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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 [120] had the largest ratio of [1]

# 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 2 2 1.00 11 0.182
2 A 2 2 1.00 11 0.182
3 A 2 2 1.00 11 0.182
4 A 1 1 1.00 9 0.111
5 A 2 2 1.00 11 0.182
6 A 2 2 1.00 11 0.182
7 A 2 2 1.00 11 0.182
8 A 2 2 1.00 11 0.182
9 A 6 5 0.77 13 0.385
10 A 5 4 0.79 13 0.308
11 A 4 3 0.82 13 0.231
12 A 3 2 1.00 13 0.154
13 A 1 1 0.60 13 0.077
14 A 2 2 0.61 13 0.154
15 A 3 3 0.64 13 0.231
16 A 4 4 0.66 13 0.308
17 A 6 5 0.72 13 0.385
18 A 5 4 0.73 13 0.308
19 A 4 3 0.69 13 0.231
20 A 3 2 1.08 13 0.154
21 A 1 1 0.59 13 0.077
22 A 2 2 0.62 13 0.154
23 A 3 3 0.66 13 0.231
24 A 4 4 0.68 13 0.308
25 A 6 5 0.68 15 0.333
26 A 5 4 0.69 15 0.267
27 A 4 3 0.66 15 0.200
28 A 3 2 0.84 15 0.133
29 A 1 1 0.59 15 0.067
30 A 2 2 0.59 15 0.133
31 A 3 3 0.62 15 0.200
32 A 3 2 0.81 13 0.154
33 A 3 2 0.61 13 0.154
34 A 3 2 1.00 13 0.154
35 A 3 2 0.88 13 0.154
36 A 3 2 1.50 16 0.125
37 A 3 2 0.77 17 0.118
38 A 3 2 1.00 15 0.133
39 A 3 2 1.00 16 0.125
40 A 4 3 0.73 13 0.231
41 A 4 3 0.69 13 0.231
42 A 4 3 0.66 11 0.273
43 A 4 3 0.62 11 0.273
44 A 4 3 0.70 11 0.273
45 A 3 2 0.86 13 0.154
46 A 3 2 1.00 11 0.182
47 A 3 2 1.00 11 0.182
48 A 5 4 0.67 11 0.364
49 A 3 2 1.00 15 0.133
50 A 3 2 1.17 13 0.154
51 B 7 6 10.00 13 0.462
52 B 8 7 19.71 13 0.538
53 B 6 5 8.94 13 0.385
54 B 7 6 18.77 13 0.462
55 B 5 4 8.42 13 0.308
56 B 8 7 20.73 13 0.538
57 B 6 5 8.80 13 0.385
58 A 6 5 0.87 13 0.385
59 A 5 4 0.95 13 0.308
60 A 5 4 0.90 13 0.308
61 A 4 3 1.15 13 0.231
62 A 4 3 1.04 13 0.231
63 A 5 4 1.13 13 0.308
64 A 6 5 0.84 13 0.385
65 A 7 6 0.80 13 0.462
66 A 4 3 1.18 13 0.231
67 A 4 3 1.18 13 0.231
68 A 4 3 1.15 13 0.231
69 A 3 2 1.21 13 0.154
70 A 3 2 1.21 13 0.154
71 A 4 3 1.14 13 0.231
72 A 4 3 1.18 13 0.231
73 A 4 3 0.90 13 0.231
74 A 4 3 0.99 13 0.231
75 A 3 2 1.21 13 0.154
76 A 3 2 1.21 13 0.154
77 A 4 3 1.14 13 0.231
78 A 5 4 0.96 13 0.308
79 A 5 4 0.99 13 0.308
80 A 5 4 1.07 13 0.308
81 A 4 3 0.85 13 0.231
82 A 4 3 0.83 13 0.231
83 A 5 4 0.92 13 0.308
84 A 1 1 1.41 11 0.091
85 A 3 2 1.16 14 0.143
86 A 1 1 1.32 13 0.077
87 A 3 2 1.28 11 0.182
88 A 3 2 1.00 11 0.182
89 A 1 1 1.29 11 0.091
90 A 1 1 1.00 11 0.091
91 A 3 3 1.00 13 0.231
92 A 3 3 1.00 13 0.231
93 A 3 3 1.00 13 0.231
94 A 1 1 1.00 11 0.091
95 A 3 3 1.00 13 0.231
96 A 3 3 1.00 13 0.231
97 A 3 3 1.00 13 0.231
98 A 3 3 1.00 13 0.231
99 A 8 8 1.16 15 0.533
100 A 6 6 1.15 15 0.400
101 A 4 4 1.11 15 0.267
102 A 2 2 1.00 15 0.133
103 A 3 2 0.94 15 0.133
104 A 6 5 1.04 15 0.333
105 A 9 8 1.12 15 0.533
106 A 12 11 1.14 15 0.733
107 A 5 5 0.80 15 0.333
108 A 4 4 0.75 15 0.267
109 A 2 2 0.67 15 0.133
110 A 1 1 1.00 15 0.067
111 A 3 3 1.08 15 0.200
112 A 4 4 1.13 15 0.267
113 A 6 6 1.15 15 0.400
114 A 13 12 1.22 15 0.800
115 A 10 9 1.24 15 0.600
116 A 7 6 1.27 15 0.400
117 A 6 5 1.22 15 0.333
118 A 9 8 1.21 15 0.533
119 A 12 11 1.22 15 0.733
120 A 16 15 1.35 15 1.000
121 A 13 12 1.44 15 0.800
122 A 10 9 1.79 15 0.600
123 B 13 12 2.08 15 0.800
124 A 16 15 1.72 15 1.000
125 A 3 3 1.15 13 0.231
126 A 3 3 1.00 15 0.200
127 A 3 3 1.00 15 0.200
128 A 1 1 1.00 13 0.077
129 A 2 2 1.00 15 0.133
130 A 2 2 1.00 15 0.133
131 A 2 2 1.00 15 0.133
132 A 3 3 1.11 17 0.176
133 A 3 3 1.08 17 0.176
134 A 3 3 1.00 17 0.176
135 A 3 3 1.00 17 0.176
136 A 3 3 1.00 17 0.176
137 A 3 3 1.11 17 0.176
138 A 3 3 1.04 15 0.200
139 A 4 4 1.19 19 0.211
140 A 3 3 1.18 19 0.158
141 A 2 2 1.09 17 0.118
142 A 2 2 1.23 19 0.105
143 A 2 2 1.25 19 0.105
144 A 2 2 1.25 19 0.105

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