  In this paper we establish an improvement of tilt-excess decay estimate for
the Allen-Cahn equation, and use this to give a new proof of Savin's theorem on
the uniform $C^{1,\alpha}$ regularity of flat level sets, which then implies
the one dimensional symmetry of minimizers in $\mathbb{R}^n$ for $n\leq 7$.
This generalizes Allard's $\varepsilon$-regularity theorem for stationary
varifolds to the setting of Allen-Cahn equations.
