# Finding Root Causes of Floating Point Error with Herbgrind

arXiv: https://arxiv.org/abs/1705.10416 · HTML: https://mlsanity.com/paper/1705.10416/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2017.

## Built on by (most cited first, 2 of 2)

- [Your Compiler is Backdooring Your Model: Understanding and Exploiting Compilation Inconsistency Vulnerabilities in Deep Learning Compilers](https://mlsanity.com/paper/2509.11173/) (2025)
- [Benchmarking Large Language Models on Floating-Point Error Classification](https://mlsanity.com/paper/2606.31308/) (2026)

## Abstract (arXiv)

Floating-point arithmetic plays a central role in science, engineering, and finance by enabling developers to approximate real arithmetic. To address numerical issues in large floating-point applications, developers must identify root causes, which is difficult because floating-point errors are generally non-local, non-compositional, and non-uniform. This paper presents Herbgrind, a tool to help developers identify and address root causes in numerical code written in low-level C/C++ and Fortran. Herbgrind dynamically tracks dependencies between operations and program outputs to avoid false positives and abstracts erroneous computations to a simplified program fragment whose improvement can reduce output error. We perform several case studies applying Herbgrind to large, expert-crafted numerical programs and show that it scales to applications spanning hundreds of thousands of lines, correctly handling the low-level details of modern floating point hardware and mathematical libraries, and tracking error across function boundaries and through the heap.