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/sub_sin_cospostode.ode#################
diff  (  y  ,  x  ,  1  )   =  m1  *  sin ( x )   -  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(0.1) 
x_end=c(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=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(cos(c(x)) - sin(c(x)))  
end
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
 
TOP MAIN SOLVE Loop
x[1]                             0.1e0+/-0.50e-31 
y[1] (closed_form)               0.8951707486311976137887477893932477e0+/-0.672e-31 
y[1] (numeric)                   0.8951707486311976137887477893932477e0+/-0.155e-30 
absolute error                   0.0e0+/-0.2222e-30 
relative error                   0.0e0+/-0.2482208007128977620449307023608317e-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]                             0.2e0+/-0.5e-31 
y[1] (closed_form)               0.7813972470461804156647838896297794e0+/-0.807e-31 
y[1] (numeric)                   0.7813972470461804156601317103007553e0+/-0.47e-30 
absolute error                   0.46521793290241e-20+/-0.55e-30 
relative error                   0.5953667416426356009390382303067693e-18+/-0.703e-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+/-0.5e-31 
y[1] (closed_form)               0.6598162824642664445369894818830228e0+/-0.955e-31 
y[1] (numeric)                   0.6598162824642664445273476115700407e0+/-0.705e-30 
absolute error                   0.96418703129821e-20+/-0.8e-30 
relative error                   0.1461296207630989023195663377983335e-17+/-0.121e-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]                             0.4e0+/-0.5e-31 
y[1] (closed_form)               0.5316426516942345911322149752560964e0+/-0.11e-30 
y[1] (numeric)                   0.5316426516942345911172957576471605e0+/-0.967e-30 
absolute error                   0.149192176089359e-19+/-0.107e-29 
relative error                   0.2806249190389720520550716832049933e-17+/-0.201e-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+/-0.5e-31 
y[1] (closed_form)               0.3981570232861697158429936473882593e0+/-0.127e-30 
y[1] (numeric)                   0.3981570232861697158225621556810945e0+/-0.106e-29 
absolute error                   0.204314917071648e-19+/-0.118e-29 
relative error                   0.5131516088435279211761450928879412e-17+/-0.296e-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+/-0.5e-31 
y[1] (closed_form)               0.2606931415146429400400070532967192e0+/-0.143e-30 
y[1] (numeric)                   0.2606931415146429400138834375097268e0+/-0.11e-29 
absolute error                   0.261236157869924e-19+/-0.124e-29 
relative error                   0.1002082971389757713034532112343175e-16+/-0.475e-27%
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]                             0.7e0+/-0.5e-31 
y[1] (closed_form)               0.1206245000467973725832456387931456e0+/-0.162e-30 
y[1] (numeric)                   0.1206245000467973725513069227669655e0+/-0.113e-29 
absolute error                   0.319387160261801e-19+/-0.129e-29 
relative error                   0.2647780178470309468388198875659343e-16+/-0.106e-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]                             0.8e0+/-0.5e-31 
y[1] (closed_form)               -0.206493815523573407064246289390596e-1+/-0.181e-30 
y[1] (numeric)                   -0.206493815523573407442433188044141e-1+/-0.117e-29 
absolute error                   0.378186898653545e-19+/-0.135e-29 
relative error                   0.1831468403519189415135471050195655e-15+/-0.653e-26%
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]                             0.9e0+/-0.5e-31 
y[1] (closed_form)               -0.161716941356818931976666164306414e0+/-0.201e-30 
y[1] (numeric)                   -0.161716941356818932020370950855989e0+/-0.121e-29 
absolute error                   0.43704786549575e-19+/-0.141e-29 
relative error                   0.2702548427078085508894077269635827e-16+/-0.871e-27%
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]                             0.1e1+/-0.5e-31 
y[1] (closed_form)               -0.301168678939756789251565714187322e0+/-0.225e-30 
y[1] (numeric)                   -0.30116867893975678930110390833378e0+/-0.131e-29 
absolute error                   0.49538194146458e-19+/-0.153e-29 
relative error                   0.1644865406351475125763794698823284e-16+/-0.508e-27%
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]                             0.11e1+/-0.5e-31 
y[1] (closed_form)               -0.437611238635857952180432526086986e0+/-0.251e-30 
y[1] (numeric)                   -0.437611238635857952235693153262551e0+/-0.145e-29 
absolute error                   0.55260627175565e-19+/-0.17e-29 
relative error                   0.1262778975874248335332047947657658e-16+/-0.388e-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+/-0.5e-31 
y[1] (closed_form)               -0.569681331490552772031761079871749e0+/-0.28e-30 
y[1] (numeric)                   -0.569681331490552772092575988849401e0+/-0.165e-29 
absolute error                   0.60814908977652e-19+/-0.193e-29 
relative error                   0.106752504630144291901237163802729e-16+/-0.338e-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+/-0.5e-31 
y[1] (closed_form)               -0.696059356792605557703364520746682e0+/-0.311e-30 
y[1] (numeric)                   -0.696059356792605557769510063751637e0+/-0.188e-29 
absolute error                   0.66145543004955e-19+/-0.219e-29 
relative error                   0.9502859542000726606045038128226205e-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]                             0.14e1+/-0.5e-31 
y[1] (closed_form)               -0.815482587088219242042726543602446e0+/-0.348e-30 
y[1] (numeric)                   -0.815482587088219242113925810926793e0+/-0.218e-29 
absolute error                   0.71199267324347e-19+/-0.252e-29 
relative error                   0.873093655850736564468831363268766e-17+/-0.309e-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+/-0.5e-31 
y[1] (closed_form)               -0.92675778493635152085353351970721e0+/-0.398e-30 
y[1] (numeric)                   -0.926757784936351520929459106500184e0+/-0.25e-29 
absolute error                   0.75925586792974e-19+/-0.289e-29 
relative error                   0.819260307569884263342756266418794e-17+/-0.311e-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+/-0.5e-31 
y[1] (closed_form)               -0.102877312534279389054788428849272e1+/-0.466e-30 
y[1] (numeric)                   -0.102877312534279389062816156608173e1+/-0.282e-29 
absolute error                   0.8027727758901e-19+/-0.328e-29 
relative error                   0.7803205158791554692755530293751932e-17+/-0.318e-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+/-0.5e-31 
y[1] (closed_form)               -0.112050930474799329943377625598272e1+/-0.54e-30 
y[1] (numeric)                   -0.112050930474799329951798711503922e1+/-0.313e-29 
absolute error                   0.842108590565e-19+/-0.367e-29 
relative error                   0.7515409171496289777543540495622136e-17+/-0.327e-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+/-0.5e-31 
y[1] (closed_form)               -0.120104972557128224184904748537391e1+/-0.641e-30 
y[1] (numeric)                   -0.120104972557128224193673451352359e1+/-0.361e-29 
absolute error                   0.8768702814968e-19+/-0.425e-29 
relative error                   0.7300865757907854349979935912010399e-17+/-0.353e-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+/-0.5e-31 
y[1] (closed_form)               -0.126958965455091791076854330671525e1+/-0.751e-30 
y[1] (numeric)                   -0.126958965455091791085921435885129e1+/-0.417e-29 
absolute error                   0.9067105213604e-19+/-0.492e-29 
relative error                   0.7141760474419773619408604320702373e-17+/-0.387e-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+/-0.5e-31 
y[1] (closed_form)               -0.132544426337282408239358809541248e1+/-0.879e-30 
y[1] (numeric)                   -0.132544426337282408248672121104681e1+/-0.473e-29 
absolute error                   0.9313311563433e-19+/-0.56e-29 
relative error                   0.7026558430856726112390974876864364e-17+/-0.422e-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+/-0.5e-31 
y[1] (closed_form)               -0.136805547124873122230169783698817e1+/-0.102e-29 
y[1] (numeric)                   -0.136805547124873122239674645550805e1+/-0.531e-29 
absolute error                   0.9504861851988e-19+/-0.633e-29 
relative error                   0.6947716705750366413009860937877745e-17+/-0.462e-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+/-0.5e-31 
y[1] (closed_form)               -0.139699752107493589282817952307102e1+/-0.116e-29 
y[1] (numeric)                   -0.139699752107493589292457794479209e1+/-0.59e-29 
absolute error                   0.9639842172107e-19+/-0.706e-29 
relative error                   0.6900400341934402286963879512107727e-17+/-0.505e-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+/-0.5e-31 
y[1] (closed_form)               -0.14119812334565443707032867828095e1+/-0.134e-29 
y[1] (numeric)                   -0.141198123345654437080045582125998e1+/-0.63e-29 
absolute error                   0.9716903845048e-19+/-0.764e-29 
relative error                   0.6881751410577122828460150866770421e-17+/-0.541e-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+/-0.5e-31 
y[1] (closed_form)               -0.141285689609239642617459375267605e1+/-0.152e-29 
y[1] (numeric)                   -0.141285689609239642627194652163654e1+/-0.699e-29 
absolute error                   0.9735276896049e-19+/-0.851e-29 
relative error                   0.6890490411997354409587098304604128e-17+/-0.602e-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+/-0.5e-31 
y[1] (closed_form)               -0.139961575965089020888535749265351e1+/-0.175e-29 
y[1] (numeric)                   -0.139961575965089020898230527013008e1+/-0.769e-29 
absolute error                   0.9694777747657e-19+/-0.944e-29 
relative error                   0.6926742343966742395646629942742631e-17+/-0.674e-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+/-0.5e-31 
y[1] (closed_form)               -0.137239012519041146905542908685456e1+/-0.199e-29 
y[1] (numeric)                   -0.137239012519041146915138719739435e1+/-0.835e-29 
absolute error                   0.9595811053979e-19+/-0.103e-28 
relative error                   0.6992043208302475056797782013926573e-17+/-0.75e-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+/-0.5e-31 
y[1] (closed_form)               -0.13314520222508910825385803678012e1+/-0.225e-29 
y[1] (numeric)                   -0.133145202225089108263297402437621e1+/-0.904e-29 
absolute error                   0.9439365657501e-19+/-0.112e-28 
relative error                   0.7089527448043712373342532592474607e-17+/-0.841e-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+/-0.5e-31 
y[1] (closed_form)               -0.127721049082456307213064187007857e1+/-0.255e-29 
y[1] (numeric)                   -0.127721049082456307222291191716766e1+/-0.969e-29 
absolute error                   0.9227004708909e-19+/-0.122e-28 
relative error                   0.7224341465400957368560450361876233e-17+/-0.955e-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+/-0.5e-31 
y[1] (closed_form)               -0.12102074943635728499653635880851e1+/-0.29e-29 
y[1] (numeric)                   -0.121020749436357285005497208857118e1+/-0.101e-28 
absolute error                   0.8960850048608e-19+/-0.130e-28 
relative error                   0.7404391470340675555979503519859288e-17+/-0.107e-26%
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+/-0.5e-31 
y[1] (closed_form)               -0.113111250466031267937231759753937e1+/-0.327e-29 
y[1] (numeric)                   -0.113111250466031267945875320759919e1+/-0.103e-28 
absolute error                   0.8643561005982e-19+/-0.135e-28 
relative error                   0.764164569869888420389895520881455e-17+/-0.119e-26%
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+/-0.5e-31 
y[1] (closed_form)               -0.104071581270657004368707432613812e1+/-0.371e-29 
y[1] (numeric)                   -0.104071581270657004376985740442078e1+/-0.105e-28 
absolute error                   0.8278307828266e-19+/-0.142e-28 
relative error                   0.7954436482267681224793446929607e-17+/-0.136e-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+/-0.5e-31 
y[1] (closed_form)               -0.939920632367173175524443307664471e0+/-0.419e-29 
y[1] (numeric)                   -0.939920632367173175603130707709192e0+/-0.108e-28 
absolute error                   0.78687400044721e-19+/-0.149e-28 
relative error                   0.8371706858540619638392913993629136e-17+/-0.158e-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+/-0.5e-31 
y[1] (closed_form)               -0.82973407576561650192493677350037e0+/-0.469e-29 
y[1] (numeric)                   -0.829734075765616501999126271509472e0+/-0.112e-28 
absolute error                   0.74189498009102e-19+/-0.158e-28 
relative error                   0.8941358463631312731874567576514283e-17+/-0.19e-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+/-0.5e-31 
y[1] (closed_form)               -0.71125709055262969503229911040197e0+/-0.532e-29 
y[1] (numeric)                   -0.711257090552629695101633424128117e0+/-0.116e-28 
absolute error                   0.69334313726147e-19+/-0.169e-28 
relative error                   0.9748136735238154418780116239771593e-17+/-0.237e-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+/-0.5e-31 
y[1] (closed_form)               -0.585673459601176489578288826628145e0+/-0.605e-29 
y[1] (numeric)                   -0.585673459601176489642459185220458e0+/-0.12e-28 
absolute error                   0.64170358592313e-19+/-0.18e-28 
relative error                   0.109566785962967845945034122270051e-16+/-0.307e-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+/-0.5e-31 
y[1] (closed_form)               -0.454237973039294621603564377773294e0+/-0.685e-29 
y[1] (numeric)                   -0.454237973039294621662313606913576e0+/-0.125e-28 
absolute error                   0.58749229140282e-19+/-0.193e-28 
relative error                   0.1293357945113932579451662078656857e-16+/-0.424e-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+/-0.5e-31 
y[1] (closed_form)               -0.318263890801914945624892480653214e0+/-0.777e-29 
y[1] (numeric)                   -0.318263890801914945678017572156848e0+/-0.131e-28 
absolute error                   0.53125091503634e-19+/-0.208e-28 
relative error                   0.166921517140311270181492250249695e-16+/-0.653e-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+/-0.5e-31 
y[1] (closed_form)               -0.179109820971697624262982088231873e0+/-0.88e-29 
y[1] (numeric)                   -0.179109820971697624310336228438319e0+/-0.139e-28 
absolute error                   0.47354140206446e-19+/-0.227e-28 
relative error                   0.2643860618560316335879754271844242e-16+/-0.126e-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]                             0.39e1+/-0.5e-31 
y[1] (closed_form)               -0.38166145016166311281442359235723e-1+/-0.858e-29 
y[1] (numeric)                   -0.381661450161663113229363959221999e-1+/-0.147e-28 
absolute error                   0.414940366864769e-19+/-0.232e-28 
relative error                   0.1087194859970818888575925197147065e-15+/-0.607e-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]                             0.4e1+/-0.5e-31 
y[1] (closed_form)               0.103158874444316336733470911414026e0+/-0.11e-28 
y[1] (numeric)                   0.1031588744443163366978675782529616e0+/-0.156e-28 
absolute error                   0.356033331610644e-19+/-0.266e-28 
relative error                   0.3451310743050280422012224589043945e-16+/-0.257e-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]                             0.41e1+/-0.5e-31 
y[1] (closed_form)               0.243453164531141592730008344698636e0+/-0.125e-28 
y[1] (numeric)                   0.2434531645311415927002674571060304e0+/-0.167e-28 
absolute error                   0.297408875926056e-19+/-0.292e-28 
relative error                   0.1221626658658662044739743049878054e-16+/-0.119e-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]                             0.42e1+/-0.5e-31 
y[1] (closed_form)               0.381314951072888482363032216531611e0+/-0.141e-28 
y[1] (numeric)                   0.3813149510728884823390669409323539e0+/-0.178e-28 
absolute error                   0.239652755992571e-19+/-0.319e-28 
relative error                   0.6284903209755373434707995218569015e-17+/-0.836e-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]                             0.43e1+/-0.5e-31 
y[1] (closed_form)               0.515366764669479687124946963948577e0+/-0.137e-28 
y[1] (numeric)                   0.5153667646694796871066127587615046e0+/-0.192e-28 
absolute error                   0.183342051870724e-19+/-0.329e-28 
relative error                   0.3557506312777208479002520142595454e-17+/-0.638e-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]                             0.44e1+/-0.5e-31 
y[1] (closed_form)               0.644269203911096270916252591162678e0+/-0.18e-28 
y[1] (numeric)                   0.6442692039110962709033486510125788e0+/-0.207e-28 
absolute error                   0.129039401500992e-19+/-0.387e-28 
relative error                   0.2002880173654836862799697905077568e-17+/-0.6e-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]                             0.45e1+/-0.5e-31 
y[1] (closed_form)               0.766734318234317349408653189704812e0+/-0.203e-28 
y[1] (numeric)                   0.7667343182343173494009244518032198e0+/-0.225e-28 
absolute error                   0.77287379015922e-20+/-0.428e-28 
relative error                   0.1008007300284981376316392845846215e-17+/-0.558e-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]                             0.46e1+/-0.5e-31 
y[1] (closed_form)               0.881538476698409938708196838679723e0+/-0.231e-28 
y[1] (numeric)                   0.8815384766984099387053365313279332e0+/-0.246e-28 
absolute error                   0.28603073517898e-20+/-0.477e-28 
relative error                   0.3244676695794824896289633652884183e-18+/-0.541e-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]                             0.47e1+/-0.5e-31 
y[1] (closed_form)               0.9875345941012101470290282452478554e0+/-0.259e-28 
y[1] (numeric)                   0.9875345941012101470306809529986102e0+/-0.269e-28 
absolute error                   0.16527077507548e-20+/-0.528e-28 
relative error                   0.1673569473542329178920376604003574e-18+/-0.534e-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]                             0.48e1+/-0.5e-31 
y[1] (closed_form)               0.1083663592275287241101811724153138e1+/-0.291e-28 
y[1] (numeric)                   0.1083663592275287241107576939003807e1+/-0.296e-28 
absolute error                   0.5765214850669e-20+/-0.587e-28 
relative error                   0.5320114924747273635471321016234435e-18+/-0.541e-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]                             0.49e1+/-0.5e-31 
y[1] (closed_form)               0.1168964982046907916770706394040314e1+/-0.329e-28 
y[1] (numeric)                   0.1168964982046907916780142517176823e1+/-0.325e-28 
absolute error                   0.9436123136509e-20+/-0.654e-28 
relative error                   0.8072203429041940071900536981075695e-18+/-0.559e-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
Finished!
diff  (  y  ,  x  ,  1  )   =  m1  *  sin ( x )   -  cos ( x )  ; 
Iterations                      98 
Total Elapsed Time              3 Minutes 9 Seconds
Elapsed Time(since restart)     3 Minutes 8 Seconds
Time to Timeout                 16 Minutes 51 Seconds
Percent Done                    0.1010204081632653061224489795918367e3+/-0.914e-29%