  The density profiles of dark matter haloes are commonly described by fitting
functions such as the NFW or Einasto models, but these approximations break
down in the transition region where halos become dominated by newly accreting
matter. Here we present a simple, accurate new fitting function that is
inspired by the asymptotic shapes of the separate orbiting and infalling halo
components. The orbiting term is described as a truncated Einasto profile,
$\rho_{\rm orb} \propto \exp \left[-2/\alpha\ (r / r_{\rm s})^\alpha - 1/\beta\
(r / r_{\rm t})^\beta \right]$, with a five-parameter space of normalization,
physically distinct scale and truncation radii, and $\alpha$ and $\beta$, which
control how rapidly the profiles steepen. The infalling profile is modelled as
a power law in overdensity that smoothly transitions to a constant at the halo
centre. We show that these formulae fit the averaged, total profiles in
simulations to about 5% accuracy across almost all of an expansive parameter
space in halo mass, redshift, cosmology, and accretion rate. When fixing
$\alpha = 0.18$ and $\beta = 3$, the formula becomes a three-parameter model
that fits individual halos better than the Einasto profile on average. By
analogy with King profiles, we show that the sharp truncation resembles a
cut-off in binding energy.
