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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 [44] had the largest ratio of [1.36363999999999996]

# 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 1.08 15 0.200
2 A 10 9 1.06 23 0.391
3 A 8 7 1.07 23 0.304
4 A 6 5 1.04 23 0.217
5 A 4 3 1.08 23 0.130
6 A 6 5 1.04 23 0.217
7 A 9 8 1.09 23 0.348
8 A 20 19 0.97 25 0.760
9 A 18 17 0.94 25 0.680
10 A 18 17 0.96 25 0.680
11 A 16 15 0.90 25 0.600
12 A 15 14 0.93 25 0.560
13 A 17 16 0.94 25 0.640
14 A 17 16 0.96 25 0.640
15 A 15 14 1.09 25 0.560
16 A 13 12 1.12 25 0.480
17 A 11 10 1.11 25 0.400
18 A 9 8 1.09 25 0.320
19 A 9 8 1.12 25 0.320
20 A 10 9 1.13 25 0.360
21 A 13 12 1.15 25 0.480
22 A 15 14 1.18 25 0.560
23 A 13 12 1.04 25 0.480
24 A 11 10 1.00 25 0.400
25 A 10 9 0.98 25 0.360
26 A 10 9 0.98 25 0.360
27 A 13 12 1.06 25 0.480
28 A 18 17 1.08 25 0.680
29 A 22 21 0.90 25 0.840
30 A 23 22 0.87 25 0.880
31 A 22 21 0.90 25 0.840
32 A 23 22 0.89 25 0.880
33 A 25 24 0.94 25 0.960
34 A 29 28 0.95 25 1.120
35 A 16 15 1.09 25 0.600
36 A 17 16 1.09 25 0.640
37 A 17 16 1.09 25 0.640
38 A 17 16 1.09 25 0.640
39 A 20 19 1.11 25 0.760
40 A 23 22 1.13 25 0.880
41 A 14 13 1.04 13 1.000
42 A 11 10 1.13 11 0.909
43 A 15 14 1.21 13 1.077
44 A 16 15 1.15 11 1.364
45 A 13 12 1.14 13 0.923
46 A 9 8 1.18 11 0.727
47 A 11 10 1.12 13 0.769
48 A 15 14 1.02 11 1.273
49 A 15 14 1.19 13 1.077
50 A 14 13 1.12 11 1.182
51 A 16 15 0.97 23 0.652
52 A 14 13 0.96 23 0.565
53 A 12 11 0.95 23 0.478
54 A 15 14 0.97 23 0.609
55 A 18 17 0.97 23 0.739
56 A 18 17 0.92 25 0.680
57 A 16 15 0.91 25 0.600
58 A 14 13 0.90 25 0.520
59 A 15 14 0.91 25 0.560
60 A 18 17 0.91 25 0.680
61 A 20 19 0.93 25 0.760
62 A 21 20 0.94 25 0.800
63 A 19 18 0.93 25 0.720
64 A 17 16 0.91 25 0.640
65 A 18 17 0.92 25 0.680
66 A 19 18 0.91 25 0.720
67 A 21 20 0.94 25 0.800
68 A 24 23 0.97 25 0.920
69 A 21 20 0.90 25 0.800
70 A 19 18 0.87 25 0.720
71 A 18 17 0.86 25 0.680
72 A 17 16 0.86 25 0.640
73 A 21 20 0.91 25 0.800
74 A 24 23 0.94 25 0.920
75 A 25 24 0.91 25 0.960
76 A 22 21 0.90 25 0.840
77 A 22 21 0.89 25 0.840
78 A 22 21 0.88 25 0.840
79 A 22 21 0.90 25 0.840
80 A 25 24 0.92 25 0.960
81 A 28 27 0.93 25 1.080
82 A 25 24 0.94 25 0.960
83 A 25 24 0.94 25 0.960
84 A 25 24 0.93 25 0.960
85 A 25 24 0.93 25 0.960
86 A 25 24 0.95 25 0.960
87 A 28 27 0.94 25 1.080
88 A 5 4 0.99 12 0.333
89 A 7 6 1.11 23 0.261
90 A 6 5 0.78 27 0.185
91 A 6 5 0.78 27 0.185
92 A 5 5 1.00 23 0.217
93 A 7 7 1.10 23 0.304
94 A 9 9 1.13 23 0.391
95 A 14 13 0.91 25 0.520
96 A 12 11 0.89 25 0.440
97 A 10 9 0.86 25 0.360
98 A 13 12 0.81 27 0.444
99 A 14 13 1.06 27 0.481
100 A 14 13 1.07 27 0.481
101 A 8 7 0.83 25 0.280
102 A 10 9 1.06 25 0.360
103 A 12 11 1.12 25 0.440
104 A 8 7 0.81 27 0.259
105 A 11 10 0.99 27 0.370
106 A 13 12 1.06 27 0.444

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