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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 [48] had the largest ratio of [1.89999999999999991]

# 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 6 0.500
2 A 5 4 1.00 8 0.500
3 C 7 7 1.24 8 0.875
4 C 4 3 1.23 8 0.375
5 C 11 11 1.27 8 1.375
6 C 5 4 1.10 8 0.500
7 A 6 6 1.00 10 0.600
8 A 6 6 1.00 10 0.600
9 A 4 4 1.00 10 0.400
10 A 4 4 1.00 10 0.400
11 A 6 6 1.00 10 0.600
12 A 6 6 1.00 10 0.600
13 A 8 8 1.02 12 0.667
14 A 6 6 1.00 12 0.500
15 A 6 6 1.00 12 0.500
16 A 4 4 1.00 12 0.333
17 A 4 4 1.00 12 0.333
18 A 6 6 1.00 12 0.500
19 A 6 6 1.00 12 0.500
20 A 8 8 1.07 12 0.667
21 A 4 4 1.00 10 0.400
22 A 6 5 1.22 10 0.500
23 A 5 4 1.08 10 0.400
24 A 4 3 1.00 10 0.300
25 A 4 3 1.15 10 0.300
26 A 5 4 1.12 10 0.400
27 A 6 5 1.22 10 0.500
28 A 7 6 1.28 10 0.600
29 A 7 6 1.26 10 0.600
30 A 6 5 1.22 10 0.500
31 A 5 4 1.15 10 0.400
32 A 4 3 1.31 10 0.300
33 A 5 4 1.39 10 0.400
34 A 6 5 1.47 10 0.500
35 A 7 6 1.51 10 0.600
36 A 14 14 1.11 10 1.400
37 A 10 10 1.33 10 1.000
38 A 8 8 1.38 10 0.800
39 A 8 8 1.31 10 0.800
40 A 10 10 1.24 10 1.000
41 A 14 14 1.14 10 1.400
42 C 8 7 0.51 10 0.700
43 C 8 7 0.58 10 0.700
44 C 8 7 0.74 10 0.700
45 A 8 7 1.00 10 0.700
46 A 7 7 0.83 10 0.700
47 A 13 13 0.73 10 1.300
48 A 19 19 0.70 10 1.900
49 A 3 3 1.00 15 0.200
50 A 3 3 1.00 15 0.200
51 A 12 11 1.04 17 0.647
52 A 7 6 1.00 17 0.353
53 A 4 3 1.00 17 0.176
54 A 10 9 1.00 17 0.529
55 A 13 12 1.05 17 0.706
56 A 4 3 1.00 17 0.176
57 A 10 9 1.00 17 0.529
58 A 4 3 1.00 12 0.250
59 A 4 3 1.00 12 0.250
60 A 4 3 1.00 12 0.250
61 A 4 3 1.00 12 0.250
62 A 17 16 1.09 13 1.231
63 A 18 17 1.13 13 1.308
64 A 15 15 1.17 13 1.154
65 A 13 13 1.20 11 1.182
66 A 4 4 0.93 11 0.364
67 A 9 9 1.53 13 0.692
68 A 13 13 1.00 13 1.000
69 A 20 19 1.27 13 1.462
70 A 5 5 1.06 12 0.417
71 A 3 3 1.03 12 0.250
72 A 11 10 1.00 12 0.833
73 A 1 1 1.00 10 0.100
74 A 7 6 0.98 12 0.500
75 A 14 13 1.20 12 1.083
76 A 17 16 1.24 12 1.333
77 C 24 23 1.36 13 1.769
78 C 18 17 1.31 13 1.308
79 C 12 11 1.35 11 1.000
80 A 8 7 1.22 11 0.636
81 A 13 12 1.16 13 0.923
82 C 17 16 1.34 13 1.231
83 C 19 18 1.34 13 1.385
84 A 19 18 1.13 13 1.385
85 A 15 14 1.21 13 1.077
86 A 15 15 1.20 13 1.154
87 A 10 9 1.00 11 0.818
88 A 18 17 1.07 11 1.545
89 A 17 16 1.21 13 1.231
90 A 20 19 1.12 13 1.462
91 A 18 17 1.38 13 1.308
92 A 12 11 0.99 13 0.846
93 C 18 17 1.22 13 1.308
94 A 12 11 0.98 13 0.846
95 C 15 14 1.25 13 1.077
96 A 12 11 0.95 11 1.000
97 A 14 13 0.84 11 1.182
98 C 14 13 1.22 13 1.000
99 A 14 13 1.29 13 1.000
100 C 16 15 1.23 13 1.154
101 A 16 15 1.40 13 1.154
102 A 7 6 0.93 13 0.462
103 A 13 13 1.17 13 1.000
104 A 7 6 0.95 13 0.462
105 A 11 11 1.14 13 0.846
106 A 7 6 1.00 11 0.545
107 A 6 5 1.00 11 0.455
108 A 5 5 1.36 13 0.385
109 A 7 6 1.67 13 0.462
110 A 7 7 1.26 13 0.538
111 A 7 6 1.20 13 0.462
112 A 12 12 1.28 13 0.923
113 A 7 6 1.32 13 0.462
114 F 0 0 N/A 0.000 N/A
115 A 6 5 1.34 13 0.385
116 C 23 22 1.12 13 1.692
117 A 7 6 1.38 11 0.545
118 A 7 6 1.16 11 0.545
119 A 19 18 1.19 13 1.385
120 A 7 6 1.28 13 0.462
121 C 19 18 1.34 13 1.385
122 A 6 5 1.07 13 0.385
123 C 9 9 1.15 13 0.692
124 A 7 6 1.04 13 0.462
125 A 7 6 0.57 25 0.240
126 A 7 6 0.63 25 0.240
127 A 5 4 1.00 25 0.160
128 A 5 4 1.00 25 0.160
129 A 6 5 0.82 25 0.200
130 A 7 6 0.46 25 0.240
131 A 7 6 0.41 25 0.240
132 A 7 6 1.25 15 0.400
133 A 4 3 0.93 15 0.200
134 A 10 9 0.90 15 0.600
135 A 7 6 1.06 15 0.400
136 A 6 5 1.20 13 0.385
137 A 7 6 1.13 11 0.545
138 A 6 5 1.00 15 0.333
139 A 6 5 1.00 15 0.333
140 A 8 7 0.73 15 0.467
141 A 4 3 1.16 15 0.200
142 A 6 5 1.09 15 0.333
143 A 9 8 1.04 15 0.533
144 A 8 7 1.10 15 0.467
145 A 4 3 0.93 15 0.200
146 A 11 10 0.84 15 0.667
147 A 8 7 1.06 15 0.467
148 A 7 6 1.17 15 0.400
149 A 8 7 0.98 15 0.467
150 A 10 9 0.85 13 0.692
151 A 8 7 1.00 11 0.636
152 A 8 7 1.00 15 0.467
153 A 4 3 1.15 15 0.200
154 A 6 5 1.04 15 0.333
155 A 7 6 0.97 15 0.400
156 A 5 4 1.00 11 0.364
157 A 5 4 1.00 13 0.308
158 A 5 4 1.00 13 0.308
159 A 5 4 1.00 13 0.308
160 C 1 1 3.26 45 0.022
161 A 4 3 1.04 15 0.200
162 A 5 4 1.00 15 0.267
163 A 4 3 1.08 20 0.150
164 A 4 3 1.62 21 0.143
165 A 5 4 1.00 15 0.267
166 A 6 5 1.00 17 0.294
167 C 9 8 1.09 17 0.471
168 C 5 4 1.07 17 0.235
169 C 13 12 1.10 17 0.706
170 A 8 7 0.98 19 0.368
171 A 8 7 0.98 19 0.368
172 A 6 5 1.00 19 0.263
173 A 6 5 1.00 19 0.263
174 A 8 7 0.98 19 0.368
175 A 8 7 0.98 19 0.368

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