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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 [72] had the largest ratio of [.740740999999999983]

# 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 1.01 29 0.172
2 A 3 2 1.00 31 0.065
3 A 3 2 1.00 27 0.074
4 A 5 4 1.00 27 0.148
5 A 7 6 1.08 27 0.222
6 A 9 8 1.14 27 0.296
7 A 5 4 1.00 31 0.129
8 A 3 2 1.00 23 0.087
9 A 2 2 1.00 31 0.065
10 A 2 2 1.00 34 0.059
11 A 4 4 0.62 22 0.182
12 A 8 7 1.07 18 0.389
13 A 4 3 1.00 26 0.115
14 A 15 14 1.01 27 0.519
15 A 2 2 1.00 23 0.087
16 A 2 2 1.00 23 0.087
17 A 2 2 1.00 23 0.087
18 A 2 2 1.00 21 0.095
19 A 2 2 1.00 23 0.087
20 A 5 4 1.00 23 0.174
21 A 6 5 1.08 23 0.217
22 A 2 2 1.00 25 0.080
23 A 2 2 1.00 25 0.080
24 A 2 2 1.00 25 0.080
25 A 2 2 1.00 23 0.087
26 A 2 2 1.00 25 0.080
27 A 4 4 1.05 25 0.160
28 A 7 6 1.08 25 0.240
29 A 8 7 1.12 25 0.280
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 2 2 1.00 23 0.087
34 A 2 2 1.00 25 0.080
35 A 4 4 1.01 25 0.160
36 A 6 6 1.10 25 0.240
37 A 2 2 1.00 25 0.080
38 A 2 2 1.00 25 0.080
39 A 2 2 1.00 25 0.080
40 A 2 2 1.00 23 0.087
41 A 8 7 1.08 25 0.280
42 A 10 9 1.12 25 0.360
43 A 12 11 1.14 25 0.440
44 A 4 4 0.95 25 0.160
45 A 4 4 0.99 25 0.160
46 A 4 4 1.02 25 0.160
47 A 5 4 1.00 23 0.174
48 A 10 9 1.12 25 0.360
49 A 12 11 1.13 25 0.440
50 A 14 13 1.14 25 0.520
51 A 6 6 1.08 25 0.240
52 A 6 6 1.12 25 0.240
53 A 7 6 1.08 25 0.240
54 A 6 5 1.08 23 0.217
55 A 12 11 1.14 25 0.440
56 A 14 13 1.13 25 0.520
57 A 16 15 1.14 25 0.600
58 A 19 18 1.19 27 0.667
59 A 15 14 1.18 27 0.519
60 A 11 10 1.16 27 0.370
61 A 7 6 1.12 25 0.240
62 A 10 9 1.03 27 0.333
63 A 8 7 1.03 27 0.259
64 A 10 9 1.05 27 0.333
65 A 20 19 1.19 27 0.704
66 A 16 15 1.19 27 0.556
67 A 12 11 1.17 27 0.407
68 A 8 7 1.14 25 0.280
69 A 12 11 1.06 27 0.407
70 A 14 13 1.07 27 0.481
71 A 10 9 1.05 27 0.333
72 A 21 20 1.20 27 0.741
73 A 17 16 1.19 27 0.593
74 A 13 12 1.18 27 0.444
75 A 9 8 1.16 25 0.320
76 A 14 13 1.08 27 0.481
77 A 16 15 1.08 27 0.556
78 A 16 15 1.02 27 0.556
79 A 18 17 1.19 27 0.630
80 A 14 13 1.17 27 0.481
81 A 10 9 1.15 27 0.333
82 A 6 5 1.08 25 0.200
83 A 6 5 1.04 27 0.185
84 A 8 7 1.03 27 0.259
85 A 10 9 1.05 27 0.333
86 A 15 14 1.16 27 0.519
87 A 12 11 1.10 27 0.407
88 A 8 7 1.10 27 0.259
89 A 5 4 1.00 25 0.160
90 A 8 7 1.03 27 0.259
91 A 10 9 1.05 27 0.333
92 A 12 11 1.07 27 0.407
93 A 14 13 1.11 27 0.481
94 A 10 9 1.10 27 0.333
95 A 7 6 1.04 27 0.222
96 A 3 3 1.00 25 0.120
97 A 10 9 1.07 27 0.333
98 A 12 11 1.07 27 0.407
99 A 14 13 1.08 27 0.481
100 A 11 10 0.88 27 0.370
101 A 7 6 0.95 25 0.240
102 A 7 6 1.14 27 0.222
103 A 6 5 1.03 27 0.185
104 A 12 11 0.76 27 0.407
105 A 8 7 0.89 25 0.280
106 A 10 9 1.01 27 0.333
107 A 12 11 1.02 27 0.407
108 A 8 7 1.03 27 0.259
109 A 14 13 1.05 27 0.481
110 A 10 9 1.07 27 0.333
111 A 6 5 1.04 25 0.200
112 A 4 3 1.00 27 0.111
113 A 6 5 0.97 27 0.185
114 A 12 11 1.09 27 0.407
115 A 8 7 1.10 27 0.259
116 A 5 4 1.00 25 0.160
117 F 0 0 N/A 0.000 N/A
118 A 10 9 1.05 27 0.333
119 A 7 6 1.05 27 0.222
120 A 3 3 1.00 25 0.120
121 A 6 5 1.00 27 0.185
122 A 4 3 1.00 29 0.103
123 A 4 3 1.00 29 0.103

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