[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 [55] had the largest ratio of [1.39999999999999991]

# 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 6 0.333
2 A 4 3 1.00 8 0.375
3 A 4 4 1.00 8 0.500
4 A 4 3 1.00 8 0.375
5 A 6 6 1.09 8 0.750
6 A 4 3 0.93 8 0.375
7 A 8 8 1.13 8 1.000
8 A 4 3 0.91 8 0.375
9 A 8 8 1.01 10 0.800
10 A 6 6 1.00 10 0.600
11 A 6 6 1.00 10 0.600
12 A 4 4 1.00 10 0.400
13 A 4 4 1.00 10 0.400
14 A 6 6 1.00 10 0.600
15 A 6 6 1.00 10 0.600
16 A 8 8 1.06 10 0.800
17 A 8 8 1.02 12 0.667
18 A 6 6 1.00 12 0.500
19 A 6 6 1.00 12 0.500
20 A 4 4 1.00 12 0.333
21 A 4 4 1.00 12 0.333
22 A 6 6 1.00 12 0.500
23 A 6 6 1.00 12 0.500
24 A 8 8 1.08 12 0.667
25 A 4 4 1.00 10 0.400
26 A 4 4 1.00 10 0.400
27 A 4 4 1.00 10 0.400
28 A 4 4 1.00 10 0.400
29 A 4 4 1.00 10 0.400
30 A 4 4 1.00 10 0.400
31 A 4 4 1.00 12 0.333
32 A 4 4 1.00 12 0.333
33 A 4 4 1.00 12 0.333
34 A 4 4 1.00 12 0.333
35 A 4 4 1.00 12 0.333
36 A 4 4 1.00 12 0.333
37 A 4 4 1.00 8 0.500
38 A 4 4 1.00 10 0.400
39 A 7 6 1.32 8 0.750
40 A 6 5 1.25 8 0.625
41 A 5 4 1.09 8 0.500
42 A 4 3 1.00 8 0.375
43 A 4 3 1.18 8 0.375
44 A 5 4 1.14 8 0.500
45 A 6 5 1.26 8 0.625
46 A 7 6 1.32 8 0.750
47 A 8 7 1.18 10 0.700
48 A 7 6 1.15 10 0.600
49 A 6 5 1.11 10 0.500
50 A 5 4 1.08 10 0.400
51 A 4 3 1.15 10 0.300
52 A 5 4 1.25 10 0.400
53 A 6 5 1.35 10 0.500
54 A 7 6 1.39 10 0.600
55 A 14 14 0.88 10 1.400
56 A 10 10 1.09 10 1.000
57 A 8 8 1.17 10 0.800
58 A 8 8 1.20 10 0.800
59 A 10 10 1.00 10 1.000
60 A 14 14 0.91 10 1.400
61 A 6 5 0.42 10 0.500
62 A 6 5 0.48 10 0.500
63 A 6 5 0.62 10 0.500
64 A 6 5 1.00 10 0.500
65 A 5 5 0.81 10 0.500
66 A 9 9 0.72 10 0.900
67 A 13 13 0.70 10 1.300
68 A 6 6 1.00 12 0.500
69 A 6 6 1.00 14 0.429
70 A 9 9 1.11 21 0.429
71 A 9 9 1.09 21 0.429
72 A 7 7 1.07 21 0.333
73 A 7 7 1.11 19 0.368
74 A 4 4 1.00 12 0.333
75 A 5 5 1.00 19 0.263
76 A 7 7 1.13 21 0.333
77 A 7 7 1.09 21 0.333
78 A 9 9 1.18 21 0.429
79 A 9 9 1.14 21 0.429
80 A 9 9 1.14 21 0.429
81 A 9 9 1.06 21 0.429
82 A 7 7 1.10 19 0.368
83 A 6 6 1.00 12 0.500
84 A 5 5 1.00 19 0.263
85 A 5 5 1.00 21 0.238
86 A 7 7 1.09 21 0.333
87 A 7 7 1.06 21 0.333
88 A 9 9 1.14 21 0.429
89 A 9 9 1.12 21 0.429
90 A 9 9 1.10 21 0.429
91 A 9 9 1.07 19 0.474
92 A 6 6 1.00 12 0.500
93 A 7 7 1.00 19 0.368
94 A 5 5 1.00 21 0.238
95 A 5 5 1.00 21 0.238
96 A 7 7 1.06 21 0.333
97 A 7 7 1.06 21 0.333
98 A 9 9 1.12 21 0.429
99 A 9 9 1.12 21 0.429
100 A 8 8 1.02 12 0.667
101 A 9 9 1.08 21 0.429
102 A 9 9 1.07 21 0.429
103 A 7 7 1.03 21 0.333
104 A 7 7 1.08 21 0.333
105 A 5 5 1.00 19 0.263
106 A 4 4 1.00 12 0.333
107 A 7 7 1.07 19 0.368
108 A 7 7 1.13 21 0.333
109 A 9 9 1.15 21 0.429
110 A 9 9 1.18 21 0.429
111 A 9 9 1.08 21 0.429
112 A 9 9 1.04 21 0.429
113 A 7 7 1.03 21 0.333
114 A 7 7 1.03 21 0.333
115 A 5 5 1.00 21 0.238
116 A 5 5 1.00 19 0.263
117 A 6 6 1.00 12 0.500
118 A 7 7 1.07 19 0.368
119 A 9 9 1.14 21 0.429
120 A 9 9 1.15 21 0.429
121 A 9 9 1.08 21 0.429
122 A 9 9 1.04 21 0.429
123 A 7 7 1.03 21 0.333
124 A 7 7 1.03 21 0.333
125 A 5 5 1.00 21 0.238
126 A 5 5 1.00 21 0.238
127 A 7 7 1.06 19 0.368
128 A 6 6 1.00 12 0.500
129 A 9 9 1.13 19 0.474
130 A 9 9 1.14 21 0.429
131 A 8 8 1.08 12 0.667
132 A 7 7 0.78 23 0.304
133 A 5 4 0.69 23 0.174
134 A 5 5 0.79 23 0.217
135 A 5 4 1.00 23 0.174
136 A 3 3 1.00 23 0.130
137 A 2 2 1.00 23 0.087
138 A 3 3 1.00 23 0.130
139 A 4 4 0.76 23 0.174
140 A 5 4 0.69 23 0.174
141 A 6 6 0.76 23 0.261
142 A 7 7 0.76 23 0.304
143 A 5 4 0.68 23 0.174
144 A 5 5 0.78 23 0.217
145 A 5 4 1.00 23 0.174
146 A 3 3 1.00 23 0.130
147 A 2 2 1.00 23 0.087
148 A 3 3 1.00 23 0.130
149 A 4 4 0.75 23 0.174
150 A 5 4 0.68 23 0.174
151 A 6 6 0.74 23 0.261
152 A 5 4 0.54 23 0.174
153 A 5 4 0.67 23 0.174
154 A 5 5 0.77 23 0.217
155 A 5 4 1.00 23 0.174
156 A 3 3 1.00 23 0.130
157 A 2 2 1.00 23 0.087
158 A 3 3 1.00 23 0.130
159 A 4 4 0.74 23 0.174
160 A 5 4 0.67 23 0.174
161 A 5 5 0.79 23 0.217
162 A 5 4 1.00 23 0.174
163 A 3 3 1.00 23 0.130
164 A 2 2 1.00 23 0.087
165 A 3 3 1.00 23 0.130
166 A 4 4 0.76 23 0.174
167 A 5 4 0.69 23 0.174
168 A 5 5 0.77 23 0.217
169 A 5 4 1.00 23 0.174
170 A 3 3 1.00 23 0.130
171 A 2 2 1.00 23 0.087
172 A 3 3 1.00 23 0.130
173 A 4 4 0.74 23 0.174
174 A 5 4 0.67 23 0.174
175 A 6 6 0.72 23 0.261
176 A 5 5 0.77 23 0.217
177 A 5 4 1.00 23 0.174
178 A 3 3 1.00 23 0.130
179 A 2 2 1.00 23 0.087
180 A 3 3 1.00 23 0.130
181 A 4 4 0.74 23 0.174
182 A 5 4 0.67 23 0.174
183 A 6 6 0.72 23 0.261
184 A 5 5 1.00 21 0.238
185 A 5 5 1.00 19 0.263
186 A 4 4 1.00 12 0.333
187 A 5 5 1.00 19 0.263
188 A 5 5 1.00 21 0.238
189 A 5 5 1.00 21 0.238
190 A 5 5 1.00 19 0.263
191 A 4 4 1.00 12 0.333
192 A 5 5 1.00 19 0.263
193 A 5 5 1.00 21 0.238
194 A 5 5 1.00 21 0.238
195 A 5 5 1.00 19 0.263
196 A 4 4 1.00 12 0.333
197 A 5 5 1.00 19 0.263
198 A 5 5 1.00 21 0.238
199 A 5 5 1.00 21 0.238
200 A 5 5 1.00 19 0.263
201 A 4 4 1.00 12 0.333
202 A 5 5 1.00 19 0.263
203 A 5 5 1.00 21 0.238
204 A 5 5 1.00 21 0.238
205 A 5 5 1.00 21 0.238
206 A 5 5 1.00 21 0.238
207 A 5 5 1.00 21 0.238
208 A 5 5 1.00 21 0.238
209 A 5 5 1.00 21 0.238
210 A 5 5 1.00 19 0.263
211 A 5 5 1.00 19 0.263
212 A 5 5 1.00 17 0.294
213 A 4 4 1.00 10 0.400
214 A 5 5 1.00 17 0.294
215 A 5 5 1.00 19 0.263
216 A 5 5 1.00 19 0.263
217 A 5 5 1.00 21 0.238
218 A 5 5 1.00 21 0.238
219 A 5 5 1.00 21 0.238
220 A 5 5 1.00 21 0.238
221 A 5 5 1.00 21 0.238
222 A 5 5 1.00 21 0.238
223 A 4 3 1.00 19 0.158
224 A 4 3 1.00 19 0.158
225 A 4 3 1.00 19 0.158
226 A 4 3 1.00 19 0.158
227 A 4 3 1.00 19 0.158
228 A 7 6 0.98 21 0.286
229 A 7 6 0.98 21 0.286
230 A 10 10 1.05 25 0.400
231 A 4 4 1.00 25 0.160
232 A 8 8 1.00 25 0.320
233 A 2 2 1.00 25 0.080
234 A 6 6 1.00 25 0.240
235 A 14 13 0.63 25 0.520
236 A 8 8 1.00 25 0.320
237 A 16 15 0.66 25 0.600
238 A 6 6 1.06 25 0.240
239 A 12 12 1.01 25 0.480
240 A 4 4 1.00 25 0.160
241 A 10 10 1.01 25 0.400
242 A 2 2 1.00 25 0.080
243 A 8 8 1.00 25 0.320
244 A 16 15 0.65 25 0.600
245 A 8 8 1.00 25 0.320
246 A 12 12 1.04 25 0.480
247 A 6 6 1.04 25 0.240
248 A 10 10 1.01 25 0.400
249 A 4 4 1.00 25 0.160
250 A 8 8 1.00 25 0.320
251 A 2 2 1.00 25 0.080
252 A 8 8 1.00 25 0.320
253 A 16 15 0.65 25 0.600
254 A 4 4 1.00 25 0.160
255 A 10 10 1.02 25 0.400
256 A 2 2 1.00 25 0.080
257 A 8 8 1.00 25 0.320
258 A 14 13 0.63 25 0.520
259 A 6 6 1.00 25 0.240
260 A 16 15 0.66 25 0.600
261 A 8 8 1.00 25 0.320
262 A 6 6 1.05 25 0.240
263 A 10 10 1.03 25 0.400
264 A 2 2 1.00 25 0.080
265 A 8 8 1.00 25 0.320
266 A 16 15 0.65 25 0.600
267 A 8 8 1.00 25 0.320
268 A 16 15 0.66 25 0.600
269 A 10 10 1.00 25 0.400
270 A 18 17 0.69 25 0.680
271 A 2 2 1.00 25 0.080
272 A 10 10 1.00 25 0.400
273 A 16 15 0.65 25 0.600
274 A 8 8 1.00 25 0.320
275 A 16 15 0.66 25 0.600
276 A 8 8 1.00 25 0.320
277 A 18 17 0.69 25 0.680
278 A 10 10 1.02 25 0.400
279 A 20 19 0.73 25 0.760
280 A 4 4 1.00 17 0.235
281 A 4 4 1.00 19 0.211
282 A 4 4 1.00 19 0.211
283 A 4 4 1.00 21 0.190
284 A 6 5 1.00 19 0.263
285 A 5 4 1.00 19 0.211
286 A 6 5 1.00 17 0.294
287 A 4 3 1.00 17 0.176
288 A 7 6 0.96 19 0.316
289 A 6 5 0.97 19 0.263
290 A 4 4 1.00 19 0.211
291 A 4 4 1.00 19 0.211
292 A 4 4 1.00 19 0.211
293 A 4 4 1.00 10 0.400
294 A 4 4 1.00 19 0.211
295 A 4 4 1.00 19 0.211
296 A 4 4 1.00 23 0.174
297 A 4 4 1.00 23 0.174
298 A 4 4 1.00 23 0.174
299 A 4 4 1.00 23 0.174

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