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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 [116] had the largest ratio of [1.90908999999999995]

# 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 10 10 1.00 8 1.250
2 C 11 11 1.26 8 1.375
3 A 7 7 1.00 8 0.875
4 C 7 7 1.33 8 0.875
5 A 4 4 1.00 8 0.500
6 A 3 3 1.00 6 0.500
7 C 3 3 1.36 6 0.500
8 A 4 4 1.00 8 0.500
9 C 7 7 1.48 8 0.875
10 A 7 7 1.00 8 0.875
11 C 11 11 1.36 8 1.375
12 A 10 10 1.00 8 1.250
13 A 12 11 1.00 12 0.917
14 A 10 9 0.95 12 0.750
15 A 10 9 0.96 12 0.750
16 A 8 7 0.88 12 0.583
17 A 8 7 0.89 12 0.583
18 A 10 9 0.95 12 0.750
19 A 10 9 0.96 12 0.750
20 A 12 11 1.01 12 0.917
21 A 12 11 1.01 8 1.375
22 A 5 4 1.00 8 0.500
23 A 5 4 1.00 10 0.400
24 C 9 9 1.00 10 0.900
25 A 5 5 1.00 10 0.500
26 A 5 5 1.00 10 0.500
27 C 13 13 0.83 14 0.929
28 C 9 9 0.93 14 0.643
29 A 5 5 1.00 14 0.357
30 C 5 5 1.13 14 0.357
31 C 9 9 1.00 14 0.643
32 C 13 13 0.88 14 0.929
33 A 12 11 0.86 8 1.375
34 A 14 13 0.74 10 1.300
35 A 12 11 0.81 10 1.100
36 A 12 11 0.80 10 1.100
37 A 12 12 0.57 10 1.200
38 A 6 6 0.71 10 0.600
39 A 6 6 0.71 10 0.600
40 A 7 6 1.00 12 0.500
41 A 12 12 1.08 12 1.000
42 A 10 10 1.09 12 0.833
43 A 8 8 1.07 12 0.667
44 A 6 6 1.00 12 0.500
45 A 3 3 1.00 12 0.250
46 A 5 5 1.08 12 0.417
47 A 7 7 1.12 12 0.583
48 A 9 9 1.14 12 0.750
49 A 11 11 1.12 12 0.917
50 A 10 9 1.11 8 1.125
51 A 8 7 1.07 8 0.875
52 A 6 5 1.00 8 0.625
53 A 4 3 1.00 8 0.375
54 A 6 5 1.00 8 0.625
55 A 8 7 1.00 8 0.875
56 A 10 9 1.08 8 1.125
57 A 12 12 1.00 12 1.000
58 A 10 10 1.00 12 0.833
59 A 8 8 1.00 12 0.667
60 A 6 6 1.00 12 0.500
61 A 5 5 1.00 12 0.417
62 A 7 7 1.15 12 0.583
63 A 9 9 1.20 12 0.750
64 A 11 11 1.23 12 0.917
65 A 5 5 1.00 12 0.417
66 A 5 5 1.00 12 0.417
67 A 8 7 1.22 14 0.500
68 A 7 6 1.15 14 0.429
69 A 7 6 1.03 11 0.545
70 C 12 12 1.40 11 1.091
71 A 7 6 1.05 11 0.545
72 C 11 11 1.47 9 1.222
73 C 12 12 2.00 9 1.333
74 A 6 5 1.00 11 0.455
75 C 11 11 1.67 11 1.000
76 A 7 6 1.00 11 0.545
77 C 12 12 1.35 11 1.091
78 A 7 6 1.00 11 0.545
79 C 11 11 1.32 11 1.000
80 A 10 9 1.65 13 0.692
81 C 24 23 1.12 13 1.769
82 A 8 7 1.69 13 0.538
83 C 15 14 1.22 11 1.273
84 C 8 8 1.15 11 0.727
85 A 6 5 1.17 13 0.385
86 C 8 8 1.20 13 0.615
87 A 6 5 1.12 13 0.385
88 C 8 8 1.37 13 0.615
89 A 6 5 1.07 13 0.385
90 A 9 9 1.00 11 0.818
91 A 4 3 1.03 23 0.130
92 A 5 4 1.03 11 0.364
93 C 6 5 1.31 11 0.455
94 A 5 4 1.05 11 0.364
95 A 4 4 1.00 9 0.444
96 A 2 2 1.00 9 0.222
97 A 4 3 1.00 11 0.273
98 A 4 4 1.00 11 0.364
99 A 4 3 1.00 11 0.273
100 A 6 6 1.00 11 0.545
101 A 5 4 1.00 11 0.364
102 A 8 8 1.15 11 0.727
103 A 6 5 0.99 13 0.385
104 A 6 5 0.99 13 0.385
105 A 6 5 0.98 13 0.385
106 A 4 3 1.00 13 0.231
107 A 5 5 1.00 8 0.625
108 A 6 5 1.18 13 0.385
109 A 6 5 1.16 13 0.385
110 A 21 20 1.05 13 1.538
111 A 15 14 1.01 13 1.077
112 A 9 8 1.00 13 0.615
113 A 4 3 1.00 11 0.273
114 A 9 8 0.88 11 0.727
115 C 15 14 0.95 13 1.077
116 C 21 21 1.63 11 1.909
117 C 15 15 1.32 11 1.364
118 C 11 11 1.42 11 1.000
119 A 4 4 1.26 11 0.364
120 C 4 4 1.50 9 0.444
121 A 3 3 1.00 6 0.500
122 C 9 9 1.68 9 1.000
123 C 13 13 1.34 11 1.182
124 C 18 18 1.62 11 1.636
125 C 20 20 1.56 11 1.818
126 C 9 8 1.24 11 0.727
127 C 7 6 1.28 11 0.545
128 C 7 6 1.37 11 0.545
129 C 9 8 1.16 11 0.727
130 A 10 9 1.00 13 0.692
131 A 8 7 1.00 13 0.538
132 A 10 9 1.00 13 0.692
133 A 9 8 1.00 13 0.615
134 C 21 20 1.39 13 1.538
135 C 16 15 1.30 13 1.154
136 C 13 12 1.27 13 0.923
137 A 11 11 0.97 13 0.846
138 C 6 6 1.23 11 0.545
139 A 5 5 1.00 8 0.625
140 C 8 8 1.24 11 0.727
141 C 12 12 1.28 13 0.923
142 C 16 16 1.43 13 1.231
143 C 19 19 1.35 13 1.462
144 A 6 6 1.05 14 0.429
145 A 9 8 1.06 24 0.333
146 A 10 9 1.01 26 0.346
147 A 6 5 1.00 11 0.455
148 A 6 5 0.93 11 0.455
149 A 5 4 1.00 9 0.444
150 A 5 4 1.00 11 0.364
151 A 5 4 1.00 11 0.364
152 A 6 5 1.00 11 0.455
153 A 11 10 1.60 11 0.909
154 A 11 10 1.52 7 1.429
155 A 11 10 1.65 11 0.909
156 A 11 10 1.55 11 0.909
157 A 8 7 1.25 13 0.538
158 A 5 4 1.00 13 0.308
159 A 7 6 1.30 11 0.545
160 A 6 5 1.00 13 0.385
161 A 7 6 1.34 13 0.462
162 A 5 4 1.09 13 0.308
163 A 8 7 1.40 13 0.538
164 A 5 4 1.12 13 0.308
165 A 14 13 1.47 13 1.000
166 A 13 12 1.56 13 0.923
167 A 3 3 1.31 9 0.333
168 A 13 12 1.54 13 0.923
169 A 13 12 1.51 13 0.923
170 A 3 3 1.00 13 0.231
171 A 5 5 1.23 15 0.333
172 A 7 7 1.58 15 0.467
173 A 3 3 1.00 9 0.333
174 A 3 3 1.00 15 0.200
175 A 2 2 1.00 11 0.182
176 A 5 4 1.03 11 0.364
177 A 6 5 1.09 11 0.455
178 A 7 6 0.94 11 0.545
179 A 3 3 1.00 7 0.429
180 A 3 3 1.00 9 0.333
181 A 3 3 1.00 9 0.333
182 A 5 4 1.61 17 0.235
183 A 5 4 1.57 17 0.235
184 A 5 4 1.65 15 0.267
185 A 5 4 1.66 13 0.308
186 A 5 4 1.00 17 0.235
187 A 5 4 1.58 17 0.235
188 A 5 4 1.64 17 0.235
189 A 7 6 1.38 19 0.316
190 A 7 6 1.36 19 0.316
191 A 7 6 1.38 17 0.353
192 A 7 6 1.39 15 0.400
193 A 6 5 1.18 19 0.263
194 A 7 6 1.35 19 0.316
195 A 7 6 1.35 19 0.316
196 C 9 8 1.14 17 0.471
197 A 9 8 1.04 17 0.471
198 C 13 12 1.08 17 0.706
199 A 5 4 1.41 19 0.211
200 A 7 6 1.26 21 0.286
201 A 9 8 1.18 21 0.381
202 A 5 4 1.00 15 0.267
203 A 5 4 1.00 21 0.190
204 A 11 10 1.00 19 0.526
205 A 11 10 1.01 19 0.526
206 A 9 8 1.02 19 0.421
207 A 9 8 1.04 19 0.421
208 A 11 10 1.00 19 0.526
209 A 11 10 1.01 19 0.526
210 C 12 11 0.68 23 0.478
211 C 10 9 0.50 23 0.391
212 C 7 6 0.50 21 0.286
213 C 7 6 1.05 21 0.286
214 C 7 6 1.35 23 0.261
215 C 12 11 0.64 21 0.524
216 A 4 3 0.89 16 0.188
217 A 5 4 0.88 16 0.250
218 A 4 3 0.88 16 0.188
219 A 5 4 0.88 14 0.286
220 A 5 4 0.88 14 0.286
221 A 4 3 0.89 16 0.188
222 A 5 4 0.89 16 0.250
223 A 4 3 0.89 16 0.188
224 A 4 3 1.28 10 0.300
225 A 12 11 1.59 8 1.375
226 A 7 6 1.44 8 0.750
227 A 4 3 1.00 10 0.300
228 A 4 3 1.00 10 0.300
229 A 4 3 1.28 10 0.300
230 A 12 11 1.49 8 1.375
231 A 12 11 1.37 8 1.375
232 A 4 3 1.15 10 0.300
233 A 4 3 1.29 10 0.300
234 A 11 10 1.33 8 1.250
235 A 16 15 1.47 8 1.875
236 A 4 3 1.23 10 0.300
237 A 6 5 1.02 14 0.357
238 A 4 3 1.00 14 0.214
239 A 2 2 1.00 18 0.111
240 A 2 2 1.00 18 0.111
241 A 2 2 1.00 16 0.125
242 A 2 2 1.00 16 0.125
243 A 2 2 1.00 18 0.111
244 A 2 2 1.00 18 0.111
245 A 6 5 0.52 25 0.200
246 A 6 5 0.53 25 0.200
247 A 6 5 0.64 25 0.200
248 A 6 5 0.64 25 0.200
249 A 6 5 0.54 25 0.200
250 A 6 5 0.53 25 0.200
251 A 4 3 0.87 9 0.333
252 A 4 3 0.88 9 0.333
253 A 4 3 0.90 7 0.429
254 N/A 4 0 1.00 7 0.000
255 A 4 3 0.87 9 0.333
256 A 4 3 0.88 9 0.333
257 A 4 3 0.90 7 0.429
258 N/A 4 0 1.00 7 0.000

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