In recent years, researchers have proposed a number of automated tools to identify and improve floating-point rounding error in mathematical expressions. However, users struggle to effectively apply these tools. In this paper, we work with novices, experts, and tool developers to investigate user needs during the expression rewriting process. We find that users follow an iterative design process. They want to compare expressions on multiple input ranges, integrate and guide various rewriting tools and understand where errors come from. We organize this investigation's results into a three-stage workflow and implement that workflow in a new, extensible workbench dubbed Odyssey. Odyssey enables users to: (1) diagnose problems in an expression, (2) generate solutions automatically or by hand, and (3) tune their results. Odyssey tracks a working set of expressions and turns a state-of-the-art automated tool "inside out," giving the user access to internal heuristics, algorithms, and functionality. In a user study, Odyssey enabled five expert numerical analysts to solve challenging rewriting problems where state-of-the-art automated tools fail. In particular, the experts unanimously praised Odyssey's novel support for interactive range modification and local error visualization.

翻译：近年来，研究者提出了多种自动化工具以识别并改进数学表达式中的浮点舍入误差。然而，用户难以有效运用这些工具。本文与初学者、专家及工具开发者合作，深入探究了表达式重写过程中的用户需求。研究发现用户遵循迭代式设计流程，希望比较表达式在多个输入区间上的表现、集成并指导多种重写工具，以及理解误差来源。我们将研究成果归纳为三阶段工作流，并在名为“奥德赛”的新型可扩展工作台中实现了该流程。奥德赛使用户能够：（1）诊断表达式中的问题，（2）通过自动或手动方式生成解决方案，（3）对结果进行调优。该工作台跟踪表达式工作集，并将最先进的自动化工具“由内而外”地开放，使用户可访问其内部启发式算法、算法逻辑及功能。用户研究表明，奥德赛帮助五位数值分析专家解决了自动化工具难以应对的重写难题。特别地，专家们一致称赞该平台在交互式区间调整与局部误差可视化方面的创新支持。