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.


Google Scholar gives 0 hits for "numeric equality testing"


Has this kind of problem been studied before? What are the right keywords to search for?



Numeric equality testing?
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](http://portal.acm.org/citation.cfm?id=32465&dl=ACM&coll=DL&CFID=111332393&CFTOKEN=61560774) by Gaston H. Gonnet might be a starting point for checking that out.


