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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 [61] had the largest ratio of [2]

# 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 12 11 1.00 12 0.917
2 A 10 9 0.95 12 0.750
3 A 10 9 0.96 12 0.750
4 A 8 7 0.88 12 0.583
5 A 8 7 0.89 12 0.583
6 A 10 9 0.95 12 0.750
7 A 10 9 0.96 12 0.750
8 A 12 11 1.01 12 0.917
9 A 15 14 1.01 12 1.167
10 A 13 12 0.99 12 1.000
11 A 12 11 0.84 12 0.917
12 A 12 11 0.84 12 0.917
13 A 13 12 0.99 12 1.000
14 A 15 14 1.01 12 1.167
15 A 5 4 1.00 8 0.500
16 A 5 4 1.00 10 0.400
17 A 7 6 1.00 12 0.500
18 C 9 9 1.00 14 0.643
19 C 5 5 1.13 14 0.357
20 A 5 5 1.00 14 0.357
21 C 9 9 0.91 14 0.643
22 A 17 16 0.77 14 1.143
23 A 17 16 0.77 14 1.143
24 A 15 14 0.79 14 1.000
25 A 15 14 0.78 14 1.000
26 A 17 16 0.78 14 1.143
27 A 17 16 0.74 14 1.143
28 A 7 6 1.00 12 0.500
29 A 14 13 0.72 14 0.929
30 A 12 11 0.74 14 0.786
31 A 12 11 0.73 14 0.786
32 A 14 13 0.70 14 0.929
33 A 9 9 0.68 14 0.643
34 A 6 6 0.76 14 0.429
35 C 5 5 1.13 14 0.357
36 A 5 5 1.00 14 0.357
37 A 6 6 0.76 14 0.429
38 A 9 9 0.65 14 0.643
39 A 7 6 1.00 12 0.500
40 A 12 12 0.63 14 0.857
41 A 6 6 0.76 14 0.429
42 A 6 6 0.76 14 0.429
43 A 12 12 0.60 14 0.857
44 A 21 20 0.73 14 1.429
45 A 17 16 0.78 14 1.143
46 A 17 16 0.77 14 1.143
47 A 17 16 0.78 14 1.143
48 A 17 16 0.77 14 1.143
49 A 21 20 0.71 14 1.429
50 A 7 6 1.00 12 0.500
51 A 7 6 1.00 14 0.429
52 A 7 6 1.26 14 0.429
53 A 7 6 1.00 14 0.429
54 A 7 6 1.00 14 0.429
55 A 7 6 1.00 14 0.429
56 A 7 6 1.00 14 0.429
57 A 7 6 1.26 14 0.429
58 A 7 6 1.00 14 0.429
59 A 7 6 1.00 14 0.429
60 A 7 6 1.00 14 0.429
61 A 12 12 1.27 6 2.000
62 A 10 10 1.26 6 1.667
63 A 8 8 1.13 6 1.333
64 A 6 6 1.00 6 1.000
65 A 3 3 1.00 6 0.500
66 A 5 5 1.19 6 0.833
67 A 7 7 1.28 6 1.167
68 A 9 9 1.33 6 1.500
69 A 11 11 1.36 6 1.833
70 A 10 9 1.11 8 1.125
71 A 8 7 1.07 8 0.875
72 A 6 5 1.00 8 0.625
73 A 4 3 1.00 8 0.375
74 A 6 5 1.00 8 0.625
75 A 8 7 1.00 8 0.875
76 A 10 9 1.08 8 1.125
77 C 12 12 1.03 12 1.000
78 C 10 10 1.04 12 0.833
79 C 8 8 1.06 12 0.667
80 C 6 6 1.11 12 0.500
81 A 5 5 1.00 12 0.417
82 A 7 7 1.15 12 0.583
83 A 9 9 1.20 12 0.750
84 A 11 11 1.23 12 0.917
85 A 5 5 1.00 12 0.417
86 A 5 5 1.00 12 0.417
87 A 8 7 1.22 14 0.500
88 A 7 6 1.15 14 0.429
89 A 4 3 1.03 23 0.130
90 A 5 4 1.03 11 0.364
91 C 9 8 1.31 11 0.727
92 A 6 5 1.05 11 0.455
93 C 7 7 1.42 9 0.778
94 A 3 3 1.00 9 0.333
95 A 5 4 1.00 11 0.364
96 C 7 7 2.25 11 0.636
97 A 4 3 1.00 11 0.273
98 A 6 5 1.16 13 0.385
99 A 7 6 1.18 13 0.462
100 A 5 5 1.00 8 0.625
101 A 5 4 1.00 13 0.308
102 A 6 5 0.98 13 0.385
103 A 7 6 1.00 13 0.462
104 A 6 5 0.99 13 0.385
105 C 24 23 0.99 13 1.769
106 C 14 13 1.03 11 1.182
107 A 5 4 1.00 11 0.364
108 C 14 13 1.19 13 1.000
109 C 26 25 1.11 13 1.923
110 A 7 6 1.03 11 0.545
111 C 11 11 1.40 11 1.000
112 A 6 5 1.05 11 0.455
113 C 11 11 1.47 9 1.222
114 C 11 11 2.40 9 1.222
115 A 5 4 0.87 11 0.364
116 C 11 11 1.50 11 1.000
117 A 7 6 1.00 11 0.545
118 A 6 5 1.00 13 0.385
119 A 10 9 1.65 13 0.692
120 C 20 19 1.16 13 1.462
121 A 7 6 1.68 13 0.462
122 C 15 14 1.22 11 1.273
123 C 8 8 1.20 11 0.727
124 A 5 4 1.21 13 0.308
125 C 8 8 1.18 13 0.615
126 A 6 5 1.10 13 0.385
127 A 9 9 1.06 13 0.692
128 C 20 20 1.56 11 1.818
129 C 18 18 1.62 11 1.636
130 C 13 13 1.34 11 1.182
131 C 9 9 1.68 9 1.000
132 A 3 3 1.00 6 0.500
133 C 4 4 1.50 9 0.444
134 A 4 4 1.26 11 0.364
135 C 11 11 1.42 11 1.000
136 C 15 15 1.32 11 1.364
137 C 9 8 1.24 11 0.727
138 C 7 6 1.28 11 0.545
139 C 7 6 1.37 11 0.545
140 C 9 8 1.16 11 0.727
141 A 10 9 1.00 13 0.692
142 A 8 7 1.00 13 0.538
143 A 10 9 1.00 13 0.692
144 A 9 8 1.00 13 0.615
145 C 19 19 1.35 13 1.462
146 C 16 16 1.43 13 1.231
147 C 12 12 1.28 13 0.923
148 C 8 8 1.24 11 0.727
149 A 5 5 1.00 8 0.625
150 C 6 6 1.23 11 0.545
151 A 11 11 0.97 13 0.846
152 C 13 12 1.27 13 0.923
153 C 16 15 1.30 13 1.154
154 C 21 20 1.39 13 1.538
155 A 6 6 1.07 14 0.429
156 A 6 5 0.93 11 0.455
157 A 5 5 1.18 11 0.455
158 A 5 4 1.00 9 0.444
159 A 5 5 1.18 7 0.714
160 C 5 4 1.33 11 0.364
161 A 5 5 1.32 11 0.455
162 A 5 4 1.00 11 0.364
163 A 5 4 1.04 13 0.308
164 A 7 7 1.31 13 0.538
165 A 7 6 1.29 11 0.545
166 A 3 3 1.00 9 0.333
167 A 6 5 1.00 13 0.385
168 A 6 6 1.31 13 0.462
169 A 7 6 1.40 13 0.462
170 A 3 3 1.00 13 0.231
171 A 5 5 1.23 15 0.333
172 A 7 7 1.57 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 0.93 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 1.62 17 0.235
183 A 5 4 1.58 17 0.235
184 A 5 4 1.67 15 0.267
185 A 5 4 1.67 13 0.308
186 C 5 4 1.16 17 0.235
187 A 5 4 1.59 17 0.235
188 A 5 4 1.65 17 0.235
189 A 7 6 1.38 19 0.316
190 A 7 6 1.37 19 0.316
191 A 7 6 1.38 17 0.353
192 A 7 6 1.40 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 1.23 17 0.471
197 A 9 8 1.04 17 0.471
198 C 13 12 1.14 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 6 5 0.53 25 0.200
217 A 6 5 0.54 25 0.200
218 A 6 5 0.64 25 0.200
219 A 6 5 0.64 25 0.200
220 A 6 5 0.53 25 0.200
221 A 6 5 0.52 25 0.200
222 A 4 3 0.87 9 0.333
223 A 4 3 0.88 9 0.333
224 A 4 3 0.90 7 0.429
225 N/A 4 0 1.00 7 0.000
226 A 4 3 0.87 9 0.333
227 A 4 3 0.88 9 0.333
228 A 4 3 0.90 7 0.429
229 N/A 4 0 1.00 7 0.000

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