Rump's Example Revisited

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Rump published an example (Algorithms for Verified Inclusions: Theory and Practice, in: Moore, R. E. (ed.), Reliability in Computing: The Role of Interval Methods in Scientific Computing, Academic Press, Boston, 1988, pp. 109–126) in which numerical evaluation of an expression gave a misleading result, even though use of increasing arithmetic precision suggested reliable computation. This oft-cited example happens not to be reproducible on many modern computers. The expression is rewritten so that Rump's result is reproducible using IEEE 754 arithmetic.

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