(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : arcsin(array_const_0D1 ),
1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
array_tmp3 : arccos(array_const_0D1 ),
1 1
array_tmp4 : array_tmp3 + array_tmp2 ,
1 1 1
array_tmp5 : arctan(array_const_0D1 ),
1 1
array_tmp6 : array_tmp5 + array_tmp4 ,
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
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
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
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 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 3.0
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 4.0
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 5.0
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
then (temporary : array_tmp6 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : arcsin(array_const_0D1 ),
1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
array_tmp3 : arccos(array_const_0D1 ),
1 1
array_tmp4 : array_tmp3 + array_tmp2 ,
1 1 1
array_tmp5 : arctan(array_const_0D1 ),
1 1
array_tmp6 : array_tmp5 + array_tmp4 ,
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
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
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
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 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 3.0
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 4.0
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 5.0
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
then (temporary : array_tmp6 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i32) log_revs(file, revs) := printf(file, revs)
(%o32) log_revs(file, revs) := printf(file, revs)
(%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i35) logstart(file) := printf(file, "")
(%o35) logstart(file) := printf(file, "
")
(%i36) logend(file) := printf(file, "
~%")
(%o36) logend(file) := printf(file, "~%")
(%i37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i40) factorial_2(nnn) := nnn!
(%o40) factorial_2(nnn) := nnn!
(%i41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i46) Si(x) := 0.0
(%o46) Si(x) := 0.0
(%i47) Ci(x) := 0.0
(%o47) Ci(x) := 0.0
(%i48) ln(x) := log(x)
(%o48) ln(x) := log(x)
(%i49) arcsin(x) := asin(x)
(%o49) arcsin(x) := asin(x)
(%i50) arccos(x) := acos(x)
(%o50) arccos(x) := acos(x)
(%i51) arctan(x) := atan(x)
(%o51) arctan(x) := atan(x)
(%i52) omniabs(x) := abs(x)
(%o52) omniabs(x) := abs(x)
(%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i54) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%o54) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%i55) exact_soln_y(x) := block((arctan(0.1) + arccos(0.1) + arcsin(0.1)) x)
(%o55) exact_soln_y(x) := block((arctan(0.1) + arccos(0.1) + arcsin(0.1)) x)
(%i56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\
########temp/arcsin_c_arccos_c_arctan_cpostode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = arcsin(0.1) + arccos(0.1) + arctan(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:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS,
"glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "glob_display_interval:0.1,"),
omniout_str(ALWAYS, "glob_max_minutes:10,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " ((arcsin(0.1) + arccos(0.1) + arctan(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_a1, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3_a1, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5_a1, 1 + max_terms), array(array_tmp5_a2, 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_a1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3_a1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp5_a1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5_a2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_a1 : 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_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_a1 : 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_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5_a1 : 0.0, term : 1 + term),
term
array(array_tmp5_a2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5_a2 : 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_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 0.05, glob_look_poles : true, glob_max_iter : 1000000,
glob_display_interval : 0.1, glob_max_minutes : 10,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 )\
= arcsin(0.1) + arccos(0.1) + arctan(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,
"2013-01-12T20:56:38-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file,
"arcsin_c_arccos_c_arctan_c"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = arcsin(0.1) + arccos(0.1) + arctan(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, " 156 | "), logitem_str(html_log_file, "arcsin_c_arccos_c_arctan_c di\
ffeq.max"), logitem_str(html_log_file, "arcsin_c_arccos_c_arctan_c maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%o56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\
########temp/arcsin_c_arccos_c_arctan_cpostode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = arcsin(0.1) + arccos(0.1) + arctan(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:-5.0,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS,
"glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "glob_display_interval:0.1,"),
omniout_str(ALWAYS, "glob_max_minutes:10,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " ((arcsin(0.1) + arccos(0.1) + arctan(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_a1, 1 + max_terms), array(array_tmp1, 1 + max_terms),
array(array_tmp2, 1 + max_terms), array(array_tmp3_a1, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5_a1, 1 + max_terms), array(array_tmp5_a2, 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_a1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3_a1 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0,
term
term : 1 + term), term : 1, while term <= max_terms do (array_tmp4 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp5_a1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5_a2 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1_a1 : 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_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_a1 : 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_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5_a1 : 0.0, term : 1 + term),
term
array(array_tmp5_a2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5_a2 : 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_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 0.05, glob_look_poles : true, glob_max_iter : 1000000,
glob_display_interval : 0.1, glob_max_minutes : 10,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "),
glob_reached_optimal_h : true, glob_optimal_clock_start_sec :
elapsed_time_seconds(), while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 )\
= arcsin(0.1) + arccos(0.1) + arctan(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,
"2013-01-12T20:56:38-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file,
"arcsin_c_arccos_c_arctan_c"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = arcsin(0.1) + arccos(0.1) + arctan(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, " 156 | "), logitem_str(html_log_file, "arcsin_c_arccos_c_arctan_c di\
ffeq.max"), logitem_str(html_log_file, "arcsin_c_arccos_c_arctan_c maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i57) main()
"##############ECHO OF PROBLEM#################"
"##############temp/arcsin_c_arccos_c_arctan_cpostode.ode#################"
"diff ( y , x , 1 ) = arcsin(0.1) + arccos(0.1) + arctan(0.1);"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:-5.0,"
"x_end:5.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.05,"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"glob_display_interval:0.1,"
"glob_max_minutes:10,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" ((arcsin(0.1) + arccos(0.1) + arctan(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 = 10. ""
estimated_steps = 10000. ""
step_error = 1.00000000000000E-14 ""
est_needed_step_err = 1.00000000000000E-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] = -5. " "
y[1] (analytic) = -8.352324896430293 " "
y[1] (numeric) = -8.352324896430293 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -5. " "
y[1] (analytic) = -8.352324896430293 " "
y[1] (numeric) = -8.352324896430293 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.999 " "
y[1] (analytic) = -8.350654431451007 " "
y[1] (numeric) = -8.350654431451007 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.998000000000000 " "
y[1] (analytic) = -8.34898396647172 " "
y[1] (numeric) = -8.348983966471721 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.127632352072822400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.996999999999999 " "
y[1] (analytic) = -8.347313501492433 " "
y[1] (numeric) = -8.347313501492435 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.128058134012400500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.995999999999999 " "
y[1] (analytic) = -8.345643036513147 " "
y[1] (numeric) = -8.345643036513149 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 2.12848408640111430000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.994999999999998 " "
y[1] (analytic) = -8.34397257153386 " "
y[1] (numeric) = -8.343972571533863 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.2578204186826700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.993999999999998 " "
y[1] (analytic) = -8.342302106554573 " "
y[1] (numeric) = -8.342302106554577 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.25867300587103200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.992999999999998 " "
y[1] (analytic) = -8.340631641575287 " "
y[1] (numeric) = -8.34063164157529 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.25952593457238800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.991999999999997 " "
y[1] (analytic) = -8.338961176596 " "
y[1] (numeric) = -8.338961176596005 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.39056880748796300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.990999999999997 " "
y[1] (analytic) = -8.337290711616713 " "
y[1] (numeric) = -8.337290711616719 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.39184922600278700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.989999999999997 " "
y[1] (analytic) = -8.335620246637427 " "
y[1] (numeric) = -8.335620246637433 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 6.39313015771140500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.988999999999996 " "
y[1] (analytic) = -8.33394978165814 " "
y[1] (numeric) = -8.333949781658147 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 8.52588213722988400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.987999999999996 " "
y[1] (analytic) = -8.332279316678854 " "
y[1] (numeric) = -8.33227931667886 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 8.527591415926200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.986999999999996 " "
y[1] (analytic) = -8.330608851699568 " "
y[1] (numeric) = -8.330608851699575 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 8.5293013801162800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.985999999999995 " "
y[1] (analytic) = -8.32893838672028 " "
y[1] (numeric) = -8.328938386720289 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 1.06637650377657180000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.984999999999995 " "
y[1] (analytic) = -8.327267921740994 " "
y[1] (numeric) = -8.327267921741003 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 1.06659042082848280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.983999999999995 " "
y[1] (analytic) = -8.325597456761708 " "
y[1] (numeric) = -8.325597456761717 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 1.06680442372190750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.982999999999994 " "
y[1] (analytic) = -8.32392699178242 " "
y[1] (numeric) = -8.32392699178243 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 1.28042221501023180000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.981999999999994 " "
y[1] (analytic) = -8.322256526803134 " "
y[1] (numeric) = -8.322256526803145 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 1.28067922468807440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.980999999999994 " "
y[1] (analytic) = -8.320586061823848 " "
y[1] (numeric) = -8.320586061823859 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 1.28093633756193230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.979999999999993 " "
y[1] (analytic) = -8.31891559684456 " "
y[1] (numeric) = -8.318915596844572 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.49472581264296880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.978999999999993 " "
y[1] (analytic) = -8.317245131865274 " "
y[1] (numeric) = -8.317245131865286 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.49502601867081450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.977999999999993 " "
y[1] (analytic) = -8.315574666885988 " "
y[1] (numeric) = -8.315574666886 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.49532634531176880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.976999999999992 " "
y[1] (analytic) = -8.3139042019067 " "
y[1] (numeric) = -8.313904201906714 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.7092877630154680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.975999999999992 " "
y[1] (analytic) = -8.312233736927414 " "
y[1] (numeric) = -8.312233736927428 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.70963126939871060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.974999999999992 " "
y[1] (analytic) = -8.310563271948128 " "
y[1] (numeric) = -8.310563271948142 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.70997491387497170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.973999999999991 " "
y[1] (analytic) = -8.30889280696884 " "
y[1] (numeric) = -8.308892806968856 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.9241085335934832000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.972999999999991 " "
y[1] (analytic) = -8.307222341989554 " "
y[1] (numeric) = -8.30722234198957 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.92449544461974350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.971999999999990 " "
y[1] (analytic) = -8.305551877010268 " "
y[1] (numeric) = -8.305551877010284 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.92488251128197600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.97099999999999 " "
y[1] (analytic) = -8.30388141203098 " "
y[1] (numeric) = -8.303881412030998 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 2.139188592971230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96999999999999 " "
y[1] (analytic) = -8.302210947051694 " "
y[1] (numeric) = -8.302210947051712 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 2.13961901321126440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96899999999999 " "
y[1] (analytic) = -8.300540482072408 " "
y[1] (numeric) = -8.300540482072426 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 2.14004960669349650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.967999999999990 " "
y[1] (analytic) = -8.29887001709312 " "
y[1] (numeric) = -8.29887001709314 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 2.3545284108747958000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.966999999999989 " "
y[1] (analytic) = -8.297199552113835 " "
y[1] (numeric) = -8.297199552113854 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 2.35500244518340780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.965999999999989 " "
y[1] (analytic) = -8.295529087134549 " "
y[1] (numeric) = -8.295529087134568 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 2.3554766704039440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.964999999999988 " "
y[1] (analytic) = -8.29385862215526 " "
y[1] (numeric) = -8.293858622155282 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 2.5701284581655565000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.963999999999988 " "
y[1] (analytic) = -8.292188157175975 " "
y[1] (numeric) = -8.292188157175996 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 2.57064621168251200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.962999999999988 " "
y[1] (analytic) = -8.290517692196689 " "
y[1] (numeric) = -8.29051769219671 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 2.5711641738448493000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.961999999999987 " "
y[1] (analytic) = -8.288847227217401 " "
y[1] (numeric) = -8.288847227217424 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 2.78598920684360930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.960999999999987 " "
y[1] (analytic) = -8.287176762238115 " "
y[1] (numeric) = -8.287176762238138 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 2.7865507849945553000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.959999999999987 " "
y[1] (analytic) = -8.285506297258829 " "
y[1] (numeric) = -8.285506297258852 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 2.7871125895883040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.958999999999986 " "
y[1] (analytic) = -8.283835832279541 " "
y[1] (numeric) = -8.283835832279566 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 3.00211113005121800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.957999999999986 " "
y[1] (analytic) = -8.282165367300255 " "
y[1] (numeric) = -8.28216536730028 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 3.00271663854860650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.956999999999986 " "
y[1] (analytic) = -8.280494902320969 " "
y[1] (numeric) = -8.280494902320994 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 3.00332239135041150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.955999999999985 " "
y[1] (analytic) = -8.278824437341681 " "
y[1] (numeric) = -8.278824437341708 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 3.21849470207627000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.954999999999985 " "
y[1] (analytic) = -8.277153972362395 " "
y[1] (numeric) = -8.277153972362422 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 3.2191442469202813000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.953999999999985 " "
y[1] (analytic) = -8.27548350738311 " "
y[1] (numeric) = -8.275483507383136 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 3.21979405399475000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.952999999999984 " "
y[1] (analytic) = -8.273813042403821 " "
y[1] (numeric) = -8.27381304240385 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 3.4351403983557430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.951999999999984 " "
y[1] (analytic) = -8.272142577424535 " "
y[1] (numeric) = -8.272142577424564 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 3.43583408583521700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.950999999999984 " "
y[1] (analytic) = -8.27047211244525 " "
y[1] (numeric) = -8.270472112445278 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 3.4365280535358506000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.949999999999983 " "
y[1] (analytic) = -8.268801647465962 " "
y[1] (numeric) = -8.268801647465992 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 3.6520486954791920000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.948999999999983 " "
y[1] (analytic) = -8.267131182486676 " "
y[1] (numeric) = -8.267131182486706 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 3.65278663217256050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.947999999999983 " "
y[1] (analytic) = -8.26546071750739 " "
y[1] (numeric) = -8.26546071750742 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 3.6535248671426840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.946999999999982 " "
y[1] (analytic) = -8.263790252528102 " "
y[1] (numeric) = -8.263790252528134 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 3.86922007119223870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.945999999999982 " "
y[1] (analytic) = -8.262119787548816 " "
y[1] (numeric) = -8.262119787548848 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 3.870002363968460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.944999999999982 " "
y[1] (analytic) = -8.26044932256953 " "
y[1] (numeric) = -8.260449322569562 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 3.87078497314216450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.943999999999981 " "
y[1] (analytic) = -8.258778857590242 " "
y[1] (numeric) = -8.258778857590276 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 4.0866550044000827000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.942999999999981 " "
y[1] (analytic) = -8.257108392610956 " "
y[1] (numeric) = -8.25710839261099 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 4.0874817604195850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.941999999999980 " "
y[1] (analytic) = -8.25543792763167 " "
y[1] (numeric) = -8.255437927631704 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 4.08830885102266450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.94099999999998 " "
y[1] (analytic) = -8.253767462652382 " "
y[1] (numeric) = -8.253767462652418 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 4.3043539751710210000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93999999999998 " "
y[1] (analytic) = -8.252096997673096 " "
y[1] (numeric) = -8.252096997673132 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 4.30522530188664200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93899999999998 " "
y[1] (analytic) = -8.25042653269381 " "
y[1] (numeric) = -8.250426532693846 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 4.30609698143754050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.937999999999980 " "
y[1] (analytic) = -8.248756067714522 " "
y[1] (numeric) = -8.24875606771456 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 4.52231746473997940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.936999999999979 " "
y[1] (analytic) = -8.247085602735236 " "
y[1] (numeric) = -8.247085602735273 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 4.52323346989791760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.935999999999979 " "
y[1] (analytic) = -8.24541513775595 " "
y[1] (numeric) = -8.245415137755987 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 4.52414984620867430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.934999999999978 " "
y[1] (analytic) = -8.243744672776662 " "
y[1] (numeric) = -8.243744672776701 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 4.7405459555120620000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.933999999999978 " "
y[1] (analytic) = -8.242074207797376 " "
y[1] (numeric) = -8.242074207797415 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 4.7415067471528220000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.932999999999978 " "
y[1] (analytic) = -8.24040374281809 " "
y[1] (numeric) = -8.24040374281813 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 4.7424679283300275000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.931999999999977 " "
y[1] (analytic) = -8.238733277838802 " "
y[1] (numeric) = -8.238733277838843 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 4.9590399310661054000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.930999999999977 " "
y[1] (analytic) = -8.237062812859516 " "
y[1] (numeric) = -8.237062812859557 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 4.9600456175254570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.929999999999977 " "
y[1] (analytic) = -8.23539234788023 " "
y[1] (numeric) = -8.235392347880271 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 4.9610517119712030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.928999999999976 " "
y[1] (analytic) = -8.233721882900943 " "
y[1] (numeric) = -8.233721882900985 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 5.1777998761582540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.927999999999976 " "
y[1] (analytic) = -8.232051417921657 " "
y[1] (numeric) = -8.2320514179217 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 5.1788505660681880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.926999999999976 " "
y[1] (analytic) = -8.23038095294237 " "
y[1] (numeric) = -8.230380952942413 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 5.179901682481030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.925999999999975 " "
y[1] (analytic) = -8.228710487963083 " "
y[1] (numeric) = -8.228710487963127 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 5.3968262767255470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.924999999999975 " "
y[1] (analytic) = -8.227040022983797 " "
y[1] (numeric) = -8.227040022983841 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 5.3979220790152380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.923999999999975 " "
y[1] (analytic) = -8.22536955800451 " "
y[1] (numeric) = -8.225369558004555 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 5.3990183263911540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.922999999999974 " "
y[1] (analytic) = -8.223699093025223 " "
y[1] (numeric) = -8.22369909302527 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 5.6161196198895090000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.921999999999974 " "
y[1] (analytic) = -8.222028628045937 " "
y[1] (numeric) = -8.222028628045983 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 5.6172606437862770000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.920999999999974 " "
y[1] (analytic) = -8.220358163066651 " "
y[1] (numeric) = -8.220358163066697 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 5.618402131419640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.919999999999973 " "
y[1] (analytic) = -8.218687698087363 " "
y[1] (numeric) = -8.218687698087411 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 5.8356803939597680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.918999999999973 " "
y[1] (analytic) = -8.217017233108077 " "
y[1] (numeric) = -8.217017233108125 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 5.836866748990050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.917999999999973 " "
y[1] (analytic) = -8.215346768128791 " "
y[1] (numeric) = -8.215346768128839 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 5.8380535864745950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.916999999999972 " "
y[1] (analytic) = -8.213676303149503 " "
y[1] (numeric) = -8.213676303149553 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 6.0555090884376790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.915999999999972 " "
y[1] (analytic) = -8.212005838170217 " "
y[1] (numeric) = -8.212005838170267 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 6.0567408844280050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.914999999999972 " "
y[1] (analytic) = -8.210335373190931 " "
y[1] (numeric) = -8.210335373190981 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 6.0579731816577960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.913999999999971 " "
y[1] (analytic) = -8.208664908211643 " "
y[1] (numeric) = -8.208664908211695 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 6.2756061940199590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.912999999999971 " "
y[1] (analytic) = -8.206994443232357 " "
y[1] (numeric) = -8.206994443232409 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 6.2768835410979200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.911999999999970 " "
y[1] (analytic) = -8.205323978253071 " "
y[1] (numeric) = -8.205323978253123 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 6.2781614082683380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.91099999999997 " "
y[1] (analytic) = -8.203653513273784 " "
y[1] (numeric) = -8.203653513273837 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 6.4959722026023390000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90999999999997 " "
y[1] (analytic) = -8.201983048294498 " "
y[1] (numeric) = -8.20198304829455 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 6.4972952111975730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90899999999997 " "
y[1] (analytic) = -8.200312583315212 " "
y[1] (numeric) = -8.200312583315265 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 6.4986187588062920000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.907999999999970 " "
y[1] (analytic) = -8.198642118335924 " "
y[1] (numeric) = -8.198642118335979 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 6.716607607283230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.906999999999969 " "
y[1] (analytic) = -8.196971653356638 " "
y[1] (numeric) = -8.196971653356693 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 6.7179763881284070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.905999999999969 " "
y[1] (analytic) = -8.195301188377352 " "
y[1] (numeric) = -8.195301188377407 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 6.7193457269763750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.904999999999968 " "
y[1] (analytic) = -8.193630723398064 " "
y[1] (numeric) = -8.19363072339812 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 6.9375129023674020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.903999999999968 " "
y[1] (analytic) = -8.191960258418778 " "
y[1] (numeric) = -8.191960258418835 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 6.9389275664992060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.902999999999968 " "
y[1] (analytic) = -8.190289793439492 " "
y[1] (numeric) = -8.190289793439549 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 6.9403428076916380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.901999999999967 " "
y[1] (analytic) = -8.188619328460204 " "
y[1] (numeric) = -8.188619328460263 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 7.1586885833696690000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.900999999999967 " "
y[1] (analytic) = -8.186948863480918 " "
y[1] (numeric) = -8.186948863480977 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 7.1601492421297930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.899999999999967 " "
y[1] (analytic) = -8.185278398501632 " "
y[1] (numeric) = -8.18527839850169 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 7.1616104970771670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.898999999999966 " "
y[1] (analytic) = -8.183607933522344 " "
y[1] (numeric) = -8.183607933522405 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 7.3801351470186000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.897999999999966 " "
y[1] (analytic) = -8.181937468543058 " "
y[1] (numeric) = -8.181937468543119 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 7.3816419120547430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.896999999999966 " "
y[1] (analytic) = -8.180267003563772 " "
y[1] (numeric) = -8.180267003563833 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 7.3831492924737850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.895999999999965 " "
y[1] (analytic) = -8.178596538584484 " "
y[1] (numeric) = -8.178596538584546 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 7.601853091260240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.894999999999965 " "
y[1] (analytic) = -8.176926073605198 " "
y[1] (numeric) = -8.17692607360526 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 7.6034060745270960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.893999999999965 " "
y[1] (analytic) = -8.175255608625912 " "
y[1] (numeric) = -8.175255608625974 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 7.6049596924417940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.892999999999964 " "
y[1] (analytic) = -8.173585143646624 " "
y[1] (numeric) = -8.173585143646688 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 7.8238429152618330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.891999999999964 " "
y[1] (analytic) = -8.171914678667338 " "
y[1] (numeric) = -8.171914678667402 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 7.8254422290221070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.890999999999964 " "
y[1] (analytic) = -8.170244213688052 " "
y[1] (numeric) = -8.170244213688116 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 7.8270421967647010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.889999999999963 " "
y[1] (analytic) = -8.168573748708765 " "
y[1] (numeric) = -8.16857374870883 " "
absolute error = 6.57252030578092700000000000000E-14 " "
relative error = 8.0461051194155750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.888999999999963 " "
y[1] (analytic) = -8.166903283729479 " "
y[1] (numeric) = -8.166903283729544 " "
absolute error = 6.57252030578092700000000000000E-14 " "
relative error = 8.0477508762409820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.887999999999963 " "
y[1] (analytic) = -8.165232818750193 " "
y[1] (numeric) = -8.165232818750258 " "
absolute error = 6.57252030578092700000000000000E-14 " "
relative error = 8.0493973064529790000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.886999999999962 " "
y[1] (analytic) = -8.163562353770905 " "
y[1] (numeric) = -8.163562353770972 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 8.2686402053423720000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.885999999999962 " "
y[1] (analytic) = -8.161891888791619 " "
y[1] (numeric) = -8.161891888791686 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 8.2703325181146490000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.884999999999962 " "
y[1] (analytic) = -8.160221423812333 " "
y[1] (numeric) = -8.1602214238124 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 8.2720255237478360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.883999999999961 " "
y[1] (analytic) = -8.158550958833045 " "
y[1] (numeric) = -8.158550958833114 " "
absolute error = 6.92779167366097700000000000000E-14 " "
relative error = 8.4914486758956150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.882999999999961 " "
y[1] (analytic) = -8.156880493853759 " "
y[1] (numeric) = -8.156880493853828 " "
absolute error = 6.92779167366097700000000000000E-14 " "
relative error = 8.4931876578075340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.881999999999960 " "
y[1] (analytic) = -8.155210028874473 " "
y[1] (numeric) = -8.155210028874542 " "
absolute error = 6.92779167366097700000000000000E-14 " "
relative error = 8.4949273521249880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.88099999999996 " "
y[1] (analytic) = -8.153539563895185 " "
y[1] (numeric) = -8.153539563895256 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 8.7145310351649670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87999999999996 " "
y[1] (analytic) = -8.151869098915899 " "
y[1] (numeric) = -8.15186909891597 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 8.7163167997213530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87899999999996 " "
y[1] (analytic) = -8.150198633936613 " "
y[1] (numeric) = -8.150198633936684 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 8.7181032962984630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.877999999999960 " "
y[1] (analytic) = -8.148528168957325 " "
y[1] (numeric) = -8.148528168957398 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 8.9378877884801590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.876999999999959 " "
y[1] (analytic) = -8.14685770397804 " "
y[1] (numeric) = -8.146857703978112 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 8.9397204494989170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.875999999999959 " "
y[1] (analytic) = -8.145187238998753 " "
y[1] (numeric) = -8.145187238998826 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 8.9415538622244100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.874999999999958 " "
y[1] (analytic) = -8.143516774019465 " "
y[1] (numeric) = -8.14351677401954 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 9.1615194424148160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.873999999999958 " "
y[1] (analytic) = -8.14184630904018 " "
y[1] (numeric) = -8.141846309040254 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 9.163399114027950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.872999999999958 " "
y[1] (analytic) = -8.140175844060893 " "
y[1] (numeric) = -8.140175844060968 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 9.165279557104910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.871999999999957 " "
y[1] (analytic) = -8.138505379081606 " "
y[1] (numeric) = -8.138505379081682 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 9.3854265047902810000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.870999999999957 " "
y[1] (analytic) = -8.13683491410232 " "
y[1] (numeric) = -8.136834914102396 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 9.387353301444930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.869999999999957 " "
y[1] (analytic) = -8.135164449123033 " "
y[1] (numeric) = -8.13516444912311 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 9.3892808893918370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.868999999999956 " "
y[1] (analytic) = -8.133493984143746 " "
y[1] (numeric) = -8.133493984143824 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 9.6096094846794560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.867999999999956 " "
y[1] (analytic) = -8.13182351916446 " "
y[1] (numeric) = -8.131823519164538 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 9.611583521138919000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.866999999999956 " "
y[1] (analytic) = -8.130153054185174 " "
y[1] (numeric) = -8.130153054185252 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 9.6135583687906860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.865999999999955 " "
y[1] (analytic) = -8.128482589205886 " "
y[1] (numeric) = -8.128482589205966 " "
absolute error = 7.99360577730112700000000000000E-14 " "
relative error = 9.8340688924106610000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.864999999999955 " "
y[1] (analytic) = -8.1268121242266 " "
y[1] (numeric) = -8.12681212422668 " "
absolute error = 7.99360577730112700000000000000E-14 " "
relative error = 9.8360902837554530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.863999999999955 " "
y[1] (analytic) = -8.125141659247314 " "
y[1] (numeric) = -8.125141659247394 " "
absolute error = 7.99360577730112700000000000000E-14 " "
relative error = 9.8381125062644480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.862999999999954 " "
y[1] (analytic) = -8.123471194268026 " "
y[1] (numeric) = -8.123471194268108 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 1.0058805239571520000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.861999999999954 " "
y[1] (analytic) = -8.12180072928874 " "
y[1] (numeric) = -8.121800729288822 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 1.006087410120039000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.860999999999954 " "
y[1] (analytic) = -8.120130264309454 " "
y[1] (numeric) = -8.120130264309536 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 1.0062943814037502000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.859999999999953 " "
y[1] (analytic) = -8.118459799330166 " "
y[1] (numeric) = -8.11845979933025 " "
absolute error = 8.34887714518117700000000000000E-14 " "
relative error = 1.028381903901282000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.858999999999953 " "
y[1] (analytic) = -8.11678933435088 " "
y[1] (numeric) = -8.116789334350964 " "
absolute error = 8.34887714518117700000000000000E-14 " "
relative error = 1.0285935486643819000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.857999999999953 " "
y[1] (analytic) = -8.115118869371594 " "
y[1] (numeric) = -8.115118869371678 " "
absolute error = 8.34887714518117700000000000000E-14 " "
relative error = 1.0288052805599489000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.856999999999952 " "
y[1] (analytic) = -8.113448404392306 " "
y[1] (numeric) = -8.113448404392392 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 1.0509110804852445000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.855999999999952 " "
y[1] (analytic) = -8.11177793941302 " "
y[1] (numeric) = -8.111777939413106 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 1.0511274954523957000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.854999999999952 " "
y[1] (analytic) = -8.110107474433734 " "
y[1] (numeric) = -8.11010747443382 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 1.0513439995709234000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.853999999999951 " "
y[1] (analytic) = -8.108437009454446 " "
y[1] (numeric) = -8.108437009454533 " "
absolute error = 8.70414851306122700000000000000E-14 " "
relative error = 1.0734681052479264000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.852999999999951 " "
y[1] (analytic) = -8.10676654447516 " "
y[1] (numeric) = -8.106766544475247 " "
absolute error = 8.70414851306122700000000000000E-14 " "
relative error = 1.073689302055107100000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.851999999999950 " "
y[1] (analytic) = -8.105096079495874 " "
y[1] (numeric) = -8.105096079495961 " "
absolute error = 8.70414851306122700000000000000E-14 " "
relative error = 1.073910590039867000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.85099999999995 " "
y[1] (analytic) = -8.103425614516587 " "
y[1] (numeric) = -8.103425614516675 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 1.0960530298557074000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.84999999999995 " "
y[1] (analytic) = -8.1017551495373 " "
y[1] (numeric) = -8.10175514953739 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 1.0962790201711416000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.84899999999995 " "
y[1] (analytic) = -8.100084684558015 " "
y[1] (numeric) = -8.100084684558103 " "
absolute error = 8.88178419700125200000000000000E-14 " "
relative error = 1.0965051036976772000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.847999999999950 " "
y[1] (analytic) = -8.098414219578727 " "
y[1] (numeric) = -8.098414219578817 " "
absolute error = 9.05941988094127700000000000000E-14 " "
relative error = 1.1186659061028545000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.846999999999949 " "
y[1] (analytic) = -8.09674375459944 " "
y[1] (numeric) = -8.096743754599531 " "
absolute error = 9.05941988094127700000000000000E-14 " "
relative error = 1.1188967016271174000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.845999999999949 " "
y[1] (analytic) = -8.095073289620155 " "
y[1] (numeric) = -8.095073289620245 " "
absolute error = 9.05941988094127700000000000000E-14 " "
relative error = 1.1191275924033509000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.844999999999948 " "
y[1] (analytic) = -8.093402824640867 " "
y[1] (numeric) = -8.09340282464096 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 1.1413067859119175000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.843999999999948 " "
y[1] (analytic) = -8.09173235966158 " "
y[1] (numeric) = -8.091732359661673 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 1.141542398378043000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.842999999999948 " "
y[1] (analytic) = -8.090061894682295 " "
y[1] (numeric) = -8.090061894682387 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 1.1417781081443816000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.841999999999947 " "
y[1] (analytic) = -8.088391429703007 " "
y[1] (numeric) = -8.088391429703101 " "
absolute error = 9.41469124882132700000000000000E-14 " "
relative error = 1.1639757213341267000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.840999999999947 " "
y[1] (analytic) = -8.086720964723721 " "
y[1] (numeric) = -8.086720964723815 " "
absolute error = 9.41469124882132700000000000000E-14 " "
relative error = 1.1642161625077137000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.839999999999947 " "
y[1] (analytic) = -8.085050499744435 " "
y[1] (numeric) = -8.08505049974453 " "
absolute error = 9.41469124882132700000000000000E-14 " "
relative error = 1.1644567030371576000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.838999999999946 " "
y[1] (analytic) = -8.083380034765147 " "
y[1] (numeric) = -8.083380034765243 " "
absolute error = 9.59232693276135300000000000000E-14 " "
relative error = 1.1866727645497921000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.837999999999946 " "
y[1] (analytic) = -8.081709569785861 " "
y[1] (numeric) = -8.081709569785957 " "
absolute error = 9.59232693276135300000000000000E-14 " "
relative error = 1.186918046229112000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.836999999999946 " "
y[1] (analytic) = -8.080039104806575 " "
y[1] (numeric) = -8.080039104806671 " "
absolute error = 9.59232693276135300000000000000E-14 " "
relative error = 1.1871634293273607000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.835999999999945 " "
y[1] (analytic) = -8.078368639827287 " "
y[1] (numeric) = -8.078368639827385 " "
absolute error = 9.76996261670137800000000000000E-14 " "
relative error = 1.2093979678687028000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.834999999999945 " "
y[1] (analytic) = -8.076698174848001 " "
y[1] (numeric) = -8.076698174848099 " "
absolute error = 9.76996261670137800000000000000E-14 " "
relative error = 1.2096481018848079000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.833999999999945 " "
y[1] (analytic) = -8.075027709868715 " "
y[1] (numeric) = -8.075027709868813 " "
absolute error = 9.76996261670137800000000000000E-14 " "
relative error = 1.2098983393903696000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.832999999999944 " "
y[1] (analytic) = -8.073357244889428 " "
y[1] (numeric) = -8.073357244889527 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 1.2321513837305294000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.831999999999944 " "
y[1] (analytic) = -8.071686779910141 " "
y[1] (numeric) = -8.071686779910241 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 1.232406381947361000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.830999999999944 " "
y[1] (analytic) = -8.070016314930855 " "
y[1] (numeric) = -8.070016314930955 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 1.2326614857316599000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.829999999999943 " "
y[1] (analytic) = -8.068345849951568 " "
y[1] (numeric) = -8.068345849951669 " "
absolute error = 1.01252339845814280000000000000E-13 " "
relative error = 1.254933064705228000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.828999999999943 " "
y[1] (analytic) = -8.066675384972282 " "
y[1] (numeric) = -8.066675384972383 " "
absolute error = 1.01252339845814280000000000000E-13 " "
relative error = 1.2551929390197247000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.827999999999943 " "
y[1] (analytic) = -8.065004919992996 " "
y[1] (numeric) = -8.065004919993097 " "
absolute error = 1.01252339845814280000000000000E-13 " "
relative error = 1.2554529209872103000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.826999999999942 " "
y[1] (analytic) = -8.063334455013708 " "
y[1] (numeric) = -8.06333445501381 " "
absolute error = 1.03028696685214530000000000000E-13 " "
relative error = 1.2777430634934440000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.825999999999942 " "
y[1] (analytic) = -8.061663990034422 " "
y[1] (numeric) = -8.061663990034525 " "
absolute error = 1.03028696685214530000000000000E-13 " "
relative error = 1.2780078258356511000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.824999999999942 " "
y[1] (analytic) = -8.059993525055136 " "
y[1] (numeric) = -8.059993525055239 " "
absolute error = 1.03028696685214530000000000000E-13 " "
relative error = 1.2782726979239073000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.823999999999941 " "
y[1] (analytic) = -8.058323060075848 " "
y[1] (numeric) = -8.058323060075953 " "
absolute error = 1.04805053524614780000000000000E-13 " "
relative error = 1.3005814329269186000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.822999999999941 " "
y[1] (analytic) = -8.056652595096562 " "
y[1] (numeric) = -8.056652595096667 " "
absolute error = 1.04805053524614780000000000000E-13 " "
relative error = 1.3008510952600985000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.821999999999940 " "
y[1] (analytic) = -8.054982130117276 " "
y[1] (numeric) = -8.05498213011738 " "
absolute error = 1.04805053524614780000000000000E-13 " "
relative error = 1.3011208694399534000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.82099999999994 " "
y[1] (analytic) = -8.053311665137988 " "
y[1] (numeric) = -8.053311665138095 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 1.323448225968898200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.81999999999994 " "
y[1] (analytic) = -8.051641200158702 " "
y[1] (numeric) = -8.051641200158809 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 1.3237228002896387000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8189999999999396 " "
y[1] (analytic) = -8.049970735179416 " "
y[1] (numeric) = -8.049970735179523 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 1.3239974885652744000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.817999999999940 " "
y[1] (analytic) = -8.048300270200128 " "
y[1] (numeric) = -8.048300270200237 " "
absolute error = 1.08357767203415280000000000000E-13 " "
relative error = 1.3463434957145412000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.816999999999939 " "
y[1] (analytic) = -8.046629805220842 " "
y[1] (numeric) = -8.04662980522095 " "
absolute error = 1.08357767203415280000000000000E-13 " "
relative error = 1.346622994052867000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8159999999999386 " "
y[1] (analytic) = -8.044959340241556 " "
y[1] (numeric) = -8.044959340241665 " "
absolute error = 1.08357767203415280000000000000E-13 " "
relative error = 1.346902608461931000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.814999999999938 " "
y[1] (analytic) = -8.043288875262268 " "
y[1] (numeric) = -8.043288875262379 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 1.3692672953913315000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.813999999999938 " "
y[1] (analytic) = -8.041618410282982 " "
y[1] (numeric) = -8.041618410283093 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 1.3695517298108148000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8129999999999376 " "
y[1] (analytic) = -8.039947945303696 " "
y[1] (numeric) = -8.039947945303807 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 1.3698362824245300000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.811999999999937 " "
y[1] (analytic) = -8.038277480324409 " "
y[1] (numeric) = -8.03827748032452 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 1.3922196783594898000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.810999999999937 " "
y[1] (analytic) = -8.036607015345123 " "
y[1] (numeric) = -8.036607015345234 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 1.3925090609573612000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8099999999999365 " "
y[1] (analytic) = -8.034936550365837 " "
y[1] (numeric) = -8.034936550365948 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 1.3927985638806373000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.808999999999936 " "
y[1] (analytic) = -8.033266085386549 " "
y[1] (numeric) = -8.033266085386662 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 1.4152006981123866000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.807999999999936 " "
y[1] (analytic) = -8.031595620407263 " "
y[1] (numeric) = -8.031595620407376 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 1.415495041019648000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8069999999999355 " "
y[1] (analytic) = -8.029925155427977 " "
y[1] (numeric) = -8.02992515542809 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 1.4157895063911935000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.805999999999935 " "
y[1] (analytic) = -8.028254690448689 " "
y[1] (numeric) = -8.028254690448804 " "
absolute error = 1.15463194561016280000000000000E-13 " "
relative error = 1.43821040827696000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.804999999999935 " "
y[1] (analytic) = -8.026584225469403 " "
y[1] (numeric) = -8.026584225469518 " "
absolute error = 1.15463194561016280000000000000E-13 " "
relative error = 1.4385097236584954000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8039999999999345 " "
y[1] (analytic) = -8.024913760490117 " "
y[1] (numeric) = -8.024913760490232 " "
absolute error = 1.15463194561016280000000000000E-13 " "
relative error = 1.4388091636509304000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.802999999999934 " "
y[1] (analytic) = -8.023243295510829 " "
y[1] (numeric) = -8.023243295510946 " "
absolute error = 1.17239551400416530000000000000E-13 " "
relative error = 1.4612488626141312000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.801999999999934 " "
y[1] (analytic) = -8.021572830531543 " "
y[1] (numeric) = -8.02157283053166 " "
absolute error = 1.17239551400416530000000000000E-13 " "
relative error = 1.4615531626688197000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8009999999999335 " "
y[1] (analytic) = -8.019902365552257 " "
y[1] (numeric) = -8.019902365552374 " "
absolute error = 1.17239551400416530000000000000E-13 " "
relative error = 1.4618575894887880000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.799999999999933 " "
y[1] (analytic) = -8.01823190057297 " "
y[1] (numeric) = -8.018231900573088 " "
absolute error = 1.19015908239816780000000000000E-13 " "
relative error = 1.484316115019224000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.798999999999933 " "
y[1] (analytic) = -8.016561435593683 " "
y[1] (numeric) = -8.016561435593802 " "
absolute error = 1.19015908239816780000000000000E-13 " "
relative error = 1.484625411980053000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7979999999999325 " "
y[1] (analytic) = -8.014890970614397 " "
y[1] (numeric) = -8.014890970614516 " "
absolute error = 1.19015908239816780000000000000E-13 " "
relative error = 1.4849348378683358000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.796999999999932 " "
y[1] (analytic) = -8.01322050563511 " "
y[1] (numeric) = -8.01322050563523 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 1.5074122195223844000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.795999999999932 " "
y[1] (analytic) = -8.011550040655823 " "
y[1] (numeric) = -8.011550040655944 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 1.5077265256565633000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7949999999999315 " "
y[1] (analytic) = -8.009879575676537 " "
y[1] (numeric) = -8.009879575676658 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 1.5080409628881913000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.793999999999931 " "
y[1] (analytic) = -8.00820911069725 " "
y[1] (numeric) = -8.008209110697372 " "
absolute error = 1.22568621918617280000000000000E-13 " "
relative error = 1.530537230289003000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.792999999999930 " "
y[1] (analytic) = -8.006538645717963 " "
y[1] (numeric) = -8.006538645718086 " "
absolute error = 1.22568621918617280000000000000E-13 " "
relative error = 1.5308565578980765000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7919999999999305 " "
y[1] (analytic) = -8.004868180738677 " "
y[1] (numeric) = -8.0048681807388 " "
absolute error = 1.22568621918617280000000000000E-13 " "
relative error = 1.531176018782445800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.79099999999993 " "
y[1] (analytic) = -8.00319771575939 " "
y[1] (numeric) = -8.003197715759514 " "
absolute error = 1.24344978758017530000000000000E-13 " "
relative error = 1.5536912016201385000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.78999999999993 " "
y[1] (analytic) = -8.001527250780104 " "
y[1] (numeric) = -8.001527250780228 " "
absolute error = 1.24344978758017530000000000000E-13 " "
relative error = 1.5540155630401010000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7889999999999295 " "
y[1] (analytic) = -7.999856785800817 " "
y[1] (numeric) = -7.999856785800942 " "
absolute error = 1.25233157177717660000000000000E-13 " "
relative error = 1.565442488920523000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.787999999999930 " "
y[1] (analytic) = -7.998186320821530 " "
y[1] (numeric) = -7.998186320821656 " "
absolute error = 1.25233157177717660000000000000E-13 " "
relative error = 1.5657694401504563000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.786999999999929 " "
y[1] (analytic) = -7.996515855842244 " "
y[1] (numeric) = -7.99651585584237 " "
absolute error = 1.26121335597417780000000000000E-13 " "
relative error = 1.5772035955543526000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7859999999999285 " "
y[1] (analytic) = -7.994845390862957 " "
y[1] (numeric) = -7.994845390863084 " "
absolute error = 1.2700951401711790000000000000E-13 " "
relative error = 1.5886425291259898000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.784999999999928 " "
y[1] (analytic) = -7.993174925883670 " "
y[1] (numeric) = -7.993174925883798 " "
absolute error = 1.2700951401711790000000000000E-13 " "
relative error = 1.5889745338342712000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.783999999999928 " "
y[1] (analytic) = -7.991504460904384 " "
y[1] (numeric) = -7.991504460904512 " "
absolute error = 1.27897692436818030000000000000E-13 " "
relative error = 1.6004207100491827000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7829999999999275 " "
y[1] (analytic) = -7.989833995925097 " "
y[1] (numeric) = -7.989833995925226 " "
absolute error = 1.28785870856518160000000000000E-13 " "
relative error = 1.611871672455277000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.781999999999927 " "
y[1] (analytic) = -7.988163530945811 " "
y[1] (numeric) = -7.98816353094594 " "
absolute error = 1.28785870856518160000000000000E-13 " "
relative error = 1.6122087430685048000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.780999999999927 " "
y[1] (analytic) = -7.986493065966524 " "
y[1] (numeric) = -7.986493065966654 " "
absolute error = 1.29674049276218280000000000000E-13 " "
relative error = 1.6236669612700047000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7799999999999265 " "
y[1] (analytic) = -7.984822600987237 " "
y[1] (numeric) = -7.984822600987368 " "
absolute error = 1.3056222769591840000000000000E-13 " "
relative error = 1.6351299737050615000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.778999999999926 " "
y[1] (analytic) = -7.983152136007951 " "
y[1] (numeric) = -7.983152136008082 " "
absolute error = 1.3056222769591840000000000000E-13 " "
relative error = 1.6354721226847027000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.777999999999926 " "
y[1] (analytic) = -7.981481671028664 " "
y[1] (numeric) = -7.981481671028796 " "
absolute error = 1.31450406115618530000000000000E-13 " "
relative error = 1.6469424040997270000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7769999999999255 " "
y[1] (analytic) = -7.979811206049377 " "
y[1] (numeric) = -7.97981120604951 " "
absolute error = 1.32338584535318660000000000000E-13 " "
relative error = 1.6584174878096705000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.775999999999925 " "
y[1] (analytic) = -7.978140741070091 " "
y[1] (numeric) = -7.978140741070224 " "
absolute error = 1.32338584535318660000000000000E-13 " "
relative error = 1.6587647276521766000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.774999999999925 " "
y[1] (analytic) = -7.976470276090804 " "
y[1] (numeric) = -7.976470276090938 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 1.6702470935591830000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7739999999999245 " "
y[1] (analytic) = -7.9747998111115175 " "
y[1] (numeric) = -7.974799811111652 " "
absolute error = 1.3411494137471890000000000000E-13 " "
relative error = 1.6817342698415166000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.772999999999924 " "
y[1] (analytic) = -7.9731293461322315 " "
y[1] (numeric) = -7.973129346132366 " "
absolute error = 1.3411494137471890000000000000E-13 " "
relative error = 1.6820866130784412000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.771999999999924 " "
y[1] (analytic) = -7.9714588811529445 " "
y[1] (numeric) = -7.9714588811530795 " "
absolute error = 1.35003119794419040000000000000E-13 " "
relative error = 1.6935810848075653000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7709999999999235 " "
y[1] (analytic) = -7.969788416173658 " "
y[1] (numeric) = -7.9697884161737935 " "
absolute error = 1.35891298214119160000000000000E-13 " "
relative error = 1.7050803750115284000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.769999999999923 " "
y[1] (analytic) = -7.968117951194372 " "
y[1] (numeric) = -7.9681179511945075 " "
absolute error = 1.35891298214119160000000000000E-13 " "
relative error = 1.7054378342096440000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.768999999999923 " "
y[1] (analytic) = -7.966447486215085 " "
y[1] (numeric) = -7.9664474862152215 " "
absolute error = 1.36779476633819290000000000000E-13 " "
relative error = 1.716944433142861000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7679999999999225 " "
y[1] (analytic) = -7.964777021235798 " "
y[1] (numeric) = -7.9647770212359355 " "
absolute error = 1.3766765505351940000000000000E-13 " "
relative error = 1.72845585866959000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.766999999999922 " "
y[1] (analytic) = -7.963106556256512 " "
y[1] (numeric) = -7.963106556256650 " "
absolute error = 1.3766765505351940000000000000E-13 " "
relative error = 1.728818446431006000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.765999999999922 " "
y[1] (analytic) = -7.961436091277225 " "
y[1] (numeric) = -7.961436091277363 " "
absolute error = 1.38555833473219540000000000000E-13 " "
relative error = 1.7403371940022885000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7649999999999215 " "
y[1] (analytic) = -7.959765626297938 " "
y[1] (numeric) = -7.959765626298077 " "
absolute error = 1.39444011892919660000000000000E-13 " "
relative error = 1.7518607763049757000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.763999999999921 " "
y[1] (analytic) = -7.958095161318652 " "
y[1] (numeric) = -7.958095161318791 " "
absolute error = 1.39444011892919660000000000000E-13 " "
relative error = 1.7522285052672565000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.762999999999920 " "
y[1] (analytic) = -7.956424696339365 " "
y[1] (numeric) = -7.956424696339505 " "
absolute error = 1.40332190312619800000000000000E-13 " "
relative error = 1.7637594229627357000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7619999999999205 " "
y[1] (analytic) = -7.954754231360078 " "
y[1] (numeric) = -7.954754231360220 " "
absolute error = 1.4122036873231990000000000000E-13 " "
relative error = 1.7752951835467898000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.76099999999992 " "
y[1] (analytic) = -7.953083766380792 " "
y[1] (numeric) = -7.953083766380933 " "
absolute error = 1.4122036873231990000000000000E-13 " "
relative error = 1.7756680663830732000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.75999999999992 " "
y[1] (analytic) = -7.951413301401505 " "
y[1] (numeric) = -7.951413301401647 " "
absolute error = 1.42108547152020040000000000000E-13 " "
relative error = 1.7872111757412004000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7589999999999195 " "
y[1] (analytic) = -7.949742836422218 " "
y[1] (numeric) = -7.949742836422361 " "
absolute error = 1.42996725571720160000000000000E-13 " "
relative error = 1.7987591361644076000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.757999999999920 " "
y[1] (analytic) = -7.948072371442932 " "
y[1] (numeric) = -7.948072371443075 " "
absolute error = 1.42996725571720160000000000000E-13 " "
relative error = 1.7991371855835256000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.756999999999919 " "
y[1] (analytic) = -7.946401906463645 " "
y[1] (numeric) = -7.946401906463790 " "
absolute error = 1.4388490399142030000000000000E-13 " "
relative error = 1.8106925081952316000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7559999999999185 " "
y[1] (analytic) = -7.944731441484358 " "
y[1] (numeric) = -7.944731441484503 " "
absolute error = 1.44773082411120400000000000000E-13 " "
relative error = 1.822252690067918000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.754999999999918 " "
y[1] (analytic) = -7.943060976505072 " "
y[1] (numeric) = -7.943060976505217 " "
absolute error = 1.44773082411120400000000000000E-13 " "
relative error = 1.822635918814515000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.753999999999918 " "
y[1] (analytic) = -7.9413905115257855 " "
y[1] (numeric) = -7.941390511525931 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 1.8342034763233742000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7529999999999175 " "
y[1] (analytic) = -7.9397200465464985 " "
y[1] (numeric) = -7.939720046546645 " "
absolute error = 1.46549439250520660000000000000E-13 " "
relative error = 1.8457759013085678000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.751999999999917 " "
y[1] (analytic) = -7.9380495815672125 " "
y[1] (numeric) = -7.938049581567359 " "
absolute error = 1.46549439250520660000000000000E-13 " "
relative error = 1.84616432216321990000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.750999999999917 " "
y[1] (analytic) = -7.936379116587926 " "
y[1] (numeric) = -7.936379116588073 " "
absolute error = 1.4743761767022080000000000000E-13 " "
relative error = 1.8577441362656125000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7499999999999165 " "
y[1] (analytic) = -7.934708651608639 " "
y[1] (numeric) = -7.934708651608787 " "
absolute error = 1.48325796089920900000000000000E-13 " "
relative error = 1.8693288260792054000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.748999999999916 " "
y[1] (analytic) = -7.933038186629353 " "
y[1] (numeric) = -7.933038186629501 " "
absolute error = 1.48325796089920900000000000000E-13 " "
relative error = 1.869722451858544000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.747999999999916 " "
y[1] (analytic) = -7.931367721650066 " "
y[1] (numeric) = -7.931367721650215 " "
absolute error = 1.49213974509621040000000000000E-13 " "
relative error = 1.881314544303818000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7469999999999155 " "
y[1] (analytic) = -7.929697256670779 " "
y[1] (numeric) = -7.929697256670929 " "
absolute error = 1.50102152929321160000000000000E-13 " "
relative error = 1.8929115207147315000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.745999999999915 " "
y[1] (analytic) = -7.928026791691493 " "
y[1] (numeric) = -7.928026791691643 " "
absolute error = 1.50102152929321160000000000000E-13 " "
relative error = 1.893310364271561200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.744999999999915 " "
y[1] (analytic) = -7.926356326712206 " "
y[1] (numeric) = -7.926356326712357 " "
absolute error = 1.5099033134902130000000000000E-13 " "
relative error = 1.9049147568621985000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7439999999999145 " "
y[1] (analytic) = -7.924685861732919 " "
y[1] (numeric) = -7.924685861733070 " "
absolute error = 1.51878509768721410000000000000E-13 " "
relative error = 1.9165240416925447000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.742999999999914 " "
y[1] (analytic) = -7.923015396753633 " "
y[1] (numeric) = -7.923015396753785 " "
absolute error = 1.51878509768721410000000000000E-13 " "
relative error = 1.9169281159159673000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.741999999999914 " "
y[1] (analytic) = -7.921344931774346 " "
y[1] (numeric) = -7.921344931774499 " "
absolute error = 1.52766688188421540000000000000E-13 " "
relative error = 1.9285448305077468000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7409999999999135 " "
y[1] (analytic) = -7.919674466795060 " "
y[1] (numeric) = -7.919674466795213 " "
absolute error = 1.53654866608121670000000000000E-13 " "
relative error = 1.9401664456329967000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.739999999999913 " "
y[1] (analytic) = -7.918004001815773 " "
y[1] (numeric) = -7.918004001815927 " "
absolute error = 1.53654866608121670000000000000E-13 " "
relative error = 1.9405757634485307000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.738999999999913 " "
y[1] (analytic) = -7.916333536836486 " "
y[1] (numeric) = -7.916333536836640 " "
absolute error = 1.5454304502782180000000000000E-13 " "
relative error = 1.9522048219506938000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7379999999999125 " "
y[1] (analytic) = -7.914663071857200 " "
y[1] (numeric) = -7.914663071857355 " "
absolute error = 1.55431223447521920000000000000E-13 " "
relative error = 1.9638387892998396000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.736999999999912 " "
y[1] (analytic) = -7.912992606877913 " "
y[1] (numeric) = -7.912992606878069 " "
absolute error = 1.55431223447521920000000000000E-13 " "
relative error = 1.9642533636695464000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.735999999999912 " "
y[1] (analytic) = -7.911322141898626 " "
y[1] (numeric) = -7.911322141898783 " "
absolute error = 1.56319401867222040000000000000E-13 " "
relative error = 1.9758947880449626000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7349999999999115 " "
y[1] (analytic) = -7.9096516769193395 " "
y[1] (numeric) = -7.909651676919497 " "
absolute error = 1.57207580286922170000000000000E-13 " "
relative error = 1.987541129600685000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.733999999999911 " "
y[1] (analytic) = -7.907981211940053 " "
y[1] (numeric) = -7.907981211940210 " "
absolute error = 1.57207580286922170000000000000E-13 " "
relative error = 1.9879609735232875000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.732999999999910 " "
y[1] (analytic) = -7.9063107469607665 " "
y[1] (numeric) = -7.906310746960925 " "
absolute error = 1.5809575870662230000000000000E-13 " "
relative error = 1.9996147857886215000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7319999999999105 " "
y[1] (analytic) = -7.90464028198148 " "
y[1] (numeric) = -7.904640281981639 " "
absolute error = 1.58983937126322420000000000000E-13 " "
relative error = 2.0112735235874570000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.73099999999991 " "
y[1] (analytic) = -7.902969817002194 " "
y[1] (numeric) = -7.902969817002353 " "
absolute error = 1.58983937126322420000000000000E-13 " "
relative error = 2.011698650098466800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.72999999999991 " "
y[1] (analytic) = -7.901299352022907 " "
y[1] (numeric) = -7.9012993520230665 " "
absolute error = 1.59872115546022540000000000000E-13 " "
relative error = 2.0233648723243444000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7289999999999095 " "
y[1] (analytic) = -7.89962888704362 " "
y[1] (numeric) = -7.8996288870437805 " "
absolute error = 1.60760293965722670000000000000E-13 " "
relative error = 2.0350360284568514000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.727999999999910 " "
y[1] (analytic) = -7.897958422064334 " "
y[1] (numeric) = -7.8979584220644945 " "
absolute error = 1.60760293965722670000000000000E-13 " "
relative error = 2.035466450628691200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.726999999999909 " "
y[1] (analytic) = -7.896287957085047 " "
y[1] (numeric) = -7.8962879570852085 " "
absolute error = 1.6164847238542280000000000000E-13 " "
relative error = 2.0471451049398676000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7259999999999085 " "
y[1] (analytic) = -7.89461749210576 " "
y[1] (numeric) = -7.8946174921059225 " "
absolute error = 1.62536650805122920000000000000E-13 " "
relative error = 2.0588287015507944000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.724999999999908 " "
y[1] (analytic) = -7.892947027126474 " "
y[1] (numeric) = -7.892947027126636 " "
absolute error = 1.62536650805122920000000000000E-13 " "
relative error = 2.059264432492921800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.723999999999908 " "
y[1] (analytic) = -7.891276562147187 " "
y[1] (numeric) = -7.89127656214735 " "
absolute error = 1.63424829224823040000000000000E-13 " "
relative error = 2.0709555410684496000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7229999999999075 " "
y[1] (analytic) = -7.8896060971679 " "
y[1] (numeric) = -7.889606097168064 " "
absolute error = 1.64313007644523170000000000000E-13 " "
relative error = 2.082651600356904000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.721999999999907 " "
y[1] (analytic) = -7.887935632188614 " "
y[1] (numeric) = -7.887935632188778 " "
absolute error = 1.64313007644523170000000000000E-13 " "
relative error = 2.0830926532159377000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.720999999999907 " "
y[1] (analytic) = -7.886265167209327 " "
y[1] (numeric) = -7.886265167209492 " "
absolute error = 1.6520118606422330000000000000E-13 " "
relative error = 2.0947962382893373000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7199999999999065 " "
y[1] (analytic) = -7.88459470223004 " "
y[1] (numeric) = -7.884594702230206 " "
absolute error = 1.66089364483923420000000000000E-13 " "
relative error = 2.106504782508954200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.718999999999906 " "
y[1] (analytic) = -7.882924237250754 " "
y[1] (numeric) = -7.88292423725092 " "
absolute error = 1.66089364483923420000000000000E-13 " "
relative error = 2.106951170468799000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.717999999999906 " "
y[1] (analytic) = -7.881253772271467 " "
y[1] (numeric) = -7.881253772271634 " "
absolute error = 1.66977542903623540000000000000E-13 " "
relative error = 2.118667254328224800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7169999999999055 " "
y[1] (analytic) = -7.87958330729218 " "
y[1] (numeric) = -7.879583307292348 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 2.1303883057873366000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.715999999999905 " "
y[1] (analytic) = -7.877912842312894 " "
y[1] (numeric) = -7.877912842313062 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 2.13084004206931000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.714999999999905 " "
y[1] (analytic) = -7.876242377333607 " "
y[1] (numeric) = -7.876242377333776 " "
absolute error = 1.6875389974302380000000000000E-13 " "
relative error = 2.142568647057724000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7139999999999045 " "
y[1] (analytic) = -7.8745719123543205 " "
y[1] (numeric) = -7.87457191235449 " "
absolute error = 1.69642078162723920000000000000E-13 " "
relative error = 2.1543022281195315000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.712999999999904 " "
y[1] (analytic) = -7.8729014473750345 " "
y[1] (numeric) = -7.872901447375204 " "
absolute error = 1.69642078162723920000000000000E-13 " "
relative error = 2.154759325982489000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.711999999999904 " "
y[1] (analytic) = -7.871230982395748 " "
y[1] (numeric) = -7.871230982395918 " "
absolute error = 1.70530256582424040000000000000E-13 " "
relative error = 2.1665004744978295000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7109999999999035 " "
y[1] (analytic) = -7.869560517416460 " "
y[1] (numeric) = -7.869560517416632 " "
absolute error = 1.71418435002124170000000000000E-13 " "
relative error = 2.178246607580572000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.709999999999903 " "
y[1] (analytic) = -7.867890052437175 " "
y[1] (numeric) = -7.867890052437346 " "
absolute error = 1.71418435002124170000000000000E-13 " "
relative error = 2.178709080321035200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.708999999999903 " "
y[1] (analytic) = -7.866219587457888 " "
y[1] (numeric) = -7.86621958745806 " "
absolute error = 1.7230661342182430000000000000E-13 " "
relative error = 2.1904627948163893000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7079999999999025 " "
y[1] (analytic) = -7.864549122478600 " "
y[1] (numeric) = -7.864549122478774 " "
absolute error = 1.73194791841524420000000000000E-13 " "
relative error = 2.2022215023935174000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.706999999999902 " "
y[1] (analytic) = -7.862878657499315 " "
y[1] (numeric) = -7.862878657499488 " "
absolute error = 1.73194791841524420000000000000E-13 " "
relative error = 2.2026893633457997000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.705999999999902 " "
y[1] (analytic) = -7.861208192520028 " "
y[1] (numeric) = -7.861208192520202 " "
absolute error = 1.74082970261224550000000000000E-13 " "
relative error = 2.2144556663295753000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7049999999999015 " "
y[1] (analytic) = -7.859537727540741 " "
y[1] (numeric) = -7.859537727540916 " "
absolute error = 1.74971148680924670000000000000E-13 " "
relative error = 2.226226970929922000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.703999999999901 " "
y[1] (analytic) = -7.857867262561455 " "
y[1] (numeric) = -7.85786726256163 " "
absolute error = 1.74971148680924670000000000000E-13 " "
relative error = 2.2267002334662594000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.702999999999900 " "
y[1] (analytic) = -7.856196797582168 " "
y[1] (numeric) = -7.856196797582344 " "
absolute error = 1.7585932710062480000000000000E-13 " "
relative error = 2.238479147502357200000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7019999999999005 " "
y[1] (analytic) = -7.854526332602881 " "
y[1] (numeric) = -7.854526332603058 " "
absolute error = 1.76747505520324920000000000000E-13 " "
relative error = 2.2502630717103123000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7009999999999 " "
y[1] (analytic) = -7.852855867623595 " "
y[1] (numeric) = -7.852855867623772 " "
absolute error = 1.76747505520324920000000000000E-13 " "
relative error = 2.2507417492409887000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6999999999999 " "
y[1] (analytic) = -7.851185402644308 " "
y[1] (numeric) = -7.851185402644486 " "
absolute error = 1.77635683940025050000000000000E-13 " "
relative error = 2.2625332969489764000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6989999999998995 " "
y[1] (analytic) = -7.849514937665021 " "
y[1] (numeric) = -7.8495149376652 " "
absolute error = 1.78523862359725170000000000000E-13 " "
relative error = 2.274329863404658800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.697999999999900 " "
y[1] (analytic) = -7.847844472685735 " "
y[1] (numeric) = -7.847844472685914 " "
absolute error = 1.78523862359725170000000000000E-13 " "
relative error = 2.274813969378138000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.696999999999899 " "
y[1] (analytic) = -7.846174007706448 " "
y[1] (numeric) = -7.846174007706628 " "
absolute error = 1.7941204077942530000000000000E-13 " "
relative error = 2.2866181734334246000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6959999999998985 " "
y[1] (analytic) = -7.844503542727161 " "
y[1] (numeric) = -7.844503542727342 " "
absolute error = 1.80300219199125420000000000000E-13 " "
relative error = 2.298427404832856800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.694999999999898 " "
y[1] (analytic) = -7.842833077747875 " "
y[1] (numeric) = -7.842833077748056 " "
absolute error = 1.80300219199125420000000000000E-13 " "
relative error = 2.29891695273591000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.693999999999898 " "
y[1] (analytic) = -7.8411626127685885 " "
y[1] (numeric) = -7.84116261276877 " "
absolute error = 1.81188397618825550000000000000E-13 " "
relative error = 2.3107338358699187000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6929999999998975 " "
y[1] (analytic) = -7.839492147789302 " "
y[1] (numeric) = -7.839492147789484 " "
absolute error = 1.82076576038525670000000000000E-13 " "
relative error = 2.322555754965203700000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.691999999999897 " "
y[1] (analytic) = -7.837821682810016 " "
y[1] (numeric) = -7.837821682810198 " "
absolute error = 1.82076576038525670000000000000E-13 " "
relative error = 2.3230507583230395000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.690999999999897 " "
y[1] (analytic) = -7.836151217830729 " "
y[1] (numeric) = -7.836151217830912 " "
absolute error = 1.8296475445822580000000000000E-13 " "
relative error = 2.334880343323385800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6899999999998965 " "
y[1] (analytic) = -7.834480752851442 " "
y[1] (numeric) = -7.834480752851626 " "
absolute error = 1.83852932877925920000000000000E-13 " "
relative error = 2.3467149729228795000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.688999999999896 " "
y[1] (analytic) = -7.832810287872156 " "
y[1] (numeric) = -7.83281028787234 " "
absolute error = 1.83852932877925920000000000000E-13 " "
relative error = 2.347215445299276000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.687999999999896 " "
y[1] (analytic) = -7.831139822892869 " "
y[1] (numeric) = -7.8311398228930535 " "
absolute error = 1.84741111297626050000000000000E-13 " "
relative error = 2.359057755009942000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6869999999998955 " "
y[1] (analytic) = -7.829469357913582 " "
y[1] (numeric) = -7.8294693579137675 " "
absolute error = 1.85629289717326170000000000000E-13 " "
relative error = 2.3709051179784318000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.685999999999895 " "
y[1] (analytic) = -7.827798892934296 " "
y[1] (numeric) = -7.8277988929344815 " "
absolute error = 1.85629289717326170000000000000E-13 " "
relative error = 2.3714110729758664000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.684999999999895 " "
y[1] (analytic) = -7.826128427955009 " "
y[1] (numeric) = -7.8261284279551955 " "
absolute error = 1.8651746813702630000000000000E-13 " "
relative error = 2.3832661302973773000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6839999999998945 " "
y[1] (analytic) = -7.824457962975722 " "
y[1] (numeric) = -7.8244579629759095 " "
absolute error = 1.87405646556726420000000000000E-13 " "
relative error = 2.3951262495562584000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.682999999999894 " "
y[1] (analytic) = -7.822787497996436 " "
y[1] (numeric) = -7.822787497996623 " "
absolute error = 1.87405646556726420000000000000E-13 " "
relative error = 2.39563770081603980000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.681999999999894 " "
y[1] (analytic) = -7.821117033017149 " "
y[1] (numeric) = -7.821117033017337 " "
absolute error = 1.88293824976426550000000000000E-13 " "
relative error = 2.4075055287056424000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6809999999998935 " "
y[1] (analytic) = -7.819446568037862 " "
y[1] (numeric) = -7.819446568038051 " "
absolute error = 1.89182003396126670000000000000E-13 " "
relative error = 2.4193784272330954000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.679999999999893 " "
y[1] (analytic) = -7.817776103058576 " "
y[1] (numeric) = -7.817776103058765 " "
absolute error = 1.89182003396126670000000000000E-13 " "
relative error = 2.4198953884354957000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.678999999999893 " "
y[1] (analytic) = -7.816105638079290 " "
y[1] (numeric) = -7.816105638079480 " "
absolute error = 1.9007018181582680000000000000E-13 " "
relative error = 2.4317760099073354000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6779999999998925 " "
y[1] (analytic) = -7.814435173100002 " "
y[1] (numeric) = -7.814435173100193 " "
absolute error = 1.90958360235526920000000000000E-13 " "
relative error = 2.4436617107385042000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.676999999999892 " "
y[1] (analytic) = -7.812764708120716 " "
y[1] (numeric) = -7.812764708120907 " "
absolute error = 1.90958360235526920000000000000E-13 " "
relative error = 2.4441841956028915000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.675999999999892 " "
y[1] (analytic) = -7.811094243141430 " "
y[1] (numeric) = -7.811094243141621 " "
absolute error = 1.91846538655227050000000000000E-13 " "
relative error = 2.456077633728192300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6749999999998915 " "
y[1] (analytic) = -7.8094237781621425 " "
y[1] (numeric) = -7.809423778162335 " "
absolute error = 1.92734717074927180000000000000E-13 " "
relative error = 2.467976159955364300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.673999999999891 " "
y[1] (analytic) = -7.8077533131828565 " "
y[1] (numeric) = -7.807753313183050 " "
absolute error = 1.92734717074927180000000000000E-13 " "
relative error = 2.4685041822403356000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.672999999999890 " "
y[1] (analytic) = -7.80608284820357 " "
y[1] (numeric) = -7.806082848203763 " "
absolute error = 1.9362289549462730000000000000E-13 " "
relative error = 2.4804104601475777000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6719999999998905 " "
y[1] (analytic) = -7.804412383224283 " "
y[1] (numeric) = -7.804412383224477 " "
absolute error = 1.94511073914327430000000000000E-13 " "
relative error = 2.4923218349203624000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.67099999999989 " "
y[1] (analytic) = -7.802741918244997 " "
y[1] (numeric) = -7.802741918245191 " "
absolute error = 1.94511073914327430000000000000E-13 " "
relative error = 2.492855408423877700000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.66999999999989 " "
y[1] (analytic) = -7.80107145326571 " "
y[1] (numeric) = -7.801071453265905 " "
absolute error = 1.95399252334027550000000000000E-13 " "
relative error = 2.5047745492989800000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6689999999998895 " "
y[1] (analytic) = -7.799400988286423 " "
y[1] (numeric) = -7.799400988286619 " "
absolute error = 1.96287430753727680000000000000E-13 " "
relative error = 2.516698795824489000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.667999999999890 " "
y[1] (analytic) = -7.797730523307137 " "
y[1] (numeric) = -7.797730523307333 " "
absolute error = 1.96287430753727680000000000000E-13 " "
relative error = 2.5172379343840057000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.666999999999889 " "
y[1] (analytic) = -7.79606005832785 " "
y[1] (numeric) = -7.796060058328047 " "
absolute error = 1.9717560917342780000000000000E-13 " "
relative error = 2.5291699614705040000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6659999999998885 " "
y[1] (analytic) = -7.794389593348563 " "
y[1] (numeric) = -7.794389593348761 " "
absolute error = 1.98063787593127930000000000000E-13 " "
relative error = 2.5411071030135330000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.664999999999888 " "
y[1] (analytic) = -7.792719128369277 " "
y[1] (numeric) = -7.792719128369475 " "
absolute error = 1.98063787593127930000000000000E-13 " "
relative error = 2.54165182050614000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.663999999999888 " "
y[1] (analytic) = -7.79104866338999 " "
y[1] (numeric) = -7.791048663390189 " "
absolute error = 1.98951966012828050000000000000E-13 " "
relative error = 2.55359675710537000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6629999999998875 " "
y[1] (analytic) = -7.789378198410703 " "
y[1] (numeric) = -7.789378198410903 " "
absolute error = 1.99840144432528180000000000000E-13 " "
relative error = 2.56554681698858000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.661999999999887 " "
y[1] (analytic) = -7.787707733431417 " "
y[1] (numeric) = -7.787707733431617 " "
absolute error = 1.99840144432528180000000000000E-13 " "
relative error = 2.5660971273311345000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.660999999999887 " "
y[1] (analytic) = -7.78603726845213 " "
y[1] (numeric) = -7.786037268452331 " "
absolute error = 2.0072832285222830000000000000E-13 " "
relative error = 2.5780549968024136000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6599999999998865 " "
y[1] (analytic) = -7.784366803472843 " "
y[1] (numeric) = -7.784366803473045 " "
absolute error = 2.01616501271928430000000000000E-13 " "
relative error = 2.5900179984065130000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.658999999999886 " "
y[1] (analytic) = -7.782696338493557 " "
y[1] (numeric) = -7.782696338493759 " "
absolute error = 2.01616501271928430000000000000E-13 " "
relative error = 2.590573915555774400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.657999999999886 " "
y[1] (analytic) = -7.78102587351427 " "
y[1] (numeric) = -7.781025873514473 " "
absolute error = 2.02504679691628550000000000000E-13 " "
relative error = 2.6025447413165853000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6569999999998855 " "
y[1] (analytic) = -7.779355408534983 " "
y[1] (numeric) = -7.779355408535187 " "
absolute error = 2.03392858111328680000000000000E-13 " "
relative error = 2.614520708080515000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.655999999999885 " "
y[1] (analytic) = -7.777684943555697 " "
y[1] (numeric) = -7.777684943555900 " "
absolute error = 2.03392858111328680000000000000E-13 " "
relative error = 2.615082246033281000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.654999999999885 " "
y[1] (analytic) = -7.7760144785764105 " "
y[1] (numeric) = -7.776014478576615 " "
absolute error = 2.0428103653102880000000000000E-13 " "
relative error = 2.6270660515594546000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6539999999998845 " "
y[1] (analytic) = -7.774344013597124 " "
y[1] (numeric) = -7.774344013597329 " "
absolute error = 2.05169214950728930000000000000E-13 " "
relative error = 2.6390550069805680000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.652999999999884 " "
y[1] (analytic) = -7.7726735486178375 " "
y[1] (numeric) = -7.772673548618043 " "
absolute error = 2.05169214950728930000000000000E-13 " "
relative error = 2.6396221797738150000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.651999999999884 " "
y[1] (analytic) = -7.771003083638550 " "
y[1] (numeric) = -7.771003083638757 " "
absolute error = 2.06057393370429050000000000000E-13 " "
relative error = 2.651618988599713000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6509999999998834 " "
y[1] (analytic) = -7.769332618659264 " "
y[1] (numeric) = -7.769332618659470 " "
absolute error = 2.06945571790129180000000000000E-13 " "
relative error = 2.6636209562339640000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.649999999999883 " "
y[1] (analytic) = -7.767662153679978 " "
y[1] (numeric) = -7.767662153680185 " "
absolute error = 2.06945571790129180000000000000E-13 " "
relative error = 2.6641937779449820000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.648999999999883 " "
y[1] (analytic) = -7.765991688700690 " "
y[1] (numeric) = -7.765991688700899 " "
absolute error = 2.0783375020982930000000000000E-13 " "
relative error = 2.6762036136636846000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6479999999998824 " "
y[1] (analytic) = -7.764321223721404 " "
y[1] (numeric) = -7.764321223721613 " "
absolute error = 2.08721928629529430000000000000E-13 " "
relative error = 2.6882186171258116000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.646999999999882 " "
y[1] (analytic) = -7.762650758742118 " "
y[1] (numeric) = -7.762650758742327 " "
absolute error = 2.08721928629529430000000000000E-13 " "
relative error = 2.688797101872341700000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.645999999999882 " "
y[1] (analytic) = -7.760980293762831 " "
y[1] (numeric) = -7.7609802937630405 " "
absolute error = 2.09610107049229550000000000000E-13 " "
relative error = 2.700819988135832000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6449999999998814 " "
y[1] (analytic) = -7.759309828783544 " "
y[1] (numeric) = -7.7593098287837545 " "
absolute error = 2.10498285468929680000000000000E-13 " "
relative error = 2.7128480510995434000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.643999999999881 " "
y[1] (analytic) = -7.757639363804258 " "
y[1] (numeric) = -7.7576393638044685 " "
absolute error = 2.10498285468929680000000000000E-13 " "
relative error = 2.7134322130399174000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.642999999999880 " "
y[1] (analytic) = -7.755968898824971 " "
y[1] (numeric) = -7.7559688988251825 " "
absolute error = 2.1138646388862980000000000000E-13 " "
relative error = 2.725468173559268000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.64199999999988 " "
y[1] (analytic) = -7.754298433845684 " "
y[1] (numeric) = -7.7542984338458965 " "
absolute error = 2.12274642308329930000000000000E-13 " "
relative error = 2.7375093197574285000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.64099999999988 " "
y[1] (analytic) = -7.752627968866398 " "
y[1] (numeric) = -7.75262796886661 " "
absolute error = 2.12274642308329930000000000000E-13 " "
relative error = 2.7380991730907100000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.63999999999988 " "
y[1] (analytic) = -7.750957503887111 " "
y[1] (numeric) = -7.750957503887324 " "
absolute error = 2.13162820728030060000000000000E-13 " "
relative error = 2.7501482316362685000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.638999999999880 " "
y[1] (analytic) = -7.749287038907824 " "
y[1] (numeric) = -7.749287038908038 " "
absolute error = 2.14050999147730180000000000000E-13 " "
relative error = 2.7622024848610890000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.637999999999879 " "
y[1] (analytic) = -7.747616573928538 " "
y[1] (numeric) = -7.747616573928752 " "
absolute error = 2.14050999147730180000000000000E-13 " "
relative error = 2.7627980438272076000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.636999999999879 " "
y[1] (analytic) = -7.745946108949251 " "
y[1] (numeric) = -7.745946108949466 " "
absolute error = 2.1493917756743030000000000000E-13 " "
relative error = 2.7748602242287884000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.635999999999878 " "
y[1] (analytic) = -7.7442756439699645 " "
y[1] (numeric) = -7.74427564397018 " "
absolute error = 2.15827355987130430000000000000E-13 " "
relative error = 2.7869276083320094000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.634999999999878 " "
y[1] (analytic) = -7.7426051789906785 " "
y[1] (numeric) = -7.742605178990894 " "
absolute error = 2.15827355987130430000000000000E-13 " "
relative error = 2.787528887211908000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.633999999999878 " "
y[1] (analytic) = -7.7409347140113915 " "
y[1] (numeric) = -7.740934714011608 " "
absolute error = 2.16715534406830560000000000000E-13 " "
relative error = 2.7996042133589766000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.632999999999877 " "
y[1] (analytic) = -7.739264249032105 " "
y[1] (numeric) = -7.739264249032322 " "
absolute error = 2.17603712826530680000000000000E-13 " "
relative error = 2.8116847522520610000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.631999999999877 " "
y[1] (analytic) = -7.737593784052819 " "
y[1] (numeric) = -7.737593784053036 " "
absolute error = 2.17603712826530680000000000000E-13 " "
relative error = 2.8122917653678325000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.630999999999877 " "
y[1] (analytic) = -7.735923319073532 " "
y[1] (numeric) = -7.73592331907375 " "
absolute error = 2.1849189124623080000000000000E-13 " "
relative error = 2.8243802612096963000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.629999999999876 " "
y[1] (analytic) = -7.734252854094245 " "
y[1] (numeric) = -7.734252854094464 " "
absolute error = 2.19380069665930930000000000000E-13 " "
relative error = 2.8364739788640186000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.628999999999876 " "
y[1] (analytic) = -7.732582389114959 " "
y[1] (numeric) = -7.732582389115178 " "
absolute error = 2.19380069665930930000000000000E-13 " "
relative error = 2.8370867405790460000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.627999999999876 " "
y[1] (analytic) = -7.730911924135672 " "
y[1] (numeric) = -7.730911924135892 " "
absolute error = 2.20268248085631060000000000000E-13 " "
relative error = 2.849188430125045000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.626999999999875 " "
y[1] (analytic) = -7.729241459156385 " "
y[1] (numeric) = -7.729241459156606 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 2.8612953505720795000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.625999999999875 " "
y[1] (analytic) = -7.727570994177099 " "
y[1] (numeric) = -7.72757099417732 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 2.8619138752911827000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.624999999999875 " "
y[1] (analytic) = -7.725900529197812 " "
y[1] (numeric) = -7.725900529198034 " "
absolute error = 2.2204460492503130000000000000E-13 " "
relative error = 2.874028782610879000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.623999999999874 " "
y[1] (analytic) = -7.724230064218525 " "
y[1] (numeric) = -7.724230064218748 " "
absolute error = 2.22932783344731430000000000000E-13 " "
relative error = 2.886148929942391500000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.622999999999874 " "
y[1] (analytic) = -7.722559599239239 " "
y[1] (numeric) = -7.722559599239462 " "
absolute error = 2.22932783344731430000000000000E-13 " "
relative error = 2.8867732321119655000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.621999999999874 " "
y[1] (analytic) = -7.720889134259952 " "
y[1] (numeric) = -7.720889134260176 " "
absolute error = 2.23820961764431560000000000000E-13 " "
relative error = 2.898901381335335400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.620999999999873 " "
y[1] (analytic) = -7.719218669280665 " "
y[1] (numeric) = -7.71921866928089 " "
absolute error = 2.24709140184131680000000000000E-13 " "
relative error = 2.9110347797035757000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.619999999999873 " "
y[1] (analytic) = -7.717548204301380 " "
y[1] (numeric) = -7.717548204301604 " "
absolute error = 2.24709140184131680000000000000E-13 " "
relative error = 2.9116648738117370000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.618999999999873 " "
y[1] (analytic) = -7.715877739322092 " "
y[1] (numeric) = -7.715877739322318 " "
absolute error = 2.2559731860383180000000000000E-13 " "
relative error = 2.9238062891293626000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.617999999999872 " "
y[1] (analytic) = -7.714207274342805 " "
y[1] (numeric) = -7.714207274343032 " "
absolute error = 2.26485497023531930000000000000E-13 " "
relative error = 2.935952962747256000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.616999999999872 " "
y[1] (analytic) = -7.712536809363520 " "
y[1] (numeric) = -7.712536809363746 " "
absolute error = 2.26485497023531930000000000000E-13 " "
relative error = 2.936588863323983000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.615999999999872 " "
y[1] (analytic) = -7.7108663443842325 " "
y[1] (numeric) = -7.71086634438446 " "
absolute error = 2.27373675443232060000000000000E-13 " "
relative error = 2.9487435689872465000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.614999999999871 " "
y[1] (analytic) = -7.7091958794049456 " "
y[1] (numeric) = -7.709195879405174 " "
absolute error = 2.2826185386293218000000000000E-13 " "
relative error = 2.960903542128588000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.613999999999871 " "
y[1] (analytic) = -7.7075254144256595 " "
y[1] (numeric) = -7.707525414425888 " "
absolute error = 2.2826185386293218000000000000E-13 " "
relative error = 2.961545263745868000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.612999999999870 " "
y[1] (analytic) = -7.705854949446373 " "
y[1] (numeric) = -7.705854949446602 " "
absolute error = 2.2915003228263230000000000000E-13 " "
relative error = 2.9737132840671443000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.61199999999987 " "
y[1] (analytic) = -7.704184484467086 " "
y[1] (numeric) = -7.704184484467316 " "
absolute error = 2.30038210702332440000000000000E-13 " "
relative error = 2.985886581066791000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.61099999999987 " "
y[1] (analytic) = -7.7025140194878 " "
y[1] (numeric) = -7.70251401948803 " "
absolute error = 2.30038210702332440000000000000E-13 " "
relative error = 2.9865341383387640000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.60999999999987 " "
y[1] (analytic) = -7.700843554508513 " "
y[1] (numeric) = -7.700843554508744 " "
absolute error = 2.30926389122032560000000000000E-13 " "
relative error = 2.9987154976916147000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.608999999999870 " "
y[1] (analytic) = -7.699173089529226 " "
y[1] (numeric) = -7.699173089529458 " "
absolute error = 2.3181456754173269000000000000E-13 " "
relative error = 3.0109021429456810000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.607999999999869 " "
y[1] (analytic) = -7.69750262454994 " "
y[1] (numeric) = -7.697502624550172 " "
absolute error = 2.3181456754173269000000000000E-13 " "
relative error = 3.011555550528786000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.606999999999869 " "
y[1] (analytic) = -7.695832159570653 " "
y[1] (numeric) = -7.695832159570886 " "
absolute error = 2.3270274596143280000000000000E-13 " "
relative error = 3.0237502733481547000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.605999999999868 " "
y[1] (analytic) = -7.694161694591366 " "
y[1] (numeric) = -7.6941616945916 " "
absolute error = 2.33590924381132940000000000000E-13 " "
relative error = 3.03595029131421000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.604999999999868 " "
y[1] (analytic) = -7.69249122961208 " "
y[1] (numeric) = -7.692491229612314 " "
absolute error = 2.33590924381132940000000000000E-13 " "
relative error = 3.036609563907329300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.603999999999868 " "
y[1] (analytic) = -7.690820764632793 " "
y[1] (numeric) = -7.6908207646330276 " "
absolute error = 2.34479102800833060000000000000E-13 " "
relative error = 3.048817674689738000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.602999999999867 " "
y[1] (analytic) = -7.689150299653506 " "
y[1] (numeric) = -7.6891502996537415 " "
absolute error = 2.3536728122053320000000000000E-13 " "
relative error = 3.061031089886999000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.601999999999867 " "
y[1] (analytic) = -7.68747983467422 " "
y[1] (numeric) = -7.6874798346744555 " "
absolute error = 2.3536728122053320000000000000E-13 " "
relative error = 3.0616962422316074000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.600999999999867 " "
y[1] (analytic) = -7.685809369694933 " "
y[1] (numeric) = -7.6858093696951695 " "
absolute error = 2.3625545964023330000000000000E-13 " "
relative error = 3.0739177655353533000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.599999999999866 " "
y[1] (analytic) = -7.684138904715646 " "
y[1] (numeric) = -7.6841389047158835 " "
absolute error = 2.37143638059933440000000000000E-13 " "
relative error = 3.086144602544883000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.598999999999866 " "
y[1] (analytic) = -7.68246843973636 " "
y[1] (numeric) = -7.682468439736597 " "
absolute error = 2.37143638059933440000000000000E-13 " "
relative error = 3.0868156494251936000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.597999999999866 " "
y[1] (analytic) = -7.680797974757073 " "
y[1] (numeric) = -7.680797974757311 " "
absolute error = 2.38031816479633560000000000000E-13 " "
relative error = 3.0990506098705450000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.596999999999865 " "
y[1] (analytic) = -7.6791275097777865 " "
y[1] (numeric) = -7.679127509778025 " "
absolute error = 2.3891999489933370000000000000E-13 " "
relative error = 3.1112908933354510000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.595999999999865 " "
y[1] (analytic) = -7.6774570447985 " "
y[1] (numeric) = -7.677457044798740 " "
absolute error = 2.3891999489933370000000000000E-13 " "
relative error = 3.1119678495785620000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.594999999999865 " "
y[1] (analytic) = -7.6757865798192135 " "
y[1] (numeric) = -7.675786579819453 " "
absolute error = 2.3980817331903380000000000000E-13 " "
relative error = 3.1242162718479594000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.593999999999864 " "
y[1] (analytic) = -7.674116114839927 " "
y[1] (numeric) = -7.674116114840167 " "
absolute error = 2.40696351738733940000000000000E-13 " "
relative error = 3.1364700264735906000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.592999999999864 " "
y[1] (analytic) = -7.672445649860640 " "
y[1] (numeric) = -7.672445649860881 " "
absolute error = 2.40696351738733940000000000000E-13 " "
relative error = 3.1371529069496350000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.591999999999864 " "
y[1] (analytic) = -7.670775184881354 " "
y[1] (numeric) = -7.670775184881595 " "
absolute error = 2.41584530158434060000000000000E-13 " "
relative error = 3.1494148157878876000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.590999999999863 " "
y[1] (analytic) = -7.669104719902067 " "
y[1] (numeric) = -7.669104719902310 " "
absolute error = 2.4247270857813420000000000000E-13 " "
relative error = 3.161682066342035000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.589999999999863 " "
y[1] (analytic) = -7.667434254922780 " "
y[1] (numeric) = -7.667434254923023 " "
absolute error = 2.4247270857813420000000000000E-13 " "
relative error = 3.1623708859643320000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.588999999999863 " "
y[1] (analytic) = -7.665763789943494 " "
y[1] (numeric) = -7.665763789943737 " "
absolute error = 2.4336088699783430000000000000E-13 " "
relative error = 3.1746463061788155000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.587999999999862 " "
y[1] (analytic) = -7.664093324964207 " "
y[1] (numeric) = -7.664093324964451 " "
absolute error = 2.44249065417534440000000000000E-13 " "
relative error = 3.186927077491911000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.586999999999862 " "
y[1] (analytic) = -7.662422859984921 " "
y[1] (numeric) = -7.662422859985165 " "
absolute error = 2.44249065417534440000000000000E-13 " "
relative error = 3.187621851217111000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.585999999999862 " "
y[1] (analytic) = -7.660752395005634 " "
y[1] (numeric) = -7.660752395005880 " "
absolute error = 2.45137243837234560000000000000E-13 " "
relative error = 3.1999108076779750000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.584999999999861 " "
y[1] (analytic) = -7.659081930026347 " "
y[1] (numeric) = -7.659081930026593 " "
absolute error = 2.4602542225693470000000000000E-13 " "
relative error = 3.2122051246432920000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.583999999999861 " "
y[1] (analytic) = -7.657411465047061 " "
y[1] (numeric) = -7.657411465047307 " "
absolute error = 2.4602542225693470000000000000E-13 " "
relative error = 3.2129058674715305000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.582999999999860 " "
y[1] (analytic) = -7.655741000067774 " "
y[1] (numeric) = -7.655741000068021 " "
absolute error = 2.4691360067663481000000000000E-13 " "
relative error = 3.2252083851118910000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.58199999999986 " "
y[1] (analytic) = -7.654070535088487 " "
y[1] (numeric) = -7.654070535088735 " "
absolute error = 2.47801779096334940000000000000E-13 " "
relative error = 3.237516272685748700000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.58099999999986 " "
y[1] (analytic) = -7.652400070109201 " "
y[1] (numeric) = -7.652400070109449 " "
absolute error = 2.47801779096334940000000000000E-13 " "
relative error = 3.238222999660795000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.57999999999986 " "
y[1] (analytic) = -7.650729605129914 " "
y[1] (numeric) = -7.650729605130163 " "
absolute error = 2.48689957516035070000000000000E-13 " "
relative error = 3.250539103476944300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.578999999999860 " "
y[1] (analytic) = -7.649059140150627 " "
y[1] (numeric) = -7.649059140150877 " "
absolute error = 2.4957813593573520000000000000E-13 " "
relative error = 3.2628605866789050000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.577999999999859 " "
y[1] (analytic) = -7.647388675171341 " "
y[1] (numeric) = -7.647388675171591 " "
absolute error = 2.4957813593573520000000000000E-13 " "
relative error = 3.263573312888315000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.576999999999859 " "
y[1] (analytic) = -7.645718210192054 " "
y[1] (numeric) = -7.645718210192305 " "
absolute error = 2.5046631435543530000000000000E-13 " "
relative error = 3.2759030279399190000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.575999999999858 " "
y[1] (analytic) = -7.6440477452127675 " "
y[1] (numeric) = -7.644047745213019 " "
absolute error = 2.51354492775135440000000000000E-13 " "
relative error = 3.288238131852997000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.574999999999858 " "
y[1] (analytic) = -7.6423772802334815 " "
y[1] (numeric) = -7.642377280233733 " "
absolute error = 2.51354492775135440000000000000E-13 " "
relative error = 3.288956872428265300000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.573999999999858 " "
y[1] (analytic) = -7.640706815254195 " "
y[1] (numeric) = -7.640706815254447 " "
absolute error = 2.52242671194835570000000000000E-13 " "
relative error = 3.3013002238385697000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.572999999999857 " "
y[1] (analytic) = -7.639036350274908 " "
y[1] (numeric) = -7.639036350275160 " "
absolute error = 2.5313084961453570000000000000E-13 " "
relative error = 3.3136489736094293000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.571999999999857 " "
y[1] (analytic) = -7.637365885295622 " "
y[1] (numeric) = -7.637365885295875 " "
absolute error = 2.5313084961453570000000000000E-13 " "
relative error = 3.314373743726141700000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.570999999999857 " "
y[1] (analytic) = -7.635695420316335 " "
y[1] (numeric) = -7.635695420316589 " "
absolute error = 2.5401902803423580000000000000E-13 " "
relative error = 3.3267307566821750000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.569999999999856 " "
y[1] (analytic) = -7.634024955337048 " "
y[1] (numeric) = -7.634024955337303 " "
absolute error = 2.54907206453935940000000000000E-13 " "
relative error = 3.339093177521341000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.568999999999856 " "
y[1] (analytic) = -7.632354490357762 " "
y[1] (numeric) = -7.632354490358017 " "
absolute error = 2.54907206453935940000000000000E-13 " "
relative error = 3.3398239923993270000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.567999999999856 " "
y[1] (analytic) = -7.630684025378475 " "
y[1] (numeric) = -7.630684025378730 " "
absolute error = 2.55795384873636070000000000000E-13 " "
relative error = 3.352194692152108400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.566999999999855 " "
y[1] (analytic) = -7.629013560399188 " "
y[1] (numeric) = -7.629013560399445 " "
absolute error = 2.5668356329333620000000000000E-13 " "
relative error = 3.3645708093341653000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.565999999999855 " "
y[1] (analytic) = -7.627343095419902 " "
y[1] (numeric) = -7.627343095420159 " "
absolute error = 2.5668356329333620000000000000E-13 " "
relative error = 3.3653076842376550000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.564999999999855 " "
y[1] (analytic) = -7.625672630440615 " "
y[1] (numeric) = -7.625672630440873 " "
absolute error = 2.5757174171303630000000000000E-13 " "
relative error = 3.377692096102396000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.563999999999854 " "
y[1] (analytic) = -7.624002165461328 " "
y[1] (numeric) = -7.624002165461587 " "
absolute error = 2.58459920132736440000000000000E-13 " "
relative error = 3.3900819349662010000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.562999999999854 " "
y[1] (analytic) = -7.622331700482042 " "
y[1] (numeric) = -7.622331700482300 " "
absolute error = 2.58459920132736440000000000000E-13 " "
relative error = 3.3908248852039760000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.561999999999854 " "
y[1] (analytic) = -7.620661235502755 " "
y[1] (numeric) = -7.6206612355030146 " "
absolute error = 2.59348098552436570000000000000E-13 " "
relative error = 3.40322303456029000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.560999999999853 " "
y[1] (analytic) = -7.618990770523468 " "
y[1] (numeric) = -7.6189907705237285 " "
absolute error = 2.6023627697213670000000000000E-13 " "
relative error = 3.415626620509175000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.559999999999853 " "
y[1] (analytic) = -7.617320305544182 " "
y[1] (numeric) = -7.6173203055444425 " "
absolute error = 2.6023627697213670000000000000E-13 " "
relative error = 3.4163756614347250000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.558999999999853 " "
y[1] (analytic) = -7.615649840564895 " "
y[1] (numeric) = -7.6156498405651565 " "
absolute error = 2.6112445539183680000000000000E-13 " "
relative error = 3.428787573726837000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.557999999999852 " "
y[1] (analytic) = -7.6139793755856084 " "
y[1] (numeric) = -7.6139793755858705 " "
absolute error = 2.62012633811536940000000000000E-13 " "
relative error = 3.4412049322288185000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.556999999999852 " "
y[1] (analytic) = -7.612308910606322 " "
y[1] (numeric) = -7.612308910606584 " "
absolute error = 2.62012633811536940000000000000E-13 " "
relative error = 3.441960079240499000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.555999999999852 " "
y[1] (analytic) = -7.6106384456270355 " "
y[1] (numeric) = -7.610638445627298 " "
absolute error = 2.62900812231237070000000000000E-13 " "
relative error = 3.454385779977449000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.554999999999851 " "
y[1] (analytic) = -7.608967980647749 " "
y[1] (numeric) = -7.608967980648012 " "
absolute error = 2.6378899065093720000000000000E-13 " "
relative error = 3.466816936565436000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.553999999999851 " "
y[1] (analytic) = -7.607297515668463 " "
y[1] (numeric) = -7.607297515668726 " "
absolute error = 2.6378899065093720000000000000E-13 " "
relative error = 3.4675782051066230000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.552999999999850 " "
y[1] (analytic) = -7.605627050689176 " "
y[1] (numeric) = -7.60562705068944 " "
absolute error = 2.6467716907063730000000000000E-13 " "
relative error = 3.4800177198624780000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.55199999999985 " "
y[1] (analytic) = -7.603956585709889 " "
y[1] (numeric) = -7.603956585710154 " "
absolute error = 2.65565347490337440000000000000E-13 " "
relative error = 3.4924627001344830000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.55099999999985 " "
y[1] (analytic) = -7.602286120730603 " "
y[1] (numeric) = -7.602286120730868 " "
absolute error = 2.65565347490337440000000000000E-13 " "
relative error = 3.4932301056937304000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.54999999999985 " "
y[1] (analytic) = -7.600615655751316 " "
y[1] (numeric) = -7.600615655751582 " "
absolute error = 2.66453525910037570000000000000E-13 " "
relative error = 3.5056834601077960000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.548999999999850 " "
y[1] (analytic) = -7.598945190772029 " "
y[1] (numeric) = -7.598945190772296 " "
absolute error = 2.6734170432973770000000000000E-13 " "
relative error = 3.5181422897271430000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.547999999999849 " "
y[1] (analytic) = -7.597274725792743 " "
y[1] (numeric) = -7.59727472579301 " "
absolute error = 2.6734170432973770000000000000E-13 " "
relative error = 3.518915847838341000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.546999999999849 " "
y[1] (analytic) = -7.595604260813456 " "
y[1] (numeric) = -7.595604260813724 " "
absolute error = 2.6822988274943780000000000000E-13 " "
relative error = 3.531383067615368000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.545999999999848 " "
y[1] (analytic) = -7.593933795834169 " "
y[1] (numeric) = -7.593933795834438 " "
absolute error = 2.69118061169137950000000000000E-13 " "
relative error = 3.5438557723109065000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.544999999999848 " "
y[1] (analytic) = -7.592263330854883 " "
y[1] (numeric) = -7.592263330855152 " "
absolute error = 2.69118061169137950000000000000E-13 " "
relative error = 3.544635498553439000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.543999999999848 " "
y[1] (analytic) = -7.590592865875596 " "
y[1] (numeric) = -7.590592865875866 " "
absolute error = 2.70006239588838070000000000000E-13 " "
relative error = 3.5571166094638396000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.542999999999847 " "
y[1] (analytic) = -7.588922400896310 " "
y[1] (numeric) = -7.58892240089658 " "
absolute error = 2.7089441800853820000000000000E-13 " "
relative error = 3.569603215030154000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.541999999999847 " "
y[1] (analytic) = -7.587251935917023 " "
y[1] (numeric) = -7.587251935917294 " "
absolute error = 2.7089441800853820000000000000E-13 " "
relative error = 3.5703891250290600000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.540999999999847 " "
y[1] (analytic) = -7.585581470937736 " "
y[1] (numeric) = -7.585581470938008 " "
absolute error = 2.7178259642823830000000000000E-13 " "
relative error = 3.582884152909115400000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.539999999999846 " "
y[1] (analytic) = -7.583911005958450 " "
y[1] (numeric) = -7.583911005958722 " "
absolute error = 2.72670774847938450000000000000E-13 " "
relative error = 3.5953846852067395000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.538999999999846 " "
y[1] (analytic) = -7.582240540979163 " "
y[1] (numeric) = -7.582240540979436 " "
absolute error = 2.72670774847938450000000000000E-13 " "
relative error = 3.59617679463287000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.537999999999846 " "
y[1] (analytic) = -7.580570075999876 " "
y[1] (numeric) = -7.58057007600015 " "
absolute error = 2.73558953267638570000000000000E-13 " "
relative error = 3.608685765384949000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.536999999999845 " "
y[1] (analytic) = -7.5788996110205895 " "
y[1] (numeric) = -7.578899611020864 " "
absolute error = 2.7444713168733870000000000000E-13 " "
relative error = 3.6212002503405780000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.535999999999845 " "
y[1] (analytic) = -7.5772291460413035 " "
y[1] (numeric) = -7.577229146041578 " "
absolute error = 2.7444713168733870000000000000E-13 " "
relative error = 3.621998574910759000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.534999999999845 " "
y[1] (analytic) = -7.575558681062017 " "
y[1] (numeric) = -7.575558681062292 " "
absolute error = 2.7533531010703880000000000000E-13 " "
relative error = 3.63452151450353000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.533999999999844 " "
y[1] (analytic) = -7.57388821608273 " "
y[1] (numeric) = -7.573888216083006 " "
absolute error = 2.76223488526738950000000000000E-13 " "
relative error = 3.647049978110236000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.532999999999844 " "
y[1] (analytic) = -7.572217751103444 " "
y[1] (numeric) = -7.57221775110372 " "
absolute error = 2.76223488526738950000000000000E-13 " "
relative error = 3.647854533587428000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.531999999999844 " "
y[1] (analytic) = -7.570547286124157 " "
y[1] (numeric) = -7.570547286124434 " "
absolute error = 2.77111666946439100000000000000E-13 " "
relative error = 3.660391468056070600000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = arcsin(0.1) + arccos(0.1) + arctan(0.1);"
Iterations = 469
"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 58 Seconds
"Expected Time Remaining "= 0 Years 0 Days 1 Hours 0 Minutes 57 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 1 Hours 0 Minutes 28 Seconds
"Expected Total Time "= 0 Years 0 Days 1 Hours 3 Minutes 28 Seconds
"Time to Timeout " Unknown
Percent Done = 4.70000000000157 "%"
(%o57) true
(%o57) diffeq.max