SW Idaho matted weed identification

I think it's some kind of Euphorbia similar to Euphorbia serpens, Euphorbia prostata and Euphorbia maculata, but is seems to grow flatter with smaller, rounder leaves than those (maybe you can't tell its flat tendancy now, with the rain we've had). It's one of the most drought-tolerant plants I know, and isn't hesitant to grow on compact, hard, dry, clay-ish soil (without rain).

It seems to root along the stem as it grows. If you don't pull it up young, it's hard to remove.

I personally like it, and think it could potentially be great for living mulch.

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