I came around these two equations
\begin{align} y&=x^2,\ x,y\in\mathbb{R} \tag{1}\\ \exp(y')&=\exp({x'}^2),\ x',y'\in\mathbb{R} \tag{2} \end{align}
Clearly they have something in common. I can define a function $f$ defined as
$$f\left(\begin{bmatrix} x' \\ y' \end{bmatrix}\right)= \begin{bmatrix} \log_2(x) \\ \log_2(y) \end{bmatrix}$$
And if I apply $f$ to each pair $(x',y')$, then the equation transforms to $(1)$. So my question is if $f$ has a proper name or how these types of similar equations are called. It seems as if there is some kind of space transformation there, but it is not linear.