Initializing...
Initialized
Initializing(2)...
PI = 0.3141592653589793238462643383279486e1+/-0.313e-31
E = 0.2718281828459045235360287471352649e1+/-0.256e-30
LOG_E_10 = 0.2302585092994045684017991454684277e1+/-0.5e-30
Initialized(2)
##############ECHO OF PROBLEM#################
##############temp/cospostode.ode#################
diff  (  y  ,  x  ,  1  )   =   cos  (  x  )   ; 
!
#BEGIN FIRST INPUT BLOCK
# Digits:=32; ELIMINATED in preodein.rb
max_terms=40 
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start=c(0.0) 
x_end=c(5.0) 
$array_y_init[0 + 1] = exact_soln_y(x_start)
$glob_look_poles=false 
#  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 
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
$glob_desired_digits_correct=8 
$glob_max_minutes=(20.0) 
$glob_subiter_method=3 
$glob_max_iter=1000 
$glob_upper_ratio_limit=c(1.11) 
$glob_lower_ratio_limit=c(0.99) 
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
def exact_soln_y (x)
x = c(x)
return(c(1.0) + sin(c(x))) 
end
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
 
TOP MAIN SOLVE Loop
x[1]                             0.0e0+/-0.50e-31 
y[1] (closed_form)               0.1e1+/-0.50e-31 
y[1] (numeric)                   0.1e1+/-0.15e-30 
absolute error                   0.0e0+/-0.200e-30 
relative error                   0.0e0+/-0.20000000000000000000000000000002e-28%
Desired digits                   8 
Estimated correct digits         14 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.1e0+/-0.2e-100 
y[1] (closed_form)               0.1099833416646828152306814198410621e1+/-0.5e-31 
y[1] (numeric)                   0.1099833416646828152310978261511985e1+/-0.58e-30 
absolute error                   0.4164063101364e-20+/-0.63e-30 
relative error                   0.3786085272858315716496665499713844e-18+/-0.572e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.2e0+/-0.4e-100 
y[1] (closed_form)               0.1198669330795061215459412627118388e1+/-0.635e-31 
y[1] (numeric)                   0.1198669330795061215467709555541537e1+/-0.94e-30 
absolute error                   0.8296928423149e-20+/-0.1e-29 
relative error                   0.6921782521661548790258987361774107e-18+/-0.834e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.3e0+/-0.6e-100 
y[1] (closed_form)               0.1295520206661339575105320745685026e1+/-0.698e-31 
y[1] (numeric)                   0.1295520206661339575117678047426228e1+/-0.112e-29 
absolute error                   0.12357301741202e-19+/-0.118e-29 
relative error                   0.9538486298911359105370864680186936e-18+/-0.91e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.4e0+/-0.8e-100 
y[1] (closed_form)               0.1389418342308650491666311756795704e1+/-0.756e-31 
y[1] (numeric)                   0.1389418342308650491682616369943215e1+/-0.136e-29 
absolute error                   0.16304613147511e-19+/-0.143e-29 
relative error                   0.1173484806629178166895796874965234e-17+/-0.102e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.5e0+/-0.10e-99 
y[1] (closed_form)               0.147942553860420300027328793521557e1+/-0.805e-31 
y[1] (numeric)                   0.1479425538604203000293387357626882e1+/-0.15e-29 
absolute error                   0.20099422411312e-19+/-0.158e-29 
relative error                   0.1358596420491378570875095697309911e-17+/-0.106e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.6e0+/-0.12e-99 
y[1] (closed_form)               0.1564642473395035357200945445658656e1+/-0.844e-31 
y[1] (numeric)                   0.1564642473395035357224649258711495e1+/-0.164e-29 
absolute error                   0.23703813052839e-19+/-0.172e-29 
relative error                   0.1514966738785081269615057936561839e-17+/-0.109e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.7e0+/-0.14e-99 
y[1] (closed_form)               0.1644217687237691053672614351398718e1+/-0.872e-31 
y[1] (numeric)                   0.1644217687237691053699696122590971e1+/-0.18e-29 
absolute error                   0.27081771192253e-19+/-0.188e-29 
relative error                   0.1647091586622617972896414768450954e-17+/-0.114e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.8e0+/-0.16e-99 
y[1] (closed_form)               0.1717356090899522761627174610581384e1+/-0.888e-31 
y[1] (numeric)                   0.1717356090899522761657374155969814e1+/-0.22e-29 
absolute error                   0.3019954538843e-19+/-0.228e-29 
relative error                   0.1758490597754364198989490444039361e-17+/-0.132e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.9e0+/-0.18e-99 
y[1] (closed_form)               0.1783326909627483388461382315713547e1+/-0.889e-31 
y[1] (numeric)                   0.1783326909627483388494408299585749e1+/-0.26e-29 
absolute error                   0.33025983872202e-19+/-0.268e-29 
relative error                   0.1851931000082354536417555780352911e-17+/-0.15e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.1e1+/-0.20e-99 
y[1] (closed_form)               0.1841470984807896506652502321630299e1+/-0.876e-31 
y[1] (numeric)                   0.1841470984807896506688035167434832e1+/-0.314e-29 
absolute error                   0.35532845804533e-19+/-0.322e-29 
relative error                   0.1929590316528381814571249372911017e-17+/-0.174e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.11e1+/-0.22e-99 
y[1] (closed_form)               0.1891207360061435339951802577871702e1+/-0.847e-31 
y[1] (numeric)                   0.1891207360061435339989497661321361e1+/-0.35e-29 
absolute error                   0.37695083449659e-19+/-0.358e-29 
relative error                   0.1993175589610357999066085018870656e-17+/-0.189e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.12e1+/-0.24e-99 
y[1] (closed_form)               0.1932039085967226349670134435494825e1+/-0.802e-31 
y[1] (numeric)                   0.193203908596722634970962552793859e1+/-0.37e-29 
absolute error                   0.39491092443765e-19+/-0.378e-29 
relative error                   0.2044011051877596281447391506266803e-17+/-0.195e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.13e1+/-0.26e-99 
y[1] (closed_form)               0.1963558185417192964701348630039554e1+/-0.742e-31 
y[1] (numeric)                   0.196355818541719296474225155769822e1+/-0.425e-29 
absolute error                   0.40902927658666e-19+/-0.432e-29 
relative error                   0.2083102398617000664303962542656671e-17+/-0.22e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.14e1+/-0.28e-99 
y[1] (closed_form)               0.1985449729988460180659474578806096e1+/-0.659e-31 
y[1] (numeric)                   0.1985449729988460180701391061309681e1+/-0.49e-29 
absolute error                   0.41916482503585e-19+/-0.496e-29 
relative error                   0.2111183268479359924923907184739415e-17+/-0.249e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.15e1+/-0.30e-99 
y[1] (closed_form)               0.1997494986604054430941723371141486e1+/-0.685e-31 
y[1] (numeric)                   0.1997494986604054430984245001015034e1+/-0.51e-29 
absolute error                   0.42521629873548e-19+/-0.516e-29 
relative error                   0.2128747764510744299054774499671138e-17+/-0.258e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.16e1+/-0.32e-99 
y[1] (closed_form)               0.1999573603041505164342113825546232e1+/-0.715e-31 
y[1] (numeric)                   0.1999573603041505164384826148882303e1+/-0.53e-29 
absolute error                   0.42712323336071e-19+/-0.537e-29 
relative error                   0.2136071574014693570784252039912594e-17+/-0.268e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.17e1+/-0.34e-99 
y[1] (closed_form)               0.1991664810452468615346133398647874e1+/-0.751e-31 
y[1] (numeric)                   0.1991664810452468615388620056192983e1+/-0.55e-29 
absolute error                   0.42486657545109e-19+/-0.557e-29 
relative error                   0.2133223287479625355679185418768755e-17+/-0.279e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.18e1+/-0.36e-99 
y[1] (closed_form)               0.1973847630878195186532373178843356e1+/-0.792e-31 
y[1] (numeric)                   0.1973847630878195186574220066122009e1+/-0.572e-29 
absolute error                   0.41846887278653e-19+/-0.579e-29 
relative error                   0.2120066748011074992029314944292896e-17+/-0.293e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.19e1+/-0.38e-99 
y[1] (closed_form)               0.194630008768741448848970961163496e1+/-0.926e-31 
y[1] (numeric)                   0.194630008768741448853050901654468e1+/-0.603e-29 
absolute error                   0.4079940490972e-19+/-0.612e-29 
relative error                   0.2096254589301163723244150602849596e-17+/-0.314e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.2e1+/-0.40e-99 
y[1] (closed_form)               0.1909297426825681695396019865911743e1+/-0.107e-30 
y[1] (numeric)                   0.1909297426825681695435374542447643e1+/-0.662e-29 
absolute error                   0.393546765359e-19+/-0.672e-29 
relative error                   0.2061212463965315479444694338642663e-17+/-0.351e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.21e1+/-0.42e-99 
y[1] (closed_form)               0.1863209366648873770680759313269029e1+/-0.123e-30 
y[1] (numeric)                   0.1863209366648873770718286450674552e1+/-0.695e-29 
absolute error                   0.37527137405523e-19+/-0.707e-29 
relative error                   0.2014112749605722551733428105800281e-17+/-0.379e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.22e1+/-0.44e-99 
y[1] (closed_form)               0.180849640381959018430403691041612e1+/-0.140e-30 
y[1] (numeric)                   0.1808496403819590184339371958101615e1+/-0.766e-29 
absolute error                   0.35335047685495e-19+/-0.78e-29 
relative error                   0.1953835662092912368156626059334811e-17+/-0.431e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.23e1+/-0.46e-99 
y[1] (closed_form)               0.1745705212176720177385406211643506e1+/-0.155e-30 
y[1] (numeric)                   0.1745705212176720177418206521655177e1+/-0.79e-29 
absolute error                   0.32800310011671e-19+/-0.805e-29 
relative error                   0.1878914594679607268959789981541155e-17+/-0.461e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.24e1+/-0.48e-99 
y[1] (closed_form)               0.1675463180551150926565771525341286e1+/-0.173e-30 
y[1] (numeric)                   0.1675463180551150926595719775986319e1+/-0.84e-29 
absolute error                   0.29948250645033e-19+/-0.857e-29 
relative error                   0.1787460983486452518014317962586448e-17+/-0.511e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.25e1+/-0.50e-99 
y[1] (closed_form)               0.1598472144103956494051854702186177e1+/-0.188e-30 
y[1] (numeric)                   0.1598472144103956494078662068606161e1+/-0.883e-29 
absolute error                   0.26807366419984e-19+/-0.901e-29 
relative error                   0.167706184426574438344544318009374e-17+/-0.563e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.26e1+/-0.52e-99 
y[1] (closed_form)               0.151550137182146423525772693520938e1+/-0.205e-30 
y[1] (numeric)                   0.1515501371821464235281135975222871e1+/-0.911e-29 
absolute error                   0.23409040013491e-19+/-0.931e-29 
relative error                   0.1544639975175735755928755217133949e-17+/-0.614e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.27e1+/-0.54e-99 
y[1] (closed_form)               0.1427379880233829934556053085857896e1+/-0.219e-30 
y[1] (numeric)                   0.1427379880233829934575840312237546e1+/-0.948e-29 
absolute error                   0.1978722637965e-19+/-0.969e-29 
relative error                   0.1386262105390507832167986834638176e-17+/-0.678e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.28e1+/-0.56e-99 
y[1] (closed_form)               0.1334988150155904919543853752712435e1+/-0.232e-30 
y[1] (numeric)                   0.1334988150155904919559831866195525e1+/-0.99e-29 
absolute error                   0.1597811348309e-19+/-0.101e-28 
relative error                   0.1196873056979870272516911132861993e-17+/-0.756e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.29e1+/-0.58e-99 
y[1] (closed_form)               0.1239249329213982328184256918739585e1+/-0.245e-30 
y[1] (numeric)                   0.1239249329213982328196276679460328e1+/-0.101e-28 
absolute error                   0.12019760720743e-19+/-0.103e-28 
relative error                   0.9699227134838768830270862010710065e-18+/-0.831e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.3e1+/-0.60e-99 
y[1] (closed_form)               0.1141120008059867222100744802808131e1+/-0.255e-30 
y[1] (numeric)                   0.1141120008059867222108696521453068e1+/-0.103e-28 
absolute error                   0.7951718644937e-20+/-0.105e-28 
relative error                   0.6968345650565286121302369611783526e-18+/-0.92e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.31e1+/-0.62e-99 
y[1] (closed_form)               0.1041580662433290579194698271596686e1+/-0.264e-30 
y[1] (numeric)                   0.1041580662433290579198512905384098e1+/-0.105e-28 
absolute error                   0.3814633787412e-20+/-0.107e-28 
relative error                   0.3662350814482707719835348299721288e-18+/-0.102e-26%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.32e1+/-0.64e-99 
y[1] (closed_form)               0.9416258565724200908627825853809178e0+/-0.284e-30 
y[1] (numeric)                   0.9416258565724200908624324279134179e0+/-0.107e-28 
absolute error                   0.3501574674999e-21+/-0.109e-28 
relative error                   0.3718647539846624004932095410038687e-19+/-0.115e-26%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.33e1+/-0.66e-99 
y[1] (closed_form)               0.84225430585675161798834572239755e0+/-0.319e-30 
y[1] (numeric)                   0.8422543058567516179838446804952603e0+/-0.109e-28 
absolute error                   0.45010419022897e-20+/-0.112e-28 
relative error                   0.5344041426670041017010527418859878e-18+/-0.132e-26%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.34e1+/-0.68e-99 
y[1] (closed_form)               0.744458897973168680750097570636293e0+/-0.359e-30 
y[1] (numeric)                   0.7444588979731686807415010253845472e0+/-0.112e-28 
absolute error                   0.85965452517458e-20+/-0.115e-28 
relative error                   0.1154737390492662400247256996559618e-17+/-0.154e-26%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.35e1+/-0.70e-99 
y[1] (closed_form)               0.649216772310380151879631199956399e0+/-0.407e-30 
y[1] (numeric)                   0.6492167723103801518670354533561829e0+/-0.115e-28 
absolute error                   0.125957466002161e-19+/-0.119e-28 
relative error                   0.194014497736886487469819723474461e-17+/-0.183e-26%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.36e1+/-0.72e-99 
y[1] (closed_form)               0.55747955670514761573327265250734e0+/-0.456e-30 
y[1] (numeric)                   0.5574795567051476157168139652575578e0+/-0.119e-28 
absolute error                   0.164586872497822e-19+/-0.123e-28 
relative error                   0.2952339157880051626475973540657703e-17+/-0.22e-26%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.37e1+/-0.74e-99 
y[1] (closed_form)               0.470163859091506786789222374298825e0+/-0.517e-30 
y[1] (numeric)                   0.4701638590915067867690756043244292e0+/-0.124e-28 
absolute error                   0.201467699743958e-19+/-0.129e-28 
relative error                   0.4285052877804179712439847850856604e-17+/-0.274e-26%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.38e1+/-0.76e-99 
y[1] (closed_form)               0.388142109057280924266413913881157e0+/-0.586e-30 
y[1] (numeric)                   0.3881421090572809242427907692105614e0+/-0.129e-28 
absolute error                   0.236231446705956e-19+/-0.134e-28 
relative error                   0.6086210209959301926433975501792736e-17+/-0.345e-26%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.39e1+/-0.78e-99 
y[1] (closed_form)               0.312233840816026181909111874621362e0+/-0.663e-30 
y[1] (numeric)                   0.3122338408160261818822587980698095e0+/-0.134e-28 
absolute error                   0.268530765515525e-19+/-0.14e-28 
relative error                   0.8600309460810437162922655471163981e-17+/-0.448e-26%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.4e1+/-0.80e-99 
y[1] (closed_form)               0.243197504692071748627360905488224e0+/-0.749e-30 
y[1] (numeric)                   0.2431975046920717485975566122826529e0+/-0.142e-28 
absolute error                   0.298042932055711e-19+/-0.149e-28 
relative error                   0.1225518051400579255915410841252922e-16+/-0.612e-26%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.41e1+/-0.82e-99 
y[1] (closed_form)               0.181722888935589495734962975641578e0+/-0.851e-30 
y[1] (numeric)                   0.1817228889355894957025156685902033e0+/-0.15e-28 
absolute error                   0.324473070513747e-19+/-0.158e-28 
relative error                   0.1785537707518805647677791772975366e-16+/-0.869e-26%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.42e1+/-0.84e-99 
y[1] (closed_form)               0.128424227586411939981422902091227e0+/-0.962e-30 
y[1] (numeric)                   0.1284242275864119399466671921228906e0+/-0.16e-28 
absolute error                   0.347557099683364e-19+/-0.169e-28 
relative error                   0.2706320343250697061257518084533631e-16+/-0.131e-25%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.43e1+/-0.86e-99 
y[1] (closed_form)               0.83834063250545015968290639715396e-1+/-0.108e-29 
y[1] (numeric)                   0.838340632505450159315842025578951e-1+/-0.17e-28 
absolute error                   0.367064371575009e-19+/-0.18e-28 
relative error                   0.437846332794352142498229447188019e-16+/-0.214e-25%
Desired digits                   8 
Estimated correct digits         11 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.44e1+/-0.88e-99 
y[1] (closed_form)               0.4839792611048404596460766661964e-1+/-0.122e-29 
y[1] (numeric)                   0.48397926110484045926327669021978e-1+/-0.183e-28 
absolute error                   0.38279997597662e-19+/-0.195e-28 
relative error                   0.7909429323536596321597891793713437e-16+/-0.402e-25%
Desired digits                   8 
Estimated correct digits         11 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
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]                             0.45e1+/-0.90e-99 
y[1] (closed_form)               0.22469882334902944610864985501343e-1+/-0.137e-29 
y[1] (numeric)                   0.224698823349029445714043167083588e-1+/-0.197e-28 
absolute error                   0.394606687929842e-19+/-0.21e-28 
relative error                   0.1756158230151882307149164218772438e-15+/-0.934e-25%
Desired digits                   8 
Estimated correct digits         11 
Correct digits                   18 
h                                0.5e-1+/-0.1e-100 
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]                             0.46e1+/-0.92e-99 
y[1] (closed_form)               0.6308996366535543861895340091119e-2+/-0.156e-29 
y[1] (numeric)                   0.630899636653554382165868622386986e-2+/-0.213e-28 
absolute error                   0.4023665386724914e-19+/-0.228e-28 
relative error                   0.6377663185966340058519515034219326e-15+/-0.361e-24%
Desired digits                   8 
Estimated correct digits         10 
Correct digits                   18 
h                                0.5e-1+/-0.1e-100 
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]                             0.47e1+/-0.94e-99 
y[1] (closed_form)               0.76742435899115820463458425033e-4+/-0.176e-29 
y[1] (numeric)                   0.7674243589911577986325899088662e-4+/-0.23e-28 
absolute error                   0.4060019943414638e-19+/-0.247e-28 
relative error                   0.5290449665621592646545714221209363e-13+/-0.321e-22%
Desired digits                   8 
Estimated correct digits         8 
Correct digits                   16 
h                                0.5e-1+/-0.1e-100 
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]                             0.48e1+/-0.96e-99 
y[1] (closed_form)               0.3835391164159328218403533496345e-2+/-0.199e-29 
y[1] (numeric)                   0.3835391164159328177855860429957232e-2+/-0.251e-28 
absolute error                   0.40547673066387768e-19+/-0.27e-28 
relative error                   0.1057197853645140052650619363225111e-14+/-0.703e-24%
Desired digits                   8 
Estimated correct digits         10 
Correct digits                   17 
h                                0.5e-1+/-0.1e-100 
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]                             0.49e1+/-0.98e-99 
y[1] (closed_form)               0.17547387375667487723622750081641e-1+/-0.226e-29 
y[1] (numeric)                   0.1754738737566748768354315049147317e-1+/-0.275e-28 
absolute error                   0.4007959959016783e-19+/-0.297e-28 
relative error                   0.2284077893313347796678206453463725e-15+/-0.169e-24%
Desired digits                   8 
Estimated correct digits         11 
Correct digits                   18 
h                                0.5e-1+/-0.1e-100 
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  )   =   cos  (  x  )   ; 
Iterations                      100 
Total Elapsed Time              1 Minutes 58 Seconds
Elapsed Time(since restart)     1 Minutes 58 Seconds
Time to Timeout                 18 Minutes 2 Seconds
Percent Done                    0.101e3+/-0.605e-29%