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, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102,
103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121,
122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
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, 86, 87,
88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 108, 109, 111, 113, 115, 118, 120,
121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139
}
B grade: { }
C grade: { 105, 107, 110, 112, 114, 116, 117, 119 }
F grade: { 140}
2.1.3 Maple
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 29, 30, 31, 32, 33, 34, 36,
38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69,
70, 71, 73, 74, 75, 76, 77, 78, 80, 82, 83, 84, 85, 86, 87, 88, 91, 93, 95, 96, 97, 106, 107, 108, 109, 111, 113,
114, 115, 116, 117, 120, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139
}
B grade: { 19, 24, 25, 26, 27, 28, 35, 37, 47, 48, 65, 72, 79, 81, 89, 90, 92, 94, 98, 99, 100, 101, 102, 103,
105, 110, 112, 118, 119 }
C grade: { }
F grade: { 104, 121, 122, 140 }
2.1.4 Maxima
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 137
B grade: { }
C grade: { }
F grade: { 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,
72, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101,
102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120,
121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140
}
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 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, 61, 62, 63, 64, 65,
66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 80, 82, 84, 86, 88, 106, 108, 109, 111, 113, 115,
120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139
}
B grade: { 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 60, 72, 79, 81, 83, 85, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97,
98, 99, 100, 101, 102, 103, 118 }
C grade: { }
F grade: { 104, 105, 107, 110, 112, 114, 116, 117, 119, 122, 140 }
2.1.6 Sympy
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 79, 81, 83, 85, 87, 90,
92, 94, 96, 98, 100, 102 }
B grade: { 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 78, 80, 82, 84, 86, 88, 89, 91,
93, 95, 97, 99, 101, 103 }
C grade: { }
F grade: { 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, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117,
118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,
140 }
2.1.7 Giac
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, 38, 39, 40, 41, 42, 50, 51, 52, 56, 57, 58, 59, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 80,
82, 84, 86, 88, 89, 91, 93, 95, 97, 99, 101, 103, 106, 113, 126, 127, 128, 129, 130, 131, 132, 139
}
B grade: { 65, 72, 111 }
C grade: { 79, 81, 83, 85, 87 }
F grade: { 33, 34, 35, 36, 37, 43, 44, 45, 46, 47, 48, 49, 53, 54, 55, 60, 61, 62, 63, 64, 90, 92, 94, 96, 98,
100, 102, 104, 105, 107, 108, 109, 110, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 133,
134, 135, 136, 137, 138, 140 }
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 \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 20 | 26 | 47 | 19 | 26 |
normalized size | 1 | 1. | 1. | 0.8 | 1.04 | 1.88 | 0.76 | 1.04 |
time (sec) |
N/A |
0.007 |
0.002 |
0. |
1.099 |
1.279 |
0.058 |
1.099 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 20 | 26 | 47 | 19 | 26 |
normalized size | 1 | 1. | 1. | 0.8 | 1.04 | 1.88 | 0.76 | 1.04 |
time (sec) |
N/A |
0.007 |
0.002 |
0. |
1.158 |
1.301 |
0.058 |
1.101 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 20 | 26 | 47 | 19 | 26 |
normalized size | 1 | 1. | 1. | 0.8 | 1.04 | 1.88 | 0.76 | 1.04 |
time (sec) |
N/A |
0.004 |
0. |
0. |
1.076 |
1.365 |
0.058 |
1.081 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 20 | 26 | 47 | 19 | 26 |
normalized size | 1 | 1. | 1. | 0.8 | 1.04 | 1.88 | 0.76 | 1.04 |
time (sec) |
N/A |
0.006 |
0.001 |
0.001 |
1.071 |
1.442 |
0.057 |
1.083 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 17 | 22 | 39 | 15 | 22 |
normalized size | 1 | 1. | 1. | 0.85 | 1.1 | 1.95 | 0.75 | 1.1 |
time (sec) |
N/A |
0.006 |
0.001 |
0.002 |
1.118 |
1.468 |
0.056 |
1.075 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 54 | 45 | 59 | 116 | 48 | 62 |
normalized size | 1 | 1. | 1. | 0.83 | 1.09 | 2.15 | 0.89 | 1.15 |
time (sec) |
N/A |
0.054 |
0.01 |
0.001 |
1.165 |
1.268 |
0.071 |
1.071 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 54 | 45 | 59 | 115 | 49 | 62 |
normalized size | 1 | 1. | 1. | 0.83 | 1.09 | 2.13 | 0.91 | 1.15 |
time (sec) |
N/A |
0.029 |
0.007 |
0. |
1.127 |
1.289 |
0.07 |
1.081 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 54 | 45 | 65 | 112 | 48 | 62 |
normalized size | 1 | 1. | 1. | 0.83 | 1.2 | 2.07 | 0.89 | 1.15 |
time (sec) |
N/A |
0.027 |
0.006 |
0. |
1.337 |
1.365 |
0.073 |
1.096 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 54 | 45 | 59 | 107 | 49 | 62 |
normalized size | 1 | 1. | 1. | 0.83 | 1.09 | 1.98 | 0.91 | 1.15 |
time (sec) |
N/A |
0.032 |
0.006 |
0.002 |
1.125 |
1.425 |
0.07 |
1.099 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 54 | 45 | 59 | 107 | 48 | 62 |
normalized size | 1 | 1. | 1. | 0.83 | 1.09 | 1.98 | 0.89 | 1.15 |
time (sec) |
N/A |
0.032 |
0.007 |
0. |
1.153 |
1.455 |
0.072 |
1.072 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 84 | 132 | 0 | 653 | 381 | 116 |
normalized size |
1 |
1. |
0.94 |
1.48 |
0. |
7.34 |
4.28 |
1.3 |
time (sec) |
N/A |
0.094 |
0.11 |
0.003 |
0. |
1.59 |
0.784 |
1.083 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 73 | 101 | 0 | 537 | 306 | 90 |
normalized size |
1 |
1. |
1.04 |
1.44 |
0. |
7.67 |
4.37 |
1.29 |
time (sec) |
N/A |
0.059 |
0.064 |
0.003 |
0. |
1.688 |
0.647 |
1.083 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 57 | 56 | 0 | 427 | 216 | 74 |
normalized size |
1 |
1. |
1.02 |
1. |
0. |
7.62 |
3.86 |
1.32 |
time (sec) |
N/A |
0.04 |
0.032 |
0.001 |
0. |
1.559 |
0.302 |
1.105 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 38 | 35 | 0 | 277 | 124 | 46 |
normalized size |
1 |
1. |
1.12 |
1.03 |
0. |
8.15 |
3.65 |
1.35 |
time (sec) |
N/A |
0.026 |
0.006 |
0.002 |
0. |
1.571 |
0.201 |
1.113 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 61 | 62 | 0 | 494 | 564 | 84 |
normalized size |
1 |
1. |
0.98 |
1. |
0. |
7.97 |
9.1 |
1.35 |
time (sec) |
N/A |
0.047 |
0.073 |
0.006 |
0. |
1.762 |
1.927 |
1.083 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 77 | 112 | 0 | 626 | 862 | 107 |
normalized size |
1 |
1. |
0.95 |
1.38 |
0. |
7.73 |
10.64 |
1.32 |
time (sec) |
N/A |
0.098 |
0.079 |
0.006 |
0. |
1.776 |
3.507 |
1.093 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 102 | 150 | 0 | 798 | 1525 | 142 |
normalized size |
1 |
1. |
0.98 |
1.44 |
0. |
7.67 |
14.66 |
1.37 |
time (sec) |
N/A |
0.146 |
0.138 |
0.007 |
0. |
1.946 |
5.173 |
1.132 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 131 | 214 | 0 | 979 | 2105 | 184 |
normalized size |
1 |
1. |
0.96 |
1.56 |
0. |
7.15 |
15.36 |
1.34 |
time (sec) |
N/A |
0.203 |
0.114 |
0.009 |
0. |
2.039 |
8.804 |
1.093 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 132 | 352 | 0 | 1760 | 842 | 217 |
normalized size |
1 |
1. |
0.88 |
2.35 |
0. |
11.73 |
5.61 |
1.45 |
time (sec) |
N/A |
0.159 |
0.193 |
0.008 |
0. |
1.598 |
1.625 |
1.116 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 114 | 109 | 209 | 0 | 1374 | 729 | 169 |
normalized size |
1 |
1. |
0.96 |
1.83 |
0. |
12.05 |
6.39 |
1.48 |
time (sec) |
N/A |
0.103 |
0.153 |
0.009 |
0. |
1.658 |
1.209 |
1.097 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 81 | 97 | 0 | 826 | 280 | 119 |
normalized size |
1 |
1. |
1.21 |
1.45 |
0. |
12.33 |
4.18 |
1.78 |
time (sec) |
N/A |
0.039 |
0.094 |
0.006 |
0. |
1.597 |
0.756 |
1.117 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 69 | 70 | 0 | 740 | 252 | 103 |
normalized size |
1 |
1. |
1.05 |
1.06 |
0. |
11.21 |
3.82 |
1.56 |
time (sec) |
N/A |
0.038 |
0.068 |
0.002 |
0. |
1.53 |
0.705 |
1.14 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 70 | 68 | 0 | 745 | 265 | 103 |
normalized size |
1 |
1. |
1.06 |
1.03 |
0. |
11.29 |
4.02 |
1.56 |
time (sec) |
N/A |
0.035 |
0.079 |
0.003 |
0. |
1.551 |
0.722 |
1.106 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 107 | 237 | 0 | 1685 | 2236 | 170 |
normalized size |
1 |
1. |
0.99 |
2.19 |
0. |
15.6 |
20.7 |
1.57 |
time (sec) |
N/A |
0.148 |
0.236 |
0.012 |
0. |
2.092 |
7.645 |
1.131 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 131 | 328 | 0 | 2049 | 2672 | 231 |
normalized size |
1 |
1. |
0.89 |
2.22 |
0. |
13.84 |
18.05 |
1.56 |
time (sec) |
N/A |
0.198 |
0.305 |
0.013 |
0. |
2.612 |
11.941 |
1.089 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 202 | 202 | 175 | 418 | 0 | 2606 | 4083 | 309 |
normalized size |
1 |
1. |
0.87 |
2.07 |
0. |
12.9 |
20.21 |
1.53 |
time (sec) |
N/A |
0.25 |
0.428 |
0.016 |
0. |
3.117 |
19.174 |
1.121 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 252 | 252 | 218 | 515 | 0 | 2989 | 4774 | 381 |
normalized size |
1 |
1. |
0.87 |
2.04 |
0. |
11.86 |
18.94 |
1.51 |
time (sec) |
N/A |
0.323 |
0.341 |
0.016 |
0. |
4.108 |
31.024 |
1.107 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 318 | 318 | 272 | 619 | 0 | 3563 | 6181 | 468 |
normalized size |
1 |
1. |
0.86 |
1.95 |
0. |
11.2 |
19.44 |
1.47 |
time (sec) |
N/A |
0.392 |
0.413 |
0.018 |
0. |
5.725 |
47.472 |
1.123 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 257 | 257 | 180 | 310 | 0 | 898 | 0 | 382 |
normalized size | 1 | 1. | 0.7 | 1.21 | 0. | 3.49 | 0. | 1.49 |
time (sec) |
N/A |
0.588 |
0.241 |
0.007 |
0. |
1.736 |
0. |
1.182 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 150 | 265 | 0 | 737 | 0 | 311 |
normalized size | 1 | 1. | 0.73 | 1.29 | 0. | 3.6 | 0. | 1.52 |
time (sec) |
N/A |
0.37 |
0.193 |
0.008 |
0. |
1.646 |
0. |
1.211 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 163 | 163 | 119 | 167 | 0 | 591 | 0 | 224 |
normalized size | 1 | 1. | 0.73 | 1.02 | 0. | 3.63 | 0. | 1.37 |
time (sec) |
N/A |
0.058 |
0.22 |
0.006 |
0. |
1.615 |
0. |
1.144 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 100 | 146 | 0 | 502 | 0 | 169 |
normalized size | 1 | 1. | 0.84 | 1.23 | 0. | 4.22 | 0. | 1.42 |
time (sec) |
N/A |
0.078 |
0.146 |
0.004 |
0. |
1.669 |
0. |
1.166 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 173 | 173 | 134 | 126 | 0 | 1457 | 0 | 0 |
normalized size |
1 |
1. |
0.77 |
0.73 |
0. |
8.42 |
0. |
0. |
time (sec) |
N/A |
0.126 |
0.11 |
0.004 |
0. |
1.842 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 173 | 173 | 131 | 174 | 0 | 1489 | 0 | 0 |
normalized size |
1 |
1. |
0.76 |
1.01 |
0. |
8.61 |
0. |
0. |
time (sec) |
N/A |
0.124 |
0.127 |
0.006 |
0. |
1.963 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 114 | 112 | 207 | 0 | 517 | 0 | 0 |
normalized size |
1 |
1. |
0.98 |
1.82 |
0. |
4.54 |
0. |
0. |
time (sec) |
N/A |
0.148 |
0.1 |
0.006 |
0. |
1.692 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 155 | 155 | 131 | 234 | 0 | 609 | 0 | 0 |
normalized size |
1 |
1. |
0.85 |
1.51 |
0. |
3.93 |
0. |
0. |
time (sec) |
N/A |
0.256 |
0.144 |
0.006 |
0. |
1.841 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 160 | 387 | 0 | 757 | 0 | 0 |
normalized size |
1 |
1. |
0.78 |
1.89 |
0. |
3.69 |
0. |
0. |
time (sec) |
N/A |
0.386 |
0.225 |
0.006 |
0. |
2.129 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 422 | 422 | 236 | 649 | 0 | 1600 | 0 | 703 |
normalized size | 1 | 1. | 0.56 | 1.54 | 0. | 3.79 | 0. | 1.67 |
time (sec) |
N/A |
1.203 |
0.426 |
0.008 |
0. |
2.031 |
0. |
1.294 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 364 | 364 | 197 | 479 | 0 | 1299 | 0 | 579 |
normalized size | 1 | 1. | 0.54 | 1.32 | 0. | 3.57 | 0. | 1.59 |
time (sec) |
N/A |
1.039 |
0.267 |
0.009 |
0. |
1.985 |
0. |
1.302 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 288 | 288 | 180 | 431 | 0 | 1099 | 0 | 493 |
normalized size | 1 | 1. | 0.62 | 1.5 | 0. | 3.82 | 0. | 1.71 |
time (sec) |
N/A |
0.519 |
0.242 |
0.009 |
0. |
1.835 |
0. |
1.325 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 198 | 198 | 163 | 289 | 0 | 878 | 0 | 383 |
normalized size | 1 | 1. | 0.82 | 1.46 | 0. | 4.43 | 0. | 1.93 |
time (sec) |
N/A |
0.178 |
0.182 |
0.006 |
0. |
1.695 |
0. |
1.273 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 132 | 265 | 0 | 725 | 0 | 313 |
normalized size | 1 | 1. | 0.8 | 1.61 | 0. | 4.39 | 0. | 1.9 |
time (sec) |
N/A |
0.128 |
0.064 |
0.006 |
0. |
1.646 |
0. |
1.28 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 227 | 227 | 166 | 222 | 0 | 1825 | 0 | 0 |
normalized size |
1 |
1. |
0.73 |
0.98 |
0. |
8.04 |
0. |
0. |
time (sec) |
N/A |
0.255 |
0.238 |
0.005 |
0. |
2.562 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 219 | 219 | 158 | 254 | 0 | 1735 | 0 | 0 |
normalized size |
1 |
1. |
0.72 |
1.16 |
0. |
7.92 |
0. |
0. |
time (sec) |
N/A |
0.242 |
0.184 |
0.006 |
0. |
2.218 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 219 | 219 | 162 | 338 | 0 | 1737 | 0 | 0 |
normalized size |
1 |
1. |
0.74 |
1.54 |
0. |
7.93 |
0. |
0. |
time (sec) |
N/A |
0.238 |
0.199 |
0.006 |
0. |
2.242 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 257 | 257 | 175 | 435 | 0 | 1871 | 0 | 0 |
normalized size |
1 |
1. |
0.68 |
1.69 |
0. |
7.28 |
0. |
0. |
time (sec) |
N/A |
0.351 |
0.307 |
0.007 |
0. |
2.5 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 197 | 197 | 141 | 501 | 0 | 743 | 0 | 0 |
normalized size |
1 |
1. |
0.72 |
2.54 |
0. |
3.77 |
0. |
0. |
time (sec) |
N/A |
0.363 |
0.117 |
0.009 |
0. |
2.341 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 249 | 249 | 177 | 534 | 0 | 898 | 0 | 0 |
normalized size |
1 |
1. |
0.71 |
2.14 |
0. |
3.61 |
0. |
0. |
time (sec) |
N/A |
0.504 |
0.176 |
0.008 |
0. |
2.71 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
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 | 143 | 143 | 105 | 144 | 0 | 514 | 0 | 0 |
normalized size | 1 | 1. | 0.73 | 1.01 | 0. | 3.59 | 0. | 0. |
time (sec) |
N/A |
0.174 |
0.137 |
0.006 |
0. |
1.569 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 89 | 88 | 0 | 429 | 0 | 146 |
normalized size | 1 | 1. | 0.86 | 0.85 | 0. | 4.17 | 0. | 1.42 |
time (sec) |
N/A |
0.078 |
0.054 |
0.006 |
0. |
1.591 |
0. |
1.156 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 66 | 65 | 0 | 298 | 0 | 50 |
normalized size | 1 | 1. | 0.93 | 0.92 | 0. | 4.2 | 0. | 0.7 |
time (sec) |
N/A |
0.037 |
0.041 |
0.006 |
0. |
1.546 |
0. |
1.159 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 70 | 66 | 0 | 300 | 0 | 80 |
normalized size | 1 | 1. | 1.56 | 1.47 | 0. | 6.67 | 0. | 1.78 |
time (sec) |
N/A |
0.016 |
0.021 |
0.005 |
0. |
1.616 |
0. |
1.157 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 89 | 88 | 0 | 444 | 0 | 0 |
normalized size |
1 |
1. |
1.16 |
1.14 |
0. |
5.77 |
0. |
0. |
time (sec) |
N/A |
0.054 |
0.056 |
0.006 |
0. |
1.732 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 112 | 152 | 0 | 527 | 0 | 0 |
normalized size |
1 |
1. |
0.94 |
1.28 |
0. |
4.43 |
0. |
0. |
time (sec) |
N/A |
0.149 |
0.096 |
0.006 |
0. |
1.791 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
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 | 262 | 262 | 183 | 283 | 0 | 1316 | 0 | 0 |
normalized size | 1 | 1. | 0.7 | 1.08 | 0. | 5.02 | 0. | 0. |
time (sec) |
N/A |
0.506 |
0.258 |
0.009 |
0. |
2.276 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 201 | 201 | 141 | 199 | 0 | 1026 | 0 | 263 |
normalized size | 1 | 1. | 0.7 | 0.99 | 0. | 5.1 | 0. | 1.31 |
time (sec) |
N/A |
0.305 |
0.159 |
0.006 |
0. |
2.09 |
0. |
1.17 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 153 | 153 | 112 | 166 | 0 | 873 | 0 | 149 |
normalized size | 1 | 1. | 0.73 | 1.08 | 0. | 5.71 | 0. | 0.97 |
time (sec) |
N/A |
0.175 |
0.123 |
0.006 |
0. |
2.159 |
0. |
1.192 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 40 | 37 | 53 | 0 | 150 | 0 | 61 |
normalized size | 1 | 1. | 0.92 | 1.32 | 0. | 3.75 | 0. | 1.52 |
time (sec) |
N/A |
0.04 |
0.074 |
0.004 |
0. |
1.985 |
0. |
1.192 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 36 | 52 | 0 | 151 | 0 | 61 |
normalized size | 1 | 1. | 0.92 | 1.33 | 0. | 3.87 | 0. | 1.56 |
time (sec) |
N/A |
0.04 |
0.024 |
0.003 |
0. |
1.946 |
0. |
1.165 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 109 | 164 | 0 | 869 | 0 | 0 |
normalized size |
1 |
1. |
1.16 |
1.74 |
0. |
9.24 |
0. |
0. |
time (sec) |
N/A |
0.068 |
0.123 |
0.006 |
0. |
2.065 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 144 | 144 | 138 | 201 | 0 | 1041 | 0 | 0 |
normalized size |
1 |
1. |
0.96 |
1.4 |
0. |
7.23 |
0. |
0. |
time (sec) |
N/A |
0.163 |
0.106 |
0.006 |
0. |
1.876 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
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 | 209 | 209 | 181 | 292 | 0 | 1328 | 0 | 0 |
normalized size | 1 | 1. | 0.87 | 1.4 | 0. | 6.35 | 0. | 0. |
time (sec) |
N/A |
0.287 |
0.167 |
0.007 |
0. |
2.208 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
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 | 271 | 271 | 225 | 340 | 0 | 1550 | 0 | 0 |
normalized size | 1 | 1. | 0.83 | 1.25 | 0. | 5.72 | 0. | 0. |
time (sec) |
N/A |
0.452 |
0.265 |
0.009 |
0. |
2.913 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
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 | 343 | 343 | 272 | 446 | 0 | 1901 | 0 | 0 |
normalized size | 1 | 1. | 0.79 | 1.3 | 0. | 5.54 | 0. | 0. |
time (sec) |
N/A |
0.621 |
0.287 |
0.008 |
0. |
4.085 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 34 | 77 | 0 | 161 | 280 | 144 |
normalized size |
1 |
1. |
0.92 |
2.08 |
0. |
4.35 |
7.57 |
3.89 |
time (sec) |
N/A |
0.013 |
0.029 |
0.003 |
0. |
1.313 |
1.09 |
1.112 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 20 | 26 | 47 | 19 | 26 |
normalized size | 1 | 1. | 1. | 0.8 | 1.04 | 1.88 | 0.76 | 1.04 |
time (sec) |
N/A |
0.008 |
0.002 |
0.002 |
1.127 |
1.051 |
0.056 |
1.098 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 20 | 26 | 47 | 19 | 26 |
normalized size | 1 | 1. | 1. | 0.8 | 1.04 | 1.88 | 0.76 | 1.04 |
time (sec) |
N/A |
0.007 |
0.002 |
0. |
1.072 |
1.087 |
0.056 |
1.091 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 20 | 26 | 47 | 19 | 26 |
normalized size | 1 | 1. | 1. | 0.8 | 1.04 | 1.88 | 0.76 | 1.04 |
time (sec) |
N/A |
0.004 |
0. |
0. |
1.114 |
1.049 |
0.056 |
1.1 |
|
|
|
|
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|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 17 | 22 | 39 | 15 | 22 |
normalized size | 1 | 1. | 1. | 0.85 | 1.1 | 1.95 | 0.75 | 1.1 |
time (sec) |
N/A |
0.006 |
0.001 |
0. |
1.131 |
1.23 |
0.056 |
1.1 |
|
|
|
|
|
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|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 21 | 18 | 23 | 46 | 17 | 27 |
normalized size | 1 | 1. | 1. | 0.86 | 1.1 | 2.19 | 0.81 | 1.29 |
time (sec) |
N/A |
0.008 |
0.002 |
0.003 |
1.142 |
1.224 |
0.089 |
1.121 |
|
|
|
|
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|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 18 | 18 | 17 | 22 | 42 | 12 | 22 |
normalized size | 1 | 1. | 1. | 0.94 | 1.22 | 2.33 | 0.67 | 1.22 |
time (sec) |
N/A |
0.007 |
0.002 |
0.003 |
1.112 |
1.191 |
0.248 |
1.091 |
|
|
|
|
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|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 76 | 76 | 69 | 300 | 0 | 602 | 1377 | 539 |
normalized size |
1 |
1. |
0.91 |
3.95 |
0. |
7.92 |
18.12 |
7.09 |
time (sec) |
N/A |
0.046 |
0.079 |
0.006 |
0. |
1.41 |
3.99 |
1.127 |
|
|
|
|
|
|
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|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 54 | 45 | 59 | 117 | 51 | 62 |
normalized size | 1 | 1. | 1. | 0.83 | 1.09 | 2.17 | 0.94 | 1.15 |
time (sec) |
N/A |
0.036 |
0.007 |
0.001 |
1.119 |
1.015 |
0.07 |
1.086 |
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 48 | 45 | 59 | 116 | 46 | 62 |
normalized size | 1 | 1. | 0.89 | 0.83 | 1.09 | 2.15 | 0.85 | 1.15 |
time (sec) |
N/A |
0.054 |
0.009 |
0.001 |
1.09 |
1.123 |
0.07 |
1.09 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 54 | 45 | 65 | 115 | 51 | 62 |
normalized size | 1 | 1. | 1. | 0.83 | 1.2 | 2.13 | 0.94 | 1.15 |
time (sec) |
N/A |
0.026 |
0.008 |
0.002 |
1.12 |
1.118 |
0.07 |
1.098 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 48 | 45 | 59 | 109 | 46 | 62 |
normalized size | 1 | 1. | 0.89 | 0.83 | 1.09 | 2.02 | 0.85 | 1.15 |
time (sec) |
N/A |
0.046 |
0.009 |
0.002 |
1.022 |
1.309 |
0.069 |
1.089 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 49 | 42 | 55 | 99 | 48 | 58 |
normalized size | 1 | 1. | 1. | 0.86 | 1.12 | 2.02 | 0.98 | 1.18 |
time (sec) |
N/A |
0.027 |
0.005 |
0.001 |
1.128 |
1.099 |
0.072 |
1.078 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 100 | 93 | 142 | 0 | 675 | 391 | 124 |
normalized size | 1 | 1. | 0.93 | 1.42 | 0. | 6.75 | 3.91 | 1.24 |
time (sec) |
N/A |
0.122 |
0.094 |
0.005 |
0. |
1.329 |
1.892 |
1.1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 203 | 203 | 250 | 467 | 0 | 3217 | 194 | 5466 |
normalized size | 1 | 1. | 1.23 | 2.3 | 0. | 15.85 | 0.96 | 26.93 |
time (sec) |
N/A |
0.602 |
0.172 |
0.023 |
0. |
1.54 |
2.207 |
2.487 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 78 | 111 | 0 | 556 | 316 | 101 |
normalized size | 1 | 1. | 0.96 | 1.37 | 0. | 6.86 | 3.9 | 1.25 |
time (sec) |
N/A |
0.087 |
0.048 |
0.003 |
0. |
1.278 |
1.541 |
1.095 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 179 | 179 | 202 | 343 | 0 | 2168 | 129 | 4593 |
normalized size | 1 | 1. | 1.13 | 1.92 | 0. | 12.11 | 0.72 | 25.66 |
time (sec) |
N/A |
0.227 |
0.145 |
0.013 |
0. |
1.412 |
1.604 |
2.336 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 62 | 60 | 0 | 443 | 223 | 80 |
normalized size | 1 | 1. | 0.98 | 0.95 | 0. | 7.03 | 3.54 | 1.27 |
time (sec) |
N/A |
0.067 |
0.028 |
0.003 |
0. |
1.316 |
0.813 |
1.089 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 165 | 208 | 0 | 1206 | 75 | 5350 |
normalized size | 1 | 1. | 1.1 | 1.39 | 0. | 8.04 | 0.5 | 35.67 |
time (sec) |
N/A |
0.094 |
0.098 |
0.011 |
0. |
1.522 |
0.768 |
2.206 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 39 | 36 | 0 | 290 | 131 | 47 |
normalized size | 1 | 1. | 1.08 | 1. | 0. | 8.06 | 3.64 | 1.31 |
time (sec) |
N/A |
0.043 |
0.009 |
0. |
0. |
1.539 |
0.445 |
1.116 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 129 | 116 | 0 | 1323 | 87 | 1365 |
normalized size | 1 | 1. | 0.86 | 0.77 | 0. | 8.82 | 0.58 | 9.1 |
time (sec) |
N/A |
0.08 |
0.083 |
0.01 |
0. |
1.571 |
0.896 |
1.359 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 113 | 66 | 0 | 510 | 253 | 92 |
normalized size | 1 | 1. | 1.64 | 0.96 | 0. | 7.39 | 3.67 | 1.33 |
time (sec) |
N/A |
0.072 |
0.073 |
0.006 |
0. |
1.588 |
2.868 |
1.096 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 174 | 174 | 191 | 232 | 0 | 2279 | 148 | 4581 |
normalized size | 1 | 1. | 1.1 | 1.33 | 0. | 13.1 | 0.85 | 26.33 |
time (sec) |
N/A |
0.195 |
0.423 |
0.019 |
0. |
1.625 |
1.808 |
2.354 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 135 | 119 | 0 | 664 | 345 | 127 |
normalized size | 1 | 1. | 1.52 | 1.34 | 0. | 7.46 | 3.88 | 1.43 |
time (sec) |
N/A |
0.133 |
0.125 |
0.006 |
0. |
2.017 |
7.246 |
1.095 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 151 | 383 | 0 | 1806 | 877 | 217 |
normalized size | 1 | 1. | 0.91 | 2.31 | 0. | 10.88 | 5.28 | 1.31 |
time (sec) |
N/A |
0.223 |
0.209 |
0.013 |
0. |
1.671 |
4.751 |
21.874 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 331 | 331 | 327 | 844 | 0 | 6311 | 450 | 0 |
normalized size |
1 |
1. |
0.99 |
2.55 |
0. |
19.07 |
1.36 |
0. |
time (sec) |
N/A |
0.703 |
0.713 |
0.033 |
0. |
2.158 |
6.661 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 121 | 222 | 0 | 1412 | 745 | 205 |
normalized size | 1 | 1. | 0.92 | 1.68 | 0. | 10.7 | 5.64 | 1.55 |
time (sec) |
N/A |
0.152 |
0.186 |
0.011 |
0. |
1.385 |
3.505 |
25.605 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 271 | 271 | 282 | 602 | 0 | 4806 | 379 | 0 |
normalized size |
1 |
1. |
1.04 |
2.22 |
0. |
17.73 |
1.4 |
0. |
time (sec) |
N/A |
0.526 |
0.572 |
0.029 |
0. |
1.723 |
4.632 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 93 | 104 | 0 | 864 | 282 | 130 |
normalized size |
1 |
1. |
1.19 |
1.33 |
0. |
11.08 |
3.62 |
1.67 |
time (sec) |
N/A |
0.072 |
0.091 |
0.009 |
0. |
1.366 |
1.746 |
29.874 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 237 | 237 | 235 | 452 | 0 | 3584 | 294 | 0 |
normalized size |
1 |
1. |
0.99 |
1.91 |
0. |
15.12 |
1.24 |
0. |
time (sec) |
N/A |
0.358 |
0.441 |
0.026 |
0. |
1.395 |
3.359 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 79 | 77 | 0 | 778 | 267 | 111 |
normalized size |
1 |
1. |
1.05 |
1.03 |
0. |
10.37 |
3.56 |
1.48 |
time (sec) |
N/A |
0.069 |
0.069 |
0.004 |
0. |
1.282 |
1.667 |
25.713 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
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 | 221 | 221 | 222 | 342 | 0 | 3623 | 298 | 0 |
normalized size |
1 |
1. |
1. |
1.55 |
0. |
16.39 |
1.35 |
0. |
time (sec) |
N/A |
0.24 |
0.462 |
0.063 |
0. |
1.612 |
3.489 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 79 | 75 | 0 | 783 | 267 | 111 |
normalized size |
1 |
1. |
1.07 |
1.01 |
0. |
10.58 |
3.61 |
1.5 |
time (sec) |
N/A |
0.065 |
0.085 |
0.004 |
0. |
1.378 |
1.574 |
31.512 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 252 | 252 | 243 | 733 | 0 | 4918 | 394 | 0 |
normalized size |
1 |
1. |
0.96 |
2.91 |
0. |
19.52 |
1.56 |
0. |
time (sec) |
N/A |
0.461 |
0.461 |
0.044 |
0. |
1.767 |
4.473 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 207 | 253 | 0 | 1728 | 772 | 224 |
normalized size | 1 | 1. | 1.7 | 2.07 | 0. | 14.16 | 6.33 | 1.84 |
time (sec) |
N/A |
0.188 |
0.322 |
0.014 |
0. |
1.784 |
40.968 |
22.145 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 308 | 308 | 302 | 712 | 0 | 6460 | 481 | 0 |
normalized size |
1 |
1. |
0.98 |
2.31 |
0. |
20.97 |
1.56 |
0. |
time (sec) |
N/A |
1.352 |
0.668 |
0.03 |
0. |
2.108 |
7.145 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 162 | 162 | 248 | 352 | 0 | 2103 | 906 | 246 |
normalized size | 1 | 1. | 1.53 | 2.17 | 0. | 12.98 | 5.59 | 1.52 |
time (sec) |
N/A |
0.25 |
0.275 |
0.017 |
0. |
2.194 |
72.952 |
25.533 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 361 | 361 | 344 | 913 | 0 | 7960 | 566 | 0 |
normalized size |
1 |
1. |
0.95 |
2.53 |
0. |
22.05 |
1.57 |
0. |
time (sec) |
N/A |
3.077 |
0.788 |
0.036 |
0. |
2.942 |
12.022 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 219 | 219 | 328 | 443 | 0 | 2627 | 1074 | 370 |
normalized size | 1 | 1. | 1.5 | 2.02 | 0. | 12. | 4.9 | 1.69 |
time (sec) |
N/A |
0.312 |
0.366 |
0.019 |
0. |
2.724 |
131.412 |
23.764 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 142 | 142 | 170 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.2 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.171 |
0.095 |
0.017 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 380 | 380 | 486 | 1042 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.28 | 2.74 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.287 |
1.52 |
0.069 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 126 | 157 | 0 | 547 | 0 | 171 |
normalized size | 1 | 1. | 0.98 | 1.22 | 0. | 4.24 | 0. | 1.33 |
time (sec) |
N/A |
0.093 |
0.078 |
0.016 |
0. |
1.397 |
0. |
1.194 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 347 | 347 | 452 | 508 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.3 | 1.46 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.224 |
0.971 |
0.019 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
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 | 194 | 194 | 155 | 136 | 0 | 1575 | 0 | 0 |
normalized size | 1 | 1. | 0.8 | 0.7 | 0. | 8.12 | 0. | 0. |
time (sec) |
N/A |
0.209 |
0.066 |
0.017 |
0. |
1.641 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 244 | 244 | 192 | 369 | 0 | 921 | 0 | 0 |
normalized size |
1 |
1. |
0.79 |
1.51 |
0. |
3.77 |
0. |
0. |
time (sec) |
N/A |
0.357 |
0.212 |
0.026 |
0. |
1.444 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 487 | 487 | 609 | 1878 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.25 | 3.86 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.457 |
2.321 |
0.024 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 177 | 152 | 295 | 0 | 768 | 0 | 624 |
normalized size |
1 |
1. |
0.86 |
1.67 |
0. |
4.34 |
0. |
3.53 |
time (sec) |
N/A |
0.138 |
0.114 |
0.02 |
0. |
1.511 |
0. |
1.518 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 425 | 425 | 540 | 1394 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.27 | 3.28 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.449 |
1.748 |
0.023 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 82 | 72 | 0 | 325 | 0 | 54 |
normalized size | 1 | 1. | 1. | 0.88 | 0. | 3.96 | 0. | 0.66 |
time (sec) |
N/A |
0.062 |
0.018 |
0.012 |
0. |
1.469 |
0. |
1.314 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 121 | 193 | 177 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.6 | 1.46 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.046 |
0.126 |
0.016 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
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 | 51 | 51 | 83 | 72 | 0 | 327 | 0 | 0 |
normalized size | 1 | 1. | 1.63 | 1.41 | 0. | 6.41 | 0. | 0. |
time (sec) |
N/A |
0.029 |
0.019 |
0.014 |
0. |
1.4 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 330 | 330 | 303 | 508 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.92 | 1.54 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.184 |
0.487 |
0.023 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 391 | 391 | 463 | 533 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.18 | 1.36 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.248 |
1.083 |
0.027 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 126 | 179 | 0 | 918 | 0 | 0 |
normalized size | 1 | 1. | 1.22 | 1.74 | 0. | 8.91 | 0. | 0. |
time (sec) |
N/A |
0.073 |
0.083 |
0.019 |
0. |
1.777 |
0. |
0. |
|
|
|
|
|
|
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|
Problem 119 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 468 | 468 | 519 | 1136 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.11 | 2.43 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.409 |
1.351 |
0.029 |
0. |
0. |
0. |
0. |
|
|
|
|
|
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Problem 120 |
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 | 154 | 154 | 160 | 220 | 0 | 1084 | 0 | 0 |
normalized size | 1 | 1. | 1.04 | 1.43 | 0. | 7.04 | 0. | 0. |
time (sec) |
N/A |
0.175 |
0.082 |
0.019 |
0. |
1.854 |
0. |
0. |
|
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Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 46 | 0 | 0 | 186 | 0 | 0 |
normalized size |
1 |
1. |
0.9 |
0. |
0. |
3.65 |
0. |
0. |
time (sec) |
N/A |
0.05 |
0.088 |
0.074 |
0. |
1.657 |
0. |
0. |
|
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Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 287 | 287 | 239 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.83 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.399 |
5.135 |
0.02 |
0. |
0. |
0. |
0. |
|
|
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Problem 123 |
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 | 45 | 45 | 73 | 58 | 0 | 142 | 0 | 0 |
normalized size | 1 | 1. | 1.62 | 1.29 | 0. | 3.16 | 0. | 0. |
time (sec) |
N/A |
0.009 |
0.018 |
0.011 |
0. |
1.268 |
0. |
0. |
|
|
|
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|
|
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Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 73 | 58 | 0 | 142 | 0 | 0 |
normalized size |
1 |
1. |
1.62 |
1.29 |
0. |
3.16 |
0. |
0. |
time (sec) |
N/A |
0.012 |
0.003 |
0.008 |
0. |
1.37 |
0. |
0. |
|
|
|
|
|
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Problem 125 |
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 | 45 | 45 | 73 | 58 | 0 | 142 | 0 | 0 |
normalized size | 1 | 1. | 1.62 | 1.29 | 0. | 3.16 | 0. | 0. |
time (sec) |
N/A |
0.012 |
0.004 |
0.003 |
0. |
1.284 |
0. |
0. |
|
|
|
|
|
|
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|
Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 70 | 81 | 0 | 157 | 0 | 93 |
normalized size | 1 | 1. | 0.81 | 0.94 | 0. | 1.83 | 0. | 1.08 |
time (sec) |
N/A |
0.041 |
0.034 |
0.007 |
0. |
1.296 |
0. |
1.089 |
|
|
|
|
|
|
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|
Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 70 | 81 | 0 | 157 | 0 | 93 |
normalized size |
1 |
1. |
0.81 |
0.94 |
0. |
1.83 |
0. |
1.08 |
time (sec) |
N/A |
0.042 |
0.009 |
0.003 |
0. |
1.288 |
0. |
1.092 |
|
|
|
|
|
|
|
|
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|
Problem 128 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 70 | 81 | 0 | 157 | 0 | 93 |
normalized size | 1 | 1. | 0.81 | 0.94 | 0. | 1.83 | 0. | 1.08 |
time (sec) |
N/A |
0.041 |
0.003 |
0.003 |
0. |
1.293 |
0. |
1.096 |
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 129 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 38 | 37 | 35 | 0 | 273 | 0 | 47 |
normalized size |
1 |
1. |
0.97 |
0.92 |
0. |
7.18 |
0. |
1.24 |
time (sec) |
N/A |
0.016 |
0.009 |
0.003 |
0. |
1.361 |
0. |
1.097 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
Problem 130 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 70 | 64 | 0 | 300 | 0 | 80 |
normalized size |
1 |
1. |
1.56 |
1.42 |
0. |
6.67 |
0. |
1.78 |
time (sec) |
N/A |
0.022 |
0.023 |
0.008 |
0. |
1.394 |
0. |
1.104 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 131 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 72 | 64 | 0 | 315 | 0 | 47 |
normalized size |
1 |
1. |
1.53 |
1.36 |
0. |
6.7 |
0. |
1. |
time (sec) |
N/A |
0.076 |
0.033 |
0.011 |
0. |
1.704 |
0. |
1.145 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 74 | 66 | 0 | 325 | 0 | 47 |
normalized size |
1 |
1. |
1.51 |
1.35 |
0. |
6.63 |
0. |
0.96 |
time (sec) |
N/A |
0.09 |
0.028 |
0.006 |
0. |
1.707 |
0. |
1.157 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 133 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 44 | 44 | 44 | 39 | 0 | 294 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0.89 |
0. |
6.68 |
0. |
0. |
time (sec) |
N/A |
0.036 |
0.012 |
0.004 |
0. |
1.467 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 134 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 81 | 72 | 0 | 311 | 0 | 0 |
normalized size |
1 |
1. |
1.65 |
1.47 |
0. |
6.35 |
0. |
0. |
time (sec) |
N/A |
0.015 |
0.016 |
0.005 |
0. |
1.325 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 135 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 83 | 72 | 0 | 327 | 0 | 0 |
normalized size |
1 |
1. |
1.63 |
1.41 |
0. |
6.41 |
0. |
0. |
time (sec) |
N/A |
0.067 |
0.02 |
0.008 |
0. |
1.372 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 85 | 74 | 0 | 338 | 0 | 0 |
normalized size |
1 |
1. |
1.6 |
1.4 |
0. |
6.38 |
0. |
0. |
time (sec) |
N/A |
0.077 |
0.019 |
0.007 |
0. |
1.362 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 137 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 40 | 40 | 31 | 27 | 131 | 0 | 0 |
normalized size | 1 | 1. | 1. | 0.78 | 0.68 | 3.28 | 0. | 0. |
time (sec) |
N/A |
0.027 |
0.009 |
0.003 |
1.646 |
1.311 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 138 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 73 | 58 | 0 | 142 | 0 | 0 |
normalized size |
1 |
1. |
1.62 |
1.29 |
0. |
3.16 |
0. |
0. |
time (sec) |
N/A |
0.012 |
0.008 |
0. |
0. |
1.289 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 139 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 62 | 50 | 0 | 132 | 0 | 69 |
normalized size |
1 |
1. |
1.44 |
1.16 |
0. |
3.07 |
0. |
1.6 |
time (sec) |
N/A |
0.047 |
0.02 |
0.011 |
0. |
1.393 |
0. |
1.144 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.067 |
0.393 |
0.121 |
0. |
0. |
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 [86] had the largest ratio of [ 0.5
]
|
|
|
|
|
|
|
| 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 |
2 |
1 |
1. |
20 |
0.05 |
|
|
|
|
|
|
|
2 |
A |
2 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
3 |
A |
1 |
0 |
1. |
16 |
0. |
|
|
|
|
|
|
|
4 |
A |
2 |
1 |
1. |
20 |
0.05 |
|
|
|
|
|
|
|
5 |
A |
2 |
1 |
1. |
20 |
0.05 |
|
|
|
|
|
|
|
6 |
A |
3 |
2 |
1. |
22 |
0.091 |
|
|
|
|
|
|
|
7 |
A |
3 |
2 |
1. |
20 |
0.1 |
|
|
|
|
|
|
|
8 |
A |
3 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
9 |
A |
3 |
2 |
1. |
22 |
0.091 |
|
|
|
|
|
|
|
10 |
A |
3 |
2 |
1. |
22 |
0.091 |
|
|
|
|
|
|
|
11 |
A |
7 |
6 |
1. |
22 |
0.273 |
|
|
|
|
|
|
|
12 |
A |
6 |
6 |
1. |
22 |
0.273 |
|
|
|
|
|
|
|
13 |
A |
5 |
5 |
1. |
22 |
0.227 |
|
|
|
|
|
|
|
14 |
A |
3 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
15 |
A |
7 |
7 |
1. |
20 |
0.35 |
|
|
|
|
|
|
|
16 |
A |
8 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
17 |
A |
8 |
7 |
1. |
22 |
0.318 |
|
|
|
|
|
|
|
18 |
A |
8 |
7 |
1. |
22 |
0.318 |
|
|
|
|
|
|
|
19 |
A |
8 |
7 |
1. |
22 |
0.318 |
|
|
|
|
|
|
|
20 |
A |
7 |
7 |
1. |
22 |
0.318 |
|
|
|
|
|
|
|
|
21 |
A |
4 |
4 |
1. |
22 |
0.182 |
|
|
|
|
|
|
|
22 |
A |
4 |
4 |
1. |
22 |
0.182 |
|
|
|
|
|
|
|
23 |
A |
4 |
4 |
1. |
22 |
0.182 |
|
|
|
|
|
|
|
24 |
A |
8 |
7 |
1. |
22 |
0.318 |
|
|
|
|
|
|
|
25 |
A |
8 |
7 |
1. |
22 |
0.318 |
|
|
|
|
|
|
|
26 |
A |
8 |
7 |
1. |
20 |
0.35 |
|
|
|
|
|
|
|
27 |
A |
8 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
28 |
A |
8 |
7 |
1. |
22 |
0.318 |
|
|
|
|
|
|
|
29 |
A |
8 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
30 |
A |
7 |
6 |
1. |
22 |
0.273 |
|
|
|
|
|
|
|
31 |
A |
5 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
32 |
A |
4 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
33 |
A |
7 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
34 |
A |
7 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
35 |
A |
5 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
36 |
A |
6 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
37 |
A |
7 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
38 |
A |
10 |
7 |
1. |
22 |
0.318 |
|
|
|
|
|
|
|
39 |
A |
10 |
7 |
1. |
20 |
0.35 |
|
|
|
|
|
|
|
40 |
A |
8 |
7 |
1. |
24 |
0.292 |
|
|
|
|
|
|
|
|
41 |
A |
6 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
42 |
A |
5 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
43 |
A |
8 |
7 |
1. |
24 |
0.292 |
|
|
|
|
|
|
|
44 |
A |
8 |
7 |
1. |
24 |
0.292 |
|
|
|
|
|
|
|
45 |
A |
8 |
7 |
1. |
24 |
0.292 |
|
|
|
|
|
|
|
46 |
A |
9 |
8 |
1. |
24 |
0.333 |
|
|
|
|
|
|
|
47 |
A |
7 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
48 |
A |
8 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
49 |
A |
6 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
50 |
A |
4 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
51 |
A |
3 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
52 |
A |
2 |
2 |
1. |
20 |
0.1 |
|
|
|
|
|
|
|
53 |
A |
3 |
3 |
1. |
24 |
0.125 |
|
|
|
|
|
|
|
54 |
A |
5 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
55 |
A |
8 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
56 |
A |
7 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
57 |
A |
6 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
58 |
A |
1 |
1 |
1. |
24 |
0.042 |
|
|
|
|
|
|
|
59 |
A |
1 |
1 |
1. |
24 |
0.042 |
|
|
|
|
|
|
|
60 |
A |
3 |
3 |
1. |
24 |
0.125 |
|
|
|
|
|
|
|
|
61 |
A |
5 |
5 |
1. |
22 |
0.227 |
|
|
|
|
|
|
|
62 |
A |
6 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
63 |
A |
7 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
64 |
A |
8 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
65 |
A |
2 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
66 |
A |
2 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
67 |
A |
2 |
1 |
1. |
16 |
0.062 |
|
|
|
|
|
|
|
68 |
A |
1 |
0 |
1. |
14 |
0. |
|
|
|
|
|
|
|
69 |
A |
2 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
70 |
A |
2 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
71 |
A |
2 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
72 |
A |
3 |
2 |
1. |
20 |
0.1 |
|
|
|
|
|
|
|
73 |
A |
3 |
2 |
1. |
20 |
0.1 |
|
|
|
|
|
|
|
74 |
A |
4 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
75 |
A |
3 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
76 |
A |
4 |
3 |
1. |
20 |
0.15 |
|
|
|
|
|
|
|
77 |
A |
3 |
2 |
1. |
20 |
0.1 |
|
|
|
|
|
|
|
78 |
A |
8 |
7 |
1. |
20 |
0.35 |
|
|
|
|
|
|
|
79 |
A |
6 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
80 |
A |
7 |
7 |
1. |
20 |
0.35 |
|
|
|
|
|
|
|
|
81 |
A |
5 |
4 |
1. |
20 |
0.2 |
|
|
|
|
|
|
|
82 |
A |
6 |
6 |
1. |
20 |
0.3 |
|
|
|
|
|
|
|
83 |
A |
4 |
3 |
1. |
20 |
0.15 |
|
|
|
|
|
|
|
84 |
A |
4 |
4 |
1. |
20 |
0.2 |
|
|
|
|
|
|
|
85 |
A |
4 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
86 |
A |
8 |
8 |
1. |
16 |
0.5 |
|
|
|
|
|
|
|
87 |
A |
5 |
4 |
1. |
20 |
0.2 |
|
|
|
|
|
|
|
88 |
A |
9 |
8 |
1. |
20 |
0.4 |
|
|
|
|
|
|
|
89 |
A |
9 |
8 |
1. |
20 |
0.4 |
|
|
|
|
|
|
|
90 |
A |
7 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
91 |
A |
8 |
8 |
1. |
20 |
0.4 |
|
|
|
|
|
|
|
92 |
A |
6 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
93 |
A |
5 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
94 |
A |
5 |
4 |
1. |
20 |
0.2 |
|
|
|
|
|
|
|
95 |
A |
5 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
96 |
A |
5 |
4 |
1. |
20 |
0.2 |
|
|
|
|
|
|
|
97 |
A |
5 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
98 |
A |
5 |
4 |
1. |
20 |
0.2 |
|
|
|
|
|
|
|
99 |
A |
9 |
8 |
1. |
18 |
0.444 |
|
|
|
|
|
|
|
100 |
A |
6 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
|
101 |
A |
9 |
8 |
1. |
20 |
0.4 |
|
|
|
|
|
|
|
102 |
A |
7 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
103 |
A |
9 |
8 |
1. |
20 |
0.4 |
|
|
|
|
|
|
|
104 |
A |
3 |
3 |
1. |
20 |
0.15 |
|
|
|
|
|
|
|
105 |
A |
5 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
106 |
A |
5 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
107 |
A |
5 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
108 |
A |
8 |
7 |
1. |
24 |
0.292 |
|
|
|
|
|
|
|
109 |
A |
8 |
8 |
1. |
24 |
0.333 |
|
|
|
|
|
|
|
110 |
A |
6 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
111 |
A |
6 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
112 |
A |
6 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
113 |
A |
4 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
114 |
A |
2 |
2 |
1. |
24 |
0.083 |
|
|
|
|
|
|
|
115 |
A |
2 |
2 |
1. |
24 |
0.083 |
|
|
|
|
|
|
|
116 |
A |
6 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
117 |
A |
5 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
118 |
A |
3 |
3 |
1. |
24 |
0.125 |
|
|
|
|
|
|
|
119 |
A |
6 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
120 |
A |
5 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
|
121 |
A |
1 |
1 |
1. |
34 |
0.029 |
|
|
|
|
|
|
|
122 |
A |
7 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
123 |
A |
2 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
124 |
A |
3 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
125 |
A |
3 |
3 |
1. |
17 |
0.176 |
|
|
|
|
|
|
|
126 |
A |
5 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
127 |
A |
6 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
128 |
A |
6 |
6 |
1. |
17 |
0.353 |
|
|
|
|
|
|
|
129 |
A |
2 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
130 |
A |
3 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
131 |
A |
3 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
132 |
A |
3 |
3 |
1. |
24 |
0.125 |
|
|
|
|
|
|
|
133 |
A |
3 |
3 |
1. |
20 |
0.15 |
|
|
|
|
|
|
|
134 |
A |
3 |
3 |
1. |
20 |
0.15 |
|
|
|
|
|
|
|
135 |
A |
3 |
3 |
1. |
24 |
0.125 |
|
|
|
|
|
|
|
136 |
A |
3 |
3 |
1. |
26 |
0.115 |
|
|
|
|
|
|
|
137 |
A |
3 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
138 |
A |
3 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
139 |
A |
3 |
3 |
1. |
20 |
0.15 |
|
|
|
|
|
|
|
140 |
A |
2 |
2 |
1. |
36 |
0.056 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|