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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 [74] had the largest ratio of [.818181999999999965]

# 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 23 0.087
2 A 2 2 1.00 23 0.087
3 A 2 2 1.00 21 0.095
4 A 2 2 1.00 23 0.087
5 A 4 4 1.16 23 0.174
6 A 6 6 1.16 23 0.261
7 A 2 2 1.00 22 0.091
8 A 2 2 1.00 22 0.091
9 A 2 2 1.00 20 0.100
10 A 2 2 1.36 22 0.091
11 A 12 11 1.27 22 0.500
12 A 14 13 1.25 22 0.591
13 A 8 8 1.32 21 0.381
14 A 8 8 1.32 19 0.421
15 A 8 8 1.32 26 0.308
16 B 7 7 5.86 19 0.368
17 B 6 6 5.10 17 0.353
18 B 6 6 4.98 22 0.273
19 A 2 2 1.00 17 0.118
20 A 2 2 1.08 22 0.091
21 A 2 2 1.11 27 0.074
22 A 2 2 1.00 23 0.087
23 A 2 2 1.00 23 0.087
24 A 2 2 1.00 21 0.095
25 A 6 6 0.95 23 0.261
26 A 5 5 0.96 23 0.217
27 A 5 5 0.99 23 0.217
28 A 2 2 1.00 22 0.091
29 A 2 2 1.00 22 0.091
30 A 2 2 1.00 20 0.100
31 A 12 11 1.21 22 0.500
32 A 12 11 1.19 22 0.500
33 A 12 11 1.18 22 0.500
34 A 3 3 1.00 17 0.176
35 A 4 4 1.03 22 0.182
36 A 2 2 0.75 27 0.074
37 A 2 2 1.00 16 0.125
38 A 2 2 1.31 15 0.133
39 A 4 4 1.05 16 0.250
40 A 4 4 1.30 15 0.267
41 A 6 6 1.10 16 0.375
42 A 6 6 1.31 15 0.400
43 A 8 8 1.14 16 0.500
44 A 8 8 1.31 15 0.533
45 A 2 2 1.00 15 0.133
46 A 2 2 1.29 13 0.154
47 A 2 2 1.01 21 0.095
48 A 2 2 1.32 20 0.100
49 A 4 4 1.03 21 0.190
50 A 4 4 1.30 20 0.200
51 A 6 6 1.08 21 0.286
52 A 6 6 1.30 20 0.300
53 A 8 8 1.10 21 0.381
54 A 8 8 1.30 20 0.400
55 A 3 3 0.96 11 0.273
56 A 3 3 0.97 12 0.250
57 A 2 2 1.00 15 0.133
58 A 3 3 0.97 14 0.214
59 A 2 2 1.00 17 0.118
60 A 3 3 1.00 19 0.158
61 A 2 2 1.00 20 0.100
62 A 2 2 1.00 14 0.143
63 A 4 4 1.00 17 0.235
64 A 4 4 1.00 19 0.211
65 A 3 3 1.00 20 0.150
66 A 4 4 1.00 21 0.190
67 A 3 3 1.00 22 0.136
68 A 4 4 1.00 24 0.167
69 A 3 3 1.00 25 0.120
70 A 3 3 1.00 25 0.120
71 A 4 4 0.98 26 0.154
72 A 6 6 1.03 26 0.231
73 A 8 8 1.06 26 0.308
74 A 10 9 1.63 11 0.818
75 A 4 3 1.00 12 0.250
76 A 2 2 1.18 15 0.133
77 A 10 9 1.63 14 0.643
78 A 9 8 1.38 17 0.471
79 A 3 3 1.18 19 0.158
80 A 2 2 1.29 20 0.100
81 A 2 2 1.00 14 0.143
82 A 2 2 1.20 17 0.118
83 A 6 5 1.03 19 0.263
84 A 2 2 1.16 20 0.100
85 A 3 3 1.20 21 0.143
86 A 2 2 1.32 22 0.091
87 A 3 3 1.16 24 0.125
88 A 2 2 1.27 25 0.080
89 A 2 2 1.00 19 0.105
90 A 2 2 1.00 17 0.118
91 A 2 2 1.00 20 0.100
92 A 2 2 1.30 19 0.105
93 A 2 2 1.00 21 0.095
94 A 2 2 1.00 21 0.095
95 A 2 2 1.00 19 0.105
96 A 2 2 1.00 19 0.105
97 A 2 2 1.00 21 0.095
98 A 2 2 1.00 21 0.095
99 A 2 2 1.00 21 0.095
100 A 2 2 1.00 31 0.065
101 A 3 3 1.05 31 0.097
102 A 5 5 1.00 31 0.161
103 A 7 7 1.01 31 0.226
104 A 3 3 1.00 30 0.100
105 A 3 3 1.00 30 0.100
106 A 2 2 1.00 28 0.071
107 A 2 2 1.29 30 0.067
108 A 4 4 1.30 30 0.133
109 A 6 6 1.22 30 0.200
110 A 8 8 1.21 30 0.267
111 A 2 2 1.00 17 0.118
112 A 2 2 1.00 20 0.100
113 A 2 2 1.00 18 0.111
114 A 2 2 1.00 19 0.105
115 A 2 2 1.00 22 0.091
116 A 1 1 1.00 23 0.043
117 A 1 1 1.07 26 0.038
118 A 1 1 0.74 28 0.036
119 A 1 1 0.81 31 0.032
120 A 2 2 0.99 42 0.048
121 A 1 1 1.05 37 0.027
122 A 1 1 0.71 44 0.023

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