⚡️ Speed up method Algorithms.fibonacci by 11%

[codeflash-ai]

📄 11% (0.11x) speedup for Algorithms.fibonacci in code_to_optimize/java/src/main/java/com/example/Algorithms.java

⏱️ Runtime : 4.23 milliseconds → 3.82 milliseconds (best of 5 runs)

📝 Explanation and details

The optimized code achieves a 10% runtime improvement (from 4.23ms to 3.82ms) by replacing the O(n) iterative Fibonacci algorithm with an O(log n) fast doubling algorithm.

Key Performance Improvements:

1. Algorithmic Complexity Reduction: The original code performs n-2 iterations with addition operations. The optimized version reduces this to approximately log₂(n) iterations by using the mathematical fast doubling formulas:

   • F(2k) = F(k) × (2×F(k+1) - F(k))
   • F(2k+1) = F(k+1)² + F(k)²

2. Bit Manipulation Efficiency: The optimization processes the binary representation of n bit-by-bit (starting from the highest bit), allowing it to "double" its way to the result exponentially faster than linear iteration. For example, computing F(1000) requires ~10 iterations instead of 998.

3. Constant Space with Minimal Operations: Both implementations use O(1) space, but the optimized version performs fewer total arithmetic operations for larger n values. The bit shift operation (b << 1) for doubling is also faster than explicit multiplication.

Performance Characteristics:

• For small n values (< 20), the overhead of bit manipulation may make performance similar to the original
• For medium to large n values (≥ 30), the logarithmic advantage becomes increasingly significant
• The 10% speedup measured suggests the test workload includes sufficiently large Fibonacci numbers where the O(log n) complexity provides measurable gains

Trade-offs:

The optimized code is slightly more complex to understand due to the mathematical doubling formulas and bitwise operations, but this is a reasonable trade-off for the consistent runtime improvement, especially as n scales.

✅ 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-mlbf0man and push.