I'm running a program that evaluates equalities after I substitute all symbols for numbers. The equalities on floats are giving me trouble. My program is reaching a point where something like the following is being evaluated: 2.304793200735844`*^-8 == 2.30479302310016`*^-8 . This gives False, despite the difference being 1.77636*10^-15, which is below the Chop threshold of 10^-10. Running Chop on both numbers obviously doesn't fix the problem, since neither number is individually below the threshold.

Chop[2.304793200735844`*^-8 - 2.30479302310016`*^-8 ]==0 gives the correct result, but I can't easily make this change as not all comparisons are between floats or even lists of floats (Chop[a-b] == 0 or {0,0,0,...} is not always a valid way to test equality between a and b).

I want to avoid overcomplicating my program: I don't want to do a ReplaceAll on a_==b_ /; (a and b are numbers) -> Chop[a-b]==0 as this is very complicated, requires something like Hold, and doesn't resolve the same exact issues which arise in the case of float inequality comparisons. There's gotta be a better way! If there's not, what's the best solution?