  Let g : $\Omega$ = [0, 1] d $\rightarrow$ R denote a Lipschitz function that
can be evaluated at each point, but at the price of a heavy computational time.
Let X stand for a random variable with values in $\Omega$ such that one is able
to simulate, at least approximately, according to the restriction of the law of
X to any subset of $\Omega$. For example, thanks to Markov chain Monte Carlo
techniques, this is always possible when X admits a density that is known up to
a normalizing constant. In this context, given a deterministic threshold T such
that the failure probability p := P(g(X) > T) may be very low, our goal is to
estimate the latter with a minimal number of calls to g. In this aim, building
on Cohen et al. [9], we propose a recursive and optimal algorithm that selects
on the fly areas of interest and estimate their respective probabilities.
