### Fast and dynamically reliable symplectic integration for solar system N-body problems

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We apply one of the exactly symplectic integrators, that we call HB15, of \cite{HB15} to solve solar system $N$-body problems. We compare the method to Wisdom-Holman methods (WH), MERCURY, and others and find HB15 to have high efficiency. Unlike WH, HB15 solved $N$-body problems exhibiting close encounters with small, acceptable error, although frequent encounters slowed the code. Switching maps like MERCURY change between two methods and are not exactly symplectic. We carry out careful tests on their properties and suggest they must be used with caution. We use different integrators to solve a 3-body problem consisting of a binary planet orbiting a star. For all tested tolerances and time steps, MERCURY unbinds the binary after 0 to 25 years. However, in the solutions of HB15, a time-symmetric Hermite code, and a symplectic Yoshida method, the binary remains bound for $>1000$ years. The methods' solutions are qualitatively different, despite small errors in the first integrals in most cases. Several checks suggest the qualitative binary behavior of HB15's solution is correct. The Bulirsch-Stoer and Radau methods in the MERCURY package also unbind the binary before a time of 50 years.