[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 [46] had the largest ratio of [.750000000000000000]

# 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 6 5 0.82 21 0.238
2 A 7 6 0.76 21 0.286
3 A 6 5 0.94 19 0.263
4 A 5 4 0.83 21 0.190
5 A 8 7 0.87 21 0.333
6 A 6 5 0.83 21 0.238
7 A 12 11 0.87 23 0.478
8 A 12 11 0.82 23 0.478
9 A 7 6 0.92 21 0.286
10 A 7 6 0.94 23 0.261
11 A 7 6 0.97 23 0.261
12 A 11 10 0.84 23 0.435
13 A 11 10 0.84 23 0.435
14 A 16 15 0.92 23 0.652
15 A 13 12 0.85 23 0.522
16 A 11 10 0.92 21 0.476
17 A 8 7 0.92 23 0.304
18 A 8 7 0.97 23 0.304
19 A 10 9 0.91 23 0.391
20 A 17 16 0.87 23 0.696
21 A 5 4 1.13 12 0.333
22 A 5 4 0.95 19 0.211
23 N/A 1 0 1.00 18 0.000
24 A 6 5 0.99 18 0.278
25 A 6 5 1.05 18 0.278
26 A 6 5 1.06 16 0.312
27 A 1 1 1.00 10 0.100
28 A 7 6 1.11 18 0.333
29 A 10 9 0.98 18 0.500
30 A 6 6 1.08 18 0.333
31 A 5 4 1.00 20 0.200
32 A 5 4 1.03 18 0.222
33 A 7 6 1.00 12 0.500
34 A 4 3 1.10 20 0.150
35 A 7 6 1.03 20 0.300
36 A 5 4 0.98 20 0.200
37 A 5 4 0.99 18 0.222
38 A 7 6 0.99 12 0.500
39 A 4 3 1.10 20 0.150
40 A 7 6 1.03 20 0.300
41 A 5 4 1.34 18 0.222
42 N/A 3 0 1.00 20 0.000
43 N/A 3 0 1.00 20 0.000
44 A 7 6 0.93 10 0.600
45 A 6 5 1.04 10 0.500
46 A 7 6 0.98 8 0.750
47 A 4 3 0.94 6 0.500
48 A 8 7 1.00 10 0.700
49 A 8 7 0.97 10 0.700
50 A 6 5 1.06 10 0.500
51 A 7 6 1.05 10 0.600
52 A 3 3 1.01 16 0.188
53 A 3 3 1.00 16 0.188
54 A 7 6 1.12 14 0.429
55 A 3 3 1.04 16 0.188
56 A 3 3 1.01 16 0.188
57 A 3 3 1.02 16 0.188
58 A 5 4 0.99 18 0.222
59 A 6 5 1.03 18 0.278
60 A 3 3 1.11 14 0.214
61 A 3 3 1.00 16 0.188
62 A 2 2 1.06 19 0.105
63 A 3 2 0.96 28 0.071
64 A 4 3 0.72 33 0.091
65 N/A 3 0 1.00 28 0.000
66 N/A 3 0 1.00 33 0.000
67 A 5 4 0.95 35 0.114
68 A 6 5 0.77 40 0.125
69 N/A 3 0 1.00 35 0.000
70 N/A 3 0 1.00 40 0.000

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