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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 [173] had the largest ratio of [1.10000000000000009]

# 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 8 7 1.34 21 0.333
2 A 6 5 0.91 21 0.238
3 A 7 6 1.35 21 0.286
4 A 6 5 0.92 19 0.263
5 A 6 5 0.96 19 0.263
6 A 6 5 0.93 21 0.238
7 A 8 7 1.09 21 0.333
8 A 5 4 0.89 21 0.190
9 A 8 7 1.23 23 0.304
10 A 6 5 0.90 23 0.217
11 A 8 7 1.20 23 0.304
12 A 6 5 0.89 21 0.238
13 A 6 5 0.92 21 0.238
14 A 6 5 0.90 23 0.217
15 A 9 8 1.45 23 0.348
16 A 5 4 0.89 23 0.174
17 A 9 8 1.57 23 0.348
18 A 6 5 0.89 23 0.217
19 A 11 10 1.74 23 0.435
20 A 6 5 0.88 21 0.238
21 A 6 5 0.92 21 0.238
22 A 6 5 0.89 23 0.217
23 A 7 6 1.28 23 0.261
24 A 5 4 0.89 23 0.174
25 A 9 8 1.24 23 0.348
26 A 7 6 0.97 23 0.261
27 A 8 7 1.24 23 0.304
28 A 6 5 0.96 21 0.238
29 A 7 6 0.98 21 0.286
30 A 6 5 0.96 23 0.217
31 A 8 7 1.13 23 0.304
32 A 6 5 1.03 23 0.217
33 A 11 10 1.13 23 0.435
34 A 7 6 0.94 23 0.261
35 A 10 9 1.14 23 0.391
36 A 7 6 1.02 21 0.286
37 A 8 7 1.07 21 0.333
38 A 7 6 1.01 23 0.261
39 A 10 9 1.06 23 0.391
40 A 6 5 1.02 23 0.217
41 A 13 12 1.11 23 0.522
42 A 9 8 0.99 23 0.348
43 A 12 11 1.18 23 0.478
44 A 8 7 1.05 21 0.333
45 A 9 8 1.12 21 0.381
46 A 8 7 1.06 23 0.304
47 A 13 12 1.11 23 0.522
48 A 7 6 1.02 23 0.261
49 A 5 5 0.97 21 0.238
50 C 6 5 1.20 21 0.238
51 A 3 3 1.00 21 0.143
52 A 4 4 1.00 19 0.211
53 A 4 4 1.00 19 0.211
54 A 6 5 1.43 21 0.238
55 A 6 6 0.97 21 0.286
56 C 6 5 1.28 21 0.238
57 A 7 6 1.46 23 0.261
58 A 5 4 0.90 23 0.174
59 A 5 4 1.26 23 0.174
60 A 5 4 1.02 21 0.190
61 A 6 5 1.23 21 0.238
62 A 5 4 0.91 23 0.174
63 A 7 6 1.10 23 0.261
64 A 5 4 0.90 23 0.174
65 A 5 4 1.18 23 0.174
66 A 5 4 0.98 23 0.174
67 A 5 4 1.12 23 0.174
68 A 5 4 1.02 21 0.190
69 A 8 7 1.30 21 0.333
70 A 5 4 0.89 23 0.174
71 A 9 8 1.13 23 0.348
72 A 5 4 0.90 23 0.174
73 A 8 7 1.24 23 0.304
74 A 5 4 0.93 23 0.174
75 A 7 6 1.24 23 0.261
76 A 5 4 0.96 21 0.190
77 A 4 3 1.00 21 0.143
78 A 4 3 1.00 23 0.130
79 A 6 5 0.96 23 0.217
80 A 5 4 0.96 23 0.174
81 A 7 6 1.08 23 0.261
82 A 5 4 0.94 23 0.174
83 A 5 4 0.94 23 0.174
84 A 9 8 1.15 23 0.348
85 A 5 4 0.95 21 0.190
86 A 5 4 0.98 21 0.190
87 A 5 4 0.97 23 0.174
88 A 5 4 0.97 23 0.174
89 A 5 4 0.98 23 0.174
90 A 7 6 1.10 23 0.261
91 A 5 4 0.95 23 0.174
92 A 9 8 1.08 23 0.348
93 A 11 10 1.20 23 0.435
94 A 5 4 0.95 21 0.190
95 A 6 5 1.10 21 0.238
96 A 6 5 1.05 23 0.217
97 A 6 5 1.00 23 0.217
98 A 6 5 1.00 23 0.217
99 A 6 5 1.05 23 0.217
100 A 7 6 1.11 23 0.261
101 A 8 7 1.14 23 0.304
102 A 7 6 1.00 21 0.286
103 A 7 6 0.94 21 0.286
104 A 9 8 1.19 21 0.381
105 A 6 5 0.93 19 0.263
106 A 1 1 1.00 12 0.083
107 A 7 6 1.32 19 0.316
108 A 8 7 1.44 21 0.333
109 A 7 6 1.32 21 0.286
110 A 7 6 1.12 21 0.286
111 A 7 6 1.29 21 0.286
112 A 6 5 0.97 23 0.217
113 A 7 6 0.92 23 0.261
114 A 8 7 1.03 23 0.304
115 A 7 6 0.96 21 0.286
116 A 5 4 1.10 14 0.286
117 A 7 6 1.04 21 0.286
118 A 8 7 1.11 23 0.304
119 A 7 6 1.16 23 0.261
120 A 6 5 1.09 23 0.217
121 A 7 6 1.33 23 0.261
122 A 8 7 1.03 23 0.304
123 A 8 7 1.22 23 0.304
124 A 6 5 0.95 23 0.217
125 A 8 7 0.91 23 0.304
126 A 8 7 0.99 23 0.304
127 A 7 6 0.90 21 0.286
128 A 5 4 1.01 14 0.286
129 A 7 6 0.99 21 0.286
130 A 8 7 1.02 23 0.304
131 A 7 6 1.02 23 0.261
132 A 6 5 1.02 23 0.217
133 A 7 6 1.16 23 0.261
134 A 8 7 1.03 23 0.304
135 A 7 6 1.22 23 0.261
136 A 5 4 0.98 14 0.286
137 A 5 4 0.97 14 0.286
138 A 7 6 0.90 23 0.261
139 A 8 7 1.19 23 0.304
140 A 7 6 1.00 23 0.261
141 A 9 8 1.17 23 0.348
142 A 5 4 1.00 21 0.190
143 A 6 5 1.00 14 0.357
144 A 7 6 1.13 21 0.286
145 A 10 9 1.24 23 0.391
146 A 7 6 1.05 23 0.261
147 A 11 10 1.23 23 0.435
148 A 7 6 0.92 23 0.261
149 A 8 7 1.15 23 0.304
150 A 7 6 0.94 23 0.261
151 A 10 9 1.14 23 0.391
152 A 7 6 0.90 21 0.286
153 A 8 7 1.20 14 0.500
154 A 7 6 1.01 21 0.286
155 A 13 12 1.17 23 0.522
156 A 7 6 0.98 23 0.261
157 A 13 12 1.13 23 0.522
158 A 11 10 1.17 23 0.435
159 A 7 6 0.95 23 0.261
160 A 11 10 1.12 23 0.435
161 A 7 6 0.93 23 0.261
162 A 12 11 1.18 23 0.478
163 A 7 6 0.95 21 0.286
164 A 10 9 1.21 14 0.643
165 A 7 6 0.98 21 0.286
166 A 15 14 1.17 23 0.609
167 A 7 6 0.99 23 0.261
168 A 15 14 1.13 23 0.609
169 A 12 11 1.20 14 0.786
170 C 11 11 1.10 12 0.917
171 A 7 7 1.00 12 0.583
172 A 7 7 1.00 12 0.583
173 C 11 11 1.00 10 1.100
174 A 7 7 1.00 10 0.700
175 A 7 7 1.00 10 0.700
176 A 7 6 1.06 17 0.353
177 A 11 10 1.10 17 0.588
178 A 10 9 1.08 17 0.529
179 A 12 11 1.05 17 0.647
180 A 8 7 1.12 15 0.467
181 A 8 7 1.00 12 0.583
182 A 9 8 1.09 15 0.533
183 A 10 9 1.00 17 0.529
184 A 10 9 1.14 17 0.529
185 A 9 8 1.05 17 0.471
186 A 13 12 1.25 17 0.706
187 A 11 10 1.11 17 0.588
188 A 16 15 1.07 17 0.882
189 A 9 8 1.14 15 0.533
190 A 10 9 1.03 12 0.750
191 A 11 10 1.09 15 0.667
192 A 12 11 1.00 17 0.647
193 A 10 9 1.00 16 0.562
194 A 7 6 1.09 17 0.353
195 A 10 9 1.08 17 0.529
196 A 9 8 1.14 17 0.471
197 A 11 10 1.00 17 0.588
198 A 7 6 1.00 15 0.400
199 A 5 4 1.00 12 0.333
200 A 9 8 1.09 15 0.533
201 A 10 9 1.00 17 0.529
202 A 10 9 1.22 17 0.529
203 A 7 6 1.07 17 0.353
204 A 10 9 1.12 17 0.529
205 A 9 8 1.10 17 0.471
206 A 9 8 1.00 17 0.471
207 A 8 7 1.12 15 0.467
208 A 6 5 1.00 12 0.417
209 A 11 10 1.25 15 0.667
210 A 13 12 1.11 17 0.706
211 A 14 13 1.24 17 0.765
212 A 7 6 1.07 17 0.353
213 A 9 8 1.08 17 0.471
214 A 10 9 1.16 17 0.529
215 A 11 10 1.08 17 0.588
216 A 9 8 1.18 15 0.533
217 A 9 8 1.16 12 0.667
218 A 13 12 1.31 15 0.800
219 A 14 13 1.17 17 0.765
220 A 11 10 1.12 16 0.625

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