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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 [23] had the largest ratio of [.727272999999999947]

# 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 9 8 0.94 17 0.471
2 A 8 7 0.96 17 0.412
3 A 7 6 0.96 17 0.353
4 A 6 5 1.00 17 0.294
5 A 7 6 0.96 17 0.353
6 A 8 7 1.00 17 0.412
7 A 9 8 0.96 19 0.421
8 A 8 7 0.97 19 0.368
9 A 7 6 0.96 19 0.316
10 A 6 5 1.00 19 0.263
11 A 7 6 0.96 19 0.316
12 A 8 7 1.01 19 0.368
13 A 6 5 0.91 21 0.238
14 A 6 5 0.97 21 0.238
15 A 7 6 1.20 21 0.286
16 A 7 6 1.18 21 0.286
17 A 4 3 1.00 17 0.176
18 A 5 4 1.00 15 0.267
19 A 5 4 1.00 13 0.308
20 A 4 3 1.00 11 0.273
21 A 5 4 1.00 15 0.267
22 A 5 4 1.00 15 0.267
23 A 9 8 0.87 11 0.727
24 A 4 3 0.92 21 0.143
25 A 4 3 0.93 21 0.143
26 A 4 3 0.96 19 0.158
27 A 5 4 1.00 21 0.190
28 A 6 5 1.01 21 0.238
29 A 8 7 1.06 21 0.333
30 A 4 3 0.75 21 0.143
31 A 4 3 0.80 21 0.143
32 A 3 2 1.00 17 0.118
33 A 5 4 1.10 21 0.190
34 A 7 6 1.05 21 0.286
35 A 9 8 1.06 21 0.381
36 A 5 4 0.82 21 0.190
37 A 5 4 1.02 21 0.190
38 A 3 2 1.00 21 0.095
39 A 6 5 1.00 21 0.238
40 A 6 5 1.08 21 0.238
41 A 5 4 1.01 21 0.190
42 A 4 3 1.03 17 0.176
43 A 4 3 1.01 21 0.143
44 A 5 4 1.01 21 0.190
45 A 7 6 1.00 21 0.286
46 A 6 5 1.03 19 0.263
47 A 6 5 1.02 21 0.238
48 A 7 6 1.03 21 0.286
49 A 4 3 1.27 23 0.130
50 A 4 3 1.28 23 0.130
51 A 5 4 1.24 23 0.174
52 A 5 4 1.12 23 0.174
53 A 3 2 1.00 19 0.105
54 A 4 3 1.00 22 0.136
55 A 4 3 1.01 21 0.143
56 A 5 4 1.06 24 0.167
57 A 3 2 1.00 11 0.182
58 A 5 4 1.07 21 0.190
59 A 5 4 1.11 21 0.190
60 A 6 5 1.04 21 0.238
61 A 7 6 1.09 21 0.286
62 A 6 5 1.06 19 0.263
63 A 5 4 1.05 21 0.190
64 A 7 6 1.11 21 0.286
65 A 9 8 1.11 21 0.381
66 A 7 6 1.07 17 0.353
67 A 8 7 1.09 21 0.333
68 A 5 4 1.07 21 0.190
69 A 5 4 1.11 21 0.190
70 A 6 5 1.04 21 0.238
71 A 7 6 1.05 21 0.286
72 A 8 7 1.13 21 0.333
73 B 8 7 3.30 21 0.333
74 A 6 5 1.83 17 0.294
75 B 7 6 2.68 21 0.286
76 A 6 5 1.48 23 0.217
77 A 6 5 1.48 23 0.217
78 A 7 6 1.75 23 0.261
79 A 7 6 1.45 23 0.261
80 A 9 8 1.11 19 0.421
81 A 8 7 1.26 17 0.412
82 A 6 5 1.08 21 0.238
83 A 5 4 1.07 21 0.190
84 A 5 4 1.05 21 0.190
85 A 5 4 1.05 21 0.190
86 A 9 8 1.13 19 0.421
87 A 8 7 1.28 17 0.412
88 A 5 4 1.03 21 0.190
89 A 5 4 1.07 21 0.190
90 A 5 4 1.05 21 0.190
91 A 5 4 1.05 21 0.190
92 A 8 7 1.10 13 0.538
93 A 7 6 1.65 23 0.261
94 A 7 6 1.32 23 0.261
95 A 6 5 1.40 23 0.217
96 A 6 5 1.45 23 0.217
97 A 7 6 1.65 23 0.261
98 A 7 6 1.29 23 0.261
99 A 6 5 1.38 23 0.217
100 A 6 5 1.45 23 0.217
101 A 1 1 1.00 13 0.077
102 A 3 2 1.00 15 0.133
103 A 3 2 1.00 15 0.133
104 A 4 3 0.90 19 0.158
105 A 4 3 0.91 19 0.158
106 A 4 3 0.92 17 0.176
107 A 3 2 1.00 15 0.133
108 A 5 4 1.31 19 0.211
109 A 4 3 1.08 19 0.158
110 A 4 3 1.02 19 0.158
111 A 4 3 0.82 19 0.158
112 A 4 3 0.80 19 0.158
113 A 4 3 0.81 17 0.176
114 A 3 2 1.60 15 0.133
115 A 4 3 1.18 19 0.158
116 A 4 3 0.93 19 0.158
117 A 4 3 0.90 19 0.158
118 A 3 2 1.00 15 0.133
119 A 4 3 0.73 13 0.231
120 A 4 3 0.76 19 0.158
121 A 4 3 0.79 19 0.158
122 A 4 3 0.84 17 0.176
123 A 3 2 1.00 15 0.133
124 A 3 2 1.00 19 0.105
125 A 3 2 1.00 19 0.105
126 A 4 3 1.29 17 0.176
127 A 4 3 1.44 17 0.176
128 A 1 1 1.00 15 0.067
129 A 3 2 1.00 17 0.118
130 A 4 3 1.12 17 0.176
131 A 5 4 1.26 17 0.235
132 A 3 2 1.00 13 0.154
133 A 3 2 1.00 13 0.154
134 A 3 2 1.00 13 0.154
135 A 3 2 1.00 13 0.154
136 A 3 2 1.00 15 0.133
137 A 3 2 1.00 15 0.133
138 A 4 3 1.28 17 0.176
139 A 4 3 1.44 17 0.176
140 A 1 1 1.00 15 0.067
141 A 10 9 0.85 17 0.529
142 A 11 10 0.94 17 0.588
143 A 12 11 1.01 17 0.647
144 A 4 3 1.00 19 0.158
145 A 4 3 1.00 17 0.176
146 A 4 3 1.00 15 0.200
147 A 4 3 1.00 13 0.231
148 A 4 3 1.00 17 0.176
149 A 4 3 1.00 17 0.176
150 A 13 12 1.07 26 0.462
151 A 9 8 1.09 24 0.333
152 A 6 5 1.09 22 0.227
153 A 10 9 0.80 26 0.346
154 A 7 6 0.88 26 0.231
155 A 9 8 0.95 26 0.308
156 A 13 12 0.97 26 0.462
157 A 16 15 1.12 26 0.577
158 A 12 11 1.12 24 0.458
159 A 8 7 1.10 22 0.318
160 A 5 4 1.02 26 0.154
161 A 6 5 0.72 26 0.192
162 A 8 7 0.94 26 0.269
163 A 12 11 1.01 26 0.423
164 A 3 2 1.00 15 0.133
165 A 6 5 1.05 16 0.312
166 A 5 4 0.90 26 0.154
167 A 5 4 0.90 26 0.154
168 A 5 4 0.86 25 0.160
169 A 5 4 0.84 25 0.160
170 A 5 4 1.22 25 0.160
171 A 5 4 1.39 23 0.174
172 A 5 4 1.24 25 0.160
173 A 5 4 0.83 25 0.160
174 A 4 3 1.00 25 0.120
175 A 5 4 0.84 25 0.160
176 A 5 4 0.84 25 0.160
177 A 3 2 1.00 13 0.154
178 A 6 5 1.00 17 0.294
179 A 7 6 1.00 21 0.286
180 A 8 7 1.00 25 0.280
181 A 10 9 1.17 20 0.450
182 A 9 8 1.13 20 0.400
183 A 8 7 1.07 18 0.389
184 A 3 3 1.00 20 0.150
185 A 6 5 1.29 20 0.250
186 A 6 5 1.18 20 0.250
187 A 2 2 1.00 18 0.111
188 A 2 2 1.00 20 0.100
189 A 4 3 1.00 22 0.136
190 A 4 3 1.00 17 0.176
191 A 4 3 1.03 22 0.136
192 A 1 1 1.00 34 0.029
193 A 6 5 1.08 31 0.161
194 A 1 1 1.00 47 0.021
195 A 9 8 0.81 58 0.138

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