  Binary neutron-star systems represent one of the most promising sources of
gravitational waves. In order to be able to extract important information,
notably about the equation of state of matter at nuclear density, it is
necessary to have in hands an accurate analytical model of the expected
waveforms. Following our recent work, we here analyze more in detail two
general-relativistic simulations spanning about 20 gravitational-wave cycles of
the inspiral of equal-mass binary neutron stars with different compactnesses,
and compare them with a tidal extension of the effective-one-body (EOB)
analytical model. The latter tidally extended EOB model is analytically
complete up to the 1.5 post-Newtonian level, and contains an analytically
undetermined parameter representing a higher-order amplification of tidal
effects. We find that, by calibrating this single parameter, the EOB model can
reproduce, within the numerical error, the two numerical waveforms essentially
up to the merger. By contrast, analytical models (either EOB, or Taylor-T4)
that do not incorporate such a higher-order amplification of tidal effects,
build a dephasing with respect to the numerical waveforms of several radians.
