Interplay of softening length and adaptive time steps for energy conservation. We show the time evolution of the mass enclosed within 10 pc (upper panel) and the energy conservation (lower panel) for simulations of collisionless DM. The shaded regions indicate the uncertainties estimated based on shot noise. The simulations employ an adaptive time step, except for the results given by the yellow curve. More details can be found in Table A.1; the corresponding names are A, B, C, D, E, and F.