Add to ORKGInternational audienceThe treatment of the axiomatic theory of floating-point numbers is out of reach of current SMT solvers, especially when it comes to automatic reasoning on approximation errors. In this paper, we describe a dedicated procedure for such a theory, which provides an interface akin to the instantiation mechanism of an SMT solver. This procedure is based on the approach of the Gappa tool: it performs saturation of consequences of the axioms, in order to refine bounds on expressions. In addition to the original approach, bounds are further refined by a constraint solver for linear arithmetic. Combined with the natural support for equalities provided by SMT solvers, our approach improves the treatment of goals coming from dedu...