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 that 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 8 times-58 times speed-up in timing simulations, while introducing less than 2% error in classification accuracy estimates. We demonstrate the use of FATE by comparing to conventional DNN accelerator that uses 2's complement (2C) arithmetic with an alternative implementation that uses signed magnitude representations (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.