What does "y depends weakly on x" mean? I have come across this phrase often, and a quick Google search indicates that it is common:

$ y $ depends weakly on $ x $.

I understand what a dependency is. If $ y $ depends on $ x $, that means it is possible to deduce $ y $ from $ x $, given all other factors:
$$ y = f(x) $$
But what does " $ y $ depends weakly on $ x $ " mean?

For context, I came across this phrase in my study of parallel algorithms:

An algorithm is said to be highly scalable if the efficiency depends only weakly on the number of processors when the problem size and the number of processors increase by the same factor.

(I'm including this as an example only, I'm not asking for a discussion of scalability.)

As Ross Millikan said, there is no specific formula as this is a soft term. The idea is that $ y $ will only change to a small degree as $ x $ changes.
For example, $ y $ could be said to depend weakly on $ x $ if $ y $ depends on $ \log x $ or $ \frac {1}{\log x} $ or $ \sqrt x $ or $ \frac {1}{\sqrt x} $.
