{
  "software": "apple-numbers",
  "function": "SQRTPI",
  "native_application_execution": false,
  "checked_date": "2026-10-12",
  "method": "Independent mathematical/text-processing models, not Apple Numbers or Zoho Sheet execution; random tests check documented bounds/transforms, not randomness.",
  "official_function_reference": "https://support.apple.com/guide/functions/sqrtpi-ffa5910f52/15.4/web/1.0",
  "passed": 6,
  "total": 6,
  "cases": [
    {
      "software": "apple-numbers",
      "function": "SQRTPI",
      "expression": "SQRTPI(0)",
      "variables": {},
      "expected": 0.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "SQRTPI",
      "expression": "SQRTPI(0.25)",
      "variables": {},
      "expected": 0.8862269254527579,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "SQRTPI",
      "expression": "SQRTPI(1)",
      "variables": {},
      "expected": 1.7724538509055159,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "SQRTPI",
      "expression": "SQRTPI(2)",
      "variables": {},
      "expected": 2.5066282746310002,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "SQRTPI",
      "expression": "SQRTPI(5)",
      "variables": {},
      "expected": 3.963327297606011,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "SQRTPI",
      "expression": "SQRTPI(8)",
      "variables": {},
      "expected": 5.0132565492620005,
      "numeric": true,
      "scope": "recovered worked example"
    }
  ],
  "independent_results": [
    {
      "case": 333,
      "software": "apple-numbers",
      "function": "SQRTPI",
      "expression": "SQRTPI(0)",
      "actual_independent_model": 0.0,
      "expected": 0.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 334,
      "software": "apple-numbers",
      "function": "SQRTPI",
      "expression": "SQRTPI(0.25)",
      "actual_independent_model": 0.8862269254527579,
      "expected": 0.8862269254527579,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 335,
      "software": "apple-numbers",
      "function": "SQRTPI",
      "expression": "SQRTPI(1)",
      "actual_independent_model": 1.7724538509055159,
      "expected": 1.7724538509055159,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 336,
      "software": "apple-numbers",
      "function": "SQRTPI",
      "expression": "SQRTPI(2)",
      "actual_independent_model": 2.5066282746310002,
      "expected": 2.5066282746310002,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 337,
      "software": "apple-numbers",
      "function": "SQRTPI",
      "expression": "SQRTPI(5)",
      "actual_independent_model": 3.963327297606011,
      "expected": 3.963327297606011,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 338,
      "software": "apple-numbers",
      "function": "SQRTPI",
      "expression": "SQRTPI(8)",
      "actual_independent_model": 5.0132565492620005,
      "expected": 5.0132565492620005,
      "passed": true,
      "scope": "recovered worked example"
    }
  ]
}