[prev] [prev-tail] [tail] [up]

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 [218] had the largest ratio of [.789474000000000009]

# 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 23 0.087
2 A 2 2 0.96 20 0.100
3 A 2 2 0.96 20 0.100
4 A 2 2 0.97 18 0.111
5 A 2 2 0.99 17 0.118
6 A 2 2 1.00 20 0.100
7 A 2 2 0.93 20 0.100
8 A 2 2 0.96 20 0.100
9 A 2 2 0.95 20 0.100
10 A 2 2 0.90 22 0.091
11 A 2 2 0.90 22 0.091
12 A 2 2 0.92 20 0.100
13 A 2 2 0.87 19 0.105
14 A 3 3 0.96 22 0.136
15 A 2 2 0.98 22 0.091
16 A 2 2 0.95 22 0.091
17 A 2 2 0.93 22 0.091
18 A 2 2 0.94 22 0.091
19 A 2 2 0.93 20 0.100
20 A 2 2 0.93 19 0.105
21 A 4 4 0.95 22 0.182
22 A 2 2 0.98 22 0.091
23 A 2 2 0.95 22 0.091
24 A 2 2 0.97 26 0.077
25 A 2 2 0.99 24 0.083
26 A 2 2 1.00 26 0.077
27 A 2 2 0.96 26 0.077
28 A 2 2 0.97 26 0.077
29 A 2 2 0.97 23 0.087
30 A 2 2 0.98 26 0.077
31 A 2 2 0.98 26 0.077
32 A 2 2 0.92 28 0.071
33 A 2 2 0.94 26 0.077
34 A 3 3 0.97 28 0.107
35 A 2 2 0.99 28 0.071
36 A 2 2 1.02 28 0.071
37 A 3 3 1.04 25 0.120
38 A 2 2 1.02 28 0.071
39 A 2 2 1.00 28 0.071
40 A 2 2 0.95 28 0.071
41 A 2 2 0.96 26 0.077
42 A 4 4 1.00 28 0.143
43 A 2 2 0.98 28 0.071
44 A 3 3 1.04 25 0.120
45 A 2 2 1.02 28 0.071
46 A 2 2 0.96 28 0.071
47 A 2 2 0.96 26 0.077
48 A 2 2 0.98 25 0.080
49 A 2 2 1.00 28 0.071
50 A 2 2 0.96 28 0.071
51 A 2 2 0.97 28 0.071
52 A 2 2 0.96 28 0.071
53 A 2 2 0.92 30 0.067
54 A 2 2 0.92 28 0.071
55 A 2 2 0.93 27 0.074
56 A 3 3 0.99 30 0.100
57 A 2 2 1.06 30 0.067
58 A 2 2 1.02 30 0.067
59 A 2 2 0.94 28 0.071
60 A 2 2 0.94 27 0.074
61 A 4 4 0.98 30 0.133
62 A 2 2 1.05 30 0.067
63 A 2 2 1.02 30 0.067
64 A 5 5 1.02 28 0.179
65 A 4 4 1.02 28 0.143
66 A 3 3 1.01 28 0.107
67 A 2 2 1.00 26 0.077
68 N/A 1 0 1.00 28 0.000
69 N/A 1 0 1.00 28 0.000
70 A 2 2 0.96 24 0.083
71 A 2 2 0.96 24 0.083
72 A 2 2 0.97 22 0.091
73 A 2 2 0.95 21 0.095
74 A 4 4 1.12 24 0.167
75 A 2 2 0.96 24 0.083
76 A 2 2 0.96 24 0.083
77 A 2 2 0.96 24 0.083
78 A 2 2 1.00 26 0.077
79 A 2 2 1.00 24 0.083
80 A 3 3 1.03 23 0.130
81 A 5 5 1.07 26 0.192
82 A 2 2 0.96 26 0.077
83 A 2 2 0.93 26 0.077
84 A 2 2 0.96 26 0.077
85 A 2 2 1.00 24 0.083
86 A 3 3 1.01 23 0.130
87 A 6 6 1.04 26 0.231
88 A 2 2 0.96 26 0.077
89 A 2 2 0.94 26 0.077
90 A 2 2 0.97 26 0.077
91 A 2 2 0.98 24 0.083
92 A 4 4 1.12 26 0.154
93 A 2 2 0.96 26 0.077
94 A 2 2 0.96 26 0.077
95 A 2 2 0.97 26 0.077
96 A 2 2 0.97 23 0.087
97 A 2 2 0.98 26 0.077
98 A 2 2 0.98 26 0.077
99 A 2 2 0.97 26 0.077
100 A 2 2 1.03 26 0.077
101 A 5 5 1.10 28 0.179
102 A 2 2 0.97 28 0.071
103 A 2 2 0.94 28 0.071
104 A 2 2 1.00 28 0.071
105 A 3 3 1.01 25 0.120
106 A 2 2 1.00 28 0.071
107 A 2 2 0.98 28 0.071
108 A 2 2 1.01 26 0.077
109 A 6 6 1.07 28 0.214
110 A 2 2 0.96 28 0.071
111 A 2 2 0.99 28 0.071
112 A 3 3 1.01 25 0.120
113 A 2 2 1.00 28 0.071
114 A 2 2 0.98 28 0.071
115 A 2 2 0.96 28 0.071
116 A 2 2 0.97 26 0.077
117 A 2 2 0.97 25 0.080
118 A 4 4 1.11 28 0.143
119 A 2 2 0.96 28 0.071
120 A 2 2 0.96 28 0.071
121 A 2 2 0.96 28 0.071
122 A 2 2 1.02 28 0.071
123 A 2 2 1.05 26 0.077
124 A 2 2 1.12 25 0.080
125 A 5 5 1.10 28 0.179
126 A 2 2 1.22 28 0.071
127 A 2 2 1.14 28 0.071
128 A 2 2 1.03 26 0.077
129 A 2 2 1.06 25 0.080
130 A 6 6 1.07 28 0.214
131 A 2 2 1.16 28 0.071
132 A 2 2 1.11 28 0.071
133 A 2 2 0.96 30 0.067
134 A 2 2 0.97 30 0.067
135 A 2 2 0.96 30 0.067
136 A 2 2 0.96 30 0.067
137 A 2 2 0.96 30 0.067
138 N/A 1 0 1.00 28 0.000
139 A 6 6 1.10 28 0.214
140 A 5 5 1.13 28 0.179
141 A 4 4 1.17 26 0.154
142 N/A 1 0 1.00 28 0.000
143 N/A 1 0 1.00 28 0.000
144 N/A 1 0 1.00 26 0.000
145 N/A 1 0 1.00 24 0.000
146 N/A 1 0 1.00 23 0.000
147 A 4 4 1.17 26 0.154
148 N/A 1 0 1.00 26 0.000
149 N/A 1 0 1.00 26 0.000
150 A 2 2 0.98 32 0.062
151 A 2 2 0.98 32 0.062
152 A 2 2 0.96 30 0.067
153 A 2 2 0.98 32 0.062
154 A 2 2 0.98 32 0.062
155 A 2 2 0.98 32 0.062
156 A 3 3 1.04 24 0.125
157 A 3 3 1.04 22 0.136
158 A 2 2 0.97 21 0.095
159 A 5 4 1.00 24 0.167
160 A 3 3 1.00 24 0.125
161 A 3 3 1.04 24 0.125
162 A 3 3 1.04 24 0.125
163 A 4 4 0.95 26 0.154
164 A 4 4 0.94 24 0.167
165 A 2 2 0.96 23 0.087
166 A 5 4 1.00 26 0.154
167 A 4 4 0.96 26 0.154
168 A 4 4 0.95 26 0.154
169 A 4 4 0.95 26 0.154
170 A 7 6 1.06 26 0.231
171 A 7 6 1.06 24 0.250
172 A 7 6 1.07 23 0.261
173 A 6 5 1.04 26 0.192
174 A 7 6 1.06 26 0.231
175 A 7 6 1.06 26 0.231
176 A 2 2 1.52 23 0.087
177 A 2 2 1.03 18 0.111
178 A 9 8 0.84 28 0.286
179 A 8 7 0.82 26 0.269
180 A 8 7 0.82 24 0.292
181 A 8 7 0.83 23 0.304
182 A 5 4 1.00 26 0.154
183 A 9 8 0.83 26 0.308
184 A 9 8 0.82 26 0.308
185 A 9 8 0.82 26 0.308
186 A 2 2 0.98 18 0.111
187 A 2 2 0.99 18 0.111
188 A 2 2 0.98 18 0.111
189 A 2 2 0.98 18 0.111
190 A 2 2 0.99 18 0.111
191 A 2 2 0.99 18 0.111
192 A 2 2 0.98 18 0.111
193 A 2 2 0.98 18 0.111
194 A 3 3 0.98 20 0.150
195 A 3 3 0.98 20 0.150
196 A 3 3 0.98 20 0.150
197 A 3 3 0.98 20 0.150
198 N/A 1 0 1.00 23 0.000
199 A 4 4 1.02 23 0.174
200 A 3 3 1.01 23 0.130
201 A 2 2 1.00 21 0.095
202 N/A 1 0 1.00 23 0.000
203 N/A 2 0 1.00 23 0.000
204 N/A 3 0 1.00 23 0.000
205 A 2 2 1.00 11 0.182
206 A 3 3 1.06 13 0.231
207 A 1 1 1.00 57 0.018
208 A 7 7 1.29 19 0.368
209 A 7 7 1.30 17 0.412
210 A 7 6 1.22 16 0.375
211 A 2 2 1.00 19 0.105
212 A 8 8 1.17 19 0.421
213 A 7 7 1.21 19 0.368
214 A 13 13 1.59 19 0.684
215 A 13 13 1.59 17 0.765
216 A 12 11 1.44 16 0.688
217 A 2 2 1.00 19 0.105
218 A 15 15 1.36 19 0.789
219 A 13 13 1.47 19 0.684
220 N/A 2 0 1.00 26 0.000
221 N/A 6 0 1.00 23 0.000
222 N/A 12 0 1.00 23 0.000
223 A 3 2 1.00 14 0.143
224 A 3 2 1.00 12 0.167
225 A 3 2 1.00 10 0.200
226 A 3 2 1.00 14 0.143
227 A 3 2 1.00 14 0.143
228 A 3 2 1.00 14 0.143
229 A 3 2 1.00 14 0.143
230 A 4 3 1.02 16 0.188
231 A 4 3 0.98 14 0.214
232 A 4 3 0.95 12 0.250
233 A 4 3 1.00 16 0.188
234 A 4 3 0.98 16 0.188
235 A 4 3 0.96 16 0.188
236 A 4 3 1.02 16 0.188
237 A 5 4 1.01 22 0.182
238 A 4 3 1.01 22 0.136
239 A 3 2 1.00 20 0.100
240 A 4 3 1.00 22 0.136
241 A 5 4 1.00 22 0.182
242 A 4 3 1.00 22 0.136
243 A 4 3 1.00 20 0.150
244 A 4 3 1.00 18 0.167
245 A 4 3 1.00 16 0.188
246 A 4 3 1.00 20 0.150
247 A 4 3 1.00 20 0.150
248 A 4 3 1.00 20 0.150
249 A 6 5 0.91 24 0.208

[prev] [prev-tail] [front] [up]