Particle radius s vs. particle count N for a disk system with I ≤.1 and a ≤ 4au. Above the black line, the numerical integration propagator with tree code for collision detection beats the analytic propagator using Kepler orbits (in terms of time efficiency). Precession due to a Jupiter has a small effect above the orange line, where T_coll = T_prec, and has a negligible effect above the orange dashed line, aT_coll = sT_prec. If the mass of three Earths is distributed over equal-sized planetoids (of Earth density), one is constrained to the blue line. On this line, precession is small for N > 10³ but only attains the much smaller error of s per orbit for N > 10⁹. Clearly, tree-code is better for these high number densities.