⚡️ Speed up function monte_carlo_pi by 15%

[codeflash-ai]

📄 15% (0.15x) speedup for monte_carlo_pi in src/numpy_pandas/np_opts.py

⏱️ Runtime : 2.10 milliseconds → 1.83 milliseconds (best of 775 runs)

📝 Explanation and details

The optimized code achieves a 14% speedup by replacing the explicit loop with a generator expression and the built-in sum() function. Here's why this optimization is effective:

Key Optimizations Applied:

1. Generator Expression with Tuple Unpacking: Instead of explicitly calling random.uniform() twice per iteration and storing in separate variables, the code creates a generator that yields coordinate tuples (x, y) and unpacks them directly in the comprehension.

2. Built-in sum() with Generator: Replaced the manual loop and counter increment with sum(x * x + y * y <= 1 for x, y in coords), which leverages Python's optimized C implementation of sum().

3. Eliminated Manual Counter Management: The original code maintained inside_circle as a separate variable and incremented it conditionally. The optimized version counts directly through the boolean evaluation in the generator expression.

Why This Leads to Speedup:

• Reduced Python Bytecode Operations: The explicit loop required more bytecode instructions for loop management, variable assignments, and conditional increments. The generator expression with sum() reduces these to fewer, more efficient operations.

• C-Level Optimization: The built-in sum() function operates at C speed rather than Python interpretation speed, making the accumulation of boolean values (which convert to 0/1) much faster.

• Better Memory Access Patterns: The generator approach processes coordinates immediately rather than storing them in separate variables, reducing variable lookup overhead.

Test Case Performance Patterns:

The optimization shows consistent speedups across different sample sizes:

• Small samples (10-100): 3-18% faster
• Medium samples (100-500): 15-19% faster
• Large samples (1000+): 17-21% faster

The speedup scales well with sample size because the optimization eliminates per-iteration overhead that compounds with more samples. However, for very small inputs or error cases (like ZeroDivisionError), the optimization may be slightly slower due to generator setup overhead, which explains the 23-44% slowdown in some edge cases.

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	🔘 None Found
🌀 Generated Regression Tests	✅ 33 Passed
⏪ Replay Tests	🔘 None Found
🔎 Concolic Coverage Tests	✅ 1 Passed
📊 Tests Coverage	100.0%

🌀 Generated Regression Tests and Runtime

import math  # used for pi and sqrt
# function to test
import random  # used for seeding RNG

# imports
import pytest  # used for our unit tests
from src.numpy_pandas.np_opts import monte_carlo_pi

# unit tests

# -------------------------------
# Basic Test Cases
# -------------------------------

def test_basic_small_sample_known_seed():
    """Test with a small sample and fixed random seed for determinism."""
    random.seed(42)
    codeflash_output = monte_carlo_pi(10); result = codeflash_output # 3.17μs -> 3.12μs (1.34% faster)

def test_basic_medium_sample_known_seed():
    """Test with a medium sample and fixed random seed for determinism."""
    random.seed(123)
    codeflash_output = monte_carlo_pi(100); result = codeflash_output # 21.5μs -> 18.6μs (15.4% faster)

def test_basic_pi_approximation_accuracy():
    """Test that with a reasonable sample size, the estimate is close to math.pi."""
    random.seed(2024)
    codeflash_output = monte_carlo_pi(500); result = codeflash_output # 104μs -> 88.2μs (18.9% faster)

def test_basic_return_type():
    """Test that the function always returns a float."""
    random.seed(0)
    codeflash_output = monte_carlo_pi(50); result = codeflash_output # 11.8μs -> 10.3μs (14.2% faster)

# -------------------------------
# Edge Test Cases
# -------------------------------

def test_edge_zero_samples():
    """Test that zero samples raises ZeroDivisionError."""
    with pytest.raises(ZeroDivisionError):
        monte_carlo_pi(0) # 375ns -> 667ns (43.8% slower)

def test_edge_one_sample_inside():
    """Test with one sample, where the point is inside the circle."""
    # Force the random point to (0,0), which is inside the circle
    class DummyRandom:
        def uniform(self, a, b):
            return 0.0
    saved_random = random.uniform
    random.uniform = DummyRandom().uniform
    try:
        codeflash_output = monte_carlo_pi(1); result = codeflash_output
    finally:
        random.uniform = saved_random

def test_edge_one_sample_outside():
    """Test with one sample, where the point is outside the circle."""
    # Force the random point to (1,1), which is outside the circle
    class DummyRandom:
        def __init__(self):
            self.calls = 0
        def uniform(self, a, b):
            self.calls += 1
            return 1.0
    saved_random = random.uniform
    random.uniform = DummyRandom().uniform
    try:
        codeflash_output = monte_carlo_pi(1); result = codeflash_output
    finally:
        random.uniform = saved_random


def test_edge_non_integer_samples():
    """Test that non-integer input raises TypeError."""
    with pytest.raises(TypeError):
        monte_carlo_pi(3.5) # 375ns -> 375ns (0.000% faster)

def test_edge_large_float_input():
    """Test that a large float input raises TypeError."""
    with pytest.raises(TypeError):
        monte_carlo_pi(1e3) # 333ns -> 333ns (0.000% faster)

# -------------------------------
# Large Scale Test Cases
# -------------------------------

def test_large_scale_accuracy_and_performance():
    """Test with a large number of samples for accuracy and performance."""
    random.seed(555)
    n_samples = 1000
    codeflash_output = monte_carlo_pi(n_samples); result = codeflash_output # 208μs -> 176μs (18.3% faster)

def test_large_scale_repeatability():
    """Test that with same seed and large n, result is repeatable."""
    random.seed(789)
    n_samples = 999
    codeflash_output = monte_carlo_pi(n_samples); result1 = codeflash_output # 212μs -> 175μs (20.8% faster)
    random.seed(789)
    codeflash_output = monte_carlo_pi(n_samples); result2 = codeflash_output # 208μs -> 173μs (20.0% faster)

def test_large_scale_extreme_seed():
    """Test with a large sample and an extreme random seed."""
    random.seed(2**31 - 1)
    n_samples = 1000
    codeflash_output = monte_carlo_pi(n_samples); result = codeflash_output # 211μs -> 177μs (19.3% faster)

def test_large_scale_all_points_inside():
    """Test with all points forced inside the circle."""
    class DummyRandom:
        def uniform(self, a, b):
            return 0.0  # Always (0,0)
    saved_random = random.uniform
    random.uniform = DummyRandom().uniform
    try:
        codeflash_output = monte_carlo_pi(1000); result = codeflash_output
    finally:
        random.uniform = saved_random

def test_large_scale_all_points_outside():
    """Test with all points forced outside the circle."""
    class DummyRandom:
        def __init__(self):
            self.calls = 0
        def uniform(self, a, b):
            # Alternate between 1.0 and -1.0 to ensure (1,1), (-1,-1), etc.
            self.calls += 1
            return 1.0 if self.calls % 2 == 1 else 1.0
    saved_random = random.uniform
    random.uniform = DummyRandom().uniform
    try:
        codeflash_output = monte_carlo_pi(1000); result = codeflash_output
    finally:
        random.uniform = saved_random
# codeflash_output is used to check that the output of the original code is the same as that of the optimized code.

import math
import random

# imports
import pytest  # used for our unit tests
from src.numpy_pandas.np_opts import monte_carlo_pi

# unit tests

# --- Basic Test Cases ---

def test_one_sample_result_in_range():
    # With 1 sample, result must be either 0.0 or 4.0, since only one point is tested
    random.seed(42)
    codeflash_output = monte_carlo_pi(1); result = codeflash_output # 1.08μs -> 1.42μs (23.6% slower)

def test_ten_samples_reasonable_range():
    # With 10 samples, result must be between 0 and 4
    random.seed(123)
    codeflash_output = monte_carlo_pi(10); result = codeflash_output # 3.42μs -> 3.29μs (3.77% faster)

def test_hundred_samples_approximate_pi():
    # With 100 samples, result should be within 1 of math.pi most of the time
    random.seed(999)
    codeflash_output = monte_carlo_pi(100); result = codeflash_output # 22.5μs -> 19.3μs (16.4% faster)

def test_repeatability_with_seed():
    # Monte Carlo is random, but with a fixed seed, result should be deterministic
    random.seed(2024)
    codeflash_output = monte_carlo_pi(20); result1 = codeflash_output # 5.38μs -> 4.96μs (8.41% faster)
    random.seed(2024)
    codeflash_output = monte_carlo_pi(20); result2 = codeflash_output # 4.75μs -> 4.29μs (10.7% faster)

def test_zero_samples_raises():
    # Should raise ZeroDivisionError if num_samples is 0
    with pytest.raises(ZeroDivisionError):
        monte_carlo_pi(0) # 375ns -> 667ns (43.8% slower)


def test_large_float_input_raises():
    # Should raise TypeError if input is not integer
    with pytest.raises(TypeError):
        monte_carlo_pi(10.5) # 375ns -> 375ns (0.000% faster)

def test_string_input_raises():
    # Should raise TypeError if input is not integer
    with pytest.raises(TypeError):
        monte_carlo_pi("100") # 375ns -> 375ns (0.000% faster)

def test_boolean_input_raises():
    # Should raise ZeroDivisionError, since bool is subclass of int (True==1, False==0)
    # monte_carlo_pi(True) is valid but with 1 sample, so allowed
    codeflash_output = monte_carlo_pi(True); result = codeflash_output # 1.25μs -> 1.46μs (14.3% slower)
    # monte_carlo_pi(False) should raise ZeroDivisionError
    with pytest.raises(ZeroDivisionError):
        monte_carlo_pi(False) # 292ns -> 459ns (36.4% slower)

def test_extreme_point_on_circle():
    # Test that a point exactly on the circle boundary is counted as inside
    # We'll monkeypatch random.uniform to always return (1,0)
    class DummyRandom:
        def __init__(self):
            self.calls = 0
        def uniform(self, a, b):
            if self.calls == 0:
                self.calls += 1
                return 1.0
            else:
                return 0.0
    dummy = DummyRandom()
    orig_uniform = random.uniform
    random.uniform = dummy.uniform
    try:
        codeflash_output = monte_carlo_pi(1); result = codeflash_output
    finally:
        random.uniform = orig_uniform

def test_all_points_outside_circle():
    # Monkeypatch to always return (1.1, 1.1), which is outside the circle
    class DummyRandom:
        def uniform(self, a, b):
            return 1.1
    orig_uniform = random.uniform
    random.uniform = DummyRandom().uniform
    try:
        codeflash_output = monte_carlo_pi(5); result = codeflash_output
    finally:
        random.uniform = orig_uniform

def test_all_points_inside_circle():
    # Monkeypatch to always return (0,0), which is inside the circle
    class DummyRandom:
        def __init__(self):
            self.toggle = False
        def uniform(self, a, b):
            # Return 0 for both x and y
            return 0.0
    orig_uniform = random.uniform
    random.uniform = DummyRandom().uniform
    try:
        codeflash_output = monte_carlo_pi(7); result = codeflash_output
    finally:
        random.uniform = orig_uniform


def test_large_sample_size_accuracy():
    # With 1000 samples, the estimate should be within 0.2 of pi most of the time
    random.seed(2023)
    codeflash_output = monte_carlo_pi(1000); result = codeflash_output # 209μs -> 179μs (16.8% faster)

def test_performance_large_sample():
    # Should not take too long for 1000 samples
    import time
    random.seed(42)
    start = time.time()
    codeflash_output = monte_carlo_pi(1000); result = codeflash_output # 210μs -> 178μs (17.8% faster)
    end = time.time()

def test_repeatability_large_sample():
    # With fixed seed, large sample should be deterministic
    random.seed(8888)
    codeflash_output = monte_carlo_pi(1000); result1 = codeflash_output # 208μs -> 177μs (17.5% faster)
    random.seed(8888)
    codeflash_output = monte_carlo_pi(1000); result2 = codeflash_output # 208μs -> 175μs (18.7% faster)

def test_result_type():
    # Should always return a float
    random.seed(1)
    codeflash_output = monte_carlo_pi(100); result = codeflash_output # 21.3μs -> 18.8μs (13.1% faster)
# codeflash_output is used to check that the output of the original code is the same as that of the optimized code.

from src.numpy_pandas.np_opts import monte_carlo_pi

def test_monte_carlo_pi():
    monte_carlo_pi(2)

To edit these changes git checkout codeflash/optimize-monte_carlo_pi-mdpaej05 and push.