# Internal versus external balancing in the evaluation of graph-based number types

## TL;DR

This paper compares internal and external balancing techniques for graph-based number types, demonstrating how restructuring and balancing can improve evaluation efficiency through theoretical analysis and experiments.

## Contribution

It provides a comparative analysis of internal versus external balancing methods for graph-based number types, highlighting their respective advantages and disadvantages.

## Key findings

- External balancing can significantly improve evaluation performance.
- Internal balancing offers a different approach to error management.
- Theoretical and experimental results illustrate the trade-offs between the methods.

## Abstract

Number types for exact computation are usually based on directed acyclic graphs. A poor graph structure can impair the efficency of their evaluation. In such cases the performance of a number type can be drastically improved by restructuring the graph or by internally balancing error bounds with respect to the graph's structure. We compare advantages and disadvantages of these two concepts both theoretically and experimentally.