Before revision:   We design a new practically efficient algorithm for solving one block quantifier elimination problems when the input semi-algebraic formula is a system of polynomial equations satisfying some mild assumptionssuch as transversality .
After revision:  This paper studies a variant of the one block quantifier elimination in which we compute an almost equivalent formula of the input. We design a new practically efficient algorithm for solving one block quantifier elimination problems when the input semi-algebraic formula is a system of polynomial equations satisfying some mild assumptionssuch as transversality .