  We study two dimensional conformal field theories in the semiclassical limit.
In this limit, the four-point function is dominated by intermediate primaries
of particular weights along with their descendants, and the crossing equations
simplify drastically. For a four-point function receiving sufficiently small
contributions from the light primaries, the structure constants involving heavy
primaries follow a universal formula. Applying our results to the four-point
function of the $\mathbb Z_2$ twist field in the symmetric product orbifold, we
produce the Hellerman bound and the logarithmically corrected Cardy formula
that is valid for $h \geq c/12$.
