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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi only. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is also given. The larger this ratio is, the harder the integral is to solve. In this test file, problem number [10] had the largest ratio of [2.20000000000000018]

# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 5 5 0.98 8 0.625
2 A 11 11 1.10 8 1.375
3 A 9 9 1.04 8 1.125
4 A 6 6 1.00 6 1.000
5 A 1 1 1.00 4 0.250
6 A 1 1 1.00 8 0.125
7 A 6 6 1.00 8 0.750
8 A 9 9 1.09 8 1.125
9 N/A 1 0 1.00 10 0.000
10 A 23 22 1.56 10 2.200
11 A 18 18 1.41 10 1.800
12 A 12 11 1.07 8 1.375
13 A 7 7 1.16 6 1.167
14 N/A 1 0 1.00 10 0.000
15 N/A 1 0 1.00 10 0.000
16 N/A 1 0 1.00 10 0.000
17 N/A 2 0 1.00 10 0.000
18 A 3 3 0.89 10 0.300
19 A 3 3 0.92 10 0.300
20 A 3 3 0.93 8 0.375
21 A 1 1 1.00 6 0.167
22 N/A 1 0 1.00 10 0.000
23 A 3 3 1.00 10 0.300
24 A 3 3 0.83 10 0.300
25 N/A 1 0 1.00 12 0.000
26 A 23 23 1.32 12 1.917
27 A 16 16 1.21 10 1.600
28 A 6 6 1.10 8 0.750
29 N/A 1 0 1.00 12 0.000
30 N/A 1 0 1.00 12 0.000
31 N/A 1 0 1.00 12 0.000
32 A 6 5 1.14 17 0.294
33 A 6 5 1.14 15 0.333
34 A 6 5 1.13 13 0.385
35 A 4 3 0.98 17 0.176
36 A 6 5 1.12 17 0.294
37 A 6 5 1.14 17 0.294
38 A 6 5 1.39 19 0.263
39 A 17 17 1.33 12 1.417
40 N/A 8 0 1.00 12 0.000
41 A 1 1 1.00 12 0.083
42 A 6 6 1.00 9 0.667
43 A 11 10 1.08 10 1.000
44 A 17 17 1.54 12 1.417
45 A 22 21 1.70 12 1.750
46 N/A 19 0 1.00 12 0.000
47 A 9 9 1.09 12 0.750
48 N/A 1 0 1.00 12 0.000
49 A 5 5 1.00 9 0.556
50 A 11 11 1.16 10 1.100
51 A 16 15 1.32 12 1.250
52 A 25 25 1.83 12 2.083
53 A 4 4 1.17 9 0.444
54 A 4 4 1.17 9 0.444
55 A 11 11 1.13 16 0.688
56 A 9 9 1.08 14 0.643
57 A 5 5 1.00 13 0.385
58 N/A 1 0 1.00 16 0.000
59 A 10 10 1.10 16 0.625
60 A 8 8 1.06 14 0.571
61 A 4 4 1.00 13 0.308
62 N/A 1 0 1.00 16 0.000
63 A 6 6 1.02 14 0.429
64 A 3 3 1.04 13 0.231
65 N/A 1 0 1.00 16 0.000
66 A 6 6 1.02 14 0.429
67 A 3 3 1.05 13 0.231
68 N/A 1 0 1.00 16 0.000
69 A 6 6 0.98 8 0.750
70 A 12 12 1.11 8 1.500
71 A 9 9 1.08 8 1.125
72 A 7 7 1.03 6 1.167
73 A 1 1 1.00 4 0.250
74 A 1 1 1.00 8 0.125
75 A 7 7 1.00 8 0.875
76 A 9 9 1.07 8 1.125
77 N/A 1 0 1.00 10 0.000
78 A 23 22 1.42 10 2.200
79 A 18 18 1.39 10 1.800
80 A 12 11 1.05 8 1.375
81 A 7 7 1.16 6 1.167
82 N/A 1 0 1.00 10 0.000
83 N/A 1 0 1.00 10 0.000
84 N/A 1 0 1.00 10 0.000
85 N/A 2 0 1.00 10 0.000
86 A 3 3 0.89 10 0.300
87 A 3 3 0.92 10 0.300
88 A 3 3 0.93 8 0.375
89 A 1 1 1.00 6 0.167
90 N/A 1 0 1.00 10 0.000
91 A 3 3 1.00 10 0.300
92 A 3 3 0.83 10 0.300
93 N/A 1 0 1.00 12 0.000
94 A 23 23 1.32 12 1.917
95 A 16 16 1.21 10 1.600
96 A 6 6 1.10 8 0.750
97 N/A 1 0 1.00 12 0.000
98 N/A 1 0 1.00 12 0.000
99 N/A 1 0 1.00 12 0.000
100 A 6 5 1.14 17 0.294
101 A 6 5 1.14 15 0.333
102 A 6 5 1.14 13 0.385
103 A 4 3 1.00 17 0.176
104 A 6 5 1.13 17 0.294
105 A 6 5 1.14 17 0.294
106 A 6 5 1.40 19 0.263
107 N/A 19 0 1.00 12 0.000
108 A 9 9 1.09 12 0.750
109 N/A 1 0 1.00 12 0.000
110 A 5 5 0.97 9 0.556
111 A 11 11 1.11 10 1.100
112 A 16 15 1.16 12 1.250
113 A 25 25 1.58 12 2.083
114 A 17 17 1.31 12 1.417
115 N/A 8 0 1.00 12 0.000
116 A 1 1 1.00 12 0.083
117 A 6 6 1.00 9 0.667
118 A 11 10 1.10 10 1.000
119 A 17 17 1.55 12 1.417
120 A 22 21 1.51 12 1.750
121 A 4 4 1.17 9 0.444
122 A 4 4 1.17 9 0.444
123 A 10 10 1.09 16 0.625
124 A 8 8 1.05 14 0.571
125 A 4 4 1.00 13 0.308
126 N/A 1 0 1.00 16 0.000
127 A 11 11 1.14 16 0.688
128 A 9 9 1.09 14 0.643
129 A 5 5 1.00 13 0.385
130 N/A 1 0 1.00 16 0.000
131 A 6 6 1.02 14 0.429
132 A 3 3 1.04 13 0.231
133 N/A 1 0 1.00 16 0.000
134 A 6 6 1.02 14 0.429
135 A 3 3 1.05 13 0.231
136 N/A 1 0 1.00 16 0.000

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