  Gravitational waveforms from numerical simulations are a critical tool to
test and analytically calibrate the waveform models used to study the
properties of merging compact objects. In this paper, we present a series of
high-accuracy waveforms produced with the SpEC code for systems involving at
least one neutron star. We provide for the first time waveforms with sub-radian
accuracy over more than twenty cycles for low-mass black hole-neutron star
binaries, including binaries with non-spinning objects, and binaries with
rapidly spinning neutron stars that maximize the impact on the gravitational
wave signal of the near-resonant growth of the fundamental excitation mode of
the neutron star (f-mode). We also provide for the first time with SpEC a
high-accuracy neutron star-neutron star waveform. These waveforms are made
publicly available as part of the SxS catalogue. We compare our results to
analytical waveform models currently implemented in data analysis pipelines.
For most simulations, the models lie outside of the predicted numerical errors
in the last few orbits before merger, but do not show systematic deviations
from the numerical results: comparing different models appears to provide
reasonable estimates of the modeling errors. The sole exception is the
equal-mass simulation using a rapidly counter-rotating neutron star to maximize
the impact of the excitation of the f-mode, for which all models perform
poorly. This is however expected, as even the single model that takes f-mode
excitation into account ignores the significant impact of the neutron star spin
on the f-mode excitation frequency.
