>Dual numbers cannot, because they use plain old floating point math in the derivative equations. There's nothing stopping you from switching out the floating

>Dual numbers cannot, because they use plain old floating point math in the derivative equations. There's nothing stopping you from switching out the floating point for rationals or something like that. For example, the Haskell `ad` package has its functions parameterized over all instances of Num: http://hackage.haskell.org/package/ad-3.4/docs/Numeric-AD.html#v:diff http://hackage.haskell.org/package/ad-3.4/docs/Numeric-AD.ht...