Wow, didn't expect this tool to be on Hacker News six years after publication! Herbgrind author here, ask me any questions you like! Also, if you're interested in this stuff, the Herbie project (which I also worked on) for numerical program synthesis is also really helpful for writing numerical code, and has had a lot of development over the years.
Thinking of all the people (some even actual friends) worked so long on numerical stability on scalar floating point operations, nearing a time when model-checking and proof tool are actually usable by the really-motivated developer ; thinking of them witnessing the arrival of GPUs and Tensor Cores, mixed-precision-everywhere and the tools now needing to scale so far it seems like starting from scratch...