  Direct N-body simulations and symplectic integrators are effective tools to
study the long-term evolution of planetary systems. The Wisdom-Holman (WH)
integrator in particular has been used extensively in planetary dynamics as it
allows for large timesteps at good accuracy. One can extend the WH method to
achieve even higher accuracy using several different approaches. In this paper
we survey integrators developed by Wisdom et al. (1996), Laskar & Robutel
(2001, and Blanes et al. (2013). Since some of these methods are harder to
implement and not as readily available to astronomers compared to the standard
WH method, they are not used as often. This is somewhat unfortunate given that
in typical simulations it is possible to improve the accuracy by up to six
orders of magnitude (!) compared to the standard WH method without the need for
any additional force evaluations. To change this, we implement a variety of
high order symplectic methods in the freely available N-body integrator
REBOUND. In this paper we catalogue these methods, discuss their differences,
describe their error scalings, and benchmark their speed using our
implementations.
