{
  "software": "apple-numbers",
  "function": "COTH",
  "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/coth-dfbc92de95/15.4/web/1.0",
  "passed": 8,
  "total": 8,
  "cases": [
    {
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B2)",
      "variables": {
        "B2": -3
      },
      "expected": -1.004969823313689,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B3)",
      "variables": {
        "B3": -2
      },
      "expected": -1.037314720727548,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B4)",
      "variables": {
        "B4": -1
      },
      "expected": -1.3130352854993312,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B5)",
      "variables": {
        "B5": -0.5
      },
      "expected": -2.1639534137386525,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B6)",
      "variables": {
        "B6": 0.5
      },
      "expected": 2.1639534137386525,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B7)",
      "variables": {
        "B7": 1
      },
      "expected": 1.3130352854993312,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B8)",
      "variables": {
        "B8": 2
      },
      "expected": 1.037314720727548,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B9)",
      "variables": {
        "B9": 3
      },
      "expected": 1.004969823313689,
      "numeric": true,
      "scope": "recovered worked example"
    }
  ],
  "independent_results": [
    {
      "case": 119,
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B2)",
      "actual_independent_model": -1.0049698233136892,
      "expected": -1.004969823313689,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 120,
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B3)",
      "actual_independent_model": -1.0373147207275482,
      "expected": -1.037314720727548,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 121,
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B4)",
      "actual_independent_model": -1.3130352854993315,
      "expected": -1.3130352854993312,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 122,
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B5)",
      "actual_independent_model": -2.163953413738653,
      "expected": -2.1639534137386525,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 123,
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B6)",
      "actual_independent_model": 2.163953413738653,
      "expected": 2.1639534137386525,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 124,
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B7)",
      "actual_independent_model": 1.3130352854993315,
      "expected": 1.3130352854993312,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 125,
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B8)",
      "actual_independent_model": 1.0373147207275482,
      "expected": 1.037314720727548,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 126,
      "software": "apple-numbers",
      "function": "COTH",
      "expression": "=COTH(B9)",
      "actual_independent_model": 1.0049698233136892,
      "expected": 1.004969823313689,
      "passed": true,
      "scope": "recovered worked example"
    }
  ]
}