{
  "experiment": "fixed_regex_patterns_and_synthetic_strings",
  "date": "2026-10-11",
  "environment": {
    "python": "3.12.14",
    "implementation": "CPython",
    "macos": "27.0.1",
    "machine": "arm64",
    "engine": "stdlib re; compiled Pattern.fullmatch; no explicit flags"
  },
  "patterns": {
    "nested": "(a+)+",
    "simple": "a+",
    "atomic": "(?>a+)+",
    "possessive": "a++"
  },
  "measurement": {
    "repeats": 3,
    "summary": "median",
    "unit": "milliseconds",
    "timer": "perf_counter_ns",
    "includes_compilation_input_creation_or_child_startup": false,
    "ordinary_case_parent_communication_timeout_seconds": 5
  },
  "measurements": [
    {
      "pattern": "nested",
      "n_a": 16,
      "input_kind": "valid",
      "input_characters": 16,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.002292,
        0.000541,
        0.00025
      ],
      "median_ms": 0.000541
    },
    {
      "pattern": "nested",
      "n_a": 18,
      "input_kind": "valid",
      "input_characters": 18,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.003125,
        0.00075,
        0.000291
      ],
      "median_ms": 0.00075
    },
    {
      "pattern": "nested",
      "n_a": 20,
      "input_kind": "valid",
      "input_characters": 20,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.001625,
        0.001667,
        0.000291
      ],
      "median_ms": 0.001625
    },
    {
      "pattern": "nested",
      "n_a": 22,
      "input_kind": "valid",
      "input_characters": 22,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.002625,
        0.000542,
        0.00025
      ],
      "median_ms": 0.000542
    },
    {
      "pattern": "nested",
      "n_a": 24,
      "input_kind": "valid",
      "input_characters": 24,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.001834,
        0.000541,
        0.00025
      ],
      "median_ms": 0.000541
    },
    {
      "pattern": "nested",
      "n_a": 16,
      "input_kind": "near_miss",
      "input_characters": 17,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        1.241375,
        1.273542,
        1.239833
      ],
      "median_ms": 1.241375
    },
    {
      "pattern": "nested",
      "n_a": 18,
      "input_kind": "near_miss",
      "input_characters": 19,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        4.995292,
        4.566,
        4.748708
      ],
      "median_ms": 4.748708
    },
    {
      "pattern": "nested",
      "n_a": 20,
      "input_kind": "near_miss",
      "input_characters": 21,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        19.453542,
        18.927125,
        19.320042
      ],
      "median_ms": 19.320042
    },
    {
      "pattern": "nested",
      "n_a": 22,
      "input_kind": "near_miss",
      "input_characters": 23,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        78.620042,
        79.566333,
        78.82475
      ],
      "median_ms": 78.82475
    },
    {
      "pattern": "nested",
      "n_a": 24,
      "input_kind": "near_miss",
      "input_characters": 25,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        310.644125,
        311.528084,
        311.556583
      ],
      "median_ms": 311.528084
    },
    {
      "pattern": "simple",
      "n_a": 16,
      "input_kind": "valid",
      "input_characters": 16,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.001417,
        0.000417,
        0.000208
      ],
      "median_ms": 0.000417
    },
    {
      "pattern": "simple",
      "n_a": 18,
      "input_kind": "valid",
      "input_characters": 18,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.001667,
        0.000625,
        0.00025
      ],
      "median_ms": 0.000625
    },
    {
      "pattern": "simple",
      "n_a": 20,
      "input_kind": "valid",
      "input_characters": 20,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.001625,
        0.000667,
        0.000291
      ],
      "median_ms": 0.000667
    },
    {
      "pattern": "simple",
      "n_a": 22,
      "input_kind": "valid",
      "input_characters": 22,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.001333,
        0.0005,
        0.000208
      ],
      "median_ms": 0.0005
    },
    {
      "pattern": "simple",
      "n_a": 24,
      "input_kind": "valid",
      "input_characters": 24,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.001583,
        0.000583,
        0.000208
      ],
      "median_ms": 0.000583
    },
    {
      "pattern": "simple",
      "n_a": 16,
      "input_kind": "near_miss",
      "input_characters": 17,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.001334,
        0.0005,
        0.000208
      ],
      "median_ms": 0.0005
    },
    {
      "pattern": "simple",
      "n_a": 18,
      "input_kind": "near_miss",
      "input_characters": 19,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.0015,
        0.000458,
        0.00025
      ],
      "median_ms": 0.000458
    },
    {
      "pattern": "simple",
      "n_a": 20,
      "input_kind": "near_miss",
      "input_characters": 21,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.001667,
        0.0005,
        0.000292
      ],
      "median_ms": 0.0005
    },
    {
      "pattern": "simple",
      "n_a": 22,
      "input_kind": "near_miss",
      "input_characters": 23,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.001541,
        0.000458,
        0.000291
      ],
      "median_ms": 0.000458
    },
    {
      "pattern": "simple",
      "n_a": 24,
      "input_kind": "near_miss",
      "input_characters": 25,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.001833,
        0.0015,
        0.000292
      ],
      "median_ms": 0.0015
    },
    {
      "pattern": "atomic",
      "n_a": 16,
      "input_kind": "valid",
      "input_characters": 16,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.002209,
        0.000458,
        0.00025
      ],
      "median_ms": 0.000458
    },
    {
      "pattern": "atomic",
      "n_a": 18,
      "input_kind": "valid",
      "input_characters": 18,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.001791,
        0.000542,
        0.000209
      ],
      "median_ms": 0.000542
    },
    {
      "pattern": "atomic",
      "n_a": 20,
      "input_kind": "valid",
      "input_characters": 20,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.001667,
        0.0015,
        0.000334
      ],
      "median_ms": 0.0015
    },
    {
      "pattern": "atomic",
      "n_a": 22,
      "input_kind": "valid",
      "input_characters": 22,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.003166,
        0.000541,
        0.00025
      ],
      "median_ms": 0.000541
    },
    {
      "pattern": "atomic",
      "n_a": 24,
      "input_kind": "valid",
      "input_characters": 24,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.001833,
        0.000625,
        0.00025
      ],
      "median_ms": 0.000625
    },
    {
      "pattern": "atomic",
      "n_a": 16,
      "input_kind": "near_miss",
      "input_characters": 17,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.001709,
        0.000542,
        0.00025
      ],
      "median_ms": 0.000542
    },
    {
      "pattern": "atomic",
      "n_a": 18,
      "input_kind": "near_miss",
      "input_characters": 19,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.001834,
        0.000459,
        0.000208
      ],
      "median_ms": 0.000459
    },
    {
      "pattern": "atomic",
      "n_a": 20,
      "input_kind": "near_miss",
      "input_characters": 21,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.001625,
        0.000417,
        0.000209
      ],
      "median_ms": 0.000417
    },
    {
      "pattern": "atomic",
      "n_a": 22,
      "input_kind": "near_miss",
      "input_characters": 23,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.002208,
        0.000458,
        0.002042
      ],
      "median_ms": 0.002042
    },
    {
      "pattern": "atomic",
      "n_a": 24,
      "input_kind": "near_miss",
      "input_characters": 25,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.001958,
        0.000458,
        0.000209
      ],
      "median_ms": 0.000458
    },
    {
      "pattern": "possessive",
      "n_a": 16,
      "input_kind": "valid",
      "input_characters": 16,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.001167,
        0.000458,
        0.000209
      ],
      "median_ms": 0.000458
    },
    {
      "pattern": "possessive",
      "n_a": 18,
      "input_kind": "valid",
      "input_characters": 18,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.000833,
        0.000459,
        0.000208
      ],
      "median_ms": 0.000459
    },
    {
      "pattern": "possessive",
      "n_a": 20,
      "input_kind": "valid",
      "input_characters": 20,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.001292,
        0.000417,
        0.000208
      ],
      "median_ms": 0.000417
    },
    {
      "pattern": "possessive",
      "n_a": 22,
      "input_kind": "valid",
      "input_characters": 22,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.00175,
        0.000417,
        0.000208
      ],
      "median_ms": 0.000417
    },
    {
      "pattern": "possessive",
      "n_a": 24,
      "input_kind": "valid",
      "input_characters": 24,
      "status": "completed",
      "matched": true,
      "samples_ms": [
        0.000916,
        0.0005,
        0.00025
      ],
      "median_ms": 0.0005
    },
    {
      "pattern": "possessive",
      "n_a": 16,
      "input_kind": "near_miss",
      "input_characters": 17,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.001584,
        0.000458,
        0.000166
      ],
      "median_ms": 0.000458
    },
    {
      "pattern": "possessive",
      "n_a": 18,
      "input_kind": "near_miss",
      "input_characters": 19,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.00125,
        0.000375,
        0.000208
      ],
      "median_ms": 0.000375
    },
    {
      "pattern": "possessive",
      "n_a": 20,
      "input_kind": "near_miss",
      "input_characters": 21,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.001375,
        0.000375,
        0.000167
      ],
      "median_ms": 0.000375
    },
    {
      "pattern": "possessive",
      "n_a": 22,
      "input_kind": "near_miss",
      "input_characters": 23,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.001542,
        0.002,
        0.000292
      ],
      "median_ms": 0.001542
    },
    {
      "pattern": "possessive",
      "n_a": 24,
      "input_kind": "near_miss",
      "input_characters": 25,
      "status": "completed",
      "matched": false,
      "samples_ms": [
        0.001667,
        0.000458,
        0.000208
      ],
      "median_ms": 0.000458
    }
  ],
  "sample_checks": [
    {
      "input_repr": "''",
      "matched": {
        "nested": false,
        "simple": false,
        "atomic": false,
        "possessive": false
      }
    },
    {
      "input_repr": "'a'",
      "matched": {
        "nested": true,
        "simple": true,
        "atomic": true,
        "possessive": true
      }
    },
    {
      "input_repr": "'aa'",
      "matched": {
        "nested": true,
        "simple": true,
        "atomic": true,
        "possessive": true
      }
    },
    {
      "input_repr": "'a!'",
      "matched": {
        "nested": false,
        "simple": false,
        "atomic": false,
        "possessive": false
      }
    },
    {
      "input_repr": "'aa!'",
      "matched": {
        "nested": false,
        "simple": false,
        "atomic": false,
        "possessive": false
      }
    },
    {
      "input_repr": "'a\\n'",
      "matched": {
        "nested": false,
        "simple": false,
        "atomic": false,
        "possessive": false
      }
    }
  ],
  "finite_equivalence_check": {
    "alphabet": [
      "a",
      "b",
      "!",
      "\n"
    ],
    "lengths": "0 through 5",
    "tested": 1365,
    "mismatches": [],
    "accepted": [
      "a",
      "aa",
      "aaa",
      "aaaa",
      "aaaaa"
    ]
  },
  "captures_for_aaa": {
    "nested": [
      "aaa"
    ],
    "simple": [],
    "atomic": [],
    "possessive": []
  },
  "possessive_counterexample_on_aa": {
    "a+a": true,
    "a++a": false
  },
  "bounded_longer_case": {
    "pattern": "nested",
    "n_a": 32,
    "input_kind": "near_miss",
    "input_characters": 33,
    "status": "terminated_after_subprocess_timeout",
    "matched": null,
    "parent_communication_timeout_seconds": 2,
    "note": "Communication wait includes remaining child initialization and calls; process creation and cleanup may add wall time. No completed match time or boolean result."
  },
  "scope": "No arbitrary user regex, external endpoint, alternate engine, throughput or load tests."
}