Wrong derivative of exp(cos(x))

It seems to me that there is a problem with cos derivatives in composite functions:

julia> D = (f, x) -> AbstractDifferentiation.derivative(DiffractorForwardBackend(), f, x)[1];

julia> D(x -> exp(cos(x)), 1.0)
-1.952024889228184

julia> exp(cos(1.0)) * (-sin(1.0))
-1.4444065708474794

julia> exp(sin(1.0)) * (-sin(1.0))
-1.952024889228184

Surprisingly, everything is OK with sin derivatives:

julia> D(x -> exp(sin(x)), 1.0)
1.253380767493447

julia> exp(sin(1.0)) * cos(1.0)
1.253380767493447

Start by running the Julia REPL reproduction in the issue with DiffractorForwardBackend and compare the derivative of exp(cos(x)) with the stated analytic value. Trace how cos is handled inside the composite derivative path, then verify that the result matches -1.4444065708474794 while the existing exp(sin(x)) behavior remains correct.