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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 [23] had the largest ratio of [1.69999999999999996]

# 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 3 3 1.02 8 0.375
2 A 5 4 1.02 8 0.500
3 A 3 3 1.02 8 0.375
4 A 5 4 1.03 8 0.500
5 A 3 3 1.03 6 0.500
6 A 2 2 1.00 4 0.500
7 A 2 2 1.00 8 0.250
8 A 6 5 1.07 8 0.625
9 A 3 3 0.97 8 0.375
10 A 5 4 1.00 8 0.500
11 A 4 4 1.05 8 0.500
12 A 16 15 1.64 10 1.500
13 A 14 13 1.34 10 1.300
14 A 11 10 1.39 10 1.000
15 A 10 9 1.16 10 0.900
16 A 5 5 1.09 8 0.625
17 A 6 5 1.19 6 0.833
18 A 4 4 1.26 10 0.400
19 A 4 4 1.15 10 0.400
20 A 9 8 1.02 10 0.800
21 A 8 8 1.02 10 0.800
22 A 14 13 1.27 10 1.300
23 B 18 17 2.30 10 1.700
24 A 17 16 1.50 10 1.600
25 A 14 13 1.73 10 1.300
26 A 11 11 1.17 10 1.100
27 A 9 8 1.14 8 1.000
28 A 5 5 1.17 6 0.833
29 A 5 5 1.24 10 0.500
30 A 5 5 1.25 10 0.500
31 A 7 7 1.01 10 0.700
32 A 15 14 1.10 10 1.400
33 A 11 11 1.49 10 1.100
34 N/A 1 0 1.00 10 0.000
35 N/A 1 0 1.00 10 0.000
36 A 2 2 1.00 8 0.250
37 A 10 9 1.22 13 0.692
38 A 9 8 0.99 13 0.615
39 A 4 4 1.00 13 0.308
40 A 5 4 1.00 11 0.364
41 A 1 1 1.00 10 0.100
42 A 3 3 1.12 13 0.231
43 A 8 7 1.10 13 0.538
44 A 7 7 1.03 13 0.538
45 A 13 12 1.30 13 0.923
46 A 9 9 1.62 15 0.600
47 A 2 2 1.00 13 0.154
48 A 6 6 1.70 12 0.500
49 A 2 2 1.00 15 0.133
50 A 13 12 1.61 15 0.800
51 A 1 1 1.00 12 0.083
52 A 1 1 1.00 12 0.083
53 A 6 5 1.00 14 0.357
54 A 6 5 1.00 14 0.357
55 A 6 5 1.00 14 0.357
56 A 6 5 1.00 12 0.417
57 A 6 6 1.56 14 0.429
58 A 4 4 1.00 14 0.286
59 N/A 1 0 1.00 16 0.000
60 N/A 1 0 1.00 16 0.000
61 A 6 5 1.00 16 0.312
62 A 7 6 1.01 16 0.375
63 A 8 7 0.97 16 0.438
64 A 6 5 0.99 16 0.312
65 A 3 3 0.79 14 0.214
66 A 2 2 0.75 14 0.143
67 A 1 1 1.00 14 0.071
68 A 2 2 1.04 14 0.143
69 A 3 3 1.09 14 0.214
70 A 3 3 1.16 11 0.273
71 A 4 4 1.23 11 0.364
72 A 2 2 1.00 10 0.200
73 A 4 4 1.09 12 0.333
74 A 5 4 1.02 10 0.400
75 A 5 4 1.03 10 0.400
76 A 2 2 1.00 8 0.250
77 A 4 3 1.11 10 0.300
78 A 6 5 1.06 10 0.500
79 A 5 4 0.97 10 0.400
80 A 11 10 1.15 10 1.000
81 A 11 10 1.09 10 1.000
82 A 10 9 1.15 6 1.500
83 A 10 9 1.10 10 0.900
84 A 11 10 1.13 10 1.000
85 A 7 6 1.02 10 0.600
86 A 6 5 1.02 8 0.625
87 A 5 4 1.32 6 0.667
88 A 4 3 1.19 10 0.300
89 A 5 4 1.39 10 0.400
90 A 6 5 1.02 10 0.500
91 A 3 3 0.97 12 0.250
92 A 3 3 0.97 12 0.250
93 A 2 2 1.00 12 0.167
94 A 4 4 1.00 12 0.333
95 A 3 3 0.86 12 0.250
96 A 3 3 1.00 4 0.750
97 A 4 3 0.96 10 0.300
98 A 4 3 1.11 10 0.300
99 A 7 6 0.93 10 0.600
100 A 6 5 1.01 10 0.500
101 A 7 6 1.00 8 0.750
102 A 4 3 0.94 6 0.500
103 A 8 7 1.00 10 0.700
104 A 8 7 0.98 10 0.700
105 A 6 5 1.07 10 0.500
106 A 7 6 1.05 10 0.600
107 A 8 7 1.12 16 0.438
108 A 7 6 1.12 14 0.429
109 A 7 7 1.42 16 0.438
110 A 7 7 1.66 16 0.438
111 A 5 4 1.63 18 0.222
112 A 5 4 1.59 18 0.222
113 A 2 2 1.06 19 0.105
114 A 3 2 0.96 28 0.071
115 A 4 3 0.72 33 0.091
116 N/A 3 0 1.00 28 0.000
117 N/A 3 0 1.00 33 0.000
118 A 5 4 0.95 35 0.114
119 A 6 5 0.77 40 0.125
120 N/A 3 0 1.00 35 0.000
121 N/A 3 0 1.00 40 0.000
122 A 6 5 0.83 14 0.357
123 A 5 4 1.00 12 0.333
124 A 4 3 0.96 14 0.214
125 A 7 6 0.96 14 0.429
126 A 5 4 1.11 12 0.333
127 A 5 4 0.96 19 0.211
128 N/A 1 0 1.00 18 0.000
129 A 6 5 0.99 18 0.278
130 A 6 5 1.06 18 0.278
131 A 6 5 1.06 16 0.312
132 A 1 1 1.00 10 0.100
133 A 7 6 1.11 18 0.333
134 A 10 9 0.97 18 0.500
135 A 6 6 1.07 18 0.333
136 A 5 4 1.00 20 0.200
137 A 5 4 1.03 18 0.222
138 A 7 6 1.00 12 0.500
139 A 4 3 1.10 20 0.150
140 A 7 6 1.03 20 0.300
141 A 5 4 0.98 20 0.200
142 A 5 4 0.99 18 0.222
143 A 7 6 0.99 12 0.500
144 A 4 3 1.10 20 0.150
145 A 7 6 1.03 20 0.300
146 A 5 4 1.33 18 0.222
147 N/A 3 0 1.00 20 0.000
148 N/A 3 0 1.00 20 0.000
149 A 5 4 0.81 12 0.333
150 A 5 4 0.80 14 0.286
151 N/A 1 0 1.00 40 0.000
152 A 7 6 1.00 40 0.150
153 A 6 5 1.01 40 0.125
154 A 4 3 0.95 38 0.079
155 N/A 1 0 1.00 40 0.000
156 N/A 1 0 1.00 40 0.000
157 A 3 2 1.00 7 0.286
158 A 7 6 1.29 15 0.400
159 A 6 5 1.30 13 0.385
160 A 5 4 1.40 11 0.364
161 N/A 1 0 1.00 15 0.000
162 A 8 7 1.29 21 0.333
163 A 7 6 1.26 19 0.316
164 A 6 5 1.26 17 0.294
165 N/A 1 0 1.00 21 0.000
166 A 9 8 1.28 22 0.364
167 A 8 7 1.26 20 0.350
168 A 7 6 1.26 18 0.333
169 N/A 1 0 1.00 22 0.000
170 A 3 2 1.00 7 0.286
171 A 7 6 1.29 15 0.400
172 A 6 5 1.30 13 0.385
173 A 5 4 1.40 11 0.364
174 N/A 1 0 1.00 15 0.000
175 A 9 8 1.29 21 0.381
176 A 8 7 1.26 19 0.368
177 A 7 6 1.26 17 0.353
178 N/A 1 0 1.00 21 0.000
179 A 8 7 1.28 22 0.318
180 A 7 6 1.26 20 0.300
181 A 6 5 1.26 18 0.278
182 N/A 1 0 1.00 22 0.000
183 A 9 8 1.09 15 0.533
184 A 8 7 1.10 15 0.467
185 A 7 6 1.10 13 0.462
186 A 6 5 1.08 7 0.714
187 N/A 1 0 1.00 15 0.000
188 A 7 6 1.24 15 0.400
189 A 6 5 1.28 13 0.385
190 A 5 4 1.36 11 0.364
191 N/A 1 0 1.00 15 0.000
192 A 9 8 1.18 19 0.421
193 A 8 7 1.17 17 0.412
194 A 7 6 1.18 15 0.400
195 N/A 1 0 1.00 19 0.000
196 A 8 7 1.17 22 0.318
197 A 7 6 1.17 20 0.300
198 A 6 5 1.16 18 0.278
199 N/A 1 0 1.00 22 0.000
200 A 9 8 1.09 15 0.533
201 A 8 7 1.10 15 0.467
202 A 7 6 1.10 13 0.462
203 A 6 5 1.08 7 0.714
204 N/A 1 0 1.00 15 0.000
205 A 7 6 1.25 15 0.400
206 A 6 5 1.28 13 0.385
207 A 5 4 1.36 11 0.364
208 N/A 1 0 1.00 15 0.000
209 A 9 8 1.18 19 0.421
210 A 8 7 1.18 17 0.412
211 A 7 6 1.18 15 0.400
212 N/A 1 0 1.00 19 0.000
213 A 8 7 1.17 22 0.318
214 A 7 6 1.16 20 0.300
215 A 6 5 1.16 18 0.278
216 N/A 1 0 1.00 22 0.000
217 A 2 2 1.00 24 0.083
218 A 4 3 1.00 4 0.750
219 A 5 4 0.89 6 0.667
220 A 6 5 1.02 8 0.625
221 A 4 3 0.96 8 0.375
222 A 5 4 0.94 10 0.400
223 A 6 5 1.05 12 0.417
224 A 9 8 0.90 12 0.667
225 A 7 7 1.94 14 0.500
226 A 7 7 1.98 16 0.438
227 A 7 6 1.22 10 0.600
228 A 1 1 1.00 19 0.053
229 A 6 5 0.94 20 0.250
230 A 8 7 1.01 20 0.350
231 A 13 12 0.97 20 0.600
232 A 13 12 0.97 20 0.600
233 A 9 8 1.01 20 0.400
234 A 7 6 0.96 20 0.300

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