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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 [68] had the largest ratio of [1.05556000000000005]

# 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 8 7 1.36 12 0.583
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 1.07 14 0.643
16 A 9 8 0.95 14 0.571
17 A 8 7 1.14 12 0.583
18 A 7 6 0.95 10 0.600
19 A 8 7 1.15 14 0.500
20 A 9 8 1.12 14 0.571
21 A 6 5 1.03 14 0.357
22 A 10 9 1.08 14 0.643
23 A 8 7 1.04 14 0.500
24 A 15 14 1.03 14 1.000
25 A 11 10 0.96 14 0.714
26 A 11 10 1.05 12 0.833
27 A 8 7 0.94 10 0.700
28 A 9 8 1.13 14 0.571
29 A 11 10 1.08 14 0.714
30 A 9 8 1.09 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 1.00 14 0.429
37 A 9 8 0.94 14 0.571
38 A 4 3 0.93 14 0.214
39 N/A 1 0 1.00 12 0.000
40 N/A 1 0 1.00 10 0.000
41 N/A 1 0 1.00 14 0.000
42 A 9 8 1.05 14 0.571
43 A 11 10 1.02 14 0.714
44 A 4 3 0.92 14 0.214
45 N/A 1 0 1.00 12 0.000
46 N/A 1 0 1.00 10 0.000
47 N/A 1 0 1.00 14 0.000
48 A 12 11 1.09 14 0.786
49 A 14 13 1.04 14 0.929
50 A 4 3 0.93 14 0.214
51 N/A 1 0 1.00 16 0.000
52 N/A 1 0 1.00 16 0.000
53 A 4 3 1.00 14 0.214
54 N/A 1 0 1.00 16 0.000
55 N/A 1 0 1.00 16 0.000
56 A 15 14 1.01 16 0.875
57 A 13 12 1.05 16 0.750
58 A 12 11 1.04 14 0.786
59 A 1 1 1.00 8 0.125
60 A 2 2 1.00 16 0.125
61 A 8 7 1.07 16 0.438
62 A 9 8 1.16 16 0.500
63 A 18 17 1.06 18 0.944
64 A 16 15 1.11 18 0.833
65 A 4 4 1.12 18 0.222
66 A 8 7 1.15 18 0.389
67 A 16 15 1.07 18 0.833
68 A 20 19 0.96 18 1.056
69 A 8 7 0.81 19 0.368
70 A 7 6 0.84 19 0.316
71 A 6 5 0.93 16 0.312
72 A 6 5 0.95 19 0.263
73 A 4 4 0.96 19 0.211
74 A 5 5 0.86 19 0.263
75 A 6 6 0.81 19 0.316
76 A 6 5 0.82 19 0.263
77 A 6 5 0.86 19 0.263
78 A 5 4 0.84 17 0.235
79 A 6 5 1.23 19 0.263
80 A 6 5 1.28 19 0.263
81 A 9 8 0.85 21 0.381
82 A 7 6 0.94 18 0.333
83 A 9 8 0.90 21 0.381
84 A 7 6 0.93 21 0.286
85 A 5 5 0.93 21 0.238
86 A 6 6 0.83 21 0.286
87 A 6 5 0.86 21 0.238
88 A 5 4 0.82 19 0.211
89 A 6 5 1.17 21 0.238
90 A 6 5 1.21 21 0.238
91 A 4 3 1.10 21 0.143
92 A 4 3 1.12 19 0.158
93 A 4 3 1.09 18 0.167
94 A 4 3 1.11 21 0.143
95 A 4 3 1.09 21 0.143
96 A 4 3 1.11 21 0.143
97 A 4 3 1.11 21 0.143
98 A 6 5 0.90 19 0.263
99 A 4 3 1.10 21 0.143
100 A 4 3 1.08 21 0.143
101 A 4 3 1.08 21 0.143
102 A 4 3 1.08 18 0.167
103 A 4 3 1.08 21 0.143
104 A 4 3 1.10 21 0.143
105 A 7 6 0.92 21 0.286
106 A 8 7 0.98 19 0.368
107 A 4 3 1.09 21 0.143
108 A 4 3 1.06 21 0.143
109 A 4 3 1.06 21 0.143
110 A 4 3 1.06 18 0.167
111 A 15 14 0.92 23 0.609
112 A 13 12 0.91 23 0.522
113 A 10 9 0.92 21 0.429
114 N/A 1 0 1.00 23 0.000
115 N/A 1 0 1.00 23 0.000
116 N/A 1 0 1.00 23 0.000
117 N/A 1 0 1.00 20 0.000
118 N/A 1 0 1.00 23 0.000
119 A 13 13 0.92 23 0.565
120 A 15 15 0.91 23 0.652
121 A 15 14 0.91 23 0.609
122 A 12 11 0.92 21 0.524
123 N/A 1 0 1.00 23 0.000
124 N/A 1 0 1.00 23 0.000
125 N/A 1 0 1.00 23 0.000
126 N/A 1 0 1.00 20 0.000
127 N/A 1 0 1.00 23 0.000
128 N/A 1 0 1.00 23 0.000
129 A 15 15 0.92 23 0.652
130 A 17 17 0.91 23 0.739
131 A 13 12 0.92 23 0.522
132 A 11 10 0.92 23 0.435
133 A 9 8 0.97 21 0.381
134 N/A 1 0 1.00 23 0.000
135 N/A 1 0 1.00 23 0.000
136 N/A 1 0 1.00 23 0.000
137 N/A 1 0 1.00 20 0.000
138 A 12 12 0.94 23 0.522
139 A 13 13 0.92 23 0.565
140 A 4 4 0.83 23 0.174
141 A 11 10 0.93 23 0.435
142 A 9 8 0.97 23 0.348
143 A 5 4 1.00 21 0.190
144 N/A 1 0 1.00 23 0.000
145 N/A 1 0 1.00 23 0.000
146 N/A 1 0 1.00 23 0.000
147 N/A 1 0 1.00 23 0.000
148 A 5 5 1.00 20 0.250
149 A 12 12 0.94 23 0.522
150 A 4 4 0.84 23 0.174
151 A 11 10 0.90 23 0.435
152 A 9 8 0.91 23 0.348
153 A 6 5 0.91 21 0.238
154 N/A 1 0 1.00 23 0.000
155 N/A 1 0 1.00 23 0.000
156 N/A 1 0 1.00 23 0.000
157 N/A 1 0 1.00 23 0.000
158 A 10 10 0.91 23 0.435
159 A 11 11 0.92 20 0.550
160 A 4 4 0.86 23 0.174
161 A 6 6 0.92 23 0.261
162 A 6 6 0.92 23 0.261
163 A 5 5 1.14 21 0.238
164 N/A 1 0 1.00 23 0.000
165 N/A 1 0 1.00 23 0.000
166 N/A 1 0 1.00 25 0.000
167 N/A 1 0 1.00 25 0.000
168 N/A 1 0 1.00 25 0.000
169 N/A 1 0 1.00 25 0.000
170 A 8 7 0.57 26 0.269
171 A 10 9 0.58 26 0.346
172 A 9 8 0.80 26 0.308
173 N/A 1 0 1.00 26 0.000
174 N/A 1 0 1.00 26 0.000

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