An operator called CID and an efficient variant 3BCID were proposed in 2007. For the numerical CSP handled by interval methods, these operators compute a partial consistency equivalent to Partition-1-AC for the discrete CSP. In addition to the constraint propagation procedure used to refute a given subproblem, the main two parameters of CID are the number of times the main CID procedure is called and the maximum number of sub-intervals treated by the procedure. The 3BCID operator is state-of-the-art in numerical CSP, but not in constrained global optimization, for which it is generally too costly. This paper proposes an adaptive variant of 3BCID called ACID. The number of variables handled is auto-adapted during the search, the other parameters are fixed and robust to modifications. On a representative sample of instances, ACID appears to work efficiently, both with the HC4 constraint propagation algorithm and with the state-of-the-art Mohc algorithm. Experiments also highlight that it is relevant to auto-adapt only a number of handled variables, instead of a specific set of selected variables. Finally, ACID appears to be the best interval constraint programming operator for solving and optimization, and has been therefore added to the default strategies of the Ibex interval solver.