  We analyze a mixed quantum-classical algorithm recently derived from the
exact factorization equations [Min, Agostini, Gross, PRL {\bf 115}, 073001
(2015)] to show the role of the different terms in the algorithm in bringing
about decoherence and wavepacket branching. The algorithm has the structure of
Ehrenfest equations plus a "coupled-trajectory" term for both the electronic
and nuclear equations, and we analyze the relative roles played by the
different non-adiabatic terms in these equations, including how they are
computed in practise. In particular, we show that while the coupled-trajectory
term in the electronic equation is essential in yielding accurate dynamics,
that in the nuclear equation has a much smaller effect. A decoherence time is
extracted from the electronic equations and compared with that of augmented
fewest-switches surface-hopping. We revisit a series of non-adiabatic Tully
model systems to illustrate our analysis.
