Then you aren't multiplying doubles, it would be a shame to get a completely wrong answer on an ill-conditioned problem because the implementation disregarded t

Then you aren't multiplying doubles, it would be a shame to get a completely wrong answer on an ill-conditioned problem because the implementation disregarded the spec, cf. "the fastest way to process UTF-8 is to truncate it to ASCII", "the fastest RSA encryption is ROT-13". Also note that floats are only faster with packed instructions (often not possible without changing APIs) or when memory bandwidth is an issue.