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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 [228] had the largest ratio of [1.42856999999999990]

# 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 11 10 0.99 19 0.526
2 A 11 10 1.01 19 0.526
3 A 11 10 1.03 19 0.526
4 A 11 10 1.07 19 0.526
5 A 10 9 0.96 17 0.529
6 A 13 12 1.30 17 0.706
7 A 12 11 1.08 19 0.579
8 A 12 11 1.00 19 0.579
9 A 12 11 0.96 19 0.579
10 A 19 18 0.99 19 0.947
11 A 17 16 0.98 19 0.842
12 A 15 14 0.98 19 0.737
13 A 13 12 0.96 19 0.632
14 A 16 15 0.95 19 0.789
15 A 16 15 0.87 19 0.789
16 A 16 15 0.83 19 0.789
17 A 16 15 0.79 19 0.789
18 A 16 15 0.80 19 0.789
19 A 9 8 0.88 21 0.381
20 A 9 8 0.90 21 0.381
21 A 9 8 0.92 21 0.381
22 A 9 8 1.00 21 0.381
23 A 9 8 0.84 19 0.421
24 A 8 7 1.04 19 0.368
25 A 8 7 0.99 21 0.333
26 A 8 7 0.96 21 0.333
27 A 8 7 0.93 21 0.333
28 A 8 7 0.92 21 0.333
29 A 5 5 1.02 21 0.238
30 A 5 5 1.03 21 0.238
31 A 5 5 1.03 21 0.238
32 A 5 5 1.05 21 0.238
33 A 5 5 1.00 21 0.238
34 A 16 15 1.10 21 0.714
35 A 5 5 1.00 21 0.238
36 A 5 5 1.00 21 0.238
37 A 5 5 1.00 21 0.238
38 A 11 10 0.88 21 0.476
39 A 11 10 0.88 21 0.476
40 A 11 10 0.89 21 0.476
41 A 10 9 0.89 21 0.429
42 A 11 10 0.82 19 0.526
43 A 12 11 0.99 19 0.579
44 A 12 11 0.95 21 0.524
45 A 12 11 0.94 21 0.524
46 A 12 11 0.93 21 0.524
47 A 12 11 0.92 21 0.524
48 A 7 7 1.02 21 0.333
49 A 7 7 1.02 21 0.333
50 A 7 7 1.03 21 0.333
51 A 7 7 1.04 21 0.333
52 A 8 8 0.96 21 0.381
53 A 8 8 1.05 21 0.381
54 A 23 22 1.07 21 1.048
55 A 8 8 1.00 21 0.381
56 A 8 8 1.00 21 0.381
57 A 15 14 0.82 21 0.667
58 A 15 14 0.86 21 0.667
59 A 15 14 0.93 21 0.667
60 A 14 13 1.00 21 0.619
61 A 11 10 1.00 19 0.526
62 A 16 15 1.00 19 0.789
63 A 18 17 1.02 21 0.810
64 A 20 19 1.04 21 0.905
65 A 18 17 1.05 21 0.810
66 A 16 15 1.04 21 0.714
67 A 14 13 1.03 21 0.619
68 A 10 10 1.00 21 0.476
69 A 15 14 1.00 21 0.667
70 A 16 15 0.95 21 0.714
71 A 16 15 0.88 21 0.714
72 A 16 15 0.84 21 0.714
73 A 16 15 0.81 21 0.714
74 A 9 8 0.89 21 0.381
75 A 9 8 0.89 21 0.381
76 A 9 8 0.95 21 0.381
77 A 9 8 0.98 21 0.381
78 A 9 8 0.95 21 0.381
79 A 9 8 0.92 19 0.421
80 A 8 7 0.92 19 0.368
81 A 7 6 1.05 21 0.286
82 A 8 7 0.95 21 0.333
83 A 7 7 1.02 21 0.333
84 A 13 13 1.07 21 0.619
85 A 7 7 1.05 21 0.333
86 A 9 9 0.88 21 0.429
87 A 5 5 1.05 21 0.238
88 A 7 7 1.04 21 0.333
89 A 7 7 1.04 21 0.333
90 A 7 7 1.03 21 0.333
91 A 11 10 0.89 21 0.476
92 A 11 10 0.91 21 0.476
93 A 11 10 0.95 21 0.476
94 A 11 10 0.92 21 0.476
95 A 11 10 0.93 21 0.476
96 A 11 10 0.89 19 0.526
97 A 12 11 0.91 19 0.579
98 A 10 9 0.88 21 0.429
99 A 12 11 0.91 21 0.524
100 A 9 9 1.03 21 0.429
101 A 9 9 1.03 21 0.429
102 A 10 10 0.94 21 0.476
103 A 9 9 1.04 21 0.429
104 F 0 0 N/A 0.000 N/A
105 F 0 0 N/A 0.000 N/A
106 F 0 0 N/A 0.000 N/A
107 F 0 0 N/A 0.000 N/A
108 A 20 19 0.96 23 0.826
109 A 20 19 0.97 23 0.826
110 A 17 16 0.93 23 0.696
111 A 19 18 0.94 23 0.783
112 A 22 21 0.97 23 0.913
113 A 22 21 0.98 23 0.913
114 A 5 5 1.00 25 0.200
115 A 5 5 1.00 25 0.200
116 A 5 5 1.00 25 0.200
117 A 5 5 1.00 25 0.200
118 A 5 5 1.00 25 0.200
119 A 5 5 1.00 25 0.200
120 A 17 16 1.02 25 0.640
121 A 15 14 1.02 25 0.560
122 A 15 14 1.02 25 0.560
123 A 15 14 1.08 25 0.560
124 A 17 16 1.08 25 0.640
125 A 19 18 1.04 25 0.720
126 A 19 18 1.07 25 0.720
127 A 7 7 1.04 25 0.280
128 A 7 7 1.06 25 0.280
129 A 7 7 1.06 25 0.280
130 A 7 7 1.07 25 0.280
131 A 7 7 1.07 25 0.280
132 A 7 7 1.05 25 0.280
133 A 7 7 1.05 25 0.280
134 A 7 7 1.00 23 0.304
135 A 5 5 1.00 23 0.217
136 A 12 11 1.00 21 0.524
137 A 11 10 1.00 23 0.435
138 A 7 7 1.04 23 0.304
139 A 9 9 1.04 23 0.391
140 A 8 7 1.58 25 0.280
141 A 8 7 1.58 25 0.280
142 A 8 7 1.55 25 0.280
143 A 8 7 1.50 25 0.280
144 A 8 7 1.52 23 0.304
145 A 9 8 0.96 21 0.381
146 A 8 7 1.03 21 0.333
147 A 7 6 1.01 21 0.286
148 A 4 3 1.00 19 0.158
149 A 6 5 1.00 19 0.263
150 A 9 8 1.10 21 0.381
151 A 12 11 1.02 21 0.524
152 A 19 18 1.38 21 0.857
153 A 11 10 1.27 21 0.476
154 A 9 8 1.00 21 0.381
155 A 13 12 1.26 21 0.571
156 A 8 7 1.00 23 0.304
157 A 8 7 1.00 23 0.304
158 A 8 7 1.00 23 0.304
159 A 8 7 1.27 23 0.304
160 A 11 10 1.04 19 0.526
161 A 11 10 1.07 19 0.526
162 A 11 10 1.10 19 0.526
163 A 10 9 0.96 17 0.529
164 A 13 12 1.00 17 0.706
165 A 16 15 0.97 19 0.789
166 A 19 18 1.01 19 0.947
167 A 21 20 0.99 19 1.053
168 A 17 16 0.98 19 0.842
169 A 15 14 0.98 19 0.737
170 A 13 12 0.96 19 0.632
171 A 16 15 0.95 19 0.789
172 A 16 15 0.87 19 0.789
173 A 16 15 0.83 19 0.789
174 A 9 8 1.03 21 0.381
175 A 9 8 1.02 21 0.381
176 A 9 8 0.98 19 0.421
177 A 10 9 1.20 19 0.474
178 A 10 9 1.30 21 0.429
179 A 17 16 1.07 21 0.762
180 A 16 16 1.12 21 0.762
181 A 5 5 1.00 21 0.238
182 A 14 13 0.92 21 0.619
183 A 14 13 0.87 21 0.619
184 A 14 13 0.85 21 0.619
185 A 11 10 0.99 21 0.476
186 A 10 9 0.89 21 0.429
187 A 11 10 0.95 19 0.526
188 A 13 12 1.16 19 0.632
189 A 14 13 1.16 21 0.619
190 A 7 7 1.00 21 0.333
191 A 21 21 1.10 21 1.000
192 A 19 19 0.95 21 0.905
193 A 8 8 0.91 21 0.381
194 A 8 8 1.00 21 0.381
195 A 8 8 1.00 21 0.381
196 A 11 10 0.91 21 0.476
197 A 11 10 0.90 21 0.476
198 A 11 10 0.90 21 0.476
199 A 11 10 0.91 19 0.526
200 A 13 12 1.03 19 0.632
201 A 14 13 1.31 21 0.619
202 A 14 13 1.27 21 0.619
203 A 18 17 1.14 21 0.810
204 A 15 14 1.16 21 0.667
205 A 13 12 1.15 21 0.571
206 A 12 11 1.13 21 0.524
207 A 14 13 1.18 21 0.619
208 A 16 15 1.20 21 0.714
209 A 9 8 0.90 21 0.381
210 A 9 8 0.89 21 0.381
211 A 9 8 0.87 21 0.381
212 A 9 8 0.84 19 0.421
213 A 10 9 1.23 19 0.474
214 A 9 8 1.13 21 0.381
215 A 10 9 1.15 21 0.429
216 A 25 24 1.22 21 1.143
217 A 19 18 1.15 21 0.857
218 A 18 17 1.41 21 0.810
219 A 5 5 1.00 21 0.238
220 A 5 5 1.00 21 0.238
221 A 11 10 0.90 21 0.476
222 A 11 10 0.89 21 0.476
223 A 11 10 0.87 21 0.476
224 A 11 10 0.81 19 0.526
225 A 14 13 1.13 19 0.684
226 A 11 10 1.12 21 0.476
227 A 14 13 1.12 21 0.619
228 A 31 30 1.26 21 1.429
229 A 25 24 1.13 21 1.143
230 A 21 20 1.15 21 0.952
231 A 8 8 1.00 21 0.381
232 A 8 8 1.00 21 0.381
233 A 27 26 0.99 25 1.040
234 A 24 23 0.97 25 0.920
235 A 24 23 0.98 25 0.920
236 A 21 20 0.98 25 0.800
237 A 22 21 1.00 25 0.840
238 A 25 24 0.94 25 0.960
239 A 25 24 0.95 25 0.960
240 A 28 27 0.97 25 1.080
241 A 5 5 1.00 25 0.200
242 A 5 5 1.00 25 0.200
243 A 5 5 1.00 25 0.200
244 A 5 5 1.00 25 0.200
245 A 5 5 1.00 25 0.200
246 A 5 5 1.00 25 0.200
247 A 5 5 1.00 25 0.200
248 A 5 5 1.00 25 0.200
249 A 2 2 1.00 14 0.143
250 A 5 5 1.00 23 0.217
251 A 8 8 1.00 14 0.571
252 A 8 8 1.05 23 0.348
253 A 2 2 1.00 14 0.143
254 A 11 11 1.14 23 0.478
255 A 11 11 1.08 14 0.786
256 A 14 14 1.11 23 0.609
257 A 7 7 1.00 23 0.304
258 A 13 12 1.08 23 0.522
259 A 12 11 1.00 21 0.524
260 A 9 9 1.00 23 0.391
261 A 5 5 1.00 23 0.217
262 A 7 7 1.00 23 0.304
263 N/A 2 0 1.00 25 0.000
264 N/A 2 0 1.00 25 0.000
265 N/A 2 0 1.00 25 0.000
266 N/A 2 0 1.00 25 0.000
267 N/A 2 0 1.00 23 0.000
268 A 5 4 0.99 21 0.190
269 A 6 5 1.00 21 0.238
270 A 4 3 1.00 19 0.158
271 A 7 6 0.99 19 0.316
272 A 5 4 0.97 21 0.190
273 N/A 2 0 1.00 21 0.000
274 N/A 2 0 1.00 21 0.000
275 A 8 7 1.00 21 0.333
276 F 0 0 N/A 0.000 N/A
277 N/A 2 0 1.00 23 0.000
278 N/A 2 0 1.00 23 0.000
279 N/A 2 0 1.00 23 0.000
280 N/A 2 0 1.00 23 0.000
281 A 21 20 0.69 23 0.870
282 A 21 20 0.73 23 0.870
283 A 18 17 0.69 23 0.739
284 A 16 15 0.68 23 0.652
285 A 19 18 0.70 23 0.783
286 A 19 18 0.65 23 0.783
287 A 7 7 0.70 25 0.280
288 A 7 7 0.74 25 0.280
289 A 7 7 0.71 25 0.280
290 A 7 7 0.71 25 0.280
291 A 7 7 0.71 25 0.280
292 A 7 7 0.68 25 0.280
293 A 19 18 0.82 25 0.720
294 A 19 18 0.83 25 0.720
295 A 17 16 0.91 25 0.640
296 A 15 14 0.91 25 0.560
297 A 15 14 0.92 25 0.560
298 A 15 14 0.82 25 0.560
299 A 17 16 0.87 25 0.640
300 A 9 9 0.75 25 0.360
301 A 9 9 0.80 25 0.360
302 A 9 9 0.86 25 0.360
303 A 9 9 0.86 25 0.360
304 A 9 9 0.81 25 0.360
305 A 9 9 0.79 25 0.360
306 A 9 9 0.86 25 0.360

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