[yes_or_gnome]

> Sometimes this is not a problem. When x is small, sin(x) can be computed by simply returning x. This rule is valid until x^3/6 > precision ~= 1e-38, or x = 4e-16. So exact precision is obtainable by simply returning x if x < 1e-16.

"This rule" seems a lot like the "skinny triangle" rule. I recently ran across it on Wikipedia after going through astrophysics articles. Specifically, to my understanding, the parsec could be calculated without using a trig function thanks to the skinny triangle rule. (To a certain level of error, of course. And, the parsec is now a defined value so the original trig-derived definition is invalid.)

https://en.wikipedia.org/wiki/Skinny_triangle

[Sean1708]

> "This rule" seems a lot like the "skinny triangle" rule

This rule is exactly the Skinny Triangle Rule, or rather the part of the Skinny Triangle Rule which overlaps with the Small Angle Approximation[0].

[0]: https://en.wikipedia.org/wiki/Small-angle_approximation