Rounding
"Nobody knows how much it would cost to compute  y^w  correctly rounded for every two floating-point arguments at which it does not over/underflow. Instead, reputable math libraries compute elementary transcendental functions mostly within slightly more than half an ulp and almost always well within one ulp. Why can't Y^W be rounded within half an ulp like SQRT? Because nobody knows how much computation it would cost... No general way exists to predict how many extra digits will have to be carried to compute a transcendental expression and round it correctly to some preassigned number of digits. Even the fact (if true) that a finite number of extra digits will ultimately suffice may be a deep theorem."