Bug or badly suboptimal result for derivative

[quinyu]

The CAS, when asked to derive the expression sin(x-cos x) returns a gigantic expression (I am not going to copy it here), containing imaginary units and otherwise close to unreadable.

The derivative could be properly determined according to the following steps (chain rule):
f(u)=sin(u) => f'(u)=cos(u)
f'(g(x))=cos(x-cos(x))
g(x)=x-cos(x) => g'(x)=1+sin(x), therefore
dy/dx=f'(g(x))g'(x)=(cos(x-cos(x)))*(1+sin(x))

I am having software 2015.6.17 (8151); HW ver C; CAS ver 1.1.2-11; OS v0.037.526.