##############ECHO OF PROBLEM#################
##############temp/sub_sin_cpostode.ode#################
diff  (  y  ,  x  ,  1  )   =  sin ( x )   -  1 , 0 ; 
!
#BEGIN FIRST INPUT BLOCK
# Digits:=32; ELIMINATED in preodein.rb
max_terms=40 
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start=0.1 
x_end=5.0 
$array_y_init[0 + 1] = exact_soln_y(x_start)
$glob_look_poles=true 
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
$glob_type_given_pole=3 
#  ELIMINATED in preodein.rb
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
$glob_desired_digits_correct=16 
$glob_max_minutes=3.0 
$glob_subiter_method=3 
$glob_max_iter=100000000 
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
def exact_soln_y (x)
return(2.0 - cos(x) - x) 
end
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size                      0.0
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   1.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               4900000.000000001
step_error                    1.129384878631564e-21
est_needed_step_err           1.129384878631564e-21
opt_iter                        1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.9049958347219743
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   1.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               4900000.000000001
step_error                    1.129384878631564e-21
est_needed_step_err           1.129384878631564e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.674790358513323e-258
estimated_step_error          2.674790358513323e-258
Double H and LOOP
opt_iter                        2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.9049958347219743
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   2.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               2450000.0000000005
step_error                    1.5971914124998497e-21
est_needed_step_err           1.5971914124998497e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.8381019356630983e-247
estimated_step_error          1.8381019356630983e-247
Double H and LOOP
opt_iter                        3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.9049958347219743
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   4.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               1225000.0000000002
step_error                    2.258769757263128e-21
est_needed_step_err           2.258769757263128e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.2631340286366648e-236
estimated_step_error          1.2631340286366648e-236
Double H and LOOP
opt_iter                        4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.9049958347219743
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   8.0e-06
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               612500.0000000001
step_error                    3.1943828249996993e-21
est_needed_step_err           3.1943828249996993e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      8.68019090245767e-226
estimated_step_error          8.68019090245767e-226
Double H and LOOP
opt_iter                        5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.9049958347219743
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   1.6e-05
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               306250.00000000006
step_error                    4.517539514526256e-21
est_needed_step_err           4.517539514526256e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      5.964981703152477e-215
estimated_step_error          5.964981703152477e-215
Double H and LOOP
opt_iter                        6
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.9049958347219743
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   3.2e-05
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               153125.00000000003
step_error                    6.388765649999399e-21
est_needed_step_err           6.388765649999399e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      4.099104124878063e-204
estimated_step_error          4.099104124878063e-204
Double H and LOOP
opt_iter                        7
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.9049958347219743
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   6.4e-05
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               76562.50000000001
step_error                    9.035079029052512e-21
est_needed_step_err           9.035079029052512e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.8168827832596326e-193
estimated_step_error          2.8168827832596326e-193
Double H and LOOP
opt_iter                        8
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
min_size                      0.9049958347219743
min_size                      1.0
$glob_desired_digits_correct  16
estimated_h                   0.000128
estimated_answer              1.0
desired_abs_gbl_error         1.0e-16
range                         4.9
estimated_steps               38281.25000000001
step_error                    1.2777531299998797e-20
est_needed_step_err           1.2777531299998797e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.9357469409419875e-182
estimated_step_error          1.9357469409419875e-182
Double H and LOOP
opt_iter                        9
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1  0.09933466539749951 
Order of pole (three term test)                   32.00996671107996 
NO COMPLEX POLE (six term test) for Equation 1
SETTING H FOR POLE ACCURACY
START of Soultion
 
TOP MAIN SOLVE Loop
x[1]                             0.1 
y[1] (closed_form)               0.9049958347219743 
y[1] (numeric)                   0.9049958347219743 
absolute error                   0.0 
relative error                   0.0%
Desired digits                   16 
Estimated correct digits         14 
Correct digits                   16 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.2000959999999943 
y[1] (closed_form)               0.8198564989306367 
y[1] (numeric)                   0.8198564989306314 
absolute error                   5.329070518200751e-15 
relative error                   6.500003994786425e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.3000639999999968 
y[1] (closed_form)               0.7446184261241386 
y[1] (numeric)                   0.7446184261241362 
absolute error                   2.4424906541753444e-15 
relative error                   3.280190992437442e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.40003200000001005 
y[1] (closed_form)               0.6789194678556437 
y[1] (numeric)                   0.6789194678556499 
absolute error                   6.217248937900877e-15 
relative error                   9.15756467779302e-13%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.5000000000000233 
y[1] (closed_form)               0.622417438109615 
y[1] (numeric)                   0.6224174381096277 
absolute error                   1.2656542480726785e-14 
relative error                   2.0334492104152483e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.6000960000000366 
y[1] (closed_form)               0.574622594570815 
y[1] (numeric)                   0.574622594570835 
absolute error                   1.9984014443252818e-14 
relative error                   3.4777634280425148e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.7000640000000499 
y[1] (closed_form)               0.5351350442138457 
y[1] (numeric)                   0.5351350442138705 
absolute error                   2.475797344914099e-14 
relative error                   4.626490774027394e-12%
Desired digits                   16 
Estimated correct digits         12 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.8000320000000631 
y[1] (closed_form)               0.5032842464044356 
y[1] (numeric)                   0.5032842464044627 
absolute error                   2.708944180085382e-14 
relative error                   5.382533229360201e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.9000000000000764 
y[1] (closed_form)               0.47839003172931915 
y[1] (numeric)                   0.47839003172934946 
absolute error                   3.0309088572266774e-14 
relative error                   6.335643839129188e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.0000960000000896 
y[1] (closed_form)               0.4596824778359767 
y[1] (numeric)                   0.45968247783600913 
absolute error                   3.241851231905457e-14 
relative error                   7.052370686755239e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.1000640000000161 
y[1] (closed_form)               0.44639691677439064 
y[1] (numeric)                   0.4463969167744136 
absolute error                   2.298161660974074e-14 
relative error                   5.1482471643852476e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.2000319999999427 
y[1] (closed_form)               0.43764007095960333 
y[1] (numeric)                   0.43764007095961943 
absolute error                   1.609823385706477e-14 
relative error                   3.678418619612811e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.2999999999998693 
y[1] (closed_form)               0.43250117137541744 
y[1] (numeric)                   0.4325011713754304 
absolute error                   1.2989609388114332e-14 
relative error                   3.0033697589316255e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.4000959999997957 
y[1] (closed_form)               0.43003146105690426 
y[1] (numeric)                   0.43003146105691553 
absolute error                   1.1268763699945339e-14 
relative error                   2.6204509949689914e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.5000639999997223 
y[1] (closed_form)               0.42926263815626675 
y[1] (numeric)                   0.4292626381562773 
absolute error                   1.0547118733938987e-14 
relative error                   2.4570316157120257e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.6000319999996488 
y[1] (closed_form)               0.4291995086416307 
y[1] (numeric)                   0.4291995086416415 
absolute error                   1.0824674490095276e-14 
relative error                   2.522061249406874e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.6999999999995754 
y[1] (closed_form)               0.42884449429552807 
y[1] (numeric)                   0.42884449429553845 
absolute error                   1.0380585280245214e-14 
relative error                   2.42059427562376e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.8000959999995019 
y[1] (closed_form)               0.4271995830185735 
y[1] (numeric)                   0.42719958301858324 
absolute error                   9.71445146547012e-15 
relative error                   2.2739843042046605e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             1.9000639999994284 
y[1] (closed_form)               0.4232861294070078 
y[1] (numeric)                   0.4232861294070146 
absolute error                   6.772360450213455e-15 
relative error                   1.5999485878975114e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.000031999999355 
y[1] (closed_form)               0.41614393385178694 
y[1] (numeric)                   0.4161439338517887 
absolute error                   1.7763568394002505e-15 
relative error                   4.268611638666622e-13%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   15 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.099999999999455 
y[1] (closed_form)               0.40484610459993187 
y[1] (numeric)                   0.4048461045999451 
absolute error                   1.3211653993039363e-14 
relative error                   3.2633768345369392e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.2000959999995553 
y[1] (closed_form)               0.3884827301982652 
y[1] (numeric)                   0.38848273019829394 
absolute error                   2.8754776337791554e-14 
relative error                   7.4018158601584e-12%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   14 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.3000639999996553 
y[1] (closed_form)               0.3662597450489251 
y[1] (numeric)                   0.36625974504897557 
absolute error                   5.0459636469213365e-14 
relative error                   1.3777008571464208e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.4000319999997553 
y[1] (closed_form)               0.33738332998555354 
y[1] (numeric)                   0.33738332998563214 
absolute error                   7.860379014346108e-14 
relative error                   2.3298065777828094e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.4999999999998552 
y[1] (closed_form)               0.30114361554699176 
y[1] (numeric)                   0.30114361554710745 
absolute error                   1.156852391659413e-13 
relative error                   3.841530525420994e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.6000959999999553 
y[1] (closed_form)               0.2568422375520445 
y[1] (numeric)                   0.2568422375522043 
absolute error                   1.5981660439479128e-13 
relative error                   6.222364589173434e-11%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   13 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.7000640000000553 
y[1] (closed_form)               0.20403549247780628 
y[1] (numeric)                   0.20403549247801855 
absolute error                   2.1227464230832993e-13 
relative error                   1.040380963774819e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.8000320000001553 
y[1] (closed_form)               0.1422010598069403 
y[1] (numeric)                   0.14220105980721431 
absolute error                   2.7400304247748863e-13 
relative error                   1.926870607360379e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             2.9000000000002553 
y[1] (closed_form)               0.07095816514939646 
y[1] (numeric)                   0.07095816514974149 
absolute error                   3.45029560477883e-13 
relative error                   4.862436334866498e-10%
Desired digits                   16 
Estimated correct digits         10 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.0000960000003554 
y[1] (closed_form)               -0.010089960440992307 
y[1] (numeric)                   -0.010089960440566146 
absolute error                   4.261608427258423e-13 
relative error                   4.223612621854156e-09%
Desired digits                   16 
Estimated correct digits         9 
Correct digits                   11 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.1000640000004553 
y[1] (closed_form)               -0.10092619061099173 
y[1] (numeric)                   -0.1009261906104749 
absolute error                   5.168226957508182e-13 
relative error                   5.120798601651886e-10%
Desired digits                   16 
Estimated correct digits         10 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.2000320000005553 
y[1] (closed_form)               -0.20173909268955104 
y[1] (numeric)                   -0.2017390926889332 
absolute error                   6.178391132038996e-13 
relative error                   3.062565142764223e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.3000000000006553 
y[1] (closed_form)               -0.31252023009189367 
y[1] (numeric)                   -0.3125202300911658 
absolute error                   7.278622149442526e-13 
relative error                   2.329008316454367e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.4000960000007554 
y[1] (closed_form)               -0.4333223438222502 
y[1] (numeric)                   -0.433322343821402 
absolute error                   8.482103908136196e-13 
relative error                   1.9574582361290777e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.5000640000008554 
y[1] (closed_form)               -0.5636297647547792 
y[1] (numeric)                   -0.5636297647537997 
absolute error                   9.795497746267756e-13 
relative error                   1.7379312376324775e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.6000320000009554 
y[1] (closed_form)               -0.7032877447805546 
y[1] (numeric)                   -0.7032877447794353 
absolute error                   1.1192158311246203e-12 
relative error                   1.5914052810259718e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.7000000000010553 
y[1] (closed_form)               -0.8518999682912063 
y[1] (numeric)                   -0.8518999682899391 
absolute error                   1.2672085603071537e-12 
relative error                   1.487508636546846e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.8000960000011554 
y[1] (closed_form)               -1.0091870300896653 
y[1] (numeric)                   -1.0091870300882404 
absolute error                   1.424860229803926e-12 
relative error                   1.411889161593098e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             3.9000640000012554 
y[1] (closed_form)               -1.1741757143228457 
y[1] (numeric)                   -1.1741757143212557 
absolute error                   1.5900614158681492e-12 
relative error                   1.3541937518143503e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.000032000001355 
y[1] (closed_form)               -1.3464125971532805 
y[1] (numeric)                   -1.3464125971515182 
absolute error                   1.7623680292899735e-12 
relative error                   1.308936081715328e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.100000000001455 
y[1] (closed_form)               -1.5251760534693775 
y[1] (numeric)                   -1.5251760534674332 
absolute error                   1.944222560723574e-12 
relative error                   1.2747528761030407e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.2000960000015555 
y[1] (closed_form)               -1.7099188521953566 
y[1] (numeric)                   -1.7099188521932236 
absolute error                   2.1329604749098507e-12 
relative error                   1.2474045023665031e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.3000640000016555 
y[1] (closed_form)               -1.8993234633639453 
y[1] (numeric)                   -1.8993234633616236 
absolute error                   2.3216983890961274e-12 
relative error                   1.222381776395318e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.400032000001755 
y[1] (closed_form)               -2.0927295814487197 
y[1] (numeric)                   -2.092729581446205 
absolute error                   2.5148771953809046e-12 
relative error                   1.2017210525785885e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.500000000001855 
y[1] (closed_form)               -2.2892042005728896 
y[1] (numeric)                   -2.289204200570182 
absolute error                   2.7076119124558318e-12 
relative error                   1.1827743072366514e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.6000960000019555 
y[1] (closed_form)               -2.4880388679218455 
y[1] (numeric)                   -2.48803886791894 
absolute error                   2.9056757000489597e-12 
relative error                   1.1678578407723785e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.7000640000020555 
y[1] (closed_form)               -2.6877393316550324 
y[1] (numeric)                   -2.687739331651935 
absolute error                   3.0975222387041867e-12 
relative error                   1.1524637833077442e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.8000320000021555 
y[1] (closed_form)               -2.887562860666427 
y[1] (numeric)                   -2.8875628606631314 
absolute error                   3.2955860262973147e-12 
relative error                   1.141303647857806e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             4.900000000002255 
y[1] (closed_form)               -3.0865123694270467 
y[1] (numeric)                   -3.086512369423548 
absolute error                   3.4985347951987933e-12 
relative error                   1.1334912601851101e-10%
Desired digits                   16 
Estimated correct digits         11 
Correct digits                   12 
h                                0.000128 
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff  (  y  ,  x  ,  1  )   =  sin ( x )   -  1 , 0 ; 
Iterations                      38282 
Total Elapsed Time              7 Seconds
Elapsed Time(since restart)     7 Seconds
Time to Timeout                 2 Minutes 53.0 Seconds
Percent Done                    100.00457142861951%