Veronicas, ugh! Grey field vs Bird's Eye vs Slender
They are tough, and there's also V. filliformis, though it's much less common. V. polita has hairs on the stems that are spreading and noticiably a mix of lengths. That's probably definitive.
Generally, V. persica flowers are nearly as large as the leaves, or at least as wide as the leaves, or more than 0.5 cm. V. polita flowers are definitely smaller than the leaves, not as wide as most of the leaves, and under 0.5 cm. V. persica has much longer flower stems, easily longer than the length of a leaf. V. polita stems tend to be shorter and they don't stick out a whole lot above the leaves.
Both of those have leaves clearly longer than wide and fairly densly bunched. If you find something similar with tiny, roundish leaves well spread out along the stem and flower stems like 4 times as long as the little leaves you probably have V. filiformis.
from srall on post by michaelmorris
