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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 [104] had the largest ratio of [1.44443999999999995]

# 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 12 11 1.31 52 0.212
2 A 9 8 1.28 50 0.160
3 F 0 0 N/A 0.000 N/A
4 A 6 6 0.91 105 0.057
5 A 7 6 1.00 179 0.034
6 A 2 2 0.83 107 0.019
7 B 12 11 2.84 231 0.048
8 F 0 0 N/A 0.000 N/A
9 F 0 0 N/A 0.000 N/A
10 F 0 0 N/A 0.000 N/A
11 F 0 0 N/A 0.000 N/A
12 A 2 2 1.04 38 0.053
13 F 0 0 N/A 0.000 N/A
14 F 0 0 N/A 0.000 N/A
15 A 2 2 0.83 33 0.061
16 A 3 3 1.23 30 0.100
17 F 0 0 N/A 0.000 N/A
18 A 10 9 1.08 11 0.818
19 A 6 5 1.13 28 0.179
20 A 5 5 0.85 82 0.061
21 A 3 3 0.98 60 0.050
22 A 10 9 0.91 19 0.474
23 A 5 5 0.87 29 0.172
24 A 4 3 1.01 30 0.100
25 A 3 3 1.00 26 0.115
26 A 3 3 1.00 22 0.136
27 A 9 9 1.11 36 0.250
28 A 2 2 1.45 26 0.077
29 A 2 2 1.00 24 0.083
30 A 3 3 0.99 28 0.107
31 A 12 11 0.94 21 0.524
32 A 3 3 0.98 23 0.130
33 A 5 4 1.05 16 0.250
34 F 0 0 N/A 0.000 N/A
35 F 0 0 N/A 0.000 N/A
36 A 3 2 1.00 34 0.059
37 A 1 1 1.00 67 0.015
38 C 2 2 10.10 90 0.022
39 A 1 1 1.00 67 0.015
40 A 8 8 1.27 122 0.066
41 A 3 3 1.00 46 0.065
42 A 3 3 1.35 93 0.032
43 F 0 0 N/A 0.000 N/A
44 A 10 10 1.09 119 0.084
45 A 7 6 1.24 44 0.136
46 A 3 3 1.76 41 0.073
47 B 8 8 2.51 86 0.093
48 F 0 0 N/A 0.000 N/A
49 B 6 5 3.46 115 0.043
50 A 4 4 1.31 60 0.067
51 F 0 0 N/A 0.000 N/A
52 F 0 0 N/A 0.000 N/A
53 F 0 0 N/A 0.000 N/A
54 A 7 6 0.97 54 0.111
55 F 0 0 N/A 0.000 N/A
56 F 0 0 N/A 0.000 N/A
57 F 0 0 N/A 0.000 N/A
58 A 6 5 1.36 79 0.063
59 A 11 10 1.68 68 0.147
60 A 2 2 1.30 31 0.065
61 A 11 10 0.97 34 0.294
62 A 10 9 0.50 20 0.450
63 A 2 2 1.82 53 0.038
64 A 2 2 1.00 29 0.069
65 A 2 2 1.27 74 0.027
66 F 0 0 N/A 0.000 N/A
67 A 11 10 1.03 24 0.417
68 F 0 0 N/A 0.000 N/A
69 F 0 0 N/A 0.000 N/A
70 A 8 7 0.81 18 0.389
71 F 0 0 N/A 0.000 N/A
72 F 0 0 N/A 0.000 N/A
73 F 0 0 N/A 0.000 N/A
74 A 3 3 0.77 30 0.100
75 A 3 3 1.12 57 0.053
76 F 0 0 N/A 0.000 N/A
77 F 0 0 N/A 0.000 N/A
78 F 0 0 N/A 0.000 N/A
79 A 10 9 1.10 9 1.000
80 A 2 2 1.00 43 0.047
81 F 0 0 N/A 0.000 N/A
82 F 0 0 N/A 0.000 N/A
83 B 8 8 2.51 86 0.093
84 A 2 2 1.09 23 0.087
85 A 2 2 0.88 24 0.083
86 A 2 2 0.90 28 0.071
87 A 10 9 1.32 25 0.360
88 F 0 0 N/A 0.000 N/A
89 F 0 0 N/A 0.000 N/A
90 F 0 0 N/A 0.000 N/A
91 F 0 0 N/A 0.000 N/A
92 F 0 0 N/A 0.000 N/A
93 A 9 8 1.30 22 0.364
94 F 0 0 N/A 0.000 N/A
95 F 0 0 N/A 0.000 N/A
96 A 3 3 1.09 38 0.079
97 F 0 0 N/A 0.000 N/A
98 A 3 3 1.14 38 0.079
99 F 0 0 N/A 0.000 N/A
100 A 9 8 1.03 9 0.889
101 A 10 9 0.76 9 1.000
102 A 10 9 0.98 9 1.000
103 A 13 12 0.54 9 1.333
104 A 14 13 0.56 9 1.444
105 A 10 10 1.28 24 0.417
106 A 14 13 0.84 24 0.542
107 A 2 2 0.96 33 0.061
108 A 2 2 0.97 59 0.034
109 A 15 14 0.95 24 0.583
110 A 14 13 0.58 13 1.000
111 A 17 16 1.35 14 1.143

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