  A new algorithm for deciding the satisfiability of polynomial formulas over
the reals is proposed. The key point of the algorithm is a new projection
operator, called sample-cell projection operator, custom-made for
Conflict-Driven Clause Learning (CDCL)-style search. Although the new operator
is also a CAD (Cylindrical Algebraic Decomposition)-like projection operator
which computes the cell (not necessarily cylindrical) containing a given sample
such that each polynomial from the problem is sign-invariant on the cell, it is
of singly exponential time complexity. The sample-cell projection operator can
efficiently guide CDCL-style search away from conflicting states. Experiments
show the effectiveness of the new algorithm.
