{
  "tid": "T490",
  "count": 7,
  "all_passed": true,
  "controls": [
    "pi_interval",
    "displaced_value_rejected",
    "integral_t_equals_half"
  ],
  "minimum_accuracy_bits": 685,
  "records": [
    {
      "params": {
        "nu": "0",
        "x": "0"
      },
      "stored_interval_contains_ball": true,
      "accuracy_bits": null,
      "argument": "0",
      "root_certificate": null,
      "mpmath_160_digits": true,
      "mpmath_210_digits": true
    },
    {
      "params": {
        "nu": "0",
        "x": "critical-1"
      },
      "stored_interval_contains_ball": true,
      "accuracy_bits": 694,
      "argument": "[6.038710806721278481086254816798963467227009841391118380840067446071377119256680921486178238575217525301638836115571335144798187450 +/- 2.25e-130]",
      "root_certificate": {
        "lower": "969373764450156801247447915702332658353944459397004306168335948358487999715474137261768041510502546274021676339171544125480695930975904648842777368514954881945835795978348011955214819512555118025167105305020761691561160553833630996707449385613435719836771661384467394878204130301762037155743418316258060949281487052024260065762682588970648476176275055799221691614331257391449320021042520202623081064329669302574104743/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "969373764450156801247447915702332658353944459397004306168335948358487999715474137261768041510502546274021676339171544125480695930975904648842777368514954881945835795978348011955214819512555118025167105305020762012614377201073224944521773291871288841805753767291075030271325655492933564077180314902350363048185980886433980291483978549629355152433835061159009939409793290791331591044272390299287990996136143380531364007/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "endpoint_signs": [
          -1,
          1
        ],
        "second_derivative_sign": 1,
        "defining_interval": [
          "6183/1024",
          "773/128"
        ]
      },
      "independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
      "mpmath_160_digits": true,
      "mpmath_210_digits": true,
      "integral_relative_error": "1.102860679e-150"
    },
    {
      "params": {
        "nu": "0",
        "x": "critical-2"
      },
      "stored_interval_contains_ball": true,
      "accuracy_bits": 692,
      "argument": "[10.51364251484559764581263577989151867767254637088694024779424251240591329886475259750218545175471206222851702213366910219406161221 +/- 1.61e-129]",
      "root_certificate": {
        "lower": "1687719374035176289925658850344418707608594965845815107538050512153895046256529236658285227710589652611430558138210369520915092346367098295445138718082629435782975936219918874757766771717753225959136696101017577405092612514090360232755871379878206105532973031526130051612531036325957324447642735068448593952994103431631442561867545240848728802554938299655725261452918468050110556249937128960023500627384707754722542243/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "1687719374035176289925658850344418707608594965845815107538050512153895046256529236658285227710589652611430558138210369520915092346367098295445138718082629435782975936219918874757766771717753225959136696101017577726145829161329954180570195286136059227501955137432737687005652561517128851369079631654540896051898597266041162787588841201507435478812498305015513509248380501449992827273166999056688410559191181832679801507/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "endpoint_signs": [
          1,
          -1
        ],
        "second_derivative_sign": -1,
        "defining_interval": [
          "10765/1024",
          "5383/512"
        ]
      },
      "independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
      "mpmath_160_digits": true,
      "mpmath_210_digits": true,
      "integral_relative_error": "2.415631893e-150"
    },
    {
      "params": {
        "nu": "0",
        "x": "critical-3"
      },
      "stored_interval_contains_ball": true,
      "accuracy_bits": 690,
      "argument": "[14.96844542184089720177199643869995239088507312346854923094696107900769333189378785885797833968630707052643707889347328624406344851 +/- 1.04e-129]",
      "root_certificate": {
        "lower": "2402833775445333611908311474222381517751582254833365090543591214923327709282903066343555040205964857665685666358522682004804185142027209395214916933659047618343734741077004186861564357334023176826679523822346858110666390953702667784927469770390872873301272507472371831669636201642970043433129947241642365445858363825315999431544194017122631196799118912827990232544034499894572376271700416473773174589977786368003792243/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "2402833775445333611908311474222381517751582254833365090543591214923327709282903066343555040205964857665685666358522682004804185142027209395214916933659047618343734741077004186861564357334023176826679523822346858431719607600942261732741793676648725995270254613378979467062757726834141570354566843827734667544762857659725719657265489977781337873056678918187778480339496533294454647294930286570438084521784260445961051507/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "endpoint_signs": [
          -1,
          1
        ],
        "second_derivative_sign": 1,
        "defining_interval": [
          "15327/1024",
          "479/32"
        ]
      },
      "independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
      "mpmath_160_digits": true,
      "mpmath_210_digits": true,
      "integral_relative_error": "3.582758219e-150"
    },
    {
      "params": {
        "nu": "0",
        "x": "critical-4"
      },
      "stored_interval_contains_ball": true,
      "accuracy_bits": 688,
      "argument": "[19.41757492600073480390474678899275562305368170664219734111257559419741762113179993320959735305062695417636801904660935492178133945 +/- 1.92e-129]",
      "root_certificate": {
        "lower": "1558518722370330309428181169209633009224278316191435297775702229319727593878728737404462875515691488884164537991205415624887881086130086444336501736243516000582554909534223294496830086993971822206542136268329183778770966503747634731781069241111270197765051227562258726858396724413936113628105634790784893572537275715339290612782288393720943514690989031198971594225559996098718381399258829201469538568758033427532169559/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "1558518722370330309428181169209633009224278316191435297775702229319727593878728737404462875515691488884164537991205415624887881086130086444336501736243516000582554909534223294496830086993971822206542136268329183939297574827367431705688231194240196758749542280515562544554957487009521877088824083083831044621989522632544150725642936374050296852819769033878865718123291012798659516910873764249801993534661270466510799191/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "endpoint_signs": [
          1,
          -1
        ],
        "second_derivative_sign": -1,
        "defining_interval": [
          "19883/1024",
          "4971/256"
        ]
      },
      "independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
      "mpmath_160_digits": true,
      "mpmath_210_digits": true,
      "integral_relative_error": "4.742207113e-150"
    },
    {
      "params": {
        "nu": "0",
        "x": "critical-5"
      },
      "stored_interval_contains_ball": true,
      "accuracy_bits": 687,
      "argument": "[23.86430432392636632558157981644551462454707095704830640599396465527183514023790369273422300297078937932218470431429471628569155110 +/- 4.14e-130]",
      "root_certificate": {
        "lower": "3830855833122594148243620120622152085630506052385333261923754402790856112018348510821648260449188909608493435985856994178801296029429490771343324642444796652973020701893049851311451409496828978609893236948636733590238603547803959674548370156227165128738894977426867180307582949335038914051281501415069791706436250526358469785134590570049714508220014308726110005394028887156798343455104823497545539072261378592124885993/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "3830855833122594148243620120622152085630506052385333261923754402790856112018348510821648260449188909608493435985856994178801296029429490771343324642444796652973020701893049851311451409496828978609893236948636733911291820195043553622362694062485018250707877083333474815700704474526210440972718398001162093805340744360768190010855886530708421184477574314085898253189490920556680614478334693594210449004067852670082145257/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "endpoint_signs": [
          -1,
          1
        ],
        "second_derivative_sign": 1,
        "defining_interval": [
          "24437/1024",
          "12219/512"
        ]
      },
      "independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
      "mpmath_160_digits": true,
      "mpmath_210_digits": true,
      "integral_relative_error": "4.854535954e-150"
    },
    {
      "params": {
        "nu": "0",
        "x": "critical-6"
      },
      "stored_interval_contains_ball": true,
      "accuracy_bits": 685,
      "argument": "[28.30979436473381819241068088541848156372252840618883677595722917778425661442746831887526024713836382846423393479377035121828479825 +/- 1.85e-129]",
      "root_certificate": {
        "lower": "568059408963730570250574658558786764097116459603910701199613853699311844114015893660506451361452954466050249957392375987576832663242483723060975052455847690874165663287496993864561400351638627855750039625806829894799736139001207798164426518569630024943801071894653903822845123498583066166881398405973670859432458594923454644448507398796093342003626612278138753515910303382635044578537839948978156508704787173106186921/20065826040452474621738395244141115820123061381619162977212070095324448220432589806036630768881181530864650607514107580997541169167266097500334986765487216377087492641938951866881041556870737904629872328704000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "568059408963730570250574658558786764097116459603910701199613853699311844114015893660506451361452954466050249957392375987576832663242483723060975052455847690874165663287496993864561400351638627855750039625806829934931388219906157041641217006851861665189923835132979858246985314147479507032061010479235208621795520324224669672663669393878431676535821612948112284490343057557620328456441573711061270250180596432850844329/20065826040452474621738395244141115820123061381619162977212070095324448220432589806036630768881181530864650607514107580997541169167266097500334986765487216377087492641938951866881041556870737904629872328704000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "endpoint_signs": [
          1,
          -1
        ],
        "second_derivative_sign": -1,
        "defining_interval": [
          "28989/1024",
          "14495/512"
        ]
      },
      "independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
      "mpmath_160_digits": true,
      "mpmath_210_digits": true,
      "integral_relative_error": "7.127262875e-150"
    }
  ],
  "retained_identifiers_and_text": []
}