[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 [135] had the largest ratio of [.562500000000000000]

# 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 11 10 1.27 25 0.400
2 A 11 10 1.03 25 0.400
3 A 7 7 1.14 25 0.280
4 A 6 6 1.57 25 0.240
5 A 7 7 1.21 25 0.280
6 A 7 7 1.05 25 0.280
7 A 5 5 1.16 23 0.217
8 A 6 6 0.95 22 0.273
9 A 12 11 1.13 25 0.440
10 A 13 12 1.02 25 0.480
11 A 15 14 1.07 25 0.560
12 A 2 2 1.00 26 0.077
13 A 2 2 1.00 26 0.077
14 A 2 2 1.00 24 0.083
15 A 2 2 1.00 23 0.087
16 A 2 2 1.00 26 0.077
17 A 2 2 1.00 26 0.077
18 A 2 2 1.00 26 0.077
19 A 2 2 1.00 26 0.077
20 A 2 2 1.00 28 0.071
21 A 2 2 1.00 28 0.071
22 A 3 3 1.00 26 0.115
23 A 3 3 1.00 25 0.120
24 A 3 3 1.00 28 0.107
25 A 3 3 1.00 28 0.107
26 A 2 2 1.00 28 0.071
27 A 2 2 1.00 28 0.071
28 A 2 2 1.00 28 0.071
29 A 2 2 1.00 28 0.071
30 A 3 3 1.00 26 0.115
31 A 3 3 1.00 25 0.120
32 A 3 3 1.00 28 0.107
33 A 3 3 1.00 28 0.107
34 A 2 2 1.00 28 0.071
35 A 2 2 1.00 28 0.071
36 A 2 2 1.00 28 0.071
37 A 2 2 1.00 28 0.071
38 A 2 2 1.00 26 0.077
39 A 2 2 1.00 25 0.080
40 A 2 2 1.00 28 0.071
41 A 2 2 1.00 28 0.071
42 A 2 2 1.00 28 0.071
43 A 2 2 1.00 28 0.071
44 A 2 2 1.00 28 0.071
45 A 4 4 1.15 28 0.143
46 A 4 4 1.19 28 0.143
47 A 4 4 1.14 28 0.143
48 A 4 4 1.18 26 0.154
49 A 6 6 1.06 25 0.240
50 A 5 5 1.09 28 0.179
51 A 4 4 1.04 28 0.143
52 A 4 4 1.04 28 0.143
53 A 6 6 1.18 28 0.214
54 A 7 7 1.23 28 0.250
55 A 8 8 1.10 28 0.286
56 A 6 6 1.21 26 0.231
57 A 5 5 1.09 25 0.200
58 A 7 7 1.11 28 0.250
59 A 6 6 1.09 28 0.214
60 A 6 6 1.11 28 0.214
61 A 14 13 1.07 30 0.433
62 A 12 11 1.07 30 0.367
63 A 10 9 1.04 28 0.321
64 A 8 7 1.04 27 0.259
65 A 11 10 1.04 30 0.333
66 A 12 11 1.04 30 0.367
67 A 14 13 0.98 30 0.433
68 A 13 12 1.01 30 0.400
69 A 13 12 1.05 30 0.400
70 A 10 9 1.00 30 0.300
71 A 12 11 1.02 30 0.367
72 A 14 13 1.05 30 0.433
73 A 16 15 1.06 30 0.500
74 A 16 15 1.02 30 0.500
75 A 12 11 1.01 30 0.367
76 A 10 9 0.98 28 0.321
77 A 9 8 0.98 27 0.296
78 A 13 12 1.03 30 0.400
79 A 13 12 1.07 30 0.400
80 A 15 14 1.05 30 0.467
81 A 15 14 1.00 30 0.467
82 A 16 15 1.02 30 0.500
83 A 15 14 1.02 30 0.467
84 A 15 14 1.04 30 0.467
85 A 11 10 0.97 30 0.333
86 A 13 12 0.98 30 0.400
87 A 15 14 1.01 30 0.467
88 A 17 16 1.03 30 0.533
89 A 14 13 1.15 30 0.433
90 A 13 12 1.15 30 0.400
91 A 11 10 1.16 30 0.333
92 A 8 7 1.14 28 0.250
93 A 7 6 1.13 27 0.222
94 A 10 9 1.04 30 0.300
95 A 11 10 1.10 30 0.333
96 A 11 10 1.04 30 0.333
97 A 9 8 1.05 30 0.267
98 A 11 10 1.08 30 0.333
99 A 13 12 1.09 30 0.400
100 A 11 10 1.28 30 0.333
101 A 10 9 1.28 30 0.300
102 A 7 6 1.27 28 0.214
103 A 7 6 1.06 27 0.222
104 A 10 9 1.11 30 0.300
105 A 7 6 1.05 30 0.200
106 A 9 8 1.10 30 0.267
107 A 11 10 1.10 30 0.333
108 A 13 12 1.07 30 0.400
109 A 12 11 1.24 30 0.367
110 A 9 8 1.29 30 0.267
111 A 9 8 1.16 30 0.267
112 A 7 6 1.20 28 0.214
113 A 4 4 1.00 27 0.148
114 A 9 8 1.06 30 0.267
115 A 9 8 0.96 30 0.267
116 A 11 10 1.14 30 0.333
117 A 2 2 1.00 30 0.067
118 A 2 2 1.00 30 0.067
119 A 2 2 1.00 30 0.067
120 A 2 2 1.00 30 0.067
121 A 2 2 1.00 30 0.067
122 A 2 2 1.30 32 0.062
123 A 2 2 1.32 32 0.062
124 A 2 2 1.34 32 0.062
125 A 2 2 1.37 32 0.062
126 A 2 2 1.46 32 0.062
127 A 2 2 1.55 32 0.062
128 A 2 2 1.51 32 0.062
129 A 4 4 1.24 32 0.125
130 A 4 4 1.27 32 0.125
131 A 4 4 1.31 32 0.125
132 A 13 12 1.11 32 0.375
133 A 15 14 1.18 32 0.438
134 A 17 16 1.16 32 0.500
135 A 19 18 1.17 32 0.562
136 A 2 2 1.00 30 0.067
137 A 2 2 1.00 28 0.071
138 A 2 2 1.00 21 0.095
139 A 2 2 1.00 30 0.067
140 A 5 5 0.93 30 0.167
141 A 5 5 0.91 30 0.167
142 A 7 7 1.06 32 0.219
143 A 7 7 1.10 32 0.219
144 A 7 7 1.06 32 0.219
145 A 5 5 0.95 32 0.156
146 A 6 6 0.92 32 0.188
147 A 6 6 0.92 32 0.188
148 A 2 2 1.00 28 0.071
149 A 2 2 1.00 28 0.071
150 A 2 2 1.00 25 0.080
151 A 2 2 1.00 28 0.071
152 A 2 2 1.00 28 0.071
153 A 2 2 1.00 28 0.071
154 A 2 2 1.00 30 0.067
155 A 2 2 1.00 30 0.067
156 A 2 2 1.00 27 0.074
157 A 2 2 1.00 30 0.067
158 A 2 2 1.00 30 0.067
159 A 2 2 1.00 30 0.067
160 A 2 2 1.00 30 0.067
161 A 2 2 1.00 30 0.067
162 A 2 2 1.00 30 0.067
163 A 2 2 1.00 27 0.074
164 A 2 2 1.00 30 0.067
165 A 2 2 1.00 30 0.067
166 A 2 2 1.00 30 0.067
167 A 2 2 1.00 30 0.067
168 A 2 2 1.00 30 0.067
169 A 2 2 1.00 30 0.067
170 A 4 4 1.09 30 0.133
171 A 5 5 1.11 30 0.167
172 A 5 5 1.15 30 0.167
173 A 4 4 1.02 27 0.148
174 A 4 4 1.03 30 0.133
175 A 4 4 1.01 30 0.133
176 A 4 4 1.03 30 0.133
177 A 4 4 1.03 30 0.133
178 A 4 4 1.03 30 0.133
179 A 5 5 1.09 30 0.167
180 A 6 6 1.11 30 0.200
181 A 5 5 1.12 30 0.167
182 A 7 7 1.04 30 0.233
183 A 7 7 1.09 27 0.259
184 A 6 6 1.09 30 0.200
185 A 5 5 1.08 30 0.167
186 A 6 6 1.07 30 0.200
187 A 6 6 1.06 30 0.200
188 A 6 6 1.05 30 0.200
189 A 9 8 0.88 32 0.250
190 A 8 7 0.98 29 0.241
191 A 10 9 0.98 32 0.281
192 A 11 10 0.96 32 0.312
193 A 9 8 1.05 32 0.250
194 A 8 7 1.16 32 0.219
195 A 6 6 1.11 32 0.188
196 A 7 7 0.98 32 0.219
197 A 7 7 0.89 32 0.219
198 A 10 9 0.81 32 0.281
199 A 9 8 0.87 29 0.276
200 A 10 9 0.86 32 0.281
201 A 11 10 0.85 32 0.312
202 A 12 11 0.87 32 0.344
203 A 10 9 1.01 32 0.281
204 A 9 8 1.12 32 0.250
205 A 5 5 1.11 32 0.156
206 A 6 6 0.98 32 0.188
207 A 8 8 0.89 32 0.250
208 A 4 3 1.02 32 0.094
209 A 4 3 1.02 32 0.094
210 A 4 3 1.04 30 0.100
211 A 4 3 1.05 32 0.094
212 A 8 7 1.01 32 0.219
213 A 9 8 1.27 32 0.250
214 A 10 9 1.24 32 0.281
215 A 10 9 1.11 32 0.281
216 A 8 7 0.90 32 0.219
217 A 7 6 0.98 32 0.188
218 A 7 6 1.11 29 0.207
219 A 9 8 1.13 32 0.250
220 A 8 7 1.09 32 0.219
221 A 7 6 1.15 32 0.188
222 A 5 5 1.11 32 0.156
223 A 7 7 0.98 32 0.219
224 A 4 3 1.02 32 0.094
225 A 4 3 1.04 32 0.094
226 A 4 3 1.04 30 0.100
227 A 4 3 1.22 32 0.094
228 A 8 7 1.00 32 0.219
229 A 9 8 1.13 32 0.250
230 A 12 11 1.16 32 0.344
231 A 14 13 1.17 32 0.406
232 A 9 8 0.95 32 0.250
233 A 8 7 1.05 32 0.219
234 A 8 7 1.09 29 0.241
235 A 9 8 1.04 32 0.250
236 A 8 7 1.12 32 0.219
237 A 5 5 1.13 32 0.156
238 A 6 6 0.98 32 0.188
239 A 7 7 0.89 32 0.219
240 A 13 12 0.85 32 0.375
241 A 13 12 0.93 32 0.375
242 A 12 11 1.01 32 0.344
243 A 8 8 0.96 29 0.276
244 A 6 6 0.86 32 0.188
245 A 7 7 0.88 32 0.219
246 A 9 9 0.84 32 0.281
247 A 10 10 0.79 32 0.312
248 A 11 11 0.74 32 0.344
249 A 5 4 1.02 33 0.121
250 A 5 4 1.02 33 0.121
251 A 5 4 1.04 31 0.129
252 A 2 2 1.00 32 0.062
253 A 2 2 1.00 32 0.062
254 A 2 2 1.00 30 0.067
255 A 2 2 1.00 23 0.087
256 A 2 2 1.00 32 0.062
257 A 4 4 1.05 32 0.125
258 A 4 4 0.90 32 0.125
259 A 5 5 1.02 34 0.147
260 A 5 5 1.02 34 0.147
261 A 5 5 1.02 34 0.147
262 A 6 6 0.97 34 0.176
263 A 7 7 1.05 34 0.206
264 A 7 7 1.14 34 0.206
265 A 5 5 1.01 32 0.156
266 A 16 15 1.00 37 0.405
267 A 11 10 1.07 34 0.294
268 A 8 8 0.97 37 0.216
269 A 9 9 0.90 37 0.243
270 A 9 9 0.88 37 0.243

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