Heuristics based on transcendentality

This is a useful heuristic, quite effective, but not widely applicable. The idea is best illustrated with an example. Suppose that our expression to match is a rational polynomial in x. Suppose that the pattern has terms in x and in e^x. Since we know that no polynomial in x is equal to any polynomial in e^x, then then only possible matching is one which eliminates all appearances of e^x in the pattern.