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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 [57] had the largest ratio of [.560000000000000053]

# 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 11 10 1.18 20 0.500
2 A 9 8 1.17 20 0.400
3 A 6 5 1.18 18 0.278
4 A 5 4 1.01 17 0.235
5 A 8 7 1.03 20 0.350
6 A 8 7 1.00 20 0.350
7 A 9 8 1.05 20 0.400
8 A 12 11 1.15 20 0.550
9 A 10 9 1.13 20 0.450
10 A 7 6 1.13 18 0.333
11 A 6 5 1.03 17 0.294
12 A 9 8 1.06 20 0.400
13 A 9 8 1.03 20 0.400
14 A 11 10 0.93 20 0.500
15 A 12 11 1.12 20 0.550
16 A 11 10 1.11 20 0.500
17 A 8 7 1.10 18 0.389
18 A 7 6 1.05 17 0.353
19 A 11 10 1.07 20 0.500
20 A 10 9 1.04 20 0.450
21 A 12 11 1.01 20 0.550
22 A 9 8 1.21 20 0.400
23 A 8 7 1.21 20 0.350
24 A 5 4 1.25 18 0.222
25 A 4 3 1.00 17 0.176
26 A 7 6 1.00 20 0.300
27 A 5 4 1.00 20 0.200
28 A 7 6 1.03 20 0.300
29 A 7 6 1.23 20 0.300
30 A 7 6 1.09 20 0.300
31 A 6 5 1.00 18 0.278
32 A 1 1 1.00 17 0.059
33 A 7 6 1.00 20 0.300
34 A 7 6 1.09 20 0.300
35 A 9 8 1.07 20 0.400
36 A 6 5 1.08 20 0.250
37 A 4 4 1.11 20 0.200
38 A 4 4 0.94 18 0.222
39 A 2 2 1.00 17 0.118
40 A 8 7 1.07 20 0.350
41 A 9 8 1.09 20 0.400
42 A 11 10 1.07 20 0.500
43 A 4 4 1.44 18 0.222
44 A 5 5 1.44 19 0.263
45 A 2 2 1.00 13 0.154
46 A 2 2 1.00 13 0.154
47 A 11 10 1.09 25 0.400
48 A 11 10 1.19 25 0.400
49 A 7 7 1.17 25 0.280
50 A 6 6 1.09 25 0.240
51 A 7 7 1.04 25 0.280
52 A 7 7 1.00 25 0.280
53 A 5 5 1.05 23 0.217
54 A 6 6 0.95 22 0.273
55 A 12 11 1.13 25 0.440
56 A 13 12 1.13 25 0.480
57 A 15 14 1.12 25 0.560
58 A 2 2 1.00 16 0.125
59 A 2 2 1.00 20 0.100
60 A 2 2 1.00 22 0.091
61 A 2 2 1.00 25 0.080
62 A 2 2 1.00 26 0.077
63 A 2 2 1.00 26 0.077
64 A 2 2 1.00 24 0.083
65 A 2 2 1.00 23 0.087
66 A 2 2 1.00 26 0.077
67 A 2 2 1.00 26 0.077
68 A 2 2 1.00 26 0.077
69 A 2 2 1.00 26 0.077
70 A 2 2 1.00 28 0.071
71 A 2 2 1.00 28 0.071
72 A 3 3 1.00 26 0.115
73 A 3 3 1.00 25 0.120
74 A 3 3 1.00 28 0.107
75 A 3 3 1.00 28 0.107
76 A 2 2 1.00 28 0.071
77 A 2 2 1.00 28 0.071
78 A 2 2 1.00 28 0.071
79 A 2 2 1.00 28 0.071
80 A 3 3 1.00 26 0.115
81 A 3 3 1.00 25 0.120
82 A 3 3 1.00 28 0.107
83 A 3 3 1.00 28 0.107
84 A 2 2 1.00 28 0.071
85 A 2 2 1.00 28 0.071
86 A 2 2 1.00 28 0.071
87 A 2 2 1.00 28 0.071
88 A 2 2 1.00 28 0.071
89 A 2 2 1.00 26 0.077
90 A 2 2 1.00 25 0.080
91 A 2 2 1.00 28 0.071
92 A 2 2 1.00 28 0.071
93 A 2 2 1.00 28 0.071
94 A 4 4 1.02 28 0.143
95 A 4 4 1.01 28 0.143
96 A 4 4 0.98 28 0.143
97 A 4 4 1.08 26 0.154
98 A 6 6 1.06 25 0.240
99 A 5 5 1.09 28 0.179
100 A 4 4 1.05 28 0.143
101 A 4 4 1.01 28 0.143
102 A 6 6 1.01 28 0.214
103 A 7 7 1.04 28 0.250
104 A 8 8 1.09 28 0.286
105 A 6 6 1.07 26 0.231
106 A 5 5 1.09 25 0.200
107 A 7 7 1.11 28 0.250
108 A 6 6 1.09 28 0.214
109 A 6 6 1.08 28 0.214
110 A 6 5 1.10 17 0.294
111 A 6 5 1.26 17 0.294
112 A 4 4 1.32 21 0.190
113 A 3 3 1.00 15 0.200
114 A 2 2 1.00 30 0.067
115 A 2 2 1.00 30 0.067
116 A 2 2 1.00 30 0.067
117 A 2 2 1.00 27 0.074
118 A 2 2 1.00 30 0.067
119 A 2 2 1.00 30 0.067
120 A 2 2 1.00 30 0.067
121 A 2 2 1.00 30 0.067
122 A 2 2 1.00 30 0.067
123 A 2 2 1.00 30 0.067
124 A 4 4 1.03 30 0.133
125 A 4 4 1.03 30 0.133
126 A 4 4 1.01 30 0.133
127 A 4 4 1.07 27 0.148
128 A 4 4 1.07 30 0.133
129 A 4 4 1.05 30 0.133
130 A 4 4 1.04 30 0.133
131 A 4 4 1.03 30 0.133
132 A 4 4 1.03 30 0.133
133 A 5 5 1.04 30 0.167
134 A 6 6 1.04 30 0.200
135 A 5 5 1.04 30 0.167
136 A 7 7 1.07 30 0.233
137 A 7 7 1.12 27 0.259
138 A 6 6 1.11 30 0.200
139 A 5 5 1.11 30 0.167
140 A 6 6 1.07 30 0.200
141 A 6 6 1.06 30 0.200
142 A 6 6 1.05 30 0.200
143 A 4 3 1.02 32 0.094
144 A 4 3 1.02 32 0.094
145 A 4 3 1.04 30 0.100
146 A 4 3 1.05 32 0.094
147 A 8 7 1.01 32 0.219
148 A 9 8 1.27 32 0.250
149 A 10 9 1.25 32 0.281
150 A 10 9 1.12 32 0.281
151 A 8 7 0.90 32 0.219
152 A 7 6 0.98 32 0.188
153 A 7 6 1.11 29 0.207
154 A 9 8 1.13 32 0.250
155 A 8 7 1.09 32 0.219
156 A 7 6 1.15 32 0.188
157 A 5 5 1.11 32 0.156
158 A 7 7 0.98 32 0.219
159 A 13 12 0.81 32 0.375
160 A 13 12 0.88 32 0.375
161 A 13 12 1.10 32 0.375
162 A 12 11 1.23 32 0.344
163 A 8 8 1.37 29 0.276
164 A 6 6 1.01 32 0.188
165 A 7 7 0.90 32 0.219
166 A 9 9 0.83 32 0.281
167 A 10 10 0.78 32 0.312
168 A 11 11 0.74 32 0.344
169 A 5 4 1.02 33 0.121
170 A 5 4 1.02 33 0.121
171 A 5 4 1.04 31 0.129
172 A 16 15 1.09 37 0.405
173 A 11 10 1.26 34 0.294
174 A 8 8 1.27 37 0.216

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