Many analysis and monitoring applications require the repeated execution of expensive functions over streams of rapidly changing data. These applications appear in fields as varied as finance, supply chain management, and power utility monitoring.While many of these applications can be expressed declaratively, current continuous query processors are not designed to optimize queries with expensive user-defined functions. Such optimizations are hindered by "black box" function interfaces, where the operator has no control over the processing inside each invocation. We are currently developing VAOs (Variable Accuracy Operators), a new class of operators that allow the query processor to speed up individual function calls. VAOs use a new function interface that exposes the trade-off between work and accuracy inherent inmany functions. Using this new interface, VAOs can eliminate unneeded work by running each function call to only the accuracy needed by the query. VAOs play a key role in our larger research agenda of optimizing queries with expensive functions, and we briefly describe this larger agenda as well.