Rational Tracer: a Tool for Faster Rational Function Reconstruction

TL;DR

Rational Tracer is a tool that accelerates rational function reconstruction in complex arithmetic expressions, especially in IBP reductions, by separating expression construction from evaluation, leading to significant speedups over existing methods.

Contribution

The paper introduces Rational Tracer, a novel tool that improves the efficiency of rational function reconstruction in symbolic computations, particularly for IBP relations in Feynman integrals.

Findings

Achieves ~10x probe time speedup over Kira+FireFly

Achieves ~5x overall time speedup over Kira+FireFly

Provides higher speedups when reconstructing fewer terms in epsilon

Abstract

Rational Tracer (Ratracer) is a tool to simplify complicated arithmetic expressions using modular arithmetics and rational function reconstruction, with the main idea of separating the construction of expressions (via tracing, i.e. recording the list of operations) and their subsequent evaluation during rational reconstruction. Ratracer can simplify arithmetic expressions (provided as text files), solutions of linear equation systems (specifically targeting Integration-by-Parts (IBP) relations between Feynman integrals), and even more generally: arbitrary sequences of rational operations, defined in C++ using the provided library ratracer.h. Any of these can also be automatically expanded into series prior to reconstruction. This paper describes the usage of Ratracer specifically focusing on IBP reduction, and demonstrates its performance benefits by comparing with Kira+FireFly and Fire6. Specifically, Ratracer achieves a typical ~10x probe time and ~5x overall time speedup over Kira+FireFly, and even higher if only a few terms in $\varepsilon$ need to be reconstructed.