This is not related to the theoretical methods (read Big $O$) of determining complexity expressions. Suppose there is input variable $x$ and output variable $y$ and 10 other variables that affect the output but are kept fixed. So I vary $x$ over 100 values and record corresponding $x,y$. This is one MC run. Then I can find the relationship between $x$ and $y$ by poly-fitting, log-log analysis etc. Then I conclude something like $y=cx,y=x^c,y=c^x$.
Now we can run 2-3 more simulations by changing the 10 variables and collecting the $x-y$ data. And I may find conclusions for them also.
My question is how many such situations we have to run to say with confidence that the relationship between the variables in the context of the simulator used has been established?
Is that dependent on the fact that the relationship is linear, polynomial or exponential? For example, if the relationship is linear then is one MC run enough to establish the exact math expression for the relationship.