TITLE: Numeric equality testing?
QUESTION [6 upvotes]: Suppose we have two closed-form expressions with $k$ unknowns which are hard to test for equality but easy to evaluate numerically over $\mathbb{R}^k$. One could then approach the problem of equality testing by checking equality numerically at several points. The interesting questions are then -- for which kinds of expressions can you do it, how to pick sampling points and how many points are needed.
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Has this kind of problem been studied before? What are the right keywords to search for?

REPLY [7 votes]: Maple has a procedure testeq which is a  "random polynomial-time equivalence tester". It works in this way. The 1986 paper  New results for random determination of equivalence of expressions by  Gaston H. Gonnet might be a starting point for checking that out.