Proving Bounds.pdf

The tactic is based on a kernel of floating-point and interval arithmetic, associated with an on-the-fly computation of Taylor expansions.

Key features of the tactic include:
- Interval arithmetic: used to compute numerical bounds on approximation errors
- Floating-point arithmetic: used to perform computations inside Coq's logic
- Taylor expansions: used to reduce the dependency effect and improve the accuracy of the bounds
- Automatic differentiation: used to compute the derivatives of the expressions
- Bisection: used to reduce the size of the intervals and improve the accuracy of the bounds

The tactic is implemented in Coq and is compared to various existing tools on a large set of examples. The results show that the tactic is able to prove tight bounds on univariate expressions in a efficient and effective way.

The paper is organized into several sections, including:
- Introduction: provides an overview of the paper and its contributions
- Floating-point and Interval Arithmetic: presents the background and preliminary results on interval arithmetic and floating-point operators
- Reducing the Dependency Effect: presents the techniques used to reduce the dependency effect, including bisection, automatic differentiation, and Taylor models
- The Interval Tactic: presents the implementation of the tactic in Coq and its performance on a set of examples
- Conclusion: summarizes the contributions of the paper and provides perspectives for future work.

The paper also includes a list of references and acknowledgements. Overall, the paper presents a significant contribution to the field of formal proof and verification, and provides a powerful tool for proving tight bounds on univariate expressions in Coq.