{
  "software": "apple-numbers",
  "function": "RAND",
  "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/rand-ffa590301a/15.4/web/1.0",
  "passed": 6,
  "total": 6,
  "cases": [
    {
      "software": "apple-numbers",
      "function": "RAND",
      "expression": "U*100",
      "variables": {
        "U": 0
      },
      "expected": 0,
      "numeric": true,
      "scope": "documented range transformation using hypothetical u, not random sampling"
    },
    {
      "software": "apple-numbers",
      "function": "RAND",
      "expression": "INT(U*6)+1",
      "variables": {
        "U": 0
      },
      "expected": 1,
      "numeric": true,
      "scope": "documented die transformation using hypothetical u, not random sampling"
    },
    {
      "software": "apple-numbers",
      "function": "RAND",
      "expression": "U*100",
      "variables": {
        "U": 0.5
      },
      "expected": 50,
      "numeric": true,
      "scope": "documented range transformation using hypothetical u, not random sampling"
    },
    {
      "software": "apple-numbers",
      "function": "RAND",
      "expression": "INT(U*6)+1",
      "variables": {
        "U": 0.5
      },
      "expected": 4,
      "numeric": true,
      "scope": "documented die transformation using hypothetical u, not random sampling"
    },
    {
      "software": "apple-numbers",
      "function": "RAND",
      "expression": "U*100",
      "variables": {
        "U": 0.999
      },
      "expected": 99.9,
      "numeric": true,
      "scope": "documented range transformation using hypothetical u, not random sampling"
    },
    {
      "software": "apple-numbers",
      "function": "RAND",
      "expression": "INT(U*6)+1",
      "variables": {
        "U": 0.999
      },
      "expected": 6,
      "numeric": true,
      "scope": "documented die transformation using hypothetical u, not random sampling"
    }
  ],
  "independent_results": [
    {
      "case": 269,
      "software": "apple-numbers",
      "function": "RAND",
      "expression": "U*100",
      "actual_independent_model": 0,
      "expected": 0,
      "passed": true,
      "scope": "documented range transformation using hypothetical u, not random sampling"
    },
    {
      "case": 270,
      "software": "apple-numbers",
      "function": "RAND",
      "expression": "INT(U*6)+1",
      "actual_independent_model": 1,
      "expected": 1,
      "passed": true,
      "scope": "documented die transformation using hypothetical u, not random sampling"
    },
    {
      "case": 271,
      "software": "apple-numbers",
      "function": "RAND",
      "expression": "U*100",
      "actual_independent_model": 50.0,
      "expected": 50,
      "passed": true,
      "scope": "documented range transformation using hypothetical u, not random sampling"
    },
    {
      "case": 272,
      "software": "apple-numbers",
      "function": "RAND",
      "expression": "INT(U*6)+1",
      "actual_independent_model": 4,
      "expected": 4,
      "passed": true,
      "scope": "documented die transformation using hypothetical u, not random sampling"
    },
    {
      "case": 273,
      "software": "apple-numbers",
      "function": "RAND",
      "expression": "U*100",
      "actual_independent_model": 99.9,
      "expected": 99.9,
      "passed": true,
      "scope": "documented range transformation using hypothetical u, not random sampling"
    },
    {
      "case": 274,
      "software": "apple-numbers",
      "function": "RAND",
      "expression": "INT(U*6)+1",
      "actual_independent_model": 6,
      "expected": 6,
      "passed": true,
      "scope": "documented die transformation using hypothetical u, not random sampling"
    }
  ]
}