Is super-accuracy matters?

[Claudio L.]

HP71B Wrote:>radians
>(sin(pi)*113 - mod(355,pi)) / 113 ! error = -1 ULP
-2.66764189063E-7

newRPL can help here: Set it to higher number of digits, then:

π0 355 113 / -
355 113 / SIN -

and you get what the error should be in the sin(π-x)~x approximation for this case:
3.16396255835E-21

Since the answer is 2.667E-7, you could be getting 21-7 = 14 good digits using that approximation if you didn't introduce any more ULP errors in intermediate operations.