Cache expensive computations

Identify the expensive computations in the following code that are called repeatedly with the same inputs: [Paste code]. Apply memoization for pure functions with a small input space. Use an LRU cache with a bounded size for functions with a large input space. Add TTL-based expiry for any result that may become stale. Show the before and after code and write a micro-benchmark that demonstrates the speedup for a representative workload.