  Expressions for the gravitational wave (GW) energy flux and center-of-mass
energy of a compact binary are integral building blocks of post-Newtonian (PN)
waveforms. In this paper, we compute the GW energy flux and GW frequency
derivative from a highly accurate numerical simulation of an equal-mass,
non-spinning black hole binary. We also estimate the (derivative of the)
center-of-mass energy from the simulation by assuming energy balance. We
compare these quantities with the predictions of various PN approximants
(adiabatic Taylor and Pade models; non-adiabatic effective-one-body (EOB)
models). We find that Pade summation of the energy flux does not accelerate the
convergence of the flux series; nevertheless, the Pade flux is markedly closer
to the numerical result for the whole range of the simulation (about 30 GW
cycles). Taylor and Pade models overestimate the increase in flux and frequency
derivative close to merger, whereas EOB models reproduce more faithfully the
shape of and are closer to the numerical flux, frequency derivative and
derivative of energy. We also compare the GW phase of the numerical simulation
with Pade and EOB models. Matching numerical and untuned 3.5 PN order
waveforms, we find that the phase difference accumulated until $M \omega = 0.1$
is -0.12 radians for Pade approximants, and 0.50 (0.45) radians for an EOB
approximant with Keplerian (non-Keplerian) flux. We fit free parameters within
the EOB models to minimize the phase difference, and confirm degeneracies among
these parameters. By tuning pseudo 4PN order coefficients in the radial
potential or in the flux, or, if present, the location of the pole in the flux,
we find that the accumulated phase difference can be reduced - if desired - to
much less than the estimated numerical phase error (0.02 radians).
