Guy's world records get deleted due to changes in atanh over time
For single-precision unary functions, it's easy enough to just exhaustively test every single input (there's only 4 billion of them). But double precision has prohibitively many inputs to test, so you have to resort to actual proof techniques to prove correct rounding for double-precision functions.
Lots of good stuff here: https://members.loria.fr/PZimmermann/papers/ .