Chapter 2
detailed summary tables of results
2.1 List of integrals sorted by grade for each CAS
2.1.1 Rubi
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 9, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 61, 63, 75, 76, 77, 78, 79, 80, 82,
83, 84, 85 }
B grade: { }
C grade: { 6, 7, 8, 10, 11, 12, 56, 57, 58, 59, 60, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 81
}
F grade: { 35}
2.1.3 Maple
A grade: { 2, 9, 10, 11, 19, 43, 44, 45, 47, 48, 49, 50, 51, 54, 55, 76, 77, 78, 79, 80, 82, 83, 84, 85
}
B grade: { 1, 4, 5, 6, 7, 8, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
35, 36, 37, 38, 39, 40, 41, 42, 46, 52, 53, 58, 59, 63, 74 }
C grade: { 3, 56, 57, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 81 }
F grade: { }
2.1.4 Maxima
A grade: { 1, 3, 37, 44, 49, 54, 76
B grade: { 2, 4, 5, 35, 36, 38, 39, 40, 63 }
C grade: { 43, 48, 53, 80 }
F grade: { 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32,
33, 34, 41, 42, 45, 46, 47, 50, 51, 52, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74,
75, 77, 78, 79, 81, 82, 83, 84, 85 }
2.1.5 FriCAS
A grade: { 1, 2, 3, 15, 25, 43, 44, 48, 49, 53, 54, 80, 84, 85 }
B grade: { 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31,
32, 33, 34, 35, 36, 37, 38, 39, 40, 58, 59, 60, 61, 62, 63, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 83
}
C grade: { 81 }
F grade: { 41, 42, 45, 46, 47, 50, 51, 52, 55, 56, 57, 64, 65, 66, 67, 68, 69, 82 }
2.1.6 Sympy
A grade: { 3, 9, 19 }
B grade: { 1, 2, 35, 36, 37, 38, 39, 40, 58, 59, 63 }
C grade: { }
F grade: { 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
34, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71,
72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85 }
2.1.7 Giac
A grade: { 1, 2, 3, 4, 5, 15, 16, 25, 27, 29, 31, 33, 37, 39, 40, 65, 66, 68, 69, 72, 74, 75, 76, 81
}
B grade: { 13, 14, 17, 18, 21, 23, 34, 35, 36, 38, 44, 49, 54, 63, 71 }
C grade: { 43, 48, 53, 62, 80 }
F grade: { 6, 7, 8, 9, 10, 11, 12, 19, 20, 22, 24, 26, 28, 30, 32, 41, 42, 45, 46, 47, 50, 51, 52, 55, 56, 57, 58,
59, 60, 61, 64, 67, 70, 73, 77, 78, 79, 82, 83, 84, 85 }
2.2 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2)
if the failure was due to an exception being raised, which could indicate a bug in the system. If
the failure was due to integral not being evaluated within the time limit, then it is given just an
F.
In this table,the column normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)
|
|
|
|
|
|
|
|
|
Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 19 | 78 | 34 | 41 | 153 | 35 |
normalized size | 1 | 1. | 0.95 | 3.9 | 1.7 | 2.05 | 7.65 | 1.75 |
time (sec) |
N/A |
0.046 |
0.004 |
0.024 |
1.072 |
1.732 |
3.668 |
1.285 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 7 | 7 | 7 | 8 | 23 | 16 | 17 | 16 |
normalized size | 1 | 1. | 1. | 1.14 | 3.29 | 2.29 | 2.43 | 2.29 |
time (sec) |
N/A |
0.044 |
0.003 |
0.01 |
1.08 |
1.608 |
1.918 |
1.229 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 6 | 6 | 6 | 11 | 8 | 8 | 3 | 8 |
normalized size | 1 | 1. | 1. | 1.83 | 1.33 | 1.33 | 0.5 | 1.33 |
time (sec) |
N/A |
0.039 |
0. |
0.013 |
1.069 |
1.834 |
1.017 |
1.345 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 22 | 37 | 82 | 317 | 0 | 28 |
normalized size | 1 | 1. | 1.16 | 1.95 | 4.32 | 16.68 | 0. | 1.47 |
time (sec) |
N/A |
0.048 |
0.004 |
0.025 |
1.08 |
1.787 |
0. |
1.271 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 32 | 53 | 182 | 694 | 0 | 36 |
normalized size |
1 |
1. |
1.1 |
1.83 |
6.28 |
23.93 |
0. |
1.24 |
time (sec) |
N/A |
0.051 |
0.004 |
0.028 |
1.085 |
1.804 |
0. |
1.281 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 148 | 395 | 0 | 6149 | 0 | 0 |
normalized size |
1 |
1. |
1.9 |
5.06 |
0. |
78.83 |
0. |
0. |
time (sec) |
N/A |
0.105 |
0.235 |
0.033 |
0. |
2.25 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 120 | 214 | 0 | 2957 | 0 | 0 |
normalized size |
1 |
1. |
2.22 |
3.96 |
0. |
54.76 |
0. |
0. |
time (sec) |
N/A |
0.087 |
0.174 |
0.025 |
0. |
2.071 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 83 | 97 | 0 | 1305 | 0 | 0 |
normalized size |
1 |
1. |
2.31 |
2.69 |
0. |
36.25 |
0. |
0. |
time (sec) |
N/A |
0.065 |
0.176 |
0.017 |
0. |
2. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 17 | 0 | 910 | 87 | 0 |
normalized size |
1 |
1. |
1. |
0.68 |
0. |
36.4 |
3.48 |
0. |
time (sec) |
N/A |
0.036 |
0.022 |
0.007 |
0. |
1.912 |
1.597 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 99 | 52 | 0 | 1085 | 0 | 0 |
normalized size |
1 |
1. |
2.36 |
1.24 |
0. |
25.83 |
0. |
0. |
time (sec) |
N/A |
0.062 |
0.135 |
0.023 |
0. |
2.087 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 61 | 61 | 154 | 94 | 0 | 3981 | 0 | 0 |
normalized size |
1 |
1. |
2.52 |
1.54 |
0. |
65.26 |
0. |
0. |
time (sec) |
N/A |
0.104 |
0.278 |
0.029 |
0. |
2.521 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 219 | 184 | 0 | 13990 | 0 | 0 |
normalized size |
1 |
1. |
2.33 |
1.96 |
0. |
148.83 |
0. |
0. |
time (sec) |
N/A |
0.172 |
0.584 |
0.035 |
0. |
3.136 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 76 | 563 | 0 | 3571 | 0 | 224 |
normalized size |
1 |
1. |
0.86 |
6.4 |
0. |
40.58 |
0. |
2.55 |
time (sec) |
N/A |
0.168 |
0.162 |
0.059 |
0. |
2.068 |
0. |
1.31 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 52 | 342 | 0 | 1667 | 0 | 139 |
normalized size |
1 |
1. |
0.88 |
5.8 |
0. |
28.25 |
0. |
2.36 |
time (sec) |
N/A |
0.116 |
0.093 |
0.04 |
0. |
2.024 |
0. |
1.216 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 36 | 183 | 0 | 845 | 0 | 70 |
normalized size |
1 |
1. |
0.92 |
4.69 |
0. |
21.67 |
0. |
1.79 |
time (sec) |
N/A |
0.067 |
0.057 |
0.03 |
0. |
1.981 |
0. |
1.275 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 78 | 0 | 828 | 0 | 53 |
normalized size |
1 |
1. |
1. |
2.69 |
0. |
28.55 |
0. |
1.83 |
time (sec) |
N/A |
0.022 |
0.063 |
0.023 |
0. |
1.984 |
0. |
1.233 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 59 | 180 | 0 | 4686 | 0 | 144 |
normalized size |
1 |
1. |
1. |
3.05 |
0. |
79.42 |
0. |
2.44 |
time (sec) |
N/A |
0.086 |
0.199 |
0.042 |
0. |
2.228 |
0. |
1.403 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 92 | 310 | 0 | 12037 | 0 | 255 |
normalized size |
1 |
1. |
1.03 |
3.48 |
0. |
135.25 |
0. |
2.87 |
time (sec) |
N/A |
0.108 |
0.354 |
0.047 |
0. |
2.455 |
0. |
1.419 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 77 | 80 | 0 | 1143 | 85 | 0 |
normalized size |
1 |
1. |
0.79 |
0.82 |
0. |
11.66 |
0.87 |
0. |
time (sec) |
N/A |
0.117 |
0.086 |
0.012 |
0. |
1.863 |
2.893 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 86 | 317 | 0 | 6260 | 0 | 0 |
normalized size |
1 |
1. |
1.1 |
4.06 |
0. |
80.26 |
0. |
0. |
time (sec) |
N/A |
0.09 |
0.274 |
0.046 |
0. |
2.124 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 76 | 323 | 0 | 3320 | 0 | 203 |
normalized size |
1 |
1. |
0.86 |
3.67 |
0. |
37.73 |
0. |
2.31 |
time (sec) |
N/A |
0.21 |
0.215 |
0.037 |
0. |
2.074 |
0. |
1.2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 61 | 177 | 0 | 3143 | 0 | 0 |
normalized size |
1 |
1. |
1.09 |
3.16 |
0. |
56.12 |
0. |
0. |
time (sec) |
N/A |
0.073 |
0.161 |
0.036 |
0. |
2.031 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 52 | 188 | 0 | 1638 | 0 | 128 |
normalized size |
1 |
1. |
0.88 |
3.19 |
0. |
27.76 |
0. |
2.17 |
time (sec) |
N/A |
0.106 |
0.127 |
0.036 |
0. |
2.09 |
0. |
1.31 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 38 | 38 | 96 | 0 | 1443 | 0 | 0 |
normalized size |
1 |
1. |
1. |
2.53 |
0. |
37.97 |
0. |
0. |
time (sec) |
N/A |
0.059 |
0.029 |
0.033 |
0. |
1.984 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 36 | 107 | 0 | 880 | 0 | 68 |
normalized size |
1 |
1. |
0.92 |
2.74 |
0. |
22.56 |
0. |
1.74 |
time (sec) |
N/A |
0.07 |
0.08 |
0.026 |
0. |
1.998 |
0. |
1.228 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 66 | 0 | 988 | 0 | 0 |
normalized size |
1 |
1. |
1. |
2.28 |
0. |
34.07 |
0. |
0. |
time (sec) |
N/A |
0.032 |
0.011 |
0.021 |
0. |
1.976 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 78 | 0 | 828 | 0 | 53 |
normalized size |
1 |
1. |
1. |
2.69 |
0. |
28.55 |
0. |
1.83 |
time (sec) |
N/A |
0.022 |
0.05 |
0. |
0. |
1.915 |
0. |
1.211 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 45 | 83 | 0 | 1096 | 0 | 0 |
normalized size |
1 |
1. |
1.1 |
2.02 |
0. |
26.73 |
0. |
0. |
time (sec) |
N/A |
0.054 |
0.095 |
0.039 |
0. |
2.296 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 38 | 38 | 99 | 0 | 1277 | 0 | 78 |
normalized size |
1 |
1. |
1. |
2.61 |
0. |
33.61 |
0. |
2.05 |
time (sec) |
N/A |
0.079 |
0.077 |
0.042 |
0. |
2.219 |
0. |
1.344 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 58 | 131 | 0 | 2944 | 0 | 0 |
normalized size |
1 |
1. |
0.98 |
2.22 |
0. |
49.9 |
0. |
0. |
time (sec) |
N/A |
0.091 |
0.165 |
0.045 |
0. |
2.524 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 55 | 139 | 0 | 3634 | 0 | 117 |
normalized size |
1 |
1. |
1. |
2.53 |
0. |
66.07 |
0. |
2.13 |
time (sec) |
N/A |
0.099 |
0.143 |
0.046 |
0. |
2.406 |
0. |
1.387 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 86 | 274 | 0 | 8682 | 0 | 0 |
normalized size |
1 |
1. |
0.96 |
3.04 |
0. |
96.47 |
0. |
0. |
time (sec) |
N/A |
0.138 |
0.291 |
0.048 |
0. |
2.708 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 68 | 230 | 0 | 3090 | 0 | 140 |
normalized size |
1 |
1. |
1.05 |
3.54 |
0. |
47.54 |
0. |
2.15 |
time (sec) |
N/A |
0.057 |
0.214 |
0.036 |
0. |
2.388 |
0. |
1.229 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 106 | 468 | 0 | 11926 | 0 | 308 |
normalized size |
1 |
1. |
0.99 |
4.37 |
0. |
111.46 |
0. |
2.88 |
time (sec) |
N/A |
0.123 |
0.588 |
0.047 |
0. |
2.821 |
0. |
1.592 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
B |
B |
B |
B |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 0 | 86 | 46 | 215 | 60 | 46 |
normalized size | 1 | 1. | 0. | 5.73 | 3.07 | 14.33 | 4. | 3.07 |
time (sec) |
N/A |
0.012 |
0.022 |
0.012 |
1.569 |
2.124 |
0.951 |
1.231 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 35 | 113 | 80 | 728 | 211 | 80 |
normalized size | 1 | 1. | 1. | 3.23 | 2.29 | 20.8 | 6.03 | 2.29 |
time (sec) |
N/A |
0.025 |
0.128 |
0.014 |
1.702 |
2.12 |
6.585 |
1.359 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 51 | 129 | 112 | 1935 | 428 | 96 |
normalized size | 1 | 1. | 1. | 2.53 | 2.2 | 37.94 | 8.39 | 1.88 |
time (sec) |
N/A |
0.051 |
0.171 |
0.015 |
1.718 |
2.149 |
35.844 |
1.298 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2 | 2 | 2 | 16 | 14 | 69 | 14 | 14 |
normalized size | 1 | 1. | 1. | 8. | 7. | 34.5 | 7. | 7. |
time (sec) |
N/A |
0.016 |
0.003 |
0.011 |
1.021 |
2.024 |
0.584 |
1.252 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 17 | 32 | 66 | 286 | 34 | 24 |
normalized size | 1 | 1. | 1.55 | 2.91 | 6. | 26. | 3.09 | 2.18 |
time (sec) |
N/A |
0.018 |
0.003 |
0.016 |
1.109 |
1.986 |
2.135 |
1.282 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 27 | 48 | 150 | 626 | 54 | 32 |
normalized size | 1 | 1. | 1.42 | 2.53 | 7.89 | 32.95 | 2.84 | 1.68 |
time (sec) |
N/A |
0.02 |
0.004 |
0.016 |
1.093 |
2. |
7.85 |
1.322 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 53 | 114 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.08 | 2.33 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.031 |
0.076 |
0.191 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 18 | 58 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.06 | 3.41 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.009 |
0.022 |
0.236 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 15 | 15 | 4 | 0 | 42 |
normalized size | 1 | 1. | 1. | 1.15 | 1.15 | 0.31 | 0. | 3.23 |
time (sec) |
N/A |
0.022 |
0.005 |
0.073 |
1.641 |
2.2 |
0. |
1.213 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 11 | 14 | 15 | 12 | 0 | 42 |
normalized size | 1 | 1. | 1. | 1.27 | 1.36 | 1.09 | 0. | 3.82 |
time (sec) |
N/A |
0.018 |
0.006 |
0.085 |
1.706 |
1.996 |
0. |
1.248 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 40 | 62 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.03 | 1.59 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.021 |
0.039 |
0.211 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 135 | 321 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.02 |
2.41 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.154 |
0.455 |
0.178 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 51 | 99 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.93 |
1.8 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.061 |
0.05 |
0.237 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F(-1) |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 25 | 21 | 31 | 4 | 0 | 89 |
normalized size |
1 |
1. |
0.76 |
0.64 |
0.94 |
0.12 |
0. |
2.7 |
time (sec) |
N/A |
0.028 |
0.031 |
0.101 |
2.113 |
2.256 |
0. |
1.257 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 23 | 21 | 31 | 73 | 0 | 89 |
normalized size |
1 |
1. |
0.79 |
0.72 |
1.07 |
2.52 |
0. |
3.07 |
time (sec) |
N/A |
0.026 |
0.022 |
0.107 |
1.733 |
2.065 |
0. |
1.275 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 78 | 96 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.77 |
0.95 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.092 |
0.07 |
0.27 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 53 | 66 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.08 | 1.35 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.03 |
0.07 |
0.122 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 18 | 45 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.06 | 2.65 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.009 |
0.034 |
0.204 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 20 | 34 | 26 | 4 | 0 | 54 |
normalized size | 1 | 1. | 1.18 | 2. | 1.53 | 0.24 | 0. | 3.18 |
time (sec) |
N/A |
0.022 |
0.007 |
0.068 |
1.668 |
2.211 |
0. |
1.212 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 18 | 16 | 23 | 78 | 0 | 53 |
normalized size | 1 | 1. | 1.2 | 1.07 | 1.53 | 5.2 | 0. | 3.53 |
time (sec) |
N/A |
0.019 |
0.008 |
0.076 |
1.629 |
2.038 |
0. |
1.297 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 40 | 61 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.03 | 1.56 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.02 |
0.044 |
0.224 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 288 | 288 | 105 | 100 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.36 |
0.35 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.478 |
0.105 |
0.292 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 288 | 288 | 105 | 94 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.36 |
0.33 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.233 |
0.086 |
0.268 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
B |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 133 | 216 | 0 | 1922 | 330 | 0 |
normalized size |
1 |
1. |
1.46 |
2.37 |
0. |
21.12 |
3.63 |
0. |
time (sec) |
N/A |
0.13 |
0.846 |
0.016 |
0. |
2.498 |
4.353 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
B |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 147 | 212 | 0 | 1924 | 405 | 0 |
normalized size |
1 |
1. |
1.55 |
2.23 |
0. |
20.25 |
4.26 |
0. |
time (sec) |
N/A |
0.121 |
0.548 |
0.016 |
0. |
2.503 |
5.28 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 361 | 485 | 121 | 121 | 0 | 1728 | 0 | 0 |
normalized size |
1 |
1.34 |
0.34 |
0.34 |
0. |
4.79 |
0. |
0. |
time (sec) |
N/A |
1.037 |
0.229 |
0.023 |
0. |
2.679 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 109 | 127 | 0 | 1706 | 0 | 0 |
normalized size |
1 |
1. |
1.08 |
1.26 |
0. |
16.89 |
0. |
0. |
time (sec) |
N/A |
0.125 |
0.191 |
0.023 |
0. |
2.704 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 176 | 176 | 45 | 37 | 0 | 1875 | 0 | 293 |
normalized size |
1 |
1. |
0.26 |
0.21 |
0. |
10.65 |
0. |
1.66 |
time (sec) |
N/A |
0.155 |
0.071 |
0.018 |
0. |
2.474 |
0. |
1.349 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 24 | 100 | 61 | 382 | 75 | 58 |
normalized size | 1 | 1. | 0.96 | 4. | 2.44 | 15.28 | 3. | 2.32 |
time (sec) |
N/A |
0.017 |
0.1 |
0.017 |
1.682 |
2.164 |
3.71 |
1.241 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 494 | 494 | 139 | 156 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.28 |
0.32 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.904 |
0.288 |
0.023 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 132 | 177 | 0 | 0 | 0 | 1 |
normalized size |
1 |
1. |
0.77 |
1.04 |
0. |
0. |
0. |
0.01 |
time (sec) |
N/A |
0.226 |
0.214 |
0.026 |
0. |
0. |
0. |
1.475 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 245 | 245 | 158 | 233 | 0 | 0 | 0 | 1 |
normalized size |
1 |
1. |
0.64 |
0.95 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.487 |
0.26 |
0.03 |
0. |
0. |
0. |
2.157 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 494 | 494 | 139 | 150 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.28 |
0.3 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.625 |
0.272 |
0.023 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 132 | 183 | 0 | 0 | 0 | 1 |
normalized size |
1 |
1. |
0.75 |
1.05 |
0. |
0. |
0. |
0.01 |
time (sec) |
N/A |
0.231 |
0.173 |
0.027 |
0. |
0. |
0. |
1.607 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 213 | 213 | 158 | 239 | 0 | 0 | 0 | 1 |
normalized size |
1 |
1. |
0.74 |
1.12 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.235 |
0.207 |
0.032 |
0. |
0. |
0. |
2.188 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 223 | 223 | 445 | 62 | 0 | 10944 | 0 | 0 |
normalized size |
1 |
1. |
2. |
0.28 |
0. |
49.08 |
0. |
0. |
time (sec) |
N/A |
0.562 |
0.1 |
0.015 |
0. |
4.288 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 68 | 208 | 0 | 506 | 0 | 189 |
normalized size |
1 |
1. |
0.82 |
2.51 |
0. |
6.1 |
0. |
2.28 |
time (sec) |
N/A |
0.105 |
0.437 |
0.023 |
0. |
2.424 |
0. |
1.311 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 127 | 47 | 0 | 11980 | 0 | 1 |
normalized size |
1 |
1. |
0.98 |
0.36 |
0. |
92.87 |
0. |
0.01 |
time (sec) |
N/A |
0.185 |
0.129 |
0.029 |
0. |
4.024 |
0. |
1.375 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 445 | 64 | 0 | 10949 | 0 | 0 |
normalized size |
1 |
1. |
2.17 |
0.31 |
0. |
53.41 |
0. |
0. |
time (sec) |
N/A |
0.463 |
0.095 |
0.019 |
0. |
4.314 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 111 | 426 | 0 | 2302 | 0 | 14 |
normalized size |
1 |
1. |
1.56 |
6. |
0. |
32.42 |
0. |
0.2 |
time (sec) |
N/A |
0.122 |
0.219 |
0.023 |
0. |
2.541 |
0. |
1.202 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 64 | 136 | 0 | 2198 | 0 | 61 |
normalized size |
1 |
1. |
0.93 |
1.97 |
0. |
31.86 |
0. |
0.88 |
time (sec) |
N/A |
0.077 |
0.434 |
0.032 |
0. |
3.067 |
0. |
1.543 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 14 | 31 | 165 | 0 | 31 |
normalized size | 1 | 1. | 1. | 0.93 | 2.07 | 11. | 0. | 2.07 |
time (sec) |
N/A |
0.033 |
0.008 |
0.02 |
1.108 |
2.572 |
0. |
1.231 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 39 | 42 | 0 | 1192 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.08 | 0. | 30.56 | 0. | 0. |
time (sec) |
N/A |
0.069 |
0.025 |
0.016 |
0. |
4.667 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 26 | 31 | 0 | 809 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.19 | 0. | 31.12 | 0. | 0. |
time (sec) |
N/A |
0.064 |
0.016 |
0.02 |
0. |
2.622 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 12 | 0 | 224 | 0 | 0 |
normalized size | 1 | 1. | 1. | 0.92 | 0. | 17.23 | 0. | 0. |
time (sec) |
N/A |
0.041 |
0.01 |
0.017 |
0. |
2.333 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 21 | 12 | 9 | 4 | 0 | 51 |
normalized size | 1 | 1. | 1.62 | 0.92 | 0.69 | 0.31 | 0. | 3.92 |
time (sec) |
N/A |
0.061 |
0.013 |
0.075 |
1.617 |
2.214 |
0. |
1.32 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 153 | 153 | 145 | 150 | 0 | 2763 | 0 | 258 |
normalized size |
1 |
1. |
0.95 |
0.98 |
0. |
18.06 |
0. |
1.69 |
time (sec) |
N/A |
0.235 |
1.35 |
0.043 |
0. |
13.749 |
0. |
1.285 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 28 | 21 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0.75 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.075 |
0.02 |
0.026 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 45 | 34 | 0 | 5227 | 0 | 0 |
normalized size | 1 | 1. | 1. | 0.76 | 0. | 116.16 | 0. | 0. |
time (sec) |
N/A |
0.082 |
0.02 |
0.017 |
0. |
11.121 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 24 | 0 | 390 | 0 | 0 |
normalized size | 1 | 1. | 1. | 0.83 | 0. | 13.45 | 0. | 0. |
time (sec) |
N/A |
0.087 |
0.022 |
0.028 |
0. |
2.239 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 45 | 38 | 0 | 552 | 0 | 0 |
normalized size | 1 | 1. | 0.96 | 0.81 | 0. | 11.74 | 0. | 0. |
time (sec) |
N/A |
0.089 |
0.02 |
0.014 |
0. |
2.278 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
2.3 Detailed conclusion table specific for Rubi results
The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the
integral was to solve. In this test, problem number [62] had the largest ratio of [ 0.75
]
|
|
|
|
|
|
|
| Table 2.1Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
3 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
2 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
3 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
4 |
A |
3 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
5 |
A |
3 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
6 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
7 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
8 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
9 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
10 |
A |
4 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
11 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
12 |
A |
6 |
6 |
1. |
15 |
0.4 |
|
|
|
|
|
|
|
13 |
A |
6 |
6 |
1. |
15 |
0.4 |
|
|
|
|
|
|
|
14 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
15 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
16 |
A |
2 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
17 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
18 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
19 |
A |
7 |
7 |
1. |
13 |
0.538 |
|
|
|
|
|
|
|
20 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
|
21 |
A |
6 |
6 |
1. |
15 |
0.4 |
|
|
|
|
|
|
|
22 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
23 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
24 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
25 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
26 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
27 |
A |
2 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
28 |
A |
4 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
29 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
30 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
31 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
32 |
A |
6 |
6 |
1. |
15 |
0.4 |
|
|
|
|
|
|
|
33 |
A |
4 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
34 |
A |
5 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
35 |
A |
2 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
36 |
A |
4 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
37 |
A |
5 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
38 |
A |
3 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
39 |
A |
3 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
40 |
A |
3 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
|
41 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
42 |
A |
1 |
1 |
1. |
10 |
0.1 |
|
|
|
|
|
|
|
43 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
44 |
A |
3 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
45 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
46 |
A |
6 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
47 |
A |
4 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
48 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
49 |
A |
4 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
50 |
A |
6 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
51 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
52 |
A |
1 |
1 |
1. |
10 |
0.1 |
|
|
|
|
|
|
|
53 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
54 |
A |
3 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
55 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
56 |
A |
8 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
57 |
A |
8 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
58 |
A |
7 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
59 |
A |
7 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
60 |
A |
10 |
6 |
1.34 |
10 |
0.6 |
|
|
|
|
|
|
|
|
61 |
A |
4 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
62 |
A |
10 |
6 |
1. |
8 |
0.75 |
|
|
|
|
|
|
|
63 |
A |
3 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
64 |
A |
12 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
65 |
A |
7 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
66 |
A |
9 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
67 |
A |
12 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
68 |
A |
7 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
69 |
A |
9 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
70 |
A |
11 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
71 |
A |
7 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
72 |
A |
9 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
73 |
A |
11 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
74 |
A |
8 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
75 |
A |
10 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
76 |
A |
4 |
4 |
1. |
11 |
0.364 |
|
|
|
|
|
|
|
77 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
78 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
79 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
80 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
|
81 |
A |
11 |
10 |
1. |
15 |
0.667 |
|
|
|
|
|
|
|
82 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
83 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
84 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
85 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|