You can imagine an infinite-precision-real package that checks whether numerator and denominator are the exact same object and optimizes that case away. (And I

You can imagine an infinite-precision-real package that checks whether numerator and denominator are the exact same object and optimizes that case away. (And I wonder idly from time to time about making one that does know a bit about some particularly nice classes of number -- e.g., algebraic numbers -- and does all the things you'd like it to as long as you stay within such a class. Obviously as soon as you ask it for sqrt(2)+pi all that would go out the window.)