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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 [53] had the largest ratio of [1.37500000000000000]

# 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 0.97 12 0.250
2 A 5 4 0.98 12 0.333
3 A 3 3 0.98 12 0.250
4 A 5 4 1.00 12 0.333
5 A 3 3 1.00 10 0.300
6 A 1 1 1.00 8 0.125
7 A 2 2 1.00 12 0.167
8 A 6 5 1.06 12 0.417
9 A 3 3 0.95 12 0.250
10 A 5 4 0.96 12 0.333
11 A 4 4 1.00 12 0.333
12 A 5 4 0.94 12 0.333
13 A 15 14 1.38 14 1.000
14 A 14 13 1.22 14 0.929
15 A 10 9 1.19 14 0.643
16 A 10 9 1.09 14 0.643
17 A 4 4 1.00 12 0.333
18 A 6 5 1.17 10 0.500
19 A 4 4 1.19 14 0.286
20 A 4 4 1.13 14 0.286
21 A 9 8 0.96 14 0.571
22 A 8 8 0.98 14 0.571
23 A 14 13 1.16 14 0.929
24 B 18 17 2.06 14 1.214
25 A 16 15 1.37 14 1.071
26 A 14 13 1.58 14 0.929
27 A 10 10 1.09 14 0.714
28 A 9 8 1.11 12 0.667
29 A 5 5 1.13 10 0.500
30 A 5 5 1.16 14 0.357
31 A 5 5 1.19 14 0.357
32 A 7 7 1.02 14 0.500
33 A 15 14 1.03 14 1.000
34 A 11 11 1.40 14 0.786
35 N/A 1 0 1.00 8 0.000
36 N/A 1 0 1.00 6 0.000
37 N/A 1 0 1.00 10 0.000
38 N/A 1 0 1.00 8 0.000
39 N/A 1 0 1.00 6 0.000
40 N/A 1 0 1.00 10 0.000
41 N/A 1 0 1.00 10 0.000
42 N/A 1 0 1.00 8 0.000
43 N/A 1 0 1.00 12 0.000
44 N/A 1 0 1.00 10 0.000
45 N/A 1 0 1.00 8 0.000
46 N/A 1 0 1.00 12 0.000
47 N/A 1 0 1.00 10 0.000
48 N/A 1 0 1.00 8 0.000
49 N/A 1 0 1.00 12 0.000
50 N/A 1 0 1.00 10 0.000
51 N/A 1 0 1.00 8 0.000
52 N/A 1 0 1.00 12 0.000
53 A 12 11 1.09 8 1.375
54 N/A 1 0 1.00 16 0.000
55 N/A 1 0 1.00 16 0.000
56 A 2 2 1.00 14 0.143
57 N/A 1 0 1.00 16 0.000
58 N/A 1 0 1.00 10 0.000
59 N/A 1 0 1.00 16 0.000
60 A 5 4 0.98 14 0.286
61 A 5 4 1.00 14 0.286
62 A 5 4 1.00 14 0.286
63 A 2 2 1.00 12 0.167
64 A 4 3 1.15 14 0.214
65 A 6 5 1.05 14 0.357
66 A 5 4 0.95 14 0.286
67 A 5 4 0.96 14 0.286
68 A 11 10 1.12 14 0.714
69 A 11 10 1.06 14 0.714
70 A 1 1 1.00 10 0.100
71 A 10 9 1.08 14 0.643
72 A 11 10 1.10 14 0.714
73 A 11 10 1.08 14 0.714
74 A 11 10 1.20 16 0.625
75 A 11 10 1.11 16 0.625
76 A 6 5 1.00 16 0.312
77 A 7 6 1.12 14 0.429
78 A 6 5 1.17 16 0.312
79 A 6 5 1.10 16 0.312
80 A 10 9 0.99 16 0.562
81 A 2 2 1.00 16 0.125
82 A 2 2 1.00 12 0.167
83 A 2 2 1.00 16 0.125
84 A 2 2 1.00 16 0.125
85 A 2 2 1.00 16 0.125
86 A 10 9 1.11 16 0.562
87 A 7 6 1.07 14 0.429
88 A 7 6 1.17 16 0.375
89 A 7 6 1.13 16 0.375
90 A 9 8 1.03 16 0.500
91 N/A 1 0 1.00 18 0.000
92 N/A 1 0 1.00 18 0.000
93 A 2 2 1.00 16 0.125
94 N/A 1 0 1.00 18 0.000
95 N/A 1 0 1.00 18 0.000
96 A 5 4 0.98 14 0.286
97 A 5 4 1.00 14 0.286
98 A 5 4 1.00 14 0.286
99 A 2 2 1.00 14 0.143
100 A 4 3 1.15 14 0.214
101 A 6 5 1.05 14 0.357
102 A 5 4 0.95 14 0.286
103 A 5 4 0.96 14 0.286
104 A 12 11 1.13 14 0.786
105 A 1 1 1.00 10 0.100
106 A 11 10 1.13 14 0.714
107 A 12 11 1.12 14 0.786
108 A 12 11 1.20 14 0.786
109 A 12 11 1.08 14 0.786
110 A 11 10 1.19 12 0.833
111 A 11 10 1.07 14 0.714
112 A 12 11 1.19 14 0.786
113 A 11 10 1.20 16 0.625
114 A 11 10 1.11 16 0.625
115 A 6 5 1.00 16 0.312
116 A 7 6 1.09 16 0.375
117 A 6 5 1.15 16 0.312
118 A 6 5 1.07 16 0.312
119 A 10 9 0.99 16 0.562
120 A 10 9 1.01 16 0.562
121 A 12 11 1.05 16 0.688
122 A 10 9 1.13 16 0.562
123 A 7 6 1.11 16 0.375
124 A 7 6 1.15 16 0.375
125 A 7 6 1.17 16 0.375
126 A 9 8 1.05 16 0.500
127 N/A 1 0 1.00 18 0.000
128 N/A 1 0 1.00 18 0.000
129 A 2 2 1.00 16 0.125
130 N/A 1 0 1.00 18 0.000
131 N/A 1 0 1.00 18 0.000
132 A 4 4 0.96 14 0.286
133 A 6 5 0.95 14 0.357
134 A 4 4 0.90 12 0.333
135 A 1 1 1.00 10 0.100
136 A 4 3 1.08 14 0.214
137 A 2 2 1.00 14 0.143
138 A 4 4 1.02 14 0.286
139 A 6 5 0.98 14 0.357
140 A 15 14 1.14 16 0.875
141 A 10 9 0.98 16 0.562
142 A 10 9 0.99 14 0.643
143 A 10 9 1.07 12 0.750
144 A 6 5 1.17 16 0.312
145 A 7 6 1.15 16 0.375
146 A 6 5 1.01 16 0.312
147 A 13 12 1.41 16 0.750
148 A 16 15 1.04 16 0.938
149 A 9 8 1.01 14 0.571
150 A 9 9 1.11 12 0.750
151 A 7 6 1.14 16 0.375
152 A 7 6 1.11 16 0.375
153 A 10 9 1.10 16 0.562
154 A 7 6 1.02 10 0.600
155 A 6 5 1.02 8 0.625
156 A 5 4 1.32 6 0.667
157 A 4 3 1.19 10 0.300
158 A 5 4 1.19 10 0.400
159 A 6 5 1.02 10 0.500
160 A 3 3 0.97 12 0.250
161 A 3 3 0.97 12 0.250
162 A 2 2 1.00 12 0.167
163 A 4 4 1.00 12 0.333
164 A 3 3 0.92 12 0.250
165 A 4 3 1.12 10 0.300
166 A 4 3 0.95 10 0.300

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