  In this paper we review different expansions for neutrino oscillation
probabilities in matter in the context of long-baseline neutrino experiments.
We examine the accuracy and computational efficiency of different exact and
approximate expressions. We find that many of the expressions used in the
literature are not precise enough for the next generation of long-baseline
experiments, but several of them are while maintaining comparable simplicity.
The results of this paper can be used as guidance to both phenomenologists and
experimentalists when implementing the various oscillation expressions into
their analysis tools.
