⚡️ Speed up function bisection_method by 19%

[codeflash-ai]

📄 19% (0.19x) speedup for bisection_method in src/numpy_pandas/numerical_methods.py

⏱️ Runtime : 191 microseconds → 161 microseconds (best of 354 runs)

📝 Explanation and details

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	🔘 None Found
🌀 Generated Regression Tests	✅ 57 Passed
⏪ Replay Tests	🔘 None Found
🔎 Concolic Coverage Tests	✅ 3 Passed
📊 Tests Coverage	100.0%

🌀 Generated Regression Tests and Runtime

import math  # for math functions
# function to test
# src/numpy_pandas/numerical_methods.py
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 0
    codeflash_output = bisection_method(lambda x: x, -1, 1); root = codeflash_output # 833ns -> 875ns (4.80% slower)

def test_basic_quadratic_root():
    # f(x) = x^2 - 4, roots at x=2 and x=-2
    codeflash_output = bisection_method(lambda x: x**2 - 4, 0, 3); root = codeflash_output # 9.29μs -> 6.50μs (42.9% faster)

def test_basic_negative_root():
    # f(x) = x^2 - 9, roots at x=3 and x=-3
    codeflash_output = bisection_method(lambda x: x**2 - 9, -4, 0); root = codeflash_output # 1.75μs -> 1.67μs (4.98% faster)

def test_basic_nonzero_epsilon():
    # f(x) = x^2 - 2, root at sqrt(2)
    codeflash_output = bisection_method(lambda x: x**2 - 2, 1, 2, epsilon=1e-6); root = codeflash_output # 6.17μs -> 4.79μs (28.7% faster)

def test_basic_trigonometric_root():
    # f(x) = sin(x), root at 0, pi, 2pi, etc.
    codeflash_output = bisection_method(math.sin, 3, 4); root = codeflash_output # 6.75μs -> 5.58μs (20.9% faster)

# ------------------- EDGE TEST CASES -------------------

def test_edge_root_at_endpoint_a():
    # f(x) = x, root at 0, interval [0, 2]
    codeflash_output = bisection_method(lambda x: x, 0, 2); root = codeflash_output # 12.2μs -> 10.6μs (15.3% faster)

def test_edge_root_at_endpoint_b():
    # f(x) = x - 2, root at 2, interval [0, 2]
    codeflash_output = bisection_method(lambda x: x - 2, 0, 2); root = codeflash_output # 6.58μs -> 5.38μs (22.5% faster)

def test_edge_no_sign_change_raises():
    # f(x) = x^2 + 1, always positive, interval [-1, 1]
    with pytest.raises(ValueError):
        bisection_method(lambda x: x**2 + 1, -1, 1) # 750ns -> 792ns (5.30% slower)

def test_edge_zero_interval_length():
    # f(x) = x, root at 0, interval [0, 0]
    codeflash_output = bisection_method(lambda x: x, 0, 0); root = codeflash_output # 791ns -> 708ns (11.7% faster)

def test_edge_max_iter_exceeded():
    # f(x) = x, root at 0, but with large epsilon and low max_iter
    codeflash_output = bisection_method(lambda x: x, -1, 1, epsilon=1e-20, max_iter=1); root = codeflash_output # 917ns -> 958ns (4.28% slower)

def test_edge_epsilon_larger_than_interval():
    # f(x) = x, root at 0, interval [-1, 1], epsilon=10
    codeflash_output = bisection_method(lambda x: x, -1, 1, epsilon=10); root = codeflash_output # 958ns -> 958ns (0.000% faster)

def test_edge_function_is_flat():
    # f(x) = 0, flat function, any x is a root
    codeflash_output = bisection_method(lambda x: 0, -5, 5); root = codeflash_output # 875ns -> 916ns (4.48% slower)



def test_edge_function_with_inf():
    # f(x) = inf for all x
    def f(x):
        return float('inf')
    with pytest.raises(ValueError):
        bisection_method(f, -1, 1) # 1.08μs -> 1.08μs (0.092% slower)

# ------------------- LARGE SCALE TEST CASES -------------------

def test_large_scale_high_precision():
    # f(x) = x - 1e-8, root at 1e-8, interval [0, 1e-7], epsilon=1e-12
    codeflash_output = bisection_method(lambda x: x - 1e-8, 0, 1e-7, epsilon=1e-12, max_iter=200); root = codeflash_output # 3.83μs -> 3.33μs (15.0% faster)

def test_large_scale_many_iterations():
    # f(x) = x, interval [-1, 1], epsilon very small, max_iter high
    codeflash_output = bisection_method(lambda x: x, -1, 1, epsilon=1e-15, max_iter=1000); root = codeflash_output # 1.04μs -> 1.04μs (0.096% slower)

def test_large_scale_small_interval():
    # f(x) = x - 1e-5, interval [1e-5, 2e-5], root at 1e-5
    codeflash_output = bisection_method(lambda x: x - 1e-5, 1e-5, 2e-5, epsilon=1e-12); root = codeflash_output # 12.5μs -> 10.8μs (16.2% faster)

def test_large_scale_nontrivial_function():
    # f(x) = x^3 - x - 2, root near x=1.521, interval [1,2]
    codeflash_output = bisection_method(lambda x: x**3 - x - 2, 1, 2, epsilon=1e-10); root = codeflash_output # 9.29μs -> 6.96μs (33.5% faster)

def test_large_scale_performance():
    # f(x) = x^2 - 2, root at sqrt(2), interval [1, 2], high max_iter
    codeflash_output = bisection_method(lambda x: x**2 - 2, 1, 2, epsilon=1e-12, max_iter=1000); root = codeflash_output # 9.96μs -> 7.21μs (38.2% faster)

def test_large_scale_large_interval():
    # f(x) = x - 500, root at 500, interval [0, 1000]
    codeflash_output = bisection_method(lambda x: x - 500, 0, 1000, epsilon=1e-8); root = codeflash_output # 1.25μs -> 1.29μs (3.25% slower)
# codeflash_output is used to check that the output of the original code is the same as that of the optimized code.
#------------------------------------------------
from math import isclose
# 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 # 875ns -> 958ns (8.66% slower)

def test_basic_quadratic_root():
    # f(x) = x^2 - 4, roots at x = -2, 2
    codeflash_output = bisection_method(lambda x: x**2 - 4, 0, 5); root = codeflash_output # 9.58μs -> 7.08μs (35.3% faster)
    codeflash_output = bisection_method(lambda x: x**2 - 4, -5, 0); root_neg = codeflash_output # 8.33μs -> 5.79μs (43.9% faster)

def test_basic_cubic_root():
    # f(x) = x^3, root at x = 0
    codeflash_output = bisection_method(lambda x: x**3, -1, 1); root = codeflash_output # 1.00μs -> 1.08μs (7.66% slower)

def test_basic_trig_root():
    # f(x) = sin(x), root at x = 0
    import math
    codeflash_output = bisection_method(math.sin, -1, 1); root = codeflash_output # 1.25μs -> 1.21μs (3.48% faster)

def test_basic_epsilon_parameter():
    # Test that changing epsilon affects precision
    codeflash_output = bisection_method(lambda x: x - 0.5, 0, 1, epsilon=1e-2); root = codeflash_output # 1.17μs -> 1.17μs (0.086% faster)

def test_basic_max_iter_parameter():
    # Test that changing max_iter affects result if epsilon is very small
    codeflash_output = bisection_method(lambda x: x - 0.5, 0, 1, epsilon=1e-15, max_iter=5); root = codeflash_output # 1.08μs -> 1.08μs (0.000% faster)

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

def test_edge_same_sign_raises():
    # f(x) = x^2 + 1, always positive, should raise
    with pytest.raises(ValueError):
        bisection_method(lambda x: x**2 + 1, -1, 1) # 791ns -> 875ns (9.60% slower)

def test_edge_root_at_endpoint_a():
    # f(x) = x - 1, root at x = 1, test [1,2]
    codeflash_output = bisection_method(lambda x: x - 1, 1, 2); root = codeflash_output # 16.2μs -> 12.8μs (27.5% faster)

def test_edge_root_at_endpoint_b():
    # f(x) = x + 2, root at x = -2, test [-3,-2]
    codeflash_output = bisection_method(lambda x: x + 2, -3, -2); root = codeflash_output # 6.21μs -> 5.04μs (23.1% faster)

def test_edge_function_with_multiple_roots_in_interval():
    # f(x) = x^3 - x, roots at x = -1, 0, 1
    codeflash_output = bisection_method(lambda x: x**3 - x, -2, 0); root = codeflash_output # 1.21μs -> 1.25μs (3.28% slower)
    codeflash_output = bisection_method(lambda x: x**3 - x, 0, 2); root2 = codeflash_output # 625ns -> 666ns (6.16% slower)


def test_edge_zero_epsilon_returns_exact_root():
    # f(x) = x - 0.123456789, root at x = 0.123456789
    codeflash_output = bisection_method(lambda x: x - 0.123456789, 0, 1, epsilon=0); root = codeflash_output # 14.1μs -> 11.9μs (18.9% faster)

def test_edge_max_iter_exceeded_returns_midpoint():
    # f(x) = x, root at x = 0, but set max_iter very low
    codeflash_output = bisection_method(lambda x: x, -1, 1, epsilon=1e-20, max_iter=1); root = codeflash_output # 1.17μs -> 1.17μs (0.000% faster)

def test_edge_non_monotonic_function():
    # f(x) = sin(5x), root near x=0
    import math
    codeflash_output = bisection_method(lambda x: math.sin(5*x), -0.5, 0.5); root = codeflash_output # 1.46μs -> 1.46μs (0.000% faster)

def test_edge_large_negative_to_positive_interval():
    # f(x) = x, root at 0, test [-1e6, 1e6]
    codeflash_output = bisection_method(lambda x: x, -1e6, 1e6); root = codeflash_output # 875ns -> 916ns (4.48% slower)

def test_edge_function_with_discontinuity():
    # f(x) = 1/x, root at no real point, but sign change between -1 and 1
    # Should return a value close to 0, but function is undefined at 0
    with pytest.raises(ZeroDivisionError):
        bisection_method(lambda x: 1/x, -1, 1) # 1.50μs -> 1.42μs (5.86% faster)

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

def test_large_scale_small_epsilon():
    # f(x) = x - 0.123456789, root at x = 0.123456789, very small epsilon
    codeflash_output = bisection_method(lambda x: x - 0.123456789, 0, 1, epsilon=1e-12, max_iter=1000); root = codeflash_output # 6.42μs -> 5.67μs (13.2% faster)

def test_large_scale_large_interval():
    # f(x) = x - 500, root at x = 500, interval [0, 1000]
    codeflash_output = bisection_method(lambda x: x - 500, 0, 1000, epsilon=1e-8, max_iter=1000); root = codeflash_output # 1.33μs -> 1.33μs (0.000% faster)

def test_large_scale_max_iter_limit():
    # f(x) = x - 1e-3, root at x = 1e-3, large interval, low max_iter
    codeflash_output = bisection_method(lambda x: x - 1e-3, -1, 1, epsilon=1e-15, max_iter=10); root = codeflash_output # 2.79μs -> 2.46μs (13.6% faster)

def test_large_scale_multiple_runs():
    # Test many roots in a loop to check performance/scalability
    for i in range(10):
        # f(x) = x - i, root at x = i, interval [i-1, i+1]
        codeflash_output = bisection_method(lambda x, i=i: x - i, i-1, i+1, epsilon=1e-10); root = codeflash_output # 4.71μs -> 4.71μs (0.042% faster)

def test_large_scale_precision_vs_iterations():
    # f(x) = x - 0.5, root at 0.5, test increasing max_iter
    for max_iter in [10, 50, 100, 500]:
        codeflash_output = bisection_method(lambda x: x - 0.5, 0, 1, epsilon=1e-15, max_iter=max_iter); root = codeflash_output # 2.75μs -> 2.75μs (0.000% faster)

# ----------- Determinism Test -----------


def test_robustness_on_non_float_inputs():
    # f(x) = x - 3, root at x = 3, test with integer interval
    codeflash_output = bisection_method(lambda x: x - 3, 0, 5); root = codeflash_output # 6.79μs -> 5.42μs (25.4% faster)

def test_robustness_on_callable_with_side_effect():
    # f(x) = x - 1, but also increments a counter
    counter = {'calls': 0}
    def f(x):
        counter['calls'] += 1
        return x - 1
    codeflash_output = bisection_method(f, 0, 2); root = codeflash_output # 1.29μs -> 1.25μs (3.36% faster)

# ----------- Failure/Mutation Detection -----------

def test_mutation_wrong_sign_logic_fails():
    # If the sign logic is reversed, this test will fail
    with pytest.raises(ValueError):
        bisection_method(lambda x: x**2 - 1, 2, 3) # 834ns -> 875ns (4.69% slower)

def test_mutation_wrong_return_logic_fails():
    # If the function returns a instead of midpoint, this will fail
    codeflash_output = bisection_method(lambda x: x - 7, 0, 10); root = codeflash_output # 6.62μs -> 5.54μs (19.5% 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 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_214yrueg/tmplia1ujyt/test_concolic_coverage.py::test_bisection_method	1.67μs	1.83μs	-9.11%⚠️
codeflash_concolic_214yrueg/tmplia1ujyt/test_concolic_coverage.py::test_bisection_method_2	1.08μs	1.17μs	-7.12%⚠️
codeflash_concolic_214yrueg/tmplia1ujyt/test_concolic_coverage.py::test_bisection_method_3	834ns	917ns	-9.05%⚠️

To edit these changes git checkout codeflash/optimize-bisection_method-mh14xvfb and push.