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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 [75] had the largest ratio of [1.33299999999999996]

# 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 3 1.00 8 0.375
2 A 4 3 1.00 8 0.375
3 A 4 3 1.00 8 0.375
4 A 4 3 1.00 8 0.375
5 A 3 3 1.00 6 0.500
6 A 2 2 1.00 4 0.500
7 A 1 1 1.00 8 0.125
8 A 5 5 1.00 8 0.625
9 A 3 3 1.00 8 0.375
10 A 4 3 1.00 8 0.375
11 A 4 3 1.00 8 0.375
12 A 15 7 1.00 10 0.700
13 A 14 9 1.00 10 0.900
14 A 10 7 1.00 10 0.700
15 A 9 8 1.00 10 0.800
16 A 5 5 1.00 8 0.625
17 A 5 5 1.00 6 0.833
18 A 6 5 1.00 10 0.500
19 A 4 4 1.00 10 0.400
20 A 8 7 1.00 10 0.700
21 A 8 7 1.00 10 0.700
22 A 13 8 1.00 10 0.800
23 A 33 11 1.00 10 1.100
24 A 22 11 1.00 10 1.100
25 A 18 10 1.00 10 1.000
26 A 11 9 1.00 10 0.900
27 A 8 8 1.00 8 1.000
28 A 5 6 1.00 6 1.000
29 A 8 6 1.00 10 0.600
30 A 5 6 1.00 10 0.600
31 A 7 6 1.00 10 0.600
32 A 14 11 1.00 10 1.100
33 A 16 8 1.00 10 0.800
34 A 1 1 1.00 14 0.071
35 A 4 4 1.00 14 0.286
36 A 4 4 1.00 14 0.286
37 A 5 5 1.00 14 0.357
38 A 5 4 1.00 12 0.333
39 A 27 13 1.00 14 0.929
40 A 25 13 1.00 14 0.929
41 A 23 11 1.00 14 0.786
42 N/A 0 0 1.00 16 0.000
43 N/A 0 0 1.00 16 0.000
44 A 5 6 1.00 16 0.375
45 A 7 9 1.00 16 0.562
46 A 8 9 1.00 16 0.562
47 A 8 9 1.00 16 0.562
48 A 3 3 1.00 15 0.200
49 A 2 2 1.00 15 0.133
50 A 1 1 1.00 15 0.067
51 A 2 2 1.00 15 0.133
52 A 3 2 1.00 15 0.133
53 A 1 1 1.00 14 0.071
54 A 1 1 1.00 14 0.071
55 A 4 4 1.00 14 0.286
56 A 4 4 1.00 13 0.308
57 A 1 1 1.00 12 0.083
58 A 3 3 1.00 13 0.231
59 A 2 2 1.00 12 0.167
60 A 4 3 1.00 13 0.231
61 A 3 3 1.00 12 0.250
62 A 7 5 1.00 10 0.500
63 A 7 5 1.00 10 0.500
64 A 7 5 1.00 8 0.625
65 A 3 3 1.00 6 0.500
66 A 5 5 1.00 10 0.500
67 A 7 5 1.00 10 0.500
68 A 5 4 1.00 10 0.400
69 A 19 15 1.00 12 1.250
70 A 15 13 1.00 12 1.083
71 A 12 10 1.00 10 1.000
72 A 6 6 1.00 8 0.750
73 A 2 2 1.00 12 0.167
74 A 17 15 1.00 12 1.250
75 A 21 16 1.00 12 1.333
76 A 15 5 1.00 16 0.312
77 A 5 5 1.00 14 0.357
78 A 37 10 1.23 16 0.625
79 A 57 11 1.00 16 0.688
80 A 55 16 1.00 18 0.889
81 A 65 19 1.00 18 1.056
82 A 12 8 1.00 19 0.421
83 A 6 4 1.00 10 0.400
84 A 5 4 1.00 8 0.500
85 A 4 4 1.00 6 0.667
86 A 2 2 1.00 10 0.200
87 A 4 4 1.00 10 0.400
88 A 5 4 1.00 10 0.400
89 A 3 2 1.00 12 0.167
90 A 3 2 1.00 12 0.167
91 A 2 2 1.00 12 0.167
92 A 4 4 1.00 12 0.333
93 A 2 2 1.00 10 0.200
94 A 3 3 1.00 4 0.750
95 A 2 2 1.00 10 0.200
96 A 4 4 1.00 12 0.333
97 A 5 4 1.00 14 0.286
98 A 2 2 1.00 14 0.143
99 A 6 6 1.00 14 0.429
100 A 3 3 1.00 12 0.250
101 A 3 3 1.00 19 0.158
102 A 7 5 1.00 18 0.278
103 A 7 5 1.00 18 0.278
104 A 7 5 1.00 16 0.312
105 A 4 3 1.00 10 0.300
106 A 5 5 1.00 18 0.278
107 A 7 5 1.00 18 0.278
108 A 5 4 1.00 18 0.222
109 A 16 13 1.00 20 0.650
110 A 13 10 1.00 18 0.556
111 A 6 6 1.00 12 0.500
112 A 2 2 1.00 20 0.100
113 A 21 19 1.01 20 0.950
114 A 21 14 1.00 20 0.700
115 A 15 11 1.00 18 0.611
116 A 6 7 1.00 12 0.583
117 A 2 2 1.00 20 0.100
118 A 30 18 1.00 20 0.900
119 A 6 4 1.00 18 0.222
120 N/A 0 0 1.00 20 0.000
121 N/A 0 0 1.00 20 0.000
122 N/A 0 0 1.00 40 0.000
123 A 9 7 1.00 40 0.175
124 A 7 6 1.00 40 0.150
125 A 2 3 1.00 38 0.079
126 N/A 0 0 1.00 40 0.000
127 N/A 0 0 1.00 40 0.000
128 A 2 2 1.00 11 0.182
129 A 2 2 1.00 11 0.182
130 A 2 2 1.00 9 0.222
131 A 2 2 1.00 7 0.286
132 A 2 2 1.00 11 0.182
133 A 2 2 1.00 11 0.182
134 A 2 2 1.00 11 0.182
135 A 2 2 1.00 11 0.182
136 A 3 2 1.00 13 0.154
137 A 3 2 1.00 13 0.154
138 A 3 2 1.00 13 0.154
139 A 3 3 1.00 11 0.273
140 A 2 2 1.00 9 0.222
141 A 3 3 1.00 13 0.231
142 A 3 3 1.00 13 0.231
143 A 3 2 1.00 13 0.154
144 A 1 1 1.00 13 0.077
145 A 2 2 1.00 13 0.154
146 A 4 2 1.00 13 0.154
147 A 4 2 1.00 13 0.154
148 A 4 2 1.00 13 0.154
149 A 4 3 1.00 13 0.231
150 A 3 3 1.00 11 0.273
151 A 2 2 1.00 9 0.222
152 A 4 3 1.00 13 0.231
153 A 4 4 1.00 13 0.308
154 A 4 3 1.00 13 0.231
155 A 4 2 1.00 13 0.154
156 A 1 1 1.00 13 0.077
157 A 2 2 1.00 13 0.154
158 A 1 1 1.00 13 0.077
159 A 5 4 1.00 13 0.308
160 A 4 4 1.00 13 0.308
161 A 3 3 1.00 11 0.273
162 A 2 2 1.00 9 0.222
163 A 4 3 1.00 13 0.231
164 A 5 4 1.00 13 0.308
165 A 6 4 1.00 13 0.308
166 A 2 2 1.00 13 0.154
167 A 6 5 1.00 13 0.385
168 A 5 5 1.00 13 0.385
169 A 4 4 1.00 13 0.308
170 A 3 3 1.00 11 0.273
171 A 2 2 1.00 9 0.222
172 A 5 4 1.00 13 0.308
173 A 6 5 1.00 13 0.385
174 A 7 5 1.00 13 0.385
175 A 3 2 1.00 13 0.154
176 A 6 5 1.00 13 0.385
177 A 5 4 1.00 13 0.308
178 A 4 3 1.00 13 0.231
179 A 3 3 1.00 11 0.273
180 A 2 2 1.00 9 0.222
181 A 6 4 1.00 13 0.308
182 A 7 5 1.00 13 0.385
183 A 8 5 1.00 13 0.385
184 A 1 1 1.00 13 0.077
185 A 6 3 1.00 13 0.231
186 A 5 3 1.00 13 0.231
187 A 4 3 1.00 13 0.231
188 A 3 3 1.00 11 0.273
189 A 2 2 1.00 9 0.222
190 A 1 1 1.00 13 0.077
191 A 2 2 1.00 13 0.154
192 A 3 2 1.00 13 0.154
193 A 2 2 1.00 11 0.182
194 A 2 2 1.00 11 0.182
195 A 2 2 1.00 9 0.222
196 A 2 2 1.00 7 0.286
197 A 2 2 1.00 11 0.182
198 A 2 2 1.00 11 0.182
199 A 2 2 1.00 11 0.182
200 A 6 4 1.00 3 1.333
201 A 8 5 1.00 5 1.000
202 A 10 6 1.00 7 0.857
203 A 11 6 1.00 15 0.400
204 A 9 5 1.00 13 0.385
205 A 7 4 1.00 11 0.364
206 N/A 0 0 1.00 15 0.000
207 A 8 7 1.00 16 0.438
208 A 7 7 1.00 16 0.438
209 A 6 6 1.00 14 0.429
210 A 5 5 1.00 12 0.417
211 N/A 0 0 1.00 16 0.000
212 A 8 7 1.00 19 0.368
213 A 7 7 1.00 19 0.368
214 A 6 6 1.00 17 0.353
215 A 5 5 1.00 15 0.333
216 N/A 0 0 1.00 19 0.000
217 A 11 6 1.00 15 0.400
218 A 9 5 1.00 13 0.385
219 A 7 4 1.00 11 0.364
220 N/A 0 0 1.00 15 0.000
221 A 8 7 1.00 16 0.438
222 A 7 7 1.00 16 0.438
223 A 6 6 1.00 14 0.429
224 A 5 5 1.00 12 0.417
225 N/A 0 0 1.00 16 0.000
226 A 8 7 1.00 19 0.368
227 A 7 7 1.00 19 0.368
228 A 6 6 1.00 17 0.353
229 A 5 5 1.00 15 0.333
230 N/A 0 0 1.00 19 0.000
231 A 12 6 1.00 15 0.400
232 A 10 6 1.00 15 0.400
233 A 8 5 1.00 13 0.385
234 A 6 4 1.00 7 0.571
235 N/A 0 0 1.00 15 0.000
236 A 11 6 1.00 15 0.400
237 A 9 5 1.00 13 0.385
238 A 7 4 1.00 11 0.364
239 N/A 0 0 1.00 15 0.000
240 A 7 7 1.00 20 0.350
241 A 6 6 1.00 18 0.333
242 A 5 5 1.00 16 0.312
243 N/A 0 0 1.00 20 0.000
244 A 7 7 1.00 21 0.333
245 A 6 6 1.00 19 0.316
246 A 5 5 1.00 17 0.294
247 N/A 0 0 1.00 21 0.000
248 A 12 6 1.00 15 0.400
249 A 10 6 1.00 15 0.400
250 A 8 5 1.00 13 0.385
251 A 6 4 1.00 7 0.571
252 N/A 0 0 1.00 15 0.000
253 A 11 6 1.00 15 0.400
254 A 9 5 1.00 13 0.385
255 A 7 4 1.00 11 0.364
256 N/A 0 0 1.00 15 0.000
257 A 7 7 1.00 20 0.350
258 A 6 6 1.00 18 0.333
259 A 5 5 1.00 16 0.312
260 N/A 0 0 1.00 20 0.000
261 A 7 7 1.00 21 0.333
262 A 6 6 1.00 19 0.316
263 A 5 5 1.00 17 0.294
264 N/A 0 0 1.00 21 0.000
265 A 11 8 1.00 24 0.333
266 A 23 11 1.00 27 0.407
267 A 14 11 1.00 27 0.407
268 A 7 8 1.00 25 0.320
269 A 21 11 1.00 27 0.407
270 A 13 13 1.00 27 0.482
271 A 17 14 1.00 27 0.518
272 A 26 15 1.00 27 0.556
273 A 21 15 1.00 27 0.556
274 A 9 8 1.00 24 0.333
275 A 6 6 1.00 27 0.222
276 A 15 14 1.00 27 0.518
277 A 24 16 1.00 27 0.593
278 A 22 17 1.00 22 0.773
279 A 38 20 1.00 21 0.952
280 N/A 0 0 1.00 24 0.000
281 A 38 22 1.00 24 0.917
282 A 32 17 1.00 24 0.708
283 A 2 2 1.00 4 0.500
284 A 7 4 1.00 6 0.667
285 A 9 5 1.00 8 0.625
286 A 2 2 1.00 8 0.250
287 A 7 4 1.00 10 0.400
288 A 9 5 1.00 12 0.417
289 A 6 6 1.00 12 0.500
290 A 25 8 1.00 14 0.571
291 A 29 9 1.00 16 0.562
292 A 1 1 1.00 20 0.050
293 A 4 4 1.00 12 0.333
294 A 4 4 1.00 14 0.286
295 A 8 7 1.00 20 0.350
296 A 5 5 1.00 20 0.250
297 A 3 2 1.00 20 0.100
298 A 3 2 1.00 20 0.100
299 A 5 5 1.00 20 0.250
300 A 8 7 1.00 20 0.350

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