  An accurate and efficient method dealing with the few-body dynamics is
important for simulating collisional N-body systems like star clusters and to
follow the formation and evolution of compact binaries. We describe such a
method which combines the time-transformed explicit symplectic integrator
(Preto & Tremaine 1999; Mikkola & Tanikawa 1999) and the slow-down method
(Mikkola & Aarseth 1996). The former conserves the Hamiltonian and the angular
momentum for a long-term evolution, while the latter significantly reduces the
computational cost for a weakly perturbed binary. In this work, the Hamilton
equations of this algorithm are analyzed in detail. We mathematically and
numerically show that it can correctly reproduce the secular evolution like the
orbit averaged method and also well conserve the angular momentum. For a weakly
perturbed binary, the method is possible to provide a few order of magnitude
faster performance than the classical algorithm. A publicly available code
written in the c++ language, SDAR, is available on GitHub
(https://github.com/lwang-astro/SDAR). It can be used either as a stand alone
tool or a library to be plugged in other $N$-body codes. The high precision of
the floating point to 62 digits is also supported.
