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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [186] had the largest ratio of [44]

# 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 6 0.167
2 A 2 2 1.00 8 0.250
3 A 2 2 1.00 8 0.250
4 A 2 1 1.00 8 0.125
5 A 3 2 1.00 8 0.250
6 A 2 1 1.00 8 0.125
7 A 2 1 1.00 6 0.167
8 A 2 1 1.00 6 0.167
9 A 3 3 1.00 10 0.300
10 A 3 3 1.00 10 0.300
11 A 2 2 1.00 10 0.200
12 A 2 2 1.00 10 0.200
13 A 3 3 1.00 10 0.300
14 A 3 3 1.00 10 0.300
15 A 4 3 1.00 12 0.250
16 A 3 3 1.00 12 0.250
17 A 3 3 1.00 12 0.250
18 A 2 2 1.00 12 0.167
19 A 2 2 1.00 12 0.167
20 A 3 3 1.00 12 0.250
21 A 3 3 1.00 12 0.250
22 A 4 3 1.00 12 0.250
23 A 2 2 1.00 10 0.200
24 A 5 3 1.00 12 0.250
25 A 4 3 1.00 12 0.250
26 A 3 3 1.00 12 0.250
27 A 2 2 1.00 12 0.167
28 A 2 2 1.00 12 0.167
29 A 3 3 1.00 12 0.250
30 A 4 3 1.00 12 0.250
31 A 5 3 1.00 12 0.250
32 A 5 4 1.00 10 0.400
33 A 4 4 1.00 10 0.400
34 A 3 3 1.00 10 0.300
35 A 2 2 1.00 10 0.200
36 A 3 3 1.00 10 0.300
37 A 4 3 1.00 10 0.300
38 A 5 3 1.00 10 0.300
39 A 7 4 1.00 10 0.400
40 A 5 4 1.00 10 0.400
41 A 4 4 1.00 10 0.400
42 A 4 4 1.00 10 0.400
43 A 5 4 1.00 10 0.400
44 A 7 4 1.00 10 0.400
45 A 3 2 1.00 10 0.200
46 A 3 2 1.00 10 0.200
47 A 3 2 1.00 10 0.200
48 A 3 3 1.00 10 0.300
49 A 3 3 1.00 10 0.300
50 A 5 3 1.00 10 0.300
51 A 7 3 1.00 10 0.300
52 A 7 7 1.00 13 0.538
53 A 6 5 1.00 13 0.385
54 A 5 5 1.00 13 0.385
55 A 5 4 1.00 11 0.364
56 A 6 6 1.00 11 0.546
57 A 6 5 1.00 13 0.385
58 A 7 7 1.00 13 0.538
59 A 7 6 1.00 13 0.462
60 A 6 5 1.00 13 0.385
61 A 5 4 1.00 13 0.308
62 A 5 5 1.00 13 0.385
63 A 5 4 1.00 11 0.364
64 A 4 3 1.00 11 0.273
65 A 5 5 1.00 13 0.385
66 A 6 5 1.00 13 0.385
67 A 6 5 1.00 13 0.385
68 A 7 5 1.00 13 0.385
69 A 6 5 1.00 13 0.385
70 A 5 5 1.00 13 0.385
71 A 4 4 1.00 11 0.364
72 A 1 1 1.00 11 0.091
73 A 3 3 1.00 13 0.231
74 A 4 4 1.00 13 0.308
75 A 6 6 1.00 13 0.462
76 A 2 2 1.00 12 0.167
77 A 2 2 1.00 13 0.154
78 A 5 5 1.00 14 0.357
79 A 4 4 1.00 14 0.286
80 A 2 2 1.00 14 0.143
81 A 5 4 1.00 14 0.286
82 A 6 5 1.00 14 0.357
83 A 2 2 1.00 15 0.133
84 A 5 4 1.00 15 0.267
85 A 2 2 1.00 10 0.200
86 A 2 2 1.00 10 0.200
87 A 6 5 1.00 12 0.417
88 A 5 4 1.00 12 0.333
89 A 4 4 1.00 12 0.333
90 A 2 1 1.00 10 0.100
91 A 3 3 1.00 12 0.250
92 A 5 5 1.00 12 0.417
93 A 6 6 1.00 12 0.500
94 A 1 1 1.00 14 0.071
95 A 8 6 1.00 13 0.462
96 A 7 6 1.00 13 0.462
97 A 6 6 1.00 13 0.462
98 A 5 5 1.00 11 0.454
99 A 3 3 1.00 11 0.273
100 A 5 5 1.00 13 0.385
101 A 6 6 1.00 13 0.462
102 A 7 7 1.00 13 0.538
103 A 5 3 1.00 13 0.231
104 A 3 2 1.00 13 0.154
105 A 4 3 1.00 13 0.231
106 A 3 2 1.00 13 0.154
107 A 3 2 1.00 13 0.154
108 A 2 2 1.00 11 0.182
109 A 3 2 1.00 11 0.182
110 A 4 3 1.00 13 0.231
111 A 3 2 1.00 13 0.154
112 A 5 3 1.00 13 0.231
113 A 3 2 1.00 13 0.154
114 A 15 8 1.00 13 0.615
115 A 3 2 1.00 13 0.154
116 A 6 6 1.00 13 0.462
117 A 3 2 1.00 13 0.154
118 A 7 7 1.00 13 0.538
119 A 4 4 1.00 11 0.364
120 A 3 2 1.00 11 0.182
121 A 9 8 1.00 13 0.615
122 A 3 2 1.00 13 0.154
123 A 15 8 1.00 13 0.615
124 A 3 2 1.00 13 0.154
125 A 5 4 1.00 23 0.174
126 A 5 4 1.00 23 0.174
127 A 4 4 1.00 21 0.190
128 A 7 5 1.00 21 0.238
129 A 13 9 1.00 23 0.391
130 A 7 7 1.00 23 0.304
131 A 1 1 1.00 14 0.071
132 A 5 4 1.00 23 0.174
133 A 5 4 1.00 23 0.174
134 A 5 4 1.00 23 0.174
135 A 3 3 1.00 21 0.143
136 A 7 5 1.00 21 0.238
137 A 11 6 1.00 23 0.261
138 A 11 8 1.00 23 0.348
139 A 6 6 1.00 23 0.261
140 A 1 1 1.00 14 0.071
141 A 9 8 1.00 23 0.348
142 A 5 4 1.00 23 0.174
143 A 5 4 1.00 23 0.174
144 A 4 4 1.00 21 0.190
145 A 7 4 1.00 21 0.190
146 A 11 5 1.00 23 0.217
147 A 17 11 1.00 23 0.478
148 A 7 7 1.00 23 0.304
149 A 6 6 1.00 14 0.429
150 A 14 11 1.00 23 0.478
151 A 6 5 1.00 25 0.200
152 A 6 5 1.00 25 0.200
153 A 4 4 1.00 25 0.160
154 A 4 4 1.00 25 0.160
155 A 5 4 1.00 25 0.160
156 A 6 5 1.00 25 0.200
157 A 6 5 1.00 25 0.200
158 A 6 6 1.00 15 0.400
159 A 3 3 1.00 15 0.200
160 A 8 8 1.00 15 0.533
161 A 6 6 1.00 15 0.400
162 A 5 5 1.00 13 0.385
163 A 6 6 1.00 11 0.546
164 A 3 2 1.00 15 0.133
165 A 5 5 1.00 15 0.333
166 A 6 6 1.00 15 0.400
167 A 3 3 1.00 15 0.200
168 A 5 5 1.00 15 0.333
169 A 8 7 1.00 15 0.467
170 A 7 6 1.00 15 0.400
171 A 3 3 1.00 15 0.200
172 A 9 8 1.00 15 0.533
173 A 7 6 1.00 15 0.400
174 A 6 5 1.00 15 0.333
175 A 7 6 1.00 15 0.400
176 A 8 7 1.00 13 0.538
177 A 7 7 1.00 11 0.636
178 A 4 3 1.00 15 0.200
179 A 3 3 1.00 15 0.200
180 A 5 5 1.00 15 0.333
181 A 6 6 1.00 15 0.400
182 A 4 4 1.00 11 0.364
183 A 4 4 1.00 13 0.308
184 A 4 4 1.00 13 0.308
185 A 4 4 1.00 13 0.308
186 C 9 4 3.48 44 0.091
187 A 3 3 1.00 15 0.200
188 A 4 4 1.00 15 0.267
189 A 3 3 1.00 20 0.150
190 A 3 3 1.00 21 0.143
191 A 2 1 1.00 15 0.067
192 A 3 2 1.00 17 0.118
193 A 3 2 1.00 17 0.118
194 A 3 1 1.00 17 0.059
195 A 4 2 1.00 17 0.118
196 A 4 3 1.00 19 0.158
197 A 4 3 1.00 19 0.158
198 A 3 2 1.00 19 0.105
199 A 3 2 1.00 19 0.105
200 A 4 3 1.00 19 0.158
201 A 4 3 1.00 19 0.158

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