The position and rotational errors ---also called pose errors--- of the end-effector of a robotic mechanical system are partly due to its joints clearances, which are the play between their pairing elements. In this paper, we model the prediction of those errors by formulating two continuous constrained optimization problems that turn out to be NP-hard. We show that techniques based on numerical constraint programming can handle globally and rigorously those hard optimization problems. In particular, we present preliminary experiments where our global optimizer is very competitive compared to the best-performing methods presented in the literature, while providing more robust results.