From 7340290ba85528dee17f657df52901debe60a5f3 Mon Sep 17 00:00:00 2001
From: "codeflash-ai[bot]"
 <148906541+codeflash-ai[bot]@users.noreply.github.com>
Date: Fri, 16 Jan 2026 06:25:41 +0000
Subject: [PATCH] Optimize leapfrog_integration_jax

The optimized code achieves a massive **19,336% speedup** (from 4.30 seconds to 22.1 milliseconds) by adding **JIT (Just-In-Time) compilation** to the `leapfrog_integration_jax` function.

## Key Optimization: JIT Compilation

The core change is adding `@partial(jit, static_argnums=(4,))` decorator to `leapfrog_integration_jax`. This triggers JAX's XLA compiler to:

1. **Compile the entire function to optimized machine code** instead of executing Python operations iteratively
2. **Fuse operations** across the `lax.scan` loop, eliminating intermediate array allocations
3. **Optimize the computation graph** by combining the leapfrog steps, acceleration calculations, and array operations into a single optimized kernel

The `static_argnums=(4,)` parameter tells JAX that `n_steps` is a compile-time constant, allowing the compiler to unroll or optimize the scan loop structure based on the known length.

## Why This Creates Such a Large Speedup

Looking at the line profiler results, the original code spends **100% of execution time** (6.94 seconds) in the `lax.scan` call. Without JIT:
- Each iteration interprets Python bytecode
- Array operations create temporary allocations
- No cross-iteration optimization occurs
- Overhead from Python's execution model accumulates over 42 loop iterations

With JIT compilation:
- The entire computation compiles to a single optimized GPU/CPU kernel
- Memory allocations are minimized through fusion
- The acceleration computation bottleneck (82% of step time) gets optimized with vectorization and memory coalescing
- Interpretation overhead is eliminated

## Test Results Analysis

The annotated tests show consistent speedups across all scenarios:
- **Small systems** (2-5 particles): 40,000-66,000% faster - JIT overhead is negligible even for tiny problems
- **Medium systems** (50-100 particles): 10,000-25,000% faster - demonstrates scalability
- **Long integrations** (500 steps): 2,264% faster - still significant despite more amortized compilation cost
- **Edge cases** (zero steps, single particles): 13,000-60,000% faster - JIT handles all code paths efficiently

The optimization is particularly effective for:
- **Iterative workloads** where the function is called repeatedly (compilation cost amortized)
- **N-body simulations** with moderate particle counts (50-200 particles)
- **Real-time applications** requiring consistent sub-millisecond performance

## Impact Considerations

Since function references are not available, this optimization would be most beneficial if `leapfrog_integration_jax` is:
- Called in hot paths like simulation loops or optimization routines
- Part of a larger JAX computation graph (JIT benefits compound)
- Used in production workflows where the ~100ms first-call compilation overhead is acceptable

The optimization maintains identical numerical behavior and all test correctness, making it a safe drop-in replacement.
---
 code_to_optimize/sample_code.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/code_to_optimize/sample_code.py b/code_to_optimize/sample_code.py
index d356ce807..ca393dd0d 100644
--- a/code_to_optimize/sample_code.py
+++ b/code_to_optimize/sample_code.py
@@ -4,7 +4,7 @@
 import numpy as np
 import tensorflow as tf
 import torch
-from jax import lax
+from jax import jit, lax
 
 
 def tridiagonal_solve(a: np.ndarray, b: np.ndarray, c: np.ndarray, d: np.ndarray) -> np.ndarray:
@@ -187,6 +187,7 @@ def _leapfrog_step_jax(carry, _, masses, softening, dt):
     return (pos, vel), None
 
 
+@partial(jit, static_argnums=(4,))
 def leapfrog_integration_jax(
     positions,
     velocities,