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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 [211] had the largest ratio of [2.66666999999999987]

# 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 N/A 2 0 1.00 32 0.000
2 A 2 2 1.00 32 0.062
3 A 2 2 1.00 32 0.062
4 A 2 2 1.00 30 0.067
5 A 3 2 1.00 14 0.143
6 N/A 2 0 1.00 32 0.000
7 N/A 2 0 1.00 32 0.000
8 N/A 2 0 1.00 32 0.000
9 A 2 2 1.00 28 0.071
10 A 2 2 1.00 28 0.071
11 A 2 2 1.00 26 0.077
12 A 1 1 1.00 10 0.100
13 N/A 2 0 1.00 28 0.000
14 N/A 2 0 1.00 28 0.000
15 N/A 2 0 1.00 28 0.000
16 A 1 1 1.00 43 0.023
17 A 1 1 1.00 43 0.023
18 A 1 1 1.00 41 0.024
19 A 2 2 1.00 25 0.080
20 A 1 1 1.00 43 0.023
21 A 1 1 1.00 43 0.023
22 A 1 1 1.00 43 0.023
23 A 3 3 1.00 39 0.077
24 A 3 3 1.00 37 0.081
25 A 1 1 1.00 15 0.067
26 A 2 2 1.00 34 0.059
27 A 3 3 1.00 37 0.081
28 A 3 3 1.00 39 0.077
29 A 2 2 1.00 45 0.044
30 N/A 2 0 1.00 40 0.000
31 A 3 3 0.84 40 0.075
32 A 3 3 0.85 40 0.075
33 A 3 3 0.89 38 0.079
34 A 2 2 1.00 22 0.091
35 N/A 2 0 1.00 40 0.000
36 N/A 2 0 1.00 40 0.000
37 N/A 2 0 1.00 40 0.000
38 A 1 1 1.00 60 0.017
39 N/A 2 0 1.00 29 0.000
40 A 1 1 1.00 39 0.026
41 A 1 1 1.00 40 0.025
42 A 1 1 1.00 41 0.024
43 A 1 1 1.00 42 0.024
44 A 1 1 1.00 40 0.025
45 A 1 1 1.00 41 0.024
46 A 4 3 1.00 19 0.158
47 A 4 3 1.00 21 0.143
48 A 4 3 1.00 19 0.158
49 A 4 3 1.00 17 0.176
50 A 1 1 1.00 15 0.067
51 A 1 1 1.00 19 0.053
52 A 4 3 1.00 19 0.158
53 A 4 3 1.00 19 0.158
54 A 4 3 1.00 19 0.158
55 A 2 2 1.00 9 0.222
56 A 1 1 1.00 13 0.077
57 A 4 3 1.00 11 0.273
58 A 1 1 1.00 15 0.067
59 A 3 3 1.12 18 0.167
60 A 3 3 0.95 18 0.167
61 A 3 3 0.95 18 0.167
62 A 3 3 0.96 18 0.167
63 A 3 3 0.89 16 0.188
64 A 3 3 1.09 14 0.214
65 A 4 4 0.96 18 0.222
66 A 3 3 1.00 18 0.167
67 A 3 3 0.93 18 0.167
68 A 3 3 0.92 18 0.167
69 A 3 3 0.93 18 0.167
70 A 3 3 0.98 19 0.158
71 A 3 3 0.97 19 0.158
72 A 3 3 0.97 19 0.158
73 A 3 3 0.97 19 0.158
74 A 3 3 0.94 17 0.176
75 A 3 3 1.03 15 0.200
76 A 3 3 0.95 19 0.158
77 A 3 3 1.00 19 0.158
78 A 3 3 0.97 19 0.158
79 A 3 3 0.95 19 0.158
80 A 3 3 0.97 19 0.158
81 A 3 3 1.00 7 0.429
82 A 3 3 1.00 23 0.130
83 A 3 3 1.00 23 0.130
84 A 3 3 1.00 23 0.130
85 A 3 3 0.99 21 0.143
86 A 3 3 1.03 15 0.200
87 A 3 3 0.93 23 0.130
88 A 3 3 0.99 23 0.130
89 A 3 3 0.96 23 0.130
90 A 3 3 0.96 23 0.130
91 A 3 3 0.96 23 0.130
92 A 9 8 0.99 25 0.320
93 A 10 9 0.96 32 0.281
94 A 2 2 1.00 25 0.080
95 A 2 2 1.00 28 0.071
96 A 3 3 0.94 16 0.188
97 A 3 3 0.99 17 0.176
98 A 2 2 1.00 21 0.095
99 A 3 3 1.04 9 0.333
100 A 4 4 1.00 13 0.308
101 A 5 5 1.03 21 0.238
102 A 5 5 1.03 21 0.238
103 A 5 5 1.00 19 0.263
104 A 5 5 1.03 17 0.294
105 N/A 2 0 1.00 21 0.000
106 A 5 5 1.04 21 0.238
107 A 5 5 1.00 21 0.238
108 A 7 6 1.03 23 0.261
109 A 7 6 1.03 23 0.261
110 A 7 6 1.10 23 0.261
111 A 7 6 1.02 23 0.261
112 A 7 6 0.99 23 0.261
113 A 7 6 1.04 12 0.500
114 A 6 5 1.03 12 0.417
115 A 5 4 1.00 10 0.400
116 A 5 4 1.21 8 0.500
117 N/A 1 0 1.00 12 0.000
118 A 6 5 1.23 20 0.250
119 A 5 4 1.15 20 0.200
120 A 4 3 1.00 18 0.167
121 A 3 2 1.00 16 0.125
122 N/A 1 0 1.00 20 0.000
123 A 7 6 1.16 20 0.300
124 A 6 5 1.10 20 0.250
125 A 5 4 1.00 18 0.222
126 A 5 4 1.35 16 0.250
127 N/A 1 0 1.00 20 0.000
128 A 4 3 1.31 16 0.188
129 A 3 2 1.00 10 0.200
130 A 3 2 1.00 12 0.167
131 A 3 2 1.00 10 0.200
132 A 3 2 1.00 10 0.200
133 A 3 2 1.00 12 0.167
134 A 4 3 1.00 14 0.214
135 A 3 2 1.00 16 0.125
136 A 3 2 1.00 14 0.143
137 A 9 8 1.02 16 0.500
138 A 3 2 1.00 15 0.133
139 A 2 2 1.00 8 0.250
140 A 5 4 1.00 9 0.444
141 A 4 3 1.00 16 0.188
142 A 4 3 1.00 16 0.188
143 A 5 4 1.12 18 0.222
144 A 4 3 1.00 16 0.188
145 A 4 3 1.00 14 0.214
146 A 4 3 1.00 16 0.188
147 A 5 4 1.00 16 0.250
148 A 4 3 1.00 20 0.150
149 A 4 3 1.00 14 0.214
150 A 4 3 1.00 14 0.214
151 A 4 3 1.00 16 0.188
152 A 4 3 1.00 16 0.188
153 A 5 4 1.00 10 0.400
154 A 8 8 0.97 9 0.889
155 A 2 2 1.00 11 0.182
156 A 5 5 0.96 11 0.455
157 A 7 7 0.94 9 0.778
158 A 3 3 0.98 11 0.273
159 A 4 4 0.95 11 0.364
160 A 1 1 1.00 12 0.083
161 A 9 8 1.15 5 1.600
162 A 10 9 1.31 7 1.286
163 A 10 9 1.13 7 1.286
164 A 8 7 1.15 5 1.400
165 A 8 7 1.31 7 1.000
166 A 9 8 1.13 7 1.143
167 A 7 6 1.06 5 1.200
168 A 8 7 1.14 7 1.000
169 A 8 7 1.02 7 1.000
170 A 8 7 1.06 5 1.400
171 A 8 7 1.14 7 1.000
172 A 9 8 1.02 7 1.143
173 A 7 6 1.17 5 1.200
174 A 8 7 1.31 7 1.000
175 A 8 7 1.18 7 1.000
176 A 10 9 1.17 5 1.800
177 A 10 9 1.31 7 1.286
178 A 11 10 1.18 7 1.429
179 A 4 4 1.00 16 0.250
180 A 4 3 1.00 10 0.300
181 A 6 5 1.00 10 0.500
182 A 5 5 1.00 8 0.625
183 A 3 2 1.00 6 0.333
184 A 6 5 1.00 10 0.500
185 A 3 3 1.00 35 0.086
186 A 4 3 1.00 8 0.375
187 A 3 2 1.00 6 0.333
188 A 3 3 1.00 6 0.500
189 A 7 6 1.00 6 1.000
190 A 3 3 1.00 6 0.500
191 A 4 4 1.04 8 0.500
192 A 10 9 1.05 8 1.125
193 A 12 11 1.20 7 1.571
194 A 5 5 1.00 8 0.625
195 A 9 9 0.94 9 1.000
196 A 3 3 0.98 11 0.273
197 A 5 5 0.96 11 0.455
198 C 10 10 1.17 9 1.111
199 A 3 3 0.98 11 0.273
200 A 4 4 0.95 11 0.364
201 C 9 8 1.36 5 1.600
202 C 10 9 1.57 7 1.286
203 C 10 9 1.27 7 1.286
204 C 8 7 1.36 5 1.400
205 C 9 8 1.57 7 1.143
206 C 9 8 1.27 7 1.143
207 C 8 7 1.28 3 2.333
208 C 8 7 1.27 5 1.400
209 C 9 8 1.46 7 1.143
210 C 9 8 1.20 7 1.143
211 C 9 8 1.28 3 2.667
212 C 9 8 1.27 5 1.600
213 C 9 8 1.46 7 1.143
214 C 10 9 1.20 7 1.286
215 C 9 8 1.39 5 1.600
216 C 9 8 1.57 7 1.143
217 C 10 9 1.30 7 1.286
218 C 10 9 1.39 5 1.800
219 C 10 9 1.57 7 1.286
220 C 11 10 1.30 7 1.429
221 A 3 3 1.00 35 0.086
222 A 5 5 1.00 8 0.625
223 A 1 1 1.00 8 0.125
224 A 4 3 1.04 10 0.300
225 A 3 2 1.00 16 0.125
226 A 3 3 1.46 9 0.333
227 A 3 2 1.32 10 0.200
228 A 3 3 1.09 10 0.300
229 A 3 3 1.12 12 0.250
230 A 5 4 1.03 8 0.500
231 A 2 2 1.00 12 0.167
232 A 3 3 1.00 12 0.250
233 A 2 2 1.00 14 0.143
234 A 7 6 0.98 14 0.429
235 A 1 1 1.00 8 0.125
236 A 2 2 1.00 4 0.500
237 A 1 1 1.00 10 0.100
238 A 4 3 1.47 11 0.273
239 A 3 3 1.00 6 0.500
240 A 2 2 1.00 8 0.250
241 A 2 2 1.00 14 0.143
242 A 3 2 1.08 6 0.333
243 A 4 4 1.17 10 0.400
244 A 4 4 1.22 14 0.286
245 A 3 2 0.94 12 0.167
246 A 3 2 0.94 14 0.143
247 A 3 2 1.00 14 0.143
248 A 3 2 0.94 14 0.143
249 A 3 2 0.95 14 0.143
250 A 3 2 1.00 15 0.133
251 A 3 2 1.00 17 0.118
252 A 10 9 0.94 17 0.529
253 A 10 9 1.44 17 0.529
254 A 4 3 1.19 17 0.176
255 A 4 3 1.12 17 0.176
256 A 11 10 1.02 17 0.588
257 A 11 10 1.49 17 0.588
258 A 4 3 1.00 18 0.167
259 A 8 7 1.02 26 0.269
260 A 8 7 1.02 21 0.333
261 A 5 4 1.05 27 0.148
262 A 2 2 1.16 10 0.200
263 A 4 3 1.00 12 0.250
264 A 4 3 1.00 12 0.250
265 A 4 3 1.00 12 0.250
266 A 5 4 1.07 15 0.267
267 A 2 2 1.00 15 0.133
268 A 1 1 1.00 8 0.125
269 A 2 2 1.00 19 0.105
270 A 2 2 1.00 19 0.105
271 A 1 1 1.00 14 0.071
272 A 4 4 1.13 24 0.167
273 A 6 5 1.00 8 0.625
274 A 2 2 1.00 9 0.222
275 A 2 2 1.00 10 0.200
276 A 4 4 1.12 22 0.182
277 A 6 5 1.08 18 0.278
278 A 5 5 1.20 20 0.250
279 A 7 7 1.06 25 0.280
280 A 1 1 1.00 39 0.026
281 A 1 1 1.00 39 0.026
282 A 3 2 1.00 8 0.250
283 A 2 2 1.00 10 0.200
284 A 6 5 1.52 12 0.417
285 A 3 3 1.00 10 0.300
286 N/A 1 0 1.00 10 0.000
287 N/A 1 0 1.00 8 0.000
288 N/A 1 0 1.00 6 0.000
289 N/A 1 0 1.00 10 0.000
290 N/A 1 0 1.00 10 0.000
291 A 3 2 1.00 14 0.143
292 A 3 2 1.00 16 0.125
293 A 2 2 1.00 14 0.143
294 A 6 5 1.09 14 0.357
295 A 7 6 1.04 14 0.429
296 A 4 4 1.00 12 0.333
297 A 5 4 1.00 14 0.286
298 A 5 4 1.00 14 0.286
299 A 1 1 1.00 14 0.071
300 A 4 3 1.00 6 0.500
301 A 5 4 1.00 13 0.308
302 A 5 4 1.00 14 0.286
303 A 5 4 1.00 17 0.235
304 A 5 4 1.00 18 0.222
305 A 4 4 1.01 10 0.400
306 A 4 4 0.99 8 0.500
307 A 2 2 1.00 6 0.333
308 N/A 1 0 1.00 10 0.000
309 N/A 3 0 1.00 10 0.000
310 A 4 4 1.01 13 0.308
311 A 4 4 0.99 11 0.364
312 A 2 2 1.00 9 0.222
313 N/A 1 0 1.00 13 0.000
314 N/A 4 0 1.00 13 0.000

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