There is a mathematical reason for why this is not completely horrible, even though this would catch you off guard. When x is approximately pi, the function x -

There is a mathematical reason for why this is not completely horrible, even though this would catch you off guard. When x is approximately pi, the function x -> sin(x) is ill-conditioned. [0] So the relative error between the computed value ybar=fl(sin(x)) and the true value y=sin(x) is (ybar-y)/y and is quite large. However: you can find a number xbar that is very close to x, in the sense that (xbar-x)/x is very small, such that the computed "inaccurate" value ybar=fl(sin(x)) matches sin(xbar) exactly. Thus this procedure is backward-stable, but not forward-stable. For "typical" numerically-stable algorithms, this might not be such an issue. Very interesting writeup, anyway. I also found this post by James Gosling [1] describing the same issue, and the slower software workaround implemented in JVM; the post is from 2005. The paper that explain K5's implementation is "The K5 transcendental functions" by Lynch, Ahmed, Schulte, Callaway, Tisdale, but it is behind an academic paywall. [0] http://en.wikipedia.org/wiki/Condition_number http://en.wikipedia.org/wiki/Condition_number [1] https://blogs.oracle.com/jag/entry/transcendental_meditation https://blogs.oracle.com/jag/entry/transcendental_meditation