# Metrics and Evaluation/Problem11

Three enhancements with the following speed-up are proposed for a new architecture:

``````Enhancement A: Speedup = 30;

Enhancement B: Speedup = 20;

Enhancement C: Speedup = 15;
``````

Only one enhancement is usable at a time. Assume, for some benchmark, the possible fraction of use is 15% for each of the enhancements A and B and 70% for enhancement C. We want to maximize performance.

If only one enhancement can be implemented, which should it be?

Solution Let the speedup when implementing only enhancement i be Speedupi, and let Speedupij denote the speedup when employing enhancement i and j.

Thus, if only one enhancement can be implemented, enhancement 3 off ers much greater speedup.

Thus, if only a pair of enhancements can be implemented, enhancements A and C off er the greatest speedup.

Selecting the fastest enhancement(s) may not yield the highest speedup. As Amdahl's Law states, an enhancement contributes to speedup only for the fraction of time it can be used.