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→一维函数映射
\int_{-\frac{L}{2}}^{\frac{L}{2}}\int_{f([-\frac{L}{2},\frac{L}{2}])}p(x_0)p(y|x_0)\ln p(y)dydx_0\approx \frac{1}{2L}\int_{-\frac{L}{2}}^{\frac{L}{2}}\ln \left(\frac{f'(x_0)}{\sigma}\right)^2dx_0
\int_{-\frac{L}{2}}^{\frac{L}{2}}\int_{f([-\frac{L}{2},\frac{L}{2}])}p(x_0)p(y|x_0)\ln p(y)dydx_0\approx \frac{1}{2L}\int_{-\frac{L}{2}}^{\frac{L}{2}}\ln \left(\frac{f'(x_0)}{\sigma}\right)^2dx_0
\end{aligned}
\end{aligned}
</math>
最终的EI可以由下式近似计算：
<math>
EI\approx \ln(\frac{L}{\sqrt{2\pi e}})+\frac{1}{2L}\int_{-\frac{L}{2}}^{\frac{L}{2}}\ln \left(\frac{f'(x)}{\sigma}\right)^2dx
</math>
</math>