Astronomical Applications Department, U.S. Naval Observatory Sensitivity Integral Page 11
1
2
1
2
(
)
cos r (
)
- +
1
g x
(
)
- +
1
g
2
r
2
1
2
(
)
cos r (
)
+
1
g x
(
)
+
1
g
2
r
2
1
16
(
)
cos 2 r g x
g
2
r
2
1
8
(
)
cos 2 s x
s
2
-
+
+
1
32
(
)
cos (
)
+
2 s
2 r x
(
)
+
s
r
2
1
32
(
)
cos (
)
-
2 s
2 r x
(
)
-
s
r
2
1
32
(
)
cos (
)
+
2 s
2 r g x
(
)
+
s
r g
2
1
16
(
)
cos 2 r x
r
2
-
-
-
+
1
4
(
)
cos (
)
- +
2 s
r
r g x
(
)
- +
2 s
r
r g
2
1
4
(
)
cos (
)
+ -
2 s
r
r g x
(
)
+ -
2 s
r
r g
2
1
4
(
)
cos (
)
+ +
2 s
r
r g x
(
)
+ +
2 s
r
r g
2
-
-
+
1
4
(
)
cos (
)
- -
2 s
r
r g x
(
)
- -
2 s
r
r g
2
1
32
(
)
cos (
)
-
2 s
2 r g x
(
)
-
s
r g
2
1
4
x
2
+
-
+
(
)
+
+
2 a
2
6 x a
3
12 x
2
a
4
x
d
(
)
ugh %
ugh[8]: polynomial factor p:
+
+
2 a
2
6 x a
3
12 x
2
a
4
ugh[8]: location of p in integrand:
[ ]
2
ugh[8]: integrating by parts...
ugh[14]: cost of evaluated part of integral:
+
+
+
+
9515 additions
83564 multiplications
2298 divisions
2562 functions
2686 subscripts
ugh[14]: simplifying...
ugh[38]: cost of evaluated part of integral:
+
+
+
+
146 additions
385 multiplications
32 divisions
26 functions
188 subscripts
ugh[38]: evaluated part of integral is stored in parts[2]
ugh[38]: new polynomial factor p:
+
6 a
3
24 x a
4
ugh[38]: location of p in integrand:
[ ]
2
ugh[38]: full non-sin/cos term:
1
32
+
6 a
3
24 x a
4
(
)
- +
1
g
2
r
2
(
)
+
1
g
2
g
2
s
2
(
)
+
s
r
2
(
)
-
s
r
2
(
)
+
s
r g
2
(
)
- +
2 s
r
r g
2
(
)
(
(
)
+ -
2 s
r
r g
2
(
)
+ +
2 s
r
r g
2
(
)
- -
2 s
r
r g
2
(
)
-
s
r g
2
)
ugh[39]: cost of new integrand:
+
+
+
+
4756 additions
41779 multiplications
1149 divisions
1281 functions
2 subscripts
ugh[39]: simplifying sin/cos part of new integrand...
ugh[45]: cost of simplified new integrand:
+
+
+
+
42 additions
99 multiplications
16 divisions
13 functions
2 subscripts
ugh[45]: new definite integral:
Page 11
