Added a test called ddxddy, which replicates the OP's test. It's sort of an unremarkable test, because I'm not too familiar with this feature and am not sure what a better test would look like.
We'd probably want to use some trivial but non-linear function like e.g. a quadratic (or perhaps e.g. a sine or cosine) over sv_position as input to ddx()/ddy(), and then probe the output in some number (e.g. 16) of places.