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<math>
<math>
\begin{aligned}
\begin{aligned}
\int_{-\frac{L}{2}}^{\frac{L}{2}}\int_{f([-\frac{L}{2},\frac{L}{2}])}p(x)p(y|x)\ln p(y)dydx\approx \frac{1}{L}\int_{-\frac{L}{2}}^{\frac{L}{2}}\ln f'(x)dx
\int_{-\frac{L}{2}}^{\frac{L}{2}}\int_{f([-\frac{L}{2},\frac{L}{2}])}p(x)p(y|x)\ln p(y)dydx\approx -\ln L - \frac{1}{L}\int_{-\frac{L}{2}}^{\frac{L}{2}}\ln f'(x)dx
\end{aligned}
\end{aligned}
</math>
</math>