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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 [.900000000000000022]

# 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 1.12 16 0.500
2 A 5 5 1.13 16 0.312
3 A 5 5 1.15 14 0.357
4 A 1 1 1.00 8 0.125
5 A 6 5 1.00 16 0.312
6 A 4 3 1.00 16 0.188
7 A 5 4 0.99 16 0.250
8 A 7 6 1.09 16 0.375
9 A 3 3 1.05 18 0.167
10 A 3 3 1.10 18 0.167
11 A 3 3 1.15 16 0.188
12 A 3 3 1.09 10 0.300
13 A 7 6 0.99 18 0.333
14 A 10 9 0.93 18 0.500
15 A 14 13 0.96 18 0.722
16 A 4 3 0.96 18 0.167
17 A 4 3 0.95 18 0.167
18 A 4 3 0.95 16 0.188
19 A 8 7 0.91 10 0.700
20 N/A 1 0 1.00 18 0.000
21 N/A 1 0 1.00 18 0.000
22 A 2 2 1.00 18 0.111
23 A 2 2 1.00 16 0.125
24 A 10 9 0.97 10 0.900
25 N/A 1 0 1.00 18 0.000
26 N/A 1 0 1.00 18 0.000
27 N/A 2 0 1.00 18 0.000
28 A 4 4 0.81 16 0.250
29 N/A 1 0 1.00 18 0.000
30 N/A 1 0 1.00 18 0.000
31 A 13 13 1.06 21 0.619
32 A 10 10 1.05 21 0.476
33 A 8 8 1.04 19 0.421
34 A 4 4 1.00 21 0.190
35 A 6 6 0.99 21 0.286
36 A 8 7 1.18 21 0.333
37 A 8 7 1.05 21 0.333
38 A 11 10 1.06 21 0.476
39 A 13 12 1.09 21 0.571
40 A 4 4 1.02 23 0.174
41 A 2 2 1.00 25 0.080
42 A 4 4 0.49 30 0.133
43 A 4 4 0.51 30 0.133
44 A 4 4 0.69 30 0.133
45 A 4 4 0.62 30 0.133
46 A 4 4 0.65 30 0.133
47 A 7 7 0.71 30 0.233
48 A 4 4 0.43 30 0.133
49 A 7 7 0.65 30 0.233
50 A 4 4 0.51 30 0.133
51 A 4 4 0.52 30 0.133
52 A 4 4 0.54 30 0.133
53 A 4 4 0.52 30 0.133
54 A 9 9 0.57 30 0.300
55 A 4 4 0.43 30 0.133
56 A 4 4 0.49 30 0.133
57 A 4 4 0.50 30 0.133
58 A 4 4 0.46 30 0.133
59 A 4 4 0.48 30 0.133
60 A 2 2 1.00 30 0.067
61 A 7 7 0.91 30 0.233
62 A 4 4 0.85 30 0.133
63 A 6 6 0.90 30 0.200
64 A 3 3 0.82 30 0.100
65 A 4 4 0.63 30 0.133
66 A 4 4 0.83 30 0.133
67 A 4 4 0.62 30 0.133
68 A 5 5 0.69 30 0.167
69 A 4 4 0.54 32 0.125
70 A 4 4 0.55 32 0.125
71 A 6 6 0.66 32 0.188
72 A 4 4 0.64 32 0.125
73 A 4 4 0.50 32 0.125
74 A 4 4 0.53 32 0.125
75 A 4 4 0.51 32 0.125
76 A 11 11 0.74 32 0.344
77 A 4 4 0.55 32 0.125
78 A 7 6 0.55 32 0.188
79 A 4 4 0.48 32 0.125
80 A 4 4 0.49 32 0.125
81 A 13 13 0.77 32 0.406
82 A 4 4 0.51 32 0.125
83 A 4 4 0.54 32 0.125
84 A 7 6 0.54 32 0.188
85 A 4 4 0.46 32 0.125
86 A 4 4 0.48 32 0.125
87 A 2 2 1.00 32 0.062
88 A 4 4 0.53 32 0.125
89 A 4 4 0.52 32 0.125
90 A 4 4 0.53 32 0.125
91 A 9 8 0.61 32 0.250
92 A 4 4 0.52 32 0.125
93 A 4 4 0.52 32 0.125
94 A 4 4 0.52 32 0.125
95 A 12 11 0.60 32 0.344
96 N/A 1 0 1.00 27 0.000
97 N/A 1 0 1.00 27 0.000
98 N/A 1 0 1.00 27 0.000
99 A 3 3 1.00 27 0.111
100 F 0 0 N/A 0.000 N/A
101 A 2 2 1.29 27 0.074
102 F 0 0 N/A 0.000 N/A
103 F 0 0 N/A 0.000 N/A
104 A 3 3 0.57 31 0.097
105 A 3 3 0.59 31 0.097
106 A 3 3 0.61 29 0.103
107 A 7 7 0.70 31 0.226
108 A 7 7 0.73 31 0.226
109 A 3 3 0.55 31 0.097
110 A 3 3 0.57 31 0.097
111 A 3 3 0.56 29 0.103
112 A 3 3 0.67 31 0.097
113 A 3 3 0.53 31 0.097
114 A 3 3 0.55 31 0.097
115 A 3 3 0.54 29 0.103
116 A 3 3 0.63 31 0.097
117 A 3 3 0.62 31 0.097
118 A 3 3 0.63 31 0.097
119 A 3 3 0.73 29 0.103
120 A 10 9 0.76 31 0.290
121 A 14 13 0.77 31 0.419
122 A 3 3 0.70 31 0.097
123 A 3 3 0.67 31 0.097
124 A 6 6 0.69 29 0.207
125 A 3 3 0.66 31 0.097
126 A 3 3 0.79 31 0.097
127 A 3 3 0.84 31 0.097
128 A 3 3 0.74 31 0.097
129 A 3 3 0.74 29 0.103
130 A 3 3 0.63 31 0.097
131 A 3 3 0.69 33 0.091
132 A 3 3 0.66 33 0.091
133 A 3 3 0.67 31 0.097
134 A 7 7 0.71 33 0.212
135 A 3 3 0.69 33 0.091
136 A 3 3 0.67 33 0.091
137 A 3 3 0.68 31 0.097
138 A 3 3 0.69 33 0.091
139 A 3 3 0.68 33 0.091
140 A 3 3 0.66 33 0.091
141 A 3 3 0.66 31 0.097
142 A 3 3 0.69 33 0.091
143 A 6 5 0.66 33 0.152
144 A 6 5 0.63 33 0.152
145 A 3 3 0.82 31 0.097
146 A 11 10 0.68 33 0.303
147 A 17 16 0.65 33 0.485
148 A 3 3 0.66 33 0.091
149 A 3 3 0.61 33 0.091
150 A 3 3 0.59 31 0.097
151 A 3 3 0.64 33 0.091
152 A 3 3 0.58 33 0.091
153 A 3 3 0.62 33 0.091
154 A 3 3 0.65 31 0.097
155 N/A 1 0 1.00 35 0.000
156 A 10 9 0.99 35 0.257
157 A 9 8 0.98 35 0.229
158 A 8 7 0.99 33 0.212
159 A 8 7 1.00 25 0.280
160 N/A 1 0 1.00 35 0.000
161 A 14 14 1.06 26 0.538
162 A 13 13 1.05 26 0.500
163 A 10 10 1.06 24 0.417
164 A 4 4 1.00 26 0.154
165 A 4 4 0.99 26 0.154
166 A 4 4 0.98 26 0.154
167 A 8 7 1.02 26 0.269
168 A 10 9 1.05 26 0.346
169 A 13 12 1.06 26 0.462
170 A 17 17 1.06 31 0.548
171 A 14 14 1.07 31 0.452
172 A 13 13 1.06 29 0.448
173 A 4 4 1.00 31 0.129
174 A 4 4 0.99 31 0.129
175 A 4 4 0.95 31 0.129
176 A 4 4 0.97 31 0.129
177 A 2 2 1.00 28 0.071
178 A 2 2 1.00 28 0.071
179 A 2 2 1.00 26 0.077
180 A 2 2 1.00 28 0.071
181 A 2 2 1.00 28 0.071
182 A 3 3 0.98 33 0.091
183 A 4 4 0.98 35 0.114

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