Preliminary: No, this isn't homework. This is how-do-I-present-my-results-accurately. It slightly crosses over into CS but the fundamental question is math - I'm just not sure how to phrase it without the CS-based word-problem.
Say there is some task T which requires x time and y memory to complete once. There is a variant of this task, T', which requires x' time and y' memory to complete once.
Take "efficiency" to be defined as a measure of how many times the task can be run in a given amount of time.
Limited to y memory, if x' = 0.5x and y' = 1y, T' can be completed twice in x time by simply running it twice in series. Thus, T' is twice as efficient as T in this case.
Assuming sufficient memory, if y' = 0.5y and x' = 1x, T' can be completed twice in x time by running it twice in parallel. Thus, T' is also twice as efficient as T in this case.
If x' = 0.5x and y' = 2y, or vice versa, T' is equally efficient to T. Runs in half the time and twice the space, or twice the space in half the time.
My question: There must be some formula here, but I can't seem to figure out how I'm figuring it out in the simple cases (in a way extensible to automation).
Well. Barely posted this, and the answer comes to me. Looking at the changes as a decimal: Multiply them.