Simionescu's function and constrained optimization

At first glance, Simionescu's function may not look particularly interesting. However, it has a constraint attached to it that makes it intriguing to work with as well as pleasant to look at.

The function is usually evaluated on the search space bounded by [-1.25, 1.25] in each dimension and can be mathematically expressed as follows:

Where the values of x, y are subject to the following condition:

This constraint effectively limits the values of x and y that are considered valid for this function. The result is depicted in the following contour diagram:

Contour diagram of the constrained Simionescu's function
Source: https://commons.wikimedia.org/wiki/File:Simionescu%27s_function.PNG.
Image by Simiprof. Licensed under Creative Commons CC BY-SA 3.0: https://creativecommons.org/licenses/by-sa/3.0/deed.en.

The...