Astronomical Applications Department, U.S. Naval Observatory Sensitivity Integral Page 10
1
2
1
8
(
)
sin 2 r g x
r g
1
4
(
)
sin 2 s x
s
1
16
(
)
sin (
)
+
2 s
2 r x
+
s
r
1
16
(
)
sin (
)
-
2 s
2 r x
-
s
r
-
-
+
+
-
1
16
(
)
sin (
)
+
2 s
2 r g x
+
s
r g
1
8
(
)
sin 2 r x
r
1
4
(
)
sin (
)
- +
2 s
r
r g x
- +
2 s
r
r g
1
4
(
)
sin (
)
+ -
2 s
r
r g x
+ -
2 s
r
r g
+
-
+
+
1
4
(
)
sin (
)
+ +
2 s
r
r g x
+ +
2 s
r
r g
1
4
(
)
sin (
)
- -
2 s
r
r g x
- -
2 s
r
r g
1
16
(
)
sin (
)
-
2 s
2 r g x
-
s
r g
1
2
(
)
sin (
)
+
r
r g x
r (
)
+
1
g
-
-
+
+
1
2
(
)
sin (
)
- +
r
r g x
r (
)
- +
1
g
1
2
x
-
+
(
)
+
+ +
2 x a
2
3 x
2
a
3
a
1
4 x
3
a
4
x
d
(
)
ugh %
ugh[0]: polynomial factor p:
+
+ +
2 x a
2
3 x
2
a
3
a
1
4 x
3
a
4
ugh[0]: location of p in integrand:
[ ]
2
ugh[0]: integrating by parts...
ugh[2]: cost of evaluated part of integral:
+
+
+
+
2697 additions
13778 multiplications
690 divisions
728 functions
774 subscripts
ugh[2]: simplifying...
ugh[6]: cost of evaluated part of integral:
+
+
+
+
174 additions
466 multiplications
32 divisions
26 functions
244 subscripts
ugh[6]: evaluated part of integral is stored in parts[1]
ugh[6]: new polynomial factor p:
+
+
2 a
2
6 x a
3
12 x
2
a
4
ugh[6]: location of p in integrand:
[ ]
2
ugh[6]: full non-sin/cos term:
1
16
+
+
2 a
2
6 x a
3
12 x
2
a
4
r g s (
)
+
s
r (
)
-
s
r (
)
+
s
r g (
)
- +
2 s
r
r g (
)
+ -
2 s
r
r g
(
)
/
(
-
(
)
+ +
2 s
r
r g (
)
- -
2 s
r
r g (
)
-
s
r g (
)
+
1
g (
)
- +
1
g )
ugh[7]: cost of new integrand:
+
+
+
+
1347 additions
6886 multiplications
345 divisions
364 functions
3 subscripts
ugh[7]: simplifying sin/cos part of new integrand...
ugh[8]: cost of simplified new integrand:
+
+
+
+
43 additions
85 multiplications
16 divisions
13 functions
3 subscripts
ugh[8]: new definite integral:
Page 10
