User blog comment:Vel!/Piecewise Puzzle/@comment-1605058-20141222082744

Just throwing it there: Solution assuming we have access to any irrational constant α:

floor(α*floor(x))+floor(-α*floor(x))

Proof of validity: floor(y)+floor(-y) is 0 for integers and -1 elsewhere, so if we put y=α*floor(x), this is integer whenever α*floor(x) is. But since α is irrational, this can only happen if floor(x), which happens exactly on interval [0,1).

Because e^1 and sin(1) are irrational, this solves both CAMFE and CAMFS.