This paper is concerned with the exact solution of mixed-integer programs
(MIPs) over the rational numbers, i.e., without any roundoff errors and error
tolerances. Here, one computational bottleneck that should be avoided whenever
possible is to employ large-scale symbolic computations. Instead it is often
possible to use safe directed rounding methods, e.g., to generate provably
correct dual bounds. In this work, we continue to leverage this paradigm and
extend an exact branch-and-bound framework by separation routines for safe
cutting planes, based on the approach first introduced by Cook, Dash, Fukasawa,
and Goycoolea in 2009. Constraints are aggregated safely using approximate dual
multipliers from an LP solve, followed by mixed-integer rounding to generate
provably valid, although slightly weaker inequalities. We generalize this
approach to problem data that is not representable in floating-point
arithmetic, add routines for controlling the encoding length of the resulting
cutting planes, and show how these cutting planes can be verified according to
the VIPR certificate standard. Furthermore, we analyze the performance impact
of these cutting planes in the context of an exact MIP framework, showing that
we can solve 21.5% more instances and reduce solving times by 26.8% on the
MIPLIB 2017 benchmark test set