/sci/ - Science & Math

>>9921439
Floating point arithmetic is both interesting and infuriating. Basically, substracting similarly sized numbers brings out the low level noise first and forfront, which if you then follow up with a large multiplication can totally destroy your results.

It's called catastrophic cancellation, see pic related. It's the reason numerical differentiation can't be done with the standard derivative formula, because f(x+h)-f(x) destroys your precision.

If you use op's retarded formula, and then multiply it by a large number (to calculate an area for an integral for eg), it will likely induce catastrophic cancellation.