  An efficient technique to solve precision problems consists in using exact
computations. For geometric predicates, using systematically expensive exact
computations can be avoided by the use of filters. The predicate is first
evaluated using rounding computations, and an error estimation gives a
certificate of the validity of the result. In this note, we studies the
statistical efficiency of filters for cosphericity predicate with an assumption
of regular distribution of the points. We prove that the expected value of the
polynomial corresponding to the in sphere test is greater than epsilon with
probability O(epsilon log 1/epsilon) improving the results of a previous paper
by the same authors.
