I know that the field of real algebraic geometry studies zero sets of real polynomials. I am looking for texts on a generalization of real algebraic geometry that talk about zero sets of classes of functions other than polynomials, for example, elementary functions.
Let me give an example of what I mean. Consider the zero set of the function defined by the expression $e^x + \sin(x) + x^3$. Such a function and its associated zero set would not be studied in real algebraic geometry, but it would be studied in a text that generalizes real algebraic geometry. Is there such a text somewhere?