Absolute accuracy tells us how much an approximation is in error at any point. In one sense this is just what we're looking for. Select an algorithm based on its relative accuracy if your code requires extremely precise answers over a wide range of inputs. Be aware that most functions behave oddly near certain points. Don't be lulled into a quest for the best possible accuracy.
High precision carries a correspondingly high computational cost.
Know what the project needs, and then select the appropriate algorithm. Every addition, multiplication, division and subtraction in even the best package will reduce the answer's precision by some small amount. Never make assumptions about your floating point libraries, whether written by your company, supplied by a compiler vendor, or implemented in a coprocessor chip. Most programmers think in terms of degrees, with 360 forming a circle. The radian is a more natural unit of measurement for angles.