Cost functions to judge time/memory/accuracy tradeoffs

I am working on an interesting algorithm: Its absolute error is exponential in a parameter $$j \in \mathbb{N}$$, and for a given $$j$$, I have complete freedom to choose between an $$\mathcal{O}(1)$$ time-complexity algorithm with memory consumption $${\sim}2^{j}$$, or a $$\mathcal{O}(2^j)$$ time-complexity algorithm with $$\mathcal{O}(1)$$ memory consumption. I can also "meet in the middle" and consume any intermediate amount of memory and compute that I wish.

I'm having trouble deciding on how make the compute/memory/accuracy tradeoffs. Have there been cost functions developed that could help answer this question?

Obviously, I could write something like $$\mathrm{cost} = c_1 t + c_2 m + c_3 e$$ for evaluation time $$t$$, memory consumption $$m$$ and error $$e$$, and just pick three positive constants $$c_1, c_2, c_3$$. But I would prefer to use a cost function that someone has already put some thought into.

• If you can modify the behaviour with parameters (as opposed to being to reprogram the whole algorithm), this is a good time to employ an autotuner. Determining the best trade-off from purely theoretical concerns will almost certainly give suboptimal performance. – Richard Mar 1 at 22:32
• @Richard: Do you have a recommendation for an autotuner? – user14717 Mar 1 at 22:41