Resistive RAM (ReRAM) is a promising technology with such advantages as small device size and in-memory-computing capability. However, designing optimal AI processors based on ReRAMs is challenging due to the limited precision, and the complex interplay between quality of result and hardware efficiency. In this paper we present a study targeting a low-power low-cost image classification application. We discover that the trade-off between accuracy and hardware efficiency in ReRAM-based hardware is not obvious and even surprising, and our solution developed for a recently fabricated ReRAM device achieves both the state-of-the-art efficiency and empirical assurance on the high quality of result.