##############ECHO OF PROBLEM#################
##############temp/mult_sin_cpostode.ode#################
diff  (  y  ,  x  ,  1  )   =   sin ( x )   *  2.0 ; 
!
#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(-cos(x) * 2.0) 
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                      1.9900083305560516
$glob_desired_digits_correct  16
estimated_h                   1.0e-06
estimated_answer              1.9900083305560516
desired_abs_gbl_error         1.9900083305560517e-16
range                         4.9
estimated_steps               4900000.000000001
step_error                    2.2474853168808475e-21
est_needed_step_err           2.2474853168808475e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      5.349580717026646e-258
estimated_step_error          5.349580717026646e-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                      1.9900083305560516
$glob_desired_digits_correct  16
estimated_h                   2.0e-06
estimated_answer              1.9900083305560516
desired_abs_gbl_error         1.9900083305560517e-16
range                         4.9
estimated_steps               2450000.0000000005
step_error                    3.178424216367288e-21
est_needed_step_err           3.178424216367288e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      3.6762038713261966e-247
estimated_step_error          3.6762038713261966e-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                      1.9900083305560516
$glob_desired_digits_correct  16
estimated_h                   4.0e-06
estimated_answer              1.9900083305560516
desired_abs_gbl_error         1.9900083305560517e-16
range                         4.9
estimated_steps               1225000.0000000002
step_error                    4.494970633761695e-21
est_needed_step_err           4.494970633761695e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      2.5262680572733296e-236
estimated_step_error          2.5262680572733296e-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                      1.9900083305560516
$glob_desired_digits_correct  16
estimated_h                   8.0e-06
estimated_answer              1.9900083305560516
desired_abs_gbl_error         1.9900083305560517e-16
range                         4.9
estimated_steps               612500.0000000001
step_error                    6.356848432734576e-21
est_needed_step_err           6.356848432734576e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.736038180491534e-225
estimated_step_error          1.736038180491534e-225
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                      1.9900083305560516
$glob_desired_digits_correct  16
estimated_h                   1.6e-05
estimated_answer              1.9900083305560516
desired_abs_gbl_error         1.9900083305560517e-16
range                         4.9
estimated_steps               306250.00000000006
step_error                    8.98994126752339e-21
est_needed_step_err           8.98994126752339e-21
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      1.1929963406304953e-214
estimated_step_error          1.1929963406304953e-214
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                      1.9900083305560516
$glob_desired_digits_correct  16
estimated_h                   3.2e-05
estimated_answer              1.9900083305560516
desired_abs_gbl_error         1.9900083305560517e-16
range                         4.9
estimated_steps               153125.00000000003
step_error                    1.2713696865469152e-20
est_needed_step_err           1.2713696865469152e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      8.198208249756126e-204
estimated_step_error          8.198208249756126e-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                      1.9900083305560516
$glob_desired_digits_correct  16
estimated_h                   6.4e-05
estimated_answer              1.9900083305560516
desired_abs_gbl_error         1.9900083305560517e-16
range                         4.9
estimated_steps               76562.50000000001
step_error                    1.797988253504678e-20
est_needed_step_err           1.797988253504678e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      5.633765566519265e-193
estimated_step_error          5.633765566519265e-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                      1.9900083305560516
$glob_desired_digits_correct  16
estimated_h                   0.000128
estimated_answer              1.9900083305560516
desired_abs_gbl_error         1.9900083305560517e-16
range                         4.9
estimated_steps               38281.25000000001
step_error                    2.5427393730938304e-20
est_needed_step_err           2.5427393730938304e-20
hn_div_ho                     0.5
hn_div_ho_2                   0.25
hn_div_ho_3                   0.125
max_estimated_step_error      3.871493881883975e-182
estimated_step_error          3.871493881883975e-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  0.09933466539752536 
Order of pole (three term test)                   32.00996671107973 
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)               -1.9900083305560516 
y[1] (numeric)                   -1.9900083305560516 
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)               -1.960095002138738 
y[1] (numeric)                   -1.9600950021387367 
absolute error                   1.3322676295501878e-15 
relative error                   6.796954372601825e-14%
Desired digits                   16 
Estimated correct digits         12 
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]                             0.3000639999999968 
y[1] (closed_form)               -1.910635147751729 
y[1] (numeric)                   -1.9106351477517327 
absolute error                   3.774758283725532e-15 
relative error                   1.975656256594747e-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)               -1.8420970642886925 
y[1] (numeric)                   -1.8420970642887062 
absolute error                   1.3766765505351941e-14 
relative error                   7.473420251428413e-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)               -1.755165123780723 
y[1] (numeric)                   -1.7551651237807504 
absolute error                   2.731148640577885e-14 
relative error                   1.5560636452796187e-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)               -1.6505628108582968 
y[1] (numeric)                   -1.650562810858335 
absolute error                   3.8191672047105385e-14 
relative error                   2.3138575397349235e-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)               -1.5296019115722088 
y[1] (numeric)                   -1.5296019115722623 
absolute error                   5.3512749786932545e-14 
relative error                   3.498475608724181e-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)               -1.3933675071910028 
y[1] (numeric)                   -1.3933675071910765 
absolute error                   7.37188088351104e-14 
relative error                   5.290693837387226e-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]                             0.9000000000000764 
y[1] (closed_form)               -1.243219936541209 
y[1] (numeric)                   -1.2432199365413044 
absolute error                   9.525713551283843e-14 
relative error                   7.662130626529004e-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]                             1.0000960000000896 
y[1] (closed_form)               -1.0804430443278676 
y[1] (numeric)                   -1.080443044327984 
absolute error                   1.163513729807164e-13 
relative error                   1.0768857608139574e-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]                             1.1000640000000161 
y[1] (closed_form)               -0.9070781664511863 
y[1] (numeric)                   -0.9070781664511761 
absolute error                   1.021405182655144e-14 
relative error                   1.126038769791192e-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)               -0.7246558580809079 
y[1] (numeric)                   -0.7246558580807643 
absolute error                   1.4366285938649526e-13 
relative error                   1.982497730259917e-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]                             1.2999999999998693 
y[1] (closed_form)               -0.5349976572494267 
y[1] (numeric)                   -0.5349976572491445 
absolute error                   2.822186928597148e-13 
relative error                   5.275138854077986e-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]                             1.4000959999997957 
y[1] (closed_form)               -0.33974507788660013 
y[1] (numeric)                   -0.339745077886174 
absolute error                   4.2615910800236634e-13 
relative error                   1.254349616051272e-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]                             1.5000639999997223 
y[1] (closed_form)               -0.14134672368802212 
y[1] (numeric)                   -0.1413467236874503 
absolute error                   5.718203688331869e-13 
relative error                   4.0455155514980185e-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]                             1.6000319999996488 
y[1] (closed_form)               0.05846301728255887 
y[1] (numeric)                   0.05846301728327768 
absolute error                   7.188069583996537e-13 
relative error                   1.2295071171670328e-09%
Desired digits                   16 
Estimated correct digits         10 
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]                             1.6999999999995754 
y[1] (closed_form)               0.2576889885902073 
y[1] (numeric)                   0.25768898859107237 
absolute error                   8.65085780787922e-13 
relative error                   3.3570925382598867e-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]                             1.8000959999995019 
y[1] (closed_form)               0.45459116603615085 
y[1] (numeric)                   0.45459116603716054 
absolute error                   1.0096923297453486e-12 
relative error                   2.2210997599215423e-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]                             1.9000639999994284 
y[1] (closed_form)               0.6467002588128724 
y[1] (numeric)                   0.646700258814022 
absolute error                   1.1496359419993496e-12 
relative error                   1.7776951939213703e-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]                             2.000031999999355 
y[1] (closed_form)               0.8323518677022848 
y[1] (numeric)                   0.8323518677035714 
absolute error                   1.286637463238094e-12 
relative error                   1.5457855183167533e-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]                             2.099999999999455 
y[1] (closed_form)               1.0096922091987743 
y[1] (numeric)                   1.009692209199884 
absolute error                   1.1095568908103814e-12 
relative error                   1.0989060633545476e-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]                             2.2000959999995553 
y[1] (closed_form)               1.177157460395641 
y[1] (numeric)                   1.1771574603965838 
absolute error                   9.42801392511683e-13 
relative error                   8.00913577181772e-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]                             2.3000639999996553 
y[1] (closed_form)               1.3326474900971612 
y[1] (numeric)                   1.3326474900979455 
absolute error                   7.842615445952106e-13 
relative error                   5.884988719245112e-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)               1.4748306599706171 
y[1] (numeric)                   1.4748306599712586 
absolute error                   6.414868636284154e-13 
relative error                   4.3495628416159705e-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)               1.6022872310936942 
y[1] (numeric)                   1.602287231094209 
absolute error                   5.146993942162226e-13 
relative error                   3.212279198311388e-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)               1.7138764751039994 
y[1] (numeric)                   1.7138764751044036 
absolute error                   4.04121180963557e-13 
relative error                   2.3579364489441084e-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)               1.8081989849557227 
y[1] (numeric)                   1.808198984956033 
absolute error                   3.1019631308026874e-13 
relative error                   1.715498767896192e-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]                             2.8000320000001553 
y[1] (closed_form)               1.884466119614191 
y[1] (numeric)                   1.8844661196144272 
absolute error                   2.362554596402333e-13 
relative error                   1.2536996934102598e-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]                             2.9000000000002553 
y[1] (closed_form)               1.9419163302993032 
y[1] (numeric)                   1.941916330299482 
absolute error                   1.787459069646502e-13 
relative error                   9.204614234697768e-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]                             3.0000960000003554 
y[1] (closed_form)               1.9800120791187261 
y[1] (numeric)                   1.9800120791188653 
absolute error                   1.3922196728799463e-13 
relative error                   7.031369593965319e-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]                             3.1000640000004553 
y[1] (closed_form)               1.998275618778927 
y[1] (numeric)                   1.9982756187790478 
absolute error                   1.2079226507921703e-13 
relative error                   6.044825045357295e-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]                             3.2000320000005553 
y[1] (closed_form)               1.9965858146220088 
y[1] (numeric)                   1.996585814622131 
absolute error                   1.2212453270876722e-13 
relative error                   6.116668355268651e-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]                             3.3000000000006553 
y[1] (closed_form)               1.974959539817523 
y[1] (numeric)                   1.974959539817665 
absolute error                   1.41886502547095e-13 
relative error                   7.184273889489637e-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]                             3.4000960000007554 
y[1] (closed_form)               1.93354731235701 
y[1] (numeric)                   1.933547312357194 
absolute error                   1.8407497748285095e-13 
relative error                   9.520065855459314e-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]                             3.5000640000008554 
y[1] (closed_form)               1.8728684704921523 
y[1] (numeric)                   1.872868470492398 
absolute error                   2.4558133304708463e-13 
relative error                   1.3112577680511155e-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]                             3.6000320000009554 
y[1] (closed_form)               1.7934885104408018 
y[1] (numeric)                   1.7934885104411284 
absolute error                   3.2662761384472105e-13 
relative error                   1.8211859844278725e-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]                             3.7000000000010553 
y[1] (closed_form)               1.696200063419698 
y[1] (numeric)                   1.696200063420123 
absolute error                   4.249933738265099e-13 
relative error                   2.5055615961343822e-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]                             3.8000960000011554 
y[1] (closed_form)               1.5818179398229804 
y[1] (numeric)                   1.5818179398235184 
absolute error                   5.380140777333509e-13 
relative error                   3.401238942792364e-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]                             3.9000640000012554 
y[1] (closed_form)               1.4517765713568191 
y[1] (numeric)                   1.4517765713574868 
absolute error                   6.676881270095691e-13 
relative error                   4.599110773536957e-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]                             4.000032000001355 
y[1] (closed_form)               1.3072388056961497 
y[1] (numeric)                   1.3072388056969644 
absolute error                   8.146816554699399e-13 
relative error                   6.23207979995739e-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]                             4.100000000001455 
y[1] (closed_form)               1.149647893064156 
y[1] (numeric)                   1.1496478930651295 
absolute error                   9.734435479913373e-13 
relative error                   8.467319027539976e-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]                             4.2000960000015555 
y[1] (closed_form)               0.9803542956123975 
y[1] (numeric)                   0.98035429561354 
absolute error                   1.1425305146417486e-12 
relative error                   1.1654261319149365e-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)               0.8014810732754198 
y[1] (numeric)                   0.8014810732767412 
absolute error                   1.3213874439088613e-12 
relative error                   1.6486820312658606e-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)               0.6146048371060711 
y[1] (numeric)                   0.614604837107579 
absolute error                   1.5079049120458876e-12 
relative error                   2.4534543514919445e-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)               0.42159159885793196 
y[1] (numeric)                   0.42159159885963177 
absolute error                   1.699806961852346e-12 
relative error                   4.0318805366544965e-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)               0.2241142641602204 
y[1] (numeric)                   0.22411426416211747 
absolute error                   1.8970658377526206e-12 
relative error                   8.464725995291397e-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]                             4.7000640000020555 
y[1] (closed_form)               0.02464933669404602 
y[1] (numeric)                   0.024649336696142825 
absolute error                   2.096805368223542e-12 
relative error                   8.506538712378495e-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]                             4.8000320000021555 
y[1] (closed_form)               -0.17506172132854317 
y[1] (numeric)                   -0.17506172132624698 
absolute error                   2.2961910151053644e-12 
relative error                   1.3116465425334412e-09%
Desired digits                   16 
Estimated correct digits         10 
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]                             4.900000000002255 
y[1] (closed_form)               -0.37302473884958254 
y[1] (numeric)                   -0.37302473884708875 
absolute error                   2.4937829579130266e-12 
relative error                   6.685301799564058e-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 )   *  2.0 ; 
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%