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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 graphu0027s structure. We compare advantages and disadvantages of these two concepts both theoretically and experimentally.

Internal Versus External Balancing in the Evaluation of Graph-Based Number Types