Expression equality is handled by https://github.com/kisonecat/math-expressions using a few heuristics, which is necessary because Richardson's theorem says this problem is undecidable. The main trick is to regard the expressions as complex-valued functions, find a point where the value is (nearly) equal, and then check for numerical equality in a neighborhood. (Doing this over the complex plane addresses the problem that many common expressions like sqrt(small number-x^2) have a restricted domain over the reals).

We rely on unit tests from Chris Sangwin (who wrote the textbook _Computer Aided Assessment of Mathematics_) to ensure that we're adjudicating expression equality mostly correctly.