back to table · edit · history · where entries came from · files · download
20729 bytes, as of the version from 2026-10-27 01:05 (current). Recorded here, not run.
{
"table": "T514",
"entries": 50,
"controls": [
"integral(t^2,0,3)=9",
"integral(exp(-t),0,1)=1-exp(-1)",
"Ai(0) gamma identity",
"exact erf/erfc/Fresnel origins",
"independent mpmath polynomial quadrature"
],
"records": [
{
"argument": "0",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 1101,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 485,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-1",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 730,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 505,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-2",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 729,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 508,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-3",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 729,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 470,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-4",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 730,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 478,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-5",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 731,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 485,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-6",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 728,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 492,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-7",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 728,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 499,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-8",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 729,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 505,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-9",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 728,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 511,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-10",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 728,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 517,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-11",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 730,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 523,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-12",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 730,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 470,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-13",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 731,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 480,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-14",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 729,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 490,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-15",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 730,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 500,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-16",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 730,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 510,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-17",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 728,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 520,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-18",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 729,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 529,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-19",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 728,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 538,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "ai-zero-20",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 727,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 542,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "gi-critical-0",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 728,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 473,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "gi-critical-1",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 727,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 505,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "gi-critical-2",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 721,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 508,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "gi-critical-3",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 717,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 470,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "gi-critical-4",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 712,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 478,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "gi-critical-5",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 707,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 485,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "gi-critical-6",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 703,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 492,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "gi-critical-7",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 698,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 499,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "gi-critical-8",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 694,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 505,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "gi-critical-9",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 689,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 511,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "gi-critical-10",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 685,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 517,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "gi-critical-11",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 680,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 523,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "gi-critical-12",
"family": "retained",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 676,
"root_bracket_checked": true,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 470,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "-1/2",
"family": "simple-real",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 732,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 489,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "1/2",
"family": "simple-real",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 733,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 475,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "-1",
"family": "simple-real",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 730,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 495,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "1",
"family": "simple-real",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 731,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 465,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "-2",
"family": "simple-real",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 729,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 504,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "2",
"family": "simple-real",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 727,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 476,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "-4",
"family": "simple-real",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 732,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 507,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "4",
"family": "simple-real",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 730,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 575,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "-8",
"family": "simple-real",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 729,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 486,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "8",
"family": "simple-real",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 726,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 548,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "-3/cbrt(3)",
"family": "unit-cubic",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 732,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 504,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "-2/cbrt(3)",
"family": "unit-cubic",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 729,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 500,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "-1/cbrt(3)",
"family": "unit-cubic",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 730,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 489,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "1/cbrt(3)",
"family": "unit-cubic",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 733,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 471,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "2/cbrt(3)",
"family": "unit-cubic",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 728,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 483,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
},
{
"argument": "3/cbrt(3)",
"family": "unit-cubic",
"digits": 100,
"certified_interval_contained": true,
"arb_accuracy_bits": 730,
"root_bracket_checked": false,
"quadrature_interval_contained": true,
"quadrature_accuracy_bits": 475,
"mpmath_decimal_precisions": [
150,
200
],
"transformed_integral": null
}
],
"versions": {
"numberdb": "0.1.10",
"python-flint": "0.6.0",
"mpmath": "1.3.0"
},
"source_sha256": {
"balanced_values.py": "1333dc603c1a65159dbffe7c263998a058f74537e1d8e961468339b0291e2d1a",
"balanced_checks.py": "875e34e73c5c5937623ab19f780d00c47330ac87242729f279b0e7fc7f0a44d3"
},
"structure": {
"all_original_entries_identical": true,
"all_original_comments_identical": true,
"parameter_order_preserved": true,
"complete_generator_enumeration": true,
"new_arguments_exactly_deduplicated": true,
"new_unresolved_citations": [],
"entries_block_bytes": 13734,
"retained_count": 34,
"added_count": 16
}
}