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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 [129] had the largest ratio of [.894737000000000005]

# 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 3 3 1.00 23 0.130
2 A 3 3 1.00 23 0.130
3 A 3 3 1.00 23 0.130
4 A 1 1 1.00 21 0.048
5 A 2 2 1.00 23 0.087
6 A 2 2 1.00 23 0.087
7 A 2 2 1.00 23 0.087
8 A 4 4 1.14 24 0.167
9 A 4 4 0.65 25 0.160
10 A 4 4 0.75 25 0.160
11 A 4 4 1.04 25 0.160
12 A 5 4 1.22 25 0.160
13 A 8 7 0.90 25 0.280
14 A 11 10 0.85 25 0.400
15 A 3 3 1.13 23 0.130
16 A 2 2 1.00 12 0.167
17 A 2 2 1.00 12 0.167
18 A 1 1 1.00 10 0.100
19 A 10 9 1.09 12 0.750
20 A 5 5 1.11 12 0.417
21 C 4 3 0.53 14 0.214
22 A 4 3 1.00 12 0.250
23 A 2 2 1.00 12 0.167
24 A 2 2 1.00 12 0.167
25 A 1 1 1.00 10 0.100
26 C 10 9 2.35 12 0.750
27 C 5 5 2.12 12 0.417
28 C 4 3 2.52 14 0.214
29 C 4 3 2.13 12 0.250
30 C 4 3 2.65 12 0.250
31 C 5 4 1.14 22 0.182
32 A 3 3 1.00 25 0.120
33 A 3 3 1.00 25 0.120
34 A 3 3 1.00 25 0.120
35 A 1 1 1.00 23 0.043
36 A 2 2 1.00 25 0.080
37 A 2 2 1.00 25 0.080
38 A 2 2 1.00 25 0.080
39 A 4 4 0.75 27 0.148
40 A 4 4 0.85 27 0.148
41 A 4 4 1.17 27 0.148
42 A 5 4 1.36 27 0.148
43 A 8 7 1.00 27 0.259
44 A 11 10 0.95 27 0.370
45 A 3 3 1.12 25 0.120
46 A 2 2 1.00 14 0.143
47 A 2 2 1.00 14 0.143
48 A 1 1 1.00 12 0.083
49 A 11 10 1.06 14 0.714
50 A 8 7 1.04 14 0.500
51 C 6 5 0.38 16 0.312
52 A 5 4 1.06 14 0.286
53 A 2 2 1.00 14 0.143
54 A 2 2 1.00 14 0.143
55 A 1 1 1.00 12 0.083
56 C 11 10 2.51 14 0.714
57 C 7 6 2.39 14 0.429
58 C 11 10 3.13 16 0.625
59 C 5 4 2.05 16 0.250
60 C 5 4 2.71 14 0.286
61 A 2 2 1.00 29 0.069
62 A 2 2 1.00 29 0.069
63 A 2 2 1.00 27 0.074
64 A 2 2 1.00 29 0.069
65 A 2 2 1.00 29 0.069
66 A 2 2 1.00 29 0.069
67 A 2 2 0.53 31 0.065
68 A 2 2 0.53 31 0.065
69 A 2 2 0.53 31 0.065
70 A 2 2 0.51 31 0.065
71 A 2 2 0.53 31 0.065
72 A 2 2 0.53 31 0.065
73 A 4 3 1.00 9 0.333
74 A 2 2 0.56 29 0.069
75 B 2 2 2.31 32 0.062
76 A 1 1 1.00 30 0.033
77 A 5 5 1.10 32 0.156
78 A 5 5 1.05 32 0.156
79 A 5 5 1.03 32 0.156
80 A 4 4 0.74 34 0.118
81 A 4 4 1.01 34 0.118
82 A 5 4 1.31 34 0.118
83 A 8 7 0.98 34 0.206
84 A 11 10 0.93 34 0.294
85 A 3 3 1.32 32 0.094
86 A 4 3 1.13 27 0.111
87 A 4 3 1.11 27 0.111
88 A 4 3 1.14 27 0.111
89 A 1 1 1.00 25 0.040
90 A 10 9 1.05 27 0.333
91 A 11 10 1.12 27 0.370
92 A 12 11 1.15 27 0.407
93 A 6 5 1.28 32 0.156
94 A 5 4 1.27 32 0.125
95 A 4 3 1.25 32 0.094
96 A 3 2 1.26 32 0.062
97 A 4 3 1.25 32 0.094
98 A 5 4 1.27 32 0.125
99 A 6 5 1.28 32 0.156
100 A 4 3 1.24 30 0.100
101 C 4 3 2.21 23 0.130
102 A 4 3 1.13 24 0.125
103 C 4 3 2.04 23 0.130
104 A 4 3 1.27 24 0.125
105 A 3 3 1.00 23 0.130
106 A 3 3 1.00 23 0.130
107 A 3 3 1.00 23 0.130
108 A 1 1 1.00 21 0.048
109 A 2 2 1.00 23 0.087
110 A 2 2 1.14 23 0.087
111 A 2 2 1.21 23 0.087
112 A 2 2 1.00 11 0.182
113 A 2 2 1.00 17 0.118
114 A 15 14 0.88 19 0.737
115 A 14 13 1.11 19 0.684
116 A 5 4 1.39 19 0.211
117 A 14 13 1.01 19 0.684
118 A 17 16 0.95 19 0.842
119 A 4 3 1.11 23 0.130
120 A 3 3 1.00 46 0.065
121 A 3 3 1.00 46 0.065
122 A 1 1 1.00 44 0.023
123 A 2 2 1.00 46 0.043
124 A 2 2 1.00 46 0.043
125 A 2 2 1.00 46 0.043
126 F 0 0 N/A 0.000 N/A
127 F 0 0 N/A 0.000 N/A
128 F 0 0 N/A 0.000 N/A
129 C 18 17 5.60 19 0.895
130 C 14 13 5.79 19 0.684
131 C 12 11 7.93 19 0.579
132 C 6 5 5.86 19 0.263
133 C 12 11 6.63 19 0.579
134 C 16 15 6.27 19 0.789
135 F 0 0 N/A 0.000 N/A
136 F 0 0 N/A 0.000 N/A
137 A 3 3 1.00 32 0.094
138 A 3 3 1.00 32 0.094
139 A 1 1 1.00 30 0.033
140 A 2 2 1.00 32 0.062
141 A 2 2 1.13 32 0.062
142 F 0 0 N/A 0.000 N/A
143 F 0 0 N/A 0.000 N/A
144 F 0 0 N/A 0.000 N/A
145 F 0 0 N/A 0.000 N/A
146 F 0 0 N/A 0.000 N/A
147 F 0 0 N/A 0.000 N/A
148 C 6 5 1.21 19 0.263
149 F 0 0 N/A 0.000 N/A
150 A 2 2 1.00 15 0.133
151 A 2 2 1.00 15 0.133
152 A 1 1 1.00 13 0.077
153 C 11 10 3.16 15 0.667
154 C 8 7 3.04 15 0.467
155 C 5 4 3.16 15 0.267
156 A 2 2 1.00 15 0.133
157 A 2 2 1.00 15 0.133
158 A 1 1 1.00 13 0.077
159 A 11 10 1.00 15 0.667
160 A 8 7 0.97 15 0.467
161 A 5 4 1.05 15 0.267
162 A 1 1 1.00 7 0.143
163 A 3 3 1.00 13 0.231
164 A 6 5 1.18 11 0.455
165 A 8 7 1.02 16 0.438
166 A 9 8 0.97 9 0.889
167 A 5 4 1.74 17 0.235
168 A 5 4 1.56 42 0.095
169 A 2 2 1.00 7 0.286
170 A 3 3 1.00 13 0.231
171 A 3 3 1.00 11 0.273
172 A 4 3 1.00 16 0.188
173 A 2 2 1.26 9 0.222

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