  We discuss through multiple numerical examples the accuracy and efficiency of
a micro-macro acceleration method for stiff stochastic differential equations
(SDEs) with a time-scale separation between the fast microscopic dynamics and
the evolution of some slow macroscopic state variables. The algorithm
interleaves a short simulation of the stiff SDE with extrapolation of the
macroscopic state variables over a longer time interval. After extrapolation,
we obtain the reconstructed microscopic state via a matching procedure: we
compute the probability distribution that is consistent with the extrapolated
state variables, while minimally altering the microscopic distribution that was
available just before the extrapolation. In this work, we numerically study the
accuracy and efficiency of micro-macro acceleration as a function of the
extrapolation time step and as a function of the chosen macroscopic state
variables. Additionally, we compare the effect of different hierarchies of
macroscopic state variables. We illustrate that the method can take
significantly larger time steps than the inner microscopic integrator, while
simultaneously being more accurate than approximate macroscopic models.
