T471-numerical-checks.json

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11892 bytes, as of the version from 2026-10-24 22:50 (current). Recorded here, not run.

{
  "all_checks_passed": true,
  "ellipse_original_n1": {
    "finite": false,
    "is_one": false,
    "result": "nan"
  },
  "ellipse_repaired_n1": {
    "exact": true,
    "result": "1"
  },
  "ellipse_stored_checks": [
    {
      "error_ulps_upper": "0.293601787084458317886775805128360092321365959175225689679211314372930807792272389633581042289733886718750000000000000000000000000000000000000000000000000",
      "n": 4,
      "radius": "1.7767399e-122",
      "recomputed": "[3.7044798810431814999553515656382943865289535738726142325336403236419950638601466298589729510502696402936017870844583178868 +/- 5.98e-122]"
    },
    {
      "error_ulps_upper": "0.265995532288854205283125597899339944067553936541733202441478451510947778047011524904519319534301757812500000000000000000000000000000000000000000000000000",
      "n": 5,
      "radius": "2.7876593e-122",
      "recomputed": "[4.2611997026079537498883789140957359663223839346815355813341008091049876596503665746474323776256741007340044677111457947169 +/- 3.02e-122]"
    },
    {
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      "n": 6,
      "radius": "2.8359160e-122",
      "recomputed": "[4.7275675557797941743078902319752164597518004058876490468352004729593239614702052498976368465391496740570138341968519738724 +/- 3.49e-122]"
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      "n": 7,
      "radius": "3.6288494e-122",
      "recomputed": "[5.1322874861014414854682896125781817270029576492213971292538488234901770563694353633757156411971645066305327826999716270443 +/- 8.51e-122]"
    },
    {
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      "n": 8,
      "radius": "4.6802500e-122",
      "recomputed": "[5.4919194964575893797146918898363167113299665220421131396176366206351705555805318198988102251455539675858667030465479226359 +/- 6.92e-122]"
    },
    {
      "error_ulps_upper": "0.436022231896448227406994603402133376967289681257654716841341314970126319394694291986525058746337890625000000000000000000000000000000000000000000000000000",
      "n": 9,
      "radius": "4.7612326e-122",
      "recomputed": "[5.8169515684039090454375672679964258975211159795235757943594952501581533324273206228095681519998370374360222318964482274069 +/- 9.47e-122]"
    },
    {
      "error_ulps_upper": "0.0347018419133017710792845518590040101223536409575401142708255333713118773175665410235524177551269531250000000000000000000000000000000000000000000000000000",
      "n": 10,
      "radius": "5.6823054e-122",
      "recomputed": "[6.1144788238475017510074064376115079121416580099454662297273146561106948628585064043019175493447741900347018419133017710792 +/- 8.46e-122]"
    },
    {
      "error_ulps_upper": "0.444198863650531521360532078638168340160312193274390745131884918051046184928054572083055973052978515625000000000000000000000000000000000000000000000000000",
      "n": 11,
      "radius": "7.8050402e-122",
      "recomputed": "[6.389543105887125138742053133536292823655200102339096508988752307062832895714436190583954360684146333555801136349468478640 +/- 5.33e-121]"
    },
    {
      "error_ulps_upper": "0.106432640091724291839847330513670591421421714390350233897172826935673128900816664099693298339843750000000000000000000000000000000000000000000000000000000",
      "n": 12,
      "radius": "7.7016449e-122",
      "recomputed": "[6.645866482340570441298673249614638350654983888797519313967937433418786463528402786500661943116637614106432640091724291840 +/- 3.07e-121]"
    },
    {
      "error_ulps_upper": "0.343287161062695264704770135762863957620023022240670687374041077088993034749364596791565418243408203125000000000000000000000000000000000000000000000000000",
      "n": 13,
      "radius": "8.7638528e-122",
      "recomputed": "[6.886281710615615159278042231712855524150106874117828228748122900275151563595217969886546842874770150656712838937304735295 +/- 4.06e-121]"
    },
    {
      "error_ulps_upper": "0.268904679650452674700457920720844017708875151991265353075316775488534659643846680410206317901611328125000000000000000000000000000000000000000000000000000",
      "n": 14,
      "radius": "7.6795101e-122",
      "recomputed": "[7.1129990770366210832012489207591964884577656971461541496824051121302923787121282559876557765063335242689046796504526747004 +/- 9.57e-122]"
    },
    {
      "error_ulps_upper": "0.117211637074543240918911980125129907238460433811352576597439398981004288202711904887109994888305664062500000000000000000000000000000000000000000000000000",
      "n": 15,
      "radius": "8.1215582e-122",
      "recomputed": "[7.327779317182812601438864931619620782977060146010610588783572147599284472294609612122706331588030433117211637074543240919 +/- 2.51e-121]"
    },
    {
      "error_ulps_upper": "0.295954980363753024999856684963843678804089370656822714916191728595773469123741961084306240081787109375000000000000000000000000000000000000000000000000000",
      "n": 16,
      "radius": "8.9621444e-122",
      "recomputed": "[7.532049871184049434569637626370679894667474231407307394245099250432850990350095283106201190372809677704045019636246975000 +/- 3.23e-121]"
    },
    {
      "error_ulps_upper": "0.135848967108886289815171150816809041680651907143095274329018702641480587089972686953842639923095703125000000000000000000000000000000000000000000000000000",
      "n": 17,
      "radius": "1.0013743e-121",
      "recomputed": "[7.726985501614797536094269226895721594828939163094485790185790267210775201682949778132964324528232517135848967108886289815 +/- 1.72e-121]"
    },
    {
      "error_ulps_upper": "0.0286351167286896751593074031393592294395745428288662206336295801278879480378236621618270874023437500000000000000000000000000000000000000000000000000000000",
      "n": 18,
      "radius": "1.0864006e-121",
      "recomputed": "[7.913565697361177510349950081563984501723144856020179004509967140874343525577719086427975190054313552028635116728689675159 +/- 3.08e-121]"
    },
    {
      "error_ulps_upper": "0.445348805832125049588396849598110500939073026105414033289000425019921181046811398118734359741210937500000000000000000000000000000000000000000000000000000",
      "n": 19,
      "radius": "1.1830075e-121",
      "recomputed": "[8.092616493589788515127220062319525840603014993919363114803975115417458273573133268783749000487982523445348805832125049588 +/- 3.97e-121]"
    },
    {
      "error_ulps_upper": "0.401181656359045641797076645844999978507339029479175805865433235286587887458154000341892242431640625000000000000000000000000000000000000000000000000000000",
      "n": 20,
      "radius": "1.3302343e-121",
      "recomputed": "[8.264841553092724186426776334570296333005260333127557471772667634613102053280288624950691397277578266401181656359045641797 +/- 1.90e-121]"
    }
  ],
  "linked_four_point_probability": {
    "closed_form": "[0.704479881043181499955351565638294386528953573872614232533640323641995063860146629858972951050269640293601787084458317886764541580457251852714434085912063 +/- 5.15e-154]",
    "comment": "This is Sylvester's four-point probability, $1-35/(12\\pi^2)$ CITE{Marckert}.",
    "e_equals_3_plus_p": true,
    "entry": "unit-disk,4",
    "tid": "T468"
  },
  "polygon_controls": [
    {
      "after": "1",
      "before": "0",
      "exact": true,
      "function": "triangle_vertices",
      "n": 1
    },
    {
      "after": "2",
      "before": "2",
      "exact": true,
      "function": "triangle_vertices",
      "n": 2
    },
    {
      "after": "3",
      "before": "3",
      "exact": true,
      "function": "triangle_vertices",
      "n": 3
    },
    {
      "after": "11/3",
      "before": "11/3",
      "exact": true,
      "function": "triangle_vertices",
      "n": 4
    },
    {
      "after": "1",
      "before": "0",
      "exact": true,
      "function": "parallelogram_vertices",
      "n": 1
    },
    {
      "after": "2",
      "before": "2",
      "exact": true,
      "function": "parallelogram_vertices",
      "n": 2
    },
    {
      "after": "3",
      "before": "3",
      "exact": true,
      "function": "parallelogram_vertices",
      "n": 3
    },
    {
      "after": "133/36",
      "before": "133/36",
      "exact": true,
      "function": "parallelogram_vertices",
      "n": 4
    }
  ],
  "polygon_stored_checks": [
    {
      "n": 4,
      "region": "equilateral-triangle",
      "value": "11/3"
    },
    {
      "n": 5,
      "region": "equilateral-triangle",
      "value": "25/6"
    },
    {
      "n": 6,
      "region": "equilateral-triangle",
      "value": "137/30"
    },
    {
      "n": 7,
      "region": "equilateral-triangle",
      "value": "49/10"
    },
    {
      "n": 8,
      "region": "equilateral-triangle",
      "value": "363/70"
    },
    {
      "n": 9,
      "region": "equilateral-triangle",
      "value": "761/140"
    },
    {
      "n": 10,
      "region": "equilateral-triangle",
      "value": "7129/1260"
    },
    {
      "n": 11,
      "region": "equilateral-triangle",
      "value": "7381/1260"
    },
    {
      "n": 12,
      "region": "equilateral-triangle",
      "value": "83711/13860"
    },
    {
      "n": 13,
      "region": "equilateral-triangle",
      "value": "86021/13860"
    },
    {
      "n": 14,
      "region": "equilateral-triangle",
      "value": "1145993/180180"
    },
    {
      "n": 15,
      "region": "equilateral-triangle",
      "value": "1171733/180180"
    },
    {
      "n": 16,
      "region": "equilateral-triangle",
      "value": "1195757/180180"
    },
    {
      "n": 17,
      "region": "equilateral-triangle",
      "value": "2436559/360360"
    },
    {
      "n": 18,
      "region": "equilateral-triangle",
      "value": "42142223/6126120"
    },
    {
      "n": 19,
      "region": "equilateral-triangle",
      "value": "14274301/2042040"
    },
    {
      "n": 20,
      "region": "equilateral-triangle",
      "value": "275295799/38798760"
    },
    {
      "n": 4,
      "region": "unit-square",
      "value": "133/36"
    },
    {
      "n": 5,
      "region": "unit-square",
      "value": "305/72"
    },
    {
      "n": 6,
      "region": "unit-square",
      "value": "281/60"
    },
    {
      "n": 7,
      "region": "unit-square",
      "value": "3647/720"
    },
    {
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      "region": "unit-square",
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      "region": "unit-square",
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    {
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      "region": "unit-square",
      "value": "107136683491/14338621440"
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      "region": "unit-square",
      "value": "327447366043/43015864320"
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    {
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      "region": "unit-square",
      "value": "12660946977401/1634602844160"
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  ]
}