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Floating-point arithmetic plays a central role in science, engineering, andfinance by enabling developers to approximate real arithmetic. To addressnumerical issues in large floating-point applications, developers must identifyroot causes, which is difficult because floating-point errors are generallynon-local, non-compositional, and non-uniform.  This paper presents Herbgrind, a tool to help developers identify and addressroot causes in numerical code written in low-level C/C++ and Fortran. Herbgrinddynamically tracks dependencies between operations and program outputs to avoidfalse positives and abstracts erroneous computations to a simplified programfragment whose improvement can reduce output error. We perform several casestudies applying Herbgrind to large, expert-crafted numerical programs and showthat it scales to applications spanning hundreds of thousands of lines,correctly handling the low-level details of modern floating point hardware andmathematical libraries, and tracking error across function boundaries andthrough the heap.

Finding Root Causes of Floating Point Error with Herbgrind