Optimize a core kernel for throughput

You are given a mocked “core kernel” function (similar in spirit to a GPU kernel / tight compute loop) that is functionally correct but slow.

Task

• Optimize the kernel to improve performance as much as possible within a fixed timebox (e.g., ~2 hours).
• You may use typical low-level optimization techniques such as:
  • loop unrolling
  • memory access optimization (e.g., coalescing / cache-friendly access)
  • reducing allocations and copies
  • operator fusion / reducing intermediate buffers
  • vectorization (SIMD) and/or parallelism where applicable
• Provide:
  1. Your optimized implementation
  2. A short write-up explaining what you changed and why
  3. Benchmarks showing speedup vs baseline
  4. Evidence you preserved correctness (tests or checks)

Constraints / expectations

• Maintain identical output semantics.
• Optimize for end-to-end runtime (not just micro-benchmarks of one line).
• Explain tradeoffs (readability vs performance, portability, precision, etc.).