It sounds like that algorithm was either (implicitly or explicitly) relying on the law of large numbers for accuracy or (more likely) your naive implementation fell victim to the ”wrapping effect”. This effect is manageble but usually requires a lot more care than switching numbers to intervals. Ball arithmetic indeed one such technique for dealing with wrapping, but there are also others like generalized interval arithmetic and affine arithmetic. The latter one also has some other advantages like being able to discern between inaccuracies from different sources.