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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 [52] had the largest ratio of [1.15789000000000009]

# 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 8 7 1.07 12 0.583
2 A 4 4 1.09 12 0.333
3 A 7 6 1.04 12 0.500
4 A 3 3 1.06 12 0.250
5 A 6 5 1.00 12 0.417
6 A 2 2 1.00 10 0.200
7 A 1 1 1.00 8 0.125
8 A 10 9 1.36 12 0.750
9 A 2 2 1.00 12 0.167
10 A 5 4 1.25 12 0.333
11 A 5 4 1.08 12 0.333
12 A 6 5 1.26 12 0.417
13 A 5 4 1.05 12 0.333
14 A 7 6 1.27 12 0.500
15 A 10 9 1.08 14 0.643
16 A 9 8 0.96 14 0.571
17 A 8 7 1.18 12 0.583
18 A 7 6 0.96 10 0.600
19 A 10 9 1.15 14 0.643
20 A 9 8 1.14 14 0.571
21 A 6 5 1.18 14 0.357
22 A 9 8 1.10 14 0.571
23 A 8 7 1.15 14 0.500
24 A 16 15 1.04 14 1.071
25 A 11 10 0.97 14 0.714
26 A 12 11 1.06 12 0.917
27 A 8 7 0.95 10 0.700
28 A 11 10 1.14 14 0.714
29 A 12 11 1.08 14 0.786
30 A 9 8 1.14 14 0.571
31 A 14 13 1.11 14 0.929
32 A 15 14 1.29 14 1.000
33 N/A 1 0 1.00 12 0.000
34 N/A 1 0 1.00 10 0.000
35 N/A 1 0 1.00 14 0.000
36 A 7 6 0.98 14 0.429
37 A 9 8 0.94 14 0.571
38 A 4 3 0.94 14 0.214
39 N/A 1 0 1.00 16 0.000
40 N/A 1 0 1.00 16 0.000
41 A 4 3 1.00 14 0.214
42 N/A 1 0 1.00 16 0.000
43 N/A 1 0 1.00 16 0.000
44 A 15 14 1.01 16 0.875
45 A 13 12 1.06 16 0.750
46 A 12 11 1.05 14 0.786
47 A 1 1 1.00 8 0.125
48 A 2 2 0.99 16 0.125
49 A 8 7 1.08 16 0.438
50 A 9 8 1.16 16 0.500
51 A 24 23 1.16 21 1.095
52 A 23 22 1.21 19 1.158
53 A 16 15 1.11 18 0.833
54 N/A 1 0 1.00 21 0.000
55 N/A 1 0 1.00 21 0.000
56 A 18 17 1.06 18 0.944
57 A 16 15 0.99 21 0.714
58 A 14 13 0.99 21 0.619
59 A 11 10 0.80 19 0.526
60 A 4 4 1.12 18 0.222
61 N/A 1 0 1.00 21 0.000
62 N/A 1 0 1.00 21 0.000
63 A 16 15 0.89 21 0.714
64 A 14 13 0.86 21 0.619
65 A 12 11 0.95 19 0.579
66 A 8 7 1.15 18 0.389
67 N/A 1 0 1.00 21 0.000
68 N/A 1 0 1.00 21 0.000
69 A 23 22 1.21 21 1.048
70 A 23 22 1.21 21 1.048
71 A 21 20 1.38 19 1.053
72 A 16 15 1.07 18 0.833
73 N/A 1 0 1.00 21 0.000
74 N/A 1 0 1.00 21 0.000
75 A 20 19 1.04 18 1.056
76 A 8 7 0.81 19 0.368
77 A 7 6 0.84 19 0.316
78 A 6 5 0.93 16 0.312
79 A 6 5 0.97 19 0.263
80 A 4 4 0.96 19 0.211
81 A 5 5 0.86 19 0.263
82 A 6 6 0.81 19 0.316
83 A 6 5 0.82 19 0.263
84 A 6 5 0.86 19 0.263
85 A 5 4 0.84 17 0.235
86 A 6 5 1.23 19 0.263
87 A 6 5 1.28 19 0.263
88 A 9 8 0.85 21 0.381
89 A 7 6 0.94 18 0.333
90 A 9 8 0.90 21 0.381
91 A 7 6 0.94 21 0.286
92 A 5 5 0.93 21 0.238
93 A 6 6 0.83 21 0.286
94 A 6 5 0.86 21 0.238
95 A 5 4 0.82 19 0.211
96 A 6 5 1.17 21 0.238
97 A 6 5 1.21 21 0.238
98 A 4 3 1.09 21 0.143
99 A 4 3 1.12 19 0.158
100 A 4 3 1.09 18 0.167
101 A 4 3 1.11 21 0.143
102 A 4 3 1.09 21 0.143
103 A 4 3 1.11 21 0.143
104 A 4 3 1.10 21 0.143
105 A 6 5 0.88 19 0.263
106 A 4 3 1.10 21 0.143
107 A 4 3 1.07 21 0.143
108 A 4 3 1.07 21 0.143
109 A 4 3 1.07 18 0.167
110 A 4 3 1.07 21 0.143
111 A 4 3 1.09 21 0.143
112 A 7 6 0.92 21 0.286
113 A 8 7 0.98 19 0.368
114 A 4 3 1.09 21 0.143
115 A 4 3 1.06 21 0.143
116 A 4 3 1.06 21 0.143
117 A 4 3 1.06 18 0.167
118 A 15 14 0.92 23 0.609
119 A 13 12 0.91 23 0.522
120 A 10 9 0.92 21 0.429
121 N/A 1 0 1.00 23 0.000
122 N/A 1 0 1.00 23 0.000
123 N/A 1 0 1.00 23 0.000
124 N/A 1 0 1.00 20 0.000
125 N/A 1 0 1.00 23 0.000
126 A 13 13 0.92 23 0.565
127 A 15 15 0.91 23 0.652
128 A 15 14 0.91 23 0.609
129 A 12 11 0.92 21 0.524
130 N/A 1 0 1.00 23 0.000
131 N/A 1 0 1.00 23 0.000
132 N/A 1 0 1.00 23 0.000
133 N/A 1 0 1.00 20 0.000
134 N/A 1 0 1.00 23 0.000
135 N/A 1 0 1.00 23 0.000
136 A 15 15 0.92 23 0.652
137 A 17 17 0.91 23 0.739
138 A 13 12 0.92 23 0.522
139 A 11 10 0.92 23 0.435
140 A 9 8 0.97 21 0.381
141 N/A 1 0 1.00 23 0.000
142 N/A 1 0 1.00 23 0.000
143 N/A 1 0 1.00 23 0.000
144 N/A 1 0 1.00 20 0.000
145 A 12 12 0.95 23 0.522
146 A 13 13 0.92 23 0.565
147 A 11 10 0.93 23 0.435
148 A 9 8 0.97 23 0.348
149 A 5 4 1.00 21 0.190
150 N/A 1 0 1.00 23 0.000
151 N/A 1 0 1.00 23 0.000
152 N/A 1 0 1.00 23 0.000
153 N/A 1 0 1.00 23 0.000
154 A 5 5 1.00 20 0.250
155 A 12 12 0.94 23 0.522
156 A 11 10 0.90 23 0.435
157 A 9 8 0.91 23 0.348
158 A 6 5 0.91 21 0.238
159 N/A 1 0 1.00 23 0.000
160 N/A 1 0 1.00 23 0.000
161 N/A 1 0 1.00 23 0.000
162 N/A 1 0 1.00 23 0.000
163 A 10 10 0.92 23 0.435
164 A 11 11 0.92 20 0.550
165 A 6 6 0.92 23 0.261
166 A 6 6 0.93 23 0.261
167 A 5 5 0.94 21 0.238
168 N/A 1 0 1.00 23 0.000
169 N/A 1 0 1.00 23 0.000
170 N/A 1 0 1.00 25 0.000
171 N/A 1 0 1.00 25 0.000
172 N/A 1 0 1.00 25 0.000
173 N/A 1 0 1.00 25 0.000
174 A 8 7 0.57 26 0.269
175 A 10 9 0.58 26 0.346
176 A 9 8 0.80 26 0.308
177 N/A 1 0 1.00 26 0.000
178 N/A 1 0 1.00 26 0.000

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