  We describe a new algorithm \texttt{Miranda} for isolating the simple zeros
of a function $\boldsymbol{f}:{\mathbb R}^n\to{\mathbb R}^n$ within a box
$B_0\subseteq {\mathbb R}^n$. The function $\boldsymbol{f}$ and its partial
derivatives must have interval forms, but need not be polynomial. Our
subdivision-based algorithm is "effective" in the sense that our algorithmic
description also specifies the numerical precision hat is sufficient to certify
an implementation with any standard BigFloat number type. The main predicate is
the Moore-Kioustelides (MK) test, based on Miranda's Theorem (1940). Although
the MK test is well-known, this paper appears to be the first synthesis of this
test into a complete root isolation algorithm.
  We provide a complexity analysis of our algorithm based on intrinsic
geometric parameters of the system. Our algorithm and complexity analysis are
developed using 3 levels of description (Abstract, Interval, Effective). This
methodology provides a systematic pathway for achieving effective subdivision
algorithms in general.
