⚡️ Speed up method Algorithms.fibonacci by 31%

[codeflash-ai]

📄 31% (0.31x) speedup for Algorithms.fibonacci in code_to_optimize/java/src/main/java/com/example/Algorithms.java

⏱️ Runtime : 4.91 milliseconds → 3.73 milliseconds (best of 5 runs)

📝 Explanation and details

The optimized code achieves a 31% runtime improvement (from 4.91ms to 3.73ms) by replacing the exponential-time recursive Fibonacci algorithm with an O(log n) fast-doubling iterative algorithm.

Key Changes:

1. Algorithm Replacement: The original recursive approach has O(φ^n) time complexity due to redundant recalculations of the same Fibonacci values. The optimized version uses the fast-doubling method, which computes F(n) in O(log n) time by processing the binary representation of n.

2. How Fast-Doubling Works:

   • Uses the mathematical identities: F(2k) = F(k) × (2×F(k+1) - F(k)) and F(2k+1) = F(k)² + F(k+1)²
   • Processes bits of n from most significant to least significant, doubling the index at each step
   • Depending on whether each bit is 0 or 1, selects either (F(2k), F(2k+1)) or (F(2k+1), F(2k+2))

3. Stack Usage: Eliminates deep recursion (which for large n would cause stack overflow), replacing it with a simple loop that iterates ~log₂(n) times.

Why This Is Faster:

For even moderately-sized inputs, the recursive version performs exponentially many redundant calculations. For example, computing F(20) recursively makes ~21,891 function calls, while the optimized version makes only ~5 iterations (since log₂(20) ≈ 4.3). This dramatic reduction in operations directly translates to the observed 31% speedup.

Impact:

This optimization particularly benefits workloads computing Fibonacci numbers for n > 15, where the exponential cost of recursion becomes prohibitive. The improvement scales dramatically with larger inputs—while the 31% speedup is measured at a specific test case, the advantage grows exponentially as n increases.

✅ 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	100.0%

⚙️ Click to see Existing Unit Tests

To edit these changes git checkout codeflash/optimize-Algorithms.fibonacci-mlbh5d2o and push.