⚡️ Speed up function bisection_method by 36%

[codeflash-ai]

📄 36% (0.36x) speedup for bisection_method in src/numpy_pandas/numerical_methods.py

⏱️ Runtime : 1.35 milliseconds → 998 microseconds (best of 77 runs)

📝 Explanation and details

Changes made:

• Cached f(a) and f(b) at the start and updated them within the loop, as their values only change when a or b changes, respectively.
• This reduces redundant function calls per iteration, significantly improving performance when f is expensive to compute.

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	🔘 None Found
🌀 Generated Regression Tests	✅ 138 Passed
⏪ Replay Tests	🔘 None Found
🔎 Concolic Coverage Tests	✅ 3 Passed
📊 Tests Coverage	100.0%

🌀 Generated Regression Tests and Runtime

import math  # used for math functions in test cases
# function to test
from typing import Callable

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

# unit tests

# --- Basic Test Cases ---

def test_basic_linear_root():
    # f(x) = x, root at x=0
    codeflash_output = bisection_method(lambda x: x, -1, 1); root = codeflash_output # 3.46μs -> 3.33μs (3.75% faster)

def test_basic_quadratic_root():
    # f(x) = x^2 - 4, roots at x=-2, x=2
    codeflash_output = bisection_method(lambda x: x**2 - 4, 1, 3); root = codeflash_output # 3.79μs -> 4.00μs (5.22% slower)

def test_basic_cubic_root():
    # f(x) = x^3 - 8, root at x=2
    codeflash_output = bisection_method(lambda x: x**3 - 8, 1, 3); root = codeflash_output # 3.67μs -> 3.67μs (0.027% slower)

def test_basic_negative_root():
    # f(x) = x + 5, root at x=-5
    codeflash_output = bisection_method(lambda x: x + 5, -10, 0); root = codeflash_output # 3.29μs -> 3.42μs (3.66% slower)

def test_basic_trigonometric_root():
    # f(x) = sin(x), root at x=0
    codeflash_output = bisection_method(math.sin, -1, 1); root = codeflash_output # 2.38μs -> 2.29μs (3.62% faster)

# --- Edge Test Cases ---

def test_edge_function_same_sign_raises():
    # f(x) = x^2 + 1, no real root, always positive
    with pytest.raises(ValueError):
        bisection_method(lambda x: x**2 + 1, -1, 1) # 54.9μs -> 57.0μs (3.66% slower)

def test_edge_root_at_endpoint_a():
    # f(x) = x, root at x=0 (endpoint a)
    codeflash_output = bisection_method(lambda x: x, 0, 1); root = codeflash_output # 111μs -> 63.4μs (76.3% faster)

def test_edge_root_at_endpoint_b():
    # f(x) = x - 1, root at x=1 (endpoint b)
    codeflash_output = bisection_method(lambda x: x - 1, 0, 1); root = codeflash_output # 41.4μs -> 25.0μs (65.2% faster)

def test_edge_small_interval():
    # f(x) = x, interval very close to zero
    codeflash_output = bisection_method(lambda x: x, -1e-8, 1e-8); root = codeflash_output # 3.46μs -> 3.46μs (0.029% faster)

def test_edge_zero_epsilon():
    # f(x) = x^2 - 2, root at sqrt(2), use very small epsilon
    codeflash_output = bisection_method(lambda x: x**2 - 2, 1, 2, epsilon=1e-15); root = codeflash_output # 65.0μs -> 39.0μs (66.5% faster)

def test_edge_max_iter_exceeded():
    # f(x) = x, set max_iter=1, should return midpoint of [-1, 1]
    codeflash_output = bisection_method(lambda x: x, -1, 1, max_iter=1); root = codeflash_output # 3.38μs -> 3.33μs (1.26% faster)

def test_edge_discontinuous_function():
    # f(x) = 1 if x < 0 else -1, root at x=0 (discontinuity)
    def f(x):
        return 1 if x < 0 else -1
    codeflash_output = bisection_method(f, -1, 1); root = codeflash_output # 116μs -> 65.2μs (78.6% faster)

def test_edge_non_monotonic_function():
    # f(x) = x^3 - x, root at x=0
    codeflash_output = bisection_method(lambda x: x**3 - x, -1, 1); root = codeflash_output # 3.96μs -> 4.25μs (6.87% slower)

# --- Large Scale Test Cases ---

def test_large_scale_small_epsilon():
    # f(x) = x^2 - 2, root at sqrt(2), very small epsilon, large max_iter
    codeflash_output = bisection_method(lambda x: x**2 - 2, 1, 2, epsilon=1e-12, max_iter=1000); root = codeflash_output # 51.9μs -> 30.3μs (71.4% faster)

def test_large_scale_large_interval():
    # f(x) = x - 100, root at x=100, interval [-500, 500]
    codeflash_output = bisection_method(lambda x: x - 100, -500, 500); root = codeflash_output # 52.2μs -> 29.0μs (80.0% faster)

def test_large_scale_many_iterations():
    # f(x) = x, interval [-1, 1], epsilon very small, max_iter=1000
    codeflash_output = bisection_method(lambda x: x, -1, 1, epsilon=1e-15, max_iter=1000); root = codeflash_output # 3.75μs -> 3.46μs (8.44% faster)

def test_large_scale_high_degree_polynomial():
    # f(x) = x^5 - 32, root at x=2
    codeflash_output = bisection_method(lambda x: x**5 - 32, 1, 3); root = codeflash_output # 3.88μs -> 3.96μs (2.12% slower)

def test_large_scale_function_with_many_roots():
    # f(x) = sin(10x), root near x=0
    codeflash_output = bisection_method(lambda x: math.sin(10*x), -0.5, 0.5); root = codeflash_output # 4.79μs -> 3.92μs (22.3% faster)

# --- Additional Robustness Tests ---

def test_bisection_method_returns_float():
    # Ensure return type is float
    codeflash_output = bisection_method(lambda x: x, -1, 1); root = codeflash_output # 3.21μs -> 3.33μs (3.75% slower)

def test_bisection_method_negative_interval():
    # f(x) = x + 2, root at x=-2, interval [0, -4] (b < a)
    codeflash_output = bisection_method(lambda x: x + 2, 0, -4); root = codeflash_output # 3.29μs -> 3.42μs (3.69% slower)

def test_bisection_method_custom_epsilon_and_iter():
    # f(x) = x^2 - 9, root at x=3, custom epsilon and max_iter
    codeflash_output = bisection_method(lambda x: x**2 - 9, 2, 4, epsilon=1e-8, max_iter=50); root = codeflash_output # 4.50μs -> 3.96μs (13.7% faster)

def test_bisection_method_non_float_inputs():
    # f(x) = x - 5, integer endpoints
    codeflash_output = bisection_method(lambda x: x - 5, 0, 10); root = codeflash_output # 3.42μs -> 3.38μs (1.21% 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 basic math functions
# function to test
from typing import Callable

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

# unit tests

# 1. BASIC TEST CASES

def test_linear_root_basic():
    # f(x) = x, root at x=0
    codeflash_output = bisection_method(lambda x: x, -1, 1); root = codeflash_output # 3.17μs -> 3.29μs (3.80% slower)

def test_quadratic_root_basic():
    # f(x) = x^2 - 4, roots at x=-2 and x=2
    codeflash_output = bisection_method(lambda x: x**2 - 4, 0, 5); root = codeflash_output # 49.1μs -> 27.9μs (76.0% faster)

def test_negative_quadratic_root_basic():
    # f(x) = x^2 - 4, root at x=-2
    codeflash_output = bisection_method(lambda x: x**2 - 4, -5, 0); root = codeflash_output # 47.2μs -> 28.4μs (66.0% faster)

def test_sine_root_basic():
    # f(x) = sin(x), root at x=0
    codeflash_output = bisection_method(math.sin, -1, 1); root = codeflash_output # 2.33μs -> 1.96μs (19.2% faster)

def test_custom_epsilon_basic():
    # f(x) = x - 0.5, root at x=0.5
    codeflash_output = bisection_method(lambda x: x - 0.5, 0, 1, epsilon=1e-6); root = codeflash_output # 3.88μs -> 3.75μs (3.33% faster)

# 2. EDGE TEST CASES

def test_function_same_sign_raises():
    # f(x) = x^2 + 1, always positive, should raise ValueError
    with pytest.raises(ValueError):
        bisection_method(lambda x: x**2 + 1, -1, 1) # 57.4μs -> 54.9μs (4.48% faster)

def test_root_at_endpoint_a():
    # f(x) = x + 3, root at x=-3 (endpoint a)
    codeflash_output = bisection_method(lambda x: x + 3, -3, 2); root = codeflash_output # 116μs -> 63.8μs (82.8% faster)

def test_root_at_endpoint_b():
    # f(x) = x - 4, root at x=4 (endpoint b)
    codeflash_output = bisection_method(lambda x: x - 4, 1, 4); root = codeflash_output # 44.3μs -> 25.4μs (74.3% faster)

def test_max_iter_exceeded():
    # Use a function with a root at x=0, but set max_iter very low
    codeflash_output = bisection_method(lambda x: x, -1, 1, epsilon=1e-2, max_iter=1); root = codeflash_output # 3.46μs -> 3.58μs (3.49% slower)

def test_non_monotonic_function():
    # f(x) = x^3 - x, roots at x=0, x=1, x=-1
    # Test interval [-2, -0.5] (should find root near -1)
    codeflash_output = bisection_method(lambda x: x**3 - x, -2, -0.5); root = codeflash_output # 46.1μs -> 25.8μs (79.0% faster)

def test_root_with_large_epsilon():
    # f(x) = x^2 - 2, root at sqrt(2) ≈ 1.4142, but with large epsilon
    codeflash_output = bisection_method(lambda x: x**2 - 2, 1, 2, epsilon=0.1); root = codeflash_output # 8.83μs -> 6.42μs (37.6% faster)

def test_root_with_small_epsilon_and_large_max_iter():
    # f(x) = x^2 - 2, root at sqrt(2), high precision
    codeflash_output = bisection_method(lambda x: x**2 - 2, 1, 2, epsilon=1e-12, max_iter=500); root = codeflash_output # 49.1μs -> 28.7μs (71.4% faster)


def test_function_with_multiple_roots_in_interval():
    # f(x) = sin(x), interval [0, 4*pi] contains multiple roots
    # Should find the root closest to the midpoint (2*pi)
    codeflash_output = bisection_method(math.sin, 0, 4*math.pi); root = codeflash_output # 2.62μs -> 2.71μs (3.06% slower)

# 3. LARGE SCALE TEST CASES

def test_large_interval():
    # f(x) = x - 1e6, root at x=1e6
    codeflash_output = bisection_method(lambda x: x - 1e6, 0, 2e6, epsilon=1e-6); root = codeflash_output # 3.92μs -> 3.83μs (2.19% faster)

def test_large_max_iter():
    # f(x) = x^2 - 100, root at x=10
    codeflash_output = bisection_method(lambda x: x**2 - 100, 0, 20, epsilon=1e-8, max_iter=1000); root = codeflash_output # 4.17μs -> 4.33μs (3.85% slower)

def test_large_scale_precision():
    # f(x) = x - 1e-7, root at x=1e-7, tiny epsilon
    codeflash_output = bisection_method(lambda x: x - 1e-7, 0, 1, epsilon=1e-12, max_iter=500); root = codeflash_output # 40.9μs -> 25.0μs (63.7% faster)

def test_large_scale_multiple_runs():
    # Run bisection_method on multiple intervals to check scalability
    for i in range(1, 100):
        # f(x) = x - i, root at x=i
        codeflash_output = bisection_method(lambda x, i=i: x - i, i-1, i+1, epsilon=1e-8); root = codeflash_output # 254μs -> 256μs (0.715% slower)

def test_large_interval_negative():
    # f(x) = x + 1e6, root at x=-1e6
    codeflash_output = bisection_method(lambda x: x + 1e6, -2e6, 0, epsilon=1e-6); root = codeflash_output # 3.67μs -> 3.83μs (4.36% slower)
# 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 bisection_method
import pytest

def test_bisection_method():
    bisection_method(((x := [0.0, 0.0, 0.0]), lambda *a: x.pop(0) if len(x) > 1 else x[0])[1], 0.0, 0.0, epsilon=0.0, max_iter=1)

def test_bisection_method_2():
    bisection_method(lambda *a: 0.0, 0.0, 0.0, epsilon=0.5, max_iter=1)

def test_bisection_method_3():
    with pytest.raises(ValueError, match='Function\\ must\\ have\\ opposite\\ signs\\ at\\ endpoints'):
        bisection_method(lambda *a: 2.0, float('inf'), 0.0, epsilon=0.0, max_iter=0)

🔎 Concolic Coverage Tests and Runtime

Test File::Test Function	Original ⏱️	Optimized ⏱️	Speedup
codeflash_concolic_214ll97i/tmpmfpfcrsk/test_concolic_coverage.py::test_bisection_method	4.96μs	4.38μs	13.3%✅
codeflash_concolic_214ll97i/tmpmfpfcrsk/test_concolic_coverage.py::test_bisection_method_2	3.54μs	3.38μs	4.95%✅
codeflash_concolic_214ll97i/tmpmfpfcrsk/test_concolic_coverage.py::test_bisection_method_3	56.2μs	57.8μs	-2.81%⚠️

To edit these changes git checkout codeflash/optimize-bisection_method-mh1684nr and push.