Current state of "recognizing zero" ?



I was curious about the current state of the problem of simplifying constant expressions.

I realize that the problem is unsolvable, in general, but I wonder if there are classes of solutions that exist.

Basically, I'm talking about finite expressions built up from constant integers, using +,-,*,/,exp(x),log(x),expt(x,y), sqrt(x), etc.  Ditto for additional standard constants like %pi, %e, %i, etc.

I'm not talking about floating point numbers here, but exact computations.

I'm not talking about "for all" or "there exists" types of computations, but merely constant expressions.