The freedom to reorder computations involving associative operators has been widely recognized and exploited in designing parallel algorithms and to a more limited extent in optimizing compilers. In this paper, we develop a novel framework utilizing the associativity and commutativity of operations in regular loop computations to enhance register reuse. Stencils represent a particular class of important computations where the optimization framework can be applied to enhance performance. We show how stencil operations can be implemented to better exploit register reuse and reduce load/stores. We develop a multi-dimensional retiming formalism to characterize the space of valid implementations in conjunction with other program transformations. Experimental results demonstrate the effectiveness of the framework on a collection of high-order stencils.