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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 [30] had the largest ratio of [1.33332999999999990]

# 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 9 0.222
2 A 2 2 1.00 9 0.222
3 A 1 1 1.00 7 0.143
4 A 10 9 1.05 9 1.000
5 A 9 8 1.01 7 1.143
6 A 4 4 1.89 11 0.364
7 A 3 3 1.46 11 0.273
8 A 2 2 1.00 11 0.182
9 A 3 3 1.47 11 0.273
10 A 2 2 1.00 9 0.222
11 A 2 2 1.00 9 0.222
12 A 2 2 1.00 9 0.222
13 A 1 1 1.00 7 0.143
14 A 10 9 1.40 9 1.000
15 A 11 10 1.41 9 1.111
16 A 9 8 1.27 9 0.889
17 A 2 2 1.00 9 0.222
18 A 1 1 1.00 9 0.111
19 A 2 2 1.00 9 0.222
20 A 8 7 1.15 9 0.778
21 A 8 7 1.14 7 1.000
22 A 5 4 1.13 11 0.364
23 A 4 3 1.12 11 0.273
24 A 3 2 1.12 11 0.182
25 A 4 3 1.12 11 0.273
26 A 2 2 1.00 11 0.182
27 A 2 2 1.00 11 0.182
28 A 2 2 1.00 11 0.182
29 A 2 2 1.00 11 0.182
30 A 13 12 1.48 9 1.333
31 A 13 12 1.46 10 1.200
32 A 4 4 1.02 11 0.364
33 A 3 3 1.01 11 0.273
34 A 4 4 1.01 11 0.364
35 A 9 8 1.99 9 0.889
36 A 2 2 1.00 9 0.222
37 A 2 2 1.00 9 0.222
38 A 1 1 1.00 7 0.143
39 A 3 2 1.00 9 0.222
40 A 4 3 1.00 9 0.333
41 A 4 3 1.00 9 0.333
42 A 2 2 1.00 10 0.200
43 A 2 2 1.00 10 0.200
44 A 2 2 1.00 9 0.222
45 A 2 2 1.00 10 0.200
46 A 2 2 1.00 10 0.200
47 A 2 2 1.00 10 0.200
48 A 4 3 1.05 11 0.273
49 A 4 3 1.05 11 0.273
50 A 4 3 1.05 11 0.273
51 A 4 3 1.19 11 0.273
52 A 1 1 1.00 9 0.111
53 A 4 3 1.04 11 0.273
54 A 4 3 1.00 11 0.273
55 A 1 1 1.00 11 0.091
56 A 4 3 1.11 11 0.273
57 A 4 3 1.05 11 0.273
58 A 4 3 1.12 11 0.273
59 A 4 3 1.19 11 0.273
60 A 1 1 1.00 9 0.111
61 A 10 9 1.02 11 0.818
62 A 11 10 1.06 11 0.909
63 A 12 11 1.10 11 1.000
64 A 13 12 1.14 11 1.091
65 A 5 4 1.24 11 0.364
66 A 5 4 1.26 11 0.364
67 A 5 4 1.43 11 0.364
68 A 1 1 1.00 9 0.111
69 A 5 4 1.11 11 0.364
70 A 5 4 1.07 11 0.364
71 A 5 4 1.10 11 0.364
72 A 5 4 1.07 11 0.364
73 A 5 4 1.14 11 0.364
74 A 5 4 1.12 11 0.364
75 A 5 4 1.20 11 0.364
76 A 1 1 1.00 9 0.111
77 A 12 11 1.10 11 1.000
78 A 13 12 1.14 11 1.091
79 A 14 13 1.17 11 1.182
80 A 4 3 1.00 11 0.273
81 A 4 3 1.00 11 0.273
82 A 4 3 1.02 11 0.273
83 A 4 3 1.00 11 0.273
84 A 5 4 1.04 11 0.364
85 A 5 4 1.04 11 0.364
86 A 4 3 1.03 11 0.273
87 A 4 3 1.03 11 0.273
88 A 4 3 1.07 11 0.273
89 A 4 3 1.12 11 0.273
90 A 4 3 1.17 11 0.273
91 A 1 1 1.00 9 0.111
92 A 4 3 1.02 11 0.273
93 A 4 3 1.02 11 0.273
94 A 4 3 1.02 11 0.273
95 A 1 1 1.00 11 0.091
96 A 4 3 1.56 11 0.273
97 A 4 3 1.07 11 0.273
98 A 4 3 1.12 11 0.273
99 A 4 3 1.17 11 0.273
100 A 1 1 1.00 9 0.111
101 A 4 3 1.02 11 0.273
102 A 4 3 1.04 11 0.273
103 A 5 4 1.09 11 0.364
104 A 4 3 1.12 11 0.273
105 A 4 3 1.17 11 0.273
106 A 1 1 1.00 9 0.111
107 A 10 9 1.50 11 0.818
108 A 11 10 1.49 11 0.909
109 A 12 11 1.48 11 1.000
110 A 5 4 1.25 11 0.364
111 A 1 1 1.07 11 0.091
112 A 1 1 1.00 9 0.111
113 A 5 4 1.08 11 0.364
114 A 5 4 1.07 11 0.364
115 A 5 4 1.06 11 0.364
116 A 5 4 1.19 11 0.364
117 A 5 4 1.20 11 0.364
118 A 1 1 1.00 9 0.111
119 A 5 4 1.09 11 0.364
120 A 6 5 1.09 11 0.455
121 A 7 6 1.12 11 0.545
122 A 5 4 1.12 11 0.364
123 A 5 4 1.19 11 0.364
124 A 1 1 1.00 9 0.111
125 A 12 11 1.55 11 1.000
126 A 13 12 1.55 11 1.091
127 A 14 13 1.53 11 1.182
128 A 1 1 1.07 11 0.091
129 A 1 1 1.00 17 0.059
130 A 4 3 1.03 13 0.231
131 A 4 3 1.06 13 0.231
132 A 4 3 1.07 13 0.231
133 A 4 3 1.07 13 0.231
134 A 4 3 1.07 13 0.231
135 A 7 6 1.08 13 0.462
136 A 6 5 1.06 13 0.385
137 A 5 4 1.03 13 0.308
138 A 5 4 1.02 13 0.308
139 A 1 1 1.00 13 0.077
140 A 4 3 1.16 13 0.231
141 A 5 4 1.31 13 0.308
142 A 8 7 1.03 13 0.538
143 A 7 6 1.02 13 0.462
144 A 6 5 1.02 13 0.385
145 A 7 6 1.02 13 0.462
146 A 9 8 1.03 13 0.615
147 A 8 7 1.05 13 0.538
148 A 8 7 1.07 13 0.538
149 A 8 7 1.11 13 0.538
150 A 8 7 1.13 13 0.538
151 A 9 8 1.14 13 0.615
152 A 8 7 1.09 13 0.538
153 A 7 6 1.10 13 0.462
154 A 1 1 1.00 13 0.077
155 A 4 3 1.28 13 0.231
156 A 6 5 1.38 13 0.385
157 A 6 5 1.10 13 0.385
158 A 5 4 1.08 13 0.308
159 A 5 4 1.06 13 0.308
160 A 6 5 1.10 13 0.385
161 A 4 3 1.00 11 0.273
162 A 4 3 1.00 11 0.273
163 A 4 3 1.00 11 0.273
164 A 4 3 1.00 11 0.273
165 A 5 4 1.04 11 0.364
166 A 5 4 1.04 11 0.364
167 A 1 1 1.07 11 0.091
168 A 1 1 1.00 17 0.059
169 A 4 3 1.00 9 0.333
170 A 1 1 1.00 13 0.077
171 A 2 2 1.00 9 0.222
172 A 2 2 1.00 9 0.222
173 A 1 1 1.00 7 0.143
174 A 1 1 1.00 9 0.111
175 A 1 1 1.00 9 0.111
176 A 1 1 1.00 9 0.111
177 A 2 2 1.00 11 0.182
178 A 2 2 1.00 11 0.182
179 A 2 2 1.00 11 0.182
180 A 2 2 1.00 11 0.182
181 A 2 2 1.00 11 0.182
182 A 2 2 1.00 9 0.222
183 A 1 1 1.00 15 0.067
184 A 4 4 0.90 15 0.267
185 A 3 3 0.95 15 0.200
186 A 2 2 1.00 15 0.133
187 A 1 1 1.00 15 0.067
188 A 3 2 0.78 13 0.154
189 A 2 2 1.00 15 0.133
190 A 2 2 1.00 15 0.133
191 A 4 4 0.90 18 0.222
192 A 3 3 0.94 18 0.167
193 A 2 2 1.00 18 0.111
194 A 1 1 1.00 16 0.062
195 A 3 2 0.78 13 0.154
196 A 2 2 1.00 18 0.111
197 A 2 2 1.00 18 0.111

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