WKB correction term ($F=f\prime \prime /(4f^2)-5(f\prime {)}^2/(16f^3)$)

The Liouville transformation of a second-order equation with $t={\int }^x\sqrt{f}dx$ gives $\ddot{U}-(1+F)U=0$. Neglecting this correction yields amplitude $f^{-1/4}$ and phase or exponent $\int \sqrt{f}$. Its smallness measures a local slowly-varying-coefficient approximation, away from zeros of $f$.