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Stencil computations are widely used in the scientific simulation domain, and their performance is critical to the overall efficiency of many large-scale numerical applications. Many optimization techniques, most of them varying strategies of tiling and parallelization, exist to systematically enhance the efficiency of stencil computations. However, the effective- ness of these optimizations vary significantly depending on the wide range of properties demonstrated by the different stencils. This paper studies several well-known optimization strategies for stencils and presents a new approach to effectively guide the composition of these optimizations, by modeling their interactions with four domain-level proper- ties of stencils: spatial dimensionality, temporal order, order of accuracy, and directional dependence. When using our prediction model to guide optimizations for five real-world stencil applications, we were able to identify optimization strategies that outperformed two highly optimized stencil libraries by an average of 2.4x.