  To detect the gravitational-wave (GW) signal from binary neutron stars and
extract information about the equation of state of matter at nuclear density,
it is necessary to match the signal with a bank of accurate templates. We
present the two longest (to date) general-relativistic simulations of
equal-mass binary neutron stars with different compactnesses, C=0.12 and
C=0.14, and compare them with a tidal extension of the effective-one-body
(EOB)model. The typical numerical phasing errors over the $\simeq 22$ GW cycles
are $\Delta \phi\simeq \pm 0.24$ rad. By calibrating only one parameter
(representing a higher-order amplification of tidal effects), the EOB model can
reproduce, within the numerical error, the two numerical waveforms essentially
up to the merger. By contrast, the third post-Newtonian Taylor-T4 approximant
with leading-order tidal corrections dephases with respect to the numerical
waveforms by several radians.
