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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 [69] had the largest ratio of [.857099999999999973]

# 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 7 5 1.00 12 0.417
2 A 4 3 1.00 12 0.250
3 A 6 5 1.00 12 0.417
4 A 3 3 1.00 12 0.250
5 A 5 5 1.00 12 0.417
6 A 2 2 1.00 10 0.200
7 A 5 4 1.00 8 0.500
8 A 6 6 1.00 12 0.500
9 A 2 2 1.00 12 0.167
10 A 4 4 1.00 12 0.333
11 A 4 3 1.00 12 0.250
12 A 5 4 1.00 12 0.333
13 A 4 3 1.00 12 0.250
14 A 6 4 1.00 12 0.333
15 A 5 5 1.00 14 0.357
16 A 8 6 1.00 14 0.429
17 A 4 4 1.00 12 0.333
18 A 7 5 1.00 10 0.500
19 A 6 6 1.00 14 0.429
20 A 4 3 1.00 14 0.214
21 A 4 3 1.00 14 0.214
22 A 5 5 1.00 14 0.357
23 A 5 3 1.00 14 0.214
24 A 10 10 1.00 14 0.714
25 A 11 8 1.00 14 0.571
26 A 7 7 1.00 12 0.583
27 A 9 6 1.00 10 0.600
28 A 7 7 1.00 14 0.500
29 A 5 3 1.00 14 0.214
30 A 6 6 1.00 14 0.429
31 A 8 6 1.00 14 0.429
32 A 10 6 1.00 14 0.429
33 N/A 0 0 1.00 12 0.000
34 N/A 0 0 1.00 10 0.000
35 N/A 0 0 1.00 14 0.000
36 A 4 4 1.00 14 0.286
37 A 6 6 1.00 14 0.429
38 A 9 5 1.00 14 0.357
39 N/A 0 0 1.00 16 0.000
40 N/A 0 0 1.00 16 0.000
41 A 3 3 1.00 14 0.214
42 N/A 0 0 1.00 16 0.000
43 N/A 0 0 1.00 16 0.000
44 A 11 9 1.00 16 0.562
45 A 10 9 1.00 16 0.562
46 A 9 9 1.00 14 0.643
47 A 5 4 1.00 8 0.500
48 A 4 2 1.00 16 0.125
49 A 7 7 1.00 16 0.438
50 A 8 8 1.00 16 0.500
51 A 31 16 1.40 21 0.762
52 A 24 15 1.24 19 0.790
53 A 15 11 1.00 18 0.611
54 N/A 0 0 1.00 21 0.000
55 N/A 0 0 1.00 21 0.000
56 A 22 13 1.00 18 0.722
57 A 27 17 1.00 21 0.810
58 A 20 15 1.00 21 0.714
59 A 14 13 1.00 19 0.684
60 A 9 9 1.00 18 0.500
61 N/A 0 0 1.00 21 0.000
62 N/A 0 0 1.00 21 0.000
63 A 23 15 1.00 21 0.714
64 A 16 13 1.00 21 0.619
65 A 11 11 1.00 19 0.579
66 A 6 6 1.00 18 0.333
67 N/A 0 0 1.00 21 0.000
68 N/A 0 0 1.00 21 0.000
69 A 31 18 1.00 21 0.857
70 A 25 17 1.00 21 0.810
71 A 19 14 1.00 19 0.737
72 A 12 11 1.00 18 0.611
73 N/A 0 0 1.00 21 0.000
74 N/A 0 0 1.00 21 0.000
75 A 19 14 1.18 18 0.778
76 A 7 7 1.00 19 0.368
77 A 6 7 1.00 19 0.368
78 A 5 5 1.00 16 0.312
79 A 4 5 1.00 19 0.263
80 A 4 5 1.00 19 0.263
81 A 5 6 1.00 19 0.316
82 A 6 6 1.00 19 0.316
83 A 5 5 1.00 19 0.263
84 A 5 5 1.00 19 0.263
85 A 6 5 1.00 17 0.294
86 A 11 11 1.00 19 0.579
87 A 13 13 1.00 19 0.684
88 A 7 8 1.00 21 0.381
89 A 6 7 1.00 18 0.389
90 A 6 7 1.00 21 0.333
91 A 6 7 1.00 21 0.333
92 A 5 6 1.00 21 0.286
93 A 6 7 1.00 21 0.333
94 A 5 6 1.00 21 0.286
95 A 6 5 1.00 19 0.263
96 A 12 13 1.00 21 0.619
97 A 14 15 1.00 21 0.714
98 A 25 12 1.00 21 0.571
99 A 26 9 1.00 19 0.474
100 A 19 7 1.00 18 0.389
101 A 19 7 1.00 21 0.333
102 A 24 10 1.00 21 0.476
103 A 31 14 1.00 21 0.667
104 A 29 12 0.99 21 0.571
105 A 7 5 0.98 19 0.263
106 A 24 10 1.00 21 0.476
107 A 51 15 1.00 21 0.714
108 A 27 10 1.00 21 0.476
109 A 47 11 1.00 18 0.611
110 A 50 13 1.00 21 0.619
111 A 33 13 1.00 21 0.619
112 A 6 7 1.00 21 0.333
113 A 8 6 1.00 19 0.316
114 A 28 11 1.00 21 0.524
115 A 35 11 1.00 21 0.524
116 A 63 12 1.00 21 0.571
117 A 81 12 1.00 18 0.667
118 A 12 12 1.00 23 0.522
119 A 11 12 1.00 23 0.522
120 A 9 9 1.00 21 0.429
121 N/A 0 0 1.00 23 0.000
122 N/A 0 0 1.00 23 0.000
123 N/A 0 0 1.00 23 0.000
124 N/A 0 0 1.00 20 0.000
125 N/A 0 0 1.00 23 0.000
126 A 11 11 1.00 23 0.478
127 A 12 12 1.00 23 0.522
128 A 12 12 1.00 23 0.522
129 A 10 10 1.00 21 0.476
130 N/A 0 0 1.00 23 0.000
131 N/A 0 0 1.00 23 0.000
132 N/A 0 0 1.00 23 0.000
133 N/A 0 0 1.00 20 0.000
134 N/A 0 0 1.00 23 0.000
135 N/A 0 0 1.00 23 0.000
136 A 12 12 1.00 23 0.522
137 A 13 12 1.00 23 0.522
138 A 11 12 1.00 23 0.522
139 A 10 12 1.00 23 0.522
140 A 9 9 1.00 21 0.429
141 N/A 0 0 1.00 23 0.000
142 N/A 0 0 1.00 23 0.000
143 N/A 0 0 1.00 23 0.000
144 N/A 0 0 1.00 20 0.000
145 A 11 11 1.00 23 0.478
146 A 11 12 1.00 23 0.522
147 A 10 11 1.00 23 0.478
148 A 9 11 1.00 23 0.478
149 A 4 4 1.00 21 0.190
150 N/A 0 0 1.00 23 0.000
151 N/A 0 0 1.00 23 0.000
152 N/A 0 0 1.00 23 0.000
153 N/A 0 0 1.00 23 0.000
154 A 5 5 1.00 20 0.250
155 A 10 11 1.00 23 0.478
156 A 10 11 1.00 23 0.478
157 A 7 8 1.00 23 0.348
158 A 5 5 1.00 21 0.238
159 N/A 0 0 1.00 23 0.000
160 N/A 0 0 1.00 23 0.000
161 N/A 0 0 1.00 23 0.000
162 N/A 0 0 1.00 23 0.000
163 A 10 10 1.00 23 0.435
164 A 10 11 1.00 20 0.550
165 A 6 7 0.97 23 0.304
166 A 6 7 0.95 23 0.304
167 A 5 6 0.94 21 0.286
168 N/A 0 0 1.00 23 0.000
169 N/A 0 0 1.00 23 0.000
170 N/A 0 0 1.00 25 0.000
171 N/A 0 0 1.00 25 0.000
172 N/A 0 0 1.00 25 0.000
173 N/A 0 0 1.00 25 0.000
174 A 16 11 1.00 26 0.423
175 A 13 11 1.00 26 0.423
176 A 8 9 1.07 26 0.346
177 N/A 0 0 1.00 26 0.000
178 N/A 0 0 1.00 26 0.000

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