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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 [10] had the largest ratio of [2.60000000000000009]

# 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 C 6 6 1.05 8 0.750
2 C 13 13 1.32 8 1.625
3 C 11 11 1.20 8 1.375
4 C 7 7 1.20 6 1.167
5 A 1 1 1.00 4 0.250
6 A 1 1 1.00 8 0.125
7 C 7 7 1.40 8 0.875
8 C 11 11 1.20 8 1.375
9 N/A 1 0 1.00 10 0.000
10 A 27 26 1.54 10 2.600
11 A 21 21 1.39 10 2.100
12 A 14 13 1.05 8 1.625
13 A 8 8 1.16 6 1.333
14 N/A 1 0 1.00 10 0.000
15 N/A 1 0 1.00 10 0.000
16 N/A 1 0 1.00 10 0.000
17 N/A 2 0 1.00 10 0.000
18 A 3 3 0.90 10 0.300
19 A 3 3 0.91 10 0.300
20 A 3 3 1.08 8 0.375
21 A 1 1 1.00 6 0.167
22 N/A 1 0 1.00 10 0.000
23 A 3 3 1.00 10 0.300
24 A 3 3 0.82 10 0.300
25 N/A 1 0 1.00 12 0.000
26 A 26 26 1.30 12 2.167
27 A 18 18 1.21 10 1.800
28 A 7 7 1.10 8 0.875
29 N/A 1 0 1.00 12 0.000
30 N/A 1 0 1.00 12 0.000
31 N/A 1 0 1.00 12 0.000
32 A 6 5 1.35 17 0.294
33 A 6 5 1.35 15 0.333
34 A 6 5 1.35 13 0.385
35 A 4 3 1.13 17 0.176
36 A 6 5 1.20 17 0.294
37 A 6 5 1.21 17 0.294
38 A 6 5 1.29 19 0.263
39 C 21 21 1.40 12 1.750
40 N/A 10 0 1.00 12 0.000
41 A 1 1 1.00 12 0.083
42 A 7 7 1.00 9 0.778
43 A 13 12 1.07 10 1.200
44 A 20 20 1.53 12 1.667
45 A 26 25 1.69 12 2.083
46 N/A 23 0 1.00 12 0.000
47 C 10 10 1.23 12 0.833
48 N/A 1 0 1.00 12 0.000
49 A 6 6 0.97 9 0.667
50 A 13 13 1.11 10 1.300
51 A 19 18 1.30 12 1.500
52 F 0 0 N/A 0.000 N/A
53 A 4 4 1.17 9 0.444
54 A 4 4 1.17 9 0.444
55 A 12 12 1.21 16 0.750
56 A 10 10 1.07 14 0.714
57 A 6 6 1.00 13 0.462
58 N/A 1 0 1.00 16 0.000
59 A 11 11 1.19 16 0.688
60 A 9 9 1.05 14 0.643
61 A 5 5 1.00 13 0.385
62 N/A 1 0 1.00 16 0.000
63 A 6 6 1.02 14 0.429
64 A 3 3 1.05 13 0.231
65 N/A 1 0 1.00 16 0.000
66 A 6 6 1.02 14 0.429
67 A 3 3 1.05 13 0.231
68 N/A 1 0 1.00 16 0.000
69 A 6 6 0.97 8 0.750
70 C 14 14 1.22 8 1.750
71 C 10 10 1.22 8 1.250
72 A 8 8 1.00 6 1.333
73 A 1 1 1.00 4 0.250
74 A 1 1 1.00 8 0.125
75 A 8 8 1.00 8 1.000
76 C 10 10 1.22 8 1.250
77 N/A 1 0 1.00 10 0.000
78 A 25 24 1.41 10 2.400
79 A 20 20 1.40 10 2.000
80 A 13 12 1.07 8 1.500
81 A 8 8 1.16 6 1.333
82 N/A 1 0 1.00 10 0.000
83 N/A 1 0 1.00 10 0.000
84 N/A 1 0 1.00 10 0.000
85 N/A 2 0 1.00 10 0.000
86 A 3 3 0.90 10 0.300
87 A 3 3 0.91 10 0.300
88 A 3 3 1.08 8 0.375
89 A 1 1 1.00 6 0.167
90 N/A 1 0 1.00 10 0.000
91 A 3 3 1.00 10 0.300
92 A 3 3 0.82 10 0.300
93 N/A 1 0 1.00 12 0.000
94 A 25 25 1.31 12 2.083
95 A 17 17 1.21 10 1.700
96 A 7 7 1.10 8 0.875
97 N/A 1 0 1.00 12 0.000
98 N/A 1 0 1.00 12 0.000
99 N/A 1 0 1.00 12 0.000
100 A 6 5 1.35 17 0.294
101 A 6 5 1.35 15 0.333
102 A 6 5 1.35 13 0.385
103 A 4 3 1.13 17 0.176
104 A 6 5 1.20 17 0.294
105 A 6 5 1.21 17 0.294
106 A 6 5 1.29 19 0.263
107 C 18 18 1.41 12 1.500
108 N/A 9 0 1.00 12 0.000
109 A 1 1 1.00 12 0.083
110 A 7 7 1.00 9 0.778
111 A 12 11 1.08 10 1.100
112 A 19 19 1.54 12 1.583
113 A 24 23 1.50 12 1.917
114 N/A 22 0 1.00 12 0.000
115 C 10 10 1.23 12 0.833
116 N/A 1 0 1.00 12 0.000
117 A 5 5 1.00 9 0.556
118 A 12 12 1.13 10 1.200
119 A 17 16 1.18 12 1.333
120 A 27 27 1.60 12 2.250
121 A 4 4 1.17 9 0.444
122 A 4 4 1.17 9 0.444
123 A 10 10 1.18 16 0.625
124 A 9 9 1.05 14 0.643
125 A 4 4 1.00 13 0.308
126 N/A 1 0 1.00 16 0.000
127 A 12 12 1.21 16 0.750
128 A 9 9 1.07 14 0.643
129 A 6 6 1.00 13 0.462
130 N/A 1 0 1.00 16 0.000
131 A 6 6 1.02 14 0.429
132 A 3 3 1.05 13 0.231
133 N/A 1 0 1.00 16 0.000
134 A 6 6 1.02 14 0.429
135 A 3 3 1.05 13 0.231
136 N/A 1 0 1.00 16 0.000

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