I have horseherb in the backyard, both plants I bought and volunteers I didn't know I had, under an oak tree. It covers the ground nicely and takes a bit of foot traffic. It seems to spread faster where it gets at least a couple hours of direct sun, but everything I planted is growing nicely now. I've been very happy with it. It tolerates being mowed with the rest of the yard, but doesn't need to be mowed. One spot even tolerated having an RV parked over it (not the wheels) for a month without protest!

Thanks! That is very helpful.