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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 [80] had the largest ratio of [1.41667000000000010]

# 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 5 4 1.06 8 0.500
2 A 4 4 1.21 8 0.500
3 A 5 4 1.08 8 0.500
4 A 3 3 1.14 6 0.500
5 A 2 2 1.00 4 0.500
6 C 9 8 1.33 8 1.000
7 A 5 4 1.00 8 0.500
8 A 2 2 1.00 8 0.250
9 A 6 5 1.00 8 0.625
10 A 3 3 1.09 8 0.375
11 A 7 6 1.06 8 0.750
12 A 7 7 1.17 10 0.700
13 A 6 6 1.18 10 0.600
14 A 5 5 1.15 10 0.500
15 A 4 4 1.12 8 0.500
16 A 3 3 1.18 6 0.500
17 C 10 9 1.28 10 0.900
18 C 8 7 1.18 10 0.700
19 A 3 3 1.00 10 0.300
20 C 10 9 1.04 10 0.900
21 A 5 5 1.01 10 0.500
22 A 15 14 1.50 10 1.400
23 A 11 11 1.47 10 1.100
24 A 10 9 1.30 10 0.900
25 A 6 6 1.19 8 0.750
26 A 4 4 1.14 6 0.667
27 C 11 10 1.23 10 1.000
28 C 9 8 1.11 10 0.800
29 C 11 10 1.10 10 1.000
30 C 14 13 1.04 10 1.300
31 C 14 13 1.09 10 1.300
32 A 13 13 1.78 10 1.300
33 A 14 14 1.65 10 1.400
34 A 10 10 1.48 10 1.000
35 A 11 11 1.37 10 1.100
36 A 7 7 1.19 8 0.875
37 A 5 5 1.21 6 0.833
38 C 12 11 1.29 10 1.100
39 C 10 9 1.12 10 0.900
40 C 12 11 1.11 10 1.100
41 C 14 13 1.06 10 1.300
42 A 4 3 0.85 10 0.300
43 A 4 3 0.88 10 0.300
44 A 4 3 0.88 10 0.300
45 A 4 3 0.93 10 0.300
46 A 4 3 0.93 10 0.300
47 A 7 6 1.00 8 0.750
48 A 4 3 1.00 6 0.500
49 N/A 1 0 1.00 10 0.000
50 N/A 1 0 1.00 10 0.000
51 A 3 2 0.91 10 0.200
52 A 3 2 0.94 10 0.200
53 A 3 2 0.94 10 0.200
54 A 3 2 0.98 10 0.200
55 A 3 2 0.98 10 0.200
56 A 4 3 1.00 8 0.375
57 A 6 5 1.00 6 0.833
58 N/A 1 0 1.00 10 0.000
59 N/A 1 0 1.00 10 0.000
60 A 6 5 1.37 10 0.500
61 A 10 9 1.33 10 0.900
62 A 9 8 1.26 10 0.800
63 A 10 9 1.10 8 1.125
64 A 6 5 1.08 6 0.833
65 N/A 1 0 1.00 10 0.000
66 N/A 1 0 1.00 10 0.000
67 A 5 4 1.34 10 0.400
68 A 7 6 1.23 10 0.600
69 A 10 9 1.25 10 0.900
70 A 7 6 1.09 8 0.750
71 A 8 7 1.16 6 1.167
72 N/A 1 0 1.00 10 0.000
73 N/A 1 0 1.00 10 0.000
74 C 7 6 1.02 12 0.500
75 A 6 5 0.95 12 0.417
76 C 7 6 1.05 12 0.500
77 A 7 6 0.97 10 0.600
78 C 9 8 1.15 8 1.000
79 N/A 1 0 1.00 12 0.000
80 A 18 17 1.28 12 1.417
81 C 17 16 1.40 12 1.333
82 A 14 13 1.28 12 1.083
83 C 13 12 1.11 10 1.200
84 A 10 9 1.06 8 1.125
85 N/A 1 0 1.00 12 0.000
86 C 17 16 1.37 12 1.333
87 A 12 11 1.38 12 0.917
88 C 15 14 1.37 12 1.167
89 A 10 9 1.07 10 0.900
90 C 11 10 1.17 8 1.250
91 N/A 1 0 1.00 12 0.000
92 A 4 3 0.91 12 0.250
93 A 4 3 0.93 12 0.250
94 A 4 3 0.92 12 0.250
95 C 10 9 1.11 10 0.900
96 A 8 7 0.95 8 0.875
97 N/A 1 0 1.00 12 0.000
98 N/A 1 0 1.00 12 0.000
99 A 3 2 0.94 12 0.167
100 A 3 2 0.96 12 0.167
101 A 3 2 0.95 12 0.167
102 A 8 7 1.07 10 0.700
103 C 9 8 1.17 8 1.000
104 N/A 1 0 1.00 12 0.000
105 A 6 5 1.46 12 0.417
106 C 13 12 1.47 12 1.000
107 A 13 12 1.33 12 1.000
108 C 13 12 1.14 10 1.200
109 A 10 9 1.08 8 1.125
110 N/A 1 0 1.00 12 0.000
111 A 5 4 1.38 12 0.333
112 A 11 10 1.39 12 0.833
113 C 13 12 1.31 12 1.000
114 A 11 10 1.13 10 1.000
115 C 11 10 1.19 8 1.250
116 N/A 1 0 1.00 12 0.000
117 N/A 2 0 1.00 10 0.000
118 N/A 2 0 1.00 10 0.000
119 A 2 2 0.96 10 0.200
120 A 2 2 1.00 8 0.250
121 N/A 1 0 1.00 10 0.000
122 N/A 1 0 1.00 10 0.000
123 N/A 1 0 1.00 12 0.000
124 N/A 1 0 1.00 12 0.000
125 N/A 1 0 1.00 12 0.000
126 N/A 1 0 1.00 12 0.000
127 N/A 1 0 1.00 12 0.000
128 N/A 1 0 1.00 12 0.000
129 A 4 3 0.92 10 0.300
130 A 4 3 0.93 10 0.300
131 A 4 3 0.93 10 0.300
132 C 8 7 1.15 8 0.875
133 A 6 5 0.96 6 0.833
134 N/A 1 0 1.00 10 0.000
135 N/A 1 0 1.00 10 0.000
136 C 8 7 1.03 16 0.438
137 A 7 6 0.98 14 0.429
138 C 10 9 1.08 12 0.750
139 A 14 13 1.34 16 0.812
140 C 14 13 1.09 14 0.929
141 A 10 9 1.04 12 0.750
142 C 16 15 1.36 16 0.938
143 A 10 9 1.04 14 0.643
144 C 12 11 1.09 12 0.917
145 A 4 3 0.97 16 0.188
146 C 11 10 1.09 14 0.714
147 A 8 7 1.01 12 0.583
148 A 3 2 0.99 16 0.125
149 A 8 7 1.07 14 0.500
150 C 10 9 1.12 12 0.750
151 A 13 12 1.41 16 0.750
152 C 14 13 1.13 14 0.929
153 A 10 9 1.09 12 0.750
154 C 14 13 1.38 16 0.812
155 A 11 10 1.13 14 0.714
156 C 12 11 1.17 12 0.917

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