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The availability of accurate numerical waveforms is an important requirementfor the creation and calibration of reliable waveform models for gravitationalwave astrophysics. For black hole-neutron star binaries, very few accuratewaveforms are however publicly available. Most recent models are calibrated toa large number of older simulations with good parameter space coverage forlow-spin non-precessing binaries but limited accuracy, and a much smallernumber of longer, more recent simulations limited to non-spinning black holes.In this paper, we present long, accurate numerical waveforms for three newsystems that include rapidly spinning black holes, and one precessingconfiguration. We study in detail the accuracy of the simulations, and inparticular perform for the first time in the context of BHNS binaries adetailed comparison of waveform extrapolation methods to the results of CauchyCharacteristic Extraction. The new waveforms have $<0.1\,{\rm rad}$ phaseerrors during inspiral, rising to $\sim (0.2-0.4)\,{\rm rad}$ errors at merger,and $\lesssim 1\%$ error in their amplitude. We compute the faithfulness ofrecent analytical models to these numerical results, and find that modelsspecifically designed for BHNS binaries perform well ($F>0.99$) for binariesseen face-on. For edge-on observations, particularly for precessing systems,disagreements between models and simulations increase, and models that includeprecession and/or higher-order modes start to perform better than BHNS modelsthat currently lack these features.

High-accuracy waveforms for black hole-neutron star systems with spinning black holes