  We investigate quantifying the difference between two hybrid dynamical
systems under noise and initial-state uncertainty. While the set of traces for
these systems is infinite, it is possible to symbolically approximate trace
sets using \emph{reachpipes} that compute upper and lower bounds on the
evolution of the reachable sets with time. We estimate distances between
corresponding sets of trajectories of two systems in terms of distances between
the reachpipes.
  In case of two individual traces, the Skorokhod distance has been proposed as
a robust and efficient notion of distance which captures both value and timing
distortions. In this paper, we extend the computation of the Skorokhod distance
to reachpipes, and provide algorithms to compute upper and lower bounds on the
distance between two sets of traces. Our algorithms use new geometric insights
that are used to compute the worst-case and best-case distances between two
polyhedral sets evolving with time.
