Neural networks offer high-accuracy solutions to a range of problems, but are costly to run in production systems because of computational and memory requirements during a forward pass. Given a trained network, we propose a techique called Deep Learning Approximation to build a faster network in a tiny fraction of the time required for training by only manipulating the network structure and coefficients without requiring re-training or access to the training data. Speedup is achieved by by applying a sequential series of independent optimizations that reduce the floating-point operations (FLOPs) required to perform a forward pass. First, lossless optimizations are applied, followed by lossy approximations using singular value decomposition (SVD) and low-rank matrix decomposition. The optimal approximation is chosen by weighing the relative accuracy loss and FLOP reduction according to a single parameter specified by the user. On PASCAL VOC 2007 with the YOLO network, we show an end-to-end 2x speedup in a network forward pass with a 5% drop in mAP that can be re-gained by finetuning.