HP HP-15C - Accuracy, Uncertainty, and Calculation Time

Appendix: Accuracy of Numerical Calculations 199
Keystrokes Display
(T][TEST]2 078-43,30, 2
GE] 079- 11
nnfRTI 080- 43 33
[f][LBL].8 081-42,21,.8
H 082- 30
r^l 083- 11
fRCLll 084- 45 1
d] 085- 11
H 086- 20
fRCLlO 087- 45 0
nnr+Pl 088- 43 1
QD [1=3 089- 43 20
0 090- 10
|x$y| 091- 34
| ENTER | 092- 36
0 093- 40
fgirRTN] 094- 43 32
GDQvR]
The results F^(p,g,r) are correct to at least nine significant digits.
They are obtained from a program "C" that is utterly reliable
though rather longer than the unreliable programs "A" and "B".
The method underlying program "C" is:
1. Ifp < q, then swap them to ensure p ^ q.
2. Calculate b = (p — q) + r, c — (p — r) + q, and s = (p + r) + q.
3. Calculate
{
r-(p-q)
g-(p-r)
Error 0 otherwise (no triangle exists).
4. Calculate Fc(p,q,r) = 2 tan'l(^fab/^/'cs).
This procedure delivers Fc(p,q,r) = Q correct to almost nine
significant digits, a result surely easier to use and interpret than
the results given by the other better-known formulas. But this
procedure's internal workings are hard to explain; indeed, the
procedure may malfunction on some calculators and computers.