证明二元函数的最小值点在$x=\pm y$上？

hbghlyj

证明Cross-in-tray函数$${\displaystyle f(x,y)=-0.0001\left[\left|\sin x\sin y\exp \left(\left|100-{\frac {\sqrt {x^{2}+y^{2}}}{\pi }}\right|\right)\right|+1\right]^{0.1}}$$的最小值点在$x=\pm y$上？

hbghlyj

WolframAlpha算出最小值是$f(1.47062, 4.41908)=-1.88994$，错误！

如何证明4个最小值点都在$x=\pm y$上？

${\displaystyle {\text{Min}}={\begin{cases}f\left(1.34941,-1.34941\right)&=-2.06261\\f\left(1.34941,1.34941\right)&=-2.06261\\f\left(-1.34941,1.34941\right)&=-2.06261\\f\left(-1.34941,-1.34941\right)&=-2.06261\\\end{cases}}}$