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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 [83] had the largest ratio of [.368420999999999998]

# 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 8 8 1.11 33 0.242
2 A 7 7 1.03 31 0.226
3 A 5 5 1.03 30 0.167
4 A 10 9 1.00 33 0.273
5 A 9 8 1.00 33 0.242
6 A 8 7 1.04 33 0.212
7 A 10 9 1.06 33 0.273
8 A 13 12 1.06 33 0.364
9 A 11 10 1.10 32 0.312
10 A 9 8 1.26 30 0.267
11 A 4 4 0.91 29 0.138
12 A 10 9 1.62 32 0.281
13 A 9 8 1.62 32 0.250
14 A 7 6 1.23 32 0.188
15 A 8 7 1.15 32 0.219
16 A 10 9 1.09 32 0.281
17 A 5 4 1.11 35 0.114
18 A 5 4 1.17 35 0.114
19 A 5 4 1.28 33 0.121
20 A 7 6 1.07 35 0.171
21 A 8 7 1.51 35 0.200
22 A 9 8 1.43 35 0.229
23 A 9 8 1.26 35 0.229
24 A 8 7 0.89 35 0.200
25 A 7 6 1.28 32 0.188
26 A 8 7 1.34 35 0.200
27 A 7 6 1.35 35 0.171
28 A 5 5 1.26 35 0.143
29 A 6 6 1.08 35 0.171
30 A 7 7 0.99 35 0.200
31 A 11 11 0.95 37 0.297
32 A 9 9 0.95 37 0.243
33 A 7 7 1.03 35 0.200
34 A 6 6 0.96 30 0.200
35 A 11 10 1.11 37 0.270
36 A 9 8 1.11 37 0.216
37 A 9 8 1.06 37 0.216
38 A 11 11 1.08 37 0.297
39 A 9 9 1.07 37 0.243
40 A 6 6 1.10 35 0.171
41 A 5 5 1.03 30 0.167
42 A 9 8 1.04 37 0.216
43 A 7 6 1.13 37 0.162
44 A 6 5 1.06 37 0.135
45 A 14 13 0.92 40 0.325
46 A 11 10 0.96 40 0.250
47 A 9 8 1.11 38 0.211
48 A 7 6 0.90 33 0.182
49 A 12 11 1.09 40 0.275
50 A 11 10 1.04 40 0.250
51 A 11 10 1.13 40 0.250
52 A 14 13 1.04 40 0.325
53 A 11 10 1.08 40 0.250
54 A 8 7 1.22 38 0.184
55 A 6 5 0.93 33 0.152
56 A 10 9 1.25 40 0.225
57 A 9 8 1.31 40 0.200
58 A 7 6 1.19 40 0.150
59 A 7 6 1.10 32 0.188
60 A 2 2 1.00 24 0.083
61 A 2 2 1.00 32 0.062
62 A 2 2 1.00 30 0.067
63 A 10 9 0.60 36 0.250
64 A 8 7 0.64 34 0.206
65 A 8 7 0.75 29 0.241
66 A 11 10 1.06 36 0.278
67 A 11 10 1.04 36 0.278
68 A 11 10 1.05 36 0.278
69 A 9 8 0.75 36 0.222
70 A 7 6 0.78 34 0.176
71 A 7 6 0.85 29 0.207
72 A 9 8 1.07 36 0.222
73 A 9 8 1.09 36 0.222
74 A 9 8 1.20 36 0.222
75 A 9 8 1.05 36 0.222
76 A 8 7 1.02 36 0.194
77 A 6 5 1.04 34 0.147
78 A 6 5 1.02 29 0.172
79 A 7 6 1.09 36 0.167
80 A 7 6 1.18 36 0.167
81 A 7 6 1.10 36 0.167
82 A 9 8 1.13 36 0.222
83 A 14 14 1.03 38 0.368
84 A 12 12 1.04 38 0.316
85 A 12 12 1.03 38 0.316
86 A 12 12 1.01 38 0.316
87 A 12 12 1.04 38 0.316
88 A 14 14 1.03 38 0.368
89 A 14 14 1.03 38 0.368
90 A 12 12 1.03 38 0.316
91 A 10 10 1.03 38 0.263
92 A 10 10 1.03 38 0.263
93 A 10 10 1.06 38 0.263
94 A 12 12 1.04 38 0.316
95 A 12 12 1.04 38 0.316
96 A 10 10 1.03 38 0.263
97 A 8 8 1.03 38 0.211
98 A 8 8 1.05 38 0.211
99 A 10 10 1.05 38 0.263
100 A 12 12 1.05 38 0.316

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