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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 [12] had the largest ratio of [1.50000000000000000]

# 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 1 1 1.00 3 0.333
2 A 1 1 1.00 3 0.333
3 A 1 1 1.00 3 0.333
4 A 1 1 1.00 3 0.333
5 A 2 2 1.00 2 1.000
6 A 2 2 1.00 2 1.000
7 A 4 3 1.00 4 0.750
8 A 4 3 1.00 4 0.750
9 A 4 3 1.00 5 0.600
10 A 5 4 1.00 5 0.800
11 A 2 2 1.00 2 1.000
12 A 3 3 1.00 2 1.500
13 A 2 2 0.71 2 1.000
14 A 2 2 0.50 2 1.000
15 A 1 1 1.00 7 0.143
16 A 1 1 1.00 9 0.111
17 A 1 1 1.00 11 0.091
18 A 1 1 1.00 9 0.111
19 A 3 2 1.00 9 0.222
20 A 3 3 1.00 2 1.500
21 A 2 2 1.00 2 1.000
22 A 5 4 1.00 4 1.000
23 A 4 3 1.00 4 0.750
24 A 3 3 1.00 2 1.500
25 A 3 3 1.00 2 1.500
26 A 3 3 0.71 2 1.500
27 A 1 1 1.00 7 0.143
28 A 1 1 1.00 7 0.143
29 A 2 2 1.00 9 0.222
30 A 2 2 1.00 11 0.182
31 A 1 1 1.00 7 0.143
32 A 2 2 0.96 9 0.222
33 A 2 2 1.00 11 0.182
34 A 1 1 1.00 7 0.143
35 A 1 1 0.74 9 0.111
36 A 2 2 1.11 11 0.182
37 A 2 2 0.88 11 0.182
38 A 1 1 1.00 7 0.143
39 A 2 2 1.20 9 0.222
40 A 1 1 0.50 11 0.091
41 A 2 2 1.16 11 0.182
42 A 1 1 1.00 7 0.143
43 A 2 2 1.20 9 0.222
44 A 2 2 1.24 11 0.182
45 A 1 1 0.36 11 0.091
46 A 3 3 1.20 11 0.273
47 A 2 2 1.17 11 0.182
48 A 2 2 1.14 11 0.182
49 A 2 2 1.05 11 0.182
50 A 2 2 1.02 11 0.182
51 A 2 2 1.13 11 0.182
52 A 2 2 1.12 11 0.182
53 A 2 2 1.19 11 0.182
54 A 2 2 1.12 11 0.182
55 A 2 2 1.13 11 0.182
56 A 2 2 1.18 11 0.182
57 A 2 2 1.11 11 0.182
58 A 2 2 1.13 11 0.182
59 A 2 2 1.18 11 0.182
60 A 1 1 1.20 9 0.111
61 A 1 1 1.08 13 0.077
62 A 9 8 1.18 9 0.889
63 A 9 8 1.15 11 0.727
64 A 1 1 1.00 13 0.077
65 A 10 9 1.23 13 0.692
66 A 10 9 1.18 13 0.692
67 A 10 9 1.21 9 1.000
68 A 10 9 1.15 11 0.818
69 A 1 1 1.00 13 0.077
70 A 10 9 1.18 13 0.692
71 A 5 4 1.24 13 0.308
72 A 10 9 1.19 13 0.692
73 A 10 9 1.21 13 0.692
74 A 4 3 1.03 13 0.231
75 A 11 10 1.20 13 0.769
76 A 11 10 1.23 13 0.769
77 B 9 8 3.17 9 0.889
78 A 3 2 1.16 11 0.182
79 B 9 8 3.17 13 0.615
80 A 1 1 1.00 13 0.077
81 B 10 9 2.78 9 1.000
82 A 4 3 1.10 11 0.273
83 B 10 9 2.64 13 0.692
84 A 1 1 1.00 13 0.077
85 A 5 4 1.24 13 0.308
86 B 10 9 2.99 13 0.692
87 A 1 1 1.00 5 0.200
88 A 1 1 1.00 7 0.143
89 A 8 7 1.05 7 1.000
90 A 9 8 1.38 7 1.143
91 A 1 1 1.00 7 0.143
92 A 1 1 1.00 9 0.111
93 A 1 1 1.00 7 0.143
94 A 7 6 1.05 9 0.667
95 A 3 3 1.44 9 0.333
96 A 2 2 1.00 7 0.286
97 A 1 1 1.00 9 0.111
98 A 8 7 1.12 9 0.778
99 A 3 2 1.00 9 0.222
100 A 2 2 1.00 9 0.222
101 A 1 1 1.00 11 0.091
102 A 7 6 1.12 11 0.545
103 A 3 2 0.40 11 0.182
104 A 5 4 1.42 11 0.364
105 A 5 4 1.36 13 0.308
106 A 2 2 1.04 13 0.154
107 A 2 2 1.44 15 0.133
108 A 2 2 1.26 16 0.125
109 A 3 2 1.81 13 0.154
110 A 4 3 1.29 13 0.231
111 A 5 4 1.31 13 0.308
112 A 6 5 1.37 13 0.385
113 A 4 3 1.50 13 0.231
114 A 4 3 1.48 13 0.231
115 A 5 4 1.30 13 0.308
116 A 6 5 1.22 13 0.385
117 A 5 4 1.26 13 0.308
118 A 5 4 1.14 13 0.308
119 A 5 4 0.84 13 0.308
120 A 6 5 0.91 13 0.385
121 B 10 9 2.16 15 0.600
122 B 10 9 2.12 15 0.600
123 B 11 10 2.04 15 0.667
124 B 11 10 2.04 15 0.667
125 A 11 10 1.90 15 0.667
126 A 11 10 1.87 15 0.667
127 A 11 10 1.94 15 0.667
128 A 11 10 1.91 15 0.667
129 A 12 11 1.86 15 0.733
130 A 12 11 1.84 15 0.733
131 A 12 11 1.94 15 0.733
132 A 12 11 1.53 15 0.733
133 A 1 1 1.00 9 0.111
134 A 2 2 1.19 11 0.182
135 A 2 2 1.31 13 0.154
136 A 4 3 1.50 11 0.273
137 B 3 3 2.43 13 0.231
138 A 3 3 1.79 15 0.200
139 A 3 2 0.55 13 0.154
140 A 4 3 0.65 13 0.231
141 A 4 3 0.64 13 0.231
142 A 5 4 0.70 13 0.308
143 A 6 5 1.11 15 0.333
144 A 6 5 0.82 15 0.333
145 A 6 5 0.61 15 0.333
146 A 4 3 0.61 13 0.231
147 A 5 4 0.85 13 0.308
148 A 5 4 1.04 15 0.267
149 A 6 5 1.18 15 0.333
150 A 7 6 1.24 15 0.400
151 A 6 5 1.23 15 0.333
152 A 6 5 0.98 13 0.385
153 A 6 5 0.79 13 0.385
154 A 7 6 0.89 13 0.462
155 A 7 6 1.18 15 0.400
156 A 8 7 1.28 15 0.467
157 A 5 4 0.96 13 0.308
158 A 7 6 1.18 15 0.400
159 A 7 6 1.01 15 0.400
160 A 3 3 0.22 15 0.200
161 A 6 5 0.96 13 0.385
162 A 7 6 1.10 13 0.462
163 A 2 2 0.91 15 0.133

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