(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "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, " ")))) (%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "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, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 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))), 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 ), hnew : sz2), return(hnew)) 1 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 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))), 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 ), hnew : sz2), return(hnew)) 1 (%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], 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(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 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(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 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))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], 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(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 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(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 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))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%i11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_2D0 array_x , 1 1 1 array_tmp2 : array_const_3D0 + array_tmp1 , array_tmp3 : sqrt(array_tmp2 ), 1 1 1 1 1 array_tmp4_g : sin(array_tmp3 ), array_tmp4 : cos(array_tmp3 ), 1 1 1 1 array_tmp5 : array_tmp4 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_2D0 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp2 2 ----------- array_tmp3 1 array_tmp3 : -----------, array_tmp4_g : att(1, array_tmp4, array_tmp3, 1), 2 2.0 2 array_tmp4 : - att(1, array_tmp4_g, array_tmp3, 1), 2 array_tmp5 : array_tmp4 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, array_tmp3 : 0.0, 2, 2 3 - ats(3, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : -----------------------------------, 3 2.0 array_tmp4_g : att(2, array_tmp4, array_tmp3, 1), 3 array_tmp4 : - att(2, array_tmp4_g, array_tmp3, 1), 3 array_tmp5 : array_tmp4 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, array_tmp3 : 0.0, 2, 3 4 - ats(4, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : -----------------------------------, 4 2.0 array_tmp4_g : att(3, array_tmp4, array_tmp3, 1), 4 array_tmp4 : - att(3, array_tmp4_g, array_tmp3, 1), 4 array_tmp5 : array_tmp4 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, array_tmp3 : 0.0, 2, 4 5 - ats(5, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : -----------------------------------, 5 2.0 array_tmp4_g : att(4, array_tmp4, array_tmp3, 1), 5 array_tmp4 : - att(4, array_tmp4_g, array_tmp3, 1), 5 array_tmp5 : array_tmp4 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp3 : 0.0, kkk - ats(kkk, array_tmp3, array_tmp3, 2) ------------------------------------- array_tmp3 1 array_tmp3 : -------------------------------------, kkk 2.0 array_tmp4 : - att(kkk - 1, array_tmp4_g, array_tmp3, 1), kkk array_tmp4_g : att(kkk - 1, array_tmp4, array_tmp3, 1), kkk array_tmp5 : array_tmp4 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp5 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_2D0 array_x , 1 1 1 array_tmp2 : array_const_3D0 + array_tmp1 , array_tmp3 : sqrt(array_tmp2 ), 1 1 1 1 1 array_tmp4_g : sin(array_tmp3 ), array_tmp4 : cos(array_tmp3 ), 1 1 1 1 array_tmp5 : array_tmp4 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_2D0 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp2 2 ----------- array_tmp3 1 array_tmp3 : -----------, array_tmp4_g : att(1, array_tmp4, array_tmp3, 1), 2 2.0 2 array_tmp4 : - att(1, array_tmp4_g, array_tmp3, 1), 2 array_tmp5 : array_tmp4 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, array_tmp3 : 0.0, 2, 2 3 - ats(3, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : -----------------------------------, 3 2.0 array_tmp4_g : att(2, array_tmp4, array_tmp3, 1), 3 array_tmp4 : - att(2, array_tmp4_g, array_tmp3, 1), 3 array_tmp5 : array_tmp4 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, array_tmp3 : 0.0, 2, 3 4 - ats(4, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : -----------------------------------, 4 2.0 array_tmp4_g : att(3, array_tmp4, array_tmp3, 1), 4 array_tmp4 : - att(3, array_tmp4_g, array_tmp3, 1), 4 array_tmp5 : array_tmp4 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, array_tmp3 : 0.0, 2, 4 5 - ats(5, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : -----------------------------------, 5 2.0 array_tmp4_g : att(4, array_tmp4, array_tmp3, 1), 5 array_tmp4 : - att(4, array_tmp4_g, array_tmp3, 1), 5 array_tmp5 : array_tmp4 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp3 : 0.0, kkk - ats(kkk, array_tmp3, array_tmp3, 2) ------------------------------------- array_tmp3 1 array_tmp3 : -------------------------------------, kkk 2.0 array_tmp4 : - att(kkk - 1, array_tmp4_g, array_tmp3, 1), kkk array_tmp4_g : att(kkk - 1, array_tmp4, array_tmp3, 1), kkk array_tmp5 : array_tmp4 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp5 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i13) log10(x) := --------- log(10.0) log(x) (%o13) log10(x) := --------- log(10.0) (%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, 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 : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, 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 : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i32) log_revs(file, revs) := printf(file, revs) (%o32) log_revs(file, revs) := printf(file, revs) (%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i35) logstart(file) := printf(file, "") (%o35) logstart(file) := printf(file, "") (%i36) logend(file) := printf(file, "~%") (%o36) logend(file) := printf(file, "~%") (%i37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i40) factorial_2(nnn) := nnn! (%o40) factorial_2(nnn) := nnn! (%i41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i46) Si(x) := 0.0 (%o46) Si(x) := 0.0 (%i47) Ci(x) := 0.0 (%o47) Ci(x) := 0.0 (%i48) ln(x) := log(x) (%o48) ln(x) := log(x) (%i49) arcsin(x) := asin(x) (%o49) arcsin(x) := asin(x) (%i50) arccos(x) := acos(x) (%o50) arccos(x) := acos(x) (%i51) arctan(x) := atan(x) (%o51) arctan(x) := atan(x) (%i52) omniabs(x) := abs(x) (%o52) omniabs(x) := abs(x) (%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i54) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], 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, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o54) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], 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, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%i55) exact_soln_y(x) := block(sqrt(3.0 + 2.0 x) sin(sqrt(3.0 + 2.0 x)) + cos(sqrt(3.0 + 2.0 x))) (%o55) exact_soln_y(x) := block(sqrt(3.0 + 2.0 x) sin(sqrt(3.0 + 2.0 x)) + cos(sqrt(3.0 + 2.0 x))) (%i56) main() := block([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, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/cos_sqrt_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-1.0,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (cos\ (sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0))) "), 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 : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4_g, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4_g : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term), term array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 1.0, x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10, 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(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 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, 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 (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), 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 < glob_check_sign x_end) 1 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")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-12T21:22:24-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "cos_sqrt_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 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) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), 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), log_revs(html_log_file, " 156 "), logitem_str(html_log_file, "cos_sqrt_lin diffeq.max"), logitem_str(html_log_file, "cos_sqrt_lin maxima results"), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o56) main() := block([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, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/cos_sqrt_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-1.0,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (cos\ (sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0))) "), 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 : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4_g, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4_g : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term), term array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 1.0, x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10, 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(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 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, 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 (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), 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 < glob_check_sign x_end) 1 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")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-12T21:22:24-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "cos_sqrt_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 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) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), 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), log_revs(html_log_file, " 156 "), logitem_str(html_log_file, "cos_sqrt_lin diffeq.max"), logitem_str(html_log_file, "cos_sqrt_lin maxima results"), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i57) main() "##############ECHO OF PROBLEM#################" "##############temp/cos_sqrt_linpostode.ode#################" "diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-1.0," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:1000000," "glob_display_interval:0.1," "glob_max_minutes:10," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.001," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0))) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 6. "" estimated_steps = 6000. "" step_error = 1.666666666666666900000000000000E-14 "" est_needed_step_err = 1.666666666666666900000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 3.69427275905390600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-92 "" max_value3 = 3.69427275905390600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-92 "" value3 = 3.69427275905390600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-92 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = -1. " " y[1] (analytic) = 1.3817732906760363 " " y[1] (numeric) = 1.3817732906760363 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1. " " y[1] (analytic) = 1.3817732906760363 " " y[1] (numeric) = 1.3817732906760363 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.999 " " y[1] (analytic) = 1.3823131722966042 " " y[1] (numeric) = 1.3823131722966042 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.998 " " y[1] (analytic) = 1.3828522127473197 " " y[1] (numeric) = 1.3828522127473197 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.997 " " y[1] (analytic) = 1.3833904123292586 " " y[1] (numeric) = 1.3833904123292586 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.996 " " y[1] (analytic) = 1.3839277713434344 " " y[1] (numeric) = 1.3839277713434346 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.604452266388755600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.995 " " y[1] (analytic) = 1.3844642900907989 " " y[1] (numeric) = 1.384464290090799 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.60383049612979700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.994 " " y[1] (analytic) = 1.3849999688722416 " " y[1] (numeric) = 1.3849999688722416 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.993 " " y[1] (analytic) = 1.38553480798859 " " y[1] (numeric) = 1.38553480798859 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.992 " " y[1] (analytic) = 1.3860688077406098 " " y[1] (numeric) = 1.38606880774061 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.60197389685855300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.991 " " y[1] (analytic) = 1.3866019684290047 " " y[1] (numeric) = 1.386601968429005 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.601357923763831700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.99 " " y[1] (analytic) = 1.3871342903544166 " " y[1] (numeric) = 1.3871342903544168 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.60074339210732300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.989 " " y[1] (analytic) = 1.387665773817425 " " y[1] (numeric) = 1.3876657738174252 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.600130298769231500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.988 " " y[1] (analytic) = 1.3881964191185476 " " y[1] (numeric) = 1.3881964191185479 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.599518640640359000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.987 " " y[1] (analytic) = 1.3887262265582407 " " y[1] (numeric) = 1.3887262265582407 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.986 " " y[1] (analytic) = 1.3892551964368978 " " y[1] (numeric) = 1.389255196436898 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.598299617626205700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.985 " " y[1] (analytic) = 1.389783329054851 " " y[1] (numeric) = 1.3897833290548514 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.19538449315026730000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.984 " " y[1] (analytic) = 1.3903106247123707 " " y[1] (numeric) = 1.390310624712371 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.194172596803224000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.983 " " y[1] (analytic) = 1.390837083709665 " " y[1] (numeric) = 1.3908370837096653 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.59648177004879700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.982 " " y[1] (analytic) = 1.39136270634688 " " y[1] (numeric) = 1.3913627063468805 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.191757316940381000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.981 " " y[1] (analytic) = 1.3918874929241007 " " y[1] (numeric) = 1.391887492924101 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.595276960629599700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.98 " " y[1] (analytic) = 1.392411443741349 " " y[1] (numeric) = 1.3924114437413493 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.594676673501096200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.979 " " y[1] (analytic) = 1.392934559098586 " " y[1] (numeric) = 1.3929345590985862 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.59407779406897400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.978 " " y[1] (analytic) = 1.3934568392957105 " " y[1] (numeric) = 1.3934568392957107 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.59348031932771200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.977 " " y[1] (analytic) = 1.3939782846325595 " " y[1] (numeric) = 1.3939782846325597 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.592884246281930600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.976 " " y[1] (analytic) = 1.394498895408908 " " y[1] (numeric) = 1.3944988954089081 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.592289571946353700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.975 " " y[1] (analytic) = 1.3950186719244697 " " y[1] (numeric) = 1.3950186719244697 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.974 " " y[1] (analytic) = 1.3955376144788956 " " y[1] (numeric) = 1.3955376144788958 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.59110440751498080000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.973 " " y[1] (analytic) = 1.3960557233717756 " " y[1] (numeric) = 1.396055723371776 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.18102782299757640000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.972 " " y[1] (analytic) = 1.396572998902638 " " y[1] (numeric) = 1.3965729989026385 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.179849604703851600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.971 " " y[1] (analytic) = 1.397089441370949 " " y[1] (numeric) = 1.3970894413709491 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.589337077139036400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.97 " " y[1] (analytic) = 1.3976050510761118 " " y[1] (numeric) = 1.3976050510761122 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.177501465869259600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.969 " " y[1] (analytic) = 1.3981198283174703 " " y[1] (numeric) = 1.3981198283174705 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.588165766823040600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.968 " " y[1] (analytic) = 1.3986337733943044 " " y[1] (numeric) = 1.3986337733943048 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.17516435179679100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.967 " " y[1] (analytic) = 1.3991468866058336 " " y[1] (numeric) = 1.399146886605834 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.173999914529138700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.966 " " y[1] (analytic) = 1.399659168251215 " " y[1] (numeric) = 1.3996591682512156 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.75925732410545200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.965 " " y[1] (analytic) = 1.4001706186295444 " " y[1] (numeric) = 1.4001706186295448 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.17167925066680230000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.964 " " y[1] (analytic) = 1.4006812380398554 " " y[1] (numeric) = 1.4006812380398557 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.585261506292220000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.963 " " y[1] (analytic) = 1.4011910267811198 " " y[1] (numeric) = 1.4011910267811203 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.16936949610821200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.962 " " y[1] (analytic) = 1.401699985152249 " " y[1] (numeric) = 1.4016999851522491 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.584109347771116800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.961 " " y[1] (analytic) = 1.4022081134520903 " " y[1] (numeric) = 1.4022081134520907 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.16707060520967370000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.96 " " y[1] (analytic) = 1.402715411979432 " " y[1] (numeric) = 1.4027154119794323 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.58296260972633520000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.959 " " y[1] (analytic) = 1.4032218810329984 " " y[1] (numeric) = 1.4032218810329988 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.164782532632266500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.958 " " y[1] (analytic) = 1.403727520911454 " " y[1] (numeric) = 1.4037275209114541 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.581821269564164200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.957 " " y[1] (analytic) = 1.4042323319133998 " " y[1] (numeric) = 1.4042323319134002 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.162505233339478000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.956 " " y[1] (analytic) = 1.404736314337377 " " y[1] (numeric) = 1.4047363143373774 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.16137060968301600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.955 " " y[1] (analytic) = 1.4052394684818639 " " y[1] (numeric) = 1.4052394684818643 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.16023866259485200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.954 " " y[1] (analytic) = 1.4057417946452775 " " y[1] (numeric) = 1.405741794645278 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.159109386529433000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.953 " " y[1] (analytic) = 1.4062432931259732 " " y[1] (numeric) = 1.4062432931259736 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.15798277595966800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.952 " " y[1] (analytic) = 1.4067439642222448 " " y[1] (numeric) = 1.4067439642222452 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.15685882537686200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.951 " " y[1] (analytic) = 1.4072438082323244 " " y[1] (numeric) = 1.4072438082323249 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.155737529290639000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.95 " " y[1] (analytic) = 1.4077428254543825 " " y[1] (numeric) = 1.4077428254543831 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.731928323343317000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.949 " " y[1] (analytic) = 1.4082410161865284 " " y[1] (numeric) = 1.4082410161865289 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.15350287873763240000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.948 " " y[1] (analytic) = 1.4087383807268092 " " y[1] (numeric) = 1.4087383807268097 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.15238951338107250000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.947 " " y[1] (analytic) = 1.4092349193732105 " " y[1] (numeric) = 1.4092349193732112 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.726918171112110500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.946 " " y[1] (analytic) = 1.4097306324236571 " " y[1] (numeric) = 1.4097306324236576 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.15017067541881600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.945 " " y[1] (analytic) = 1.410225520176011 " " y[1] (numeric) = 1.4102255201760117 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.723597788047073600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.944 " " y[1] (analytic) = 1.410719582928074 " " y[1] (numeric) = 1.4107195829280745 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.14796232521502200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.943 " " y[1] (analytic) = 1.4112128209775852 " " y[1] (numeric) = 1.4112128209775856 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.14686206962341840000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.942 " " y[1] (analytic) = 1.4117052346222225 " " y[1] (numeric) = 1.4117052346222232 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.71864662989192500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.941 " " y[1] (analytic) = 1.412196824159603 " " y[1] (numeric) = 1.4121968241596037 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.717004056226436500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.94 " " y[1] (analytic) = 1.4126875898872813 " " y[1] (numeric) = 1.412687589887282 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.7153653754985200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.939 " " y[1] (analytic) = 1.413177532102751 " " y[1] (numeric) = 1.4131775321027518 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.71373057979427200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.938 " " y[1] (analytic) = 1.4136666511034441 " " y[1] (numeric) = 1.4136666511034448 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.712099661225933600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9369999999999999 " " y[1] (analytic) = 1.4141549471867312 " " y[1] (numeric) = 1.4141549471867318 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.710472611931786300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9359999999999999 " " y[1] (analytic) = 1.4146424206499213 " " y[1] (numeric) = 1.414642420649922 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.708849424076055300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9349999999999999 " " y[1] (analytic) = 1.4151290717902618 " " y[1] (numeric) = 1.4151290717902625 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.707230089848811000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9339999999999999 " " y[1] (analytic) = 1.415614900904939 " " y[1] (numeric) = 1.4156149009049397 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.70561460146586800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9329999999999999 " " y[1] (analytic) = 1.4160999082910775 " " y[1] (numeric) = 1.4160999082910781 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.7040029511686900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9319999999999999 " " y[1] (analytic) = 1.4165840942457404 " " y[1] (numeric) = 1.416584094245741 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.70239513122428900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9309999999999999 " " y[1] (analytic) = 1.4170674590659298 " " y[1] (numeric) = 1.4170674590659305 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.700791133925133500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9299999999999999 " " y[1] (analytic) = 1.4175500030485857 " " y[1] (numeric) = 1.4175500030485864 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.699190951589046000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9289999999999999 " " y[1] (analytic) = 1.4180317264905873 " " y[1] (numeric) = 1.418031726490588 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.697594576559113000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9279999999999999 " " y[1] (analytic) = 1.418512629688752 " " y[1] (numeric) = 1.4185126296887527 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.69600200120358500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9269999999999999 " " y[1] (analytic) = 1.4189927129398359 " " y[1] (numeric) = 1.4189927129398365 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.69441321791578100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9259999999999999 " " y[1] (analytic) = 1.419471976540534 " " y[1] (numeric) = 1.4194719765405344 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.12855214607599800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9249999999999999 " " y[1] (analytic) = 1.4199504207874791 " " y[1] (numeric) = 1.4199504207874796 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.12749799816094100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9239999999999999 " " y[1] (analytic) = 1.4204280459772436 " " y[1] (numeric) = 1.4204280459772443 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.68966954476598600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9229999999999999 " " y[1] (analytic) = 1.4209048524063383 " " y[1] (numeric) = 1.4209048524063388 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.12539723612025300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9219999999999999 " " y[1] (analytic) = 1.4213808403712123 " " y[1] (numeric) = 1.4213808403712127 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.124350612001234300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9209999999999999 " " y[1] (analytic) = 1.4218560101682534 " " y[1] (numeric) = 1.4218560101682538 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.12330648584811300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9199999999999999 " " y[1] (analytic) = 1.4223303620937884 " " y[1] (numeric) = 1.4223303620937886 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.56113242635250500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9189999999999999 " " y[1] (analytic) = 1.4228038964440823 " " y[1] (numeric) = 1.4228038964440826 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.56061285381613320000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9179999999999999 " " y[1] (analytic) = 1.4232766135153392 " " y[1] (numeric) = 1.4232766135153396 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.12018904570637400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9169999999999999 " " y[1] (analytic) = 1.4237485136037018 " " y[1] (numeric) = 1.4237485136037022 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.11915486201992400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9159999999999999 " " y[1] (analytic) = 1.4242195970052516 " " y[1] (numeric) = 1.424219597005252 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.118123151681539000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9149999999999999 " " y[1] (analytic) = 1.4246898640160084 " " y[1] (numeric) = 1.4246898640160088 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.117093909815818500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9139999999999999 " " y[1] (analytic) = 1.4251593149319308 " " y[1] (numeric) = 1.4251593149319315 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.67410069734491500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9129999999999999 " " y[1] (analytic) = 1.4256279500489168 " " y[1] (numeric) = 1.4256279500489173 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.115042812080282600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9119999999999999 " " y[1] (analytic) = 1.4260957696628023 " " y[1] (numeric) = 1.4260957696628027 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.11402094653900200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9109999999999999 " " y[1] (analytic) = 1.4265627740693623 " " y[1] (numeric) = 1.4265627740693627 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.11300153012733900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9099999999999999 " " y[1] (analytic) = 1.4270289635643105 " " y[1] (numeric) = 1.427028963564311 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.111984558048876000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9089999999999999 " " y[1] (analytic) = 1.4274943384432999 " " y[1] (numeric) = 1.4274943384433 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.555485012761407500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9079999999999999 " " y[1] (analytic) = 1.4279588990019207 " " y[1] (numeric) = 1.4279588990019212 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.109957927783923400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9069999999999999 " " y[1] (analytic) = 1.4284226455357039 " " y[1] (numeric) = 1.4284226455357043 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.10894826008247100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9059999999999999 " " y[1] (analytic) = 1.4288855783401182 " " y[1] (numeric) = 1.4288855783401184 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.553970508842087000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9049999999999999 " " y[1] (analytic) = 1.4293476977105706 " " y[1] (numeric) = 1.429347697710571 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.10693619587014250000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9039999999999999 " " y[1] (analytic) = 1.4298090039424085 " " y[1] (numeric) = 1.4298090039424087 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.55296689496840700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9029999999999999 " " y[1] (analytic) = 1.4302694973309162 " " y[1] (numeric) = 1.4302694973309167 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.10493379519590900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9019999999999999 " " y[1] (analytic) = 1.4307291781713185 " " y[1] (numeric) = 1.430729178171319 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.103936206974360300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9009999999999999 " " y[1] (analytic) = 1.4311880467587783 " " y[1] (numeric) = 1.4311880467587785 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.551470510307134700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8999999999999999 " " y[1] (analytic) = 1.4316461033883967 " " y[1] (numeric) = 1.4316461033883972 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.10194823147284400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8989999999999999 " " y[1] (analytic) = 1.432103348355215 " " y[1] (numeric) = 1.4321033483552152 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.550478917461171600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8979999999999999 " " y[1] (analytic) = 1.4325597819542122 " " y[1] (numeric) = 1.4325597819542124 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.549984913175011800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8969999999999999 " " y[1] (analytic) = 1.4330154044803067 " " y[1] (numeric) = 1.4330154044803072 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.0989842011580800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8959999999999999 " " y[1] (analytic) = 1.4334702162283561 " " y[1] (numeric) = 1.4334702162283566 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.098000954763596700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8949999999999999 " " y[1] (analytic) = 1.4339242174931564 " " y[1] (numeric) = 1.4339242174931566 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.548510041299243600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8939999999999999 " " y[1] (analytic) = 1.4343774085694423 " " y[1] (numeric) = 1.4343774085694425 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.54802079005472220000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8929999999999999 " " y[1] (analytic) = 1.4348297897518878 " " y[1] (numeric) = 1.434829789751888 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.547532721378941400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8919999999999999 " " y[1] (analytic) = 1.4352813613351056 " " y[1] (numeric) = 1.435281361335106 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.09409166601988600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8909999999999999 " " y[1] (analytic) = 1.435732123613648 " " y[1] (numeric) = 1.4357321236136484 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.09312024538615100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8899999999999999 " " y[1] (analytic) = 1.436182076882005 " " y[1] (numeric) = 1.4361820768820057 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.6382267645429100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8889999999999999 " " y[1] (analytic) = 1.4366312214346069 " " y[1] (numeric) = 1.4366312214346075 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.636776681700532400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8879999999999999 " " y[1] (analytic) = 1.4370795575658217 " " y[1] (numeric) = 1.4370795575658224 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.63533011285343130000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8869999999999999 " " y[1] (analytic) = 1.4375270855699571 " " y[1] (numeric) = 1.4375270855699578 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.63388705132454800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8859999999999999 " " y[1] (analytic) = 1.4379738057412594 " " y[1] (numeric) = 1.4379738057412603 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.17659665394446600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8849999999999999 " " y[1] (analytic) = 1.4384197183739147 " " y[1] (numeric) = 1.4384197183739154 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.63101142362074900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8839999999999999 " " y[1] (analytic) = 1.438864823762047 " " y[1] (numeric) = 1.4388648237620476 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.629578844199030400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8829999999999999 " " y[1] (analytic) = 1.4393091221997194 " " y[1] (numeric) = 1.4393091221997203 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.17086632746902800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8819999999999999 " " y[1] (analytic) = 1.439752613980935 " " y[1] (numeric) = 1.4397526139809358 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.16896549501167600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8809999999999999 " " y[1] (analytic) = 1.440195299399635 " " y[1] (numeric) = 1.4401952993996356 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.625301964620915400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8799999999999999 " " y[1] (analytic) = 1.4406371787496997 " " y[1] (numeric) = 1.4406371787497005 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.16517769221364700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8789999999999999 " " y[1] (analytic) = 1.4410782523249492 " " y[1] (numeric) = 1.4410782523249497 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.08164535224645700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8779999999999999 " " y[1] (analytic) = 1.4415185204191412 " " y[1] (numeric) = 1.4415185204191419 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.62105623576314800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8769999999999999 " " y[1] (analytic) = 1.441957983325974 " " y[1] (numeric) = 1.4419579833259746 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.61964788487533500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8759999999999999 " " y[1] (analytic) = 1.4423966413390836 " " y[1] (numeric) = 1.4423966413390845 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.15765729234895700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8749999999999999 " " y[1] (analytic) = 1.4428344947520466 " " y[1] (numeric) = 1.4428344947520473 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.61684148249844900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8739999999999999 " " y[1] (analytic) = 1.4432715438583772 " " y[1] (numeric) = 1.4432715438583779 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.6154434181822895000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8729999999999999 " " y[1] (analytic) = 1.4437077889515293 " " y[1] (numeric) = 1.44370778895153 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.61404876993053700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8719999999999999 " " y[1] (analytic) = 1.444143230324896 " " y[1] (numeric) = 1.4441432303248967 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.612657531380945400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8709999999999999 " " y[1] (analytic) = 1.4445778682718091 " " y[1] (numeric) = 1.44457786827181 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.14835959492221100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8699999999999999 " " y[1] (analytic) = 1.44501170308554 " " y[1] (numeric) = 1.4450117030855412 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 7.68314209673521900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8689999999999999 " " y[1] (analytic) = 1.4454447350592994 " " y[1] (numeric) = 1.4454447350593003 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.14467228083741100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8679999999999999 " " y[1] (analytic) = 1.445876964486236 " " y[1] (numeric) = 1.445876964486237 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 7.67854424611884200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8669999999999999 " " y[1] (analytic) = 1.4463083916594388 " " y[1] (numeric) = 1.44630839165944 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 7.67625377151638600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8659999999999999 " " y[1] (analytic) = 1.4467390168719354 " " y[1] (numeric) = 1.4467390168719365 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 7.673968916837700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8649999999999999 " " y[1] (analytic) = 1.4471688404166927 " " y[1] (numeric) = 1.4471688404166938 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 7.67168967171434500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8639999999999999 " " y[1] (analytic) = 1.4475978625866166 " " y[1] (numeric) = 1.4475978625866177 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 7.66941602581101200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8629999999999999 " " y[1] (analytic) = 1.4480260836745522 " " y[1] (numeric) = 1.4480260836745535 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 9.200577562590500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8619999999999999 " " y[1] (analytic) = 1.4484535039732842 " " y[1] (numeric) = 1.4484535039732855 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 9.19786258858579600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8609999999999999 " " y[1] (analytic) = 1.448880123775536 " " y[1] (numeric) = 1.4488801237755373 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 9.19515429667517400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8599999999999999 " " y[1] (analytic) = 1.4493059433739703 " " y[1] (numeric) = 1.4493059433739717 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 9.19245267461390200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8589999999999999 " " y[1] (analytic) = 1.4497309630611892 " " y[1] (numeric) = 1.4497309630611905 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 9.18975771019630600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8579999999999999 " " y[1] (analytic) = 1.4501551831297341 " " y[1] (numeric) = 1.4501551831297352 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 7.65589115937968900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8569999999999999 " " y[1] (analytic) = 1.4505786038720845 " " y[1] (numeric) = 1.450578603872086 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.07151189899412180000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8559999999999999 " " y[1] (analytic) = 1.4510012255806612 " " y[1] (numeric) = 1.4510012255806626 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 9.18171264133179100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8549999999999999 " " y[1] (analytic) = 1.4514230485478223 " " y[1] (numeric) = 1.451423048547824 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.07088848839098940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8539999999999999 " " y[1] (analytic) = 1.4518440730658664 " " y[1] (numeric) = 1.451844073065868 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.07057793829951050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8529999999999999 " " y[1] (analytic) = 1.4522642994270305 " " y[1] (numeric) = 1.452264299427032 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.07026815648394720000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8519999999999999 " " y[1] (analytic) = 1.4526837279234919 " " y[1] (numeric) = 1.4526837279234932 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 9.17107835615787900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8509999999999999 " " y[1] (analytic) = 1.4531023588473655 " " y[1] (numeric) = 1.453102358847367 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.06965089211480980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8499999999999999 " " y[1] (analytic) = 1.4535201924907075 " " y[1] (numeric) = 1.453520192490709 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.06934340678941480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8489999999999999 " " y[1] (analytic) = 1.4539372291455122 " " y[1] (numeric) = 1.4539372291455135 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 9.16317157882510300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8479999999999999 " " y[1] (analytic) = 1.454353469103713 " " y[1] (numeric) = 1.4543534691037143 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 9.16054905394653500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8469999999999999 " " y[1] (analytic) = 1.4547689126571834 " " y[1] (numeric) = 1.4547689126571848 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 9.15793304324022800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8459999999999999 " " y[1] (analytic) = 1.4551835600977359 " " y[1] (numeric) = 1.4551835600977372 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 9.1553235349958710000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8449999999999999 " " y[1] (analytic) = 1.4555974117171222 " " y[1] (numeric) = 1.4555974117171235 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 9.15272051754031300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8439999999999999 " " y[1] (analytic) = 1.4560104678070334 " " y[1] (numeric) = 1.456010467807035 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.06751446424436960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8429999999999999 " " y[1] (analytic) = 1.4564227286591003 " " y[1] (numeric) = 1.4564227286591016 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 9.14753390848809700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8419999999999999 " " y[1] (analytic) = 1.456834194564892 " " y[1] (numeric) = 1.4568341945648937 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.2193267058306449000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8409999999999999 " " y[1] (analytic) = 1.4572448658159187 " " y[1] (numeric) = 1.4572448658159203 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.06661019773430600000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8399999999999999 " " y[1] (analytic) = 1.4576547427036284 " " y[1] (numeric) = 1.45765474270363 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.06631027838067630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8389999999999999 " " y[1] (analytic) = 1.458063825519409 " " y[1] (numeric) = 1.4580638255194107 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.21829840937687020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8379999999999999 " " y[1] (analytic) = 1.458472114554588 " " y[1] (numeric) = 1.4584721145545898 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.217957355285290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8369999999999999 " " y[1] (analytic) = 1.4588796101004327 " " y[1] (numeric) = 1.4588796101004342 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.06541501006256210000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8359999999999999 " " y[1] (analytic) = 1.4592863124481483 " " y[1] (numeric) = 1.4592863124481499 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.06511807944504880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8349999999999999 " " y[1] (analytic) = 1.459692221888881 " " y[1] (numeric) = 1.4596922218888826 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.06482189270276250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8339999999999999 " " y[1] (analytic) = 1.4600973387137157 " " y[1] (numeric) = 1.4600973387137173 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.06452644852055050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8329999999999999 " " y[1] (analytic) = 1.4605016632136767 " " y[1] (numeric) = 1.4605016632136785 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.21626485209990680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8319999999999999 " " y[1] (analytic) = 1.4609051956797285 " " y[1] (numeric) = 1.46090519567973 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.06393778259651560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8309999999999998 " " y[1] (analytic) = 1.461307936402774 " " y[1] (numeric) = 1.4613079364027755 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.06364455824512190000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8299999999999998 " " y[1] (analytic) = 1.4617098856736557 " " y[1] (numeric) = 1.4617098856736574 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.21525950998243680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8289999999999998 " " y[1] (analytic) = 1.4621110437831564 " " y[1] (numeric) = 1.4621110437831581 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.2149260803091912000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8279999999999998 " " y[1] (analytic) = 1.4625114110219979 " " y[1] (numeric) = 1.4625114110219997 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.2145934903570690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8269999999999998 " " y[1] (analytic) = 1.4629109876808415 " " y[1] (numeric) = 1.462910987680843 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.06247902132396750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8259999999999998 " " y[1] (analytic) = 1.4633097740502876 " " y[1] (numeric) = 1.4633097740502892 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.06218947077285370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8249999999999998 " " y[1] (analytic) = 1.4637077704208765 " " y[1] (numeric) = 1.4637077704208783 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.21360074414954720000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8239999999999998 " " y[1] (analytic) = 1.4641049770830885 " " y[1] (numeric) = 1.4641049770830903 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.21327149842715240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8229999999999998 " " y[1] (analytic) = 1.4645013943273426 " " y[1] (numeric) = 1.4645013943273444 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.21294308512157170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8219999999999998 " " y[1] (analytic) = 1.4648970224439977 " " y[1] (numeric) = 1.4648970224439994 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.21261550278573230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8209999999999998 " " y[1] (analytic) = 1.465291861723352 " " y[1] (numeric) = 1.465291861723354 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.36382484372426100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8199999999999998 " " y[1] (analytic) = 1.4656859124556436 " " y[1] (numeric) = 1.4656859124556456 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.36345817841498820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8189999999999998 " " y[1] (analytic) = 1.4660791749310498 " " y[1] (numeric) = 1.4660791749310522 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.66600187489206740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8179999999999998 " " y[1] (analytic) = 1.4664716494396886 " " y[1] (numeric) = 1.4664716494396908 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.51414181794697800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8169999999999998 " " y[1] (analytic) = 1.4668633362716155 " " y[1] (numeric) = 1.466863336271618 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.66511125731966250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8159999999999998 " " y[1] (analytic) = 1.4672542357168277 " " y[1] (numeric) = 1.46725423571683 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.51333422333963380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8149999999999998 " " y[1] (analytic) = 1.4676443480652601 " " y[1] (numeric) = 1.4676443480652626 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.66422516285719160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8139999999999998 " " y[1] (analytic) = 1.4680336736067887 " " y[1] (numeric) = 1.4680336736067914 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.81503688028757630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8129999999999998 " " y[1] (analytic) = 1.4684222126312287 " " y[1] (numeric) = 1.4684222126312314 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.81455662831867840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8119999999999998 " " y[1] (analytic) = 1.4688099654283346 " " y[1] (numeric) = 1.4688099654283373 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.81407760147061900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8109999999999998 " " y[1] (analytic) = 1.4691969322878005 " " y[1] (numeric) = 1.4691969322878033 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.96473311411730880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8099999999999998 " " y[1] (analytic) = 1.4695831134992607 " " y[1] (numeric) = 1.4695831134992636 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.96421681598674620000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8089999999999998 " " y[1] (analytic) = 1.469968509352289 " " y[1] (numeric) = 1.4699685093522916 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.81264785071786870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8079999999999998 " " y[1] (analytic) = 1.4703531201363977 " " y[1] (numeric) = 1.4703531201364006 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.9631881787401060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8069999999999998 " " y[1] (analytic) = 1.4707369461410407 " " y[1] (numeric) = 1.4707369461410438 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.11365089937186330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8059999999999998 " " y[1] (analytic) = 1.4711199876556107 " " y[1] (numeric) = 1.4711199876556134 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.8112290509672171000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8049999999999998 " " y[1] (analytic) = 1.471502244969439 " " y[1] (numeric) = 1.471502244969442 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.96165508676159530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8039999999999998 " " y[1] (analytic) = 1.4718837183717988 " " y[1] (numeric) = 1.4718837183718014 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.81028924081576950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8029999999999998 " " y[1] (analytic) = 1.4722644081519005 " " y[1] (numeric) = 1.4722644081519034 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.96063957536599280000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8019999999999998 " " y[1] (analytic) = 1.4726443145988966 " " y[1] (numeric) = 1.4726443145988994 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.96013377800030640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8009999999999998 " " y[1] (analytic) = 1.4730234380018776 " " y[1] (numeric) = 1.4730234380018805 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.95962928325226520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7999999999999998 " " y[1] (analytic) = 1.4734017786498748 " " y[1] (numeric) = 1.4734017786498776 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.95912608892767380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7989999999999998 " " y[1] (analytic) = 1.4737793368318584 " " y[1] (numeric) = 1.4737793368318612 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.95862419283921150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7979999999999998 " " y[1] (analytic) = 1.4741561128367386 " " y[1] (numeric) = 1.4741561128367417 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.10874848456074960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7969999999999998 " " y[1] (analytic) = 1.4745321069533661 " " y[1] (numeric) = 1.4745321069533692 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.1082107702445250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7959999999999998 " " y[1] (analytic) = 1.4749073194705304 " " y[1] (numeric) = 1.4749073194705336 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.1076744470061940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7949999999999998 " " y[1] (analytic) = 1.4752817506769613 " " y[1] (numeric) = 1.4752817506769642 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.95662954733958060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7939999999999998 " " y[1] (analytic) = 1.4756554008613276 " " y[1] (numeric) = 1.4756554008613307 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.10660596446566100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7929999999999998 " " y[1] (analytic) = 1.4760282703122392 " " y[1] (numeric) = 1.4760282703122423 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.10607380053285800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7919999999999998 " " y[1] (analytic) = 1.4764003593182449 " " y[1] (numeric) = 1.4764003593182478 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.95514708852979300000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7909999999999998 " " y[1] (analytic) = 1.4767716681678331 " " y[1] (numeric) = 1.4767716681678362 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.1050136158199560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7899999999999998 " " y[1] (analytic) = 1.477142197149433 " " y[1] (numeric) = 1.477142197149436 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.1044855904525750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7889999999999998 " " y[1] (analytic) = 1.477511946551413 " " y[1] (numeric) = 1.477511946551416 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.95367615860083530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7879999999999998 " " y[1] (analytic) = 1.477880916662081 " " y[1] (numeric) = 1.4778809166620839 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.953188400689950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7869999999999998 " " y[1] (analytic) = 1.4782491077696853 " " y[1] (numeric) = 1.4782491077696882 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.95270191529528260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used" Radius of convergence = 0.8108682847738087 " " Order of pole = 13.44774039007337 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7859999999999998 " " y[1] (analytic) = 1.478616520162414 " " y[1] (numeric) = 1.4786165201624168 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.95221670031682030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7849999999999998 " " y[1] (analytic) = 1.4789831541283944 " " y[1] (numeric) = 1.4789831541283975 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.10186604240427370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7839999999999998 " " y[1] (analytic) = 1.4793490099556952 " " y[1] (numeric) = 1.479349009955698 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.95125007324124050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7829999999999998 " " y[1] (analytic) = 1.479714087932323 " " y[1] (numeric) = 1.479714087932326 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.10082778443656750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7819999999999998 " " y[1] (analytic) = 1.4800783883462256 " " y[1] (numeric) = 1.4800783883462287 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.10031069531653540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7809999999999998 " " y[1] (analytic) = 1.4804419114852907 " " y[1] (numeric) = 1.4804419114852938 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.09979496313477950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7799999999999998 " " y[1] (analytic) = 1.4808046576373453 " " y[1] (numeric) = 1.4808046576373484 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.09928058567178860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7789999999999998 " " y[1] (analytic) = 1.4811666270901565 " " y[1] (numeric) = 1.4811666270901596 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.09876756071497750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7779999999999998 " " y[1] (analytic) = 1.4815278201314315 " " y[1] (numeric) = 1.4815278201314346 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.09825588605866450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7769999999999998 " " y[1] (analytic) = 1.4818882370488173 " " y[1] (numeric) = 1.4818882370488204 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.09774555950404760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7759999999999998 " " y[1] (analytic) = 1.4822478781299009 " " y[1] (numeric) = 1.482247878129904 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.09723657885918430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7749999999999998 " " y[1] (analytic) = 1.4826067436622092 " " y[1] (numeric) = 1.4826067436622123 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.0967289419389650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7739999999999998 " " y[1] (analytic) = 1.482964833933209 " " y[1] (numeric) = 1.4829648339332122 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.0962226465650950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7729999999999998 " " y[1] (analytic) = 1.4833221492303077 " " y[1] (numeric) = 1.4833221492303106 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.94602356981134960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7719999999999998 " " y[1] (analytic) = 1.4836786898408512 " " y[1] (numeric) = 1.4836786898408543 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.0952140717771509000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7709999999999998 " " y[1] (analytic) = 1.484034456052127 " " y[1] (numeric) = 1.4840344560521301 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.09471178804034960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7699999999999998 " " y[1] (analytic) = 1.4843894481513615 " " y[1] (numeric) = 1.4843894481513649 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 2.24379732557614180000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7689999999999998 " " y[1] (analytic) = 1.484743666425722 " " y[1] (numeric) = 1.4847436664257252 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.09371121712473380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7679999999999998 " " y[1] (analytic) = 1.485097111162315 " " y[1] (numeric) = 1.4850971111623181 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.09321292566347070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7669999999999998 " " y[1] (analytic) = 1.485449782648187 " " y[1] (numeric) = 1.4854497826481903 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 2.2421956721671980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7659999999999998 " " y[1] (analytic) = 1.4858016811703254 " " y[1] (numeric) = 1.4858016811703285 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.09222032007788520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7649999999999998 " " y[1] (analytic) = 1.4861528070156569 " " y[1] (numeric) = 1.48615280701566 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.09172600171099930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7639999999999998 " " y[1] (analytic) = 1.4865031604710481 " " y[1] (numeric) = 1.4865031604710515 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 2.24060678944001450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7629999999999998 " " y[1] (analytic) = 1.4868527418233066 " " y[1] (numeric) = 1.4868527418233097 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.0907413232721190000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7619999999999998 " " y[1] (analytic) = 1.487201551359179 " " y[1] (numeric) = 1.487201551359182 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.09025095899705940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7609999999999998 " " y[1] (analytic) = 1.4875495893653525 " " y[1] (numeric) = 1.4875495893653556 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.08976190856044050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7599999999999998 " " y[1] (analytic) = 1.4878968561284545 " " y[1] (numeric) = 1.4878968561284576 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.08927416987704280000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7589999999999998 " " y[1] (analytic) = 1.488243351935052 " " y[1] (numeric) = 1.488243351935055 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.08878774086813520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7579999999999998 " " y[1] (analytic) = 1.4885890770716528 " " y[1] (numeric) = 1.4885890770716557 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.93913814664277700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.7569999999999998 " " y[1] (analytic) = 1.488934031824704 " " y[1] (numeric) = 1.4889340318247068 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.93868888904894840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));" Iterations = 244 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds "Expected Time Remaining "= 0 Years 0 Days 1 Hours 10 Minutes 47 Seconds "Optimized Time Remaining "= 0 Years 0 Days 1 Hours 10 Minutes 22 Seconds "Expected Total Time "= 0 Years 0 Days 1 Hours 13 Minutes 23 Seconds "Time to Timeout " Unknown Percent Done = 4.083333333333337 "%" (%o57) true (%o57) diffeq.max