The delicate flowers in question appear to commonly be known as Rue Anemone, which closely resembles Liverwort. However the leaves denote Rue Anemone.

The Bloodroot bloom has several more petals, is much taller with a broad leaf, and is almost rubbery. The root of Bloodroot is a rhizome which when snapped open will ooze a bit of reddish liquid resembling blood, hence its name. Cynthia A. Meyer, Sycamore Spring.