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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 [160] had the largest ratio of [.782599999999999962]

# 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 12 0.000
40 N/A 0 0 1.00 10 0.000
41 N/A 0 0 1.00 14 0.000
42 A 5 5 1.00 14 0.357
43 A 7 7 1.00 14 0.500
44 A 11 6 1.00 14 0.429
45 N/A 0 0 1.00 12 0.000
46 N/A 0 0 1.00 10 0.000
47 N/A 0 0 1.00 14 0.000
48 A 6 5 1.00 14 0.357
49 A 8 7 1.00 14 0.500
50 A 13 6 1.00 14 0.429
51 N/A 0 0 1.00 16 0.000
52 N/A 0 0 1.00 16 0.000
53 A 3 3 1.00 14 0.214
54 N/A 0 0 1.00 16 0.000
55 N/A 0 0 1.00 16 0.000
56 A 11 9 1.00 16 0.562
57 A 10 9 1.00 16 0.562
58 A 9 9 1.00 14 0.643
59 A 5 4 1.00 8 0.500
60 A 4 2 1.00 16 0.125
61 A 7 7 1.00 16 0.438
62 A 8 8 1.00 16 0.500
63 A 22 13 1.00 18 0.722
64 A 15 11 1.00 18 0.611
65 A 9 9 1.00 18 0.500
66 A 6 6 1.00 18 0.333
67 A 12 11 1.00 18 0.611
68 A 19 14 1.18 18 0.778
69 A 7 7 1.00 19 0.368
70 A 6 7 1.00 19 0.368
71 A 5 5 1.00 16 0.312
72 A 4 5 1.00 19 0.263
73 A 4 5 1.00 19 0.263
74 A 5 6 1.00 19 0.316
75 A 6 6 1.00 19 0.316
76 A 5 5 1.00 19 0.263
77 A 5 5 1.00 19 0.263
78 A 6 5 1.00 17 0.294
79 A 11 11 1.00 19 0.579
80 A 13 13 1.00 19 0.684
81 A 7 8 1.00 21 0.381
82 A 6 7 1.00 18 0.389
83 A 6 7 1.00 21 0.333
84 A 6 7 1.00 21 0.333
85 A 5 6 1.00 21 0.286
86 A 6 7 1.00 21 0.333
87 A 5 6 1.00 21 0.286
88 A 6 5 1.00 19 0.263
89 A 12 13 1.00 21 0.619
90 A 14 15 1.00 21 0.714
91 A 25 12 1.00 21 0.571
92 A 26 9 1.00 19 0.474
93 A 19 7 1.00 18 0.389
94 A 19 7 1.00 21 0.333
95 A 24 10 1.00 21 0.476
96 A 31 14 1.00 21 0.667
97 A 29 12 1.00 21 0.571
98 A 7 5 1.00 19 0.263
99 A 24 10 1.00 21 0.476
100 A 51 15 1.00 21 0.714
101 A 27 10 1.00 21 0.476
102 A 47 11 1.00 18 0.611
103 A 50 13 1.00 21 0.619
104 A 33 13 1.00 21 0.619
105 A 6 7 1.00 21 0.333
106 A 8 6 1.00 19 0.316
107 A 28 11 1.00 21 0.524
108 A 35 11 1.00 21 0.524
109 A 63 12 1.00 21 0.571
110 A 81 12 1.00 18 0.667
111 A 12 12 1.00 23 0.522
112 A 11 12 1.00 23 0.522
113 A 9 9 1.00 21 0.429
114 N/A 0 0 1.00 23 0.000
115 N/A 0 0 1.00 23 0.000
116 N/A 0 0 1.00 23 0.000
117 N/A 0 0 1.00 20 0.000
118 N/A 0 0 1.00 23 0.000
119 A 11 11 1.00 23 0.478
120 A 12 12 1.00 23 0.522
121 A 12 12 1.00 23 0.522
122 A 10 10 1.00 21 0.476
123 N/A 0 0 1.00 23 0.000
124 N/A 0 0 1.00 23 0.000
125 N/A 0 0 1.00 23 0.000
126 N/A 0 0 1.00 20 0.000
127 N/A 0 0 1.00 23 0.000
128 N/A 0 0 1.00 23 0.000
129 A 12 12 1.00 23 0.522
130 A 13 12 1.00 23 0.522
131 A 11 12 1.00 23 0.522
132 A 10 12 1.00 23 0.522
133 A 9 9 1.00 21 0.429
134 N/A 0 0 1.00 23 0.000
135 N/A 0 0 1.00 23 0.000
136 N/A 0 0 1.00 23 0.000
137 N/A 0 0 1.00 20 0.000
138 A 11 11 1.00 23 0.478
139 A 11 12 1.00 23 0.522
140 A 32 15 1.00 23 0.652
141 A 10 11 1.00 23 0.478
142 A 9 11 1.00 23 0.478
143 A 4 4 1.00 21 0.190
144 N/A 0 0 1.00 23 0.000
145 N/A 0 0 1.00 23 0.000
146 N/A 0 0 1.00 23 0.000
147 N/A 0 0 1.00 23 0.000
148 A 5 5 1.00 20 0.250
149 A 10 11 1.00 23 0.478
150 A 25 14 1.00 23 0.609
151 A 10 11 1.00 23 0.478
152 A 7 8 1.00 23 0.348
153 A 5 5 1.00 21 0.238
154 N/A 0 0 1.00 23 0.000
155 N/A 0 0 1.00 23 0.000
156 N/A 0 0 1.00 23 0.000
157 N/A 0 0 1.00 23 0.000
158 A 10 10 1.00 23 0.435
159 A 10 11 1.00 20 0.550
160 A 26 18 1.00 23 0.783
161 A 6 7 0.97 23 0.304
162 A 6 7 0.95 23 0.304
163 A 5 6 1.15 21 0.286
164 N/A 0 0 1.00 23 0.000
165 N/A 0 0 1.00 23 0.000
166 N/A 0 0 1.00 25 0.000
167 N/A 0 0 1.00 25 0.000
168 N/A 0 0 1.00 25 0.000
169 N/A 0 0 1.00 25 0.000
170 A 16 11 1.00 26 0.423
171 A 13 11 1.00 26 0.423
172 A 8 9 1.07 26 0.346
173 N/A 0 0 1.00 26 0.000
174 N/A 0 0 1.00 26 0.000

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