  It is shown that the complex field equipped with the "approximate exponential
map", defined up to ambiguity from a small group, is quasiminimal: every
automorphism-invariant subset of the field is countable or co-countable. If the
ambiguity is taken to be from a subfield analogous to a field of constants then
the resulting "blurred exponential field" is isomorphic to the result of an
equivalent blurring of Zilber's exponential field, and to a suitable reduct of
a differentially closed field. These results are progress towards Zilber's
conjecture that the complex exponential field itself is quasiminimal. A key
ingredient in the proofs is to prove the analogue of the exponential-algebraic
closedness property using the density of the group governing the ambiguity with
respect to the complex topology.
