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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 [274] had the largest ratio of [.538461999999999996]

# 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 3 3 0.99 30 0.100
2 A 3 3 1.00 30 0.100
3 A 3 3 0.92 30 0.100
4 A 6 6 1.00 28 0.214
5 A 4 4 1.00 30 0.133
6 A 2 2 1.00 30 0.067
7 A 4 4 1.00 30 0.133
8 A 6 6 1.03 30 0.200
9 A 8 8 1.04 30 0.267
10 A 3 3 0.92 32 0.094
11 A 3 3 0.93 32 0.094
12 A 3 3 0.86 32 0.094
13 A 8 8 0.92 32 0.250
14 A 3 3 0.92 30 0.100
15 A 9 8 0.93 32 0.250
16 A 6 6 1.00 32 0.188
17 A 2 2 1.00 32 0.062
18 A 4 4 1.00 32 0.125
19 A 6 6 1.04 32 0.188
20 A 8 8 1.06 32 0.250
21 A 3 3 0.92 32 0.094
22 A 3 3 0.92 32 0.094
23 A 3 3 0.86 32 0.094
24 A 10 10 0.94 32 0.312
25 A 3 3 0.86 32 0.094
26 A 3 3 1.00 30 0.100
27 A 11 10 0.98 32 0.312
28 A 11 10 0.98 32 0.312
29 A 8 8 1.02 32 0.250
30 A 2 2 1.00 32 0.062
31 A 4 4 1.00 32 0.125
32 A 6 6 1.04 32 0.188
33 A 8 8 1.06 32 0.250
34 A 5 5 0.96 32 0.156
35 A 11 10 0.98 32 0.312
36 A 9 8 0.95 32 0.250
37 A 4 4 1.00 30 0.133
38 A 7 6 1.00 32 0.188
39 A 3 3 0.86 32 0.094
40 A 3 3 0.95 32 0.094
41 A 3 3 0.91 32 0.094
42 A 7 7 0.99 32 0.219
43 A 13 12 0.97 32 0.375
44 A 11 10 0.99 32 0.312
45 A 6 6 1.00 32 0.188
46 A 2 2 1.00 30 0.067
47 A 3 3 0.86 32 0.094
48 A 7 6 0.84 32 0.188
49 A 3 3 0.86 32 0.094
50 A 3 3 0.92 32 0.094
51 A 3 3 0.91 32 0.094
52 A 9 9 0.98 32 0.281
53 A 15 14 1.01 32 0.438
54 A 13 12 1.01 32 0.375
55 A 8 8 1.02 32 0.250
56 A 2 2 1.00 32 0.062
57 A 4 4 1.00 30 0.133
58 A 3 3 0.95 32 0.094
59 A 3 3 0.86 32 0.094
60 A 8 7 0.69 32 0.219
61 A 3 3 0.82 32 0.094
62 A 3 3 0.92 32 0.094
63 A 3 3 0.90 32 0.094
64 A 8 8 1.05 32 0.250
65 A 6 6 1.03 32 0.188
66 A 4 4 1.00 32 0.125
67 A 2 2 1.00 32 0.062
68 A 6 5 1.00 32 0.156
69 A 6 5 1.00 32 0.156
70 A 8 7 1.04 32 0.219
71 A 8 8 1.05 34 0.235
72 A 6 6 1.03 34 0.176
73 A 4 4 1.00 34 0.118
74 A 2 2 1.00 34 0.059
75 A 8 7 1.05 34 0.206
76 A 8 7 1.12 34 0.206
77 A 8 7 1.09 34 0.206
78 A 10 9 1.02 34 0.265
79 A 8 8 1.05 34 0.235
80 A 6 6 1.03 34 0.176
81 A 4 4 1.00 34 0.118
82 A 2 2 1.00 34 0.059
83 A 10 9 1.02 34 0.265
84 A 10 9 1.02 34 0.265
85 A 10 9 1.01 34 0.265
86 A 8 8 1.00 34 0.235
87 A 6 6 0.99 34 0.176
88 A 4 4 1.00 34 0.118
89 A 2 2 1.00 34 0.059
90 A 6 5 1.00 34 0.147
91 A 8 7 1.02 34 0.206
92 A 10 9 1.03 34 0.265
93 A 8 8 1.00 34 0.235
94 A 6 6 0.99 34 0.176
95 A 4 4 0.99 34 0.118
96 A 2 2 1.00 34 0.059
97 A 8 7 0.99 34 0.206
98 A 10 9 1.02 34 0.265
99 A 12 11 1.02 34 0.324
100 A 8 8 1.02 34 0.235
101 A 6 6 1.02 34 0.176
102 A 4 4 1.00 34 0.118
103 A 2 2 1.00 34 0.059
104 A 10 9 1.02 34 0.265
105 A 12 11 1.04 34 0.324
106 A 14 13 1.04 34 0.382
107 A 2 2 1.00 36 0.056
108 A 2 2 1.00 36 0.056
109 A 2 2 1.00 36 0.056
110 A 2 2 1.00 36 0.056
111 A 2 2 1.00 36 0.056
112 A 2 2 1.00 36 0.056
113 A 4 4 1.00 36 0.111
114 A 4 4 1.00 36 0.111
115 A 4 4 1.00 36 0.111
116 A 2 2 1.00 36 0.056
117 A 4 4 1.00 36 0.111
118 A 4 4 1.00 36 0.111
119 A 2 2 1.00 36 0.056
120 A 4 4 1.00 36 0.111
121 A 4 4 1.00 36 0.111
122 A 4 4 1.00 36 0.111
123 A 6 6 1.03 36 0.167
124 A 6 6 1.03 36 0.167
125 A 4 4 1.00 36 0.111
126 A 2 2 1.00 36 0.056
127 A 6 6 1.01 36 0.167
128 A 6 6 0.99 36 0.167
129 A 6 6 1.03 36 0.167
130 A 2 2 1.00 36 0.056
131 A 4 4 1.00 36 0.111
132 A 6 6 1.04 36 0.167
133 A 6 6 1.01 36 0.167
134 A 4 4 1.00 36 0.111
135 A 2 2 1.00 36 0.056
136 A 5 5 1.00 36 0.139
137 A 7 7 1.00 36 0.194
138 A 9 9 1.04 36 0.250
139 A 6 6 0.99 36 0.167
140 A 4 4 1.00 36 0.111
141 A 2 2 1.00 36 0.056
142 A 7 7 1.00 36 0.194
143 A 7 7 0.74 36 0.194
144 A 9 9 0.84 36 0.250
145 A 6 6 1.00 36 0.167
146 A 2 2 1.00 36 0.056
147 A 2 2 1.00 36 0.056
148 A 9 9 1.04 36 0.250
149 A 9 9 0.84 36 0.250
150 A 9 9 0.64 36 0.250
151 A 5 4 1.00 32 0.125
152 A 5 4 1.00 32 0.125
153 A 5 4 1.00 30 0.133
154 A 5 4 1.00 32 0.125
155 A 5 4 1.00 32 0.125
156 A 6 6 0.99 34 0.176
157 A 4 4 1.02 34 0.118
158 A 2 2 1.00 34 0.059
159 A 5 4 1.00 34 0.118
160 A 5 4 1.00 34 0.118
161 A 5 4 1.00 34 0.118
162 A 6 6 0.99 36 0.167
163 A 4 4 1.02 36 0.111
164 A 2 2 1.00 36 0.056
165 A 5 4 1.00 34 0.118
166 A 5 4 1.00 36 0.111
167 A 5 4 1.00 36 0.111
168 A 3 3 0.99 32 0.094
169 A 3 3 0.91 32 0.094
170 A 6 5 1.00 30 0.167
171 A 10 9 1.02 32 0.281
172 A 8 8 1.04 32 0.250
173 A 7 7 1.02 32 0.219
174 A 3 3 0.99 34 0.088
175 A 4 4 1.00 32 0.125
176 A 8 8 1.01 34 0.235
177 A 10 10 1.01 34 0.294
178 A 6 5 1.22 40 0.125
179 A 7 6 1.22 36 0.167
180 A 11 10 1.12 38 0.263
181 A 7 6 1.16 40 0.150
182 A 10 9 1.11 40 0.225
183 A 7 6 1.00 38 0.158
184 A 4 3 1.00 34 0.088
185 A 15 14 1.07 29 0.483
186 A 13 12 1.06 29 0.414
187 A 11 10 1.06 29 0.345
188 A 9 8 1.05 27 0.296
189 A 9 8 1.00 29 0.276
190 A 10 9 1.14 29 0.310
191 A 13 12 1.14 29 0.414
192 A 15 14 1.14 29 0.483
193 A 14 13 1.19 31 0.419
194 A 11 10 1.25 31 0.323
195 A 11 10 1.53 31 0.323
196 A 11 10 0.89 29 0.345
197 B 10 9 2.12 31 0.290
198 A 10 9 1.97 31 0.290
199 A 7 6 1.72 31 0.194
200 A 8 7 1.44 31 0.226
201 A 14 13 1.67 31 0.419
202 A 12 11 1.20 31 0.355
203 A 12 11 1.20 31 0.355
204 A 5 5 0.88 29 0.172
205 A 13 12 1.73 31 0.387
206 A 12 11 1.76 31 0.355
207 A 12 11 1.76 31 0.355
208 A 8 7 1.62 31 0.226
209 A 9 8 1.39 31 0.258
210 A 12 11 1.67 31 0.355
211 A 9 8 1.84 31 0.258
212 B 8 7 2.49 31 0.226
213 A 5 5 1.00 29 0.172
214 A 6 5 1.86 31 0.161
215 A 9 8 1.61 31 0.258
216 A 11 10 1.58 31 0.323
217 A 14 13 1.52 31 0.419
218 A 11 10 1.56 31 0.323
219 A 9 8 1.67 31 0.258
220 A 8 7 2.00 31 0.226
221 A 4 4 0.98 29 0.138
222 A 10 9 1.70 31 0.290
223 A 12 11 1.46 31 0.355
224 A 14 13 1.48 31 0.419
225 A 16 15 1.38 31 0.484
226 A 13 12 1.39 31 0.387
227 A 11 10 1.51 31 0.323
228 A 9 8 1.69 31 0.258
229 A 7 6 1.67 31 0.194
230 A 6 6 0.97 29 0.207
231 A 13 12 1.62 31 0.387
232 A 15 14 1.36 31 0.452
233 A 17 16 1.38 31 0.516
234 A 4 3 1.00 35 0.086
235 A 8 7 1.00 35 0.200
236 A 4 3 1.00 35 0.086
237 A 8 7 1.00 37 0.189
238 A 4 3 1.00 33 0.091
239 A 8 7 1.00 39 0.179
240 A 8 7 1.00 33 0.212
241 A 8 7 1.00 35 0.200
242 A 8 7 1.00 39 0.179
243 A 12 11 1.06 39 0.282
244 A 15 14 1.06 29 0.483
245 A 13 12 1.06 29 0.414
246 A 11 10 1.05 29 0.345
247 A 9 8 1.05 27 0.296
248 A 9 8 1.00 29 0.276
249 A 10 9 1.11 29 0.310
250 A 12 11 1.15 29 0.379
251 A 15 14 1.17 29 0.483
252 A 5 5 1.00 31 0.161
253 A 5 5 1.00 31 0.161
254 A 5 5 1.00 31 0.161
255 A 9 8 1.00 29 0.276
256 A 8 7 1.00 31 0.226
257 A 11 10 1.18 31 0.323
258 A 5 5 1.00 31 0.161
259 A 5 5 1.00 31 0.161
260 A 5 5 1.00 31 0.161
261 A 5 5 1.00 31 0.161
262 A 10 9 1.11 29 0.310
263 A 11 10 1.17 31 0.323
264 A 5 5 1.00 33 0.152
265 A 2 2 1.00 35 0.057
266 A 2 2 1.00 35 0.057
267 A 2 2 1.00 35 0.057
268 A 2 2 1.00 35 0.057
269 A 5 5 1.00 37 0.135
270 A 13 13 1.00 39 0.333
271 A 6 6 1.00 39 0.154
272 A 15 15 1.04 39 0.385
273 A 2 2 1.00 33 0.061
274 A 21 21 1.05 39 0.538
275 A 5 5 1.00 33 0.152
276 A 5 5 1.00 35 0.143
277 A 14 14 1.00 39 0.359
278 A 21 21 0.99 39 0.538
279 A 5 5 1.00 33 0.152
280 A 13 13 1.00 39 0.333
281 A 2 2 1.00 33 0.061
282 A 5 5 1.00 35 0.143
283 A 6 6 1.00 39 0.154
284 A 13 13 1.00 39 0.333
285 A 6 5 0.88 28 0.179
286 A 6 5 0.84 28 0.179

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