234152819813391 absolute error = 1e-32 relative error = 1.0990433840758425715664382970075e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2029.4MB, alloc=4.5MB, time=144.72 x[1] = 1.144 y1[1] (analytic) = -0.41395663891440010281852198793779 y1[1] (numeric) = -0.41395663891440010281852198793778 absolute error = 1e-32 relative error = 2.4157119514316684136152202680444e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91029660061910204326884541778702 y2[1] (numeric) = -0.91029660061910204326884541778703 absolute error = 1e-32 relative error = 1.0985430455522845585491589251749e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2033.2MB, alloc=4.5MB, time=145.26 x[1] = 1.145 y1[1] (analytic) = -0.41304613548719488428529374283065 y1[1] (numeric) = -0.41304613548719488428529374283064 absolute error = 1e-32 relative error = 2.4210370563580824487734665174080e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91071010204076129314164235880843 y2[1] (numeric) = -0.91071010204076129314164235880844 absolute error = 1e-32 relative error = 1.0980442599232772055478633103521e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2037.0MB, alloc=4.5MB, time=145.82 x[1] = 1.146 y1[1] (analytic) = -0.41213521901388859906732446164759 y1[1] (numeric) = -0.41213521901388859906732446164758 absolute error = 1e-32 relative error = 2.4263881218224663983261506727792e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91112269275239439475911980472364 y2[1] (numeric) = -0.91112269275239439475911980472365 absolute error = 1e-32 relative error = 1.0975470240776439481977340435454e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2040.8MB, alloc=4.5MB, time=146.37 x[1] = 1.147 y1[1] (analytic) = -0.41122389040539764456119578382428 y1[1] (numeric) = -0.41122389040539764456119578382428 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.91153437234141067087073429472838 y2[1] (numeric) = -0.91153437234141067087073429472839 absolute error = 1e-32 relative error = 1.0970513349171379000574926588386e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2044.7MB, alloc=4.5MB, time=146.92 x[1] = 1.148 y1[1] (analytic) = -0.41031215057305055331381403937818 y1[1] (numeric) = -0.41031215057305055331381403937818 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.91194514039613056676684099167677 y2[1] (numeric) = -0.91194514039613056676684099167678 absolute error = 1e-32 relative error = 1.0965571893563906476742655753430e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.149 y1[1] (analytic) = -0.40940000042858708169395364604402 y1[1] (numeric) = -0.40940000042858708169395364604402 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.91235499650578606195821408509776 y2[1] (numeric) = -0.91235499650578606195821408509777 absolute error = 1e-32 relative error = 1.0960645843228613286877568580101e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2048.5MB, alloc=4.5MB, time=147.46 x[1] = 1.15 y1[1] (analytic) = -0.40848744088415729815257671880992 y1[1] (numeric) = -0.40848744088415729815257671880992 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.91276394026052108094403304975368 y2[1] (numeric) = -0.91276394026052108094403304975369 absolute error = 1e-32 relative error = 1.0955735167567859913055575004014e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2052.3MB, alloc=4.5MB, time=148.01 x[1] = 1.151 y1[1] (analytic) = -0.40757447285232067107284063145842 y1[1] (numeric) = -0.40757447285232067107284063145842 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = -0.91317197125139190306792399178895 y2[1] (numeric) = -0.91317197125139190306792399178897 absolute error = 2e-32 relative error = 2.1901679672222544669864717897391e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2056.1MB, alloc=4.5MB, time=148.56 x[1] = 1.152 y1[1] (analytic) = -0.40666109724604515621070568002894 y1[1] (numeric) = -0.40666109724604515621070568002895 absolute error = 1e-32 relative error = 2.4590500708627229252387386981069e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91357908907036757146164622646176 y2[1] (numeric) = -0.91357908907036757146164622646177 absolute error = 1e-32 relative error = 1.0945959818515241202345778083907e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2059.9MB, alloc=4.5MB, time=149.11 x[1] = 1.153 y1[1] (analytic) = -0.40574731497870628372705540751796 y1[1] (numeric) = -0.40574731497870628372705540751797 absolute error = 1e-32 relative error = 2.4645880898866336047491144581099e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91398529331033030107601514380608 y2[1] (numeric) = -0.91398529331033030107601514380609 absolute error = 1e-32 relative error = 1.0941095084562423772289773224181e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2063.7MB, alloc=4.5MB, time=149.66 x[1] = 1.154 y1[1] (analytic) = -0.4048331269640862448122425576204 y1[1] (numeric) = -0.40483312696408624481224255762041 absolute error = 1e-32 relative error = 2.4701535852541842286957413555891e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91439058356507588579865333133538 y2[1] (numeric) = -0.91439058356507588579865333133539 absolute error = 1e-32 relative error = 1.0936245604161248594045236119792e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.155 y1[1] (analytic) = -0.40391853411637297790397403289031 y1[1] (numeric) = -0.40391853411637297790397403289032 absolute error = 1e-32 relative error = 2.4757467546955643724434236212255e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91479495942931410465816283607061 y2[1] (numeric) = -0.91479495942931410465816283607063 absolute error = 2e-32 relative error = 2.1862822694690845852735658293548e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2067.6MB, alloc=4.5MB, time=150.21 x[1] = 1.156 y1[1] (analytic) = -0.40300353735015925449944863935961 y1[1] (numeric) = -0.40300353735015925449944863935962 absolute error = 1e-32 relative error = 2.4813677978491938192745631345535e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91519842049866912711431236175425 y2[1] (numeric) = -0.91519842049866912711431236175427 absolute error = 2e-32 relative error = 2.1853184568546885741492826974984e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2071.4MB, alloc=4.5MB, time=150.78 x[1] = 1.157 y1[1] (analytic) = -0.40208813758044176456266180540106 y1[1] (numeric) = -0.40208813758044176456266180540107 absolute error = 1e-32 relative error = 2.4870169162847784106957462034421e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.9156009663696799174338341110968 y2[1] (numeric) = -0.91560096636967991743383411109682 absolute error = 2e-32 relative error = 2.1843576770456212409717062959997e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2075.2MB, alloc=4.5MB, time=151.33 x[1] = 1.158 y1[1] (analytic) = -0.40117233572262020152779186745441 y1[1] (numeric) = -0.40117233572262020152779186745442 absolute error = 1e-32 relative error = 2.4926943135267010194313486341035e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91600259663980063815142589729275 y2[1] (numeric) = -0.91600259663980063815142589729277 absolute error = 2e-32 relative error = 2.1833999241232055800922623003052e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2079.0MB, alloc=4.5MB, time=151.89 x[1] = 1.159 y1[1] (analytic) = -0.40025613269249634689958291915336 y1[1] (numeric) = -0.40025613269249634689958291915337 absolute error = 1e-32 relative error = 2.4984001950777533417413089982429e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91640331090740105261555506383741 y2[1] (numeric) = -0.91640331090740105261555506383744 absolute error = 3e-32 relative error = 3.2736677882901474930201682697926e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.16 y1[1] (analytic) = -0.39933952940627315445163962339401 y1[1] (numeric) = -0.39933952940627315445163962339402 absolute error = 1e-32 relative error = 2.5041347684432143166386845864530e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91680310877176692661866166687433 y2[1] (numeric) = -0.91680310877176692661866166687436 absolute error = 3e-32 relative error = 3.2722402130802912020593074638272e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2082.8MB, alloc=4.5MB, time=152.43 TOP MAIN SOLVE Loop x[1] = 1.161 y1[1] (analytic) = -0.3984225267805538340235497889738 y1[1] (numeric) = -0.39842252678055383402354978897382 absolute error = 2e-32 relative error = 5.0197964863105621859150278645253e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91720198983310042911135928990347 y2[1] (numeric) = -0.9172019898331004291113592899035 absolute error = 3e-32 relative error = 3.2708171517877953787350472891140e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2086.6MB, alloc=4.5MB, time=152.98 x[1] = 1.162 y1[1] (analytic) = -0.39750512573234093491775091460202 y1[1] (numeric) = -0.39750512573234093491775091460203 absolute error = 1e-32 relative error = 2.5156908307978585810924644574134e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91759995369252053200023277668282 y2[1] (numeric) = -0.91759995369252053200023277668285 absolute error = 3e-32 relative error = 3.2693985956817876441168850825183e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2090.4MB, alloc=4.5MB, time=153.53 x[1] = 1.163 y1[1] (analytic) = -0.3965873271790354288970573033388 y1[1] (numeric) = -0.39658732717903542889705730333881 absolute error = 1e-32 relative error = 2.5215127450317137446599518616457e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91799699995206340902883308455898 y2[1] (numeric) = -0.91799699995206340902883308455901 absolute error = 3e-32 relative error = 3.2679845360678259711149187278070e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2094.3MB, alloc=4.5MB, time=154.08 x[1] = 1.164 y1[1] (analytic) = -0.39566913203843579278376474985931 y1[1] (numeric) = -0.39566913203843579278376474985932 absolute error = 1e-32 relative error = 2.5273642016200009083787425973873e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91839312821468283374147037726515 y2[1] (numeric) = -0.91839312821468283374147037726518 absolute error = 3e-32 relative error = 3.2665749642877580743807152030846e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2098.1MB, alloc=4.5MB, time=154.64 x[1] = 1.165 y1[1] (analytic) = -0.39475054122873709066125020136176 y1[1] (numeric) = -0.39475054122873709066125020136177 absolute error = 1e-32 relative error = 2.5332454184541644822010594151621e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91878833808425057652940739342648 y2[1] (numeric) = -0.91878833808425057652940739342652 absolute error = 4e-32 relative error = 4.3535598289594420978108874967513e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.166 y1[1] (analytic) = -0.39383155566853005567898419044329 y1[1] (numeric) = -0.3938315556685300556789841904433 absolute error = 1e-32 relative error = 2.5391566155802256282092243848323e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.9191826291655568007590560446127 y2[1] (numeric) = -0.91918262916555680075905604461274 absolute error = 4e-32 relative error = 4.3516923330364065653538148792137e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2101.9MB, alloc=4.5MB, time=155.18 x[1] = 1.167 y1[1] (analytic) = -0.39291217627680017146187423485461 y1[1] (numeric) = -0.39291217627680017146187423485462 absolute error = 1e-32 relative error = 2.5450980152254595260960225401892e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91957600106431045798178111477418 y2[1] (numeric) = -0.91957600106431045798178111477422 absolute error = 4e-32 relative error = 4.3498307865477454864264811503626e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2105.7MB, alloc=4.5MB, time=155.74 x[1] = 1.168 y1[1] (analytic) = -0.3919924039729267531248577947136 y1[1] (numeric) = -0.39199240397292675312485779471361 absolute error = 1e-32 relative error = 2.5510698418254700252392414376318e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.91996845338713968222491585129093 y2[1] (numeric) = -0.91996845338713968222491585129096 absolute error = 3e-32 relative error = 3.2609813836057101225508207354083e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2109.5MB, alloc=4.5MB, time=156.30 x[1] = 1.169 y1[1] (analytic) = -0.39107223967668202789366377250818 y1[1] (numeric) = -0.39107223967668202789366377250819 absolute error = 1e-32 relative error = 2.5570723220516686065341426362337e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92035998574159218336359515665156 y2[1] (numeric) = -0.9203599857415921833635951566516 absolute error = 4e-32 relative error = 4.3461254965109628314297540974436e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2113.3MB, alloc=4.5MB, time=156.85 x[1] = 1.17 y1[1] (analytic) = -0.3901516843082302153326619350505 y1[1] (numeric) = -0.39015168430823021533266193505051 absolute error = 1e-32 relative error = 2.5631056848391647153358290323670e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92075059773613563957301300896203 y2[1] (numeric) = -0.92075059773613563957301300896206 absolute error = 3e-32 relative error = 3.2582112978000214562228130181959e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2117.1MB, alloc=4.5MB, time=157.41 x[1] = 1.171 y1[1] (analytic) = -0.38923073878812660718072002945622 y1[1] (numeric) = -0.38923073878812660718072002945623 absolute error = 1e-32 relative error = 2.5691701614150746681624984506760e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92114028898015808886071165905919 y2[1] (numeric) = -0.92114028898015808886071165905922 absolute error = 3e-32 relative error = 3.2568329014481113300061550642827e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.172 y1[1] (analytic) = -0.38830940403731664679598875721517 y1[1] (numeric) = -0.38830940403731664679598875721519 absolute error = 2e-32 relative error = 5.1505319706545129605968482010513e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92152905908396831967851107197284 y2[1] (numeric) = -0.92152905908396831967851107197287 absolute error = 3e-32 relative error = 3.2554589249546872772995678622652e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2121.0MB, alloc=4.5MB, time=157.95 x[1] = 1.173 y1[1] (analytic) = -0.38738768097713500821053516149177 y1[1] (numeric) = -0.38738768097713500821053516149178 absolute error = 1e-32 relative error = 2.5813933924734781091923386753764e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.9219169076587962606136880008392 y2[1] (numeric) = -0.92191690765879626061368800083923 absolute error = 3e-32 relative error = 3.2540893599820033433241581024949e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2124.8MB, alloc=4.5MB, time=158.50 x[1] = 1.174 y1[1] (analytic) = -0.38646557052930467479574537294483 y1[1] (numeric) = -0.38646557052930467479574537294484 absolute error = 1e-32 relative error = 2.5875526211310267596551054837283e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92230383431679336915901500211929 y2[1] (numeric) = -0.92230383431679336915901500211932 absolute error = 3e-32 relative error = 3.2527241982272390101530654388788e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2128.6MB, alloc=4.5MB, time=159.05 x[1] = 1.175 y1[1] (analytic) = -0.38554307361593601753941804858756 y1[1] (numeric) = -0.38554307361593601753941804858757 absolute error = 1e-32 relative error = 2.5937439119867670514048111716719e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92268983867103301956127062211557 y2[1] (numeric) = -0.9226898386710330195612706221156 absolute error = 3e-32 relative error = 3.2513634314223668505619273247742e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2132.4MB, alloc=4.5MB, time=159.61 x[1] = 1.176 y1[1] (analytic) = -0.38462019115952587293547022651722 y1[1] (numeric) = -0.38462019115952587293547022651724 absolute error = 2e-32 relative error = 5.1999350163353120151494873517578e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92307492033551088974783290630898 y2[1] (numeric) = -0.92307492033551088974783290630901 absolute error = 3e-32 relative error = 3.2500070513340209075555771687932e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2136.2MB, alloc=4.5MB, time=160.16 x[1] = 1.177 y1[1] (analytic) = -0.38369692408295662048717770673193 y1[1] (numeric) = -0.38369692408295662048717770673195 absolute error = 2e-32 relative error = 5.2124473105434459689591810020634e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92345907892514534733096930495515 y2[1] (numeric) = -0.92345907892514534733096930495518 absolute error = 3e-32 relative error = 3.2486550497633657954339407982257e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.178 y1[1] (analytic) = -0.38277327330949525982487245471722 y1[1] (numeric) = -0.38277327330949525982487245471724 absolute error = 2e-32 relative error = 5.2250252027990456566391522183249e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92384231405577783468943697068198 y2[1] (numeric) = -0.92384231405577783468943697068201 absolute error = 3e-32 relative error = 3.2473074185459665182889217268066e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2140.0MB, alloc=4.5MB, time=160.71 x[1] = 1.179 y1[1] (analytic) = -0.38184923976279248743901991002817 y1[1] (numeric) = -0.38184923976279248743901991002819 absolute error = 2e-32 relative error = 5.2376691943721414273714102612865e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.9242246253441732531270083665204 y2[1] (numeric) = -0.92422462534417325312700836652043 absolute error = 3e-32 relative error = 3.2459641495516590018526745328467e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2143.8MB, alloc=4.5MB, time=161.26 x[1] = 1.18 y1[1] (analytic) = -0.38092482436688177302959946671276 y1[1] (numeric) = -0.38092482436688177302959946671278 absolute error = 2e-32 relative error = 5.2503797916665345836180073297707e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92460601240802034610753802587476 y2[1] (numeric) = -0.9246060124080203461075380258748 absolute error = 4e-32 relative error = 4.3261669795792284461947461557086e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2147.7MB, alloc=4.5MB, time=161.81 x[1] = 1.181 y1[1] (analytic) = -0.38000002804617843547271177611907 y1[1] (numeric) = -0.38000002804617843547271177611909 absolute error = 2e-32 relative error = 5.2631575062856459071452217794394e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92498647486593208156618722939801 y2[1] (numeric) = -0.92498647486593208156618722939805 absolute error = 4e-32 relative error = 4.3243875545096609525390047470385e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2151.5MB, alloc=4.5MB, time=162.37 x[1] = 1.182 y1[1] (analytic) = -0.37907485172547871840533690540195 y1[1] (numeric) = -0.37907485172547871840533690540197 absolute error = 2e-32 relative error = 5.2760028550993803869611046397148e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92536601233744603329642428757874 y2[1] (numeric) = -0.92536601233744603329642428757879 absolute error = 5e-32 relative error = 5.4032673918616851596407651191691e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.183 y1[1] (analytic) = -0.37814929632995886542916776689402 y1[1] (numeric) = -0.37814929632995886542916776689404 memory used=2155.3MB, alloc=4.5MB, time=162.92 absolute error = 2e-32 relative error = 5.2889163603120264923134493131569e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92574462444302476141241904207182 y2[1] (numeric) = -0.92574462444302476141241904207187 absolute error = 5e-32 relative error = 5.4010575573239275589806981257014e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.184 y1[1] (analytic) = -0.37722336278517419493444361443051 y1[1] (numeric) = -0.37722336278517419493444361443053 absolute error = 2e-32 relative error = 5.3018985495312087132814930925079e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92612231080405619188645112340955 y2[1] (numeric) = -0.9261223108040561918864511234096 absolute error = 5e-32 relative error = 5.3988549262559253835999844668224e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2159.1MB, alloc=4.5MB, time=163.47 x[1] = 1.185 y1[1] (analytic) = -0.37629705201705817454470878271726 y1[1] (numeric) = -0.37629705201705817454470878271729 absolute error = 3e-32 relative error = 7.9724249337568687195970564731252e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92649907104285399516095242771696 y2[1] (numeric) = -0.92649907104285399516095242771701 absolute error = 5e-32 relative error = 5.3966594854456487420756454814525e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2162.9MB, alloc=4.5MB, time=164.02 x[1] = 1.186 y1[1] (analytic) = -0.37537036495192149518342222490618 y1[1] (numeric) = -0.37537036495192149518342222490621 absolute error = 3e-32 relative error = 7.9921066767864014500837816477765e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92687490478265796383480520042016 y2[1] (numeric) = -0.92687490478265796383480520042021 absolute error = 5e-32 relative error = 5.3944712217367082123847146461815e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2166.7MB, alloc=4.5MB, time=164.57 x[1] = 1.187 y1[1] (analytic) = -0.37444330251645114476334378169122 y1[1] (numeric) = -0.37444330251645114476334378169125 absolute error = 3e-32 relative error = 8.0118938697486655516297239530934e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92724981164763438942351804068117 y2[1] (numeric) = -0.92724981164763438942351804068122 absolute error = 5e-32 relative error = 5.3922901220281483338321570881954e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2170.6MB, alloc=4.5MB, time=165.12 x[1] = 1.188 y1[1] (analytic) = -0.37351586563770948149962349246169 y1[1] (numeric) = -0.37351586563770948149962349246171 absolute error = 2e-32 relative error = 5.3545248916946773000942267917666e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92762379126287643819290306641467 y2[1] (numeric) = -0.92762379126287643819290306641472 absolute error = 5e-32 relative error = 5.3901161732742422287913338647761e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.189 y1[1] (analytic) = -0.37258805524313330684752063534609 y1[1] (numeric) = -0.37258805524313330684752063534612 absolute error = 3e-32 relative error = 8.0517879137116786487005881899003e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92799684325440452606587840624079 y2[1] (numeric) = -0.92799684325440452606587840624084 absolute error = 5e-32 relative error = 5.3879493624842873479152915371494e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2174.4MB, alloc=4.5MB, time=165.66 TOP MAIN SOLVE Loop x[1] = 1.19 y1[1] (analytic) = -0.37165987226053293806567955835047 y1[1] (numeric) = -0.37165987226053293806567955835049 absolute error = 2e-32 relative error = 5.3812642937088548613935325903777e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92836896724916669260202111160267 y2[1] (numeric) = -0.92836896724916669260202111160272 absolute error = 5e-32 relative error = 5.3857896767224023325210638158632e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2178.2MB, alloc=4.5MB, time=166.21 x[1] = 1.191 y1[1] (analytic) = -0.37073131761809128040588973823783 y1[1] (numeric) = -0.37073131761809128040588973823785 absolute error = 2e-32 relative error = 5.3947425128521222089558317695293e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92874016287503897404949650952708 y2[1] (numeric) = -0.92874016287503897404949650952712 absolute error = 4e-32 relative error = 4.3069096824858599903142019053079e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2182.0MB, alloc=4.5MB, time=166.76 x[1] = 1.192 y1[1] (analytic) = -0.36980239224436289893025787731161 y1[1] (numeric) = -0.36980239224436289893025787731163 absolute error = 2e-32 relative error = 5.4082938400204118717164918402662e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92911042976082577546899094412978 y2[1] (numeric) = -0.92911042976082577546899094412982 absolute error = 4e-32 relative error = 4.3051933030497690890339289232176e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2185.8MB, alloc=4.5MB, time=167.32 x[1] = 1.193 y1[1] (analytic) = -0.36887309706827308995672022085341 y1[1] (numeric) = -0.36887309706827308995672022085344 absolute error = 3e-32 relative error = 8.1328782821067139776763717275742e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92947976753626024192927578296402 y2[1] (numeric) = -0.92947976753626024192927578296406 absolute error = 4e-32 relative error = 4.3034825928515487348085560234730e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2189.6MB, alloc=4.5MB, time=167.87 x[1] = 1.194 y1[1] (analytic) = -0.3679434330191169521338236496256 y1[1] (numeric) = -0.36794343301911695213382364962563 absolute error = 3e-32 relative error = 8.1534272140253997201326903965476e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.92984817583200462877403149267892 y2[1] (numeric) = -0.92984817583200462877403149267896 absolute error = 4e-32 relative error = 4.3017775417163142502654825223370e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.195 y1[1] (analytic) = -0.36701340102655845714570447258002 y1[1] (numeric) = -0.36701340102655845714570447258005 absolute error = 3e-32 relative error = 8.1740884436612406487136004392341e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.93021565427965067095956151719464 y2[1] (numeric) = -0.93021565427965067095956151719469 absolute error = 5e-32 relative error = 5.3750976743902982403299508181407e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2193.4MB, alloc=4.5MB, time=168.42 x[1] = 1.196 y1[1] (analytic) = -0.36608300202062952004819421471675 y1[1] (numeric) = -0.36608300202062952004819421471678 absolute error = 3e-32 relative error = 8.1948628683692446123591783707891e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.93058220251171995146302662071125 y2[1] (numeric) = -0.93058220251171995146302662071129 absolute error = 4e-32 relative error = 4.2983843761503951003641566082779e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2197.3MB, alloc=4.5MB, time=168.96 x[1] = 1.197 y1[1] (analytic) = -0.36515223693172906923698206390959 y1[1] (numeric) = -0.36515223693172906923698206390962 absolute error = 3e-32 relative error = 8.2157513951116695326772345797749e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.93094782016166426876083128734747 y2[1] (numeric) = -0.93094782016166426876083128734752 absolute error = 5e-32 relative error = 5.3708703019807513809109265779072e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2201.1MB, alloc=4.6MB, time=169.52 x[1] = 1.198 y1[1] (analytic) = -0.36422110669062211604876400845833 y1[1] (numeric) = -0.36422110669062211604876400845836 absolute error = 3e-32 relative error = 8.2367549405868721774645944526507e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.93131250686386600337679469905388 y2[1] (numeric) = -0.93131250686386600337679469905392 absolute error = 4e-32 relative error = 4.2950137258112623886905567051929e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2204.9MB, alloc=4.6MB, time=170.07 x[1] = 1.199 y1[1] (analytic) = -0.3632896122284388239963090641411 y1[1] (numeric) = -0.36328961222843882399630906414113 absolute error = 3e-32 relative error = 8.2578744313602362959689532357004e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.93167626225363848349973974365966 y2[1] (numeric) = -0.9316762622536384834997397436597 absolute error = 4e-32 relative error = 4.2933368188692185012527609108929e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2208.7MB, alloc=4.6MB, time=170.63 x[1] = 1.2 y1[1] (analytic) = -0.36235775447667357763837335562308 y1[1] (numeric) = -0.36235775447667357763837335562311 absolute error = 3e-32 relative error = 8.2791108039972193706502988177133e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.93203908596722634967013443549483 y2[1] (numeric) = -0.93203908596722634967013443549487 absolute error = 4e-32 relative error = 4.2916655108395889148204676897409e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.201 y1[1] (analytic) = -0.36142553436718405108539318222982 y1[1] (numeric) = -0.36142553436718405108539318222985 absolute error = 3e-32 relative error = 8.3004650051985580894200304635554e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.93240097764180591853542106197658 y2[1] (numeric) = -0.93240097764180591853542106197662 absolute error = 4e-32 relative error = 4.2899997918456200234952742677276e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2212.5MB, alloc=4.6MB, time=171.17 x[1] = 1.202 y1[1] (analytic) = -0.36049295283219027614188856231455 y1[1] (numeric) = -0.36049295283219027614188856231458 absolute error = 3e-32 relative error = 8.3219379919376735122791357309856e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.93276193691548554567366930086106 y2[1] (numeric) = -0.9327619369154855456736693008611 absolute error = 4e-32 relative error = 4.2883396520525329772962065889838e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2216.3MB, alloc=4.6MB, time=171.72 x[1] = 1.203 y1[1] (analytic) = -0.35956001080427371008650911373818 y1[1] (numeric) = -0.35956001080427371008650911373822 absolute error = 4e-32 relative error = 1.1124707642133757063343452158956e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93312196342730598748519048453766 y2[1] (numeric) = -0.9331219634273059874851904845377 absolute error = 4e-32 relative error = 4.2866850816673723477025146834251e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2220.1MB, alloc=4.6MB, time=172.27 x[1] = 1.204 y1[1] (analytic) = -0.35862670921637630309065449033859 y1[1] (numeric) = -0.35862670921637630309065449033863 absolute error = 4e-32 relative error = 1.1153658936168673687541158951459e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93348105681724076215175111978172 y2[1] (numeric) = -0.93348105681724076215175111978176 absolute error = 4e-32 relative error = 4.2850360709388556199454191769670e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2224.0MB, alloc=4.6MB, time=172.83 x[1] = 1.205 y1[1] (analytic) = -0.35769304900179956527660195569084 y1[1] (numeric) = -0.35769304900179956527660195569088 absolute error = 4e-32 relative error = 1.1182772522873028686871964482202e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93383921672619650966302470378221 y2[1] (numeric) = -0.93383921672619650966302470378225 absolute error = 4e-32 relative error = 4.2833926101572235075073472082404e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2227.8MB, alloc=4.6MB, time=173.38 x[1] = 1.206 y1[1] (analytic) = -0.35675903109420363341607403595321 y1[1] (numeric) = -0.35675903109420363341607403595324 absolute error = 3e-32 relative error = 8.4090373011688052619993838633107e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.93419644279601335090992181002254 y2[1] (numeric) = -0.93419644279601335090992181002259 absolute error = 5e-32 relative error = 5.3521933620676138553980044989885e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.207 y1[1] (analytic) = -0.35582465642760633727017955315342 y1[1] (numeric) = -0.35582465642760633727017955315345 absolute error = 3e-32 relative error = 8.4311189396464985583475719818926e-30 % Correct digits = 31 h = 0.001 y2[1] (analytic) = -0.93455273466946524584443935071444 y2[1] (numeric) = -0.93455273466946524584443935071449 absolute error = 5e-32 relative error = 5.3501528747528746627135037943112e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2231.6MB, alloc=4.6MB, time=173.93 x[1] = 1.208 y1[1] (analytic) = -0.35488992593638226557166169889642 y1[1] (numeric) = -0.35488992593638226557166169889646 absolute error = 4e-32 relative error = 1.1271100438948616068747356639018e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.9349080919902603507056708559653 y2[1] (numeric) = -0.93490809199026035070567085596535 absolute error = 5e-32 relative error = 5.3481192887697123561284289457607e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2235.4MB, alloc=4.6MB, time=174.48 x[1] = 1.209 y1[1] (analytic) = -0.35395484055526183165038716616764 y1[1] (numeric) = -0.35395484055526183165038716616768 absolute error = 4e-32 relative error = 1.1300876670382737302725264786990e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93526251440304137431162054369872 y2[1] (numeric) = -0.93526251440304137431162054369876 absolute error = 4e-32 relative error = 4.2768740737493546069337287300018e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2239.2MB, alloc=4.6MB, time=175.03 x[1] = 1.21 y1[1] (analytic) = -0.35301940121933033870301071366479 y1[1] (numeric) = -0.35301940121933033870301071366483 absolute error = 4e-32 relative error = 1.1330822006337286180955577608168e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93561600155338593341646488854361 y2[1] (numeric) = -0.93561600155338593341646488854365 absolute error = 4e-32 relative error = 4.2752582184986939317636653606433e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2243.0MB, alloc=4.6MB, time=175.58 x[1] = 1.211 y1[1] (analytic) = -0.3520836088640270447077498929158 y1[1] (numeric) = -0.35208360886402704470774989291584 absolute error = 4e-32 relative error = 1.1360937854805902921227880495529e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93596855308780690713290633246015 y2[1] (numeric) = -0.9359685530878069071329063324602 absolute error = 5e-32 relative error = 5.3420598197500875325976616677608e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.212 y1[1] (analytic) = -0.35114746442514422698520502333014 y1[1] (numeric) = -0.35114746442514422698520502333019 absolute error = 5e-32 relative error = 1.4239032049356784551229594332863e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93632016865375279041926471477826 y2[1] (numeric) = -0.9363201686537527904192647147783 absolute error = 4e-32 relative error = 4.2720429762302631331320900420155e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2246.8MB, alloc=4.6MB, time=176.13 TOP MAIN SOLVE Loop x[1] = 1.213 y1[1] (analytic) = -0.35021096883882624640615985428573 y1[1] (numeric) = -0.35021096883882624640615985428578 absolute error = 5e-32 relative error = 1.4277108499994171134629941393719e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93667084789960804663095293458658 y2[1] (numeric) = -0.93667084789960804663095293458663 absolute error = 5e-32 relative error = 5.3380544630080103813925185290088e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2250.7MB, alloc=4.6MB, time=176.68 x[1] = 1.214 y1[1] (analytic) = -0.3492741230415686112472987063726 y1[1] (numeric) = -0.34927412304156861124729870637264 absolute error = 4e-32 relative error = 1.1452322792100870427141779504246e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93702059047469345913598429402594 y2[1] (numeric) = -0.93702059047469345913598429402598 absolute error = 4e-32 relative error = 4.2688496289858529182217247895092e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2254.5MB, alloc=4.6MB, time=177.24 x[1] = 1.215 y1[1] (analytic) = -0.34833692797021704069577623599835 y1[1] (numeric) = -0.34833692797021704069577623599839 absolute error = 4e-32 relative error = 1.1483135087939920469784411214671e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93736939602926648199415990700887 y2[1] (numeric) = -0.93736939602926648199415990700891 absolute error = 4e-32 relative error = 4.2672611426660149662105960656628e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2258.3MB, alloc=4.6MB, time=177.78 x[1] = 1.216 y1[1] (analytic) = -0.3473993845619665280035763187075 y1[1] (numeric) = -0.34739938456196652800357631870755 absolute error = 5e-32 relative error = 1.4392656470317197841167261666546e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93771726421452158969958549420736 y2[1] (numeric) = -0.9377172642145215896995854942074 absolute error = 4e-32 relative error = 4.2656781021842421282037156614096e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2262.1MB, alloc=4.6MB, time=178.34 x[1] = 1.217 y1[1] (analytic) = -0.34646149375436040329259689677779 y1[1] (numeric) = -0.34646149375436040329259689677784 absolute error = 5e-32 relative error = 1.4431618203277091668051867763728e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93806419468259062598616782182097 y2[1] (numeric) = -0.93806419468259062598616782182101 absolute error = 4e-32 relative error = 4.2641004983176716065824066503774e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 1.218 y1[1] (analytic) = -0.34552325648528939601139798593043 y1[1] (numeric) = -0.34552325648528939601139798593048 absolute error = 5e-32 relative error = 1.4470805962124504044504785844819e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.938410187086543151695741978658 y2[1] (numeric) = -0.93841018708654315169574197865804 absolute error = 4e-32 relative error = 4.2625283218830907308041352131918e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2265.9MB, alloc=4.6MB, time=178.89 x[1] = 1.219 y1[1] (analytic) = -0.34458467369299069704455038432832 y1[1] (numeric) = -0.34458467369299069704455038432837 absolute error = 5e-32 relative error = 1.4510221671828541745292883758840e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93875524108038679170848162343145 y2[1] (numeric) = -0.93875524108038679170848162343149 absolute error = 4e-32 relative error = 4.2609615637367983230232041369159e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2269.7MB, alloc=4.6MB, time=179.44 x[1] = 1.22 y1[1] (analytic) = -0.3436457463160470204755229744352 y1[1] (numeric) = -0.34364574631604702047552297443524 absolute error = 4e-32 relative error = 1.1639893823452847975735699500606e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93909935631906758093524527188837 y2[1] (numeric) = -0.93909935631906758093524527188841 absolute error = 4e-32 relative error = 4.2594002147744668214178252652873e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2273.5MB, alloc=4.6MB, time=179.99 x[1] = 1.221 y1[1] (analytic) = -0.3427064752933856650040468547703 y1[1] (numeric) = -0.34270647529338566500404685477035 absolute error = 5e-32 relative error = 1.4589744753785518739239845816055e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93944253245847030937151263145524 y2[1] (numeric) = -0.93944253245847030937151263145528 absolute error = 4e-32 relative error = 4.2578442659310051571551488637049e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2277.4MB, alloc=4.6MB, time=180.54 x[1] = 1.222 y1[1] (analytic) = -0.34176686156427757501889488411627 y1[1] (numeric) = -0.34176686156427757501889488411632 absolute error = 5e-32 relative error = 1.4629856087026238288028211904539e-29 % Correct digits = 30 h = 0.001 y2[1] (analytic) = -0.93978476915541886621256592949169 y2[1] (numeric) = -0.93978476915541886621256592949173 absolute error = 4e-32 relative error = 4.2562937081804223809536125839066e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 Finished! Maximum Time Reached before Solution Completed! diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 2 ) = diff ( y1, x , 1) ; Iterations = 723 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 3 Minutes 0 Seconds Expected Time Remaining = 15 Minutes 42 Seconds Optimized Time Remaining = 15 Minutes 41 Seconds Expected Total Time = 18 Minutes 41 Seconds Time to Timeout Unknown Percent Done = 16.09 % > quit memory used=2278.6MB, alloc=4.6MB, time=180.70