⚡️ Speed up method Algorithms.fibonacci by 97%

[codeflash-ai]

📄 97% (0.97x) speedup for Algorithms.fibonacci in code_to_optimize/java/src/main/java/com/example/Algorithms.java

⏱️ Runtime : 6.98 milliseconds → 3.53 milliseconds (best of 5 runs)

📝 Explanation and details

This optimization achieves a 97% speedup (reducing runtime from 6.98ms to 3.53ms) by introducing a hybrid approach that selects the most efficient algorithm based on input size.

Key Changes:

1. Small-n Fast Path (n < 50): For smaller Fibonacci numbers, the optimization adds a simple iterative loop that directly computes F(n) = F(n-1) + F(n-2). This linear O(n) approach is actually faster than the logarithmic O(log n) fast-doubling method for small inputs because:

   • Avoids bit manipulation overhead (Integer.numberOfLeadingZeros, bit shifting, masking)
   • Eliminates multiple multiplications per iteration
   • Uses simpler arithmetic (just addition)
   • Has better cache locality with straightforward sequential access

2. Minor Optimization in Fast-Doubling Path: The expression (b << 1) - a is extracted into a local variable twoBminusA to avoid recomputing it, though this has minimal impact compared to the fast path addition.

Why This Works:

The original fast-doubling algorithm has O(log n) time complexity, which is theoretically superior for large n. However, for small n, the constant overhead of bit operations and multiplications dominates. The threshold of n=50 is well-chosen: below this, the simple loop completes quickly with minimal operations, while above it, the logarithmic scaling of fast-doubling becomes beneficial.

Impact:

This optimization is particularly effective for workloads that frequently compute Fibonacci numbers in the small-to-medium range (n < 50), which are common in real-world applications. The 97% speedup indicates the test cases heavily favor this range, making the fast path highly beneficial while maintaining the theoretical efficiency for large inputs.

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	✅ 12 Passed
🌀 Generated Regression Tests	🔘 None Found
⏪ Replay Tests	🔘 None Found
🔎 Concolic Coverage Tests	🔘 None Found
📊 Tests Coverage	No coverage data found for fibonacci

⚙️ Click to see Existing Unit Tests

To edit these changes git checkout codeflash/optimize-Algorithms.fibonacci-mlbd0zet and push.