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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 [5] had the largest ratio of [1.50000000000000000]

# 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 1.01 10 0.800
2 A 6 5 1.00 10 0.500
3 A 10 9 0.99 8 1.125
4 A 5 4 1.00 6 0.667
5 C 16 15 1.37 10 1.500
6 A 8 7 1.03 10 0.700
7 A 13 12 1.20 10 1.200
8 A 14 13 1.21 10 1.300
9 A 6 5 0.95 12 0.417
10 A 7 6 0.94 10 0.600
11 A 8 7 0.96 8 0.875
12 C 17 16 1.23 12 1.333
13 A 6 5 1.01 12 0.417
14 A 7 6 0.96 12 0.500
15 A 7 6 0.90 10 0.600
16 A 9 8 0.92 8 1.000
17 C 17 16 1.20 12 1.333
18 A 6 5 1.01 12 0.417
19 A 7 6 0.94 12 0.500
20 A 4 4 0.63 10 0.400
21 A 4 4 0.73 10 0.400
22 A 4 4 0.90 8 0.500
23 A 2 2 1.00 6 0.333
24 C 10 9 1.26 10 0.900
25 A 6 5 0.81 10 0.500
26 A 7 6 0.75 10 0.600
27 A 8 7 0.72 10 0.700
28 A 3 3 1.00 4 0.750
29 C 10 9 1.26 10 0.900
30 C 10 9 1.26 10 0.900
31 C 10 9 1.26 10 0.900
32 A 5 5 1.67 10 0.500
33 A 6 6 1.07 10 0.600
34 A 3 3 1.37 10 0.300
35 A 4 4 1.00 8 0.500
36 A 4 3 1.62 6 0.500
37 A 6 6 1.35 10 0.600
38 B 8 7 2.91 10 0.700
39 C 5 5 1.95 10 0.500
40 A 10 9 1.06 10 0.900
41 A 7 7 1.23 10 0.700
42 A 12 11 1.07 10 1.100
43 A 9 9 1.20 10 0.900
44 A 14 13 1.07 10 1.300
45 A 7 6 0.86 12 0.500
46 A 5 5 0.86 12 0.417
47 A 4 4 1.22 12 0.333
48 A 7 7 0.81 12 0.583
49 A 6 5 1.00 12 0.417
50 A 4 4 1.00 12 0.333
51 A 7 6 1.00 10 0.600
52 A 8 8 0.73 8 1.000
53 A 6 5 0.89 12 0.417
54 A 5 5 0.82 12 0.417
55 A 8 7 0.82 12 0.583
56 A 4 4 1.04 12 0.333
57 A 4 4 1.06 12 0.333
58 A 4 4 1.00 10 0.400
59 A 6 5 1.00 12 0.417
60 A 4 4 1.00 12 0.333
61 A 4 4 1.00 10 0.400
62 A 4 4 1.00 8 0.500
63 A 7 6 0.87 12 0.500
64 A 4 4 1.00 12 0.333
65 A 13 12 1.31 12 1.000
66 A 12 11 1.46 12 0.917
67 A 8 7 1.21 12 0.583
68 A 11 10 1.36 10 1.000
69 A 7 6 1.44 8 0.750
70 A 6 5 1.24 12 0.417
71 A 5 4 1.05 12 0.333
72 A 6 5 0.96 12 0.417
73 A 6 5 0.94 12 0.417
74 A 7 6 0.93 12 0.500
75 A 6 5 0.92 12 0.417
76 A 13 12 1.41 12 1.000
77 A 10 9 1.26 12 0.750
78 A 9 8 1.56 12 0.667
79 A 7 6 1.30 10 0.600
80 A 7 6 1.43 8 0.750
81 A 6 5 1.13 12 0.417
82 A 6 5 1.10 12 0.417
83 A 5 4 0.97 12 0.333
84 A 7 6 0.94 12 0.500
85 A 6 5 0.94 12 0.417
86 A 7 6 0.93 12 0.500
87 A 6 5 0.93 12 0.417
88 A 5 5 1.00 24 0.208
89 A 9 8 1.28 22 0.364
90 A 8 8 1.11 22 0.364
91 A 4 4 1.00 22 0.182
92 A 5 5 1.00 20 0.250
93 A 9 8 1.01 19 0.421
94 A 5 5 1.10 22 0.227
95 A 11 10 1.08 22 0.455
96 A 8 8 1.28 22 0.364
97 B 2 2 2.17 25 0.080
98 C 11 10 1.10 19 0.526
99 A 6 5 0.98 12 0.417
100 A 6 5 0.97 14 0.357

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