Collaborative collection of useful userRPL snippets

[Paul Dale]

It comes down to taking an arccosine of a number near to ±1. The result is close to zero but you are also likely to lose up to half the possible digits. Remember that there are more numbers close to zero than any other number in floating point arithmetic and that cosine is very flat when it takes a value of ±1.

For fun, try plotting: \( arccos(1-x) \) and \( 2 \, arcsin(\sqrt{\frac{x}{2}}) \) for very small \( x > 0 \). These two are mathematically equivalent.

There is also a worse possibility here, where the number rounds to > 1 or < -1 causing an error.