Enforcing exact symmetry can provide a strong inductive bias in scientific machine learning, but exact symmetry may be more restrictive than needed in practice. This work compares the cost of enforcing exact and approximate symmetry through a notion of averaging complexity. It proves an exponential separation: exact symmetry requires complexity that scales linearly with the group size, while approximate symmetry can be achieved with only logarithmic complexity under standard assumptions. The result gives a theoretical explanation for the practical appeal of approximate symmetries and introduces tools for studying symmetry enforcement more broadly.