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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 [35] had the largest ratio of [.500000000000000000]

# 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 1.04 20 0.150
2 A 5 4 1.01 20 0.200
3 A 4 3 1.01 18 0.167
4 A 7 6 1.01 20 0.300
5 A 4 3 0.99 20 0.150
6 A 7 6 1.02 20 0.300
7 A 2 2 1.00 20 0.100
8 A 2 2 1.00 20 0.100
9 A 2 2 1.00 17 0.118
10 A 2 2 1.00 20 0.100
11 A 2 2 1.00 20 0.100
12 A 4 3 1.00 22 0.136
13 A 7 6 1.01 22 0.273
14 A 6 5 1.04 20 0.250
15 A 9 8 1.02 22 0.364
16 A 4 3 1.01 22 0.136
17 A 9 8 0.98 22 0.364
18 A 2 2 0.99 22 0.091
19 A 2 2 0.99 22 0.091
20 F 0 0 N/A 0.000 N/A
21 A 2 2 1.01 22 0.091
22 A 2 2 1.00 22 0.091
23 A 7 6 1.03 22 0.273
24 A 4 3 1.39 22 0.136
25 A 7 6 1.01 22 0.273
26 A 4 3 1.01 20 0.150
27 A 9 8 1.02 22 0.364
28 A 4 3 1.43 22 0.136
29 A 9 8 1.01 22 0.364
30 F 0 0 N/A 0.000 N/A
31 F 0 0 N/A 0.000 N/A
32 A 2 2 1.00 19 0.105
33 F 0 0 N/A 0.000 N/A
34 F 0 0 N/A 0.000 N/A
35 A 12 11 0.90 22 0.500
36 A 4 3 1.66 22 0.136
37 A 4 3 0.99 22 0.136
38 A 4 3 1.01 20 0.150
39 A 4 3 1.01 22 0.136
40 A 4 3 1.96 22 0.136
41 A 4 3 0.97 22 0.136
42 F 0 0 N/A 0.000 N/A
43 F 0 0 N/A 0.000 N/A
44 A 2 2 1.00 19 0.105
45 F 0 0 N/A 0.000 N/A
46 F 0 0 N/A 0.000 N/A
47 A 4 3 0.99 25 0.120
48 A 4 3 0.98 25 0.120
49 A 6 5 1.03 25 0.200
50 A 4 3 1.04 25 0.120
51 A 4 3 1.02 25 0.120
52 A 4 3 1.00 25 0.120
53 A 8 7 1.03 25 0.280
54 A 5 4 1.01 25 0.160
55 A 4 3 0.99 23 0.130
56 A 5 4 0.98 25 0.160
57 A 7 6 0.96 25 0.240
58 A 5 5 0.85 25 0.200
59 A 5 5 0.88 25 0.200
60 A 4 4 0.87 22 0.182
61 A 6 6 0.88 25 0.240
62 A 6 6 0.88 25 0.240
63 A 10 9 1.61 23 0.391
64 A 7 6 1.03 23 0.261
65 B 5 4 2.08 21 0.190
66 A 4 3 1.07 23 0.130
67 A 10 9 1.44 23 0.391
68 A 10 9 1.48 23 0.391
69 A 10 9 1.86 23 0.391
70 A 11 10 1.26 23 0.435
71 A 9 8 1.22 20 0.400
72 A 9 8 1.87 23 0.348
73 A 11 10 1.32 23 0.435
74 A 4 3 0.99 27 0.111
75 A 7 6 0.87 27 0.222
76 A 4 3 1.01 27 0.111
77 A 4 3 1.00 27 0.111
78 A 4 3 0.99 27 0.111
79 A 4 3 0.99 27 0.111
80 A 4 3 0.98 27 0.111
81 A 4 3 0.99 25 0.120
82 A 4 3 0.99 27 0.111
83 A 4 3 0.98 27 0.111
84 A 2 2 1.11 27 0.074
85 A 2 2 1.11 27 0.074
86 A 2 2 1.11 24 0.083
87 A 2 2 1.10 27 0.074
88 A 2 2 1.10 27 0.074
89 A 8 7 1.16 25 0.280
90 A 5 4 0.99 25 0.160
91 A 5 4 0.98 25 0.160
92 A 6 5 1.21 25 0.200
93 A 6 5 1.09 25 0.200
94 A 8 7 1.00 25 0.280
95 A 6 5 0.99 25 0.200
96 A 5 4 0.98 25 0.160
97 A 6 5 0.97 23 0.217
98 A 7 6 0.96 25 0.240
99 A 7 7 0.77 25 0.280
100 A 7 7 0.81 25 0.280
101 A 6 6 0.81 25 0.240
102 A 7 7 0.81 25 0.280
103 A 6 6 0.81 22 0.273
104 A 8 8 0.77 25 0.320
105 A 6 5 1.17 27 0.185
106 A 6 5 1.17 27 0.185
107 A 5 4 1.19 27 0.148
108 A 4 3 0.99 27 0.111
109 A 4 3 0.99 27 0.111
110 A 9 8 0.97 27 0.296
111 A 10 9 1.10 27 0.333
112 A 10 9 0.95 27 0.333
113 A 4 3 0.89 25 0.120
114 A 4 3 0.96 27 0.111
115 A 12 12 1.04 27 0.444
116 A 10 10 0.94 27 0.370
117 A 11 11 0.78 27 0.407
118 F 0 0 N/A 0.000 N/A
119 F 0 0 N/A 0.000 N/A

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