If you are drafting the oval/egg and then magic wanding the walls over, you need to set the magic wand to "best match" so the wall tool understands not to make facets and to follow the arcs closely.
So what is the math in making an "egg"?
Don't forget the oval/circle tool..... you might squatify an oval.
See my sketch - four circular arcs....
Dwight Atkinson