Eccentricity as a function of semimajor axis for a planetary system orbited by a secondary star of 1 M_⊙ after 0.5 Myr of integration using Nemesis (big black bullets) and the single 8th order symplectic integrator in Huayno (smaller white bullets). The final eccentricity of the planets in the direct integration and the component method are indistinguishable in the figure, with an absolute mean error < 2 × 10⁻⁴ for each of the planets.