[lntue]

I think the function inputs are in double-double format, so the assumption is that the magnitude of y is significantly smaller than the magnitude of x, ideally |y| < 2^(-52) |x|. So that 1 is a very good approximation for cos(y), since |cos(y) - 1| < |y|^2 < 2^(-104) |x|^2. Similarly, if we assume |x| is also small, |sin(x) - x| < |x|^3 is also a very good approximation (same with sin(y) ~ y).

So using the cosine of sum formula:

  *  cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
  *             ~ cos(x) - x*y.