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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 0.84 12 1.167
10 A 13 12 0.81 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 0.81 12 1.000
14 A 15 14 0.84 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 0.63 14 1.143
23 A 17 16 0.63 14 1.143
24 A 15 14 0.63 14 1.000
25 A 15 14 0.62 14 1.000
26 A 17 16 0.64 14 1.143
27 A 17 16 0.61 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 0.61 14 1.429
45 A 17 16 0.64 14 1.143
46 A 17 16 0.63 14 1.143
47 A 17 16 0.64 14 1.143
48 A 17 16 0.63 14 1.143
49 A 21 20 0.60 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 5 4 1.03 11 0.364
90 C 9 8 1.31 11 0.727
91 A 6 5 1.05 11 0.455
92 C 7 7 1.42 9 0.778
93 A 3 3 1.00 9 0.333
94 A 5 4 1.00 11 0.364
95 C 7 7 2.25 11 0.636
96 A 4 3 1.09 11 0.273
97 A 6 5 1.26 13 0.385
98 C 24 23 0.99 13 1.769
99 A 7 6 1.28 13 0.462
100 C 14 13 1.03 11 1.182
101 A 5 4 1.00 11 0.364
102 A 5 4 1.00 13 0.308
103 C 14 13 1.19 13 1.000
104 A 6 5 0.98 13 0.385
105 A 7 6 1.03 11 0.545
106 C 11 11 1.40 11 1.000
107 A 6 5 1.05 11 0.455
108 C 11 11 1.47 9 1.222
109 C 11 11 2.40 9 1.222
110 A 5 4 0.87 11 0.364
111 C 11 11 1.50 11 1.000
112 A 7 6 1.00 11 0.545
113 A 6 5 1.00 13 0.385
114 A 10 9 1.65 13 0.692
115 C 20 19 1.16 13 1.462
116 A 7 6 1.68 13 0.462
117 C 15 14 1.22 11 1.273
118 C 8 8 1.20 11 0.727
119 A 5 4 1.21 13 0.308
120 C 8 8 1.18 13 0.615
121 A 6 5 1.10 13 0.385
122 A 9 9 1.06 13 0.692
123 C 20 20 1.56 11 1.818
124 C 18 18 1.62 11 1.636
125 C 13 13 1.34 11 1.182
126 C 9 9 1.68 9 1.000
127 A 3 3 1.00 6 0.500
128 C 4 4 1.50 9 0.444
129 A 4 4 1.26 11 0.364
130 C 11 11 1.42 11 1.000
131 C 15 15 1.32 11 1.364
132 C 9 8 1.24 11 0.727
133 C 7 6 1.28 11 0.545
134 C 7 6 1.37 11 0.545
135 C 9 8 1.16 11 0.727
136 A 10 9 1.00 13 0.692
137 A 8 7 1.00 13 0.538
138 A 10 9 1.00 13 0.692
139 A 9 8 1.00 13 0.615
140 C 19 19 1.35 13 1.462
141 C 16 16 1.43 13 1.231
142 C 12 12 1.28 13 0.923
143 C 8 8 1.24 11 0.727
144 A 5 5 1.00 8 0.625
145 C 6 6 1.23 11 0.545
146 A 11 11 0.97 13 0.846
147 C 13 12 1.27 13 0.923
148 C 16 15 1.30 13 1.154
149 C 21 20 1.39 13 1.538
150 A 6 6 1.07 14 0.429
151 A 6 5 0.93 11 0.455
152 A 5 5 1.18 11 0.455
153 A 5 4 1.00 9 0.444
154 A 5 5 1.18 7 0.714
155 C 5 4 1.33 11 0.364
156 A 5 5 1.32 11 0.455
157 A 5 4 1.00 11 0.364
158 A 5 4 1.04 13 0.308
159 A 7 7 1.31 13 0.538
160 A 7 6 1.29 11 0.545
161 A 3 3 1.00 9 0.333
162 A 6 5 1.00 13 0.385
163 A 6 6 1.08 13 0.462
164 A 7 6 1.00 13 0.462
165 A 3 3 1.00 13 0.231
166 A 5 5 1.23 15 0.333
167 A 7 7 1.12 15 0.467
168 A 3 3 1.00 9 0.333
169 A 3 3 1.00 15 0.200
170 A 2 2 1.00 11 0.182
171 A 5 4 1.03 11 0.364
172 A 6 5 1.09 11 0.455
173 A 7 6 1.08 11 0.545
174 A 3 3 1.00 7 0.429
175 A 3 3 1.00 9 0.333
176 A 3 3 1.00 9 0.333
177 A 5 4 1.62 17 0.235
178 A 5 4 1.58 17 0.235
179 A 5 4 1.67 15 0.267
180 A 5 4 1.67 13 0.308
181 C 5 4 1.16 17 0.235
182 A 5 4 1.59 17 0.235
183 A 5 4 1.65 17 0.235
184 A 7 6 1.38 19 0.316
185 A 7 6 1.37 19 0.316
186 A 7 6 1.38 17 0.353
187 A 7 6 1.40 15 0.400
188 A 6 5 1.18 19 0.263
189 A 7 6 1.35 19 0.316
190 A 7 6 1.35 19 0.316
191 C 9 8 1.23 17 0.471
192 A 9 8 1.04 17 0.471
193 C 13 12 1.14 17 0.706
194 A 5 4 1.41 19 0.211
195 A 7 6 1.26 21 0.286
196 A 9 8 1.18 21 0.381
197 A 5 4 1.00 15 0.267
198 A 5 4 1.00 21 0.190
199 A 11 10 1.00 19 0.526
200 A 11 10 1.01 19 0.526
201 A 9 8 1.02 19 0.421
202 A 9 8 1.04 19 0.421
203 A 11 10 1.00 19 0.526
204 A 11 10 1.01 19 0.526
205 C 12 11 0.68 23 0.478
206 C 10 9 0.50 23 0.391
207 C 7 6 0.50 21 0.286
208 C 7 6 1.05 21 0.286
209 C 7 6 1.04 23 0.261
210 C 12 11 0.64 21 0.524
211 A 6 5 0.53 25 0.200
212 A 6 5 0.54 25 0.200
213 A 6 5 0.64 25 0.200
214 A 6 5 0.64 25 0.200
215 A 6 5 0.53 25 0.200
216 A 6 5 0.52 25 0.200
217 A 4 3 0.87 9 0.333
218 A 4 3 0.88 9 0.333
219 A 4 3 0.90 7 0.429
220 N/A 4 0 1.00 7 0.000
221 A 4 3 0.87 9 0.333
222 A 4 3 0.88 9 0.333
223 A 4 3 0.90 7 0.429
224 N/A 4 0 1.00 7 0.000

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