[prev] [prev-tail] [tail] [up]

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 [39] had the largest ratio of [.479999999999999982]

# 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 5 4 0.94 17 0.235
2 A 1 1 1.00 15 0.067
3 A 6 5 1.30 17 0.294
4 A 5 4 0.99 17 0.235
5 A 7 6 0.81 19 0.316
6 A 6 5 0.85 19 0.263
7 A 5 4 1.00 19 0.211
8 A 6 5 0.86 19 0.263
9 A 7 6 0.84 19 0.316
10 A 9 8 0.87 19 0.421
11 A 8 7 0.91 19 0.368
12 A 8 7 0.91 19 0.368
13 A 7 6 0.96 19 0.316
14 A 7 6 0.96 19 0.316
15 A 8 7 0.92 19 0.368
16 A 8 7 0.92 19 0.368
17 A 9 8 0.90 19 0.421
18 A 4 3 0.99 17 0.176
19 A 2 2 1.00 23 0.087
20 A 2 2 1.00 23 0.087
21 A 2 2 1.00 21 0.095
22 A 1 1 1.00 15 0.067
23 A 2 2 1.00 23 0.087
24 A 2 2 1.00 23 0.087
25 A 2 2 1.00 23 0.087
26 A 2 2 1.00 25 0.080
27 A 2 2 1.00 25 0.080
28 A 2 2 1.00 23 0.087
29 A 5 4 0.94 17 0.235
30 A 2 2 1.00 25 0.080
31 A 2 2 1.00 25 0.080
32 A 2 2 1.00 25 0.080
33 A 7 6 1.14 25 0.240
34 A 6 5 1.11 25 0.200
35 A 5 4 1.05 23 0.174
36 A 6 5 1.30 17 0.294
37 N/A 2 0 1.00 25 0.000
38 N/A 2 0 1.00 25 0.000
39 A 13 12 1.17 25 0.480
40 A 12 11 1.15 25 0.440
41 A 12 11 1.10 23 0.478
42 A 5 4 0.99 17 0.235
43 N/A 2 0 1.00 25 0.000
44 N/A 2 0 1.00 25 0.000
45 F 0 0 N/A 0.000 N/A
46 F 0 0 N/A 0.000 N/A
47 F 0 0 N/A 0.000 N/A
48 F 0 0 N/A 0.000 N/A
49 A 2 2 1.00 25 0.080
50 A 2 2 1.00 25 0.080
51 A 2 2 1.00 25 0.080
52 N/A 1 0 1.00 25 0.000
53 A 2 2 1.00 25 0.080
54 A 2 2 1.00 23 0.087
55 N/A 1 0 1.00 25 0.000
56 N/A 1 0 1.00 25 0.000
57 A 3 2 1.00 13 0.154
58 A 3 2 1.00 13 0.154
59 A 4 3 1.00 19 0.158
60 A 3 2 1.00 21 0.095
61 A 3 2 1.00 13 0.154
62 A 4 3 1.00 19 0.158
63 A 3 2 1.00 21 0.095
64 A 3 2 1.00 13 0.154
65 A 4 3 1.00 19 0.158
66 A 3 2 1.00 21 0.095
67 A 3 2 1.00 13 0.154
68 A 4 3 1.00 19 0.158
69 A 3 2 1.00 21 0.095
70 A 3 2 1.00 17 0.118
71 A 4 3 1.00 17 0.176
72 A 3 2 1.00 29 0.069
73 A 4 3 1.00 44 0.068
74 A 4 3 1.00 15 0.200
75 A 4 3 1.00 15 0.200
76 A 3 2 1.00 15 0.133
77 A 4 3 1.00 15 0.200
78 A 4 3 0.97 17 0.176
79 A 4 3 0.95 17 0.176
80 A 3 2 1.00 17 0.118
81 A 4 3 1.11 17 0.176
82 A 4 3 1.05 19 0.158
83 A 4 3 1.38 16 0.188
84 A 4 3 1.09 18 0.167
85 A 4 3 1.00 18 0.167
86 A 4 3 1.08 18 0.167
87 A 4 3 1.00 18 0.167
88 A 4 3 0.96 18 0.167
89 A 3 2 1.10 22 0.091
90 A 4 3 1.00 23 0.130
91 A 4 3 0.80 23 0.130
92 A 4 3 0.82 23 0.130
93 A 4 3 0.71 23 0.130
94 A 3 2 1.00 13 0.154
95 A 3 2 1.00 15 0.133
96 A 4 3 1.00 16 0.188
97 A 6 5 1.32 18 0.278
98 A 7 6 1.17 18 0.333
99 A 3 2 1.00 15 0.133
100 A 6 5 0.90 16 0.312
101 A 7 6 0.90 18 0.333
102 A 8 7 0.88 18 0.389
103 A 4 3 0.95 15 0.200
104 A 2 2 1.00 16 0.125
105 A 4 4 1.00 18 0.222
106 A 4 4 0.97 18 0.222
107 A 5 4 1.01 15 0.267
108 A 2 2 1.00 16 0.125
109 A 4 4 0.99 18 0.222
110 A 3 2 1.00 15 0.133
111 A 6 5 0.90 17 0.294
112 A 7 6 0.90 19 0.316
113 A 8 7 0.88 19 0.368
114 A 3 2 1.00 15 0.133
115 A 7 6 0.97 17 0.353
116 A 7 6 1.03 19 0.316
117 A 8 7 1.05 19 0.368
118 A 5 4 0.98 15 0.267
119 A 3 3 1.00 17 0.176
120 A 3 3 1.00 19 0.158
121 A 3 3 1.00 25 0.120
122 A 2 2 1.00 25 0.080
123 A 2 2 1.00 34 0.059
124 A 2 2 1.00 34 0.059

[prev] [prev-tail] [front] [up]