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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 [106] had the largest ratio of [.740740999999999983]

# 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 5 4 1.43 21 0.190
2 A 3 3 1.14 29 0.103
3 A 3 3 1.17 34 0.088
4 A 3 3 1.24 41 0.073
5 B 3 3 2.50 31 0.097
6 B 2 2 2.27 29 0.069
7 A 1 1 1.00 21 0.048
8 A 2 2 1.00 31 0.065
9 A 2 2 1.00 31 0.065
10 A 2 2 1.00 31 0.065
11 A 2 2 1.00 31 0.065
12 A 2 2 1.00 31 0.065
13 A 3 3 1.32 45 0.067
14 A 4 4 1.44 52 0.077
15 B 2 2 4.64 35 0.057
16 B 2 2 2.76 33 0.061
17 A 1 1 1.00 22 0.045
18 A 2 2 1.00 33 0.061
19 A 1 1 1.00 28 0.036
20 A 2 2 1.00 35 0.057
21 B 2 2 2.17 35 0.057
22 A 2 2 1.00 35 0.057
23 A 4 4 1.28 69 0.058
24 A 3 3 1.27 67 0.045
25 A 4 4 1.43 65 0.062
26 B 2 2 5.54 54 0.037
27 B 2 2 2.92 52 0.038
28 A 1 1 1.00 41 0.024
29 A 2 2 1.00 50 0.040
30 A 2 2 1.90 39 0.051
31 A 2 2 1.00 54 0.037
32 A 2 2 1.00 54 0.037
33 A 2 2 1.00 54 0.037
34 A 6 5 1.01 29 0.172
35 A 3 2 1.00 31 0.065
36 A 3 2 1.00 27 0.074
37 A 5 4 1.00 27 0.148
38 A 7 6 1.08 27 0.222
39 A 9 8 1.14 27 0.296
40 A 5 4 1.00 31 0.129
41 A 3 2 1.00 23 0.087
42 A 2 2 1.26 31 0.065
43 A 2 2 1.52 34 0.059
44 A 2 2 1.00 23 0.087
45 A 2 2 1.00 23 0.087
46 A 2 2 1.00 23 0.087
47 A 2 2 1.00 21 0.095
48 A 2 2 1.00 23 0.087
49 A 5 4 1.00 23 0.174
50 A 6 5 1.08 23 0.217
51 A 2 2 1.00 25 0.080
52 A 2 2 1.00 25 0.080
53 A 2 2 1.00 25 0.080
54 A 2 2 1.00 23 0.087
55 A 2 2 1.00 25 0.080
56 A 4 4 1.05 25 0.160
57 A 7 6 1.08 25 0.240
58 A 8 7 1.12 25 0.280
59 A 2 2 1.00 25 0.080
60 A 2 2 1.00 25 0.080
61 A 2 2 1.00 25 0.080
62 A 2 2 1.00 23 0.087
63 A 2 2 1.00 25 0.080
64 A 4 4 1.01 25 0.160
65 A 6 6 1.10 25 0.240
66 A 2 2 1.00 25 0.080
67 A 2 2 1.00 25 0.080
68 A 2 2 1.00 25 0.080
69 A 2 2 1.00 23 0.087
70 A 8 7 1.08 25 0.280
71 A 10 9 1.12 25 0.360
72 A 12 11 1.14 25 0.440
73 A 4 4 0.95 25 0.160
74 A 4 4 0.99 25 0.160
75 A 4 4 1.02 25 0.160
76 A 5 4 1.00 23 0.174
77 A 10 9 1.12 25 0.360
78 A 12 11 1.13 25 0.440
79 A 14 13 1.14 25 0.520
80 A 6 6 1.08 25 0.240
81 A 6 6 1.12 25 0.240
82 A 7 6 1.08 25 0.240
83 A 6 5 1.08 23 0.217
84 A 12 11 1.14 25 0.440
85 A 14 13 1.13 25 0.520
86 A 16 15 1.14 25 0.600
87 A 4 4 1.00 20 0.200
88 A 5 5 1.00 19 0.263
89 A 2 2 1.00 25 0.080
90 A 2 2 1.03 25 0.080
91 A 3 3 1.00 15 0.200
92 A 19 18 1.19 27 0.667
93 A 15 14 1.18 27 0.519
94 A 11 10 1.16 27 0.370
95 A 7 6 1.12 25 0.240
96 A 10 9 1.03 27 0.333
97 A 8 7 1.03 27 0.259
98 A 10 9 1.05 27 0.333
99 A 20 19 1.19 27 0.704
100 A 16 15 1.19 27 0.556
101 A 12 11 1.17 27 0.407
102 A 8 7 1.14 25 0.280
103 A 12 11 1.06 27 0.407
104 A 14 13 1.01 27 0.481
105 A 10 9 1.05 27 0.333
106 A 21 20 1.20 27 0.741
107 A 17 16 1.19 27 0.593
108 A 13 12 1.18 27 0.444
109 A 9 8 1.16 25 0.320
110 A 14 13 1.02 27 0.481
111 A 16 15 0.96 27 0.556
112 A 16 15 0.98 27 0.556
113 A 18 17 1.19 27 0.630
114 A 14 13 1.17 27 0.481
115 A 10 9 1.15 27 0.333
116 A 6 5 1.08 25 0.200
117 A 6 5 1.04 27 0.185
118 A 8 7 1.03 27 0.259
119 A 10 9 1.05 27 0.333
120 A 15 14 1.16 27 0.519
121 A 12 11 1.10 27 0.407
122 A 8 7 1.10 27 0.259
123 A 5 4 1.00 25 0.160
124 A 8 7 1.03 27 0.259
125 A 10 9 1.05 27 0.333
126 A 12 11 1.07 27 0.407
127 A 14 13 1.11 27 0.481
128 A 10 9 1.10 27 0.333
129 A 7 6 1.04 27 0.222
130 A 3 3 1.00 25 0.120
131 A 10 9 1.07 27 0.333
132 A 12 11 1.07 27 0.407
133 A 14 13 1.08 27 0.481
134 A 15 14 1.18 25 0.560
135 A 11 10 0.88 27 0.370
136 A 7 6 0.95 25 0.240
137 A 7 6 1.14 27 0.222
138 A 6 5 1.03 27 0.185
139 A 8 7 1.13 25 0.280
140 A 12 11 0.76 27 0.407
141 A 8 7 0.89 25 0.280
142 A 10 9 1.01 27 0.333
143 A 12 11 0.98 27 0.407
144 A 8 7 1.04 27 0.259
145 A 10 9 1.07 25 0.360
146 A 15 14 1.01 27 0.519
147 A 14 13 1.05 27 0.481
148 A 10 9 1.07 27 0.333
149 A 6 5 1.04 25 0.200
150 A 4 3 1.00 27 0.111
151 A 6 5 0.97 27 0.185
152 A 8 7 1.06 25 0.280
153 A 12 11 1.09 27 0.407
154 A 8 7 1.10 27 0.259
155 A 5 4 1.03 25 0.160
156 F 0 0 N/A 0.000 N/A
157 A 8 7 1.06 25 0.280
158 A 10 9 1.04 25 0.360
159 A 7 6 1.06 27 0.222
160 A 3 3 0.99 25 0.120
161 A 8 7 1.10 25 0.280
162 A 10 9 1.08 25 0.360
163 A 6 5 1.00 27 0.185
164 B 4 3 2.05 29 0.103
165 A 4 3 1.00 29 0.103
166 A 8 8 1.21 25 0.320
167 A 6 6 1.16 25 0.240
168 A 4 4 1.18 23 0.174
169 A 1 1 1.44 12 0.083
170 F 0 0 N/A 0.000 N/A
171 F 0 0 N/A 0.000 N/A
172 F 0 0 N/A 0.000 N/A
173 F 0 0 N/A 0.000 N/A
174 F 0 0 N/A 0.000 N/A
175 F 0 0 N/A 0.000 N/A
176 F 0 0 N/A 0.000 N/A
177 F 0 0 N/A 0.000 N/A
178 F 0 0 N/A 0.000 N/A
179 F 0 0 N/A 0.000 N/A
180 A 2 2 1.00 19 0.105

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