Simplify non-linear but simple expression with max and min

Question

I have this code:

max(n+1,min(numPages+n-4,currentPage+n-2))

which is equivalent to the expression

$\max\{n+1, \min\{N+n-4, m+n-2\}\}$

$0<m<N, 0\le n\le5$

Is there any neat/weird trick to simplify it? Even only w.r.t. a computational standpoint?

Answer 1

though it hardly matters to have 2-3 more or less additions(or any basic arithmetic operations, as at hardware level it's very fast, so definitely other components of a code make the bottleneck for efficiency, but as you have asked:

$\max\{n+1, \min\{N+n-4, m+n-2\}\}$

assuming all are positive numbers (as it shows, they are page numbers etc),

it is equivalent to

       n + max{1, min{N-4, m-2}}

// by doing this you are avoiding 2 extra additions during evaluation.

Now in all cases you can write

       n+1 + min{N-5, m-3} 

note that you don't have to check whether $min\{N-5, m-3\}$ > 0 if you constrain N & m accordingly.

any other optimization I could think of, is subjective to the implementation and scenario you are dealing with.

So overall we have saved 1 addition and 1 comparison.