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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 [93] had the largest ratio of [.800000000000000044]

# 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 0.95 22 0.227
2 A 6 5 0.97 22 0.227
3 A 6 5 1.03 20 0.250
4 A 6 5 0.78 22 0.227
5 A 9 8 0.84 22 0.364
6 A 11 10 0.88 22 0.455
7 A 9 9 1.18 24 0.375
8 A 8 8 1.12 24 0.333
9 A 5 5 1.10 22 0.227
10 A 7 6 0.70 24 0.250
11 A 11 10 0.78 24 0.417
12 A 18 17 1.49 24 0.708
13 A 14 13 1.32 24 0.542
14 A 10 9 1.20 22 0.409
15 A 8 7 0.69 24 0.292
16 A 16 15 0.74 24 0.625
17 A 5 4 0.76 20 0.200
18 A 5 4 0.80 20 0.200
19 A 5 4 0.93 18 0.222
20 N/A 1 0 1.00 20 0.000
21 N/A 1 0 1.00 20 0.000
22 A 5 4 0.84 20 0.200
23 A 5 4 0.88 20 0.200
24 A 5 4 0.98 18 0.222
25 N/A 2 0 1.00 20 0.000
26 N/A 2 0 1.00 20 0.000
27 A 6 5 0.77 24 0.208
28 A 6 5 0.79 24 0.208
29 A 6 5 0.85 22 0.227
30 N/A 1 0 1.00 24 0.000
31 N/A 1 0 1.00 24 0.000
32 A 5 4 0.80 24 0.167
33 A 5 4 0.82 24 0.167
34 A 5 4 0.89 22 0.182
35 N/A 2 0 1.00 24 0.000
36 N/A 2 0 1.00 24 0.000
37 A 8 8 1.07 24 0.333
38 A 6 6 1.07 24 0.250
39 A 3 3 1.00 24 0.125
40 A 1 1 1.00 24 0.042
41 A 2 2 1.00 24 0.083
42 A 4 4 1.04 24 0.167
43 A 6 6 1.08 24 0.250
44 A 10 10 1.20 26 0.385
45 A 5 5 0.97 26 0.192
46 A 1 1 1.00 26 0.038
47 A 10 9 0.91 26 0.346
48 A 13 12 0.96 26 0.462
49 A 3 3 1.00 14 0.214
50 A 1 1 1.00 21 0.048
51 A 8 8 1.06 24 0.333
52 A 6 6 1.10 24 0.250
53 A 3 3 1.00 24 0.125
54 A 1 1 1.00 24 0.042
55 A 2 2 1.00 24 0.083
56 A 4 4 1.03 24 0.167
57 A 6 6 1.06 24 0.250
58 A 10 10 1.12 26 0.385
59 A 5 5 0.88 26 0.192
60 A 1 1 1.00 26 0.038
61 A 10 9 0.68 26 0.346
62 A 13 12 0.84 26 0.462
63 A 14 14 1.04 22 0.636
64 A 6 6 0.79 22 0.273
65 A 1 1 1.00 22 0.045
66 A 11 10 0.64 22 0.455
67 A 15 14 0.75 22 0.636
68 A 5 4 0.47 26 0.154
69 A 5 4 0.52 26 0.154
70 A 5 4 0.60 26 0.154
71 A 1 1 1.11 26 0.038
72 N/A 1 0 1.00 26 0.000
73 N/A 1 0 1.00 26 0.000
74 A 6 5 0.56 26 0.192
75 A 6 5 0.65 26 0.192
76 A 12 11 0.80 26 0.423
77 A 1 1 1.00 26 0.038
78 N/A 2 0 1.00 26 0.000
79 N/A 2 0 1.00 26 0.000
80 A 6 5 1.00 18 0.278
81 A 6 5 1.00 18 0.278
82 A 6 5 1.01 18 0.278
83 A 6 5 1.04 16 0.312
84 A 1 1 1.00 8 0.125
85 A 2 2 1.00 18 0.111
86 A 2 2 1.00 20 0.100
87 A 2 2 1.00 20 0.100
88 A 2 2 1.00 18 0.111
89 A 3 3 1.11 10 0.300
90 A 2 2 1.00 20 0.100
91 A 2 2 1.00 20 0.100
92 A 2 2 1.00 18 0.111
93 A 9 8 0.93 10 0.800
94 N/A 1 0 1.00 20 0.000
95 N/A 1 0 1.00 20 0.000
96 A 2 2 1.00 20 0.100
97 A 2 2 1.00 18 0.111
98 A 9 8 0.94 10 0.800
99 N/A 1 0 1.00 20 0.000
100 N/A 1 0 1.00 20 0.000
101 N/A 1 0 1.00 20 0.000
102 N/A 1 0 1.00 20 0.000
103 A 6 5 1.00 20 0.250
104 A 7 6 1.01 20 0.300
105 A 9 8 1.07 20 0.400
106 N/A 1 0 1.00 22 0.000
107 N/A 1 0 1.00 22 0.000
108 N/A 1 0 1.00 22 0.000
109 N/A 1 0 1.00 22 0.000
110 N/A 1 0 1.00 22 0.000
111 N/A 1 0 1.00 22 0.000
112 N/A 1 0 1.00 22 0.000
113 N/A 1 0 1.00 22 0.000
114 N/A 1 0 1.00 22 0.000
115 N/A 1 0 1.00 22 0.000
116 N/A 1 0 1.00 22 0.000
117 N/A 1 0 1.00 22 0.000

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