In[]:=
Ex1:
Param-extract time: 0.000011 s
Conversion time: 0.000049 s
Direct time: 0.003120 s
Direct result: -
Sec
ArcCsc[x]
2
Sec
ArcSec[x]
2
Sin
1
2
(ArcCsc[x]-ArcSec[x])-2
2-
2
2
x
xArcTanh
x
2
-1+
2
x

2
Csc
1
2
(ArcCsc[x]+ArcSec[x])
+
-1+
2
x
2
Csc
1
2
(ArcCsc[x]+ArcSec[x])
21+
1-
1
2
x
x+4Log1+
1-
1
2
x
x+Log[2-
2
x
]-2
3
Cot
1
2
(ArcCsc[x]+ArcSec[x])
Log-
21+
2
-
1-
1
2
x
x
3
Tan
1
2
(ArcCsc[x]+ArcSec[x])
2
+x
+Log-
2-1+
2
+
1-
1
2
x
x
3
Tan
1
2
(ArcCsc[x]+ArcSec[x])
2
-x
-
2
ArcTanh
x
2

4
Csc
1
2
(ArcCsc[x]+ArcSec[x])
Sin[ArcCsc[x]+ArcSec[x]]
8
-1+
2
x
Tan
ArcCsc[x]
2
-Tan
ArcSec[x]
2

Direct LeafCount: 311
Direct ByteCount: 9920
USM time (upper): 0.015700 s
USM result (upper):
1
2
-
1
x-
-1+
2
x
+3Logx-
-1+
2
x
+(-1+
2
)Log1+
2
+x-
-1+
2
x
+(-1-
2
)Log-1+
2
-x+
-1+
2
x

USM LeafCount (upper): 96
USM ByteCount (upper): 2984
USM time (lower): 0.012500 s
USM result (lower):
1
2
-
1
x+
-1+
2
x
+(-1-
2
)Log-1+
2
-x-
-1+
2
x
+3Logx+
-1+
2
x
+(-1+
2
)Log1+
2
+x+
-1+
2
x

USM LeafCount (lower): 92
USM ByteCount (lower): 2840
Ex2:
Param-extract time: 0.000012 s
Conversion time: 0.000091 s
Direct time: 1.170000 s
Direct result:
4(-1+x)-7+12-5
1-
1
2
x
x+59-29
1-
1
2
x
2
x
+4+8
1-
1
2
x
3
x
+60-1+
1-
1
2
x
4
x
+24-1+
1-
1
2
x
5
x
-12
x-
1-
1
2
x
x
-1+3-
1-
1
2
x
x+8-4
1-
1
2
x
2
x
+-4+4
1-
1
2
x
3
x
+-8+8
1-
1
2
x
4
x
ArcTanh
x-
1-
1
2
x
x

3
2
-1+
1-
1
2
x
2
x
-1+-1+
1-
1
2
x
x
2
1+-1+
1-
1
2
x
x
x-
1-
1
2
x
x
Direct LeafCount: 295
Direct ByteCount: 9208
USM time (upper): 0.001370 s
USM result (upper):
1
2
2
3
3/2
x-
-1+
2
x

+
8
x-
-1+
2
x
+2
x-
-1+
2
x
-16ArcTanh
x-
-1+
2
x

USM LeafCount (upper): 84
USM ByteCount (upper): 2544
USM time (lower): 0.001090 s
USM result (lower):
1
2
2
3
3/2
x+
-1+
2
x

+
8
x+
-1+
2
x
+2
x+
-1+
2
x
-16ArcTanh
x+
-1+
2
x

USM LeafCount (lower): 76
USM ByteCount (lower): 2256
Ex3:
Param-extract time: 0.000013 s
Conversion time: 0.000063 s
Direct time: 6.180000 s
Direct LeafCount: 8962
Direct ByteCount: 283576
USM time (upper): 0.001460 s
USM result (upper):
15-15x-
-1+
2
x
+5
2
x-
-1+
2
x

+3
3
x-
-1+
2
x

30
x-
-1+
2
x
USM LeafCount (upper): 72
USM ByteCount (upper): 2216
USM time (lower): 0.000955 s
USM result (lower):
15-15x+
-1+
2
x
+5
2
x+
-1+
2
x

+3
3
x+
-1+
2
x

30
x+
-1+
2
x
USM LeafCount (lower): 64
USM ByteCount (lower): 1928
Ex4:
Param-extract time: 0.000015 s
Conversion time: 0.000054 s
Direct time: 0.258000 s
Direct result:
Log-1+
1-
1
2
x
x+Log1+
1-
1
2
x
x
2Cos
1
2
(ArcCsc[x]+ArcSec[x])-Sin
1
2
(ArcCsc[x]+ArcSec[x])
3
Cos
1
2
(ArcCsc[x]+ArcSec[x])+Sin
1
2
(ArcCsc[x]+ArcSec[x])
Direct LeafCount: 85
Direct ByteCount: 2768
USM time (upper): 0.000980 s
USM result (upper):
1
4x-
-1+
2
x

+
1
4
x-
-1+
2
x
+
1
8
2
x-
-1+
2
x

-
1
4
Logx-
-1+
2
x

USM LeafCount (upper): 74
USM ByteCount (upper): 2248
USM time (lower): 0.000702 s
USM result (lower):
1
4x+
-1+
2
x

+
1
4
x+
-1+
2
x
+
1
8
2
x+
-1+
2
x

-
1
4
Logx+
-1+
2
x

USM LeafCount (lower): 66
USM ByteCount (lower): 1960
Ex5:
Param-extract time: 0.000011 s
Conversion time: 0.000035 s
Direct time: 0.011300 s
Direct result:
1
2
x+
1-
1
2
x
x+ArcSin
1
x

Direct LeafCount: 23
Direct ByteCount: 680
USM time (upper): 0.004640 s
USM result (upper):
1
2
1
x-
-1+
2
x
+2ArcTanx-
-1+
2
x

USM LeafCount (upper): 36
USM ByteCount (upper): 1128
USM time (lower): 0.005140 s
USM result (lower):
1
2
1
x+
-1+
2
x
+2ArcTanx+
-1+
2
x

USM LeafCount (lower): 32
USM ByteCount (lower): 984
Ex6:
Param-extract time: 0.000013 s
Conversion time: 0.000036 s
Direct time: 0.026800 s
Direct result:
1-
1
2
x
x(5+x)
1+x
-3Log1+
1-
1
2
x
x
Direct LeafCount: 40
Direct ByteCount: 1248
USM time (upper): 0.011200 s
USM result (upper):
1
2
-x+
-1+
2
x
+
1
x-
-1+
2
x
+
16
1+x-
-1+
2
x
+6Logx-
-1+
2
x

USM LeafCount (upper): 66
USM ByteCount (upper): 2032