More important than just increasing accuracy is knowing how much accuracy you have. With interval artihmetic, you keep an upper and lower bound of every calcula

More important than just increasing accuracy is knowing how much accuracy you have. With interval artihmetic, you keep an upper and lower bound of every calculation, and use the the appropriate floating point rounding modes when you manipulate the numbers. You can then try different methods of calculating your result and measure which is the least destructive - compiler optimisations can optimise for width rather than runtime. Some methods might produce a better upper bound, and others a better lower bound. In those cases you can take the intersection as your best result. See https://pypi.python.org/pypi/pyinterval https://pypi.python.org/pypi/pyinterval for an implementation in python.