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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 [67] had the largest ratio of [.500000000000000000]

# 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 4 3 0.83 23 0.130
2 A 2 2 1.00 15 0.133
3 A 6 5 1.00 21 0.238
4 A 6 5 1.00 20 0.250
5 A 3 2 1.00 27 0.074
6 A 5 4 0.76 38 0.105
7 A 5 4 0.89 23 0.174
8 A 9 8 1.07 26 0.308
9 A 8 7 0.90 26 0.269
10 A 2 2 1.65 24 0.083
11 A 2 2 1.25 24 0.083
12 A 2 2 0.49 23 0.087
13 A 7 6 1.00 27 0.222
14 A 8 7 1.00 25 0.280
15 A 8 7 0.70 25 0.280
16 A 9 8 0.70 23 0.348
17 A 2 2 1.00 15 0.133
18 A 2 2 1.00 27 0.074
19 A 2 2 1.00 17 0.118
20 A 2 2 1.00 20 0.100
21 A 4 3 1.32 15 0.200
22 A 4 3 1.62 15 0.200
23 A 4 3 0.95 17 0.176
24 A 4 3 1.68 15 0.200
25 A 5 4 1.00 15 0.267
26 A 4 3 1.60 12 0.250
27 A 3 2 1.07 16 0.125
28 A 5 4 1.00 21 0.190
29 A 3 2 1.12 21 0.095
30 A 4 3 1.00 26 0.115
31 A 4 3 1.00 25 0.120
32 A 4 3 1.78 22 0.136
33 A 9 8 1.09 20 0.400
34 A 3 2 1.00 13 0.154
35 A 4 3 1.00 15 0.200
36 A 4 3 1.00 13 0.231
37 A 5 4 1.00 11 0.364
38 A 4 3 1.00 18 0.167
39 A 5 4 1.00 17 0.235
40 A 4 4 0.90 18 0.222
41 A 5 5 0.90 17 0.294
42 A 9 8 0.93 26 0.308
43 A 8 7 0.94 26 0.269
44 A 5 4 0.87 24 0.167
45 A 6 5 1.04 26 0.192
46 A 5 4 0.85 26 0.154
47 A 7 6 0.91 26 0.231
48 A 9 8 0.91 26 0.308
49 A 7 7 0.80 26 0.269
50 A 6 6 0.81 26 0.231
51 A 5 5 1.08 22 0.227
52 A 7 7 1.21 26 0.269
53 A 8 8 1.09 26 0.308
54 A 10 10 1.03 26 0.385
55 A 13 12 0.89 26 0.462
56 A 9 8 0.87 26 0.308
57 A 6 5 0.70 24 0.208
58 A 8 7 0.98 26 0.269
59 A 6 5 0.69 26 0.192
60 A 10 9 0.85 26 0.346
61 A 12 11 0.87 26 0.423
62 A 11 11 0.79 26 0.423
63 A 8 8 0.79 26 0.308
64 A 7 7 1.23 22 0.318
65 A 9 9 1.16 26 0.346
66 A 11 11 1.05 26 0.423
67 A 13 13 1.00 26 0.500
68 A 5 4 1.33 21 0.190
69 A 5 4 1.13 23 0.174
70 A 5 4 1.31 23 0.174
71 A 9 8 1.11 23 0.348
72 A 7 6 1.15 25 0.240
73 A 6 5 1.11 23 0.217
74 A 6 5 0.84 28 0.179
75 A 9 8 0.92 26 0.308
76 A 7 6 0.90 26 0.231
77 A 5 4 0.87 24 0.167
78 A 6 5 1.04 26 0.192
79 A 5 4 0.85 26 0.154
80 A 7 6 0.87 26 0.231
81 A 8 8 0.89 26 0.308
82 A 6 6 0.94 26 0.231
83 A 5 5 1.09 22 0.227
84 A 7 7 1.20 26 0.269
85 A 10 10 0.94 26 0.385
86 A 10 9 0.83 26 0.346
87 A 12 11 0.83 26 0.423
88 A 6 5 0.62 24 0.208
89 A 7 6 0.90 26 0.231
90 A 6 5 0.61 26 0.192
91 A 12 11 0.81 26 0.423
92 A 10 10 0.85 26 0.385
93 A 7 7 0.91 26 0.269
94 A 7 7 1.22 22 0.318
95 A 11 11 0.95 26 0.423
96 A 12 12 0.91 26 0.462
97 A 5 4 1.00 11 0.364
98 A 3 3 1.00 15 0.200
99 A 8 7 1.01 15 0.467
100 A 3 3 1.30 15 0.200
101 A 8 7 0.83 23 0.304
102 A 8 7 1.01 21 0.333
103 A 8 7 1.01 23 0.304
104 A 8 7 1.01 25 0.280

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