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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 [8] had the largest ratio of [.933332999999999968]

# 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 9 8 0.97 15 0.533
2 A 12 11 0.96 17 0.647
3 A 2 2 1.00 17 0.118
4 A 2 2 1.00 17 0.118
5 A 11 10 1.01 15 0.667
6 A 10 9 1.09 13 0.692
7 A 13 12 1.05 15 0.800
8 A 15 14 1.08 15 0.933
9 A 8 7 0.96 16 0.438
10 A 4 3 1.00 11 0.273
11 A 4 3 1.00 15 0.200
12 A 4 3 1.00 19 0.158
13 A 4 3 1.00 21 0.143
14 A 4 4 1.00 13 0.308
15 A 3 3 1.00 13 0.231
16 A 5 5 1.00 20 0.250
17 A 4 4 1.00 20 0.200
18 A 8 7 1.02 15 0.467
19 A 4 3 1.00 19 0.158
20 A 4 3 1.00 21 0.143
21 A 4 3 0.90 31 0.097
22 A 4 3 0.90 36 0.083
23 A 2 2 1.00 22 0.091
24 A 2 2 1.00 22 0.091
25 A 2 2 1.00 22 0.091
26 A 1 1 1.00 35 0.029
27 A 1 1 1.00 33 0.030
28 A 1 1 1.00 36 0.028
29 A 13 12 1.02 19 0.632
30 A 11 10 0.97 18 0.556
31 A 5 4 1.00 27 0.148
32 A 5 4 1.00 28 0.143
33 A 5 4 1.00 24 0.167
34 A 5 4 0.91 24 0.167
35 A 8 7 1.15 13 0.538
36 A 2 2 1.00 31 0.065
37 A 2 2 1.00 42 0.048
38 A 3 3 1.00 20 0.150
39 A 7 6 1.09 20 0.300
40 A 2 2 1.00 16 0.125
41 A 6 5 1.00 20 0.250
42 A 4 4 1.00 18 0.222
43 A 2 2 1.00 18 0.111
44 A 2 2 1.00 30 0.067
45 A 2 2 1.00 30 0.067
46 A 2 2 1.00 28 0.071
47 A 2 2 1.00 30 0.067
48 A 10 9 0.97 30 0.300
49 A 12 11 1.01 30 0.367
50 A 3 3 1.00 17 0.176
51 A 3 3 1.00 19 0.158
52 A 10 10 1.02 32 0.312
53 A 8 8 1.01 32 0.250
54 A 6 6 1.01 32 0.188
55 A 4 4 1.01 32 0.125
56 A 6 6 1.01 32 0.188
57 A 8 8 1.02 32 0.250
58 A 10 10 1.03 32 0.312
59 A 9 9 1.01 32 0.281
60 A 7 7 1.02 32 0.219
61 A 7 7 1.01 32 0.219
62 A 9 9 1.02 32 0.281
63 A 3 3 1.00 18 0.167
64 A 3 3 1.00 22 0.136
65 A 1 1 1.00 20 0.050
66 A 1 1 1.00 20 0.050
67 A 3 3 1.00 33 0.091
68 A 3 3 1.00 35 0.086
69 A 1 1 1.00 36 0.028
70 A 1 1 1.00 36 0.028
71 A 3 3 0.99 30 0.100
72 A 3 3 0.99 32 0.094
73 A 1 1 1.00 33 0.030
74 A 1 1 1.00 33 0.030
75 A 1 1 1.00 20 0.050
76 A 1 1 1.00 24 0.042
77 A 3 3 1.00 22 0.136
78 A 3 3 1.00 22 0.136
79 A 1 1 1.00 20 0.050
80 A 1 1 1.00 20 0.050
81 A 3 3 1.00 18 0.167
82 A 3 3 1.00 22 0.136
83 A 1 1 1.00 35 0.029
84 A 1 1 1.00 37 0.027
85 A 3 3 1.00 38 0.079
86 A 3 3 1.00 38 0.079
87 A 1 1 1.00 32 0.031
88 A 1 1 1.00 34 0.029
89 A 3 3 0.99 35 0.086
90 A 3 3 0.99 35 0.086
91 A 3 3 1.01 17 0.176
92 A 3 3 1.01 18 0.167
93 A 3 3 1.01 19 0.158
94 A 3 3 1.01 20 0.150
95 A 3 3 1.00 15 0.200
96 A 3 3 1.00 17 0.176
97 A 3 3 1.01 15 0.200
98 A 3 3 1.00 17 0.176
99 A 6 6 0.98 22 0.273
100 A 2 2 1.35 22 0.091
101 A 3 3 1.00 22 0.136
102 A 4 4 1.08 22 0.182
103 A 5 5 0.97 22 0.227
104 A 6 6 1.11 22 0.273
105 A 7 7 1.08 22 0.318
106 A 8 8 1.18 22 0.364
107 A 8 8 0.95 27 0.296
108 A 2 2 1.31 27 0.074
109 A 5 5 0.99 27 0.185
110 A 6 6 1.09 27 0.222
111 A 7 7 1.00 27 0.259
112 A 6 6 1.05 27 0.222
113 A 7 7 1.03 27 0.259
114 A 8 8 1.12 27 0.296
115 A 2 2 1.07 25 0.080

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