Quadts test:  Quadlevel =    11
Digits1 =    70  Digits2 =   140  Epsilon1 =   -70  Epsilon2 =  -140
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
       11264       24576
initqes: Table spaced used =   12287
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
       11264       24576
       12288       24576
initqss: Table spaced used =   12291
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
       10240       24576
initqts: Table spaced used =   10945
Quadrature initialization completed: cpu time =    1.452613

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 =
2.499605565626265642937956650364502706040995938475912221549654945378881e-1      
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
2.499999999962861931752600367692878233467888640566284230669655567505079e-1      
quadts: Iteration  3 of 11; est error = 10^    -23; approx value =
2.499999999999999999999994079541174289312135764700202391674583766259619e-1      
quadts: Iteration  4 of 11; est error = 10^    -48; approx value =
2.499999999999999999999999999999999999999999999999982171636485004914394e-1      
quadts: Iteration  5 of 11; est error = 10^    -71; approx value =
2.499999999999999999999999999999999999999999999999999999999999999999278e-1      
quadts: Estimated error = 10^    -71
Quadrature completed: CPU time =    0.009726
Result =
2.499999999999999999999999999999999999999999999999999999999999999999278e-1      
Actual error =   7.211124D-68

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 =
2.104723124581668627558485022252152104985371769219415448028672815593772e-1      
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
2.106572512378272684316281924203025308278485396881668616378600379308970e-1      
quadts: Iteration  3 of 11; est error = 10^    -22; approx value =
2.106572512258069878271517634196170465600193251197711374032939764404351e-1      
quadts: Iteration  4 of 11; est error = 10^    -32; approx value =
2.106572512258069881080923021829880017002044931018003164151338019845675e-1      
quadts: Iteration  5 of 11; est error = 10^    -71; approx value =
2.106572512258069881080923021829880016956808056746346941013587176078514e-1      
quadts: Estimated error = 10^    -71
Quadrature completed: CPU time =    0.012347
Result =
2.106572512258069881080923021829880016956808056746346941013587176078514e-1      
Actual error =   3.013730D-68

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 =
1.905309488698257830527909238858130141351402721731212790129745423787285e0       
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
1.905238687997661482581173300283858306124324271389243758922510301590325e0       
quadts: Iteration  3 of 11; est error = 10^    -17; approx value =
1.905238690482675827737211562087715196977746239314373878018110204959556e0       
quadts: Iteration  4 of 11; est error = 10^    -42; approx value =
1.905238690482675827736517833351916563195085437331975334634348239808685e0       
quadts: Iteration  5 of 11; est error = 10^    -66; approx value =
1.905238690482675827736517833351916563195085437332267470010407744619368e0       
quadts: Estimated error = 10^    -66
Adjust nq1 and neps2 in initqts for greater accuracy.
Quadrature completed: CPU time =    0.008709
Result =
1.905238690482675827736517833351916563195085437332267470010407744619368e0       
Actual error =   4.135765D-66

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 =
5.139748784314219123378733676733350426679388134587228369585360873232567e-1      
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
5.140418936267092496270487473101845724239183856118601678322839063598493e-1      
quadts: Iteration  3 of 11; est error = 10^    -17; approx value =
5.140418958900707602881076687394558317202044974872838457306886922214171e-1      
quadts: Iteration  4 of 11; est error = 10^    -36; approx value =
5.140418958900707613976297395768828700674688789878061008969596040004905e-1      
quadts: Iteration  5 of 11; est error = 10^    -71; approx value =
5.140418958900707613976297395768828716309218441271245117923619466778624e-1      
quadts: Estimated error = 10^    -71
Quadrature completed: CPU time =    0.017190
Result =
5.140418958900707613976297395768828716309218441271245117923619466778624e-1      
Actual error =   2.550079D-67

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 =
-4.444392576516707717488134233627802823671186708727753169210730664085988e-1     
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
-4.444444444441117476326162579634883374927278854151820703558623322337171e-1     
quadts: Iteration  3 of 11; est error = 10^    -25; approx value =
-4.444444444444444444444444444120514627410087635323248692822329982436404e-1     
quadts: Iteration  4 of 11; est error = 10^    -57; approx value =
-4.444444444444444444444444444444444444444444444444444444444444256134436e-1     
quadts: Iteration  5 of 11; est error = 10^    -71; approx value =
-4.444444444444444444444444444444444444444444444444444444444444444442078e-1     
quadts: Estimated error = 10^    -71
Quadrature completed: CPU time =    0.014360
Result =
-4.444444444444444444444444444444444444444444444444444444444444444442078e-1     
Actual error =  -2.341436D-67

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

quadts: Iteration  1 of 11; est error = 10^      0; approx value =
7.854273838441508557994186844091915254335075669608786987870825631512139e-1      
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
7.853981633989281068079393217819579652775141898980881589723706794846849e-1      
quadts: Iteration  3 of 11; est error = 10^    -24; approx value =
7.853981633974483096156608912069304127976696865145262608355143744473072e-1      
quadts: Iteration  4 of 11; est error = 10^    -51; approx value =
7.853981633974483096156608458198757210492923498437700697813167817135655e-1      
quadts: Iteration  5 of 11; est error = 10^    -71; approx value =
7.853981633974483096156608458198757210492923498437764552437361480766414e-1      
quadts: Estimated error = 10^    -71
Quadrature completed: CPU time =    0.000707
Result =
7.853981633974483096156608458198757210492923498437764552437361480766414e-1      
Actual error =   3.060095D-67

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 =
1.198138873892717159649221840146312698527256908847473256667751322566978e0       
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
1.198140234734772955716118571727365769354102156571468921819245240208580e0       
quadts: Iteration  3 of 11; est error = 10^    -24; approx value =
1.198140234735592207439922488923140307710184504874539856706189694756093e0       
quadts: Iteration  4 of 11; est error = 10^    -53; approx value =
1.198140234735592207439922492280323878227212663215965064155626790716291e0       
quadts: Iteration  5 of 11; est error = 10^    -70; approx value =
1.198140234735592207439922492280323878227212663215651728736260158644403e0       
quadts: Estimated error = 10^    -70
Quadrature completed: CPU time =    0.001114
Result =
1.198140234735592207439922492280323878227212663215651728736260158644403e0       
Actual error =  -1.704726D-52

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

quadts: Iteration  1 of 11; est error = 10^      0; approx value =
2.000010783144524300179818284259782315397196179533808594129381867293461e0       
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
2.000000000000407064154154548063307434134156668531719407263262904453190e0       
quadts: Iteration  3 of 11; est error = 10^    -25; approx value =
2.000000000000000000000000000024221280727881763216811769600235569567658e0       
quadts: Iteration  4 of 11; est error = 10^    -57; approx value =
2.000000000000000000000000000000000000000000000000000000000000009501561e0       
quadts: Iteration  5 of 11; est error = 10^    -70; approx value =
2.000000000000000000000000000000000000000000000000000000000000000000378e0       
quadts: Estimated error = 10^    -70
Quadrature completed: CPU time =    0.014674
Result =
2.000000000000000000000000000000000000000000000000000000000000000000378e0       
Actual error =  -3.780231D-67

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 =
-1.088721155239041938600668717669823079820911175131967011699918512748344e0      
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
-1.088793045146372183847035105991429335526928098210812268850895962023095e0      
quadts: Iteration  3 of 11; est error = 10^    -23; approx value =
-1.088793045151801065250343518968911954091052332343470856954130471315490e0      
quadts: Iteration  4 of 11; est error = 10^    -48; approx value =
-1.088793045151801065250344449118806973669291850184630800382360439337948e0      
quadts: Iteration  5 of 11; est error = 10^    -64; approx value =
-1.088793045151801065250344449118806973669291850184642568352701908097484e0      
quadts: Estimated error = 10^    -64
Adjust nq1 and neps2 in initqts for greater accuracy.
Quadrature completed: CPU time =    0.015497
Result =
-1.088793045151801065250344449118806973669291850184642568352701908097484e0      
Actual error =  -5.788102D-52

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 =
2.221441920026155786640011214084157297898181095952010861275105852275341e0       
quadts: Iteration  2 of 11; est error = 10^      0; approx value =
2.221441469077981403393767856584169751077988552278505040068613605770329e0       
quadts: Iteration  3 of 11; est error = 10^    -22; approx value =
2.221441469079183123507940554202063002925912741773041745025999757723496e0       
quadts: Iteration  4 of 11; est error = 10^    -31; approx value =
2.221441469079183123507940495030346644136706768539654228785743603929019e0       
quadts: Estimated error = 10^    -31
Adjust nq1 and neps2 in initqts for greater accuracy.
Quadrature completed: CPU time =    0.001793
Result =
2.221441469079183123507940495030346644136706768539654228785743603929019e0       
Actual error =   2.051706D-34

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 =
1.570796336652852395884114686177691782892268943699117605655891813352365e0       
quades: Iteration  2 of 11; est error = 10^      0; approx value =
1.570796326794897078079303428702199460003781848391136447993367332760709e0       
quades: Iteration  3 of 11; est error = 10^    -29; approx value =
1.570796326794896619231321691639748910799848711227538904828787956446415e0       
quades: Iteration  4 of 11; est error = 10^    -65; approx value =
1.570796326794896619231321691639751442098584699687552910487472296153950e0       
quades: Iteration  5 of 11; est error = 10^    -71; approx value =
1.570796326794896619231321691639751442098584699687552910487472296153656e0       
quades: Estimated error = 10^    -71
Quadrature completed: CPU time =    0.000955
Result =
1.570796326794896619231321691639751442098584699687552910487472296153656e0       
Actual error =   2.410984D-67

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

quades: Iteration  1 of 11; est error = 10^      0; approx value =
1.772324013687165707303653496992060986640299278705717944532956634099942e0       
quades: Iteration  2 of 11; est error = 10^      0; approx value =
1.772450486757275822569400452567859246001945574897612661054825628622014e0       
quades: Iteration  3 of 11; est error = 10^     -8; approx value =
1.772453850930051744191977852711112681794385815573375573343217611779267e0       
quades: Iteration  4 of 11; est error = 10^    -21; approx value =
1.772453850905516024710841331726073111276767772682616623022928613473050e0       
quades: Iteration  5 of 11; est error = 10^    -29; approx value =
1.772453850905516027298167483341128318096502568634581489528977616569922e0       
quades: Iteration  6 of 11; est error = 10^    -57; approx value =
1.772453850905516027298167483341145182797549456122387128217863904195618e0       
quades: Iteration  7 of 11; est error = 10^    -67; approx value =
1.772453850905516027298167483341145182797549456122387128213807789853010e0       
quades: Estimated error = 10^    -67
Adjust nq1 and neps2 in initqss for greater accuracy.
Quadrature completed: CPU time =    0.016186
Result =
1.772453850905516027298167483341145182797549456122387128213807789853010e0       
Actual error =  -1.344587D-67

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

quades: Iteration  1 of 11; est error = 10^      0; approx value =
1.248819950811887890691638613329367294755402452195570256986783256699314e0       
quades: Iteration  2 of 11; est error = 10^      0; approx value =
1.253454840255305062125624067930674646260261835895120041676926010571681e0       
quades: Iteration  3 of 11; est error = 10^     -6; approx value =
1.253314069186494613809379110351547328133218095763434147034295460403079e0       
quades: Iteration  4 of 11; est error = 10^    -13; approx value =
1.253314137315476654941971674411632583714605117484178821050937401775060e0       
quades: Iteration  5 of 11; est error = 10^    -26; approx value =
1.253314137315500251207882759159192960384928823300923460153498995580603e0       
quades: Iteration  6 of 11; est error = 10^    -46; approx value =
1.253314137315500251207882642405522626503493370207855486041534551917290e0       
quades: Iteration  7 of 11; est error = 10^    -71; approx value =
1.253314137315500251207882642405522626503493370304969158314961788171059e0       
quades: Estimated error = 10^    -71
Quadrature completed: CPU time =    0.012451
Result =
1.253314137315500251207882642405522626503493370304969158314961788171059e0       
Actual error =   8.113888D-68

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

quades: Iteration  1 of 11; est error = 10^      0; approx value =
4.979996755488653107411428325926132861814998375504777515806683579564905e-1      
quades: Iteration  2 of 11; est error = 10^      0; approx value =
4.992362278358806422713606542575497359142105647791737775069935196817048e-1      
quades: Iteration  3 of 11; est error = 10^     -4; approx value =
4.999918777105267240043638424302177284304736493706860646145232243505120e-1      
quades: Iteration  4 of 11; est error = 10^     -8; approx value =
5.000000002384274797621304595421375285844301727700595643156794668264884e-1      
quades: Iteration  5 of 11; est error = 10^    -18; approx value =
4.999999999999999680054595397319774266052105807356727277308095952305459e-1      
quades: Iteration  6 of 11; est error = 10^    -28; approx value =
5.000000000000000000000000000009896465478244991410086424332219181287956e-1      
quades: Iteration  7 of 11; est error = 10^    -55; approx value =
5.000000000000000000000000000000000000000000000000000037545233694134228e-1      
quades: Iteration  8 of 11; est error = 10^    -71; approx value =
4.999999999999999999999999999999999999999999999999999999999999999999088e-1      
quades: Estimated error = 10^    -71
Quadrature completed: CPU time =    0.051471
Result =
4.999999999999999999999999999999999999999999999999999999999999999999088e-1      
Actual error =   9.117810D-68

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 =
3.141592673305704791768229372355383565784537887398235211311783626704654e0       
quadss: Iteration  2 of 11; est error = 10^      0; approx value =
3.141592653589794156158606857404398920007563696782272895986734665521347e0       
quadss: Iteration  3 of 11; est error = 10^    -29; approx value =
3.141592653589793238462643383279497821599697422455077809657575912892829e0       
quadss: Iteration  4 of 11; est error = 10^    -65; approx value =
3.141592653589793238462643383279502884197169399375105820974944592307903e0       
quadss: Iteration  5 of 11; est error = 10^    -71; approx value =
3.141592653589793238462643383279502884197169399375105820974944592307235e0       
quadss: Estimated error = 10^    -71
Quadrature completed: CPU time =    0.000665
Result =
3.141592653589793238462643383279502884197169399375105820974944592307235e0       
Actual error =   5.563809D-67

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

quadss: Iteration  1 of 11; est error = 10^      0; approx value =
2.287333312070842418165965832127758340945389170963942044770464832660896e0       
quadss: Iteration  2 of 11; est error = 10^      0; approx value =
2.222377947431867716225788423187419755136974798893959262741520953389958e0       
quadss: Iteration  3 of 11; est error = 10^     -6; approx value =
2.221441653351209624012697009494336641383706491652198766441392953994745e0       
quadss: Iteration  4 of 11; est error = 10^    -13; approx value =
2.221441469079187530310192033504044537795911488096559123461475548589982e0       
quadss: Iteration  5 of 11; est error = 10^    -29; approx value =
2.221441469079183123507940494987246339704340609785679667982970188500388e0       
quadss: Iteration  6 of 11; est error = 10^    -56; approx value =
2.221441469079183123507940495030346849307310844687845111541043991240703e0       
quadss: Iteration  7 of 11; est error = 10^    -71; approx value =
2.221441469079183123507940495030346849307310844687845111542697803478796e0       
quadss: Estimated error = 10^    -71
Quadrature completed: CPU time =    0.002518
Result =
2.221441469079183123507940495030346849307310844687845111542697803478796e0       
Actual error =  -5.934730D-67

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

quadss: Iteration  1 of 11; est error = 10^      0; approx value =
2.433154622201186700450448044201775371575733942658997249415562001648569e0       
quadss: Iteration  2 of 11; est error = 10^      0; approx value =
2.505176288137098807082097461583730125981829685063404369544796496541585e0       
quadss: Iteration  3 of 11; est error = 10^     -6; approx value =
2.506627882721064777048365935915532497489208817733082735354537804069057e0       
quadss: Iteration  4 of 11; est error = 10^    -13; approx value =
2.506628274615202070628532661572574351125624486034734359713639925360708e0       
quadss: Iteration  5 of 11; est error = 10^    -18; approx value =
2.506628274631000502414244627677355069146254794371596576579780442652904e0       
quadss: Iteration  6 of 11; est error = 10^    -40; approx value =
2.506628274631000502415765284811045253009140799868208653757189754795079e0       
quadss: Iteration  7 of 11; est error = 10^    -71; approx value =
2.506628274631000502415765284811045253006986740609938316629923576341840e0       
quadss: Estimated error = 10^    -71
Quadrature completed: CPU time =    0.008281
Result =
2.506628274631000502415765284811045253006986740609938316629923576341840e0       
Actual error =   4.451047D-67

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 =
1.685174789051493718169102018252170246918805551975761663380691421559958e0       
quadss: Iteration  2 of 11; est error = 10^      0; approx value =
1.528097509306032656389987302112351302396796841578677907433246165743574e0       
quadss: Iteration  3 of 11; est error = 10^     -4; approx value =
1.520354053640467153718329709254895884404326675856798566481464378916138e0       
quadss: Iteration  4 of 11; est error = 10^    -10; approx value =
1.520346900914117791484499655117345625474495687665625631142770149422471e0       
quadss: Iteration  5 of 11; est error = 10^    -19; approx value =
1.520346901066280805479380234581060847808932628315693436486703354734760e0       
quadss: Iteration  6 of 11; est error = 10^    -36; approx value =
1.520346901066280805611940146754975627675063178335266930410717935408646e0       
quadss: Iteration  7 of 11; est error = 10^    -69; approx value =
1.520346901066280805611940146754975627036107418779046337528363868526744e0       
quadss: Iteration  8 of 11; est error = 10^    -71; approx value =
1.520346901066280805611940146754975627036107418779046337528363868526578e0       
quadss: Estimated error = 10^    -71
Quadrature completed: CPU time =    0.030439
Result =
1.520346901066280805611940146754975627036107418779046337528363868526578e0       
Actual error =   1.020032D-67

Total CPU time =    1.671696
Max abs error =   2.051706D-34
ALL TESTS PASSED
