{
  "software": "apple-numbers",
  "function": "ATANH",
  "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/atanh-ffa5c8e90c/15.4/web/1.0",
  "passed": 8,
  "total": 8,
  "cases": [
    {
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B2)",
      "variables": {
        "B2": -0.95
      },
      "expected": -1.8317808230648227,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B3)",
      "variables": {
        "B3": -0.5
      },
      "expected": -0.5493061443340548,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B4)",
      "variables": {
        "B4": -0.1
      },
      "expected": -0.10033534773107558,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B5)",
      "variables": {
        "B5": 0
      },
      "expected": 0.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B6)",
      "variables": {
        "B6": 0.1
      },
      "expected": 0.10033534773107558,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B7)",
      "variables": {
        "B7": 0.5
      },
      "expected": 0.5493061443340548,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B8)",
      "variables": {
        "B8": 0.95
      },
      "expected": 1.8317808230648227,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B9)",
      "variables": {
        "B9": 1
      },
      "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": 62,
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B2)",
      "actual_independent_model": -1.8317808230648227,
      "expected": -1.8317808230648227,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 63,
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B3)",
      "actual_independent_model": -0.5493061443340548,
      "expected": -0.5493061443340548,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 64,
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B4)",
      "actual_independent_model": -0.10033534773107558,
      "expected": -0.10033534773107558,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 65,
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B5)",
      "actual_independent_model": 0.0,
      "expected": 0.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 66,
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B6)",
      "actual_independent_model": 0.10033534773107558,
      "expected": 0.10033534773107558,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 67,
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B7)",
      "actual_independent_model": 0.5493061443340548,
      "expected": 0.5493061443340548,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 68,
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B8)",
      "actual_independent_model": 1.8317808230648227,
      "expected": 1.8317808230648227,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 69,
      "software": "apple-numbers",
      "function": "ATANH",
      "expression": "=ATANH(B9)",
      "passed": true,
      "model_domain_error": "math domain error",
      "scope": "recovered mathematically invalid input; independent domain error only, not a native Numbers error string"
    }
  ]
}