Astronomical Applications Department, U.S. Naval Observatory Sensitivity Integral Page 12
1
2
1
32
(
)
sin 2 r g x
g
3
r
3
1
16
(
)
sin 2 s x
s
3
1
64
(
)
sin (
)
+
2 s
2 r x
(
)
+
s
r
3
1
64
(
)
sin (
)
-
2 s
2 r x
(
)
-
s
r
3
+
-
-
-
1
64
(
)
sin (
)
+
2 s
2 r g x
(
)
+
s
r g
3
1
32
(
)
sin 2 r x
r
3
1
4
(
)
sin (
)
- +
2 s
r
r g x
(
)
- +
2 s
r
r g
3
1
4
(
)
sin (
)
+ -
2 s
r
r g x
(
)
+ -
2 s
r
r g
3
-
+
-
-
1
4
(
)
sin (
)
+ +
2 s
r
r g x
(
)
+ +
2 s
r
r g
3
1
4
(
)
sin (
)
- -
2 s
r
r g x
(
)
- -
2 s
r
r g
3
1
64
(
)
sin (
)
-
2 s
2 r g x
(
)
-
s
r g
3
1
2
(
)
sin r (
)
+
1
g x
(
)
+
1
g
3
r
3
+
+
-
-
1
2
(
)
sin r (
)
- +
1
g x
r
3
(
)
- +
1
g
3
1
12
x
3
+
+
(
)
+
6 a
3
24 x a
4
x
d
(
)
ugh %
ugh[45]: polynomial factor p:
+
6 a
3
24 x a
4
ugh[45]: location of p in integrand:
[ ]
2
ugh[45]: integrating by parts...
ugh[62]: cost of evaluated part of integral:
+
+
+
+
20389 additions
250998 multiplications
4874 divisions
5436 functions
5662 subscripts
ugh[62]: simplifying...
ugh[147]: cost of evaluated part of integral:
+
+
+
+
117 additions
333 multiplications
32 divisions
26 functions
129 subscripts
ugh[147]: evaluated part of integral is stored in parts[3]
ugh[147]: no new polynomial factor!
ugh[150]: cost of new integrand:
+
+
+
+
10193 additions
125496 multiplications
2437 divisions
2718 functions
subscripts
ugh[150]: simplifying sin/cos part of new integrand...
ugh[169]: cost of simplified new integrand:
+
+
+
+
41 additions
126 multiplications
16 divisions
13 functions
14 subscripts
ugh[169]: new definite integral:
1
2
12
a
4
(
)
cos r (
)
- +
1
g x
(
)
- +
1
g
4
r
4
12
a
4
(
)
cos r (
)
+
1
g x
(
)
+
1
g
4
r
4
3
8
a
4
(
)
cos 2 r g x
r
4
g
4
3
4
a
4
(
)
cos 2 s x
s
4
-
+
-
-
3
16
a
4
(
)
cos (
)
+
2 s
2 r x
(
)
+
s
r
4
3
16
a
4
(
)
cos (
)
-
2 s
2 r x
(
)
-
s
r
4
3
16
a
4
(
)
cos (
)
+
2 s
2 r g x
(
)
+
s
r g
4
3
8
a
4
(
)
cos 2 r x
r
4
+
+
+
-
Page 12
