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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 [32] had the largest ratio of [1.42856999999999990]

# 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 1.06 12 0.583
2 A 4 4 1.09 12 0.333
3 A 7 6 1.03 12 0.500
4 A 3 3 1.06 12 0.250
5 A 6 5 0.98 12 0.417
6 A 2 2 1.00 10 0.200
7 A 1 1 1.00 8 0.125
8 C 10 9 1.73 12 0.750
9 A 2 2 1.00 12 0.167
10 A 5 4 1.26 12 0.333
11 A 5 4 1.09 12 0.333
12 A 6 5 1.27 12 0.417
13 A 5 4 1.05 12 0.333
14 A 7 6 1.28 12 0.500
15 A 13 12 1.09 14 0.857
16 C 12 11 1.05 14 0.786
17 A 10 9 1.20 12 0.750
18 C 8 7 1.07 10 0.700
19 C 10 9 1.19 14 0.643
20 C 10 9 1.29 14 0.643
21 A 7 6 1.01 14 0.429
22 C 12 11 1.21 14 0.786
23 A 10 9 1.05 14 0.643
24 C 19 18 1.06 14 1.286
25 C 14 13 1.04 14 0.929
26 C 14 13 1.09 12 1.083
27 C 9 8 0.99 10 0.800
28 C 11 10 1.15 14 0.714
29 C 14 13 1.17 14 0.929
30 A 12 11 1.14 14 0.786
31 C 18 17 1.19 14 1.214
32 A 21 20 1.29 14 1.429
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 9 8 1.02 14 0.571
37 C 12 11 1.05 14 0.786
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 0.99 16 0.875
45 A 13 12 1.05 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 1.00 16 0.125
49 A 8 7 1.08 16 0.438
50 A 9 8 1.20 16 0.500
51 B 21 20 2.31 21 0.952
52 B 20 19 3.01 19 1.000
53 B 13 12 3.06 18 0.667
54 N/A 1 0 1.00 21 0.000
55 N/A 1 0 1.00 21 0.000
56 B 16 15 2.79 18 0.833
57 A 19 18 1.65 21 0.857
58 B 17 16 2.06 21 0.762
59 B 15 14 2.91 19 0.737
60 B 7 6 2.60 18 0.333
61 N/A 1 0 1.00 21 0.000
62 N/A 1 0 1.00 21 0.000
63 B 17 16 2.04 21 0.762
64 B 15 14 2.84 21 0.667
65 B 12 11 3.17 19 0.579
66 B 7 6 4.94 18 0.333
67 N/A 1 0 1.00 21 0.000
68 N/A 1 0 1.00 21 0.000
69 B 26 25 2.81 21 1.190
70 B 26 25 3.73 21 1.190
71 B 22 21 5.30 19 1.105
72 B 16 15 3.68 18 0.833
73 N/A 1 0 1.00 21 0.000
74 N/A 1 0 1.00 21 0.000
75 B 17 16 2.30 18 0.889
76 A 8 7 0.80 19 0.368
77 A 7 6 0.84 19 0.316
78 A 6 5 0.92 16 0.312
79 A 6 5 0.95 19 0.263
80 A 4 4 0.95 19 0.211
81 A 5 5 0.85 19 0.263
82 A 6 6 0.80 19 0.316
83 A 6 5 0.81 19 0.263
84 A 6 5 0.85 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 1.29 19 0.263
88 A 9 8 0.85 21 0.381
89 A 8 7 0.93 18 0.389
90 A 9 8 0.89 21 0.381
91 A 8 7 0.92 21 0.333
92 A 6 6 0.93 21 0.286
93 A 7 7 0.83 21 0.333
94 A 6 5 0.85 21 0.238
95 A 5 4 0.81 19 0.211
96 A 6 5 1.17 21 0.238
97 A 6 5 1.22 21 0.238
98 A 4 3 1.10 21 0.143
99 A 4 3 1.14 19 0.158
100 A 4 3 1.10 18 0.167
101 A 4 3 1.12 21 0.143
102 A 4 3 1.10 21 0.143
103 A 4 3 1.12 21 0.143
104 A 4 3 1.12 21 0.143
105 A 7 6 0.90 19 0.316
106 A 4 3 1.11 21 0.143
107 A 4 3 1.08 21 0.143
108 A 4 3 1.08 21 0.143
109 A 4 3 1.08 18 0.167
110 A 4 3 1.08 21 0.143
111 A 4 3 1.10 21 0.143
112 A 7 6 0.92 21 0.286
113 A 9 8 0.99 19 0.421
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 0.91 23 0.609
119 A 13 12 0.90 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 9 9 0.87 23 0.391
127 A 10 10 0.85 23 0.435
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 10 10 0.85 23 0.435
137 A 11 11 0.84 23 0.478
138 A 13 12 0.91 23 0.522
139 A 11 10 0.91 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 9 9 0.91 23 0.391
146 A 9 9 0.87 23 0.391
147 A 11 10 0.92 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 3 3 1.00 20 0.150
155 A 9 9 0.91 23 0.391
156 A 11 10 0.90 23 0.435
157 A 8 7 0.91 23 0.304
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 7 7 0.81 23 0.304
164 A 5 5 0.97 20 0.250
165 A 8 8 0.92 23 0.348
166 A 7 7 0.92 23 0.304
167 A 5 5 0.95 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 0.58 26 0.269
175 A 10 9 0.59 26 0.346
176 A 9 8 0.78 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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