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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 [47] had the largest ratio of [1]

# 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 18 0.111
2 A 2 2 1.00 23 0.087
3 A 2 2 1.00 28 0.071
4 A 2 2 1.00 33 0.061
5 A 2 2 1.00 38 0.053
6 A 2 2 1.00 20 0.100
7 A 2 2 1.00 25 0.080
8 A 2 2 1.00 30 0.067
9 A 2 2 1.00 35 0.057
10 A 8 7 1.11 18 0.389
11 A 8 7 1.08 23 0.304
12 A 7 6 1.09 28 0.214
13 A 7 6 1.08 33 0.182
14 A 7 6 1.03 38 0.158
15 A 12 11 1.03 16 0.688
16 A 12 11 1.04 21 0.524
17 A 13 12 1.05 26 0.462
18 A 9 8 1.01 31 0.258
19 A 7 6 0.99 36 0.167
20 A 8 7 1.01 20 0.350
21 A 8 7 1.00 25 0.280
22 A 9 8 1.01 30 0.267
23 A 9 8 1.01 35 0.229
24 A 7 6 1.00 40 0.150
25 A 7 6 1.00 55 0.109
26 A 10 9 1.12 18 0.500
27 A 10 9 1.10 23 0.391
28 A 9 8 1.07 28 0.286
29 A 9 8 1.06 33 0.242
30 A 11 10 1.03 38 0.263
31 A 14 13 1.06 16 0.812
32 A 14 13 1.08 21 0.619
33 A 13 12 1.08 26 0.462
34 A 13 12 1.07 31 0.387
35 A 14 13 1.07 36 0.361
36 A 11 10 0.96 20 0.500
37 A 11 10 0.97 25 0.400
38 A 10 9 0.97 30 0.300
39 A 10 9 0.98 35 0.257
40 A 11 10 0.98 40 0.250
41 A 12 11 1.02 55 0.200
42 A 12 11 1.12 18 0.611
43 A 12 11 1.10 23 0.478
44 A 11 10 1.10 28 0.357
45 A 11 10 1.09 33 0.303
46 A 13 12 1.01 38 0.316
47 A 17 16 1.09 16 1.000
48 A 17 16 1.08 21 0.762
49 A 16 15 1.07 26 0.577
50 A 16 15 1.06 31 0.484
51 A 17 16 1.06 36 0.444
52 A 14 13 1.04 20 0.650
53 A 14 13 0.97 25 0.520
54 A 13 12 0.97 30 0.400
55 A 13 12 1.02 35 0.343
56 A 14 13 1.01 40 0.325
57 A 14 13 1.02 55 0.236
58 A 12 11 1.01 50 0.220
59 A 17 16 1.05 50 0.320
60 A 2 2 1.00 63 0.032
61 A 2 2 1.00 63 0.032
62 A 2 2 1.00 61 0.033
63 A 2 2 1.00 63 0.032
64 A 9 8 1.00 63 0.127
65 A 12 11 0.97 63 0.175
66 A 15 14 0.97 63 0.222
67 A 2 2 1.00 26 0.077
68 A 3 3 1.00 31 0.097
69 A 3 3 1.00 36 0.083
70 A 3 3 1.00 41 0.073
71 A 3 3 1.00 46 0.065
72 A 3 3 1.00 51 0.059
73 A 3 3 1.00 21 0.143
74 A 3 3 1.00 26 0.115
75 A 3 3 1.00 31 0.097
76 A 3 3 1.00 36 0.083
77 A 3 3 1.00 41 0.073
78 A 3 3 1.00 46 0.065
79 A 3 3 1.00 16 0.188
80 A 3 3 1.00 21 0.143
81 A 3 3 1.00 26 0.115
82 A 3 3 1.00 31 0.097
83 A 3 3 1.00 36 0.083
84 A 3 3 1.00 41 0.073
85 A 3 3 1.00 26 0.115
86 A 3 3 1.00 31 0.097
87 A 3 3 1.00 36 0.083
88 A 3 3 1.00 41 0.073
89 A 3 3 1.00 46 0.065
90 A 3 3 1.00 51 0.059
91 A 3 3 0.98 21 0.143
92 A 7 7 1.06 26 0.269
93 A 7 7 1.05 31 0.226
94 A 3 3 1.00 36 0.083
95 A 3 3 1.00 41 0.073
96 A 3 3 1.00 46 0.065
97 A 3 3 1.00 16 0.188
98 A 3 3 1.00 21 0.143
99 A 3 3 1.00 26 0.115
100 A 3 3 1.00 31 0.097
101 A 3 3 1.00 36 0.083
102 A 3 3 1.00 41 0.073
103 A 15 14 0.97 32 0.438
104 A 12 11 0.99 32 0.344
105 A 10 9 1.01 32 0.281
106 A 9 8 0.97 32 0.250
107 A 13 12 0.96 32 0.375
108 A 1 1 1.00 28 0.036
109 A 6 5 1.00 31 0.161
110 A 6 5 1.00 33 0.152
111 A 5 4 1.00 36 0.111

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