(%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 # 0.0 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 # 0.0 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 (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 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 (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 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_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , 1 1 1 array_tmp3 : array_tmp2 + array_const_0D0 , 1 1 1 array_tmp4 : array_const_0D3 array_x , 1 1 1 array_tmp5 : array_const_0D1 + array_tmp4 , 1 1 1 array_tmp6 : array_tmp3 - array_tmp5 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1), 1 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 2 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_tmp2 , array_tmp4 : array_const_0D3 array_x , 2 2 2 1 2 array_tmp5 : array_tmp4 , array_tmp6 : array_tmp3 - array_tmp5 , 2 2 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(1, 2), 2 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 3 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (order_d : 1, if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp6 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d temporary convfp(adj2) then (if adj2 > 1 then temporary : ---------------------- glob_h temporary else temporary : ---------, array_y_higher : temporary), glob_h adj3, term term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , 1 1 1 array_tmp3 : array_tmp2 + array_const_0D0 , 1 1 1 array_tmp4 : array_const_0D3 array_x , 1 1 1 array_tmp5 : array_const_0D1 + array_tmp4 , 1 1 1 array_tmp6 : array_tmp3 - array_tmp5 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1), 1 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 2 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_tmp2 , array_tmp4 : array_const_0D3 array_x , 2 2 2 1 2 array_tmp5 : array_tmp4 , array_tmp6 : array_tmp3 - array_tmp5 , 2 2 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(1, 2), 2 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 3 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (order_d : 1, if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp6 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d temporary convfp(adj2) then (if adj2 > 1 then temporary : ---------------------- glob_h temporary else temporary : ---------, array_y_higher : temporary), glob_h adj3, term term : term - 1, adj2 : adj2 - 1, 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 # 0.0 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 # 0.0 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) arcsin(x) := asin(x) (%o46) arcsin(x) := asin(x) (%i47) arccos(x) := acos(x) (%o47) arccos(x) := acos(x) (%i48) arctan(x) := atan(x) (%o48) arctan(x) := atan(x) (%i49) omniabs(x) := abs(x) (%o49) omniabs(x) := abs(x) y (%i50) expt(x, y) := x y (%o50) expt(x, y) := x (%i51) 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) (%o51) 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) - 0.2 x x (%i52) exact_soln_y(x) := block(0.1 x + ---------) 2.0 - 0.2 x x (%o52) exact_soln_y(x) := block(0.1 x + ---------) 2.0 (%i53) 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], 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/sub_lin_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.1 * x + 0.2) - (0.3 * x + 0.1) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (- 0.2 * x * x / 2.0 + 0.1 * x) "), 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, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 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 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term 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, 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_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 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_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, 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), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05, 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_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(), 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 : 1, 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 display_alot(current_iter)), 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 ) = (0.1 * x + 0.2) - (0.3 * x + 0.1) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-12-15T04:00:28-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sub_lin_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.1 * x + 0.2) - (0.3 * x + 0.1) ;"), 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, " 151 "), logitem_str(html_log_file, "sub_lin_lin diffeq.max"), logitem_str(html_log_file, "sub_lin_lin maxima results"), logitem_str(html_log_file, "Languages compared"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o53) 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], 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/sub_lin_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.1 * x + 0.2) - (0.3 * x + 0.1) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (- 0.2 * x * x / 2.0 + 0.1 * x) "), 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, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 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 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term 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, 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_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 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_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, 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), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05, 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_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(), 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 : 1, 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 display_alot(current_iter)), 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 ) = (0.1 * x + 0.2) - (0.3 * x + 0.1) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-12-15T04:00:28-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sub_lin_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.1 * x + 0.2) - (0.3 * x + 0.1) ;"), 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, " 151 "), logitem_str(html_log_file, "sub_lin_lin diffeq.max"), logitem_str(html_log_file, "sub_lin_lin maxima results"), logitem_str(html_log_file, "Languages compared"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i54) main() "##############ECHO OF PROBLEM#################" "##############temp/sub_lin_linpostode.ode#################" "diff ( y , x , 1 ) = (0.1 * x + 0.2) - (0.3 * x + 0.1) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h:0.05," "glob_look_poles:true," "glob_max_iter:1000000," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.001," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (- 0.2 * x * x / 2.0 + 0.1 * x) " "));" "/* 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 = 4.9 "" estimated_steps = 4900. "" step_error = 2.040816326530612300000000000000E-14 "" est_needed_step_err = 2.040816326530612300000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_value3 = 0.0 "" value3 = 0.0 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = 0.1 " " y[1] (analytic) = 9.000000000000001000E-3 " " y[1] (numeric) = 9.000000000000001000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.101 " " y[1] (analytic) = 9.079900000000002000E-3 " " y[1] (numeric) = 9.079900000000002000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10200000000000001 " " y[1] (analytic) = 9.1596000E-3 " " y[1] (numeric) = 9.159600000000002000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.89388562380104700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10300000000000001 " " y[1] (analytic) = 9.239100000000002000E-3 " " y[1] (numeric) = 9.239100000000002000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10400000000000001 " " y[1] (analytic) = 9.318400000000001000E-3 " " y[1] (numeric) = 9.318400000000001000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10500000000000001 " " y[1] (analytic) = 9.397500000000001000E-3 " " y[1] (numeric) = 9.397500000000001000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10600000000000001 " " y[1] (analytic) = 9.476400000000001000E-3 " " y[1] (numeric) = 9.476400000000001000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10700000000000001 " " y[1] (analytic) = 9.5551000E-3 " " y[1] (numeric) = 9.5551000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10800000000000001 " " y[1] (analytic) = 9.633600000000002000E-3 " " y[1] (numeric) = 9.6336000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.80070116672563400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10900000000000001 " " y[1] (analytic) = 9.7119000E-3 " " y[1] (numeric) = 9.7119000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11000000000000001 " " y[1] (analytic) = 9.790000000000002000E-3 " " y[1] (numeric) = 9.79000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.771934091906850800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11100000000000002 " " y[1] (analytic) = 9.867900000000003000E-3 " " y[1] (numeric) = 9.8679000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.757945941868894700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11200000000000002 " " y[1] (analytic) = 9.9456000E-3 " " y[1] (numeric) = 9.9456000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11300000000000002 " " y[1] (analytic) = 1.002310000000000100E-2 " " y[1] (numeric) = 1.0023100E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.73072550007164120000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11400000000000002 " " y[1] (analytic) = 1.010040000000000200E-2 " " y[1] (numeric) = 1.0100400E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.717479977007649600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11500000000000002 " " y[1] (analytic) = 1.017750000000000300E-2 " " y[1] (numeric) = 1.0177500E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.704469148589345700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11600000000000002 " " y[1] (analytic) = 1.025440000000000200E-2 " " y[1] (numeric) = 1.0254400E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.69168695972149200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11700000000000002 " " y[1] (analytic) = 1.033110000000000100E-2 " " y[1] (numeric) = 1.033110000000000100E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11800000000000002 " " y[1] (analytic) = 1.040760000000000300E-2 " " y[1] (numeric) = 1.040760000000000200E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.66678530686883300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11900000000000002 " " y[1] (analytic) = 1.048390000000000300E-2 " " y[1] (numeric) = 1.0483900E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.654654733426307600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12000000000000002 " " y[1] (analytic) = 1.056000000000000300E-2 " " y[1] (numeric) = 1.056000000000000100E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.642730564371975800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12100000000000002 " " y[1] (analytic) = 1.063590000000000200E-2 " " y[1] (numeric) = 1.063590000000000200E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12200000000000003 " " y[1] (analytic) = 1.071160000000000200E-2 " " y[1] (numeric) = 1.071160000000000200E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12300000000000003 " " y[1] (analytic) = 1.078710000000000200E-2 " " y[1] (numeric) = 1.0787100E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.60814628211178800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12400000000000003 " " y[1] (analytic) = 1.086240000000000300E-2 " " y[1] (numeric) = 1.086240000000000100E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.596998339203865300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12500000000000003 " " y[1] (analytic) = 1.093750000000000300E-2 " " y[1] (numeric) = 1.093750000000000100E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.58603289232165180000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12600000000000003 " " y[1] (analytic) = 1.101240000000000300E-2 " " y[1] (numeric) = 1.1012400E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.575245610381757800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12700000000000003 " " y[1] (analytic) = 1.108710000000000300E-2 " " y[1] (numeric) = 1.1087100E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.564632298776782400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12800000000000003 " " y[1] (analytic) = 1.116160000000000200E-2 " " y[1] (numeric) = 1.1161600E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.554188894044587500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12900000000000003 " " y[1] (analytic) = 1.123590000000000400E-2 " " y[1] (numeric) = 1.1235900E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.087822917571011500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13000000000000003 " " y[1] (analytic) = 1.131000000000000300E-2 " " y[1] (numeric) = 1.13100E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.06759235362830500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13100000000000003 " " y[1] (analytic) = 1.138390000000000200E-2 " " y[1] (numeric) = 1.1383900E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.523839348533285500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13200000000000003 " " y[1] (analytic) = 1.145760000000000100E-2 " " y[1] (numeric) = 1.1457600E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.514037386517950400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13300000000000003 " " y[1] (analytic) = 1.153110000000000400E-2 " " y[1] (numeric) = 1.1531100E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.008773622597681300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13400000000000004 " " y[1] (analytic) = 1.160440000000000200E-2 " " y[1] (numeric) = 1.1604400E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.49488424733446500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13500000000000004 " " y[1] (analytic) = 1.167750000000000500E-2 " " y[1] (numeric) = 1.1677500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.971052838324652600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13600000000000004 " " y[1] (analytic) = 1.175040000000000300E-2 " " y[1] (numeric) = 1.175040000000000100E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.476310147719913000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13700000000000004 " " y[1] (analytic) = 1.182310000000000300E-2 " " y[1] (numeric) = 1.182310000000000200E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.467232346826811000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13800000000000004 " " y[1] (analytic) = 1.189560000000000500E-2 " " y[1] (numeric) = 1.189560000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.91658003963954140000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13900000000000004 " " y[1] (analytic) = 1.196790000000000400E-2 " " y[1] (numeric) = 1.196790000000000200E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.449480256333029700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14000000000000004 " " y[1] (analytic) = 1.204000000000000300E-2 " " y[1] (numeric) = 1.204000000000000200E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.440800229216617000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14100000000000004 " " y[1] (analytic) = 1.211190000000000300E-2 " " y[1] (numeric) = 1.211190000000000200E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.432247191585801200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14200000000000004 " " y[1] (analytic) = 1.218360000000000300E-2 " " y[1] (numeric) = 1.218360000000000100E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.423818473995212300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14300000000000004 " " y[1] (analytic) = 1.225510000000000500E-2 " " y[1] (numeric) = 1.225510000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.831022963463058500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14400000000000004 " " y[1] (analytic) = 1.232640000000000300E-2 " " y[1] (numeric) = 1.232640000000000100E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.407323692218982500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14500000000000005 " " y[1] (analytic) = 1.239750000000000400E-2 " " y[1] (numeric) = 1.2397500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.798505305064419000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14600000000000005 " " y[1] (analytic) = 1.246840000000000400E-2 " " y[1] (numeric) = 1.246840000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.782591954022659600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14700000000000005 " " y[1] (analytic) = 1.253910000000000300E-2 " " y[1] (numeric) = 1.253910000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.76690268994873100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14800000000000005 " " y[1] (analytic) = 1.260960000000000400E-2 " " y[1] (numeric) = 1.2609600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.75143299704480200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14900000000000005 " " y[1] (analytic) = 1.267990000000000500E-2 " " y[1] (numeric) = 1.267990000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.73617848086626300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15000000000000005 " " y[1] (analytic) = 1.275000000000000600E-2 " " y[1] (numeric) = 1.275000000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.721134864277343600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15100000000000005 " " y[1] (analytic) = 1.281990000000000400E-2 " " y[1] (numeric) = 1.2819900E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.70629798356743300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15200000000000005 " " y[1] (analytic) = 1.288960000000000400E-2 " " y[1] (numeric) = 1.288960000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.69166378472071500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15300000000000005 " " y[1] (analytic) = 1.295910000000000400E-2 " " y[1] (numeric) = 1.295910000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.67722831983209730000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15400000000000005 " " y[1] (analytic) = 1.302840000000000400E-2 " " y[1] (numeric) = 1.3028400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.662987743662777500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15500000000000005 " " y[1] (analytic) = 1.309750000000000600E-2 " " y[1] (numeric) = 1.309750000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.648938310329156400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15600000000000006 " " y[1] (analytic) = 1.316640000000000600E-2 " " y[1] (numeric) = 1.316640000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.635076370119100500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15700000000000006 " " y[1] (analytic) = 1.323510000000000200E-2 " " y[1] (numeric) = 1.323510000000000200E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.31069918321494100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15800000000000006 " " y[1] (analytic) = 1.330360000000000400E-2 " " y[1] (numeric) = 1.330360000000000200E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.30395041641120200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15900000000000006 " " y[1] (analytic) = 1.337190000000000600E-2 " " y[1] (numeric) = 1.337190000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.594580390186595000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16000000000000006 " " y[1] (analytic) = 1.344000000000000500E-2 " " y[1] (numeric) = 1.344000000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.581433744013104700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16100000000000006 " " y[1] (analytic) = 1.350790000000000600E-2 " " y[1] (numeric) = 1.350790000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.568457681766679300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16200000000000006 " " y[1] (analytic) = 1.357560000000000400E-2 " " y[1] (numeric) = 1.357560000000000200E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.277824535178413200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16300000000000006 " " y[1] (analytic) = 1.364310000000000200E-2 " " y[1] (numeric) = 1.364310000000000200E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.271502426850793800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16400000000000006 " " y[1] (analytic) = 1.371040000000000600E-2 " " y[1] (numeric) = 1.371040000000000000E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.795783075570675600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16500000000000006 " " y[1] (analytic) = 1.377750000000000400E-2 " " y[1] (numeric) = 1.377750000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.518197751372609500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16600000000000006 " " y[1] (analytic) = 1.384440000000000400E-2 " " y[1] (numeric) = 1.384440000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.506029117876985000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16700000000000007 " " y[1] (analytic) = 1.391110000000000400E-2 " " y[1] (numeric) = 1.391110000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.49401337921056800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16800000000000007 " " y[1] (analytic) = 1.397760000000000400E-2 " " y[1] (numeric) = 1.397760000000000000E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.24107391539091600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16900000000000007 " " y[1] (analytic) = 1.404390000000000600E-2 " " y[1] (numeric) = 1.404390000000000000E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.70564474820414500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17000000000000007 " " y[1] (analytic) = 1.411000000000000600E-2 " " y[1] (numeric) = 1.411000000000000000E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.688285207604832000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17100000000000007 " " y[1] (analytic) = 1.417590000000000500E-2 " " y[1] (numeric) = 1.417590000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.447426231811463700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17200000000000007 " " y[1] (analytic) = 1.424160000000000400E-2 " " y[1] (numeric) = 1.424160000000000100E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.218067826632405600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17300000000000007 " " y[1] (analytic) = 1.430710000000000300E-2 " " y[1] (numeric) = 1.430710000000000000E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.212491333657279700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17400000000000007 " " y[1] (analytic) = 1.437240000000000700E-2 " " y[1] (numeric) = 1.437240000000000200E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.620947390784015600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17500000000000007 " " y[1] (analytic) = 1.443750000000000600E-2 " " y[1] (numeric) = 1.443750000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.403080139881290400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17600000000000007 " " y[1] (analytic) = 1.450240000000000400E-2 " " y[1] (numeric) = 1.450240000000000100E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.39232606461938200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17700000000000007 " " y[1] (analytic) = 1.456710000000000500E-2 " " y[1] (numeric) = 1.456710000000000200E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.19085025569729500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17800000000000007 " " y[1] (analytic) = 1.463160000000000600E-2 " " y[1] (numeric) = 1.463160000000000300E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.185600669767357300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17900000000000008 " " y[1] (analytic) = 1.469590000000000600E-2 " " y[1] (numeric) = 1.469590000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.360826456327011200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18000000000000008 " " y[1] (analytic) = 1.476000000000000600E-2 " " y[1] (numeric) = 1.476000000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.350573815686729500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18100000000000008 " " y[1] (analytic) = 1.482390000000000400E-2 " " y[1] (numeric) = 1.482390000000000400E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.170220708434896700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18200000000000008 " " y[1] (analytic) = 1.488760000000000400E-2 " " y[1] (numeric) = 1.488760000000000400E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.16521365161396510000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18300000000000008 " " y[1] (analytic) = 1.495110000000000600E-2 " " y[1] (numeric) = 1.495110000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.32052956100461700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18400000000000008 " " y[1] (analytic) = 1.501440000000000800E-2 " " y[1] (numeric) = 1.501440000000000300E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.46611947725544700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18500000000000008 " " y[1] (analytic) = 1.507750000000000500E-2 " " y[1] (numeric) = 1.507750000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.301075743295382700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18600000000000008 " " y[1] (analytic) = 1.514040000000000400E-2 " " y[1] (numeric) = 1.514040000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.291516044459600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18700000000000008 " " y[1] (analytic) = 1.520310000000000300E-2 " " y[1] (numeric) = 1.520310000000000300E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.141032734098181700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18800000000000008 " " y[1] (analytic) = 1.526560000000000700E-2 " " y[1] (numeric) = 1.526560000000000100E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.409083447706227600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18900000000000008 " " y[1] (analytic) = 1.532790000000000800E-2 " " y[1] (numeric) = 1.532790000000000300E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.39522728353552600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.19000000000000009 " " y[1] (analytic) = 1.539000000000000600E-2 " " y[1] (numeric) = 1.539000000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.25435149574633700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1910000000000001 " " y[1] (analytic) = 1.545190000000000700E-2 " " y[1] (numeric) = 1.545190000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.245320609086011000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1920000000000001 " " y[1] (analytic) = 1.551360000000000500E-2 " " y[1] (numeric) = 1.551360000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.236390619813333500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1930000000000001 " " y[1] (analytic) = 1.557510000000000800E-2 " " y[1] (numeric) = 1.557510000000000300E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.34133997722673940000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1940000000000001 " " y[1] (analytic) = 1.56364000000000100E-2 " " y[1] (numeric) = 1.5636400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.437654385860699000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1950000000000001 " " y[1] (analytic) = 1.569750000000000600E-2 " " y[1] (numeric) = 1.569750000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.210190764104865700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1960000000000001 " " y[1] (analytic) = 1.575840000000000600E-2 " " y[1] (numeric) = 1.575840000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.201649248625249200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1970000000000001 " " y[1] (analytic) = 1.581910000000000500E-2 " " y[1] (numeric) = 1.581910000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.193201226336272700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1980000000000001 " " y[1] (analytic) = 1.587960000000000800E-2 " " y[1] (numeric) = 1.587960000000000500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.184845305897889500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1990000000000001 " " y[1] (analytic) = 1.593990000000000700E-2 " " y[1] (numeric) = 1.593990000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.17658012406201580000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2000000000000001 " " y[1] (analytic) = 1.600000000000001000E-2 " " y[1] (numeric) = 1.600000000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.16840434497100800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2010000000000001 " " y[1] (analytic) = 1.605990000000000500E-2 " " y[1] (numeric) = 1.605990000000000500E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2020000000000001 " " y[1] (analytic) = 1.611960000000000600E-2 " " y[1] (numeric) = 1.611960000000000600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2030000000000001 " " y[1] (analytic) = 1.61791000000000070E-2 " " y[1] (numeric) = 1.617910000000000500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.144400462296179600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2040000000000001 " " y[1] (analytic) = 1.623840000000000800E-2 " " y[1] (numeric) = 1.623840000000000800E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2050000000000001 " " y[1] (analytic) = 1.629750000000000600E-2 " " y[1] (numeric) = 1.629750000000000600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2060000000000001 " " y[1] (analytic) = 1.635640000000000700E-2 " " y[1] (numeric) = 1.635640000000000700E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2070000000000001 " " y[1] (analytic) = 1.641510000000000500E-2 " " y[1] (numeric) = 1.641510000000000500E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2080000000000001 " " y[1] (analytic) = 1.64736000000000080E-2 " " y[1] (numeric) = 1.647360000000000500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.106064826117917400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2090000000000001 " " y[1] (analytic) = 1.65319000000000100E-2 " " y[1] (numeric) = 1.653190000000000500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.09863775606773100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2100000000000001 " " y[1] (analytic) = 1.659000000000000800E-2 " " y[1] (numeric) = 1.659000000000000500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.091288096415679600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2110000000000001 " " y[1] (analytic) = 1.664790000000000700E-2 " " y[1] (numeric) = 1.664790000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.084014771805220200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2120000000000001 " " y[1] (analytic) = 1.670560000000001000E-2 " " y[1] (numeric) = 1.670560000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.07681672729720100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2130000000000001 " " y[1] (analytic) = 1.67631000000000090E-2 " " y[1] (numeric) = 1.676310000000000300E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.139385855782775600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2140000000000001 " " y[1] (analytic) = 1.682040000000000800E-2 " " y[1] (numeric) = 1.682040000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.062642358061409200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2150000000000001 " " y[1] (analytic) = 1.687750000000000600E-2 " " y[1] (numeric) = 1.687750000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.055664021302688600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2160000000000001 " " y[1] (analytic) = 1.693440000000000500E-2 " " y[1] (numeric) = 1.693440000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.048756939692940600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2170000000000001 " " y[1] (analytic) = 1.699110000000000600E-2 " " y[1] (numeric) = 1.699110000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.041920153464821800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2180000000000001 " " y[1] (analytic) = 1.70476000000000100E-2 " " y[1] (numeric) = 1.704760000000000200E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.07030544118070800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2190000000000001 " " y[1] (analytic) = 1.71039000000000080E-2 " " y[1] (numeric) = 1.710390000000000200E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.0569074327534804000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2200000000000001 " " y[1] (analytic) = 1.71600000000000090E-2 " " y[1] (numeric) = 1.71600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.043644466146401600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2210000000000001 " " y[1] (analytic) = 1.721590000000000600E-2 " " y[1] (numeric) = 1.721590000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.015257379488503700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22200000000000011 " " y[1] (analytic) = 1.727160000000000400E-2 " " y[1] (numeric) = 1.7271600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.00875828061882700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22300000000000011 " " y[1] (analytic) = 1.73271000000000100E-2 " " y[1] (numeric) = 1.7327100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.00464815457129250000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22400000000000012 " " y[1] (analytic) = 1.738240000000000600E-2 " " y[1] (numeric) = 1.738240000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.995953925783328400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22500000000000012 " " y[1] (analytic) = 1.74375000000000090E-2 " " y[1] (numeric) = 1.7437500E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.979293995072243400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22600000000000012 " " y[1] (analytic) = 1.749240000000000500E-2 " " y[1] (numeric) = 1.7492400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.98340247876427100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22700000000000012 " " y[1] (analytic) = 1.754710000000000700E-2 " " y[1] (numeric) = 1.754710000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.97721957015895100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22800000000000012 " " y[1] (analytic) = 1.76016000000000100E-2 " " y[1] (numeric) = 1.760160000000000000E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.94219497313154750000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22900000000000012 " " y[1] (analytic) = 1.76559000000000080E-2 " " y[1] (numeric) = 1.765590000000000200E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.93007091335317100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23000000000000012 " " y[1] (analytic) = 1.771000000000000600E-2 " " y[1] (numeric) = 1.771000000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.959032722729312500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23100000000000012 " " y[1] (analytic) = 1.776390000000000500E-2 " " y[1] (numeric) = 1.776390000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.953088540215613000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23200000000000012 " " y[1] (analytic) = 1.781760000000000600E-2 " " y[1] (numeric) = 1.781760000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.947202177596092000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23300000000000012 " " y[1] (analytic) = 1.787110000000000600E-2 " " y[1] (numeric) = 1.787110000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.941372916022859600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23400000000000012 " " y[1] (analytic) = 1.792440000000000700E-2 " " y[1] (numeric) = 1.792440000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.935600049069208800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23500000000000013 " " y[1] (analytic) = 1.797750000000000700E-2 " " y[1] (numeric) = 1.797750000000000500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.92988288246620100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23600000000000013 " " y[1] (analytic) = 1.80304000000000080E-2 " " y[1] (numeric) = 1.803040000000000500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.92422073384595580000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23700000000000013 " " y[1] (analytic) = 1.808310000000000500E-2 " " y[1] (numeric) = 1.808310000000000500E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23800000000000013 " " y[1] (analytic) = 1.81356000000000070E-2 " " y[1] (numeric) = 1.813560000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.913058819092620400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23900000000000013 " " y[1] (analytic) = 1.818790000000000700E-2 " " y[1] (numeric) = 1.818790000000000700E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24000000000000013 " " y[1] (analytic) = 1.824000000000000600E-2 " " y[1] (numeric) = 1.824000000000000600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24100000000000013 " " y[1] (analytic) = 1.829190000000000500E-2 " " y[1] (numeric) = 1.829190000000000500E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24200000000000013 " " y[1] (analytic) = 1.83436000000000100E-2 " " y[1] (numeric) = 1.834360000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.891366444947345500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24300000000000013 " " y[1] (analytic) = 1.839510000000001000E-2 " " y[1] (numeric) = 1.839510000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.886071264605037600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24400000000000013 " " y[1] (analytic) = 1.84464000000000070E-2 " " y[1] (numeric) = 1.844640000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.880826042996797700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24500000000000013 " " y[1] (analytic) = 1.849750000000000600E-2 " " y[1] (numeric) = 1.849750000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.875630194325510500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24600000000000014 " " y[1] (analytic) = 1.854840000000000700E-2 " " y[1] (numeric) = 1.854840000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.870483142456283400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24700000000000014 " " y[1] (analytic) = 1.859910000000000700E-2 " " y[1] (numeric) = 1.859910000000000500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.865384320721762400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24800000000000014 " " y[1] (analytic) = 1.86496000000000100E-2 " " y[1] (numeric) = 1.864960000000000200E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.72066634346432400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24900000000000014 " " y[1] (analytic) = 1.86999000000000080E-2 " " y[1] (numeric) = 1.869990000000000300E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.710658294379769500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2500000000000001 " " y[1] (analytic) = 1.875000000000000600E-2 " " y[1] (numeric) = 1.875000000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.850371707708593500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2510000000000001 " " y[1] (analytic) = 1.879990000000000500E-2 " " y[1] (numeric) = 1.8799900E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.845460322636616700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2520000000000001 " " y[1] (analytic) = 1.884960000000000800E-2 " " y[1] (numeric) = 1.8849600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.68118893976913300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2530000000000001 " " y[1] (analytic) = 1.88991000000000080E-2 " " y[1] (numeric) = 1.889910000000000200E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.671547271514107000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2540000000000001 " " y[1] (analytic) = 1.894840000000000700E-2 " " y[1] (numeric) = 1.8948400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.66199462957675900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2550000000000001 " " y[1] (analytic) = 1.899750000000000600E-2 " " y[1] (numeric) = 1.8997500E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.65253001916421900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2560000000000001 " " y[1] (analytic) = 1.904640000000000500E-2 " " y[1] (numeric) = 1.9046400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.82157623065440900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2570000000000001 " " y[1] (analytic) = 1.909510000000000700E-2 " " y[1] (numeric) = 1.9095100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.633860992562084600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2580000000000001 " " y[1] (analytic) = 1.914360000000000800E-2 " " y[1] (numeric) = 1.9143600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.62465466469589100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2590000000000001 " " y[1] (analytic) = 1.919190000000000600E-2 " " y[1] (numeric) = 1.9191900E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.807766272205260000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2600000000000001 " " y[1] (analytic) = 1.924000000000000700E-2 " " y[1] (numeric) = 1.92400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.606493713049494000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2610000000000001 " " y[1] (analytic) = 1.928790000000000200E-2 " " y[1] (numeric) = 1.9287900E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.798768633160485700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2620000000000001 " " y[1] (analytic) = 1.93356000000000080E-2 " " y[1] (numeric) = 1.9335600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.58866231402554140000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2630000000000001 " " y[1] (analytic) = 1.938310000000001000E-2 " " y[1] (numeric) = 1.9383100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.57986797979024330000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2640000000000001 " " y[1] (analytic) = 1.943040000000001000E-2 " " y[1] (numeric) = 1.9430400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.57115340080864300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2650000000000001 " " y[1] (analytic) = 1.947750000000000600E-2 " " y[1] (numeric) = 1.947750000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.781258863793409600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2660000000000001 " " y[1] (analytic) = 1.952440000000000300E-2 " " y[1] (numeric) = 1.9524400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.776980061847541500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2670000000000001 " " y[1] (analytic) = 1.957110000000000800E-2 " " y[1] (numeric) = 1.9571100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.54547976552530300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2680000000000001 " " y[1] (analytic) = 1.961760000000000700E-2 " " y[1] (numeric) = 1.961760000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.768537921026839800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.26900000000000013 " " y[1] (analytic) = 1.966390000000000600E-2 " " y[1] (numeric) = 1.9663900E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.76437377730440710000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27000000000000013 " " y[1] (analytic) = 1.971000000000000500E-2 " " y[1] (numeric) = 1.971000000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.760247058322482700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27100000000000013 " " y[1] (analytic) = 1.975590000000000700E-2 " " y[1] (numeric) = 1.975590000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.756157376760164300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27200000000000013 " " y[1] (analytic) = 1.98016000000000080E-2 " " y[1] (numeric) = 1.980160000000000300E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.504208702280232600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27300000000000013 " " y[1] (analytic) = 1.984710000000000600E-2 " " y[1] (numeric) = 1.984710000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.748087605722555600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27400000000000013 " " y[1] (analytic) = 1.989240000000000700E-2 " " y[1] (numeric) = 1.989240000000000500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.744106770401566700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27500000000000013 " " y[1] (analytic) = 1.993750000000000800E-2 " " y[1] (numeric) = 1.993750000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.74016148060369300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27600000000000013 " " y[1] (analytic) = 1.998240000000000600E-2 " " y[1] (numeric) = 1.998240000000000600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27700000000000014 " " y[1] (analytic) = 2.002710000000000600E-2 " " y[1] (numeric) = 2.002710000000000600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27800000000000014 " " y[1] (analytic) = 2.00716000000000100E-2 " " y[1] (numeric) = 2.007160000000000600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.728535319532878700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27900000000000014 " " y[1] (analytic) = 2.011590000000000600E-2 " " y[1] (numeric) = 2.011590000000000600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28000000000000014 " " y[1] (analytic) = 2.016000000000000600E-2 " " y[1] (numeric) = 2.016000000000000600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28100000000000014 " " y[1] (analytic) = 2.020390000000000200E-2 " " y[1] (numeric) = 2.020390000000000200E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28200000000000014 " " y[1] (analytic) = 2.024760000000000700E-2 " " y[1] (numeric) = 2.024760000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.71351021945989300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28300000000000014 " " y[1] (analytic) = 2.029110000000000600E-2 " " y[1] (numeric) = 2.029110000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.709836801333398700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28400000000000014 " " y[1] (analytic) = 2.03344000000000080E-2 " " y[1] (numeric) = 2.033440000000000200E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.41239176169802150000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28500000000000014 " " y[1] (analytic) = 2.037750000000000700E-2 " " y[1] (numeric) = 2.037750000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.702587143640590400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28600000000000014 " " y[1] (analytic) = 2.042040000000000500E-2 " " y[1] (numeric) = 2.042040000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.699010279893446200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28700000000000014 " " y[1] (analytic) = 2.04631000000000100E-2 " " y[1] (numeric) = 2.0463100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.390929968532248600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28800000000000014 " " y[1] (analytic) = 2.050560000000000700E-2 " " y[1] (numeric) = 2.050560000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.691950955813833000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28900000000000015 " " y[1] (analytic) = 2.054790000000000800E-2 " " y[1] (numeric) = 2.0547900E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.37693579582693400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29000000000000015 " " y[1] (analytic) = 2.059000000000000300E-2 " " y[1] (numeric) = 2.05900E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.68501551819019570000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29100000000000015 " " y[1] (analytic) = 2.06319000000000090E-2 " " y[1] (numeric) = 2.0631900E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.36318705689113700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29200000000000015 " " y[1] (analytic) = 2.067360000000001000E-2 " " y[1] (numeric) = 2.0673600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.35640328917422500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29300000000000015 " " y[1] (analytic) = 2.071510000000000900E-2 " " y[1] (numeric) = 2.0715100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.34967917311875200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29400000000000015 " " y[1] (analytic) = 2.075640000000000800E-2 " " y[1] (numeric) = 2.0756400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.343014156552786600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29500000000000015 " " y[1] (analytic) = 2.079750000000000800E-2 " " y[1] (numeric) = 2.0797500E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.3364076951110600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29600000000000015 " " y[1] (analytic) = 2.083840000000000700E-2 " " y[1] (numeric) = 2.0838400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.329859252105356600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29700000000000015 " " y[1] (analytic) = 2.087910000000001000E-2 " " y[1] (numeric) = 2.0879100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.323368298397548000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29800000000000015 " " y[1] (analytic) = 2.091960000000000800E-2 " " y[1] (numeric) = 2.0919600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.31693431227519930000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29900000000000015 " " y[1] (analytic) = 2.095990000000000600E-2 " " y[1] (numeric) = 2.0959900E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.31055677932968500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30000000000000016 " " y[1] (analytic) = 2.100000000000000500E-2 " " y[1] (numeric) = 2.100E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.652117596168387300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30100000000000016 " " y[1] (analytic) = 2.103990000000000600E-2 " " y[1] (numeric) = 2.1039900E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.29796905113960900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30200000000000016 " " y[1] (analytic) = 2.107960000000000700E-2 " " y[1] (numeric) = 2.1079600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.291757862534026600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30300000000000016 " " y[1] (analytic) = 2.11191000000000070E-2 " " y[1] (numeric) = 2.111910000000000200E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.28560114015617400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30400000000000016 " " y[1] (analytic) = 2.115840000000000800E-2 " " y[1] (numeric) = 2.1158400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.279498404372365000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30500000000000016 " " y[1] (analytic) = 2.119750000000000800E-2 " " y[1] (numeric) = 2.1197500E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.27344918217111700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30600000000000016 " " y[1] (analytic) = 2.123640000000000500E-2 " " y[1] (numeric) = 2.123640000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.633726503528664400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30700000000000016 " " y[1] (analytic) = 2.12751000000000080E-2 " " y[1] (numeric) = 2.1275100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.26150941894854800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30800000000000016 " " y[1] (analytic) = 2.13136000000000100E-2 " " y[1] (numeric) = 2.131360000000000200E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.2556179640732796000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30900000000000016 " " y[1] (analytic) = 2.135190000000000700E-2 " " y[1] (numeric) = 2.135190000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.624889097435644200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31000000000000016 " " y[1] (analytic) = 2.139000000000000600E-2 " " y[1] (numeric) = 2.139000000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.621994834947925700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31100000000000017 " " y[1] (analytic) = 2.142790000000000500E-2 " " y[1] (numeric) = 2.142790000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.619125976858961000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31200000000000017 " " y[1] (analytic) = 2.14656000000000070E-2 " " y[1] (numeric) = 2.146560000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.616282308416076300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31300000000000017 " " y[1] (analytic) = 2.150310000000000300E-2 " " y[1] (numeric) = 2.150310000000000300E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31400000000000017 " " y[1] (analytic) = 2.154040000000001000E-2 " " y[1] (numeric) = 2.154040000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.610669695991538100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31500000000000017 " " y[1] (analytic) = 2.15775000000000100E-2 " " y[1] (numeric) = 2.157750000000000500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.607900336903539700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31600000000000017 " " y[1] (analytic) = 2.161440000000000600E-2 " " y[1] (numeric) = 2.161440000000000600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31700000000000017 " " y[1] (analytic) = 2.165110000000000600E-2 " " y[1] (numeric) = 2.165110000000000600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31800000000000017 " " y[1] (analytic) = 2.168760000000000400E-2 " " y[1] (numeric) = 2.168760000000000400E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3190000000000002 " " y[1] (analytic) = 2.172390000000000700E-2 " " y[1] (numeric) = 2.172390000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.597064501288264500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3200000000000002 " " y[1] (analytic) = 2.17600000000000070E-2 " " y[1] (numeric) = 2.176000000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.59441495953750600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3210000000000002 " " y[1] (analytic) = 2.179590000000000700E-2 " " y[1] (numeric) = 2.179590000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.591788800624710800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3220000000000002 " " y[1] (analytic) = 2.183160000000000700E-2 " " y[1] (numeric) = 2.183160000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.58918583702230400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3230000000000002 " " y[1] (analytic) = 2.186710000000000600E-2 " " y[1] (numeric) = 2.186710000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.58660588370365200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3240000000000002 " " y[1] (analytic) = 2.19024000000000100E-2 " " y[1] (numeric) = 2.190240000000000200E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.168097516211569000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3250000000000002 " " y[1] (analytic) = 2.19375000000000100E-2 " " y[1] (numeric) = 2.193750000000000100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.163028560185629500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3260000000000002 " " y[1] (analytic) = 2.197240000000000600E-2 " " y[1] (numeric) = 2.197240000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.579002271920051000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3270000000000002 " " y[1] (analytic) = 2.20071000000000070E-2 " " y[1] (numeric) = 2.2007100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.15302511639753760000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3280000000000002 " " y[1] (analytic) = 2.204160000000000600E-2 " " y[1] (numeric) = 2.2041600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.574044965861649500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3290000000000002 " " y[1] (analytic) = 2.20759000000000100E-2 " " y[1] (numeric) = 2.207590000000000400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.143198648257704600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3300000000000002 " " y[1] (analytic) = 2.211000000000000700E-2 " " y[1] (numeric) = 2.21100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.138350928949446600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3310000000000002 " " y[1] (analytic) = 2.214390000000000800E-2 " " y[1] (numeric) = 2.2143900E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.13354644119022700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3320000000000002 " " y[1] (analytic) = 2.217760000000000600E-2 " " y[1] (numeric) = 2.217760000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.564392428375303600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3330000000000002 " " y[1] (analytic) = 2.221110000000000600E-2 " " y[1] (numeric) = 2.2211100E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.562032925858518300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3340000000000002 " " y[1] (analytic) = 2.224440000000000900E-2 " " y[1] (numeric) = 2.2244400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.119389106430034400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3350000000000002 " " y[1] (analytic) = 2.22775000000000080E-2 " " y[1] (numeric) = 2.227750000000000300E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.11475430542351050000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3360000000000002 " " y[1] (analytic) = 2.231040000000000800E-2 " " y[1] (numeric) = 2.2310400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.110161137365186600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3370000000000002 " " y[1] (analytic) = 2.234310000000000700E-2 " " y[1] (numeric) = 2.2343100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.10560929499810960000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3380000000000002 " " y[1] (analytic) = 2.237560000000000700E-2 " " y[1] (numeric) = 2.237560000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.550549237541613600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3390000000000002 " " y[1] (analytic) = 2.24079000000000080E-2 " " y[1] (numeric) = 2.2407900E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.096628378343006500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3400000000000002 " " y[1] (analytic) = 2.24400000000000100E-2 " " y[1] (numeric) = 2.24400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.09219870940607160000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3410000000000002 " " y[1] (analytic) = 2.247190000000000600E-2 " " y[1] (numeric) = 2.247190000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.543904588376422700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3420000000000002 " " y[1] (analytic) = 2.250360000000000700E-2 " " y[1] (numeric) = 2.250360000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.541729746331081700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3430000000000002 " " y[1] (analytic) = 2.253510000000000500E-2 " " y[1] (numeric) = 2.253510000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.539574686579430800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3440000000000002 " " y[1] (analytic) = 2.256640000000001000E-2 " " y[1] (numeric) = 2.256640000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.53743926898114600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3450000000000002 " " y[1] (analytic) = 2.259750000000000600E-2 " " y[1] (numeric) = 2.259750000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.53532335521788380000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3460000000000002 " " y[1] (analytic) = 2.262840000000000700E-2 " " y[1] (numeric) = 2.262840000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.53322680876845600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3470000000000002 " " y[1] (analytic) = 2.26591000000000100E-2 " " y[1] (numeric) = 2.265910000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.531149494884445000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3480000000000002 " " y[1] (analytic) = 2.268960000000000400E-2 " " y[1] (numeric) = 2.268960000000000400E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3490000000000002 " " y[1] (analytic) = 2.271990000000001000E-2 " " y[1] (numeric) = 2.271990000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.527052034539594400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3500000000000002 " " y[1] (analytic) = 2.275000000000000600E-2 " " y[1] (numeric) = 2.275000000000000600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3510000000000002 " " y[1] (analytic) = 2.277990000000000600E-2 " " y[1] (numeric) = 2.277990000000000600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3520000000000002 " " y[1] (analytic) = 2.280960000000000800E-2 " " y[1] (numeric) = 2.280960000000000800E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3530000000000002 " " y[1] (analytic) = 2.283910000000000400E-2 " " y[1] (numeric) = 2.283910000000000400E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3540000000000002 " " y[1] (analytic) = 2.286840000000000800E-2 " " y[1] (numeric) = 2.286840000000000500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.5171358520725600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3550000000000002 " " y[1] (analytic) = 2.289750000000001000E-2 " " y[1] (numeric) = 2.289750000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.515207752791184000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3560000000000002 " " y[1] (analytic) = 2.292640000000000800E-2 " " y[1] (numeric) = 2.292640000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.513297749299328800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3570000000000002 " " y[1] (analytic) = 2.295510000000000600E-2 " " y[1] (numeric) = 2.295510000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.51140572332667400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3580000000000002 " " y[1] (analytic) = 2.298360000000000700E-2 " " y[1] (numeric) = 2.298360000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.509531558134327700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3590000000000002 " " y[1] (analytic) = 2.30119000000000070E-2 " " y[1] (numeric) = 2.301190000000000200E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.015350276990264600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3600000000000002 " " y[1] (analytic) = 2.30400000000000080E-2 " " y[1] (numeric) = 2.30400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.011672701348623000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3610000000000002 " " y[1] (analytic) = 2.306790000000000500E-2 " " y[1] (numeric) = 2.306790000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.50401508241045500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3620000000000002 " " y[1] (analytic) = 2.309560000000000800E-2 " " y[1] (numeric) = 2.3095600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.00442244579366900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3630000000000002 " " y[1] (analytic) = 2.312310000000000500E-2 " " y[1] (numeric) = 2.3123100E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.500424662763043800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3640000000000002 " " y[1] (analytic) = 2.31504000000000100E-2 " " y[1] (numeric) = 2.3150400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.997310588113909500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3650000000000002 " " y[1] (analytic) = 2.31775000000000120E-2 " " y[1] (numeric) = 2.3177500E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 4.490709030680979000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3660000000000002 " " y[1] (analytic) = 2.320440000000000800E-2 " " y[1] (numeric) = 2.3204400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.9903354122094200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3670000000000002 " " y[1] (analytic) = 2.323110000000000700E-2 " " y[1] (numeric) = 2.3231100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.986898555775329700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3680000000000002 " " y[1] (analytic) = 2.325760000000000300E-2 " " y[1] (numeric) = 2.3257600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.49174762312259820000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3690000000000002 " " y[1] (analytic) = 2.328390000000000700E-2 " " y[1] (numeric) = 2.3283900E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.98012528137778800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3700000000000002 " " y[1] (analytic) = 2.331000000000000800E-2 " " y[1] (numeric) = 2.33100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.97678846156466100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3710000000000002 " " y[1] (analytic) = 2.333590000000000700E-2 " " y[1] (numeric) = 2.3335900E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.97348458979821930000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3720000000000002 " " y[1] (analytic) = 2.336160000000000700E-2 " " y[1] (numeric) = 2.3361600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.9702134716403100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3730000000000002 " " y[1] (analytic) = 2.338710000000000500E-2 " " y[1] (numeric) = 2.3387100E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.48348745759568900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3740000000000002 " " y[1] (analytic) = 2.341240000000000500E-2 " " y[1] (numeric) = 2.3412400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.963768731060133500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3750000000000002 " " y[1] (analytic) = 2.343750000000000600E-2 " " y[1] (numeric) = 2.3437500E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.9605947323337495000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3760000000000002 " " y[1] (analytic) = 2.346240000000000500E-2 " " y[1] (numeric) = 2.3462400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.47872636727428290000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3770000000000002 " " y[1] (analytic) = 2.348710000000000800E-2 " " y[1] (numeric) = 2.3487100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.95434255566128900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3780000000000002 " " y[1] (analytic) = 2.351160000000000700E-2 " " y[1] (numeric) = 2.3511600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.95126401602069900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3790000000000002 " " y[1] (analytic) = 2.353590000000000400E-2 " " y[1] (numeric) = 2.353590000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.474108469169912200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3800000000000002 " " y[1] (analytic) = 2.356000000000001000E-2 " " y[1] (numeric) = 2.35600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.94520114766860240000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3810000000000002 " " y[1] (analytic) = 2.358390000000000500E-2 " " y[1] (numeric) = 2.3583900E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.471108235683501700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38200000000000023 " " y[1] (analytic) = 2.360760000000000600E-2 " " y[1] (numeric) = 2.360760000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.469631369539306500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38300000000000023 " " y[1] (analytic) = 2.36311000000000100E-2 " " y[1] (numeric) = 2.363110000000000200E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.93633978270466700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38400000000000023 " " y[1] (analytic) = 2.365440000000000600E-2 " " y[1] (numeric) = 2.365440000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.466723718189264200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38500000000000023 " " y[1] (analytic) = 2.367750000000000700E-2 " " y[1] (numeric) = 2.367750000000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.46529276822029900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38600000000000023 " " y[1] (analytic) = 2.370040000000000500E-2 " " y[1] (numeric) = 2.370040000000000500E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38700000000000023 " " y[1] (analytic) = 2.372310000000000800E-2 " " y[1] (numeric) = 2.372310000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.462476215989315700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38800000000000023 " " y[1] (analytic) = 2.37456000000000080E-2 " " y[1] (numeric) = 2.374560000000000600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.461090455475377600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38900000000000023 " " y[1] (analytic) = 2.37679000000000080E-2 " " y[1] (numeric) = 2.376790000000000600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.459719601628083600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39000000000000024 " " y[1] (analytic) = 2.379000000000000600E-2 " " y[1] (numeric) = 2.379000000000000600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39100000000000024 " " y[1] (analytic) = 2.381190000000000300E-2 " " y[1] (numeric) = 2.381190000000000300E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39200000000000024 " " y[1] (analytic) = 2.383360000000000800E-2 " " y[1] (numeric) = 2.383360000000000500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.45569572030814200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39300000000000024 " " y[1] (analytic) = 2.38551000000000120E-2 " " y[1] (numeric) = 2.385510000000000400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.90876747693668200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39400000000000024 " " y[1] (analytic) = 2.387640000000000600E-2 " " y[1] (numeric) = 2.387640000000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.45308629104622700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39500000000000024 " " y[1] (analytic) = 2.38975000000000100E-2 " " y[1] (numeric) = 2.389750000000000200E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.903606613205242000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = (0.1 * x + 0.2) - (0.3 * x + 0.1) ;" Iterations = 295 "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 0 Hours 46 Minutes 50 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 46 Minutes 26 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 49 Minutes 27 Seconds "Time to Timeout " Unknown Percent Done = 6.040816326530617 "%" (%o54) true (%o54) diffeq.max