⚡️ Speed up function tridiagonal_solve_jax by 1,995%

[codeflash-ai]

📄 1,995% (19.95x) speedup for tridiagonal_solve_jax in code_to_optimize/sample_code.py

⏱️ Runtime : 42.9 milliseconds → 2.05 milliseconds (best of 5 runs)

📝 Explanation and details

The optimized code achieves a 20x speedup (1995%) by applying JAX's Just-In-Time (JIT) compilation via the @jit decorator to tridiagonal_solve_jax.

Key optimization:

• JIT compilation: The @jit decorator compiles the entire function into optimized XLA (Accelerated Linear Algebra) machine code on first execution, then reuses this compiled version for subsequent calls.

Why this is dramatically faster:

1. Eliminates Python interpreter overhead: Without JIT, every array operation and function call goes through Python's interpreter. The line profiler shows that even simple operations like c[0] / b[0] took ~1.17 seconds across 31 calls (~38ms each). JIT removes this overhead entirely by compiling to native code.

2. Operator fusion: JAX can fuse multiple array operations into single kernels. For example, operations like (d_i - a_i * d_prev) / denom become a single fused kernel instead of separate subtract, multiply, and divide operations, reducing memory bandwidth requirements.

3. Optimizes the scan operations: The two lax.scan calls (forward and backward passes) benefit significantly from JIT. The profiler shows these took ~515ms and ~348ms respectively in the original code. JIT enables better loop unrolling and vectorization within the scan kernels.

4. Reduces array creation overhead: Multiple jnp.concatenate and jnp.array calls (totaling ~644ms in the profiler) are optimized away or compiled into efficient buffer operations.

Impact: This optimization is particularly effective for the tridiagonal solver because it's called repeatedly (31 times in the profile), and JIT compilation amortizes the one-time compilation cost across all invocations. The optimization benefits any workload that calls this function multiple times with similarly-shaped inputs, making it ideal for numerical PDE solvers, time-stepping algorithms, or batch processing scenarios.

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	✅ 18 Passed
🌀 Generated Regression Tests	🔘 None Found
⏪ Replay Tests	🔘 None Found
🔎 Concolic Coverage Tests	🔘 None Found
📊 Tests Coverage	100.0%

⚙️ Click to see Existing Unit Tests

Test File::Test Function	Original ⏱️	Optimized ⏱️	Speedup
test_jax_jit_code.py::TestTridiagonalSolveJax.test_diagonal_system	14.8ms	223μs	6515%✅
test_jax_jit_code.py::TestTridiagonalSolveJax.test_larger_system	14.6ms	1.54ms	846%✅
test_jax_jit_code.py::TestTridiagonalSolveJax.test_simple_system	13.5ms	278μs	4745%✅

To edit these changes git checkout codeflash/optimize-tridiagonal_solve_jax-mkggf6xm and push.