{
  "software": "apple-numbers",
  "function": "ACOSH",
  "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/acosh-ffa5c9a390/15.4/web/1.0",
  "passed": 7,
  "total": 7,
  "cases": [
    {
      "software": "apple-numbers",
      "function": "ACOSH",
      "expression": "=ACOSH(B2)",
      "variables": {
        "B2": 1
      },
      "expected": 0.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOSH",
      "expression": "=ACOSH(B3)",
      "variables": {
        "B3": 1.125
      },
      "expected": 0.4949329230945269,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOSH",
      "expression": "=ACOSH(B4)",
      "variables": {
        "B4": 2
      },
      "expected": 1.3169578969248166,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOSH",
      "expression": "=ACOSH(B5)",
      "variables": {
        "B5": 10
      },
      "expected": 2.993222846126381,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOSH",
      "expression": "=ACOSH(B6)",
      "variables": {
        "B6": 100
      },
      "expected": 5.298292365610484,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOSH",
      "expression": "=ACOSH(B7)",
      "variables": {
        "B7": 3.7621956910836314
      },
      "expected": 2.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOSH",
      "expression": "=ACOSH(B8)",
      "variables": {
        "B8": 0.5
      },
      "expected": null,
      "numeric": true,
      "scope": "recovered mathematically invalid input; independent domain error only, not a native Numbers error string",
      "expected_domain_error": true
    }
  ],
  "independent_results": [
    {
      "case": 8,
      "software": "apple-numbers",
      "function": "ACOSH",
      "expression": "=ACOSH(B2)",
      "actual_independent_model": 0.0,
      "expected": 0.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 9,
      "software": "apple-numbers",
      "function": "ACOSH",
      "expression": "=ACOSH(B3)",
      "actual_independent_model": 0.4949329230945269,
      "expected": 0.4949329230945269,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 10,
      "software": "apple-numbers",
      "function": "ACOSH",
      "expression": "=ACOSH(B4)",
      "actual_independent_model": 1.3169578969248166,
      "expected": 1.3169578969248166,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 11,
      "software": "apple-numbers",
      "function": "ACOSH",
      "expression": "=ACOSH(B5)",
      "actual_independent_model": 2.993222846126381,
      "expected": 2.993222846126381,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 12,
      "software": "apple-numbers",
      "function": "ACOSH",
      "expression": "=ACOSH(B6)",
      "actual_independent_model": 5.298292365610484,
      "expected": 5.298292365610484,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 13,
      "software": "apple-numbers",
      "function": "ACOSH",
      "expression": "=ACOSH(B7)",
      "actual_independent_model": 2.0,
      "expected": 2.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 14,
      "software": "apple-numbers",
      "function": "ACOSH",
      "expression": "=ACOSH(B8)",
      "passed": true,
      "model_domain_error": "math domain error",
      "scope": "recovered mathematically invalid input; independent domain error only, not a native Numbers error string"
    }
  ]
}