ExactCalc
Software for exact computing based on interval arithmetic.
1/3 is not 0.33. Pi is not 3.14. Actually 1/3 is in interval [0.33, 0.34] and pi is in interval [3.14, 3.15].
During computation truncating error is accumulating. At end of computation it is needed to know real boundaries of result. The solution is given by interval arithmetic. Simply speaking, because 1/3 is in interval [0.33, 0.34] and 1/7 is in interval [0.14, 0.15], value 1/3 - 1/7 must be in [0.18, 0.2]. Computation can be arbitrary long and complex but interval arithmetic gives...