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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 [170] had the largest ratio of [1.19999999999999996]

# 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 6 6 1.10 12 0.500
2 A 4 4 1.17 12 0.333
3 A 4 4 1.12 10 0.400
4 A 6 5 1.00 12 0.417
5 A 4 3 1.00 12 0.250
6 A 5 4 1.15 12 0.333
7 A 10 9 1.17 12 0.750
8 A 3 3 1.08 14 0.214
9 A 3 3 1.13 14 0.214
10 A 3 3 1.17 12 0.250
11 A 7 6 0.99 14 0.429
12 A 10 9 0.91 14 0.643
13 A 16 15 0.96 14 1.071
14 A 6 6 1.08 16 0.375
15 A 4 4 1.13 16 0.250
16 A 4 4 1.08 14 0.286
17 A 6 5 1.00 16 0.312
18 A 4 3 1.00 16 0.188
19 A 5 4 1.14 16 0.250
20 A 10 9 1.16 16 0.562
21 A 3 3 1.05 18 0.167
22 A 3 3 1.09 18 0.167
23 A 3 3 1.15 16 0.188
24 A 7 6 0.98 18 0.333
25 A 10 9 0.90 18 0.500
26 A 16 15 0.94 18 0.833
27 A 4 3 0.96 18 0.167
28 A 4 3 0.95 18 0.167
29 A 4 3 0.95 16 0.188
30 N/A 1 0 1.00 18 0.000
31 N/A 1 0 1.00 18 0.000
32 A 2 2 1.00 18 0.111
33 A 2 2 1.00 16 0.125
34 N/A 1 0 1.00 18 0.000
35 N/A 1 0 1.00 18 0.000
36 N/A 2 0 1.00 18 0.000
37 N/A 2 0 1.00 18 0.000
38 A 3 3 1.00 16 0.188
39 N/A 1 0 1.00 18 0.000
40 N/A 1 0 1.00 18 0.000
41 A 7 6 0.87 14 0.429
42 A 7 6 0.88 14 0.429
43 A 7 6 0.92 14 0.429
44 A 4 4 1.07 12 0.333
45 A 2 2 1.00 14 0.143
46 A 2 2 1.00 14 0.143
47 N/A 1 0 1.00 16 0.000
48 N/A 1 0 1.00 16 0.000
49 A 7 6 1.00 16 0.375
50 A 8 7 0.93 16 0.438
51 A 10 9 0.96 16 0.562
52 A 11 10 0.97 16 0.625
53 A 3 3 0.56 31 0.097
54 A 3 3 0.59 31 0.097
55 A 3 3 0.60 29 0.103
56 A 6 6 0.69 31 0.194
57 A 7 7 0.68 31 0.226
58 A 3 3 0.52 31 0.097
59 A 3 3 0.55 31 0.097
60 A 3 3 0.53 29 0.103
61 F 0 0 N/A 0.000 N/A
62 A 3 3 0.49 31 0.097
63 A 3 3 0.51 31 0.097
64 A 3 3 0.49 29 0.103
65 A 3 3 0.61 31 0.097
66 A 3 3 0.59 31 0.097
67 A 3 3 0.60 31 0.097
68 A 3 3 0.70 29 0.103
69 A 10 9 0.70 31 0.290
70 A 16 15 0.69 31 0.484
71 A 3 3 0.86 31 0.097
72 A 3 3 0.94 31 0.097
73 A 3 3 1.00 29 0.103
74 A 3 3 0.82 31 0.097
75 A 6 5 0.72 30 0.167
76 A 6 5 0.79 35 0.143
77 A 6 5 0.68 37 0.135
78 N/A 2 0 1.00 35 0.000
79 A 10 9 0.61 35 0.257
80 A 9 8 0.62 33 0.242
81 A 8 7 1.00 25 0.280
82 N/A 2 0 1.00 35 0.000
83 A 9 8 1.11 10 0.800
84 A 7 6 1.16 10 0.600
85 A 8 7 1.06 8 0.875
86 A 4 3 0.95 6 0.500
87 A 9 8 1.00 10 0.800
88 A 6 5 1.06 10 0.500
89 A 8 7 1.09 10 0.700
90 A 11 10 1.14 10 1.000
91 C 10 9 1.09 14 0.643
92 C 9 8 1.09 15 0.533
93 A 9 8 0.93 21 0.381
94 A 8 7 0.92 21 0.333
95 A 7 6 0.93 21 0.286
96 A 6 5 0.96 19 0.263
97 A 1 1 1.00 10 0.100
98 C 11 10 1.09 21 0.476
99 A 6 5 0.91 21 0.238
100 A 5 4 0.92 21 0.190
101 A 7 6 0.93 21 0.286
102 A 7 6 0.93 21 0.286
103 A 9 8 0.93 21 0.381
104 A 10 9 0.88 23 0.391
105 A 9 8 0.89 23 0.348
106 A 8 7 0.89 23 0.304
107 A 7 6 0.94 21 0.286
108 A 5 4 1.03 12 0.333
109 C 12 11 1.08 23 0.478
110 A 9 8 0.84 23 0.348
111 A 6 5 0.88 23 0.217
112 A 11 10 0.83 23 0.435
113 A 18 17 1.11 23 0.739
114 A 15 14 1.05 23 0.609
115 A 11 10 0.96 23 0.435
116 A 9 8 0.94 21 0.381
117 A 5 4 0.94 12 0.333
118 C 13 12 1.08 23 0.522
119 A 10 9 0.82 23 0.391
120 C 13 12 0.95 23 0.522
121 A 14 13 0.84 23 0.565
122 A 13 12 1.08 23 0.522
123 A 14 13 1.01 23 0.565
124 A 10 9 0.94 21 0.429
125 A 7 6 0.97 12 0.500
126 C 14 13 1.10 23 0.565
127 A 11 10 0.82 23 0.435
128 C 14 13 0.99 23 0.565
129 A 15 14 0.83 23 0.609
130 A 7 6 0.79 23 0.261
131 A 7 6 0.82 23 0.261
132 A 7 6 0.82 23 0.261
133 C 15 14 0.99 21 0.667
134 C 12 11 1.05 12 0.917
135 N/A 4 0 1.00 23 0.000
136 A 5 4 0.82 23 0.174
137 A 5 4 0.85 23 0.174
138 A 5 4 0.85 23 0.174
139 A 12 11 0.94 21 0.524
140 A 11 10 0.94 12 0.833
141 N/A 4 0 1.00 23 0.000
142 A 9 8 1.19 23 0.348
143 C 18 17 1.15 23 0.739
144 C 19 18 1.12 23 0.783
145 C 18 17 0.98 21 0.810
146 C 14 13 1.00 12 1.083
147 N/A 4 0 1.00 23 0.000
148 A 7 6 1.16 23 0.261
149 A 15 14 1.07 23 0.609
150 A 16 15 1.06 23 0.652
151 A 15 14 0.94 21 0.667
152 A 13 12 0.98 12 1.000
153 N/A 4 0 1.00 23 0.000
154 A 8 7 0.92 25 0.280
155 A 8 7 0.91 25 0.280
156 A 8 7 0.93 25 0.280
157 A 8 7 0.95 23 0.304
158 A 10 9 1.00 14 0.643
159 N/A 4 0 1.00 25 0.000
160 C 21 20 1.24 25 0.800
161 C 18 17 1.21 25 0.680
162 C 16 15 1.02 23 0.652
163 C 12 11 1.03 14 0.786
164 N/A 4 0 1.00 25 0.000
165 A 13 12 1.18 25 0.480
166 A 17 16 1.14 25 0.640
167 A 11 10 0.96 23 0.435
168 A 12 11 0.98 14 0.786
169 N/A 4 0 1.00 25 0.000
170 C 31 30 1.37 25 1.200
171 C 19 18 0.99 23 0.783
172 C 14 13 1.00 14 0.929
173 N/A 4 0 1.00 25 0.000
174 A 7 6 0.92 25 0.240
175 A 7 6 0.94 25 0.240
176 A 7 6 0.93 25 0.240
177 C 13 12 1.08 23 0.522
178 C 10 9 1.09 14 0.643
179 N/A 4 0 1.00 25 0.000
180 A 5 4 0.92 25 0.160
181 A 5 4 0.94 25 0.160
182 A 5 4 0.94 25 0.160
183 A 11 10 1.03 23 0.435
184 A 10 9 1.05 14 0.643
185 N/A 4 0 1.00 25 0.000
186 A 9 8 1.38 25 0.320
187 C 16 15 1.31 25 0.600
188 C 17 16 1.26 25 0.640
189 C 16 15 1.03 23 0.652
190 C 12 11 1.06 14 0.786
191 N/A 4 0 1.00 25 0.000
192 A 7 6 1.29 25 0.240
193 A 14 13 1.23 25 0.520
194 A 15 14 1.18 25 0.560
195 A 14 13 1.02 23 0.565
196 A 12 11 1.04 14 0.786
197 N/A 4 0 1.00 25 0.000
198 A 10 9 1.03 23 0.391
199 A 9 8 1.03 23 0.348
200 A 8 7 1.03 23 0.304
201 A 7 6 1.02 23 0.261
202 A 6 5 0.98 23 0.217
203 A 5 4 0.98 23 0.174
204 A 9 8 0.99 23 0.348
205 A 8 7 1.02 23 0.304
206 A 4 3 1.01 25 0.120
207 A 4 3 1.01 25 0.120
208 A 4 3 1.01 25 0.120
209 A 4 3 1.01 25 0.120
210 A 4 3 0.99 25 0.120
211 A 4 3 0.99 25 0.120
212 A 4 3 0.98 25 0.120
213 A 4 3 1.01 25 0.120
214 N/A 4 0 1.00 25 0.000
215 N/A 4 0 1.00 25 0.000
216 N/A 4 0 1.00 25 0.000
217 N/A 4 0 1.00 25 0.000
218 N/A 4 0 1.00 25 0.000
219 N/A 4 0 1.00 25 0.000
220 N/A 4 0 1.00 25 0.000
221 N/A 4 0 1.00 25 0.000
222 N/A 4 0 1.00 25 0.000
223 N/A 4 0 1.00 25 0.000
224 N/A 4 0 1.00 25 0.000
225 N/A 4 0 1.00 25 0.000
226 N/A 4 0 1.00 23 0.000
227 N/A 4 0 1.00 23 0.000
228 A 4 3 0.96 23 0.130
229 A 6 5 1.03 21 0.238
230 N/A 3 0 1.00 23 0.000
231 C 8 7 1.24 10 0.700
232 A 8 7 1.07 10 0.700
233 A 7 6 1.03 8 0.750
234 A 6 5 1.02 6 0.833
235 C 8 7 1.41 10 0.700
236 A 3 3 1.00 10 0.300
237 A 4 4 1.07 10 0.400
238 A 3 3 1.00 4 0.750
239 C 8 7 1.13 10 0.700
240 A 3 3 1.00 14 0.214
241 A 2 2 0.98 14 0.143
242 A 2 2 1.00 14 0.143
243 A 1 1 1.00 12 0.083
244 A 1 1 1.00 14 0.071
245 A 1 1 1.00 14 0.071
246 A 2 2 1.02 14 0.143
247 A 3 3 1.00 14 0.214
248 A 2 2 0.97 14 0.143
249 A 2 2 1.00 14 0.143
250 A 1 1 1.00 12 0.083
251 A 1 1 1.00 14 0.071
252 A 1 1 1.00 14 0.071
253 A 2 2 1.02 14 0.143
254 A 2 2 1.01 16 0.125
255 A 2 2 1.02 16 0.125
256 A 1 1 1.00 16 0.062
257 A 1 1 1.00 16 0.062
258 A 1 1 1.00 16 0.062
259 A 2 2 1.01 16 0.125
260 A 2 2 1.00 16 0.125
261 A 2 2 1.01 16 0.125
262 A 2 2 1.02 16 0.125
263 A 1 1 1.00 16 0.062
264 A 1 1 1.00 16 0.062
265 A 1 1 1.00 16 0.062
266 A 2 2 1.01 16 0.125
267 A 2 2 1.00 16 0.125
268 N/A 1 0 1.00 40 0.000
269 C 12 11 0.93 40 0.275
270 C 11 10 0.97 40 0.250
271 C 10 9 1.02 38 0.237
272 N/A 1 0 1.00 40 0.000
273 N/A 1 0 1.00 40 0.000
274 C 9 8 1.08 10 0.800
275 A 7 6 0.86 12 0.500
276 A 6 5 0.89 12 0.417
277 A 7 6 0.87 10 0.600
278 A 6 5 1.06 8 0.625
279 A 3 3 1.00 12 0.250
280 A 3 3 1.00 12 0.250
281 A 3 3 1.00 12 0.250
282 A 3 3 1.00 12 0.250
283 A 3 3 1.00 12 0.250
284 A 7 6 0.91 14 0.429
285 A 6 5 0.92 14 0.357
286 A 7 6 0.94 12 0.500
287 A 4 3 0.97 10 0.300
288 N/A 1 0 1.00 14 0.000
289 N/A 1 0 1.00 14 0.000
290 C 10 9 1.07 19 0.474
291 A 4 3 1.00 20 0.150
292 A 5 4 0.93 12 0.333
293 A 5 4 0.91 14 0.286
294 A 6 5 1.00 10 0.500
295 A 3 2 1.00 26 0.077
296 A 3 2 1.00 26 0.077

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