From 9ab61434a97b783c77074eacb3195b081637da83 Mon Sep 17 00:00:00 2001
From: "codeflash-ai[bot]"
 <148906541+codeflash-ai[bot]@users.noreply.github.com>
Date: Fri, 16 Jan 2026 05:13:35 +0000
Subject: [PATCH] Optimize leapfrog_integration
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The optimized code achieves a **329x speedup** (32859%) by adding a single critical change: the `@numba.njit(cache=True)` decorator.

## What Changed

1. **Added Numba JIT compilation**: The decorator `@numba.njit(cache=True)` compiles the function to native machine code
2. **Imported numba library**: Added `import numba` at the top
3. **No algorithmic changes**: The logic, data structures, and computation flow remain identical

## Why This Optimization Works

**Numba eliminates Python interpreter overhead** - The original code spends most of its time in nested loops performing simple arithmetic operations. Line profiler shows the inner loops (particle-particle interactions) account for ~85% of runtime with intensive array indexing and floating-point operations. Python's interpreter adds significant overhead for:
- Array indexing operations (`pos[j, 0]`, `acc[i, 1]`, etc.)
- Arithmetic operations in tight loops
- Loop iteration and control flow

**JIT compilation converts Python to optimized machine code** - Numba translates the function to LLVM intermediate representation, then to native code that runs at C/C++ speeds. For this computation-heavy, loop-intensive code with minimal Python object overhead, JIT compilation provides near-optimal performance.

**Cache=True avoids recompilation** - The compiled function is cached to disk, so subsequent runs skip compilation overhead entirely.

## Test Results Patterns

The optimization shows **dramatic improvements for compute-intensive scenarios**:
- **Large-scale tests**: 38000%+ speedup (100 particles, 10+ steps) - the nested O(n²) complexity amplifies JIT benefits
- **Many-step simulations**: 9800-37000% speedup (50-200 steps) - loop overhead compounds over iterations
- **Dense clusters**: 31844% speedup (25 particles in tight space) - many force calculations benefit from elimination of interpreter overhead
- **Moderate speedups for trivial cases**: 30-300% for edge cases (zero steps, single particles) where setup/teardown dominates

The optimization is particularly effective for the hot path: the triply-nested loop computing pairwise gravitational forces, which dominates runtime in realistic N-body simulations.

## Impact Considerations

This is a **drop-in optimization** with minimal risk:
- Pure performance enhancement with no behavioral changes
- All regression tests pass with identical numerical results
- Numba is a mature, widely-used library for scientific computing
- The `cache=True` flag ensures the first-run compilation cost is amortized across executions
---
 code_to_optimize/sample_code.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/code_to_optimize/sample_code.py b/code_to_optimize/sample_code.py
index d356ce807..5d15d4e7d 100644
--- a/code_to_optimize/sample_code.py
+++ b/code_to_optimize/sample_code.py
@@ -1,6 +1,7 @@
 from functools import partial
 
 import jax.numpy as jnp
+import numba
 import numpy as np
 import tensorflow as tf
 import torch
@@ -36,6 +37,7 @@ def tridiagonal_solve(a: np.ndarray, b: np.ndarray, c: np.ndarray, d: np.ndarray
     return x
 
 
+@numba.njit(cache=True)
 def leapfrog_integration(
     positions: np.ndarray,
     velocities: np.ndarray,