Time to Call a Memoized Function

Let's suppose we make N calls to m
Suppose the cache hit rate is h
- Cache miss rate is 1-h
- The real f gets called about N(1-h) times
Suppose the average time for f to execute is f
- Time spent in f is N(1-h)f
Suppose the average time to manage the cache is K
- Time spent managing the cache is NK
Total time spent for N calls: N(1-h)f + NK
- Average time per call: (1-h)f + K