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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 [27] had the largest ratio of [.684211000000000014]

# 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 2 2 1.00 17 0.118
2 A 2 2 1.00 17 0.118
3 A 2 2 1.00 17 0.118
4 A 2 2 1.00 15 0.133
5 A 10 9 1.34 17 0.529
6 A 10 9 1.33 17 0.529
7 A 11 10 1.27 17 0.588
8 A 2 2 1.00 19 0.105
9 A 2 2 1.00 19 0.105
10 A 2 2 1.00 19 0.105
11 A 2 2 1.00 17 0.118
12 A 2 2 1.32 19 0.105
13 A 2 2 1.30 19 0.105
14 A 11 10 1.15 19 0.526
15 A 2 2 1.23 19 0.105
16 A 2 2 1.27 19 0.105
17 A 2 2 1.32 19 0.105
18 A 10 9 1.34 17 0.529
19 A 10 9 1.30 19 0.474
20 A 11 10 1.27 19 0.526
21 A 2 2 1.21 19 0.105
22 A 2 2 1.24 19 0.105
23 A 2 2 1.28 19 0.105
24 A 2 2 1.30 19 0.105
25 A 10 9 1.33 17 0.529
26 A 12 11 1.27 19 0.579
27 A 14 13 1.21 19 0.684
28 A 4 4 0.99 21 0.190
29 A 3 3 0.97 19 0.158
30 A 8 8 1.29 21 0.381
31 A 10 10 1.44 21 0.476
32 A 3 3 1.07 21 0.143
33 A 2 2 1.00 19 0.105
34 A 6 6 1.38 21 0.286
35 A 9 9 1.41 21 0.429
36 A 4 4 1.20 21 0.190
37 A 3 3 1.14 21 0.143
38 A 2 2 1.00 19 0.105
39 A 10 10 1.48 21 0.476
40 A 11 11 1.37 21 0.524
41 A 1 1 1.00 15 0.067
42 A 9 9 1.01 23 0.391
43 A 8 8 0.98 23 0.348
44 A 7 7 0.97 23 0.304
45 A 4 4 1.00 23 0.174
46 A 8 8 0.96 23 0.348
47 A 9 9 1.02 23 0.391
48 A 11 11 1.45 22 0.500
49 A 9 9 1.31 22 0.409
50 A 7 7 1.41 22 0.318
51 A 11 11 1.52 22 0.500
52 A 13 13 1.43 22 0.591
53 A 11 11 0.99 23 0.478
54 A 10 10 0.98 23 0.435
55 A 9 9 0.97 23 0.391
56 A 9 9 0.98 23 0.391
57 A 9 9 0.92 23 0.391
58 A 11 11 0.96 23 0.478
59 A 13 13 1.00 23 0.565
60 A 5 4 0.98 25 0.160
61 A 1 1 1.00 25 0.040
62 C 3 3 0.64 24 0.125
63 A 5 5 1.12 21 0.238
64 A 3 3 1.00 19 0.158
65 A 2 2 1.00 21 0.095
66 A 2 2 1.00 21 0.095
67 A 5 5 1.12 21 0.238
68 A 3 3 1.00 19 0.158
69 A 2 2 1.00 21 0.095
70 A 2 2 1.00 21 0.095
71 A 5 5 1.15 21 0.238
72 A 3 3 1.19 19 0.158
73 A 2 2 1.00 21 0.095
74 A 2 2 1.00 21 0.095
75 A 5 5 1.15 21 0.238
76 A 3 3 1.12 19 0.158
77 A 2 2 1.00 21 0.095
78 A 2 2 1.00 21 0.095
79 A 7 6 0.93 19 0.316
80 A 6 5 0.99 19 0.263
81 A 6 5 1.05 19 0.263
82 A 2 2 0.77 19 0.105
83 A 3 3 0.97 19 0.158
84 A 4 4 0.95 19 0.211
85 A 8 7 0.93 19 0.368
86 A 7 6 0.97 19 0.316
87 A 6 5 1.00 19 0.263
88 A 6 5 1.00 19 0.263
89 A 7 6 1.00 19 0.316
90 A 8 7 0.98 19 0.368
91 A 8 7 0.89 21 0.333
92 A 7 6 0.97 21 0.286
93 A 8 7 1.14 21 0.333
94 A 7 6 1.13 21 0.286
95 A 3 3 0.72 21 0.143
96 A 4 4 0.93 21 0.190
97 A 9 8 0.89 21 0.381
98 A 8 7 0.97 21 0.333
99 A 7 6 1.08 21 0.286
100 A 7 6 1.16 21 0.286
101 A 7 6 1.10 21 0.286
102 A 8 7 0.97 21 0.333
103 A 12 11 1.04 21 0.524
104 A 10 9 1.05 21 0.429
105 A 5 4 1.00 21 0.190
106 A 6 5 1.09 21 0.238
107 A 9 8 1.14 21 0.381
108 A 11 10 1.20 21 0.476
109 A 14 13 0.91 21 0.619
110 A 11 10 0.87 21 0.476
111 A 5 4 0.85 21 0.190
112 A 10 9 0.87 21 0.429
113 A 12 11 0.94 21 0.524
114 A 14 13 1.00 21 0.619
115 A 13 12 1.02 21 0.571
116 A 11 10 1.06 21 0.476
117 A 6 5 1.05 21 0.238
118 A 6 5 1.06 21 0.238
119 A 8 7 1.07 21 0.333
120 A 10 9 1.11 21 0.429
121 A 13 12 0.88 21 0.571
122 A 11 10 0.88 21 0.476
123 A 12 11 0.87 21 0.524
124 A 11 10 0.91 21 0.476
125 A 13 12 0.96 21 0.571
126 A 5 4 1.00 17 0.235
127 A 5 4 1.00 26 0.154
128 A 3 3 1.00 19 0.158
129 A 7 7 1.02 19 0.368
130 A 5 5 1.01 19 0.263
131 A 3 3 1.00 17 0.176
132 A 2 2 1.00 9 0.222
133 A 2 2 1.00 19 0.105
134 A 2 2 1.00 19 0.105

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