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Compensated Horner Scheme Langlois, Philippe Graillat, Stef Louvet, Nicolas Polynomial evaluation Horner scheme error-free transformation floating point arithmetic accuracy Using error-free transformations, we improve the classic Horner Scheme (HS) to evaluate (univariate) polynomials in floating point arithmetic. We prove that this Compensated Horner Scheme (CHS) is as accurate as HS performed with twice the working precision. Theoretical analysis and experiments exhibit a reasonable running time overhead being also more interesting than double-double implementations. We introduce a dynamic and validated error bound of the CHS computed value. The talk presents these results together with a survey about error-free transformations and related hypothesis. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Philippe Langlois and Stef Graillat and Nicolas Louvet 2006 Is Part Of Dagstuhl Seminar Proceedings, Volume 5391, Algebraic and Numerical Algorithms and Computer-assisted Proofs (2006) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.05391.3 urn:nbn:de:0030-drops-4423 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05391.3 eng https://creativecommons.org/licenses/by/4.0/legalcode