Performance of our analytic density profile for different redshifts. Upper panel: most probable (mode) average matter density within spheres of enclosed mass M as a function of M (normalized to M₂₀₀; $\tilde{M}$ is equivalent to β in Eq. (8)), from our analytic result (Eq. (8), dashed lines), and from the MDPL2 simulation halos (solid lines; the shaded region includes 68% of the densities PDF), for z = 0 (blue) and z = 1 (green). Lower panel: ratio of MDPL2 over analytic mode profile as a function of enclosed mass. In the bottom panel, the ratio of the mode to the analytic profiles is displayed.