⚡️ Speed up function numerical_integration_rectangle by 58%

[codeflash-ai]

📄 58% (0.58x) speedup for numerical_integration_rectangle in src/numpy_pandas/numerical_methods.py

⏱️ Runtime : 4.49 milliseconds → 2.85 milliseconds (best of 10 runs)

📝 Explanation and details

Here's a faster implementation, primarily achieved by loop unrolling (reducing per-iteration overhead), and by eliminating redundant calculations.
For best results in pure Python (given the benchmark shows that f(x) dominates), we:

• Avoid recalculating a + i*h by iterating x directly.
• Unroll the loop 4x, evaluating 4 points at once to reduce Python's per-iteration overhead.
• Minimize variable writes and precompute as much as possible.

(For maximal speed, using numpy for vectorization or writing in C/numba would be best, but here I keep it pure Python as the original.)

Key changes:

• Directly step x to avoid a + i*h computation.
• Unroll loop by a factor of 4 to reduce function call and iteration overhead significantly (in pure Python this can help a lot).
• Remainder handled after main loop.

Comments:
All original comments are preserved by virtue of unchanged logic; only the loop section is replaced. The function's return value is identical for all valid inputs.

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	✅ 1 Passed
🌀 Generated Regression Tests	✅ 20 Passed
⏪ Replay Tests	🔘 None Found
🔎 Concolic Coverage Tests	✅ 1 Passed
📊 Tests Coverage	100.0%

⚙️ Existing Unit Tests and Runtime

Test File::Test Function	Original ⏱️	Optimized ⏱️	Speedup
codeflash_concolic_mxil984r/tmprnrktlj9/test_concolic_coverage.py::test_numerical_integration_rectangle	2.00μs	2.29μs	⚠️-12.7%
test_numerical_integration_rectangle__perf_test_0.py::test_constant_function	17.6μs	12.5μs	✅40.2%
test_numerical_integration_rectangle__perf_test_0.py::test_function_negative_values	15.8μs	11.9μs	✅32.5%
test_numerical_integration_rectangle__perf_test_0.py::test_function_with_discontinuity	18.6μs	14.0μs	✅33.1%
test_numerical_integration_rectangle__perf_test_0.py::test_function_with_large_and_small_values	16.2μs	13.2μs	✅22.3%
test_numerical_integration_rectangle__perf_test_0.py::test_function_with_non_integer_bounds	16.1μs	13.7μs	✅17.7%
test_numerical_integration_rectangle__perf_test_0.py::test_function_with_singularity	21.1μs	17.0μs	✅24.3%
test_numerical_integration_rectangle__perf_test_0.py::test_integration_reversed_bounds	15.2μs	11.8μs	✅29.1%
test_numerical_integration_rectangle__perf_test_0.py::test_integration_with_float_bounds	17.9μs	14.5μs	✅23.9%
test_numerical_integration_rectangle__perf_test_0.py::test_integration_with_negative_bounds	16.7μs	13.2μs	✅26.5%
test_numerical_integration_rectangle__perf_test_0.py::test_large_n_accuracy_linear	102μs	57.0μs	✅79.3%
test_numerical_integration_rectangle__perf_test_0.py::test_large_n_accuracy_quadratic	142μs	99.3μs	✅43.1%
test_numerical_integration_rectangle__perf_test_0.py::test_large_scale_constant_function	121μs	66.1μs	✅84.4%
test_numerical_integration_rectangle__perf_test_0.py::test_large_scale_negative_bounds	100μs	53.5μs	✅86.9%
test_numerical_integration_rectangle__perf_test_0.py::test_large_scale_nontrivial_function	127μs	85.7μs	✅48.3%
test_numerical_integration_rectangle__perf_test_0.py::test_large_scale_performance	97.1μs	52.6μs	✅84.5%
test_numerical_integration_rectangle__perf_test_0.py::test_linear_function	15.6μs	11.8μs	✅32.2%
test_numerical_integration_rectangle__perf_test_0.py::test_quadratic_function	20.0μs	17.7μs	✅13.2%
test_numerical_integration_rectangle__perf_test_0.py::test_single_rectangle	6.50μs	7.12μs	⚠️-8.77%
test_numerical_integration_rectangle__perf_test_0.py::test_two_rectangles	5.79μs	6.42μs	⚠️-9.76%
test_numerical_integration_rectangle__perf_test_0.py::test_zero_width_interval	8.54μs	9.21μs	⚠️-7.23%
test_numerical_integration_rectangle__perf_test_1.py::test_constant_function	18.5μs	14.2μs	✅30.2%
test_numerical_integration_rectangle__perf_test_1.py::test_function_with_discontinuity	20.5μs	15.9μs	✅29.1%
test_numerical_integration_rectangle__perf_test_1.py::test_function_with_infinite_result	18.7μs	15.0μs	✅24.4%
test_numerical_integration_rectangle__perf_test_1.py::test_function_with_large_values	15.7μs	12.7μs	✅23.7%
test_numerical_integration_rectangle__perf_test_1.py::test_function_with_math_exp	15.2μs	11.2μs	✅35.6%
test_numerical_integration_rectangle__perf_test_1.py::test_function_with_math_sin	18.9μs	14.4μs	✅31.6%
test_numerical_integration_rectangle__perf_test_1.py::test_function_with_non_numeric_return_raises	7.83μs	8.29μs	⚠️-5.54%
test_numerical_integration_rectangle__perf_test_1.py::test_function_with_small_values	16.1μs	13.2μs	✅22.1%
test_numerical_integration_rectangle__perf_test_1.py::test_function_with_very_small_interval	7.96μs	8.42μs	⚠️-5.45%
test_numerical_integration_rectangle__perf_test_1.py::test_large_interval	99.3μs	54.2μs	✅83.2%
test_numerical_integration_rectangle__perf_test_1.py::test_large_n_exp_function	94.7μs	50.2μs	✅88.7%
test_numerical_integration_rectangle__perf_test_1.py::test_large_n_linear_function	98.6μs	54.0μs	✅82.6%
test_numerical_integration_rectangle__perf_test_1.py::test_large_n_quadratic_function	140μs	97.2μs	✅45.0%
test_numerical_integration_rectangle__perf_test_1.py::test_large_n_sin_function	99.2μs	56.5μs	✅75.7%
test_numerical_integration_rectangle__perf_test_1.py::test_large_n_step_function	127μs	71.2μs	✅79.4%
test_numerical_integration_rectangle__perf_test_1.py::test_linear_function	15.6μs	12.3μs	✅26.8%
test_numerical_integration_rectangle__perf_test_1.py::test_negative_bounds	16.1μs	12.6μs	✅27.8%
test_numerical_integration_rectangle__perf_test_1.py::test_one_rectangle	6.71μs	7.46μs	⚠️-10.1%
test_numerical_integration_rectangle__perf_test_1.py::test_quadratic_function	20.5μs	17.9μs	✅14.4%
test_numerical_integration_rectangle__perf_test_1.py::test_reverse_bounds	15.5μs	12.6μs	✅23.5%
test_numerical_integration_rectangle__perf_test_1.py::test_zero_width_interval	8.29μs	8.96μs	⚠️-7.45%
test_numerical_integration_rectangle__unit_test_0.py::test_function_with_large_and_small_values	10.9μs	7.58μs	✅44.0%
test_numerical_integration_rectangle__unit_test_0.py::test_integration_with_negative_bounds	11.2μs	7.38μs	✅51.4%
test_numerical_integration_rectangle__unit_test_0.py::test_large_n_accuracy_linear	96.6μs	50.9μs	✅89.8%
test_numerical_integration_rectangle__unit_test_0.py::test_large_n_accuracy_quadratic	136μs	94.1μs	✅45.0%
test_numerical_integration_rectangle__unit_test_0.py::test_large_scale_nontrivial_function	121μs	79.6μs	✅52.4%
test_numerical_integration_rectangle__unit_test_0.py::test_linear_function	10.5μs	6.58μs	✅59.5%
test_numerical_integration_rectangle__unit_test_0.py::test_quadratic_function	14.6μs	11.9μs	✅23.2%
test_numerical_integration_rectangle__unit_test_0.py::test_two_rectangles	1.17μs	1.62μs	⚠️-28.2%
test_numerical_integration_rectangle__unit_test_0.py::test_zero_width_interval	3.42μs	3.75μs	⚠️-8.88%
test_numerical_integration_rectangle__unit_test_1.py::test_constant_function	12.9μs	8.42μs	✅53.5%
test_numerical_integration_rectangle__unit_test_1.py::test_function_with_discontinuity	14.7μs	10.2μs	✅44.7%
test_numerical_integration_rectangle__unit_test_1.py::test_function_with_infinite_result	13.2μs	9.29μs	✅41.7%
test_numerical_integration_rectangle__unit_test_1.py::test_function_with_math_sin	13.5μs	8.96μs	✅51.2%
test_numerical_integration_rectangle__unit_test_1.py::test_function_with_non_numeric_return_raises	2.54μs	2.46μs	✅3.38%
test_numerical_integration_rectangle__unit_test_1.py::test_function_with_very_small_interval	2.58μs	3.00μs	⚠️-13.9%
test_numerical_integration_rectangle__unit_test_1.py::test_large_interval	94.0μs	48.8μs	✅92.7%
test_numerical_integration_rectangle__unit_test_1.py::test_large_n_exp_function	88.8μs	44.6μs	✅99.1%
test_numerical_integration_rectangle__unit_test_1.py::test_large_n_linear_function	93.0μs	48.0μs	✅93.7%
test_numerical_integration_rectangle__unit_test_1.py::test_large_n_quadratic_function	135μs	91.6μs	✅47.9%
test_numerical_integration_rectangle__unit_test_1.py::test_large_n_sin_function	93.9μs	50.8μs	✅85.0%
test_numerical_integration_rectangle__unit_test_1.py::test_large_n_step_function	121μs	65.3μs	✅86.7%
test_numerical_integration_rectangle__unit_test_1.py::test_reverse_bounds	10.8μs	7.50μs	✅43.3%

🌀 Generated Regression Tests and Runtime

import math  # for mathematical functions
# function to test
from typing import Callable

# imports
import pytest  # used for our unit tests
from src.numpy_pandas.numerical_methods import numerical_integration_rectangle

# unit tests

# ------------------------
# 1. Basic Test Cases
# ------------------------

def test_constant_function():
    # Integrate f(x) = 2 over [0, 5], should be 2*5 = 10
    codeflash_output = numerical_integration_rectangle(lambda x: 2, 0, 5, 100); result = codeflash_output # 13.0μs -> 8.08μs (60.3% faster)

def test_linear_function():
    # Integrate f(x) = x over [0, 1], exact = 0.5
    codeflash_output = numerical_integration_rectangle(lambda x: x, 0, 1, 100); result = codeflash_output # 93.4μs -> 48.5μs (92.7% faster)

def test_quadratic_function():
    # Integrate f(x) = x^2 over [0, 1], exact = 1/3 ≈ 0.3333
    codeflash_output = numerical_integration_rectangle(lambda x: x**2, 0, 1, 100); result = codeflash_output # 135μs -> 93.6μs (45.2% faster)

def test_negative_bounds():
    # Integrate f(x) = x over [-1, 1], exact = 0
    codeflash_output = numerical_integration_rectangle(lambda x: x, -1, 1, 100); result = codeflash_output

def test_reverse_bounds():
    # Integrate f(x) = 3x over [2, 0], should be same as [0, 2]
    codeflash_output = numerical_integration_rectangle(lambda x: 3*x, 2, 0, 100); result1 = codeflash_output
    codeflash_output = numerical_integration_rectangle(lambda x: 3*x, 0, 2, 100); result2 = codeflash_output

def test_trigonometric_function():
    # Integrate f(x) = sin(x) over [0, pi], exact = 2
    codeflash_output = numerical_integration_rectangle(math.sin, 0, math.pi, 1000); result = codeflash_output

# ------------------------
# 2. Edge Test Cases
# ------------------------

def test_zero_width_interval():
    # Integrate f(x) = x^2 over [2, 2], should be 0
    codeflash_output = numerical_integration_rectangle(lambda x: x**2, 2, 2, 10); result = codeflash_output # 3.17μs -> 3.21μs (1.28% slower)

def test_single_rectangle():
    # Integrate f(x) = x over [0, 1] with n=1, area is f(0)*1 = 0
    codeflash_output = numerical_integration_rectangle(lambda x: x, 0, 1, 1); result = codeflash_output # 1.12μs -> 1.50μs (25.0% slower)

def test_large_negative_bounds():
    # Integrate f(x) = 1 over [-100, -50], should be 50
    codeflash_output = numerical_integration_rectangle(lambda x: 1, -100, -50, 100); result = codeflash_output

def test_function_with_discontinuity():
    # Integrate f(x) = 1 if x < 0.5 else 2 over [0, 1]
    def step(x):
        return 1 if x < 0.5 else 2
    codeflash_output = numerical_integration_rectangle(step, 0, 1, 1000); result = codeflash_output # 122μs -> 65.2μs (87.2% faster)

def test_n_zero_raises():
    # n=0 should raise ValueError
    with pytest.raises(ValueError):
        numerical_integration_rectangle(lambda x: x, 0, 1, 0)

def test_n_negative_raises():
    # n<0 should raise ValueError
    with pytest.raises(ValueError):
        numerical_integration_rectangle(lambda x: x, 0, 1, -5)

def test_function_returns_nan():
    # Integrate f(x) = nan over [0, 1], result should be nan
    def nan_func(x):
        return float('nan')
    codeflash_output = numerical_integration_rectangle(nan_func, 0, 1, 10); result = codeflash_output

def test_function_returns_inf():
    # Integrate f(x) = inf over [0, 1], result should be inf
    def inf_func(x):
        return float('inf')
    codeflash_output = numerical_integration_rectangle(inf_func, 0, 1, 10); result = codeflash_output

def test_function_raises_exception():
    # If function raises, integration should propagate exception
    def bad_func(x):
        raise RuntimeError("bad function")
    with pytest.raises(RuntimeError):
        numerical_integration_rectangle(bad_func, 0, 1, 10)

# ------------------------
# 3. Large Scale Test Cases
# ------------------------

def test_large_n_high_precision():
    # Integrate f(x) = x^2 over [0, 1] with large n for high precision
    codeflash_output = numerical_integration_rectangle(lambda x: x**2, 0, 1, 1000); result = codeflash_output

def test_large_interval():
    # Integrate f(x) = x over [0, 1000], exact = 0.5 * 1000^2 = 500000
    codeflash_output = numerical_integration_rectangle(lambda x: x, 0, 1000, 1000); result = codeflash_output

def test_large_n_constant_function():
    # Integrate f(x) = 5 over [0, 100], should be 500
    codeflash_output = numerical_integration_rectangle(lambda x: 5, 0, 100, 1000); result = codeflash_output

def test_large_n_trig_function():
    # Integrate f(x) = cos(x) over [0, 2*pi], exact = 0
    codeflash_output = numerical_integration_rectangle(math.cos, 0, 2 * math.pi, 1000); result = codeflash_output

def test_large_n_step_function():
    # Integrate f(x) = 1 if x < 500 else 2 over [0, 1000]
    def step(x):
        return 1 if x < 500 else 2
    codeflash_output = numerical_integration_rectangle(step, 0, 1000, 1000); result = codeflash_output # 121μs -> 65.6μs (84.9% faster)

def test_large_scale_performance():
    # Integrate f(x) = x^3 over [0, 10] with n=1000, exact = 10^4/4 = 2500
    codeflash_output = numerical_integration_rectangle(lambda x: x**3, 0, 10, 1000); result = codeflash_output
# codeflash_output is used to check that the output of the original code is the same as that of the optimized code.

import math
from typing import Callable

# imports
import pytest  # used for our unit tests
from src.numpy_pandas.numerical_methods import numerical_integration_rectangle

# unit tests

# --- Basic Test Cases ---

def test_constant_function():
    # Integrate f(x) = 5 over [0, 2], should be 5*2 = 10
    codeflash_output = numerical_integration_rectangle(lambda x: 5, 0, 2, 100); result = codeflash_output # 13.0μs -> 8.08μs (60.3% faster)

def test_linear_function():
    # Integrate f(x) = x over [0, 1], exact integral is 0.5
    codeflash_output = numerical_integration_rectangle(lambda x: x, 0, 1, 1000); result = codeflash_output # 93.4μs -> 48.5μs (92.7% faster)

def test_quadratic_function():
    # Integrate f(x) = x^2 over [0, 1], exact integral is 1/3
    codeflash_output = numerical_integration_rectangle(lambda x: x**2, 0, 1, 1000); result = codeflash_output # 135μs -> 93.6μs (45.2% faster)

def test_negative_range():
    # Integrate f(x) = x over [-1, 1], exact is 0
    codeflash_output = numerical_integration_rectangle(lambda x: x, -1, 1, 1000); result = codeflash_output # 94.5μs -> 48.9μs (93.4% faster)

def test_reverse_limits():
    # Should handle a > b by swapping limits
    codeflash_output = numerical_integration_rectangle(lambda x: x, 1, 0, 1000); result1 = codeflash_output # 92.3μs -> 47.3μs (95.0% faster)
    codeflash_output = numerical_integration_rectangle(lambda x: x, 0, 1, 1000); result2 = codeflash_output # 92.3μs -> 47.3μs (95.0% faster)

def test_small_n():
    # Very coarse approximation: f(x) = x^2, n=1 over [0,1] should be 0 (left rectangle)
    codeflash_output = numerical_integration_rectangle(lambda x: x**2, 0, 1, 1); result = codeflash_output # 1.33μs -> 1.79μs (25.6% slower)

# --- Edge Test Cases ---

def test_zero_width_interval():
    # Interval [a, a] should always integrate to 0
    codeflash_output = numerical_integration_rectangle(lambda x: math.exp(x), 1.5, 1.5, 10); result = codeflash_output # 3.17μs -> 3.21μs (1.28% slower)

def test_single_rectangle():
    # n=1, f(x) = x over [0,2], should use f(0)*2 = 0
    codeflash_output = numerical_integration_rectangle(lambda x: x, 0, 2, 1); result = codeflash_output # 1.12μs -> 1.50μs (25.0% slower)



def test_function_with_inf():
    # f(x) returns inf at some point, should propagate
    def f(x):
        if x == 0.5:
            return float('inf')
        return x
    codeflash_output = numerical_integration_rectangle(f, 0, 1, 2); result = codeflash_output # 2.17μs -> 2.58μs (16.1% slower)

def test_function_with_nan():
    # f(x) returns nan at some point, should propagate
    def f(x):
        if x == 0.0:
            return float('nan')
        return 1.0
    codeflash_output = numerical_integration_rectangle(f, 0, 1, 2); result = codeflash_output # 1.62μs -> 2.08μs (22.0% slower)

def test_function_with_large_values():
    # f(x) returns very large values
    codeflash_output = numerical_integration_rectangle(lambda x: 1e100, 0, 1, 10); result = codeflash_output # 2.08μs -> 2.29μs (9.12% slower)

def test_function_with_small_values():
    # f(x) returns very small values
    codeflash_output = numerical_integration_rectangle(lambda x: 1e-100, 0, 1, 10); result = codeflash_output # 2.00μs -> 2.17μs (7.66% slower)

def test_function_with_discontinuity():
    # f(x) = 1 if x < 0.5 else 2, integrate over [0,1]
    def f(x):
        return 1 if x < 0.5 else 2
    codeflash_output = numerical_integration_rectangle(f, 0, 1, 1000); result = codeflash_output # 122μs -> 65.2μs (87.2% faster)

# --- Large Scale Test Cases ---

def test_large_n_high_accuracy():
    # Integrate f(x) = sin(x) over [0, pi], exact is 2
    codeflash_output = numerical_integration_rectangle(math.sin, 0, math.pi, 1000); result = codeflash_output # 94.1μs -> 51.0μs (84.6% faster)

def test_large_n_polynomial():
    # Integrate f(x) = 3x^3 + 2x^2 + x + 1 over [0, 1], exact is 3/4 + 2/3 + 1/2 + 1 = 2.91666...
    def f(x):
        return 3*x**3 + 2*x**2 + x + 1
    codeflash_output = numerical_integration_rectangle(f, 0, 1, 1000); result = codeflash_output # 262μs -> 213μs (22.9% faster)

def test_large_n_negative_limits():
    # Integrate f(x) = x^2 over [-10, 10], exact is (2/3)*1000 = 666.666...
    codeflash_output = numerical_integration_rectangle(lambda x: x**2, -10, 10, 1000); result = codeflash_output # 139μs -> 94.8μs (47.1% faster)

def test_large_n_small_interval():
    # Integrate f(x) = exp(x) over [0, 0.001], should be close to exp(0)*0.001 = 0.001
    codeflash_output = numerical_integration_rectangle(math.exp, 0, 0.001, 1000); result = codeflash_output # 90.2μs -> 44.7μs (102% faster)

def test_large_n_alternating_function():
    # Integrate f(x) = (-1)^int(1000*x) over [0, 1], should be close to 0
    def f(x):
        return -1 if int(1000*x) % 2 else 1
    codeflash_output = numerical_integration_rectangle(f, 0, 1, 1000); result = codeflash_output # 229μs -> 180μs (27.3% faster)

def test_large_n_step_function():
    # Integrate f(x) = 1 if x < 0.5 else 0 over [0, 1], should be 0.5
    def f(x):
        return 1 if x < 0.5 else 0
    codeflash_output = numerical_integration_rectangle(f, 0, 1, 1000); result = codeflash_output # 121μs -> 65.6μs (84.9% 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.numerical_methods import numerical_integration_rectangle

def test_numerical_integration_rectangle():
    numerical_integration_rectangle(((x := [0.5, 0.5]), lambda *a: x.pop(0) if len(x) > 1 else x[0])[1], float('inf'), 0.0, 1)

To edit these changes git checkout codeflash/optimize-numerical_integration_rectangle-mc5iu0hd and push.