Quadts test:  Quadlevel =    11
Digits1 =    34  Digits2 =    68  Epsilon1 =   -34  Epsilon2 =   -68
initqes: Exp-sinh quadrature initialization
           0       24576
        1024       24576
        2048       24576
        3072       24576
        4096       24576
        5120       24576
        6144       24576
        7168       24576
        8192       24576
        9216       24576
       10240       24576
initqes: Table spaced used =   10778
initqss: Sinh-sinh quadrature initialization
           0       24576
        1024       24576
        2048       24576
        3072       24576
        4096       24576
        5120       24576
        6144       24576
        7168       24576
        8192       24576
        9216       24576
       10240       24576
initqss: Table spaced used =   10787
initqts: Tanh-sinh quadrature initialization
           0       24576
        1024       24576
        2048       24576
        3072       24576
        4096       24576
        5120       24576
        6144       24576
        7168       24576
        8192       24576
        9216       24576
initqts: Table spaced used =    9500
Quadrature initialization completed: cpu time =    0.000000

Continuous functions on finite intervals:

Problem 1: Int_0^1 t*log(1+t) dt = 1/4

quadts: Iteration  1 of 11; est error = 10^      0; approx value =
      0.24996055656262656429379566503645
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
      0.24999999999628619317526003676929
quadts: Iteration  3 of 11; est error = 10^    -23; approx value =
      0.24999999999999999999999940795412
quadts: Iteration  4 of 11; est error = 10^    -30; approx value =
      0.25000000000000000000000000000000
quadts: Estimated error = 10^    -30
Adjust nq1 and neps2 in initqts for greater accuracy.
Quadrature completed: CPU time =    0.000000
Result =
      0.25000000000000000000000000000000
Actual error =  -4.814825D-35

Problem 2: Int_0^1 t^2*arctan(t) dt = (pi - 2 + 2*log(2))/12

quadts: Iteration  1 of 11; est error = 10^      0; approx value =
      0.21047231245816686275584850222522
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
      0.21065725123782726843162819242030
quadts: Iteration  3 of 11; est error = 10^    -22; approx value =
      0.21065725122580698782715176341962
quadts: Iteration  4 of 11; est error = 10^    -30; approx value =
      0.21065725122580698810809230218299
quadts: Estimated error = 10^    -30
Adjust nq1 and neps2 in initqts for greater accuracy.
Quadrature completed: CPU time =    0.000000
Result =
      0.21065725122580698810809230218299
Actual error =   0.000000D+00

Problem 3: Int_0^(pi/2) e^t*cos(t) dt = 1/2*(e^(pi/2) - 1)

quadts: Iteration  1 of 11; est error = 10^      0; approx value =
      1.90530948869825783052790923885813
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
      1.90523868799766148258117330028386
quadts: Iteration  3 of 11; est error = 10^    -17; approx value =
      1.90523869048267582773721156208772
quadts: Iteration  4 of 11; est error = 10^    -30; approx value =
      1.90523869048267582773651783335192
quadts: Estimated error = 10^    -30
Adjust nq1 and neps2 in initqts for greater accuracy.
Quadrature completed: CPU time =    0.000000
Result =
      1.90523869048267582773651783335192
Actual error =  -5.777790D-34

Problem 4: Int_0^1 arctan(sqrt(2+t^2))/((1+t^2)sqrt(2+t^2)) dt = 5*Pi^2/96

quadts: Iteration  1 of 11; est error = 10^      0; approx value =
      0.51397487843142191233787336767334
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
      0.51404189362670924962704874731018
quadts: Iteration  3 of 11; est error = 10^    -17; approx value =
      0.51404189589007076028810766873946
quadts: Terms too large -- adjust neps2 in call to initqss.
Quadrature completed: CPU time =    0.000000
Result =
      0.51404189589007076028810766873946
Actual error =   1.109522D-18

Continuous functions on finite intervals, but non-diff at an endpoint:

Problem 5: Int_0^1 sqrt(t)*log(t) dt = -4/9

quadts: Iteration  1 of 11; est error = 10^      0; approx value =
     -0.44443925765167077174881342336278
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
     -0.44444444444411174763261625796349
quadts: Iteration  3 of 11; est error = 10^    -25; approx value =
     -0.44444444444444444444444444441205
quadts: Iteration  4 of 11; est error = 10^    -35; approx value =
     -0.44444444444444444444444444444444
quadts: Estimated error = 10^    -35
Quadrature completed: CPU time =    0.000000
Result =
     -0.44444444444444444444444444444444
Actual error =   4.814825D-35

Problem 6: Int_0^1 sqrt(1-t^2) dt = pi/4

quadts: Iteration  1 of 11; est error = 10^      0; approx value =
      0.78542738384415085579941868440919
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
      0.78539816339892810680793932178196
quadts: Iteration  3 of 11; est error = 10^    -24; approx value =
      0.78539816339744830961566089120693
quadts: Iteration  4 of 11; est error = 10^    -30; approx value =
      0.78539816339744830961566084581988
quadts: Estimated error = 10^    -30
Adjust nq1 and neps2 in initqts for greater accuracy.
Quadrature completed: CPU time =    0.000000
Result =
      0.78539816339744830961566084581988
Actual error =   9.629650D-35

Functions on finite intervals with integrable singularity at an endpoint:

Problem 7: Int_0^1 sqrt(t)/sqrt(1-t^2) dt = 2*sqrt(pi)*gamma(3/4)/gamma(1/4)

quadts: Iteration  1 of 11; est error = 10^      0; approx value =
      1.19813887389271715232039250627725
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
      1.19814023473477295213240452207519
quadts: Iteration  3 of 11; est error = 10^    -15; approx value =
      1.19814023473559220992348163384568
quadts: Estimated error = 10^    -15
Adjust nq1 and neps2 in initqts for greater accuracy.
Quadrature completed: CPU time =    0.000000
Result =
      1.19814023473559220992348163384568
Actual error =  -2.483559D-18

Problem 8: Int_0^1 log(t)^2 dt = 2

quadts: Iteration  1 of 11; est error = 10^      0; approx value =
      2.00001078314452430017981828425975
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
      2.00000000000040706415415454806329
quadts: Iteration  3 of 11; est error = 10^    -25; approx value =
      2.00000000000000000000000000002421
quadts: Iteration  4 of 11; est error = 10^    -26; approx value =
      1.99999999999999999999999999999966
quadts: Estimated error = 10^    -26
Adjust nq1 and neps2 in initqts for greater accuracy.
Quadrature completed: CPU time =    0.000000
Result =
      1.99999999999999999999999999999966
Actual error =   3.412748D-31

Problem 9: Int_0^(pi/2) log(cos(t)) dt = -pi*log(2)/2

quadts: Iteration  1 of 11; est error = 10^      0; approx value =
     -1.08872115523904193860066871766982
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
     -1.08879304514637218384703510599143
quadts: Iteration  3 of 11; est error = 10^    -23; approx value =
     -1.08879304515180106525034351896891
quadts: Iteration  4 of 11; est error = 10^    -28; approx value =
     -1.08879304515180106525034444911880
quadts: Estimated error = 10^    -28
Adjust nq1 and neps2 in initqts for greater accuracy.
Quadrature completed: CPU time =    0.000000
Result =
     -1.08879304515180106525034444911880
Actual error =  -8.474092D-33

Problem 10: Int_0^(pi/2) sqrt(tan(t)) dt = pi*sqrt(2)/2

quadts: Iteration  1 of 11; est error = 10^      0; approx value =
      2.22144192002615577364991865702346
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
      2.22144146907798139684508060396083
quadts: Iteration  3 of 11; est error = 10^    -15; approx value =
      2.22144146907918310853773234747200
quadts: Estimated error = 10^    -15
Adjust nq1 and neps2 in initqts for greater accuracy.
Quadrature completed: CPU time =    0.000000
Result =
      2.22144146907918310853773234747200
Actual error =   1.497021D-17

Functions on a semi-infinite interval:

Problem 11: Int_0^inf 1/(1+t^2) dt = pi/2

quades: Iteration  1 of 11; est error = 10^      0; approx value =
      1.57079633665285239588411468617769
quades: Iteration  2 of 11; est error = 10^      0; approx value =
      1.57079632679489707807930342870220
quades: Iteration  3 of 11; est error = 10^    -29; approx value =
      1.57079632679489661923132169163975
quades: Iteration  4 of 11; est error = 10^    -35; approx value =
      1.57079632679489661923132169163975
quades: Estimated error = 10^    -35
Quadrature completed: CPU time =    0.000000
Result =
      1.57079632679489661923132169163975
Actual error =  -3.851860D-34

Problem 12: Int_0^inf e^(-t)/sqrt(t) dt = sqrt(pi)

quades: Iteration  1 of 11; est error = 10^      0; approx value =
      1.77232401368716570730365349699206
quades: Iteration  2 of 11; est error = 10^      0; approx value =
      1.77245048675727582256940045256786
quades: Iteration  3 of 11; est error = 10^     -8; approx value =
      1.77245385093005174419197785271111
quades: Iteration  4 of 11; est error = 10^    -21; approx value =
      1.77245385090551602471084133172607
quades: Iteration  5 of 11; est error = 10^    -29; approx value =
      1.77245385090551602729816748334113
quades: Iteration  6 of 11; est error = 10^    -31; approx value =
      1.77245385090551602729816748334114
quades: Estimated error = 10^    -31
Adjust nq1 and neps2 in initqss for greater accuracy.
Quadrature completed: CPU time =    0.000000
Result =
      1.77245385090551602729816748334114
Actual error =   3.081488D-33

Problem 13: Int_0^inf e^(-t^2/2) dt = sqrt(pi/2)

quades: Iteration  1 of 11; est error = 10^      0; approx value =
      1.24881995081188789069163861332937
quades: Iteration  2 of 11; est error = 10^      0; approx value =
      1.25345484025530506212562406793067
quades: Iteration  3 of 11; est error = 10^     -6; approx value =
      1.25331406918649461380937911035155
quades: Iteration  4 of 11; est error = 10^    -13; approx value =
      1.25331413731547665494197167441163
quades: Iteration  5 of 11; est error = 10^    -26; approx value =
      1.25331413731550025120788275915919
quades: Iteration  6 of 11; est error = 10^    -35; approx value =
      1.25331413731550025120788264240552
quades: Estimated error = 10^    -35
Quadrature completed: CPU time =    0.000000
Result =
      1.25331413731550025120788264240552
Actual error =   5.777790D-34

Problem 14: Int_0^inf e^(-t)*cos(t) dt = 1/2

quades: Iteration  1 of 11; est error = 10^      0; approx value =
      0.49799967554886531074114283259261
quades: Iteration  2 of 11; est error = 10^      0; approx value =
      0.49923622783588064227136065425755
quades: Iteration  3 of 11; est error = 10^     -4; approx value =
      0.49999187771052672400436384243022
quades: Iteration  4 of 11; est error = 10^     -8; approx value =
      0.50000000023842747976213045954214
quades: Iteration  5 of 11; est error = 10^    -18; approx value =
      0.49999999999999996800545953973198
quades: Iteration  6 of 11; est error = 10^    -28; approx value =
      0.50000000000000000000000000000099
quades: Iteration  7 of 11; est error = 10^    -35; approx value =
      0.50000000000000000000000000000000
quades: Estimated error = 10^    -35
Quadrature completed: CPU time =    0.000000
Result =
      0.50000000000000000000000000000000
Actual error =  -3.851860D-34

Functions on the entire real line:

Problem 15: Int_-inf^inf 1/(1+t^2) dt = Pi

quadss: Iteration  1 of 11; est error = 10^      0; approx value =
      3.14159267330570479176822937235538
quadss: Iteration  2 of 11; est error = 10^      0; approx value =
      3.14159265358979415615860685740440
quadss: Iteration  3 of 11; est error = 10^    -29; approx value =
      3.14159265358979323846264338327950
quadss: Iteration  4 of 11; est error = 10^    -35; approx value =
      3.14159265358979323846264338327950
quadss: Estimated error = 10^    -35
Quadrature completed: CPU time =    0.000000
Result =
      3.14159265358979323846264338327950
Actual error =   0.000000D+00

Problem 16: Int_-inf^inf 1/(1+t^4) dt = Pi/Sqrt(2)

quadss: Iteration  1 of 11; est error = 10^      0; approx value =
      2.28733331207084241816596583212776
quadss: Iteration  2 of 11; est error = 10^      0; approx value =
      2.22237794743186771622578842318742
quadss: Iteration  3 of 11; est error = 10^     -6; approx value =
      2.22144165335120962401269700949434
quadss: Iteration  4 of 11; est error = 10^    -13; approx value =
      2.22144146907918753031019203350404
quadss: Iteration  5 of 11; est error = 10^    -29; approx value =
      2.22144146907918312350794049498725
quadss: Iteration  6 of 11; est error = 10^    -35; approx value =
      2.22144146907918312350794049503034
quadss: Estimated error = 10^    -35
Quadrature completed: CPU time =    0.000000
Result =
      2.22144146907918312350794049503034
Actual error =   6.548162D-33

Problem 17: Int_-inf^inf e^(-t^2/2) dt = sqrt (2*Pi)

quadss: Iteration  1 of 11; est error = 10^      0; approx value =
      2.43315462220118670045044804420178
quadss: Iteration  2 of 11; est error = 10^      0; approx value =
      2.50517628813709880708209746158373
quadss: Iteration  3 of 11; est error = 10^     -6; approx value =
      2.50662788272106477704836593591553
quadss: Iteration  4 of 11; est error = 10^    -13; approx value =
      2.50662827461520207062853266157257
quadss: Iteration  5 of 11; est error = 10^    -18; approx value =
      2.50662827463100050241424462767736
quadss: Iteration  6 of 11; est error = 10^    -35; approx value =
      2.50662827463100050241576528481105
quadss: Estimated error = 10^    -35
Quadrature completed: CPU time =    0.000000
Result =
      2.50662827463100050241576528481105
Actual error =   0.000000D+00

Problem 18: Int_-inf^inf e^(-t^2/2) cos(t) dt = sqrt (2*Pi/e)

quadss: Iteration  1 of 11; est error = 10^      0; approx value =
      1.68517478905149371816910201825217
quadss: Iteration  2 of 11; est error = 10^      0; approx value =
      1.52809750930603265638998730211235
quadss: Iteration  3 of 11; est error = 10^     -4; approx value =
      1.52035405364046715371832970925490
quadss: Iteration  4 of 11; est error = 10^    -10; approx value =
      1.52034690091411779148449965511735
quadss: Iteration  5 of 11; est error = 10^    -19; approx value =
      1.52034690106628080547938023458106
quadss: Iteration  6 of 11; est error = 10^    -35; approx value =
      1.52034690106628080561194014675497
quadss: Estimated error = 10^    -35
Quadrature completed: CPU time =    0.000000
Result =
      1.52034690106628080561194014675497
Actual error =   5.777790D-34

Total CPU time =    0.000000
Max abs error =   1.497021D-17
ALL TESTS PASSED
