I am regularly reminded of William Kahan's (the godfather of IEEE-754 floating point) admonition: A floating-point calculation should usually carry twice as many bits in intermediate results as the input and output deserve. He makes this observation on the basis of having seen many real world numerical bugs which are corrupt in half of the carried digits.
These bugs are so subtle and so pervasive that its almost always cheaper to throw more hardware at the problem than it is to hire a numerical analyst. Chances are that you aren't clever enough to unit test your way out of them, either.
These bugs are so subtle and so pervasive that its almost always cheaper to throw more hardware at the problem than it is to hire a numerical analyst. Chances are that you aren't clever enough to unit test your way out of them, either.