Many analysis applications require the ability to repeatedly execute sophisticated modeling functions, which can each take minutes or even hours to produce a single answer. Because of this expense, such applications have largely been unable to directly use such models in queries, with either on-demand or continuous query processing technology. Query processors are hindered in their ability to optimize expenseive modeling functions due to the "black box" nature of exisiting user-defined function (UDF) interfaces. In this paper, we address the problem of querying over sophisticated models with the development of VAOs (Variable-Accuracy Operators). VAOs use a new function interface that exposes the trade-off between compute time and accuracy that exists in many modeling functions. Using this interface, VAOs adaptively run each function call in a query only to an accuracy needed to answer the query, thus eliminating unneeded work. In this paper, we present the design of VAOs for a set of common query operations. We show the effectiveness of VAOs using a prototype implementation running financial queries over real bond market data.