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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 [128] had the largest ratio of [1.50000000000000000]

# 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 16 0.125
2 A 2 2 1.00 16 0.125
3 A 2 2 1.00 14 0.143
4 A 2 2 1.00 16 0.125
5 A 2 2 1.00 16 0.125
6 A 2 2 1.00 16 0.125
7 A 2 2 1.00 16 0.125
8 A 2 2 1.00 16 0.125
9 A 1 1 1.00 12 0.083
10 A 2 2 1.00 16 0.125
11 A 2 2 1.00 16 0.125
12 A 5 4 1.02 18 0.222
13 A 5 4 1.05 18 0.222
14 A 4 3 1.07 16 0.188
15 A 3 3 1.00 18 0.167
16 A 3 3 1.00 18 0.167
17 A 3 3 1.00 18 0.167
18 A 3 3 1.00 18 0.167
19 A 3 3 1.00 18 0.167
20 A 2 2 1.00 14 0.143
21 A 3 3 1.00 18 0.167
22 A 3 3 1.00 18 0.167
23 A 13 12 1.11 14 0.857
24 A 8 7 1.05 14 0.500
25 A 5 4 0.70 12 0.333
26 A 2 2 1.00 14 0.143
27 A 2 2 1.00 14 0.143
28 A 2 2 1.00 14 0.143
29 A 2 2 1.00 10 0.200
30 A 3 3 1.02 14 0.214
31 A 2 2 1.00 10 0.200
32 A 3 3 1.06 14 0.214
33 A 5 4 0.52 12 0.333
34 A 2 2 1.00 12 0.167
35 A 10 9 0.94 18 0.500
36 A 9 8 0.97 18 0.444
37 A 6 5 1.12 16 0.312
38 N/A 1 0 1.00 18 0.000
39 N/A 1 0 1.00 18 0.000
40 N/A 1 0 1.00 18 0.000
41 N/A 1 0 1.00 14 0.000
42 N/A 1 0 1.00 18 0.000
43 A 16 15 0.94 18 0.833
44 A 13 12 1.01 18 0.667
45 A 10 9 1.09 16 0.562
46 N/A 1 0 1.00 18 0.000
47 N/A 1 0 1.00 18 0.000
48 N/A 1 0 1.00 18 0.000
49 N/A 1 0 1.00 14 0.000
50 N/A 1 0 1.00 18 0.000
51 N/A 1 0 1.00 20 0.000
52 A 4 4 1.00 20 0.200
53 A 3 3 1.00 20 0.150
54 A 2 2 1.00 18 0.111
55 N/A 1 0 1.00 20 0.000
56 N/A 1 0 1.00 20 0.000
57 A 2 2 1.00 16 0.125
58 A 2 2 1.00 16 0.125
59 A 2 2 1.00 16 0.125
60 A 2 2 1.00 16 0.125
61 A 2 2 1.00 16 0.125
62 A 2 2 1.00 14 0.143
63 A 2 2 1.00 16 0.125
64 A 2 2 1.00 16 0.125
65 A 2 2 1.00 16 0.125
66 A 1 1 1.00 12 0.083
67 A 2 2 1.00 16 0.125
68 A 2 2 1.00 16 0.125
69 A 5 4 1.00 18 0.222
70 A 4 3 1.03 18 0.167
71 A 3 3 1.00 18 0.167
72 A 3 3 1.00 18 0.167
73 A 3 3 1.00 18 0.167
74 A 3 3 1.00 16 0.188
75 A 3 3 0.99 18 0.167
76 A 3 3 0.99 18 0.167
77 A 3 3 1.00 18 0.167
78 A 2 2 1.00 14 0.143
79 A 3 3 0.99 18 0.167
80 A 3 3 0.99 18 0.167
81 A 9 8 0.98 18 0.444
82 A 6 5 1.12 18 0.278
83 N/A 1 0 1.00 18 0.000
84 N/A 1 0 1.00 18 0.000
85 N/A 1 0 1.00 16 0.000
86 N/A 1 0 1.00 18 0.000
87 N/A 1 0 1.00 14 0.000
88 N/A 1 0 1.00 18 0.000
89 A 13 12 1.01 18 0.667
90 A 10 9 1.05 18 0.500
91 N/A 1 0 1.00 18 0.000
92 N/A 1 0 1.00 18 0.000
93 N/A 1 0 1.00 16 0.000
94 N/A 1 0 1.00 18 0.000
95 N/A 1 0 1.00 14 0.000
96 N/A 1 0 1.00 18 0.000
97 N/A 1 0 1.00 20 0.000
98 A 4 4 1.00 20 0.200
99 A 3 3 1.00 20 0.150
100 A 2 2 1.00 18 0.111
101 N/A 1 0 1.00 20 0.000
102 N/A 1 0 1.00 20 0.000
103 A 14 13 0.97 12 1.083
104 A 12 11 0.92 10 1.100
105 A 9 8 1.06 8 1.000
106 A 3 3 1.00 12 0.250
107 A 4 3 1.00 12 0.250
108 A 6 5 1.00 12 0.417
109 A 9 8 1.09 12 0.667
110 A 11 10 1.16 12 0.833
111 A 2 2 0.97 14 0.143
112 A 12 11 1.02 12 0.917
113 A 10 9 1.00 10 0.900
114 A 2 2 1.00 14 0.143
115 A 5 4 1.00 14 0.286
116 A 5 4 1.00 14 0.286
117 A 8 7 1.06 14 0.500
118 A 8 7 1.05 14 0.500
119 A 6 5 1.10 8 0.625
120 A 3 3 1.00 12 0.250
121 A 5 4 1.00 12 0.333
122 A 4 3 1.00 12 0.250
123 A 6 5 1.03 12 0.417
124 A 4 3 1.00 12 0.250
125 A 5 4 0.86 14 0.286
126 A 6 5 1.00 6 0.833
127 A 8 7 1.10 8 0.875
128 A 13 12 1.13 8 1.500
129 N/A 1 0 1.00 18 0.000
130 N/A 1 0 1.00 20 0.000
131 A 5 4 1.00 20 0.200
132 N/A 2 0 1.00 22 0.000
133 A 7 6 1.00 22 0.273
134 N/A 2 0 1.00 24 0.000
135 A 3 3 1.00 12 0.250
136 A 2 2 1.00 14 0.143
137 A 2 2 1.00 14 0.143
138 A 2 2 1.00 14 0.143
139 A 2 2 1.00 8 0.250
140 A 2 2 1.00 10 0.200
141 A 2 2 1.00 10 0.200
142 A 2 2 1.00 12 0.167
143 A 2 2 1.00 14 0.143
144 A 2 2 1.00 14 0.143
145 A 6 5 0.94 16 0.312
146 A 7 6 0.94 16 0.375
147 A 9 8 0.91 16 0.500
148 A 2 2 0.99 18 0.111
149 A 2 2 0.99 18 0.111
150 A 12 11 0.83 16 0.688
151 A 2 2 0.98 18 0.111
152 A 2 2 0.99 18 0.111
153 A 3 2 0.94 18 0.111
154 A 3 2 0.95 18 0.111
155 A 3 2 0.97 16 0.125
156 A 1 1 1.00 10 0.100
157 N/A 1 0 1.00 18 0.000
158 N/A 1 0 1.00 18 0.000
159 A 3 2 0.92 18 0.111
160 A 3 2 0.93 18 0.111
161 A 3 2 0.93 16 0.125
162 A 4 3 0.98 10 0.300
163 N/A 1 0 1.00 18 0.000
164 N/A 1 0 1.00 18 0.000
165 A 3 2 0.94 20 0.100
166 A 3 2 0.95 20 0.100
167 A 3 2 0.96 18 0.111
168 A 3 3 1.00 12 0.250
169 N/A 1 0 1.00 20 0.000
170 N/A 1 0 1.00 20 0.000
171 A 3 2 0.95 20 0.100
172 A 3 2 0.96 20 0.100
173 A 3 2 0.97 18 0.111
174 A 2 2 1.00 12 0.167
175 N/A 1 0 1.00 20 0.000
176 N/A 1 0 1.00 20 0.000
177 A 3 2 0.93 20 0.100
178 A 3 2 0.93 18 0.111
179 A 6 5 1.05 12 0.417
180 N/A 1 0 1.00 20 0.000
181 N/A 1 0 1.00 20 0.000
182 A 3 2 0.95 20 0.100
183 A 3 2 0.97 18 0.111
184 A 2 2 1.00 12 0.167
185 N/A 1 0 1.00 20 0.000
186 N/A 1 0 1.00 20 0.000
187 A 3 2 1.01 22 0.091
188 A 3 2 1.02 20 0.100
189 A 6 5 0.96 14 0.357
190 A 3 2 1.08 22 0.091
191 A 6 5 1.05 22 0.227
192 A 3 2 0.96 22 0.091
193 A 3 2 0.97 20 0.100
194 A 4 3 0.99 14 0.214
195 N/A 1 0 1.00 22 0.000
196 N/A 1 0 1.00 22 0.000
197 A 3 2 1.03 22 0.091
198 A 3 2 1.06 20 0.100
199 A 12 11 1.00 14 0.786
200 A 3 2 1.07 22 0.091
201 A 6 5 1.06 22 0.227
202 A 3 2 0.95 22 0.091
203 A 3 2 0.97 20 0.100
204 A 4 3 0.99 14 0.214
205 N/A 1 0 1.00 22 0.000
206 N/A 1 0 1.00 22 0.000
207 A 3 2 1.01 22 0.091
208 A 3 2 1.02 20 0.100
209 A 9 8 1.00 14 0.571
210 A 3 2 1.07 22 0.091
211 A 6 5 1.02 22 0.227
212 A 3 2 0.94 22 0.091
213 A 3 2 0.94 20 0.100
214 A 6 5 0.99 14 0.357
215 N/A 1 0 1.00 22 0.000
216 N/A 1 0 1.00 22 0.000
217 A 3 2 1.01 22 0.091
218 A 3 2 1.02 20 0.100
219 A 14 13 0.93 14 0.929
220 A 3 2 1.06 22 0.091
221 A 6 5 1.03 22 0.227
222 A 3 2 0.95 22 0.091
223 A 3 2 0.96 20 0.100
224 A 8 7 1.06 14 0.500
225 N/A 1 0 1.00 22 0.000
226 N/A 1 0 1.00 22 0.000
227 A 20 19 0.81 27 0.704
228 A 15 14 0.83 27 0.519
229 A 12 11 0.84 27 0.407
230 A 7 6 0.85 27 0.222
231 A 5 4 1.00 27 0.148
232 A 10 9 0.73 27 0.333
233 A 13 12 0.69 27 0.444
234 A 18 17 0.69 27 0.630
235 A 10 9 0.83 27 0.333
236 A 9 8 0.80 27 0.296
237 A 8 7 0.83 27 0.259
238 A 6 5 1.00 27 0.185
239 A 7 6 0.83 27 0.222
240 A 8 7 0.85 27 0.259
241 A 11 10 0.71 27 0.370
242 A 18 17 0.73 27 0.630
243 A 13 12 0.70 27 0.444
244 A 10 9 0.73 27 0.333
245 A 5 4 1.00 27 0.148
246 A 7 6 0.82 27 0.222
247 A 12 11 0.81 27 0.407
248 A 15 14 0.80 27 0.519
249 A 12 11 0.79 27 0.407
250 A 11 10 0.78 27 0.370
251 A 14 13 0.71 27 0.481
252 A 11 10 0.71 27 0.370
253 A 9 8 0.85 27 0.296
254 A 7 6 0.80 27 0.222
255 A 6 5 1.00 27 0.185
256 A 8 7 0.81 27 0.259
257 A 10 9 0.78 27 0.333
258 A 11 10 0.81 27 0.370
259 N/A 1 0 1.00 18 0.000
260 A 3 2 0.96 16 0.125
261 A 3 2 0.96 16 0.125
262 A 3 2 0.97 14 0.143
263 A 2 2 1.00 12 0.167
264 N/A 1 0 1.00 16 0.000
265 N/A 1 0 1.00 16 0.000
266 A 2 2 1.00 20 0.100
267 A 2 2 1.00 20 0.100
268 A 2 2 1.00 18 0.111
269 A 1 1 1.00 16 0.062
270 N/A 2 0 1.00 20 0.000
271 N/A 2 0 1.00 20 0.000
272 A 3 2 0.96 22 0.091
273 A 3 2 0.96 20 0.100
274 A 2 2 1.00 18 0.111
275 N/A 1 0 1.00 22 0.000
276 N/A 1 0 1.00 22 0.000
277 N/A 1 0 1.00 22 0.000
278 N/A 1 0 1.00 20 0.000
279 N/A 1 0 1.00 18 0.000
280 N/A 1 0 1.00 22 0.000
281 N/A 1 0 1.00 22 0.000
282 N/A 1 0 1.00 22 0.000
283 N/A 1 0 1.00 20 0.000
284 N/A 1 0 1.00 18 0.000
285 N/A 1 0 1.00 22 0.000
286 N/A 1 0 1.00 22 0.000
287 N/A 1 0 1.00 24 0.000
288 A 3 2 1.00 20 0.100
289 A 3 2 1.00 18 0.111
290 A 1 1 1.00 12 0.083
291 A 3 2 1.03 20 0.100
292 A 5 4 1.00 20 0.200
293 A 3 2 1.00 20 0.100
294 A 3 2 1.00 20 0.100
295 A 5 4 1.00 14 0.286
296 A 3 2 1.03 22 0.091
297 A 5 4 1.01 22 0.182
298 A 3 2 1.01 22 0.091
299 N/A 1 0 1.00 22 0.000
300 N/A 1 0 1.00 20 0.000
301 N/A 1 0 1.00 14 0.000
302 N/A 1 0 1.00 20 0.000
303 N/A 1 0 1.00 22 0.000
304 N/A 1 0 1.00 22 0.000
305 N/A 1 0 1.00 20 0.000
306 N/A 1 0 1.00 14 0.000
307 N/A 1 0 1.00 20 0.000
308 N/A 1 0 1.00 22 0.000
309 N/A 1 0 1.00 22 0.000
310 A 4 4 0.83 18 0.222
311 A 10 10 0.86 18 0.556
312 A 8 8 0.85 18 0.444
313 A 5 5 0.98 16 0.312
314 A 4 4 1.00 14 0.286
315 A 6 6 0.65 18 0.333
316 A 8 8 0.66 18 0.444
317 A 11 11 0.60 18 0.611
318 A 3 3 0.85 20 0.150
319 A 7 6 0.98 20 0.300
320 A 5 5 0.77 20 0.250
321 A 6 5 1.00 18 0.278
322 A 4 4 0.80 16 0.250
323 A 4 4 0.68 20 0.200
324 A 5 5 0.83 20 0.250
325 A 10 9 0.65 20 0.450
326 A 3 3 0.85 20 0.150
327 A 3 3 0.84 20 0.150
328 A 3 3 0.84 20 0.150
329 A 3 3 0.84 18 0.167
330 A 3 3 0.83 16 0.188
331 A 4 4 0.68 20 0.200
332 A 3 3 0.83 20 0.150
333 A 3 3 0.84 20 0.150
334 A 4 4 0.75 18 0.222
335 A 7 7 0.73 18 0.389
336 A 7 7 0.73 18 0.389
337 A 4 4 0.84 16 0.250
338 A 5 5 0.87 14 0.357
339 A 4 4 0.57 18 0.222
340 A 9 9 0.70 18 0.500
341 A 7 7 0.85 18 0.389
342 A 3 3 0.76 20 0.150
343 A 6 5 0.89 20 0.250
344 A 3 3 0.61 20 0.150
345 A 7 6 0.94 18 0.333
346 A 3 3 0.66 16 0.188
347 A 3 3 0.56 20 0.150
348 A 7 7 0.84 20 0.350
349 A 3 3 0.52 20 0.150
350 A 3 3 0.76 20 0.150
351 A 3 3 0.73 20 0.150
352 A 3 3 0.73 20 0.150
353 A 3 3 0.73 18 0.167
354 A 3 3 0.71 16 0.188
355 A 3 3 0.58 20 0.150
356 A 3 3 0.72 20 0.150
357 A 3 3 0.72 20 0.150

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