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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 [24] 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 10 10 1.00 36 0.278
2 A 6 6 1.00 30 0.200
3 A 6 6 1.00 36 0.167
4 A 10 10 1.05 38 0.263
5 A 9 9 1.05 38 0.237
6 A 12 12 1.03 38 0.316
7 A 14 14 1.02 38 0.368
8 A 17 17 1.02 38 0.447
9 A 13 13 1.08 38 0.342
10 A 8 8 1.00 32 0.250
11 A 8 8 1.00 38 0.211
12 A 9 9 1.03 40 0.225
13 A 9 9 1.03 40 0.225
14 A 12 12 1.03 40 0.300
15 A 14 14 1.03 40 0.350
16 A 17 17 1.01 40 0.425
17 A 10 10 1.00 32 0.312
18 A 10 10 1.00 38 0.263
19 A 13 13 1.02 40 0.325
20 A 12 12 1.02 40 0.300
21 A 13 13 1.02 40 0.325
22 A 15 15 1.05 40 0.375
23 A 19 19 1.07 40 0.475
24 A 20 20 1.04 40 0.500
25 A 14 13 1.13 40 0.325
26 A 12 11 1.07 38 0.289
27 A 5 4 1.12 32 0.125
28 A 6 6 1.00 38 0.158
29 A 8 8 1.02 40 0.200
30 A 10 10 1.08 40 0.250
31 A 14 14 1.12 40 0.350
32 A 15 14 1.08 40 0.350
33 A 12 11 1.09 38 0.289
34 A 6 6 1.10 32 0.188
35 A 8 8 1.10 38 0.211
36 A 10 10 1.18 40 0.250
37 A 12 12 1.16 40 0.300
38 A 18 17 1.10 40 0.425
39 A 14 13 1.14 40 0.325
40 A 11 11 1.14 38 0.289
41 A 8 8 1.12 32 0.250
42 A 10 10 1.13 38 0.263
43 A 13 13 1.20 40 0.325
44 A 15 15 1.16 40 0.375
45 A 9 8 1.03 39 0.205
46 A 9 8 0.96 39 0.205
47 A 9 8 0.96 41 0.195
48 A 9 8 0.96 41 0.195
49 C 5 4 0.79 43 0.093
50 A 13 13 1.05 43 0.302
51 A 11 11 1.05 43 0.256
52 A 8 8 1.08 41 0.195
53 A 6 6 1.00 31 0.194
54 A 10 9 1.04 43 0.209
55 A 9 8 1.06 43 0.186
56 A 8 8 1.08 43 0.186
57 A 17 17 1.05 45 0.378
58 A 14 14 1.06 45 0.311
59 A 10 10 1.04 43 0.233
60 A 8 8 1.00 33 0.242
61 A 13 12 1.06 45 0.267
62 A 11 10 1.03 45 0.222
63 A 12 11 1.06 45 0.244
64 A 16 16 1.05 45 0.356
65 A 12 12 1.04 43 0.279
66 A 10 10 1.00 33 0.303
67 A 16 15 1.07 45 0.333
68 A 14 13 1.03 45 0.289
69 A 14 13 1.04 45 0.289
70 A 16 15 1.07 45 0.333
71 A 13 12 1.07 45 0.267
72 A 9 8 1.04 43 0.186
73 A 7 6 1.00 33 0.182
74 A 4 4 0.99 45 0.089
75 A 7 7 1.13 45 0.156
76 A 10 10 1.13 45 0.222
77 A 14 13 1.03 45 0.289
78 A 11 10 1.04 45 0.222
79 A 9 8 1.04 43 0.186
80 A 6 6 1.08 33 0.182
81 A 7 7 1.12 45 0.156
82 A 9 9 1.11 45 0.200
83 A 11 11 1.09 45 0.244
84 A 14 13 1.04 45 0.289
85 A 12 11 1.06 45 0.244
86 A 9 9 1.08 43 0.209
87 A 9 9 1.12 33 0.273
88 A 9 9 1.13 45 0.200
89 A 11 11 1.08 45 0.244
90 A 21 20 1.03 47 0.426
91 A 18 17 1.02 47 0.362
92 A 15 14 0.97 45 0.311
93 A 12 11 0.86 35 0.314
94 A 16 15 0.96 47 0.319
95 A 17 16 1.03 47 0.340
96 A 20 19 1.08 47 0.404
97 A 23 22 1.03 47 0.468
98 A 20 19 1.02 47 0.404
99 A 17 16 0.98 45 0.356
100 A 14 13 0.89 35 0.371
101 A 20 19 1.01 47 0.404
102 A 20 19 1.04 47 0.404
103 A 20 19 1.06 47 0.404
104 A 22 21 1.02 47 0.447
105 A 19 18 0.98 45 0.400
106 A 16 15 0.91 35 0.429
107 A 24 23 1.01 47 0.489
108 F 0 0 N/A 0.000 N/A
109 F 0 0 N/A 0.000 N/A
110 A 19 18 1.03 47 0.383
111 A 16 15 1.00 47 0.319
112 A 13 12 0.95 45 0.267
113 A 10 9 0.84 35 0.257
114 A 13 12 0.93 47 0.255
115 A 17 16 1.09 47 0.340
116 A 19 18 1.00 47 0.383
117 A 16 15 1.01 47 0.319
118 A 12 11 1.09 45 0.244
119 A 10 9 1.03 35 0.257
120 A 17 16 1.18 47 0.340
121 A 20 19 1.15 47 0.404
122 A 19 18 1.03 47 0.383
123 A 15 14 1.08 47 0.298
124 A 13 12 1.10 45 0.267
125 A 13 12 1.11 35 0.343
126 A 19 18 1.22 47 0.383
127 A 23 22 1.13 47 0.468
128 A 17 16 1.04 49 0.327
129 A 14 13 1.04 49 0.265
130 A 11 10 1.02 49 0.204
131 A 8 7 1.02 49 0.143
132 A 8 7 1.10 49 0.143
133 A 13 12 1.19 49 0.245
134 A 16 15 1.16 49 0.306
135 A 17 16 1.04 49 0.327
136 A 14 13 1.03 49 0.265
137 A 12 11 1.02 49 0.224
138 A 11 10 1.10 49 0.204
139 A 11 10 1.14 49 0.204
140 A 16 15 1.16 49 0.306
141 A 17 16 1.03 49 0.327
142 A 14 13 1.04 49 0.265
143 A 14 13 1.05 49 0.265
144 A 14 13 1.11 49 0.265
145 A 14 13 1.12 49 0.265
146 F 0 0 N/A 0.000 N/A
147 A 14 13 1.04 49 0.265
148 A 11 10 1.02 49 0.204
149 A 8 7 1.01 49 0.143
150 A 5 4 0.97 49 0.082
151 A 10 9 1.21 49 0.184
152 A 13 12 1.22 49 0.245
153 A 14 13 1.05 49 0.265
154 A 11 10 1.10 49 0.204
155 A 8 7 1.10 49 0.143
156 A 10 9 1.20 49 0.184
157 A 13 12 1.22 49 0.245
158 A 16 15 1.18 49 0.306
159 A 14 13 1.10 49 0.265
160 A 11 10 1.14 49 0.204
161 A 13 12 1.19 49 0.245
162 A 13 12 1.22 49 0.245
163 A 16 15 1.15 49 0.306
164 A 5 4 0.99 45 0.089
165 A 17 16 1.04 45 0.356
166 A 13 12 1.06 45 0.267
167 A 11 10 1.06 43 0.233
168 A 9 8 1.00 33 0.242
169 A 11 10 1.03 45 0.222
170 A 14 13 1.12 45 0.289
171 F 0 0 N/A 0.000 N/A

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