How to efficiently track and store deltas between two HAMTs

Ideally, I would like to be able to do

x = Map({'a': 2, 'c': 1})
y = x.update({'b': 3: 'c': 2)
z = y - x # magic
z == Map({'b': 3, 'c': 2})

Is there any particularly efficient way to do this in terms of memory and computational time? Ideally, I'd like z to share its data with y in the same way y shares its data with x. One way that comes to mind is

def diff(y, x):
  z = y
  for k, v in y.items():
    if k in x and x[k] == v:
      z = z.delete('k')
  return z

But this is O(N log N) (for log N get/set). Is there a more efficient way to go about this?

No files or tests are named. Start by reviewing the HAMT and Map update/delete implementation, then determine whether a delta representation can preserve structural sharing without requiring the proposed scan. Done means an efficient, documented approach or a clearly scoped API change with coverage for the example.