  A simple approximate solution for the quantum-mechanical quartic oscillator
$V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is
presented. It is based on a combining of perturbation theory near true minima
of the potential, semi-classical approximation at large distances and a
description of tunneling under the barrier. It provides 9-10 significant digits
in energies and gives for wavefunctions the relative deviation in real
$x$-space less than $\lesssim 10^{-3}$.
