A. Ieee, IEEE-754 Standard for Binary Floating-point Arithmetic, 2008.

J. Bertrane, P. , R. Cousot, J. Feret, L. Mauborgne et al., Static analysis and verification of aerospace software by abstract interpretation, AIAA Infotech@Aerospace. American Inst. of Aeronautics and Astronautics, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00528611

O. Bouissou and M. Matthieu, Abstract Interpretation of the Physical Inputs of Embedded Programs, VMCAI, pp.37-51, 2008.
DOI : 10.1007/978-3-540-78163-9_8

P. Caspi, D. Pilaud, N. Halbwachs, and J. Plaice, Lustre: A declarative language for programming synchronous systems, POPL, pp.178-188, 1987.

P. and R. Cousot, Abstract interpretation: A unified lattice model for static analysis of programs by construction of approximations of fixed points, Principles of Programming Languages 4, pp.238-252, 1977.

D. Delmas, E. Goubault, S. Putot, J. Souyris, K. Tekkal et al., Towards an Industrial Use of FLUCTUAT on Safety-Critical Avionics Software, Formal Methods for Industrial Critical Systems, 14th International Workshop, 2009.
DOI : 10.1007/978-3-642-04570-7_6

E. Goubault and S. Putot, Static Analysis of Finite Precision Computations, VMCAI'11, number 6538 in LNCS, pp.232-247, 2011.
DOI : 10.1007/978-3-540-24738-8_18

A. Ioualalen and M. Martel, A New Abstract Domain for the Representation of Mathematically Equivalent Expressions, Static Analysis Symposium, SAS, number 7460 in LNCS, pp.75-93, 2012.
DOI : 10.1007/978-3-642-33125-1_8

URL : https://hal.archives-ouvertes.fr/hal-00698618

A. Ioualalen and M. Martel, Synthesis of arithmetic expressions for the fixed-point arithmetic: The sardana approach, The 6th Conference on Design & Architectures for Signal & Image Processing, DASIP, pp.346-353, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00698621

M. Martel, Enhancing the implementation of mathematical formulas for fixed-point and floating-point arithmetics, Formal Methods in System Design, vol.2006, issue.3, pp.265-278, 2009.
DOI : 10.1007/s10703-009-0068-y

D. Monniaux, The pitfalls of verifying floating-point computations, ACM Transactions on Programming Languages and Systems, vol.30, issue.3, 2008.
DOI : 10.1145/1353445.1353446

URL : https://hal.archives-ouvertes.fr/hal-00128124

C. Mouilleron, Efficient computation with structured matrices and arithmetic expressions, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00688388

J. Muller, On the definition of ulp(x), 2005.
URL : https://hal.archives-ouvertes.fr/inria-00070503

R. Tate, M. Stepp, Z. Tatlock, and S. Lerner, Equality saturation: A new approach to optimization, Logical Methods in Computer Science, vol.7, issue.1, 2011.