In[]:=
ClearSystemCache[];N[(Timing[(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->1000,Method->"Trapezoidal"]+I/Pi)])]
NIntegrate
:NIntegrate failed to converge to prescribed accuracy after 9 iterated refinements in t in the region {{1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,∞}}. NIntegrate obtained 1009-1008 and 1013 for the integral and error estimates.
Out[]=
{3.10938,0.070776-0.0473806}
In[]:=
ClearSystemCache[];N[(Timing[(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->2000,Method->"Trapezoidal"]+I/Pi)])]
Out[]=
{9.64063,0.070776-0.0473806}
In[]:=
N[(Timing[(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->3000,Method->"Trapezoidal",MaxRecursion->10]+I/Pi)])]
Out[]=
{37.7344,0.070776-0.0473806}
In[]:=
N[(Timing[(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->4000,Method->"Trapezoidal",MaxRecursion->10]+I/Pi)])]
Out[]=
{64.8281,0.070776-0.0473806}
In[]:=
N[(Timing[(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->4000,Method->"Trapezoidal",MaxRecursion->10]+I/Pi)])]
Out[]=
{64.1563,0.070776-0.0473806}
In[]:=
N[(Timing[M2-(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->4000,Method->"Trapezoidal",MaxRecursion->10]+I/Pi)]),20]
Out[]=
{64.7031,1.201996624892726351×
-2410
10
+1.02559174313687893296×
-2408
10
}
N[(Timing[M2-(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->4000,Method->"Trapezoidal",MaxRecursion->11]+I/Pi)]),20]
In[]:=
N[(Timing[M2-(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->5000,Method->"Trapezoidal",MaxRecursion->11]+I/Pi)]),20]
Out[]=
{193.172,-2.8152588260798214×
-4456
10
-1.6474664892865609980×
-4453
10
}
N[(Timing[M2-(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->5000,Method->"Trapezoidal",MaxRecursion->12]+I/Pi)]),20]
In[]:=
N[(Timing[M2-(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->10000,Method->"Trapezoidal",MaxRecursion->12]+I/Pi)])]
General
:1767+1771 is too small to represent as a normalized machine number; precision may be lost.
Out[]=
{1366.25,0.+0.}
Orange BACKGROUNDS ARE REDOS
In[]:=
N[(Timing[M2-(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->10000,Method->"Trapezoidal",MaxRecursion->13]+I/Pi)]),20]
Out[]=
{2742.81,0.×
-10001
10
+0.×
-10001
10
}
In[]:=
N[(Timing[(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->40000,Method->"Trapezoidal",MaxRecursion->14]+I/Pi)])]
Out[]=
{67348.3,0.070776-0.0473806}
In[]:=
N[(Timing[M2-(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->40000,Method->"Trapezoidal",MaxRecursion->15]+I/Pi)]),20]
Out[]=
{134440.,0.×
-10002
10
+0.×
-10002
10
}
In[]:=
N[(Timing[M2-(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->5000,Method->"Trapezoidal",MaxRecursion->12]+I/Pi)]),20]
Out[]=
{378.438,0.×
-5001
10
+0.×
-5001
10
}
In[]:=
N[(Timing[M2-(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->4000,Method->"Trapezoidal",MaxRecursion->12]+I/Pi)]),20]
Out[]=
{259.984,0.×
-4001
10
+0.×
-4001
10
}
Now that we know the program works, let' s try it from a fresh kennel .
In[]:=
CloseKernels[]
Out[]=
{}
In[]:=
(Timing[(NIntegrate[(Exp[Log[t]/t-Pit/I]),{t,1,InfinityI},WorkingPrecision->4000,Method->"Trapezoidal",MaxRecursion->12]+I/Pi)])
Out[]=
{248.641,0.0707760393115288035395280218302820013657546962033630275831727881636184572643820365808318812661772382094407339691097179269990446453847536429225844386065219333047122290612020548398576433662343489843827071049989705395231226917848529903218507274354522005125732810542217424931317767029586377171448965877929118571617511540562365603991484881752820025072306153573457106503145899219683164868123907954938255650974196758814736254874320591902869577457241143992751659339102999273310798274679484513088932825130726310257008303152743086102342833436910409821702262269045940297055093272952022662549075225941956559080574835998923469310063614655255062971317960148313404503841687805492907298185104582941328637784284366753787303942475197280648872877809986710218877979777725224197655941725692774900310719381777491848349627938468198411955193898347075098152638657614980900350262780319142430252921925131515239611841070722530473939496294305264627977744876814858325335947117076721493110160508928494597906728688873533031986215124467678736429981544321187124269147141804397293341468345902382977472975053271988386946291215512340931334841526712825988330652119397517437992225419804561517899441213313555349094245152157337720540864293004858914416964903391069077239158225378137007134225157259436267756749980892097547020923938358076198570370106085596863039832425037481494682633055245925697703500997321958201037926268378037273021499168580036766118335796488501619742893070662953852922641481467895325340185006631153014589399140567464642817322554124276739871343784769014864816430102142673821103099429482190262551342893689261414565078351300454655173124597023403312281112674354963160553141145567801875089895942712157634242627126275368184624967147795406349712434902034403655110657336828783643528206451755699785097293845034301399072335418076018544901955694165639769553876705231326512333366413569309147544153147040751278651787331897291338831573491539276810505393193420241588397347561526288661290728125579362948181618288086569973506768636781006386650904534717662131801845803474823423298157834525912125581020582196401078634352065556973647371001379876626633998647899439636865809171008260727796700323541873379525993158697583430323304307895358482051309957606629650194455591037743888293996355687016945561468756667810137028618261442580752084968748790834555683286810992293714710797655441238658361507793595620533974776960070520467919307350751324617559160904358483933727879354374654770015405315934911669904273679391713646599364840768394803265618888420669169340277261914455191828151652360399692719061991655729677744654356588953602124646688591824365597199025929668876773171577235647694709665048098037194956104125531479498893907745459337858730796977515966494235608105257022978810125350663109530591734669918469930734550933587377397856349258234049411471938885385086011030918278312344618497246818765182307767075040597982052236224255617202772645301508653393621700356912690450255099693218917315607411892180967322579047180170212691588040910818933109805057252902227931659575733486175457651130811956867582907068883066723837899816837670787899360869933819422195746218699516733809670530135357903631293882837719370519875606291578527801296043186418096608100829755823649276027221806346169998542692832027777478286102979116280990177760284464151299277101106571545737336647958718244776566375647148433054675834244246049240504686922677421785867393122980814858147770340450055348706971250452311783103291070960442874005786179693433856757309587531165347866491655486207901573141523303786002863792972865839185688715489251955650764768156301356832542206804033891636152122872196025946652394388825789606358890573428609585537496268723416265793405419332522961262899388287613272932643580198488578410174917159464026574904398378971234285839661098451230709606672960619995390673778745129567435608627407535165639492342814598465513325229158297855621032058214589809423668291556295887639710813223944274544167064098025396411543916290237014533917149169483476622031228574697692918713580737506511407117583-0.0473806170703507861072094065026036785731528996931736393319610009025658675880704977905046231477091348479465936090596564623870306654248309678968694089850886419182319688715463982960670062314183486702689720252148875994794102259752445460322817818484531652353688273727307707219133267390790687239387283711452184754907210375883544247175994258945122936989872295281707693556302515688717082931442635088618016377844080077616675520615150089637450932283351202836099023933261710638813450869288035610728520113330960534483984278315793912516000573432689333227969650194719611548152118905143659377033086635522268001967438573058978803038852670704717015491961016945819567398212848032265673541450688861365368893780336286619266615487378956008502150262386454789352080333273200092975067206267668206619476807133830303208043819214307156314491128256764646618272424439040624798981625171397881038895093575197275081861558292549054719826047380102953691405495840261060256916800998870191029190930079440319323897139184114325329921275442168451906986138527317621679779988402520683910593358480457531679161275731336221874397415119398071035280746777234013421669370972789893492419277008472723448844886362216728816688501141657014881030219705838325518944402795918902708368412462132838462832322059131294157560229243803446741005230698330662386728047762411095471276431856288068024246833578221221694199608670998685451353821879036080883177518942867977212189596443064064664656115235251869424401377636333268109772375770600393688616007125925279769013463922774753248722444666223152491097529226104949110013368482223584678614486999090623485347142704810101335898862608678587515881863532041208546852300176483829199352049706786906909793565829346445606508115688089228469999979712827796160763038635490066249070281795265516438177569415281000045197261974836063101294195246094792410345429999163534465195437729204090863124169037952825984586434103992823836926381851655906615017036787844276325854811426904539507063735934074278093784965283359195407022540569503233260294631421382605362266780820302441953025920710615230730153641611954529758903518719515565207605145709875476529267016730825019160756905822828399780005144949773355112404678363927645859673813554015270887845597184892944989299425939066634525349489305667791819593164921949854142903510299694304888090510053152888410344953296862128357158420768074153309659717320557261759784591592461478597497689796428547032978054351762378277766281262689434644439710227499357286713766475399000307291151914517981839462742761918546463610889243027034074796786900203514746805647415878359791756851446918279672536629933796650706083887704125710668996359112105677855424339485517001649443351150891147671019361713110327756401279911019979834349979099881557149180226416179674299960710088689846290641393130630552170595971214883456717685413743518308713048474242302221343126436325069947350303145966410841105277990411741449936565467457025426752003608366929422811827226546384744423531438886265357214045977357951367706910006802680492429267781201522689098452648446559927188321752876177957452796467319088192306698386600737182236402386216554955479991806049961689405928629528095328052943620407400592497246811575340542867852369574578183134540530333161765109482571573678588730432310398474768856021068559638658326822903118970884787785947734545302853686063420431385365369331627020658933505579147656351705295929282594460336418522093967399855759897821993402303724365369600332306022539942509314574408281889899825873193193430366068780836933912994569062284172987471674049651242397700911635502256963493878554458233247538227388742700171957999270207657187973363061447487610711034139851583223477005101362041167512991776417893202857972412840628673422113991702030428315374456212137739417368792290389878275491224589912164781769333386688157173214394727461527115865424971615604008324584387923471668279850087082727624706922186631883875072168310581431172869917369746416558836150912220430421741962335046107764697996627445637759348598712732435943192759240232635586581735957}
Here is the same from 11.3 :