We present FARA, a novel approach for fast approximation of RFD-like descriptors in the context of document retrieval systems. RFD-like descriptors are widely used for document representation, but their computation is expensive, especially for large document collections. Our method is a CPU-friendly gradient maps computation approximation with sequential memory access and integer-only calculations. There are three types of operations that we use: addition, subtraction, and absolute values. It allows us to effectively use SIMD extensions, resulting in an additional increase in the running speed. Experimental results demonstrate that FARA achieves the same accuracy as RFDoc descriptors and significantly reduces the computational overhead. The proposed approach achieves a twofold speed improvement of gradient maps computation and 25% acceleration of overall descriptor computing time compared to the most efficient RFDoc implementation.