{
  "software": "apple-numbers",
  "function": "TANH",
  "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/tanh-ffa5c5b63d/15.4/web/1.0",
  "passed": 9,
  "total": 9,
  "cases": [
    {
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B2)",
      "variables": {
        "B2": -5
      },
      "expected": -0.9999092042625951,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B3)",
      "variables": {
        "B3": -2
      },
      "expected": -0.9640275800758169,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B4)",
      "variables": {
        "B4": -1
      },
      "expected": -0.7615941559557649,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B5)",
      "variables": {
        "B5": -0.5
      },
      "expected": -0.46211715726000974,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B6)",
      "variables": {
        "B6": 0
      },
      "expected": 0.0,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B7)",
      "variables": {
        "B7": 0.5
      },
      "expected": 0.46211715726000974,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B8)",
      "variables": {
        "B8": 1
      },
      "expected": 0.7615941559557649,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B9)",
      "variables": {
        "B9": 2
      },
      "expected": 0.9640275800758169,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B10)",
      "variables": {
        "B10": 5
      },
      "expected": 0.9999092042625951,
      "numeric": true,
      "scope": "recovered worked example"
    }
  ],
  "independent_results": [
    {
      "case": 364,
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B2)",
      "actual_independent_model": -0.9999092042625951,
      "expected": -0.9999092042625951,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 365,
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B3)",
      "actual_independent_model": -0.9640275800758169,
      "expected": -0.9640275800758169,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 366,
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B4)",
      "actual_independent_model": -0.7615941559557649,
      "expected": -0.7615941559557649,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 367,
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B5)",
      "actual_independent_model": -0.46211715726000974,
      "expected": -0.46211715726000974,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 368,
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B6)",
      "actual_independent_model": 0.0,
      "expected": 0.0,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 369,
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B7)",
      "actual_independent_model": 0.46211715726000974,
      "expected": 0.46211715726000974,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 370,
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B8)",
      "actual_independent_model": 0.7615941559557649,
      "expected": 0.7615941559557649,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 371,
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B9)",
      "actual_independent_model": 0.9640275800758169,
      "expected": 0.9640275800758169,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 372,
      "software": "apple-numbers",
      "function": "TANH",
      "expression": "=TANH(B10)",
      "actual_independent_model": 0.9999092042625951,
      "expected": 0.9999092042625951,
      "passed": true,
      "scope": "recovered worked example"
    }
  ]
}