The number of digits out is only a simple function of the digits in if you're doing fairly trivial calculations. Checkout https://en.wikipedia.org/wiki/Interva

The number of digits out is only a simple function of the digits in if you're doing fairly trivial calculations. Checkout https://en.wikipedia.org/wiki/Interval_arithmetic https://en.wikipedia.org/wiki/Interval_arithmetic for what it takes to monitor precision through complex calculations (in particular, see the bits about using the taylor expansions of non-trivial functions).