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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 [135] had the largest ratio of [1]

# 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 7 6 1.02 22 0.273
2 A 7 6 1.08 22 0.273
3 A 4 4 1.03 20 0.200
4 C 7 6 0.98 22 0.273
5 C 10 9 0.98 22 0.409
6 C 12 11 0.97 22 0.500
7 A 11 11 1.17 24 0.458
8 A 10 10 1.11 24 0.417
9 A 7 7 1.09 22 0.318
10 C 8 7 0.88 24 0.292
11 C 14 13 0.95 24 0.542
12 C 16 15 0.97 24 0.625
13 A 22 21 1.47 24 0.875
14 A 17 16 1.26 24 0.667
15 A 10 10 1.21 22 0.455
16 C 9 8 0.87 24 0.333
17 C 20 19 0.91 24 0.792
18 C 6 5 0.91 20 0.250
19 C 6 5 0.96 20 0.250
20 C 6 5 1.14 18 0.278
21 N/A 1 0 1.00 20 0.000
22 N/A 1 0 1.00 20 0.000
23 A 5 4 0.85 20 0.200
24 A 5 4 0.89 20 0.200
25 A 5 4 0.98 18 0.222
26 N/A 2 0 1.00 20 0.000
27 N/A 2 0 1.00 20 0.000
28 C 7 6 0.84 24 0.250
29 C 7 6 0.86 24 0.250
30 C 7 6 0.93 22 0.273
31 N/A 1 0 1.00 24 0.000
32 N/A 1 0 1.00 24 0.000
33 A 5 4 0.80 24 0.167
34 A 5 4 0.82 24 0.167
35 A 5 4 0.89 22 0.182
36 N/A 2 0 1.00 24 0.000
37 N/A 2 0 1.00 24 0.000
38 A 11 11 1.20 24 0.458
39 A 8 8 1.21 24 0.333
40 A 3 3 1.17 24 0.125
41 A 1 1 1.20 24 0.042
42 A 2 2 1.17 24 0.083
43 A 5 5 1.19 24 0.208
44 A 9 9 1.22 24 0.375
45 A 12 12 1.18 26 0.462
46 A 5 5 0.97 26 0.192
47 A 1 1 1.20 26 0.038
48 C 10 9 0.86 26 0.346
49 C 14 13 0.96 26 0.500
50 A 3 3 1.00 14 0.214
51 A 1 1 1.00 21 0.048
52 A 11 11 1.10 24 0.458
53 A 8 8 1.10 24 0.333
54 A 3 3 1.00 24 0.125
55 A 1 1 0.95 24 0.042
56 A 2 2 1.00 24 0.083
57 A 5 5 1.10 24 0.208
58 A 9 9 1.16 24 0.375
59 A 12 12 1.10 26 0.462
60 A 5 5 0.89 26 0.192
61 A 1 1 0.95 26 0.038
62 C 10 9 0.71 26 0.346
63 C 14 13 0.87 26 0.500
64 C 18 17 1.00 22 0.773
65 A 18 18 1.01 22 0.818
66 A 6 6 0.79 22 0.273
67 A 1 1 0.94 22 0.045
68 C 11 10 0.59 22 0.455
69 C 16 15 0.73 22 0.682
70 A 6 5 0.45 26 0.192
71 A 5 4 0.50 26 0.154
72 A 6 5 0.57 26 0.192
73 A 1 1 0.92 26 0.038
74 N/A 1 0 1.00 26 0.000
75 N/A 1 0 1.00 26 0.000
76 A 7 6 0.54 26 0.231
77 A 8 7 0.64 26 0.269
78 C 14 13 0.83 26 0.500
79 A 1 1 0.96 26 0.038
80 N/A 3 0 1.00 26 0.000
81 N/A 4 0 1.00 26 0.000
82 C 18 17 1.00 24 0.708
83 C 12 11 0.88 24 0.458
84 A 1 1 0.94 24 0.042
85 N/A 2 0 1.00 24 0.000
86 N/A 4 0 1.00 24 0.000
87 A 8 7 0.67 24 0.292
88 A 1 1 0.94 24 0.042
89 N/A 2 0 1.00 24 0.000
90 N/A 6 0 1.00 24 0.000
91 C 15 14 0.78 24 0.583
92 A 1 1 0.94 24 0.042
93 N/A 2 0 1.00 24 0.000
94 N/A 6 0 1.00 24 0.000
95 C 19 18 1.00 24 0.750
96 C 12 11 0.88 24 0.458
97 A 1 1 0.96 24 0.042
98 N/A 3 0 1.00 24 0.000
99 N/A 6 0 1.00 24 0.000
100 A 8 7 0.69 24 0.292
101 A 1 1 0.96 24 0.042
102 N/A 3 0 1.00 24 0.000
103 N/A 8 0 1.00 24 0.000
104 A 6 5 0.47 24 0.208
105 A 5 4 0.50 24 0.167
106 A 6 5 0.59 24 0.208
107 A 1 1 0.94 24 0.042
108 N/A 1 0 1.00 24 0.000
109 N/A 1 0 1.00 24 0.000
110 A 6 5 0.56 24 0.208
111 A 7 6 0.64 24 0.250
112 C 11 10 0.87 24 0.417
113 A 1 1 0.94 24 0.042
114 N/A 3 0 1.00 24 0.000
115 N/A 4 0 1.00 24 0.000
116 A 13 12 0.76 24 0.500
117 A 10 9 0.91 24 0.375
118 A 1 1 0.94 24 0.042
119 N/A 3 0 1.00 24 0.000
120 N/A 4 0 1.00 24 0.000
121 A 7 6 1.02 18 0.333
122 A 7 6 1.03 14 0.429
123 A 7 6 1.07 14 0.429
124 A 7 6 1.14 14 0.429
125 A 4 4 1.07 12 0.333
126 A 2 2 1.00 14 0.143
127 A 2 2 1.00 14 0.143
128 A 2 2 1.00 20 0.100
129 A 2 2 1.00 20 0.100
130 A 2 2 1.00 18 0.111
131 A 3 3 1.08 10 0.300
132 A 2 2 1.00 20 0.100
133 A 2 2 1.00 20 0.100
134 A 2 2 1.29 18 0.111
135 C 11 10 1.06 10 1.000
136 N/A 1 0 1.00 20 0.000
137 N/A 1 0 1.00 20 0.000
138 A 2 2 1.00 20 0.100
139 A 2 2 1.00 18 0.111
140 A 10 9 0.96 10 0.900
141 N/A 1 0 1.00 20 0.000
142 N/A 1 0 1.00 20 0.000
143 N/A 1 0 1.00 20 0.000
144 N/A 1 0 1.00 20 0.000
145 A 7 6 1.00 20 0.300
146 A 8 7 0.98 20 0.350
147 A 10 9 1.02 20 0.450
148 N/A 1 0 1.00 22 0.000
149 N/A 1 0 1.00 22 0.000
150 N/A 1 0 1.00 22 0.000
151 N/A 1 0 1.00 22 0.000
152 N/A 1 0 1.00 22 0.000
153 N/A 1 0 1.00 22 0.000
154 N/A 1 0 1.00 22 0.000
155 N/A 1 0 1.00 22 0.000
156 N/A 1 0 1.00 22 0.000
157 N/A 1 0 1.00 22 0.000
158 N/A 1 0 1.00 22 0.000
159 N/A 1 0 1.00 22 0.000
160 A 2 2 1.00 22 0.091
161 A 2 2 1.00 20 0.100
162 A 9 8 1.02 12 0.667
163 N/A 1 0 1.00 22 0.000
164 N/A 1 0 1.00 22 0.000
165 A 2 2 1.00 20 0.100
166 C 11 10 1.08 12 0.833
167 N/A 1 0 1.00 22 0.000
168 N/A 1 0 1.00 22 0.000
169 A 2 2 1.00 22 0.091
170 A 2 2 1.00 20 0.100
171 C 9 8 1.09 12 0.667
172 N/A 1 0 1.00 22 0.000
173 N/A 1 0 1.00 22 0.000
174 A 2 2 1.00 20 0.100
175 A 9 8 1.08 12 0.667
176 N/A 1 0 1.00 22 0.000
177 N/A 1 0 1.00 22 0.000

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