Before revision: The existential theory of the reals (ETR) consists of existentially quantified boolean formulas over equalities and inequalities of real-valued polynomials. We propose the approximate existential theory of the reals (\epsilon-ETR), in which the constraints only need to be satisfied approximately.
After revision: The existential theory of the reals (ETR) consists of existentially quantified boolean formulas over equalities and inequalities of polynomial functions of variables in \mathbb{R the approximate existential theory of the reals (\epsilon-ETR), in which the constraints only need to be satisfied approximately.