  Conformal prediction constructs a confidence set for an unobserved response
of a feature vector based on previous identically distributed and exchangeable
observations of responses and features. It has a coverage guarantee at any
nominal level without additional assumptions on their distribution. Its
computation deplorably requires a refitting procedure for all replacement
candidates of the target response. In regression settings, this corresponds to
an infinite number of model fits. Apart from relatively simple estimators that
can be written as pieces of linear function of the response, efficiently
computing such sets is difficult, and is still considered as an open problem.
We exploit the fact that, \emph{often}, conformal prediction sets are intervals
whose boundaries can be efficiently approximated by classical root-finding
algorithms. We investigate how this approach can overcome many limitations of
formerly used strategies; we discuss its complexity and drawbacks.
