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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 [200] had the largest ratio of [2.33333000000000013]

# 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 1.02 8 0.375
2 A 5 4 1.04 8 0.500
3 A 3 3 1.02 8 0.375
4 A 5 4 1.05 8 0.500
5 A 3 3 1.03 6 0.500
6 A 2 2 1.00 4 0.500
7 A 1 1 1.00 8 0.125
8 A 6 5 1.10 8 0.625
9 A 3 3 0.94 8 0.375
10 A 5 4 1.00 8 0.500
11 A 4 4 1.00 8 0.500
12 A 16 15 1.69 10 1.500
13 A 14 13 1.35 10 1.300
14 A 11 10 1.42 10 1.000
15 A 10 9 1.17 10 0.900
16 A 5 5 1.13 8 0.625
17 A 6 5 1.22 6 0.833
18 A 4 4 1.32 10 0.400
19 A 4 4 1.09 10 0.400
20 A 9 8 0.98 10 0.800
21 A 8 8 0.94 10 0.800
22 A 14 13 1.27 10 1.300
23 B 18 17 2.26 10 1.700
24 A 17 16 1.55 10 1.600
25 A 14 13 1.72 10 1.300
26 A 11 11 1.19 10 1.100
27 A 9 8 1.15 8 1.000
28 A 5 5 1.19 6 0.833
29 A 5 5 1.21 10 0.500
30 A 5 5 1.18 10 0.500
31 A 7 7 0.95 10 0.700
32 A 15 14 1.03 10 1.400
33 A 11 11 1.35 10 1.100
34 A 1 1 1.00 14 0.071
35 A 6 5 1.01 14 0.357
36 A 6 5 1.01 14 0.357
37 A 6 5 1.02 14 0.357
38 A 6 5 1.04 12 0.417
39 A 6 6 1.58 14 0.429
40 A 4 4 1.05 14 0.286
41 A 4 4 1.04 14 0.286
42 N/A 1 0 1.00 16 0.000
43 N/A 1 0 1.00 16 0.000
44 A 6 5 1.00 16 0.312
45 A 7 6 1.02 16 0.375
46 A 7 6 0.97 16 0.375
47 A 6 5 0.99 16 0.312
48 A 3 3 0.75 15 0.200
49 A 2 2 0.69 15 0.133
50 A 1 1 1.00 15 0.067
51 A 2 2 1.04 15 0.133
52 A 3 3 1.09 15 0.200
53 A 1 1 1.00 14 0.071
54 A 1 1 1.00 14 0.071
55 A 4 4 1.08 14 0.286
56 A 5 4 1.05 13 0.308
57 A 1 1 1.00 12 0.083
58 A 3 3 1.14 13 0.231
59 A 2 2 1.00 12 0.167
60 A 4 4 1.20 13 0.308
61 A 3 3 1.07 12 0.250
62 A 7 6 0.98 10 0.600
63 A 6 5 1.05 10 0.500
64 A 7 6 1.09 8 0.750
65 A 4 3 0.94 6 0.500
66 A 8 7 1.00 10 0.700
67 A 6 5 1.05 10 0.500
68 A 5 4 1.03 10 0.400
69 A 6 5 0.93 12 0.417
70 A 5 4 0.95 12 0.333
71 A 6 5 0.93 10 0.500
72 A 7 6 0.94 8 0.750
73 A 5 4 1.00 12 0.333
74 A 8 7 1.02 12 0.583
75 A 7 6 0.94 12 0.500
76 A 8 7 1.05 16 0.438
77 A 7 6 1.15 14 0.429
78 A 7 7 1.49 16 0.438
79 A 7 7 1.58 16 0.438
80 A 5 4 1.00 18 0.222
81 A 5 4 1.00 18 0.222
82 A 2 2 1.06 19 0.105
83 A 7 6 1.02 10 0.600
84 A 6 5 1.02 8 0.625
85 A 5 4 1.32 6 0.667
86 A 3 2 1.42 10 0.200
87 A 5 4 1.28 10 0.400
88 A 6 5 1.02 10 0.500
89 A 3 3 0.92 12 0.250
90 A 3 3 0.90 12 0.250
91 A 2 2 1.00 12 0.167
92 A 4 4 1.00 12 0.333
93 A 3 2 1.14 10 0.200
94 A 3 3 1.00 4 0.750
95 A 3 2 0.95 10 0.200
96 A 5 4 1.00 12 0.333
97 A 6 5 0.76 14 0.357
98 A 3 2 0.94 14 0.143
99 A 7 6 0.94 14 0.429
100 A 4 3 1.16 12 0.250
101 A 4 3 0.94 19 0.158
102 A 6 5 0.99 18 0.278
103 A 6 5 1.07 18 0.278
104 A 6 5 1.09 16 0.312
105 A 1 1 1.00 10 0.100
106 A 7 6 1.14 18 0.333
107 A 4 4 1.05 18 0.222
108 A 4 4 1.02 18 0.222
109 A 5 4 1.00 20 0.200
110 A 5 4 1.05 18 0.222
111 A 7 6 0.96 12 0.500
112 A 4 3 1.13 20 0.150
113 A 7 6 1.02 20 0.300
114 A 5 4 0.98 20 0.200
115 A 5 4 0.99 18 0.222
116 A 7 6 0.98 12 0.500
117 A 4 3 1.12 20 0.150
118 A 7 6 1.00 20 0.300
119 A 5 4 1.37 18 0.222
120 N/A 3 0 1.00 20 0.000
121 N/A 3 0 1.00 20 0.000
122 N/A 1 0 1.00 40 0.000
123 A 7 6 0.98 40 0.150
124 A 6 5 1.01 40 0.125
125 A 3 2 0.94 38 0.053
126 N/A 1 0 1.00 40 0.000
127 N/A 1 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 3 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 3 0.93 13 0.231
137 A 3 3 1.07 13 0.231
138 A 3 3 1.07 13 0.231
139 A 4 3 1.00 11 0.273
140 A 3 2 1.00 9 0.222
141 A 3 3 1.02 13 0.231
142 A 3 3 1.00 13 0.231
143 A 3 3 1.00 13 0.231
144 A 1 1 1.00 13 0.077
145 A 2 2 1.00 13 0.154
146 A 4 4 0.86 13 0.308
147 A 4 4 1.10 13 0.308
148 A 4 4 1.10 13 0.308
149 A 5 4 1.15 13 0.308
150 A 4 3 1.00 11 0.273
151 A 3 2 1.00 9 0.222
152 A 4 4 1.03 13 0.308
153 A 4 4 1.00 13 0.308
154 A 4 4 1.02 13 0.308
155 A 4 4 1.00 13 0.308
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 6 5 1.07 13 0.385
160 A 5 4 1.05 13 0.308
161 A 4 3 1.00 11 0.273
162 A 3 2 1.00 9 0.222
163 A 5 4 1.00 13 0.308
164 A 6 5 1.25 13 0.385
165 A 7 6 1.32 13 0.462
166 A 2 2 1.00 13 0.154
167 A 7 6 1.12 13 0.462
168 A 6 5 1.09 13 0.385
169 A 5 4 1.08 13 0.308
170 A 4 3 1.00 11 0.273
171 A 3 2 1.00 9 0.222
172 A 6 5 1.26 13 0.385
173 A 7 6 1.32 13 0.462
174 A 8 7 1.31 13 0.538
175 A 3 3 1.03 13 0.231
176 A 7 6 1.16 13 0.462
177 A 6 5 1.14 13 0.385
178 A 5 4 1.11 13 0.308
179 A 4 3 1.00 11 0.273
180 A 3 2 1.00 9 0.222
181 A 7 6 1.38 13 0.462
182 A 8 7 1.38 13 0.538
183 A 9 8 1.36 13 0.615
184 A 1 1 1.00 13 0.077
185 A 7 6 0.91 13 0.462
186 A 6 5 0.96 13 0.385
187 A 5 4 1.00 13 0.308
188 A 4 3 1.00 11 0.273
189 A 3 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 3 0.97 13 0.231
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 3 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 C 8 7 1.48 3 2.333
201 C 9 8 1.35 5 1.600
202 C 10 9 1.29 7 1.286
203 A 7 6 1.29 15 0.400
204 A 6 5 1.32 13 0.385
205 A 5 4 1.38 11 0.364
206 N/A 1 0 1.00 15 0.000
207 A 9 8 1.28 16 0.500
208 A 8 7 1.29 16 0.438
209 A 7 6 1.30 14 0.429
210 A 6 5 1.30 12 0.417
211 N/A 1 0 1.00 16 0.000
212 A 9 8 1.30 19 0.421
213 A 8 7 1.31 19 0.368
214 A 7 6 1.33 17 0.353
215 A 6 5 1.36 15 0.333
216 N/A 1 0 1.00 19 0.000
217 A 7 6 1.29 15 0.400
218 A 6 5 1.31 13 0.385
219 A 5 4 1.38 11 0.364
220 N/A 1 0 1.00 15 0.000
221 A 9 8 1.28 16 0.500
222 A 8 7 1.29 16 0.438
223 A 7 6 1.28 14 0.429
224 A 6 5 1.29 12 0.417
225 N/A 1 0 1.00 16 0.000
226 A 9 8 1.30 19 0.421
227 A 8 7 1.31 19 0.368
228 A 7 6 1.31 17 0.353
229 A 6 5 1.34 15 0.333
230 N/A 1 0 1.00 19 0.000
231 A 9 8 1.18 15 0.533
232 A 8 7 1.16 15 0.467
233 A 7 6 1.12 13 0.462
234 A 6 5 1.09 7 0.714
235 N/A 1 0 1.00 15 0.000
236 A 7 6 1.32 15 0.400
237 A 6 5 1.36 13 0.385
238 A 5 4 1.48 11 0.364
239 N/A 1 0 1.00 15 0.000
240 A 8 7 1.28 20 0.350
241 A 7 6 1.29 18 0.333
242 A 6 5 1.32 16 0.312
243 N/A 1 0 1.00 20 0.000
244 A 8 7 1.30 21 0.333
245 A 7 6 1.31 19 0.316
246 A 6 5 1.36 17 0.294
247 N/A 1 0 1.00 21 0.000
248 A 9 8 1.18 15 0.533
249 A 8 7 1.16 15 0.467
250 A 7 6 1.12 13 0.462
251 A 6 5 1.09 7 0.714
252 N/A 1 0 1.00 15 0.000
253 A 7 6 1.31 15 0.400
254 A 6 5 1.34 13 0.385
255 A 5 4 1.46 11 0.364
256 N/A 1 0 1.00 15 0.000
257 A 8 7 1.30 20 0.350
258 A 7 6 1.30 18 0.333
259 A 6 5 1.35 16 0.312
260 N/A 1 0 1.00 20 0.000
261 A 8 7 1.28 21 0.333
262 A 7 6 1.27 19 0.316
263 A 6 5 1.31 17 0.294
264 N/A 1 0 1.00 21 0.000
265 A 2 2 1.00 24 0.083
266 A 2 2 0.98 27 0.074
267 A 2 2 0.99 27 0.074
268 A 2 2 1.00 25 0.080
269 A 16 15 0.88 27 0.556
270 A 2 2 0.91 27 0.074
271 A 2 2 0.96 27 0.074
272 A 2 2 0.91 27 0.074
273 A 2 2 0.90 27 0.074
274 A 8 7 1.12 24 0.292
275 A 8 7 0.81 27 0.259
276 A 17 16 0.90 27 0.593
277 A 26 25 1.14 27 0.926
278 A 2 2 0.98 22 0.091
279 A 16 15 1.44 21 0.714
280 N/A 8 0 1.00 24 0.000
281 A 13 12 1.39 24 0.500
282 A 2 2 1.01 24 0.083
283 A 3 2 1.00 4 0.500
284 A 5 4 0.98 6 0.667
285 A 6 5 1.20 8 0.625
286 A 3 2 0.95 8 0.250
287 A 5 4 1.00 10 0.400
288 A 6 5 1.16 12 0.417
289 A 9 8 0.89 12 0.667
290 A 6 6 2.00 14 0.429
291 B 6 6 2.07 16 0.375
292 A 1 1 1.00 20 0.050
293 A 5 4 0.82 12 0.333
294 A 5 4 0.81 14 0.286
295 A 8 7 0.85 20 0.350
296 A 7 6 0.94 20 0.300
297 A 4 3 0.91 20 0.150
298 A 4 3 0.91 20 0.150
299 A 7 6 0.94 20 0.300
300 A 9 8 0.85 20 0.400

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