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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 [78] 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 1 1 1.00 24 0.042
2 A 1 1 1.00 24 0.042
3 B 2 2 4.33 19 0.105
4 A 1 1 1.00 24 0.042
5 A 1 1 1.00 24 0.042
6 A 1 1 1.00 24 0.042
7 A 1 1 1.00 24 0.042
8 A 1 1 1.26 29 0.034
9 A 1 1 1.20 27 0.037
10 A 2 2 1.83 20 0.100
11 A 1 1 1.27 29 0.034
12 A 1 1 1.26 29 0.034
13 A 1 1 1.26 29 0.034
14 A 1 1 1.43 31 0.032
15 A 2 2 1.60 20 0.100
16 A 2 2 1.24 18 0.111
17 A 2 2 1.00 20 0.100
18 A 3 3 1.01 20 0.150
19 A 2 2 1.51 20 0.100
20 A 2 2 1.18 18 0.111
21 A 2 2 1.00 20 0.100
22 A 3 3 1.00 20 0.150
23 B 2 2 2.20 22 0.091
24 A 2 2 1.69 20 0.100
25 A 2 2 1.00 22 0.091
26 A 3 3 1.29 22 0.136
27 A 2 2 1.00 20 0.100
28 A 2 2 1.00 18 0.111
29 A 2 2 1.00 17 0.118
30 A 2 2 1.00 20 0.100
31 A 2 2 1.00 20 0.100
32 A 2 2 1.00 23 0.087
33 A 2 2 1.00 23 0.087
34 A 2 2 1.00 21 0.095
35 A 2 2 1.00 20 0.100
36 A 2 2 1.00 23 0.087
37 A 2 2 1.00 23 0.087
38 A 5 5 1.21 17 0.294
39 A 4 4 1.18 17 0.235
40 A 3 3 1.13 17 0.176
41 A 2 2 1.00 15 0.133
42 A 1 1 1.00 9 0.111
43 A 1 1 1.00 17 0.059
44 A 2 2 1.00 17 0.118
45 A 3 3 0.97 17 0.176
46 A 4 4 0.99 17 0.235
47 A 5 5 1.01 17 0.294
48 A 6 6 1.21 48 0.125
49 A 5 5 1.18 37 0.135
50 A 4 4 1.13 26 0.154
51 A 3 3 1.00 28 0.107
52 A 4 4 0.97 39 0.103
53 A 5 5 0.99 50 0.100
54 A 6 6 1.01 61 0.098
55 B 2 2 4.10 16 0.125
56 B 2 2 2.47 21 0.095
57 A 1 1 1.00 7 0.143
58 A 1 1 1.00 7 0.143
59 A 1 1 1.00 7 0.143
60 A 7 6 1.21 13 0.462
61 A 6 5 1.17 13 0.385
62 A 5 4 1.11 13 0.308
63 A 4 3 1.00 13 0.231
64 A 3 2 1.00 13 0.154
65 A 4 3 1.00 13 0.231
66 A 5 4 1.01 13 0.308
67 A 6 5 1.02 13 0.385
68 A 7 6 1.02 13 0.462
69 A 7 6 1.15 19 0.316
70 A 6 5 1.13 19 0.263
71 A 5 4 1.09 19 0.211
72 A 4 3 1.00 19 0.158
73 A 3 2 1.00 19 0.105
74 A 4 3 1.00 19 0.158
75 A 5 4 1.03 19 0.211
76 A 6 5 1.04 19 0.263
77 A 7 6 1.04 19 0.316
78 A 10 9 1.24 12 0.750
79 A 1 1 1.00 19 0.053
80 A 2 2 1.00 21 0.095
81 A 2 2 1.00 50 0.040
82 A 2 2 1.00 39 0.051
83 A 2 2 1.00 28 0.071
84 A 1 1 1.00 17 0.059
85 A 1 1 1.00 19 0.053
86 A 2 2 1.00 30 0.067
87 A 2 2 1.00 41 0.049
88 A 1 1 1.00 17 0.059
89 A 2 2 1.00 19 0.105
90 A 2 2 1.00 15 0.133
91 A 2 2 1.69 20 0.100
92 A 2 2 1.94 25 0.080
93 B 2 2 2.15 30 0.067
94 A 2 2 1.00 21 0.095
95 A 2 2 1.75 21 0.095
96 A 2 2 1.70 21 0.095
97 A 2 2 1.34 19 0.105
98 A 4 4 1.08 18 0.222
99 A 2 2 1.00 21 0.095
100 A 2 2 1.00 21 0.095
101 A 2 2 1.00 21 0.095
102 A 2 2 1.00 21 0.095
103 A 2 2 1.00 22 0.091
104 A 2 2 1.89 22 0.091
105 A 2 2 1.93 22 0.091
106 A 2 2 1.88 20 0.100
107 A 4 4 1.12 19 0.211
108 A 2 2 1.00 22 0.091
109 A 2 2 1.00 22 0.091
110 A 2 2 1.00 22 0.091
111 A 2 2 1.00 22 0.091
112 A 2 2 1.00 22 0.091
113 A 2 2 0.94 25 0.080
114 A 2 2 0.99 25 0.080
115 A 2 2 0.99 23 0.087
116 A 5 5 1.09 18 0.278
117 A 2 2 1.00 25 0.080
118 A 2 2 1.00 25 0.080
119 A 2 2 1.00 25 0.080
120 A 2 2 1.00 25 0.080
121 A 2 2 1.00 25 0.080
122 A 1 1 1.00 39 0.026
123 A 1 1 1.00 38 0.026
124 A 1 1 1.00 36 0.028
125 A 1 1 1.00 35 0.029
126 A 1 1 1.00 35 0.029
127 A 1 1 1.00 38 0.026
128 A 1 1 1.00 38 0.026
129 A 5 5 1.20 15 0.333
130 A 4 4 1.17 15 0.267
131 A 3 3 1.11 15 0.200
132 A 2 2 1.00 13 0.154
133 A 1 1 1.00 11 0.091
134 A 2 2 1.44 15 0.133
135 A 3 3 1.25 15 0.200
136 A 4 4 1.18 15 0.267
137 A 5 5 1.17 15 0.333

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