Any way to determine the dimension of matrix given the norm of applied vector?

Question

Let $r \in [1, 95]$ and two full rank matrices $W_1 \in \mathbb{R}^{r \times 100}$ and $W_2 \in \mathbb{R}^{100 \times r}$. I can choose any $x \in \mathbb{R}^{100}$ and obtain result of $$ ||\sin(W_2 \cos(W_1 x))||^2_2,$$where trigonometric functions are applied element-wise. How can I find out the $r$? I can use numeric calculations using JAX.