Stencil computations are a key part of many high-performance computing applications, such as imageprocessing, convolutional neural networks, and finite-difference solvers for partial differential equations. Devitois a framework capable of generating highly-optimized code given symbolic equations expressed in Python,specialized in, but not limited to, affine (stencil) codes. The lowering process—from mathematical equations down to C++ code—is performed by the Devito compiler through a series of intermediate representations.Several performance optimizations are introduced, including advanced common sub-expressions elimination, tiling and parallelization. Some of these are obtained through well-established stencil optimizers, integratedin the back-end of the Devito compiler. The architecture of the Devito compiler, as well as the performance optimizations that are applied when generating code, are presented. The effectiveness of such performanceoptimizations is demonstrated using operators drawn from seismic imaging applications.