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Recurrent Neural Networks (RNNs) are a key technology for applications such as automatic speech recognition or machine translation. Unlike conventional feed-forward DNNs, RNNs remember past information to improve the accuracy of future predictions and, therefore, they are very effective for sequence processing problems. For each application run, recurrent layers are executed many times for processing a potentially large sequence of inputs (words, images, audio frames, etc.). In this paper, we observe that the output of a neuron exhibits small changes in consecutive invocations.~We exploit this property to build a neuron-level fuzzy memoization scheme, which dynamically caches each neuron's output and reuses it whenever it is predicted that the current output will be similar to a previously computed result, avoiding in this way the output computations. The main challenge in this scheme is determining whether the new neuron's output for the current input in the sequence will be similar to a recently computed result. To this end, we extend the recurrent layer with a much simpler Bitwise Neural Network (BNN), and show that the BNN and RNN outputs are highly correlated: if two BNN outputs are very similar, the corresponding outputs in the original RNN layer are likely to exhibit negligible changes. The BNN provides a low-cost and effective mechanism for deciding when fuzzy memoization can be applied with a small impact on accuracy. We evaluate our memoization scheme on top of a state-of-the-art accelerator for RNNs, for a variety of different neural networks from multiple application domains. We show that our technique avoids more than 26.7\% of computations, resulting in 21\% energy savings and 1.4x speedup on average.