Interactive tools make data analysis both more efficient and more accessible to a broad population. Simple interfaces such as Google Finance as well as complex visual exploration interfaces such as Tableau are effective because they are tailored to the desired user tasks. Yet, designing interactive interfaces requires technical expertise and domain knowledge. Experts are scarce and expensive, and therefore it is currently infeasible to provide tailored (or precise) interfaces for every user and every task. We envision a data-driven approach to generate tailored interactive interfaces. We observe that interactive interfaces are designed to express sets of programs; thus, samples of programs-increasingly collected by data systems-may help us build interactive interfaces. Based on this idea, Precision Interfaces is a language-agnostic system that examines an input query log, identifies how the queries structurally change, and generates interactive web interfaces to express these changes. The focus of this paper is on applying this idea towards logs of structured queries. Our experiments show that Precision Interfaces can support multiple query languages (SQL and SPARQL), derive Tableau's salient interaction components from OLAP queries, analyze <75k queries in <12 minutes, and generate interaction designs that improve upon existing interfaces and are comparable to human-crafted interfaces.