  For a spherical dark matter halo with isotropic velocity distribution, the
phase space distribution function (DF), the energy distribution, and the
density profile form a set of self-consistent description of its equilibrium
state, and knowing one is sufficient to determine the other two. The
Navarro-Frenk-White density profile (NFW profile) is known to be a good
approximation to the spherically-averaged density distribution in simulated
haloes. The DARKexp energy distribution is also known to compare well with the
simulated energy distribution. We present a quantitative assessment of the NFW
and DARKexp fits to the simulated DF and energy distribution for a wide range
of haloes in a dark-matter-only simulation from the IllustrisTNG Project. As
expected, we find that the NFW fits work well except at low energy when the
density at small radii deviates from the NFW profile. Further, the NFW and
DARKexp fits have comparable accuracy in the region where both fit well, but
the DARKexp fits are better at low energy because they require matching of the
central gravitational potential. We also find an approximate relation between
the energy scale parameterizing the DARKexp energy distribution and that
defined by the characteristic density and radius of the NFW profile. This
relation may be linked to the relaxation process during halo formation.
