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 [324] had the largest ratio of [1]

# 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 4 4 0.84 22 0.182
2 A 3 3 0.92 22 0.136
3 A 2 2 1.00 22 0.091
4 A 2 2 1.00 22 0.091
5 A 3 3 1.16 22 0.136
6 A 4 4 0.98 22 0.182
7 A 5 5 0.94 22 0.227
8 A 2 2 1.96 19 0.105
9 A 3 3 1.00 20 0.150
10 A 3 3 1.00 20 0.150
11 B 2 2 2.12 21 0.095
12 A 7 7 1.40 25 0.280
13 A 6 6 1.60 25 0.240
14 A 5 5 1.82 25 0.200
15 A 1 1 1.96 25 0.040
16 B 6 6 2.14 25 0.240
17 A 8 8 1.92 25 0.320
18 A 10 10 1.73 25 0.400
19 A 9 9 0.94 27 0.333
20 A 7 7 0.88 27 0.259
21 A 5 5 0.77 27 0.185
22 A 2 2 1.00 27 0.074
23 A 7 7 0.86 27 0.259
24 A 9 9 0.94 27 0.333
25 A 11 11 0.98 27 0.407
26 A 1 1 1.08 16 0.062
27 A 1 1 1.05 16 0.062
28 A 1 1 1.28 16 0.062
29 A 1 1 1.03 16 0.062
30 A 1 1 1.08 16 0.062
31 A 1 1 1.00 16 0.062
32 A 1 1 1.00 16 0.062
33 A 1 1 1.00 16 0.062
34 A 1 1 1.00 14 0.071
35 A 1 1 1.00 11 0.091
36 A 1 1 1.00 16 0.062
37 A 1 1 1.00 16 0.062
38 A 1 1 1.00 16 0.062
39 A 1 1 1.00 16 0.062
40 A 1 1 1.84 16 0.062
41 A 1 1 0.87 16 0.062
42 A 1 1 1.64 16 0.062
43 A 1 1 0.90 16 0.062
44 A 1 1 0.92 16 0.062
45 A 1 1 1.09 16 0.062
46 A 1 1 1.05 16 0.062
47 A 1 1 1.28 16 0.062
48 A 1 1 1.03 16 0.062
49 A 1 1 0.93 16 0.062
50 A 1 1 1.00 16 0.062
51 A 1 1 1.00 16 0.062
52 A 1 1 1.00 16 0.062
53 A 1 1 1.00 14 0.071
54 A 1 1 1.00 11 0.091
55 A 1 1 1.00 16 0.062
56 A 1 1 1.00 16 0.062
57 A 1 1 1.00 16 0.062
58 A 1 1 1.00 16 0.062
59 A 1 1 1.84 16 0.062
60 A 1 1 0.94 16 0.062
61 A 1 1 1.64 16 0.062
62 A 1 1 0.84 16 0.062
63 A 1 1 0.92 16 0.062
64 A 1 1 0.70 19 0.053
65 A 3 3 1.00 16 0.188
66 A 3 3 1.00 16 0.188
67 A 3 3 1.00 16 0.188
68 A 1 1 1.00 16 0.062
69 A 1 1 1.00 16 0.062
70 A 1 1 1.00 16 0.062
71 A 1 1 1.00 14 0.071
72 A 1 1 1.00 11 0.091
73 A 1 1 1.00 16 0.062
74 A 1 1 1.00 16 0.062
75 A 1 1 1.00 16 0.062
76 A 1 1 1.00 16 0.062
77 A 3 3 1.32 16 0.188
78 A 3 3 1.48 16 0.188
79 A 3 3 1.55 16 0.188
80 A 3 3 1.00 16 0.188
81 A 3 3 1.00 16 0.188
82 A 3 3 1.00 16 0.188
83 A 1 1 1.00 16 0.062
84 A 1 1 1.00 16 0.062
85 A 1 1 1.00 16 0.062
86 A 1 1 1.00 14 0.071
87 A 1 1 1.00 11 0.091
88 A 1 1 1.00 16 0.062
89 A 1 1 1.00 16 0.062
90 A 1 1 1.00 16 0.062
91 A 1 1 1.00 16 0.062
92 A 3 3 1.53 16 0.188
93 A 3 3 1.42 16 0.188
94 A 3 3 1.55 16 0.188
95 A 2 2 1.00 16 0.125
96 A 3 3 1.00 16 0.188
97 A 3 3 1.09 16 0.188
98 A 2 2 1.00 16 0.125
99 A 3 3 1.00 16 0.188
100 A 3 3 1.00 14 0.214
101 A 1 1 1.00 11 0.091
102 A 3 3 1.00 16 0.188
103 A 3 3 1.00 16 0.188
104 A 2 2 1.00 16 0.125
105 A 3 3 1.09 16 0.188
106 A 3 3 1.00 16 0.188
107 A 2 2 1.00 16 0.125
108 A 3 3 1.10 16 0.188
109 A 3 3 1.00 16 0.188
110 A 3 3 1.00 16 0.188
111 A 2 2 1.00 16 0.125
112 A 3 3 1.00 16 0.188
113 A 3 3 1.00 14 0.214
114 A 1 1 1.00 11 0.091
115 A 3 3 1.00 16 0.188
116 A 3 3 1.00 16 0.188
117 A 2 2 1.00 16 0.125
118 A 3 3 1.00 16 0.188
119 A 3 3 1.00 16 0.188
120 A 3 3 1.11 16 0.188
121 A 2 2 1.00 16 0.125
122 A 3 3 1.00 16 0.188
123 A 1 1 1.24 16 0.062
124 A 1 1 1.41 16 0.062
125 A 1 1 1.49 16 0.062
126 A 1 1 1.44 16 0.062
127 A 1 1 1.17 14 0.071
128 B 1 1 2.88 11 0.091
129 A 1 1 1.30 16 0.062
130 A 1 1 1.51 16 0.062
131 A 1 1 1.56 16 0.062
132 A 1 1 1.51 16 0.062
133 A 1 1 1.29 16 0.062
134 A 1 1 1.48 16 0.062
135 A 1 1 1.57 16 0.062
136 A 1 1 1.24 16 0.062
137 A 1 1 1.41 16 0.062
138 A 1 1 1.49 16 0.062
139 A 1 1 1.46 16 0.062
140 A 1 1 1.31 14 0.071
141 B 1 1 2.80 11 0.091
142 A 1 1 1.16 16 0.062
143 A 1 1 1.53 16 0.062
144 A 1 1 1.56 16 0.062
145 A 1 1 1.50 16 0.062
146 A 1 1 1.29 16 0.062
147 A 1 1 1.65 16 0.062
148 A 1 1 1.56 16 0.062
149 A 1 1 1.00 16 0.062
150 A 1 1 1.00 16 0.062
151 A 1 1 1.08 16 0.062
152 A 1 1 1.23 16 0.062
153 A 1 1 1.08 14 0.071
154 A 2 2 1.00 16 0.125
155 A 2 2 1.00 16 0.125
156 A 3 3 1.00 16 0.188
157 A 2 2 1.00 16 0.125
158 A 2 2 1.00 16 0.125
159 A 2 2 1.00 16 0.125
160 A 3 3 1.00 16 0.188
161 A 2 2 1.00 16 0.125
162 A 2 2 1.00 16 0.125
163 A 1 1 1.00 16 0.062
164 A 1 1 1.00 17 0.059
165 A 1 1 1.00 19 0.053
166 A 1 1 1.00 20 0.050
167 A 1 1 1.00 17 0.059
168 A 1 1 1.00 18 0.056
169 A 2 2 1.30 17 0.118
170 A 2 2 1.46 18 0.111
171 A 2 2 1.46 18 0.111
172 A 2 2 1.30 19 0.105
173 A 7 7 1.09 16 0.438
174 A 7 7 1.18 16 0.438
175 A 6 6 1.13 16 0.375
176 A 7 7 1.17 16 0.438
177 A 7 7 1.09 14 0.500
178 A 2 2 1.00 11 0.182
179 A 7 7 1.01 16 0.438
180 A 7 7 1.15 16 0.438
181 A 6 6 1.12 16 0.375
182 A 7 7 1.17 16 0.438
183 A 7 7 1.01 16 0.438
184 A 6 6 1.09 16 0.375
185 A 7 7 1.19 16 0.438
186 A 7 7 1.09 16 0.438
187 A 7 7 1.12 16 0.438
188 A 6 6 1.09 16 0.375
189 A 7 7 1.17 16 0.438
190 A 7 7 1.00 14 0.500
191 A 2 2 1.00 11 0.182
192 A 7 7 1.08 16 0.438
193 A 7 7 1.16 16 0.438
194 A 6 6 1.07 16 0.375
195 A 7 7 1.11 16 0.438
196 A 7 7 1.01 16 0.438
197 A 7 7 1.19 16 0.438
198 A 6 6 1.09 16 0.375
199 A 7 7 1.02 16 0.438
200 A 6 6 1.09 16 0.375
201 A 7 7 1.07 33 0.212
202 A 5 5 1.60 16 0.312
203 A 6 6 1.57 16 0.375
204 A 6 6 1.52 16 0.375
205 A 6 6 1.50 16 0.375
206 A 5 5 1.61 16 0.312
207 A 6 6 1.52 16 0.375
208 A 6 6 1.50 14 0.429
209 B 2 2 2.20 11 0.182
210 A 6 6 1.61 16 0.375
211 A 6 6 1.59 16 0.375
212 A 6 6 1.66 16 0.375
213 A 6 6 1.59 16 0.375
214 A 6 6 1.64 16 0.375
215 A 6 6 1.63 16 0.375
216 A 6 6 1.67 16 0.375
217 A 5 5 1.56 16 0.312
218 A 6 6 1.66 16 0.375
219 A 6 6 1.52 16 0.375
220 A 6 6 1.58 16 0.375
221 A 5 5 1.55 16 0.312
222 A 6 6 1.58 16 0.375
223 A 6 6 1.63 14 0.429
224 B 2 2 2.20 11 0.182
225 A 6 6 1.50 16 0.375
226 A 6 6 1.64 16 0.375
227 A 6 6 1.62 16 0.375
228 A 6 6 1.66 16 0.375
229 A 6 6 1.64 16 0.375
230 A 6 6 1.71 16 0.375
231 A 6 6 1.63 16 0.375
232 A 5 5 1.22 16 0.312
233 A 5 5 1.44 16 0.312
234 A 6 6 1.01 16 0.375
235 A 6 6 1.03 16 0.375
236 A 6 6 1.01 16 0.375
237 A 6 6 1.00 14 0.429
238 A 2 2 1.00 11 0.182
239 A 6 6 1.01 16 0.375
240 A 6 6 1.01 16 0.375
241 A 6 6 1.04 16 0.375
242 A 6 6 1.01 16 0.375
243 B 6 6 2.05 16 0.375
244 A 6 6 1.17 16 0.375
245 A 5 5 1.27 16 0.312
246 A 5 5 1.25 16 0.312
247 A 5 5 1.50 16 0.312
248 A 5 5 1.19 16 0.312
249 A 5 5 1.28 16 0.312
250 A 6 6 1.07 16 0.375
251 A 6 6 1.02 16 0.375
252 A 6 6 1.05 16 0.375
253 A 6 6 1.02 14 0.429
254 A 2 2 1.00 11 0.182
255 A 6 6 1.03 16 0.375
256 A 6 6 1.05 16 0.375
257 A 6 6 1.03 16 0.375
258 A 6 6 1.07 16 0.375
259 B 6 6 2.07 16 0.375
260 A 6 6 1.17 16 0.375
261 A 6 6 1.78 16 0.375
262 A 4 4 0.88 19 0.211
263 A 7 7 1.07 16 0.438
264 A 7 7 1.02 16 0.438
265 A 7 7 1.05 16 0.438
266 A 6 6 1.07 16 0.375
267 A 6 6 1.03 16 0.375
268 A 6 6 1.05 16 0.375
269 A 6 6 1.03 14 0.429
270 A 2 2 1.00 11 0.182
271 A 6 6 1.02 16 0.375
272 A 6 6 1.05 16 0.375
273 A 6 6 1.02 16 0.375
274 A 6 6 1.07 16 0.375
275 A 8 8 1.67 16 0.500
276 A 8 8 1.52 16 0.500
277 A 8 8 1.77 16 0.500
278 A 7 7 1.07 16 0.438
279 A 7 7 1.03 16 0.438
280 A 7 7 1.16 16 0.438
281 A 6 6 1.01 16 0.375
282 A 6 6 1.04 16 0.375
283 A 6 6 1.01 16 0.375
284 A 6 6 1.01 14 0.429
285 A 2 2 1.00 11 0.182
286 A 6 6 1.00 16 0.375
287 A 6 6 1.01 16 0.375
288 A 6 6 1.03 16 0.375
289 A 6 6 1.01 16 0.375
290 A 8 8 1.83 16 0.500
291 A 8 8 1.53 16 0.500
292 A 8 8 1.77 16 0.500
293 A 5 5 1.06 16 0.312
294 A 8 8 1.83 16 0.500
295 A 5 5 1.41 21 0.238
296 A 9 9 1.75 19 0.474
297 A 6 6 1.03 16 0.375
298 A 5 5 1.02 16 0.312
299 A 5 5 1.44 16 0.312
300 A 5 5 1.41 16 0.312
301 A 4 4 1.20 14 0.286
302 A 6 6 1.09 16 0.375
303 A 6 6 1.09 16 0.375
304 A 7 7 1.09 16 0.438
305 A 6 6 1.09 16 0.375
306 A 6 6 1.13 16 0.375
307 A 6 6 1.13 16 0.375
308 A 7 7 1.08 16 0.438
309 A 6 6 1.09 16 0.375
310 A 6 6 1.09 16 0.375
311 A 6 6 0.99 16 0.375
312 A 6 6 0.99 17 0.353
313 A 6 6 0.98 19 0.316
314 A 6 6 0.98 20 0.300
315 A 5 5 1.02 17 0.294
316 A 5 5 1.02 18 0.278
317 A 7 7 0.93 17 0.412
318 A 8 8 1.63 18 0.444
319 A 8 8 1.63 18 0.444
320 A 7 7 0.92 19 0.368
321 A 2 2 1.00 14 0.143
322 A 2 2 1.00 14 0.143
323 A 1 1 1.00 12 0.083
324 A 1 1 1.00 1 1.000
325 A 2 2 1.00 14 0.143
326 A 4 4 0.94 14 0.286
327 A 6 6 1.02 14 0.429
328 A 8 7 1.42 16 0.438
329 A 3 3 1.00 16 0.188
330 A 8 7 1.42 16 0.438
331 A 2 2 1.00 12 0.167
332 A 2 2 1.00 12 0.167
333 A 7 6 1.25 12 0.500
334 A 7 6 1.47 12 0.500
335 A 2 2 1.33 64 0.031
336 A 11 11 1.10 16 0.688
337 A 9 9 1.08 16 0.562
338 A 7 7 1.10 16 0.438
339 A 3 3 1.00 16 0.188
340 A 7 7 1.02 16 0.438
341 A 9 9 1.07 16 0.562
342 A 11 11 1.10 16 0.688
343 A 8 8 1.02 17 0.471
344 A 4 4 1.00 17 0.235