HP -15C Advanced Functions Handbook page 198

196
Appendix: Accuracy of Numerical Calculations
The three bottom lines in the table below show results for three
programs "A", "B", and "C" based upon three different formulas
F(p,q,r) all algebraically equivalent to
Q = f(p,Q,r) = cos-
l
((p
2
+ q
2
- rV(2p<7)).
Disparate Results from Three Programs F
A
, F
B
, F
c
p
q
r
FA
FB
FC
P
q
r
FA
FB
FC
P
q
r
FA
FB
FC
Case 1
1.
1.
1 .00005 X 1 0~
5
0.
5.73072X10'
4
5.72986X10~
4
Case 4
0.527864055
9.472135941
9.999999996
Error 0
Error 0
180.
Case?
1 .00002
1 .00002
2.00004
Error 0
180.
180.
Case 2
9.999999996
9.999999994
3 X 1 0~
9
0.
Error 0
1.281 17 X10'
8
Case 5
9.999999996
3 X 1 0"
9
9.999999994
48.18968509
Error 0
48.18968510
CaseS
3.162277662
2.3 X10'
9
3.162277661
90.
70.52877936
64.22853822
CaseS
10.
5.000000001
15.
180.
180.
179.9985965
Case 6
9.999999999
9.999999999
20.
180.
180.
Error 0
Case9
3.162277662
1.5555X10"
6
3.162277661
90.
89.96318706
89.96315156
To use a program, key in p \R | q \R | r, run program "A",
"B", or "C", and wait to see the program's approximation Ftod — f.
Only program "C" is reliable.