Using floating points in the reachability computation produces ungauged approximation due to their inexact arithmetic. In order to estimate this reached set approximation, floating point types must be replaced by their exact interval-based approximations and the set-level functions (such as Bundle::is_empty(), intersect(const Bundle&, const Boundle&), and Polytope::includes) must be provided in two versions: a correct/under-approximated version and a complete/over-approximated version.