Tree code relative errors Err(a_k) (averaged over all the three Cartesian coordinates) for the gravitational field computation as a function of the CPU time. The data are illustrated for different particle numbers (N = 10⁴, N = 10⁵, and N = 10⁶) in panels a, b, and c. In each panel, the full line connects the points related to a computation of the gravitational field made with the quadrupole approximation, while the dashed line refers to computations made by using just the monopole term. The shape of the “void” markers distinguishes different choices of θ with the “standard” criterion (Eq. (20)): θ = 0.8 (void squares), θ = 0.6 (void triangles), and θ = 0.4 (void circles). Results for different opening angles with the “opening law” (Eq. (21)) criterion are also marked: θ = 0.8 (solid squares), θ = 0.6 (solid triangles), and θ = 0.4 (solid circles).