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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 [1.30000000000000004]

# 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 1 1 1.00 10 0.100
2 C 5 4 3.27 37 0.108
3 A 2 2 1.00 15 0.133
4 A 5 4 1.00 19 0.211
5 A 2 2 1.00 17 0.118
6 A 8 7 1.00 17 0.412
7 A 4 3 1.00 17 0.176
8 A 2 2 1.00 23 0.087
9 A 2 2 1.66 27 0.074
10 B 2 2 2.46 39 0.051
11 A 1 1 1.00 45 0.022
12 A 5 4 1.21 32 0.125
13 A 4 3 1.00 32 0.094
14 A 3 2 1.00 27 0.074
15 A 3 2 1.00 29 0.069
16 A 2 2 1.00 30 0.067
17 A 4 3 0.98 13 0.231
18 A 4 3 0.98 15 0.200
19 A 3 2 1.00 23 0.087
20 A 3 2 1.00 25 0.080
21 A 4 3 1.07 11 0.273
22 A 3 2 1.00 18 0.111
23 A 7 6 1.00 20 0.300
24 A 8 7 1.09 31 0.226
25 A 3 2 1.00 29 0.069
26 A 3 2 1.00 35 0.057
27 A 7 6 1.10 32 0.188
28 A 8 7 1.12 21 0.333
29 A 5 5 1.22 14 0.357
30 A 3 2 1.00 23 0.087
31 A 4 3 0.98 13 0.231
32 A 2 2 1.00 33 0.061
33 A 6 5 1.05 15 0.333
34 A 6 5 1.07 15 0.333
35 A 1 1 1.00 11 0.091
36 A 6 5 1.11 15 0.333
37 A 1 1 1.00 17 0.059
38 A 3 3 1.00 18 0.167
39 A 3 3 1.09 16 0.188
40 A 6 5 1.06 17 0.294
41 A 6 5 1.30 13 0.385
42 A 6 5 1.19 16 0.312
43 F 0 0 N/A 0.000 N/A
44 F 0 0 N/A 0.000 N/A
45 F 0 0 N/A 0.000 N/A
46 A 2 2 1.16 32 0.062
47 A 27 26 1.24 20 1.300
48 F 0 0 N/A 0.000 N/A
49 F 0 0 N/A 0.000 N/A
50 A 24 23 1.12 23 1.000
51 F 0 0 N/A 0.000 N/A
52 C 11 10 6.50 48 0.208
53 A 8 7 1.03 24 0.292
54 A 8 7 1.00 24 0.292
55 A 1 1 1.00 18 0.056
56 A 2 2 1.04 13 0.154
57 A 7 6 1.12 15 0.400
58 A 2 2 1.00 17 0.118
59 A 2 2 1.46 22 0.091
60 A 2 2 1.00 17 0.118
61 A 2 2 1.00 21 0.095
62 A 1 1 1.00 38 0.026
63 A 1 1 1.00 33 0.030
64 A 3 3 1.09 38 0.079
65 A 1 1 1.00 19 0.053
66 A 5 4 1.00 19 0.211
67 A 5 4 1.35 24 0.167
68 A 1 1 1.00 24 0.042
69 A 8 7 1.10 24 0.292
70 A 8 7 1.09 24 0.292
71 A 3 3 1.01 26 0.115
72 A 3 3 1.01 22 0.136
73 A 1 1 1.00 22 0.045
74 A 1 1 1.00 23 0.043
75 A 10 9 1.00 18 0.500
76 A 9 8 1.00 23 0.348
77 A 1 1 1.00 21 0.048
78 A 1 1 1.00 19 0.053
79 A 1 1 1.00 19 0.053
80 A 1 1 1.00 19 0.053
81 A 6 5 1.00 34 0.147
82 C 6 5 7.69 40 0.125
83 C 8 7 5.07 51 0.137
84 A 3 2 1.00 29 0.069
85 A 3 2 1.00 18 0.111
86 A 1 1 1.00 25 0.040
87 A 1 1 1.00 25 0.040
88 A 1 1 1.00 25 0.040
89 A 1 1 1.00 25 0.040
90 A 3 2 1.12 40 0.050
91 A 3 2 1.11 40 0.050
92 A 1 1 1.00 18 0.056
93 A 3 3 1.03 15 0.200
94 A 1 1 1.00 21 0.048
95 A 2 2 1.00 23 0.087
96 A 6 5 1.04 24 0.208
97 A 1 1 1.00 19 0.053
98 A 12 11 1.07 20 0.550
99 A 6 5 1.05 22 0.227
100 B 2 2 2.84 25 0.080
101 B 3 3 2.84 24 0.125
102 B 2 2 3.00 23 0.087
103 A 2 2 1.00 20 0.100
104 A 2 2 1.00 25 0.080
105 A 3 3 1.00 19 0.158
106 A 2 2 1.04 11 0.182
107 A 7 6 1.09 15 0.400
108 A 6 6 0.98 19 0.316
109 A 2 2 1.00 22 0.091
110 A 2 2 1.26 27 0.074
111 A 5 5 1.03 17 0.294
112 A 6 6 1.03 27 0.222
113 A 3 3 1.05 19 0.158
114 A 14 13 1.09 20 0.650
115 A 2 2 1.71 24 0.083
116 A 11 10 1.08 19 0.526

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