Deep neural networks (DNN) are increasingly being accelerated on application-specific hardware such as the Google TPU designed especially for deep learning. Timing speculation is a promising approach to further increase the energy efficiency of DNN accelerators. Architectural exploration for timing speculation requires detailed gate-level timing simulations that can be time-consuming for large DNNs which execute millions of multiply-and-accumulate (MAC) operations. In this paper we propose FATE, a new methodology for fast and accurate timing simulations of DNN accelerators like the Google TPU. FATE proposes two novel ideas: (i) DelayNet, a DNN based timing model for MAC units; and (ii) a statistical sampling methodology that reduces the number of MAC operations for which timing simulations are performed. We show that FATE results in between 8X - 58X speed-up in timing simulations, while introducing less than 2% error in classification accuracy estimates. We demonstrate the use of FATE by comparing a conventional DNN accelerator that uses 2's complement (2C) arithmetic with one that uses signed magnitude representation (SMR). We show that that the SMR implementation provides 18% more energy savings for the same classification accuracy than 2C, a result that might be of independent interest.