this is basically how affine arithmetic works. but in interval arithmetic or modal interval arithmetic the representation of a float is two floats, and in affine arithmetic the representation of a float is a potentially unboundedly large set of float coefficients, none of which can be safely ignored, so there are some drawbacks to this approach
i'm not sure why wayne doesn't mention affine arithmetic and modal interval arithmetic in this post; i'd think they were relevant
Or more accurately speaking, they can be ignored but at some expense of accuracy. (You can always approximate every variable with a (-inf, +inf) interval!) There are several working ways to "compress" affine variables when they get too many.
Probably a worse problem with AA is that every multiplication introduces a new variable, so it can be very frequent to head into the maximum number of variables set for the reasonable performance...
i'm not sure why wayne doesn't mention affine arithmetic and modal interval arithmetic in this post; i'd think they were relevant