Actually I find that Computer Science is one of the most narrow disciplines.
I disagree; having any sort of thorough knowledge about computers requires at least some education from almost all parts of the STEM curricula. Any person who actually gives a shit about computers should know (with at least some rudimentary level of competency) a whole spectrum of things from semiconductor theory to abstract models of computation. The set of sciences and fields of mathematics you need to now master to have a solid understanding of the operation of a computer is mind boggling.
Numeric stability is probably not all that important when you're guessing.