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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 [64] had the largest ratio of [.484848000000000001]

# 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 3 3 1.00 29 0.103
2 A 3 3 1.00 29 0.103
3 A 3 3 1.00 29 0.103
4 A 3 3 1.00 27 0.111
5 A 2 2 1.05 22 0.091
6 A 3 3 1.00 29 0.103
7 A 3 3 1.00 29 0.103
8 A 3 3 1.00 29 0.103
9 A 3 3 1.00 29 0.103
10 A 3 3 1.00 29 0.103
11 A 3 3 1.00 29 0.103
12 A 3 3 1.00 29 0.103
13 A 3 3 1.00 29 0.103
14 A 3 3 1.00 29 0.103
15 A 3 3 1.00 29 0.103
16 A 3 3 1.00 27 0.111
17 A 2 2 1.09 22 0.091
18 A 3 3 1.00 29 0.103
19 A 3 3 1.00 29 0.103
20 A 3 3 1.00 29 0.103
21 A 3 3 1.00 29 0.103
22 A 3 3 1.00 29 0.103
23 A 3 3 1.00 29 0.103
24 A 3 3 1.00 29 0.103
25 A 3 3 1.00 29 0.103
26 A 3 3 1.00 29 0.103
27 A 3 3 1.00 29 0.103
28 A 3 3 1.00 27 0.111
29 A 2 2 1.25 22 0.091
30 A 3 3 1.00 29 0.103
31 A 3 3 1.00 29 0.103
32 A 8 8 1.08 29 0.276
33 A 6 6 1.11 29 0.207
34 A 3 3 1.06 27 0.111
35 A 3 3 1.00 22 0.136
36 A 2 2 1.00 29 0.069
37 A 2 2 1.48 29 0.069
38 A 2 2 1.81 29 0.069
39 A 9 9 0.89 29 0.310
40 A 7 7 1.01 29 0.241
41 A 4 4 1.14 27 0.148
42 A 3 3 1.54 22 0.136
43 A 2 2 1.00 29 0.069
44 A 2 2 1.50 29 0.069
45 B 2 2 2.12 29 0.069
46 A 13 12 1.08 31 0.387
47 A 10 9 1.10 31 0.290
48 A 10 9 1.10 31 0.290
49 A 5 5 1.15 31 0.161
50 A 3 3 0.92 29 0.103
51 A 4 4 1.29 24 0.167
52 A 10 9 1.34 31 0.290
53 A 8 7 0.93 31 0.226
54 A 10 9 1.10 31 0.290
55 A 8 7 1.05 29 0.241
56 A 6 6 1.14 29 0.207
57 A 8 8 0.99 30 0.267
58 A 14 14 1.10 33 0.424
59 A 12 12 1.10 33 0.364
60 A 8 7 1.58 31 0.226
61 A 4 3 1.00 26 0.115
62 A 6 6 1.09 33 0.182
63 A 14 14 1.10 33 0.424
64 A 16 16 1.11 33 0.485
65 A 11 11 1.12 31 0.355
66 A 10 10 1.14 31 0.323
67 A 6 5 1.48 29 0.172
68 A 3 2 1.00 24 0.083
69 A 6 6 1.00 31 0.194
70 A 12 12 1.15 31 0.387
71 A 13 13 1.16 31 0.419
72 A 10 10 1.14 31 0.323
73 A 9 9 1.14 29 0.310
74 A 3 2 1.00 25 0.080
75 A 4 3 0.83 30 0.100
76 A 3 3 1.00 29 0.103
77 A 4 4 1.00 32 0.125
78 A 2 2 1.00 29 0.069
79 A 3 3 1.00 28 0.107
80 A 3 3 1.00 28 0.107
81 A 3 3 1.00 26 0.115
82 A 3 3 1.00 21 0.143
83 A 6 5 0.99 28 0.179
84 A 6 5 1.28 28 0.179
85 A 6 5 1.05 28 0.179
86 A 9 8 1.11 36 0.222
87 A 7 6 1.10 36 0.167
88 A 5 4 1.00 34 0.118
89 A 3 2 1.00 29 0.069
90 A 5 4 1.08 36 0.111
91 A 7 6 1.12 36 0.167
92 A 9 8 1.08 36 0.222
93 A 8 7 0.91 30 0.233
94 A 7 6 0.95 30 0.200
95 A 6 5 0.97 30 0.167
96 A 6 5 1.29 30 0.167
97 A 6 5 1.06 30 0.167
98 A 3 3 1.00 30 0.100
99 A 4 4 1.03 30 0.133
100 A 5 5 1.03 30 0.167
101 A 6 6 1.05 30 0.200
102 A 2 2 0.88 36 0.056
103 A 2 2 0.88 36 0.056
104 A 3 3 0.71 36 0.083
105 A 1 1 0.84 36 0.028
106 A 5 5 1.04 36 0.139
107 A 1 1 0.01 36 0.028
108 A 1 1 0.02 36 0.028
109 A 1 1 0.01 36 0.028
110 A 1 1 0.01 36 0.028
111 A 3 3 1.00 29 0.103
112 A 3 3 1.00 27 0.111
113 A 4 4 1.00 22 0.182
114 A 3 3 1.00 29 0.103
115 A 3 3 1.00 29 0.103
116 B 7 7 3.33 29 0.241
117 A 3 3 1.00 27 0.111
118 A 4 4 1.00 22 0.182
119 A 3 3 1.00 29 0.103
120 A 3 3 1.00 29 0.103
121 A 2 2 1.00 45 0.044
122 A 3 3 1.00 26 0.115
123 A 3 3 1.00 27 0.111
124 A 4 4 1.00 30 0.133
125 A 2 2 1.00 27 0.074
126 A 3 3 1.00 29 0.103
127 A 3 3 1.00 30 0.100
128 A 2 2 1.00 27 0.074
129 A 2 2 1.00 27 0.074
130 A 3 3 1.00 27 0.111
131 A 3 3 1.12 27 0.111
132 A 4 4 1.17 29 0.138
133 A 4 4 0.94 29 0.138
134 A 3 3 1.00 27 0.111
135 A 4 4 0.96 29 0.138
136 A 4 4 0.98 27 0.148
137 A 3 2 1.00 22 0.091
138 A 4 4 0.87 29 0.138
139 A 4 4 0.97 29 0.138
140 A 4 4 0.98 29 0.138
141 A 3 3 1.00 25 0.120
142 A 3 3 1.00 30 0.100
143 A 2 2 1.00 25 0.080

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