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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 [85] had the largest ratio of [1.80000000000000004]

# 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 3 3 1.00 8 0.375
3 C 4 3 1.23 8 0.375
4 A 5 5 1.11 8 0.625
5 C 4 3 1.12 8 0.375
6 A 7 7 1.15 8 0.875
7 A 6 6 1.07 10 0.600
8 A 4 4 1.00 10 0.400
9 A 4 4 1.00 10 0.400
10 A 2 2 1.00 10 0.200
11 A 2 2 1.00 10 0.200
12 A 4 4 1.00 10 0.400
13 A 4 4 1.00 10 0.400
14 A 6 6 1.01 10 0.600
15 A 8 8 1.09 8 1.000
16 A 6 6 1.00 8 0.750
17 A 6 6 1.00 8 0.750
18 A 4 4 1.00 8 0.500
19 A 4 4 1.00 8 0.500
20 A 6 6 1.00 8 0.750
21 A 6 6 1.00 8 0.750
22 A 8 8 1.06 8 1.000
23 A 2 2 1.00 10 0.200
24 C 10 9 1.15 13 0.692
25 A 4 4 1.00 13 0.308
26 A 7 7 0.96 13 0.538
27 A 4 4 1.00 11 0.364
28 A 5 5 1.00 11 0.455
29 A 10 9 1.04 13 0.692
30 A 12 11 1.02 13 0.846
31 C 12 11 1.12 13 0.846
32 A 2 2 1.00 10 0.200
33 A 4 4 1.00 10 0.400
34 A 6 6 1.07 10 0.600
35 A 8 8 1.11 10 0.800
36 A 2 2 1.00 12 0.167
37 A 4 4 1.00 12 0.333
38 A 6 6 1.07 12 0.500
39 A 8 8 1.10 12 0.667
40 A 6 5 1.00 13 0.385
41 A 6 5 1.00 14 0.357
42 A 6 6 1.04 14 0.429
43 A 4 4 1.00 14 0.286
44 A 2 2 1.00 14 0.143
45 A 4 3 1.00 14 0.214
46 A 6 5 1.00 14 0.357
47 A 8 7 1.05 14 0.500
48 A 6 6 1.04 15 0.400
49 A 4 4 1.00 15 0.267
50 A 2 2 1.00 15 0.133
51 A 4 3 1.00 15 0.200
52 A 6 5 1.00 15 0.333
53 A 8 7 1.05 15 0.467
54 A 14 13 1.15 13 1.000
55 A 10 9 1.12 13 0.692
56 A 10 9 1.05 13 0.692
57 A 6 5 1.00 11 0.455
58 A 7 6 1.00 11 0.545
59 A 11 10 1.05 13 0.769
60 A 13 12 1.13 13 0.923
61 A 16 15 1.15 13 1.154
62 A 8 8 1.07 12 0.667
63 A 6 6 1.06 12 0.500
64 A 4 4 1.03 12 0.333
65 A 2 2 1.00 12 0.167
66 A 1 1 1.00 10 0.100
67 A 4 3 1.00 12 0.250
68 A 8 7 1.13 12 0.583
69 A 11 10 1.20 12 0.833
70 A 13 12 1.23 12 1.000
71 A 4 3 1.00 12 0.250
72 A 7 6 1.00 12 0.500
73 A 10 9 1.07 12 0.750
74 A 13 12 1.10 12 1.000
75 A 2 2 1.00 12 0.167
76 A 5 5 1.09 12 0.417
77 A 8 8 1.12 12 0.667
78 A 11 11 1.14 12 0.917
79 A 15 15 1.04 10 1.500
80 A 12 12 1.01 10 1.200
81 A 4 4 1.00 14 0.286
82 A 4 4 1.00 10 0.400
83 A 7 7 1.00 10 0.700
84 A 15 15 1.06 10 1.500
85 A 18 18 1.11 10 1.800
86 A 9 9 1.00 13 0.692
87 A 8 8 0.95 17 0.471
88 A 6 6 0.97 17 0.353
89 A 4 4 1.00 17 0.235
90 A 8 8 0.95 18 0.444
91 A 6 6 0.97 18 0.333
92 A 4 4 1.00 18 0.222
93 A 4 4 1.00 13 0.308
94 A 4 4 1.00 13 0.308
95 A 6 6 0.96 13 0.462
96 A 8 8 0.95 13 0.615
97 A 4 4 1.00 15 0.267
98 A 4 4 1.00 15 0.267
99 A 6 6 0.97 15 0.400
100 A 8 8 0.95 15 0.533
101 A 6 5 1.00 17 0.294
102 A 6 5 1.00 17 0.294
103 A 8 7 0.98 17 0.412
104 A 6 5 1.00 18 0.278
105 A 6 5 1.00 18 0.278
106 A 8 7 0.98 18 0.389
107 A 18 18 1.05 17 1.059
108 A 15 15 1.03 17 0.882
109 A 12 12 1.01 17 0.706
110 A 6 5 1.00 15 0.333
111 A 8 7 1.13 15 0.467
112 A 11 10 1.19 15 0.667
113 A 13 12 1.21 15 0.800
114 A 6 5 1.12 20 0.250
115 A 2 2 1.00 20 0.100
116 A 3 3 1.00 15 0.200
117 A 4 4 1.06 13 0.308
118 A 9 9 1.00 17 0.529
119 A 12 12 1.07 17 0.706
120 A 15 15 1.04 17 0.882
121 A 10 10 1.08 10 1.000
122 A 8 8 1.06 10 0.800
123 A 6 6 1.00 10 0.600
124 A 4 4 1.00 10 0.400
125 A 4 4 1.00 10 0.400
126 A 6 6 1.00 10 0.600
127 A 8 8 1.13 10 0.800
128 A 12 12 0.82 10 1.200
129 A 8 8 0.89 10 0.800
130 A 6 6 0.94 10 0.600
131 A 6 6 0.89 10 0.600
132 A 8 8 0.87 10 0.800
133 A 12 12 0.79 10 1.200
134 A 13 13 0.70 10 1.300
135 A 9 9 0.77 10 0.900
136 A 5 5 0.81 10 0.500
137 A 6 5 1.00 10 0.500
138 C 6 5 0.72 10 0.500
139 C 6 5 0.58 10 0.500
140 A 5 4 1.00 9 0.444
141 A 5 4 1.00 11 0.364
142 A 4 4 1.00 11 0.364
143 A 4 4 1.00 13 0.308
144 A 6 5 1.00 11 0.455
145 A 6 5 1.00 13 0.385
146 A 5 4 1.00 9 0.444
147 A 5 4 1.00 11 0.364
148 A 3 3 1.00 11 0.273
149 A 3 3 1.00 13 0.231
150 A 6 5 1.00 11 0.455
151 A 6 5 1.00 13 0.385
152 A 13 13 1.05 13 1.000
153 A 6 5 1.02 13 0.385
154 A 10 10 1.05 13 0.769
155 A 6 5 0.97 13 0.385
156 A 7 7 0.97 13 0.538
157 A 5 4 1.00 13 0.308
158 A 4 4 1.00 13 0.308
159 A 5 4 1.22 11 0.364
160 A 6 5 1.26 11 0.455
161 A 9 8 1.00 13 0.615
162 A 6 5 1.11 13 0.385
163 C 6 5 1.16 13 0.385
164 A 6 5 0.99 13 0.385
165 A 6 5 1.00 13 0.385
166 A 16 15 1.19 13 1.154
167 A 6 5 0.99 13 0.385
168 A 12 11 1.20 13 0.846
169 A 6 5 1.00 13 0.385
170 A 10 9 1.24 13 0.692
171 A 5 4 1.00 11 0.364
172 A 6 5 1.25 11 0.455
173 A 8 7 1.16 13 0.538
174 A 6 5 1.18 13 0.385
175 A 10 9 1.22 13 0.692
176 A 6 5 1.17 13 0.385
177 A 14 13 1.26 13 1.000
178 A 10 9 1.07 13 0.692
179 A 12 11 1.18 13 0.846
180 A 6 5 1.04 13 0.385
181 A 13 12 1.23 13 0.923
182 A 7 6 1.10 11 0.545
183 A 9 8 1.09 11 0.727
184 A 13 12 1.14 13 0.923
185 A 9 8 1.44 13 0.615
186 C 20 19 1.15 13 1.462
187 A 15 14 1.02 13 1.077
188 C 11 10 1.27 13 0.769
189 A 11 10 1.00 13 0.769
190 C 10 9 1.42 13 0.692
191 A 9 8 1.00 13 0.615
192 A 7 6 1.22 11 0.545
193 C 14 13 1.27 11 1.182
194 C 11 10 1.20 13 0.769
195 C 18 17 1.28 13 1.308
196 C 11 10 1.12 13 0.769
197 A 7 6 1.00 13 0.462
198 A 6 5 1.00 13 0.385
199 A 3 3 1.00 15 0.200
200 A 3 3 1.00 13 0.231
201 A 3 3 1.00 15 0.200
202 A 3 3 1.00 15 0.200
203 A 3 3 1.00 15 0.200
204 A 9 8 1.00 15 0.533
205 C 8 8 1.13 15 0.533
206 A 12 11 1.00 31 0.355
207 A 14 13 1.09 31 0.419
208 A 17 16 1.14 31 0.516
209 A 19 18 1.16 31 0.581
210 A 9 8 1.01 12 0.667
211 A 10 9 0.95 14 0.643
212 A 11 10 0.91 14 0.714
213 A 5 4 0.98 36 0.111
214 A 5 4 0.98 36 0.111
215 A 4 3 1.00 34 0.088
216 N/A 4 0 1.00 34 0.000
217 N/A 4 0 1.00 36 0.000
218 A 5 4 1.00 12 0.333
219 A 9 8 1.18 12 0.667
220 A 2 2 1.00 20 0.100
221 N/A 1 0 1.00 22 0.000
222 A 7 6 1.03 22 0.273
223 A 6 5 1.02 22 0.227
224 A 5 4 1.00 20 0.200
225 A 5 4 1.00 19 0.211
226 N/A 1 0 1.00 22 0.000
227 N/A 1 0 1.00 24 0.000
228 C 23 22 0.94 24 0.917
229 C 18 17 0.96 24 0.708
230 A 15 14 0.99 22 0.636
231 A 10 9 1.19 21 0.429
232 N/A 1 0 1.00 24 0.000
233 N/A 1 0 1.00 24 0.000
234 C 29 28 0.92 24 1.167
235 C 21 20 0.90 24 0.833
236 C 16 15 0.92 22 0.682
237 A 6 5 0.90 21 0.238
238 N/A 1 0 1.00 24 0.000
239 A 1 1 1.00 11 0.091
240 A 2 2 1.00 13 0.154
241 A 2 2 0.96 13 0.154
242 A 3 3 0.93 13 0.231
243 A 1 1 1.01 15 0.067
244 A 2 2 1.02 17 0.118
245 A 2 2 0.93 17 0.118
246 A 3 3 0.89 17 0.176
247 A 4 3 1.00 15 0.200
248 A 5 4 1.13 17 0.235
249 C 5 4 1.07 17 0.235
250 A 7 6 1.10 17 0.353
251 C 5 4 0.98 17 0.235
252 A 6 5 0.97 19 0.263
253 A 6 5 0.97 19 0.263
254 A 4 3 1.00 19 0.158
255 A 4 3 1.00 19 0.158
256 A 6 5 0.97 19 0.263
257 A 6 5 0.97 19 0.263
258 A 9 8 0.99 18 0.444
259 A 8 7 0.89 18 0.389
260 A 7 6 1.07 18 0.333
261 A 4 3 1.00 18 0.167
262 A 5 4 1.62 18 0.222
263 C 13 12 1.15 14 0.857
264 C 13 12 1.14 16 0.750
265 A 5 4 0.86 16 0.250
266 A 6 5 0.82 16 0.312
267 A 5 4 0.88 16 0.250
268 A 5 4 1.30 14 0.286
269 A 4 3 1.00 14 0.214
270 A 5 4 1.08 16 0.250
271 A 4 3 1.00 16 0.188
272 A 7 6 1.12 16 0.375
273 A 6 5 1.00 16 0.312
274 A 5 4 1.08 10 0.400
275 A 5 4 1.11 8 0.500
276 A 11 10 1.60 8 1.250
277 A 12 11 1.45 10 1.100
278 A 5 4 1.08 10 0.400
279 A 5 4 1.21 8 0.500
280 A 11 10 0.64 8 1.250
281 A 12 11 1.42 10 1.100
282 A 5 4 1.08 10 0.400
283 A 5 4 1.21 8 0.500
284 A 11 10 1.35 8 1.250
285 A 11 10 1.33 10 1.000
286 A 2 2 0.94 18 0.111
287 A 2 2 1.00 18 0.111
288 A 1 1 1.00 16 0.062
289 A 1 1 1.00 16 0.062
290 A 1 1 1.00 18 0.056
291 A 2 2 1.12 18 0.111
292 A 2 2 1.11 18 0.111
293 A 7 6 0.41 25 0.240
294 A 7 6 0.46 25 0.240
295 A 6 5 0.80 25 0.200
296 A 5 4 1.00 25 0.160
297 A 5 4 1.00 25 0.160
298 A 7 6 0.62 25 0.240
299 A 7 6 0.55 25 0.240
300 A 1 1 1.00 10 0.100
301 A 2 2 1.00 12 0.167
302 A 2 2 1.00 15 0.133
303 A 2 2 1.00 12 0.167
304 A 2 2 1.00 14 0.143
305 A 2 2 1.00 17 0.118
306 A 2 2 1.00 16 0.125
307 A 2 2 1.00 18 0.111
308 A 2 2 1.00 18 0.111
309 A 2 2 1.00 19 0.105
310 A 2 2 1.00 21 0.095
311 A 2 2 1.00 21 0.095
312 A 2 2 1.00 16 0.125
313 A 2 2 1.00 18 0.111
314 A 2 2 1.00 18 0.111
315 A 2 2 1.00 18 0.111
316 A 2 2 1.00 20 0.100
317 A 2 2 1.00 20 0.100
318 A 2 2 1.00 21 0.095
319 A 2 2 1.00 23 0.087
320 A 2 2 1.00 23 0.087
321 A 2 2 1.00 19 0.105
322 A 2 2 1.00 21 0.095
323 A 2 2 1.00 21 0.095
324 A 2 2 1.00 21 0.095
325 A 2 2 1.00 23 0.087
326 A 2 2 1.00 23 0.087
327 A 2 2 1.00 24 0.083
328 A 2 2 1.00 26 0.077
329 A 2 2 1.00 26 0.077
330 A 1 1 1.00 17 0.059
331 A 1 1 1.00 20 0.050
332 A 1 1 1.00 20 0.050
333 A 1 1 1.00 21 0.048
334 A 2 2 1.00 6 0.333
335 A 2 2 1.00 6 0.333
336 A 2 2 1.00 16 0.125
337 A 2 2 1.00 19 0.105

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