{
  "software": "apple-numbers",
  "function": "ACOTH",
  "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/acoth-af3aad5cff/15.4/web/1.0",
  "passed": 8,
  "total": 8,
  "cases": [
    {
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B2)",
      "variables": {
        "B2": -5
      },
      "expected": -0.20273255405408222,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B3)",
      "variables": {
        "B3": -3
      },
      "expected": -0.34657359027997264,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B4)",
      "variables": {
        "B4": -2
      },
      "expected": -0.5493061443340549,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B5)",
      "variables": {
        "B5": -1.5
      },
      "expected": -0.8047189562170501,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B6)",
      "variables": {
        "B6": 1.5
      },
      "expected": 0.8047189562170501,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B7)",
      "variables": {
        "B7": 2
      },
      "expected": 0.5493061443340549,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B8)",
      "variables": {
        "B8": 3
      },
      "expected": 0.34657359027997264,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B9)",
      "variables": {
        "B9": 5
      },
      "expected": 0.2027325540540822,
      "numeric": true,
      "scope": "recovered worked example"
    }
  ],
  "independent_results": [
    {
      "case": 23,
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B2)",
      "actual_independent_model": -0.20273255405408222,
      "expected": -0.20273255405408222,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 24,
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B3)",
      "actual_independent_model": -0.34657359027997264,
      "expected": -0.34657359027997264,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 25,
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B4)",
      "actual_independent_model": -0.5493061443340549,
      "expected": -0.5493061443340549,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 26,
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B5)",
      "actual_independent_model": -0.8047189562170501,
      "expected": -0.8047189562170501,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 27,
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B6)",
      "actual_independent_model": 0.8047189562170501,
      "expected": 0.8047189562170501,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 28,
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B7)",
      "actual_independent_model": 0.5493061443340549,
      "expected": 0.5493061443340549,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 29,
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B8)",
      "actual_independent_model": 0.34657359027997264,
      "expected": 0.34657359027997264,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 30,
      "software": "apple-numbers",
      "function": "ACOTH",
      "expression": "=ACOTH(B9)",
      "actual_independent_model": 0.2027325540540822,
      "expected": 0.2027325540540822,
      "passed": true,
      "scope": "recovered worked example"
    }
  ]
}