Sometimes when the problem space is simple enough you can get the best of both worlds by using regex to perform your tokenization when lexing and then passing the tokens to a traditional stack based parser. It’s possible for this approach to be bad performance wise but it depends on the use case.

The lexer that yacc implements is indeed regex based and as I also recently discovered was originally written by a little known developer by the name of Eric Schmidt [1]

1: https://en.m.wikipedia.org/wiki/Lex_(software)