⚡️ Speed up function monte_carlo_pi by 37%

[codeflash-ai]

📄 37% (0.37x) speedup for monte_carlo_pi in src/numerical/monte_carlo.py

⏱️ Runtime : 2.88 milliseconds → 2.11 milliseconds (best of 250 runs)

📝 Explanation and details

Brief: The only meaningful change is replacing the float power expressions x2 and y2 with x * x and y * y. That small micro-optimization reduces per-iteration Python overhead on the inner loop, producing a ~36% end-to-end speedup for typical workloads (largest gains when num_samples is large) while keeping behavior identical.

What changed

• Replaced x2 and y2 with x * x and y * y inside the inner loop.

Why this speeds things up

• The body of this function is a tight hot loop; the cost of the distance check (x2 + y2 <= 1) is executed num_samples times. Any per-iteration overhead accumulates.
• x**2 triggers Python's power machinery (BINARY_POWER / PyNumber_Power), which is more general and therefore heavier than a plain multiplication. Multiplication for floats is implemented as a very cheap C fast-path (BINARY_MULTIPLY).
• Using x * x and y * y reduces bytecode and C-level calls, so the distance check executes fewer and cheaper operations per iteration.
• Line-profiler confirms the conditional line dropped from ~8.5e6 ns to ~6.84e6 ns total in the measured run; the optimized runtime moved from 2.88 ms -> 2.11 ms (36% speedup). The savings are concentrated in the conditional computation inside the loop.

Impact on workloads and tests

• Big wins when monte_carlo_pi is called with large num_samples (see annotated_tests: 1000-sample tests show ~33–40% faster). For micro-calls (num_samples small or 0/negative), the improvement is negligible because loop overhead dominates or there are no iterations.
• Behavior and numeric results are unchanged; the optimization is purely local and safe for floats. All regression tests remain valid.

Risks / notes

• No API or semantic change. Readability stays clear; this is a standard micro-optimization for numeric loops in Python.
• This is most valuable in hot paths where the function is invoked many times or with large sample counts.

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	🔘 None Found
🌀 Generated Regression Tests	✅ 35 Passed
⏪ Replay Tests	🔘 None Found
🔎 Concolic Coverage Tests	✅ 1 Passed
📊 Tests Coverage	100.0%

🌀 Click to see Generated Regression Tests

import math  # used for reference value of pi in some assertions
import random  # used by the function under test and to make deterministic expectations

# imports
import pytest  # used for our unit tests
from src.numerical.monte_carlo import monte_carlo_pi


# Helper used by tests: reproduce the algorithm deterministically using a local RNG
def _expected_monte_carlo_pi(seed: int, num_samples: int) -> float:
    """
    Using random.Random(seed) produce the same sequence of uniform draws that the
    global random generator would produce after random.seed(seed). This helper
    computes the expected numeric result deterministically for assertions.
    """
    rnd = random.Random(seed)  # independent RNG seeded the same way
    inside = 0
    for _ in range(num_samples):
        x = rnd.uniform(-1, 1)
        y = rnd.uniform(-1, 1)
        if x * x + y * y <= 1:
            inside += 1
    return 4 * inside / num_samples


# ===============
# Basic Test Cases
# ===============


def test_single_sample_deterministic():
    """
    Basic case: single sample (num_samples=1). Seeded so outcome is deterministic.
    The expected value is either 0.0 or 4.0 depending on whether the point falls
    inside the unit circle; we compute the expected outcome using an independent RNG.
    """
    seed = 12345
    num_samples = 1

    # Compute expected result using a local RNG seeded with the same seed.
    expected = _expected_monte_carlo_pi(seed, num_samples)

    # Seed the global random generator so monte_carlo_pi uses the same sequence.
    random.seed(seed)
    codeflash_output = monte_carlo_pi(num_samples)
    result = codeflash_output  # 1.46μs -> 1.29μs (12.9% faster)


def test_small_number_of_samples_reproducible_and_in_bounds():
    """
    Small multiple-sample case. Verify:
    - deterministic reproducibility with a fixed seed
    - returned value is a float
    - value lies between 0 and 4 (inclusive), the theoretical possible range
    """
    seed = 42
    num_samples = 10

    expected = _expected_monte_carlo_pi(seed, num_samples)

    # Seed and run the real function
    random.seed(seed)
    codeflash_output = monte_carlo_pi(num_samples)
    result = codeflash_output  # 5.00μs -> 3.79μs (31.9% faster)


# ==============
# Edge Test Cases
# ==============


def test_zero_samples_raises_zero_division_error():
    """
    Edge: num_samples = 0. The implementation divides by num_samples at the end,
    so a ZeroDivisionError is the expected and correct Python exception here.
    """
    with pytest.raises(ZeroDivisionError):
        monte_carlo_pi(0)  # 792ns -> 792ns (0.000% faster)


def test_negative_num_samples_returns_zero_float():
    """
    Edge: negative num_samples. The for-loop will not execute (range(negative) empty),
    so inside_circle remains 0. The function computes 4 * 0 / num_samples which yields
    0.0 (possibly -0.0). We assert the numeric equality with 0.0.
    """
    codeflash_output = monte_carlo_pi(-5)
    result = codeflash_output  # 542ns -> 542ns (0.000% faster)


def test_non_integer_inputs_raise_type_error():
    """
    Edge: If a non-integer (that is not an int subclass) is passed to range(),
    Python raises a TypeError. We check a few such examples.
    """
    with pytest.raises(TypeError):
        monte_carlo_pi(10.5)  # 625ns -> 667ns (6.30% slower)

    with pytest.raises(TypeError):
        monte_carlo_pi("100")  # 500ns -> 500ns (0.000% faster)

    with pytest.raises(TypeError):
        monte_carlo_pi(None)  # 417ns -> 417ns (0.000% faster)


def test_bool_is_treated_as_integer_subclass():
    """
    Edge: bool is a subclass of int in Python. Passing True should be treated as 1.
    Confirm behavior is consistent and deterministic with seeding.
    """
    seed = 7
    # Expected for 1 sample with this seed
    expected = _expected_monte_carlo_pi(seed, 1)

    # Seed global RNG and call with True (equivalent to num_samples=1)
    random.seed(seed)
    codeflash_output = monte_carlo_pi(True)
    result = codeflash_output  # 1.54μs -> 1.29μs (19.3% faster)


# =====================
# Large Scale Test Cases
# =====================


def test_large_scale_1000_samples_deterministic_and_reasonably_accurate():
    """
    Large-scale case (upper limit allowed by the test constraint): num_samples = 1000.
    We:
    - keep test deterministic by seeding the RNG
    - assert exact reproducibility via deterministic expected computation
    - also confirm the estimate is reasonably close to math.pi to catch gross errors
      in the algorithm (tolerance is intentionally generous).
    """
    seed = 999
    num_samples = 1000  # at the upper bound allowed by instructions

    expected = _expected_monte_carlo_pi(seed, num_samples)

    # Seed and run the real function
    random.seed(seed)
    codeflash_output = monte_carlo_pi(num_samples)
    result = codeflash_output  # 329μs -> 240μs (36.8% faster)


def test_reproducible_when_reseeded():
    """
    Ensure that seeding the global RNG before each call produces identical results:
    this checks that the function is deterministic when the global RNG state is set.
    """
    seed = 2021
    num_samples = 100

    random.seed(seed)
    codeflash_output = monte_carlo_pi(num_samples)
    first = codeflash_output  # 35.5μs -> 26.6μs (33.5% faster)

    random.seed(seed)
    codeflash_output = monte_carlo_pi(num_samples)
    second = codeflash_output  # 32.1μs -> 24.5μs (31.0% faster)


# codeflash_output is used to check that the output of the original code is the same as that of the optimized code.

import math  # used for reference value of pi and numeric checks

# imports
import random  # used by the function under test and to control randomness in tests

import pytest  # used for our unit tests
from src.numerical.monte_carlo import monte_carlo_pi

# unit tests


def test_deterministic_with_fixed_seed_and_consistency():
    # Arrange: set a fixed seed so the random draws are deterministic
    random.seed(42)
    # Act: run the estimator twice with the same seed and same sample count
    codeflash_output = monte_carlo_pi(1000)
    result_first = codeflash_output  # 330μs -> 247μs (33.5% faster)
    # Reset the seed to reproduce the exact same sequence
    random.seed(42)
    codeflash_output = monte_carlo_pi(1000)
    result_second = codeflash_output  # 326μs -> 236μs (38.2% faster)


def test_estimate_reasonable_accuracy_for_1000_samples():
    # Arrange: fix RNG seed to make this test deterministic
    random.seed(0)
    # Act: compute estimate with 1000 samples (balance between speed and statistical accuracy)
    codeflash_output = monte_carlo_pi(1000)
    estimate = codeflash_output  # 328μs -> 245μs (33.8% faster)


def test_single_sample_returns_extreme_value_only():
    # For a single random point, the returned value must be either 0.0 (outside) or 4.0 (inside).
    random.seed(123)
    codeflash_output = monte_carlo_pi(1)
    single = codeflash_output  # 2.00μs -> 1.79μs (11.6% faster)


def test_zero_samples_raises_zero_division_error():
    # num_samples == 0 will cause division by zero in the current implementation.
    with pytest.raises(ZeroDivisionError):
        monte_carlo_pi(0)  # 750ns -> 667ns (12.4% faster)


def test_negative_samples_behavior_returns_zero():
    # Negative sample counts produce no iterations; inside_circle stays 0,
    # and the returned value is 4*0 / negative -> -0.0 which compares equal to 0.0.
    codeflash_output = monte_carlo_pi(-10)
    result = codeflash_output  # 583ns -> 584ns (0.171% slower)


def test_non_integer_num_samples_raises_type_error():
    # Passing a non-integer to range() in the implementation should raise a TypeError.
    with pytest.raises(TypeError):
        monte_carlo_pi(100.5)  # 625ns -> 625ns (0.000% faster)


def test_value_range_for_various_seeds_and_samples():
    # Validate that for multiple different RNG seeds the output always stays within [0, 4]
    # (property-based style check but with a small, deterministic sample of seeds).
    seeds = [
        0,
        1,
        2,
        999,
        12345,
    ]  # small fixed set to keep test deterministic and quick
    for s in seeds:
        random.seed(s)
        codeflash_output = monte_carlo_pi(500)
        val = codeflash_output  # 817μs -> 587μs (39.0% faster)


def test_different_seeds_yield_different_results_most_of_the_time():
    # While it's possible two distinct RNG seeds produce identical estimates by chance,
    # it is extraordinarily unlikely for moderate sample sizes; verify diversity of outputs.
    random.seed(1)
    codeflash_output = monte_carlo_pi(1000)
    res1 = codeflash_output  # 333μs -> 245μs (35.9% faster)
    random.seed(2)
    codeflash_output = monte_carlo_pi(1000)
    res2 = codeflash_output  # 330μs -> 235μs (40.3% faster)


def test_statistical_average_over_multiple_seeds_is_close_to_pi():
    # Average the estimates over several distinct seeds and assert the mean is near pi.
    # This is a light-weight large-scale style test using up to 1000 samples per run and a small number of runs.
    seeds = list(range(10))  # 10 independent experiments
    estimates = []
    for s in seeds:
        random.seed(s)
        estimates.append(
            monte_carlo_pi(1000)
        )  # 1000 samples balances speed and accuracy
    mean_estimate = sum(estimates) / len(estimates)


# codeflash_output is used to check that the output of the original code is the same as that of the optimized code.

from src.numerical.monte_carlo import monte_carlo_pi


def test_monte_carlo_pi():
    monte_carlo_pi(4)

🔎 Click to see Concolic Coverage Tests

Test File::Test Function	Original ⏱️	Optimized ⏱️	Speedup
codeflash_concolic_bn6q47k8/tmpgxezq4o2/test_concolic_coverage.py::test_monte_carlo_pi	2.83μs	2.25μs	25.9%✅

To edit these changes git checkout codeflash/optimize-monte_carlo_pi-mkaetbj5 and push.