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, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155,
156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174
}
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, 66, 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, 100, 101, 102, 103, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 122, 123, 124, 125,
126, 127, 128, 131, 132, 133, 134, 135, 136, 137, 138, 141, 142, 143, 144, 145, 146, 147, 148,
151, 152, 153, 154, 155, 156, 157, 158, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174
}
B grade: { 96, 97, 104 }
C grade: { 63, 64, 65, 67, 68, 98, 105, 106, 111, 119, 120, 121, 129, 130, 139, 140, 149, 150, 159, 160
}
F grade: { 99, 107, 161, 162, 163}
2.1.3 Maple
A grade: { 1, 2, 3, 4, 6, 7, 8, 9, 11, 13, 14, 18, 19, 22, 26, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44,
45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 58, 59, 60, 64, 65, 66, 69, 72, 73, 74, 75, 76, 77, 78, 79,
80, 83, 84, 85, 86, 87, 88, 89, 90, 114, 115, 116, 117, 118, 123, 124, 125, 126, 127, 128, 134,
135, 136, 137, 144, 145, 146, 147, 154, 155, 156, 157, 164, 165, 166, 167, 168, 169, 173, 174
}
B grade: { 5, 10, 12, 15, 16, 17, 20, 21, 23, 24, 25, 28, 29, 30, 31, 32, 56, 57, 61, 62, 63, 67, 68, 70, 71, 81,
82, 98, 105, 106 }
C grade: { 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 107, 108, 109, 110 }
F grade: { 27, 53, 111, 112, 113, 119, 120, 121, 122, 129, 130, 131, 132, 133, 138, 139, 140, 141, 142, 143,
148, 149, 150, 151, 152, 153, 158, 159, 160, 161, 162, 163, 170, 171, 172 }
2.1.4 Maxima
A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 20, 22, 29, 33, 34, 35, 39, 40, 41, 45, 46, 47, 54, 55,
56, 57, 58, 59, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 164, 165, 166, 167, 168,
169, 173, 174
B grade: { 31 }
C grade: { }
F grade: { 8, 16, 18, 19, 21, 23, 24, 25, 26, 27, 28, 30, 32, 36, 37, 38, 42, 43, 44, 48, 49, 50, 51, 52, 53, 60,
61, 62, 63, 64, 65, 66, 67, 68, 79, 80, 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, 141, 142, 143, 144, 145, 146, 147,
148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 170, 171, 172
}
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 29, 30, 31, 32, 33, 34, 35, 39, 40, 41, 45,
46, 47, 51, 52, 54, 55, 56, 57, 58, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 98, 111,
112, 113, 114, 115, 116, 117, 118, 121, 122, 123, 124, 125, 126, 127, 128, 131, 132, 133, 134, 135, 136, 137,
141, 142, 143, 144, 145, 146, 147, 154, 155, 156, 157, 164, 165, 166, 167, 168, 169, 173, 174
}
B grade: { 7, 17, 59, 61, 62, 105, 106, 151, 152, 153 }
C grade: { }
F grade: { 8, 16, 18, 19, 24, 25, 26, 27, 28, 36, 37, 38, 42, 43, 44, 48, 49, 50, 53, 60, 63, 64, 65, 66, 67,
68, 79, 80, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 107, 108, 109, 110,
119, 120, 129, 130, 138, 139, 140, 148, 149, 150, 158, 159, 160, 161, 162, 163, 170, 171, 172
}
2.1.6 Sympy
A grade: { 9, 33, 34, 35, 39, 40, 41, 45, 46, 47, 52, 54, 55, 114, 117, 118, 134, 137, 173 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,
29, 30, 31, 32, 36, 37, 38, 42, 43, 44, 48, 49, 50, 51, 53, 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, 115, 116, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133,
135, 136, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154,
155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 174
}
2.1.7 Giac
A grade: { 7, 33, 34, 35, 39, 40, 41, 45, 46, 47, 51, 52, 54, 55, 59, 114, 115, 116, 117, 118, 123, 124, 125,
126, 127, 128, 134, 135, 136, 137, 144, 145, 146, 147, 154, 155, 156, 157, 164, 165, 166, 167, 168, 169, 173,
174 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 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, 36, 37, 38, 42, 43, 44, 48, 49, 50, 53, 56, 57, 58, 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, 119, 120, 121, 122, 129, 130, 131, 132, 133, 138,
139, 140, 141, 142, 143, 148, 149, 150, 151, 152, 153, 158, 159, 160, 161, 162, 163, 170, 171, 172
}
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 |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 114 | 107 | 177 | 219 | 275 | 0 | 0 |
normalized size | 1 | 1. | 0.94 | 1.55 | 1.92 | 2.41 | 0. | 0. |
time (sec) |
N/A |
0.061 |
0.133 |
0.19 |
0.987 |
3.107 |
0. |
0. |
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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 |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 72 | 83 | 109 | 143 | 0 | 0 |
normalized size | 1 | 1. | 0.81 | 0.93 | 1.22 | 1.61 | 0. | 0. |
time (sec) |
N/A |
0.041 |
0.081 |
0.16 |
0.987 |
2.78 |
0. |
0. |
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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 |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 97 | 150 | 177 | 248 | 0 | 0 |
normalized size | 1 | 1. | 1.09 | 1.69 | 1.99 | 2.79 | 0. | 0. |
time (sec) |
N/A |
0.046 |
0.069 |
0.19 |
1.007 |
2.79 |
0. |
0. |
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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 |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 62 | 74 | 81 | 119 | 0 | 0 |
normalized size | 1 | 1. | 0.97 | 1.16 | 1.27 | 1.86 | 0. | 0. |
time (sec) |
N/A |
0.027 |
0.1 |
0.162 |
0.977 |
2.665 |
0. |
0. |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 85 | 123 | 132 | 219 | 0 | 0 |
normalized size | 1 | 1. | 1.33 | 1.92 | 2.06 | 3.42 | 0. | 0. |
time (sec) |
N/A |
0.035 |
0.05 |
0.162 |
1.028 |
2.67 |
0. |
0. |
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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 |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 50 | 65 | 50 | 90 | 0 | 0 |
normalized size | 1 | 1. | 1.28 | 1.67 | 1.28 | 2.31 | 0. | 0. |
time (sec) |
N/A |
0.012 |
0.021 |
0.161 |
0.995 |
2.686 |
0. |
0. |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 59 | 38 | 72 | 154 | 0 | 62 |
normalized size | 1 | 1. | 1.84 | 1.19 | 2.25 | 4.81 | 0. | 1.94 |
time (sec) |
N/A |
0.02 |
0.063 |
0.155 |
0.962 |
2.641 |
0. |
1.132 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 59 | 86 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.92 | 1.34 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.084 |
0.016 |
0.281 |
0. |
0. |
0. |
0. |
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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 |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 40 | 62 | 45 | 62 | 36 | 0 |
normalized size | 1 | 1. | 1.29 | 2. | 1.45 | 2. | 1.16 | 0. |
time (sec) |
N/A |
0.02 |
0.028 |
0.164 |
0.982 |
2.441 |
2.787 |
0. |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 66 | 118 | 112 | 93 | 0 | 0 |
normalized size | 1 | 1. | 1.29 | 2.31 | 2.2 | 1.82 | 0. | 0. |
time (sec) |
N/A |
0.033 |
0.033 |
0.163 |
1.445 |
2.852 |
0. |
0. |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 59 | 75 | 78 | 97 | 0 | 0 |
normalized size | 1 | 1. | 0.98 | 1.25 | 1.3 | 1.62 | 0. | 0. |
time (sec) |
N/A |
0.039 |
0.045 |
0.161 |
0.97 |
2.655 |
0. |
0. |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 76 | 76 | 78 | 147 | 169 | 122 | 0 | 0 |
normalized size | 1 | 1. | 1.03 | 1.93 | 2.22 | 1.61 | 0. | 0. |
time (sec) |
N/A |
0.045 |
0.059 |
0.16 |
1.497 |
2.685 |
0. |
0. |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 69 | 83 | 103 | 123 | 0 | 0 |
normalized size | 1 | 1. | 0.84 | 1.01 | 1.26 | 1.5 | 0. | 0. |
time (sec) |
N/A |
0.049 |
0.066 |
0.165 |
0.977 |
2.722 |
0. |
0. |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 88 | 174 | 223 | 150 | 0 | 0 |
normalized size | 1 | 1. | 0.87 | 1.72 | 2.21 | 1.49 | 0. | 0. |
time (sec) |
N/A |
0.059 |
0.071 |
0.16 |
1.464 |
2.489 |
0. |
0. |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 124 | 208 | 220 | 339 | 0 | 0 |
normalized size | 1 | 1. | 1.16 | 1.94 | 2.06 | 3.17 | 0. | 0. |
time (sec) |
N/A |
0.107 |
0.21 |
0.248 |
2.094 |
2.845 |
0. |
0. |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 225 | 343 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.53 | 2.33 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.123 |
1.197 |
0.392 |
0. |
0. |
0. |
0. |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 90 | 134 | 117 | 266 | 0 | 0 |
normalized size | 1 | 1. | 1.61 | 2.39 | 2.09 | 4.75 | 0. | 0. |
time (sec) |
N/A |
0.068 |
0.149 |
0.249 |
1.02 |
2.757 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 18 |
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 | 92 | 92 | 163 | 212 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.77 | 2.3 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.072 |
0.166 |
0.294 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 93 | 93 | 129 | 215 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.39 | 2.31 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.119 |
0.12 |
0.358 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 50 | 50 | 75 | 117 | 105 | 140 | 0 | 0 |
normalized size | 1 | 1. | 1.5 | 2.34 | 2.1 | 2.8 | 0. | 0. |
time (sec) |
N/A |
0.059 |
0.123 |
0.24 |
1.022 |
2.666 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 102 | 199 | 0 | 196 | 0 | 0 |
normalized size | 1 | 1. | 1.09 | 2.12 | 0. | 2.09 | 0. | 0. |
time (sec) |
N/A |
0.079 |
0.114 |
0.244 |
0. |
2.389 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
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 | 102 | 102 | 108 | 154 | 221 | 224 | 0 | 0 |
normalized size | 1 | 1. | 1.06 | 1.51 | 2.17 | 2.2 | 0. | 0. |
time (sec) |
N/A |
0.094 |
0.184 |
0.243 |
2.186 |
2.226 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 134 | 134 | 148 | 265 | 0 | 275 | 0 | 0 |
normalized size | 1 | 1. | 1.1 | 1.98 | 0. | 2.05 | 0. | 0. |
time (sec) |
N/A |
0.111 |
0.174 |
0.253 |
0. |
2.211 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 207 | 207 | 288 | 447 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.39 | 2.16 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.211 |
0.836 |
0.472 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 236 | 236 | 403 | 687 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.71 | 2.91 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.192 |
1.322 |
0.52 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 126 | 184 | 285 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.46 | 2.26 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.142 |
0.46 |
0.401 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
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 | 158 | 158 | 289 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.83 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.118 |
0.236 |
0.508 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 204 | 390 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.59 | 3.05 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.141 |
0.17 |
0.431 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 141 | 198 | 197 | 238 | 0 | 0 |
normalized size | 1 | 1. | 1.76 | 2.48 | 2.46 | 2.98 | 0. | 0. |
time (sec) |
N/A |
0.083 |
0.161 |
0.319 |
1.044 |
2.221 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 185 | 324 | 0 | 342 | 0 | 0 |
normalized size | 1 | 1. | 1.35 | 2.36 | 0. | 2.5 | 0. | 0. |
time (sec) |
N/A |
0.105 |
0.202 |
0.323 |
0. |
2.219 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 170 | 170 | 204 | 299 | 787 | 401 | 0 | 0 |
normalized size | 1 | 1. | 1.2 | 1.76 | 4.63 | 2.36 | 0. | 0. |
time (sec) |
N/A |
0.147 |
0.28 |
0.319 |
3.223 |
2.244 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 208 | 208 | 283 | 472 | 0 | 512 | 0 | 0 |
normalized size | 1 | 1. | 1.36 | 2.27 | 0. | 2.46 | 0. | 0. |
time (sec) |
N/A |
0.173 |
0.336 |
0.342 |
0. |
2.344 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.014 |
2.556 |
0.973 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.006 |
2.187 |
0.447 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.025 |
0.269 |
0.74 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
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 | 46 | 46 | 43 | 47 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.93 | 1.02 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.105 |
0.074 |
0.247 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
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 | 63 | 63 | 56 | 58 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.89 | 0.92 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.136 |
0.072 |
0.24 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
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 | 117 | 117 | 91 | 102 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.78 | 0.87 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.225 |
0.165 |
0.246 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.015 |
9.877 |
1.09 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.006 |
21.574 |
0.461 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
3.249 |
0.75 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
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 | 75 | 75 | 69 | 78 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.92 | 1.04 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.129 |
0.256 |
0.241 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
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 | 84 | 84 | 80 | 77 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.95 | 0.92 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.149 |
0.351 |
0.243 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
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 | 178 | 178 | 223 | 153 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.25 | 0.86 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.267 |
0.446 |
0.247 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.014 |
3.353 |
1.274 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.006 |
11.262 |
0.545 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.025 |
1.688 |
0.799 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
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 | 103 | 103 | 88 | 154 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.85 | 1.5 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.147 |
0.372 |
0.27 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
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 | 112 | 112 | 114 | 157 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.02 | 1.4 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.18 |
0.401 |
0.248 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
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 | 228 | 228 | 169 | 307 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.74 | 1.35 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.313 |
0.445 |
0.25 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.022 |
4.393 |
1.964 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.022 |
2.863 |
1.876 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 82 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.22 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.043 |
0.24 |
1.828 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.026 |
0.245 |
1.791 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
0.5 |
1.411 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 166 | 486 | 367 | 633 | 0 | 0 |
normalized size | 1 | 1. | 0.99 | 2.91 | 2.2 | 3.79 | 0. | 0. |
time (sec) |
N/A |
0.401 |
0.279 |
0.135 |
0.976 |
4.563 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 124 | 362 | 270 | 462 | 0 | 0 |
normalized size | 1 | 1. | 1. | 2.92 | 2.18 | 3.73 | 0. | 0. |
time (sec) |
N/A |
0.266 |
0.177 |
0.129 |
1.01 |
3.902 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
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 | 84 | 84 | 114 | 141 | 126 | 302 | 0 | 0 |
normalized size | 1 | 1. | 1.36 | 1.68 | 1.5 | 3.6 | 0. | 0. |
time (sec) |
N/A |
0.167 |
0.208 |
0.163 |
0.995 |
2.829 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
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 | 32 | 32 | 59 | 38 | 72 | 154 | 0 | 62 |
normalized size | 1 | 1. | 1.84 | 1.19 | 2.25 | 4.81 | 0. | 1.94 |
time (sec) |
N/A |
0.022 |
0.051 |
0.158 |
0.982 |
2.824 |
0. |
1.118 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 247 | 247 | 333 | 456 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.35 | 1.85 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.373 |
0.588 |
0.374 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 142 | 214 | 0 | 960 | 0 | 0 |
normalized size |
1 |
1. |
1.37 |
2.06 |
0. |
9.23 |
0. |
0. |
time (sec) |
N/A |
0.156 |
0.223 |
0.25 |
0. |
3.283 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
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 | 172 | 172 | 247 | 1005 | 0 | 2223 | 0 | 0 |
normalized size | 1 | 1. | 1.44 | 5.84 | 0. | 12.92 | 0. | 0. |
time (sec) |
N/A |
0.292 |
0.48 |
0.28 |
0. |
7.152 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 372 | 372 | 333 | 812 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.9 |
2.18 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.759 |
1.406 |
0.371 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 315 | 315 | 277 | 388 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.88 |
1.23 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.463 |
6.018 |
0.255 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 212 | 212 | 212 | 254 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1. |
1.2 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.304 |
2.658 |
0.257 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 124 | 217 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.04 |
1.82 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.219 |
0.267 |
0.247 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 298 | 298 | 326 | 886 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.09 |
2.97 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.406 |
6.175 |
0.267 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 540 | 637 | 407 | 1640 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.18 |
0.75 |
3.04 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.711 |
8.302 |
0.276 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
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 | 206 | 206 | 141 | 338 | 400 | 459 | 0 | 0 |
normalized size | 1 | 1. | 0.68 | 1.64 | 1.94 | 2.23 | 0. | 0. |
time (sec) |
N/A |
0.128 |
0.223 |
0.167 |
0.974 |
4.522 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 123 | 282 | 313 | 398 | 0 | 0 |
normalized size | 1 | 1. | 0.76 | 1.75 | 1.94 | 2.47 | 0. | 0. |
time (sec) |
N/A |
0.103 |
0.166 |
0.179 |
0.98 |
3.411 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 150 | 195 | 208 | 327 | 0 | 0 |
normalized size | 1 | 1. | 1.38 | 1.79 | 1.91 | 3. | 0. | 0. |
time (sec) |
N/A |
0.051 |
0.264 |
0.171 |
0.965 |
2.541 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
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 | 87 | 87 | 104 | 137 | 120 | 286 | 0 | 0 |
normalized size | 1 | 1. | 1.2 | 1.57 | 1.38 | 3.29 | 0. | 0. |
time (sec) |
N/A |
0.063 |
0.118 |
0.172 |
0.981 |
2.321 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
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 | 105 | 105 | 69 | 121 | 127 | 157 | 0 | 0 |
normalized size | 1 | 1. | 0.66 | 1.15 | 1.21 | 1.5 | 0. | 0. |
time (sec) |
N/A |
0.075 |
0.079 |
0.171 |
0.983 |
1.999 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
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 | 152 | 152 | 94 | 140 | 185 | 217 | 0 | 0 |
normalized size | 1 | 1. | 0.62 | 0.92 | 1.22 | 1.43 | 0. | 0. |
time (sec) |
N/A |
0.094 |
0.125 |
0.172 |
0.985 |
1.835 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
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 | 197 | 197 | 110 | 158 | 232 | 273 | 0 | 0 |
normalized size | 1 | 1. | 0.56 | 0.8 | 1.18 | 1.39 | 0. | 0. |
time (sec) |
N/A |
0.117 |
0.144 |
0.184 |
0.991 |
2.058 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
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 | 196 | 196 | 118 | 152 | 250 | 304 | 0 | 0 |
normalized size | 1 | 1. | 0.6 | 0.78 | 1.28 | 1.55 | 0. | 0. |
time (sec) |
N/A |
0.147 |
0.224 |
0.181 |
0.963 |
2.411 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
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 | 153 | 153 | 98 | 134 | 194 | 247 | 0 | 0 |
normalized size | 1 | 1. | 0.64 | 0.88 | 1.27 | 1.61 | 0. | 0. |
time (sec) |
N/A |
0.122 |
0.253 |
0.171 |
0.968 |
2.182 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
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 | 138 | 138 | 79 | 115 | 135 | 192 | 0 | 0 |
normalized size | 1 | 1. | 0.57 | 0.83 | 0.98 | 1.39 | 0. | 0. |
time (sec) |
N/A |
0.093 |
0.099 |
0.171 |
0.979 |
2.05 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 104 | 142 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.84 | 1.15 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.284 |
0.122 |
0.531 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 136 | 145 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.99 | 1.06 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.291 |
0.442 |
0.386 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 252 | 252 | 186 | 494 | 547 | 641 | 0 | 0 |
normalized size | 1 | 1. | 0.74 | 1.96 | 2.17 | 2.54 | 0. | 0. |
time (sec) |
N/A |
0.236 |
0.355 |
0.167 |
1.022 |
4.634 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 191 | 191 | 153 | 372 | 400 | 547 | 0 | 0 |
normalized size | 1 | 1. | 0.8 | 1.95 | 2.09 | 2.86 | 0. | 0. |
time (sec) |
N/A |
0.115 |
0.229 |
0.168 |
0.999 |
3.529 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
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 | 162 | 162 | 136 | 286 | 267 | 502 | 0 | 0 |
normalized size | 1 | 1. | 0.84 | 1.77 | 1.65 | 3.1 | 0. | 0. |
time (sec) |
N/A |
0.127 |
0.195 |
0.174 |
0.993 |
2.58 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
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 | 158 | 158 | 127 | 255 | 215 | 501 | 0 | 0 |
normalized size | 1 | 1. | 0.8 | 1.61 | 1.36 | 3.17 | 0. | 0. |
time (sec) |
N/A |
0.131 |
0.213 |
0.179 |
0.973 |
2.227 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
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 | 183 | 183 | 127 | 191 | 244 | 302 | 0 | 0 |
normalized size | 1 | 1. | 0.69 | 1.04 | 1.33 | 1.65 | 0. | 0. |
time (sec) |
N/A |
0.157 |
0.211 |
0.177 |
0.974 |
1.67 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
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 | 241 | 241 | 153 | 223 | 325 | 401 | 0 | 0 |
normalized size | 1 | 1. | 0.63 | 0.93 | 1.35 | 1.66 | 0. | 0. |
time (sec) |
N/A |
0.193 |
0.229 |
0.175 |
1.001 |
1.658 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
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 | 242 | 242 | 162 | 214 | 346 | 431 | 0 | 0 |
normalized size | 1 | 1. | 0.67 | 0.88 | 1.43 | 1.78 | 0. | 0. |
time (sec) |
N/A |
0.224 |
0.275 |
0.171 |
0.986 |
2.189 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
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 | 195 | 195 | 125 | 182 | 259 | 336 | 0 | 0 |
normalized size | 1 | 1. | 0.64 | 0.93 | 1.33 | 1.72 | 0. | 0. |
time (sec) |
N/A |
0.148 |
0.286 |
0.166 |
0.974 |
1.934 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 186 | 186 | 160 | 242 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.86 | 1.3 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.412 |
0.333 |
0.714 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 187 | 218 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.99 | 1.15 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.417 |
0.638 |
0.608 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 546 | 546 | 1023 | 374 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.87 |
0.68 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.294 |
1.362 |
1.723 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 487 | 487 | 891 | 453 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.83 | 0.93 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.152 |
0.376 |
0.5 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 509 | 509 | 871 | 272 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.71 |
0.53 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.869 |
0.326 |
0.961 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 459 | 459 | 402 | 2933 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.88 | 6.39 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.896 |
0.828 |
0.605 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 551 | 551 | 997 | 331 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.81 |
0.6 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.096 |
1.291 |
1.541 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
C |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 608 | 608 | 1255 | 783 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.06 |
1.29 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.306 |
3.904 |
0.695 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
C |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 570 | 570 | 1213 | 594 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.13 |
1.04 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.216 |
1.113 |
0.647 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 286 | 354 | 0 | 833 | 0 | 0 |
normalized size |
1 |
1. |
2.18 |
2.7 |
0. |
6.36 |
0. |
0. |
time (sec) |
N/A |
0.121 |
0.575 |
0.256 |
0. |
1.943 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
C |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 546 | 546 | 0 | 3095 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
5.67 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.14 |
35.01 |
0.879 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 784 | 784 | 1331 | 1887 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.7 |
2.41 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.354 |
2.257 |
9.726 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 745 | 745 | 1245 | 1756 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.67 |
2.36 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.217 |
1.532 |
1.681 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 739 | 739 | 1239 | 1748 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.68 |
2.37 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.211 |
1.97 |
1.806 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 785 | 785 | 1291 | 1817 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.64 |
2.31 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.307 |
1.952 |
8.437 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
C |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 707 | 707 | 1805 | 1626 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.55 |
2.3 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.404 |
7.807 |
0.819 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 389 | 1870 | 0 | 2093 | 0 | 0 |
normalized size |
1 |
1. |
2.48 |
11.91 |
0. |
13.33 |
0. |
0. |
time (sec) |
N/A |
0.175 |
1.311 |
0.277 |
0. |
4.356 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 193 | 193 | 386 | 1840 | 0 | 1839 | 0 | 0 |
normalized size |
1 |
1. |
2. |
9.53 |
0. |
9.53 |
0. |
0. |
time (sec) |
N/A |
0.19 |
0.877 |
0.262 |
0. |
5.009 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
C |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 685 | 685 | 0 | 5373 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
7.84 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.291 |
50.101 |
1.949 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1124 | 1124 | 1819 | 3223 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.62 |
2.87 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.583 |
6.177 |
2.084 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1124 | 1124 | 1827 | 2357 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.63 |
2.1 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
3.022 |
6.113 |
2.354 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1114 | 1114 | 1812 | 3214 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.63 |
2.89 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
3.791 |
6.055 |
2.15 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 403 | 403 | 366 | 0 | 0 | 3776 | 0 | 0 |
normalized size |
1 |
1. |
0.91 |
0. |
0. |
9.37 |
0. |
0. |
time (sec) |
N/A |
1.275 |
0.647 |
1.842 |
0. |
33.813 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 294 | 294 | 327 | 0 | 0 | 3039 | 0 | 0 |
normalized size |
1 |
1. |
1.11 |
0. |
0. |
10.34 |
0. |
0. |
time (sec) |
N/A |
0.398 |
0.737 |
1.681 |
0. |
15.325 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 195 | 195 | 266 | 0 | 0 | 2425 | 0 | 0 |
normalized size |
1 |
1. |
1.36 |
0. |
0. |
12.44 |
0. |
0. |
time (sec) |
N/A |
0.19 |
0.457 |
1.386 |
0. |
6.691 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.098 |
4.094 |
1.288 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.101 |
4.428 |
1.26 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.094 |
8.824 |
1.629 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.034 |
4.207 |
1.29 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.086 |
1.408 |
1.257 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 119 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 328 | 328 | 247 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.75 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.424 |
0.613 |
1.7 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 453 | 453 | 325 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.72 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.601 |
0.667 |
2.864 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 374 | 374 | 339 | 0 | 0 | 3771 | 0 | 0 |
normalized size |
1 |
1. |
0.91 |
0. |
0. |
10.08 |
0. |
0. |
time (sec) |
N/A |
0.508 |
0.595 |
1.519 |
0. |
31.276 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 262 | 262 | 305 | 0 | 0 | 3004 | 0 | 0 |
normalized size |
1 |
1. |
1.16 |
0. |
0. |
11.47 |
0. |
0. |
time (sec) |
N/A |
0.27 |
0.714 |
1.191 |
0. |
10.902 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.115 |
4.984 |
1.133 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.119 |
5.339 |
1.036 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.112 |
8.753 |
1.458 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.042 |
4.864 |
1.105 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.103 |
8.089 |
1.031 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 128 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.104 |
10.674 |
1.447 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 129 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 416 | 416 | 303 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.73 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.539 |
0.642 |
1.676 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 130 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 554 | 554 | 383 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.69 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.778 |
0.835 |
2.136 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 131 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 321 | 321 | 328 | 0 | 0 | 3060 | 0 | 0 |
normalized size |
1 |
1. |
1.02 |
0. |
0. |
9.53 |
0. |
0. |
time (sec) |
N/A |
1.012 |
0.718 |
2.826 |
0. |
11.84 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 225 | 225 | 272 | 0 | 0 | 2452 | 0 | 0 |
normalized size |
1 |
1. |
1.21 |
0. |
0. |
10.9 |
0. |
0. |
time (sec) |
N/A |
0.308 |
0.507 |
2.027 |
0. |
5.059 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 133 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 211 | 0 | 0 | 1925 | 0 | 0 |
normalized size |
1 |
1. |
1.6 |
0. |
0. |
14.58 |
0. |
0. |
time (sec) |
N/A |
0.146 |
0.22 |
1.591 |
0. |
2.6 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 134 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.097 |
1.422 |
1.52 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 135 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.108 |
11.006 |
1.239 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.091 |
8.703 |
1.276 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 137 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.03 |
0.795 |
1.261 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 138 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 246 | 246 | 143 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.58 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.255 |
0.194 |
1.273 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 139 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 362 | 362 | 249 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.69 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.447 |
0.635 |
1.717 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1006 | 1006 | 329 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.33 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.78 |
0.806 |
1.97 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 141 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 252 | 252 | 303 | 0 | 0 | 3171 | 0 | 0 |
normalized size |
1 |
1. |
1.2 |
0. |
0. |
12.58 |
0. |
0. |
time (sec) |
N/A |
1.006 |
0.65 |
1.828 |
0. |
4.994 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 142 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 221 | 0 | 0 | 2360 | 0 | 0 |
normalized size |
1 |
1. |
1.41 |
0. |
0. |
15.03 |
0. |
0. |
time (sec) |
N/A |
0.259 |
0.352 |
1.589 |
0. |
3.339 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 143 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 95 | 0 | 0 | 626 | 0 | 0 |
normalized size |
1 |
1. |
1.19 |
0. |
0. |
7.82 |
0. |
0. |
time (sec) |
N/A |
0.102 |
0.145 |
1.233 |
0. |
2.355 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 144 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.11 |
15.089 |
1.081 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 145 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.123 |
21.066 |
1.079 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 146 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.106 |
7.663 |
1.148 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 147 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.099 |
3.641 |
1.159 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 148 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 113 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.04 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.088 |
0.188 |
1.088 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 149 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 274 | 274 | 212 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.77 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.31 |
0.475 |
1.032 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 150 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 701 | 701 | 292 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.42 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.392 |
0.717 |
1.481 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 151 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 244 | 244 | 312 | 0 | 0 | 4483 | 0 | 0 |
normalized size |
1 |
1. |
1.28 |
0. |
0. |
18.37 |
0. |
0. |
time (sec) |
N/A |
1.063 |
0.522 |
1.862 |
0. |
5.146 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 152 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 163 | 163 | 172 | 0 | 0 | 1380 | 0 | 0 |
normalized size |
1 |
1. |
1.06 |
0. |
0. |
8.47 |
0. |
0. |
time (sec) |
N/A |
0.243 |
0.256 |
1.631 |
0. |
3.348 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 153 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 158 | 0 | 0 | 1189 | 0 | 0 |
normalized size |
1 |
1. |
1.14 |
0. |
0. |
8.62 |
0. |
0. |
time (sec) |
N/A |
0.131 |
0.205 |
1.233 |
0. |
3.091 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 154 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.12 |
25.452 |
1.078 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 155 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.138 |
31.587 |
1.08 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 156 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.116 |
9.905 |
1.224 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 157 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.106 |
9.378 |
1.169 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 158 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 276 | 276 | 186 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.67 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.276 |
0.285 |
1.157 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 159 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 296 | 296 | 248 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.84 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.235 |
0.556 |
1.08 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 160 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 631 | 631 | 323 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.51 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.396 |
0.791 |
1.022 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 161 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 589 | 570 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.97 |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.415 |
0.212 |
4.007 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 162 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 374 | 355 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.95 |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.432 |
0.141 |
3.049 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 163 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
NO |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 178 | 204 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.15 |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.187 |
0.101 |
2.319 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 164 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.071 |
1.937 |
1.646 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 165 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.071 |
1.916 |
1.95 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 166 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.105 |
0.885 |
1.532 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 167 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.094 |
0.108 |
1.655 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 168 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.096 |
1.108 |
2.517 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 169 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.105 |
1.365 |
1.757 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 170 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-1) |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 401 | 401 | 194 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.48 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.484 |
0.249 |
17.217 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 171 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-1) |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 268 | 268 | 159 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.59 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.018 |
0.316 |
4.461 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 172 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-1) |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 135 | 118 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.07 |
0.94 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.208 |
0.213 |
1.641 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 173 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.088 |
0.333 |
1.9 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 174 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.099 |
6.369 |
1.836 |
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 [160] had the largest ratio of [ 0.7826
]
|
|
|
|
|
|
|
| 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 |
7 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
2 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
3 |
A |
6 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
4 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
5 |
A |
5 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
6 |
A |
2 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
7 |
A |
5 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
8 |
A |
6 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
9 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
10 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
11 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
12 |
A |
5 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
13 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
14 |
A |
6 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
15 |
A |
5 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
16 |
A |
8 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
17 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
18 |
A |
7 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
19 |
A |
6 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
20 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
|
21 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
22 |
A |
5 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
23 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
24 |
A |
10 |
10 |
1. |
14 |
0.714 |
|
|
|
|
|
|
|
25 |
A |
11 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
26 |
A |
7 |
7 |
1. |
12 |
0.583 |
|
|
|
|
|
|
|
27 |
A |
9 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
28 |
A |
7 |
7 |
1. |
14 |
0.5 |
|
|
|
|
|
|
|
29 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
30 |
A |
6 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
31 |
A |
8 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
32 |
A |
10 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
33 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
34 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
35 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
36 |
A |
4 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
37 |
A |
6 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
38 |
A |
9 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
39 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
40 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
41 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
42 |
A |
5 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
43 |
A |
7 |
7 |
1. |
14 |
0.5 |
|
|
|
|
|
|
|
44 |
A |
11 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
45 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
46 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
47 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
48 |
A |
6 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
49 |
A |
8 |
7 |
1. |
14 |
0.5 |
|
|
|
|
|
|
|
50 |
A |
13 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
51 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
52 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
53 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
54 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
55 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
56 |
A |
11 |
9 |
1. |
16 |
0.562 |
|
|
|
|
|
|
|
57 |
A |
10 |
9 |
1. |
16 |
0.562 |
|
|
|
|
|
|
|
58 |
A |
9 |
9 |
1. |
14 |
0.643 |
|
|
|
|
|
|
|
59 |
A |
5 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
60 |
A |
4 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
|
61 |
A |
7 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
62 |
A |
8 |
8 |
1. |
16 |
0.5 |
|
|
|
|
|
|
|
63 |
A |
22 |
13 |
1. |
18 |
0.722 |
|
|
|
|
|
|
|
64 |
A |
15 |
11 |
1. |
18 |
0.611 |
|
|
|
|
|
|
|
65 |
A |
9 |
9 |
1. |
18 |
0.5 |
|
|
|
|
|
|
|
66 |
A |
6 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
67 |
A |
12 |
11 |
1. |
18 |
0.611 |
|
|
|
|
|
|
|
68 |
A |
19 |
14 |
1.18 |
18 |
0.778 |
|
|
|
|
|
|
|
69 |
A |
7 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
70 |
A |
6 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
71 |
A |
5 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
72 |
A |
4 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
73 |
A |
4 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
74 |
A |
5 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
75 |
A |
6 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
76 |
A |
5 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
77 |
A |
5 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
78 |
A |
6 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
79 |
A |
11 |
11 |
1. |
19 |
0.579 |
|
|
|
|
|
|
|
80 |
A |
13 |
13 |
1. |
19 |
0.684 |
|
|
|
|
|
|
|
|
81 |
A |
7 |
8 |
1. |
21 |
0.381 |
|
|
|
|
|
|
|
82 |
A |
6 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
83 |
A |
6 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
84 |
A |
6 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
85 |
A |
5 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
86 |
A |
6 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
87 |
A |
5 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
88 |
A |
6 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
89 |
A |
12 |
13 |
1. |
21 |
0.619 |
|
|
|
|
|
|
|
90 |
A |
14 |
15 |
1. |
21 |
0.714 |
|
|
|
|
|
|
|
91 |
A |
25 |
12 |
1. |
21 |
0.571 |
|
|
|
|
|
|
|
92 |
A |
26 |
9 |
1. |
19 |
0.474 |
|
|
|
|
|
|
|
93 |
A |
19 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
94 |
A |
19 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
95 |
A |
24 |
10 |
1. |
21 |
0.476 |
|
|
|
|
|
|
|
96 |
A |
31 |
14 |
1. |
21 |
0.667 |
|
|
|
|
|
|
|
97 |
A |
29 |
12 |
1. |
21 |
0.571 |
|
|
|
|
|
|
|
98 |
A |
7 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
99 |
A |
24 |
10 |
1. |
21 |
0.476 |
|
|
|
|
|
|
|
100 |
A |
51 |
15 |
1. |
21 |
0.714 |
|
|
|
|
|
|
|
|
101 |
A |
27 |
10 |
1. |
21 |
0.476 |
|
|
|
|
|
|
|
102 |
A |
47 |
11 |
1. |
18 |
0.611 |
|
|
|
|
|
|
|
103 |
A |
50 |
13 |
1. |
21 |
0.619 |
|
|
|
|
|
|
|
104 |
A |
33 |
13 |
1. |
21 |
0.619 |
|
|
|
|
|
|
|
105 |
A |
6 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
106 |
A |
8 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
107 |
A |
28 |
11 |
1. |
21 |
0.524 |
|
|
|
|
|
|
|
108 |
A |
35 |
11 |
1. |
21 |
0.524 |
|
|
|
|
|
|
|
109 |
A |
63 |
12 |
1. |
21 |
0.571 |
|
|
|
|
|
|
|
110 |
A |
81 |
12 |
1. |
18 |
0.667 |
|
|
|
|
|
|
|
111 |
A |
12 |
12 |
1. |
23 |
0.522 |
|
|
|
|
|
|
|
112 |
A |
11 |
12 |
1. |
23 |
0.522 |
|
|
|
|
|
|
|
113 |
A |
9 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
114 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
115 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
116 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
117 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
118 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
119 |
A |
11 |
11 |
1. |
23 |
0.478 |
|
|
|
|
|
|
|
120 |
A |
12 |
12 |
1. |
23 |
0.522 |
|
|
|
|
|
|
|
|
121 |
A |
12 |
12 |
1. |
23 |
0.522 |
|
|
|
|
|
|
|
122 |
A |
10 |
10 |
1. |
21 |
0.476 |
|
|
|
|
|
|
|
123 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
124 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
125 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
126 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
127 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
128 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
129 |
A |
12 |
12 |
1. |
23 |
0.522 |
|
|
|
|
|
|
|
130 |
A |
13 |
12 |
1. |
23 |
0.522 |
|
|
|
|
|
|
|
131 |
A |
11 |
12 |
1. |
23 |
0.522 |
|
|
|
|
|
|
|
132 |
A |
10 |
12 |
1. |
23 |
0.522 |
|
|
|
|
|
|
|
133 |
A |
8 |
8 |
1. |
21 |
0.381 |
|
|
|
|
|
|
|
134 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
135 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
136 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
137 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
138 |
A |
11 |
11 |
1. |
23 |
0.478 |
|
|
|
|
|
|
|
139 |
A |
11 |
12 |
1. |
23 |
0.522 |
|
|
|
|
|
|
|
140 |
A |
32 |
15 |
1. |
23 |
0.652 |
|
|
|
|
|
|
|
|
141 |
A |
10 |
11 |
1. |
23 |
0.478 |
|
|
|
|
|
|
|
142 |
A |
9 |
11 |
1. |
23 |
0.478 |
|
|
|
|
|
|
|
143 |
A |
4 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
144 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
145 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
146 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
147 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
148 |
A |
5 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
149 |
A |
10 |
11 |
1. |
23 |
0.478 |
|
|
|
|
|
|
|
150 |
A |
25 |
14 |
1. |
23 |
0.609 |
|
|
|
|
|
|
|
151 |
A |
10 |
11 |
1. |
23 |
0.478 |
|
|
|
|
|
|
|
152 |
A |
7 |
8 |
1. |
23 |
0.348 |
|
|
|
|
|
|
|
153 |
A |
5 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
154 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
155 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
156 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
157 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
158 |
A |
10 |
10 |
1. |
23 |
0.435 |
|
|
|
|
|
|
|
159 |
A |
10 |
11 |
1. |
20 |
0.55 |
|
|
|
|
|
|
|
160 |
A |
26 |
18 |
1. |
23 |
0.783 |
|
|
|
|
|
|
|
|
161 |
A |
6 |
7 |
0.97 |
23 |
0.304 |
|
|
|
|
|
|
|
162 |
A |
6 |
7 |
0.95 |
23 |
0.304 |
|
|
|
|
|
|
|
163 |
A |
5 |
6 |
1.15 |
21 |
0.286 |
|
|
|
|
|
|
|
164 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
165 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
166 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
167 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
168 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
169 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
170 |
A |
16 |
11 |
1. |
26 |
0.423 |
|
|
|
|
|
|
|
171 |
A |
13 |
11 |
1. |
26 |
0.423 |
|
|
|
|
|
|
|
172 |
A |
8 |
9 |
1.07 |
26 |
0.346 |
|
|
|
|
|
|
|
173 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
174 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|