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, 78, 81, 82, 83, 84, 85, 88, 91, 92, 93, 94, 95, 96, 97,
98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 117, 124, 127, 128, 129, 130, 131,
132, 133, 134, 135, 136, 137, 138, 139, 144, 151, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165,
166 }
B grade: { 75, 77, 79, 86, 87, 114, 116, 118, 120, 121, 122, 123, 141, 143, 145, 152 }
C grade: { 74, 76, 80, 113, 115, 119, 140, 142, 146 }
F grade: { 89, 90, 125, 126, 147, 148, 149, 150, 153 }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 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, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78,
79, 80, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 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, 160, 161, 162, 163, 164, 165, 166
}
B grade: { 83 }
C grade: { 9, 11, 66, 82, 102, 158, 159 }
F grade: { 81, 84, 85 }
2.1.3 Maple
A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 18, 21, 23, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46,
47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 80,
91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 116, 119,
127, 128, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 142, 145, 146, 154, 155, 156, 158, 159, 160, 161,
162, 163, 164 }
B grade: { 7, 14, 16, 20, 22, 24, 26, 28, 29, 32, 34, 87, 123, 136, 141, 143, 147, 149, 152, 153, 157, 166
}
C grade: { 19, 25, 27, 30, 31, 33, 64, 86, 100, 122, 144, 148, 150, 151, 165 }
F grade: { 56, 75, 78, 79, 81, 82, 83, 84, 85, 88, 89, 90, 93, 114, 117, 118, 120, 121, 124, 125, 126, 129
}
2.1.4 Maxima
A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 35, 36, 37, 38, 39, 40, 53, 54, 55, 57, 58, 59,
60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 80, 91, 92, 94, 95, 96, 97, 98, 99, 101,
102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 119, 127, 128, 130, 131, 132,
133, 134, 135, 137, 138, 139, 140, 142, 146, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164
}
B grade: { 157, 165 }
C grade: { }
F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 41, 42, 43, 44, 45, 46, 47, 48,
49, 50, 51, 52, 56, 64, 75, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 93, 100, 114, 116, 117, 118, 120,
121, 122, 123, 124, 125, 126, 129, 136, 141, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 166
}
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 35, 36, 37, 38, 39, 40, 53, 54, 55, 57, 58, 59, 60,
61, 62, 63, 65, 66, 67, 74, 76, 80, 91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 105, 107, 109, 111, 113, 115,
119, 127, 128, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 142, 146, 154, 155, 156, 158, 159, 160, 161,
162, 163, 164 }
B grade: { 68, 69, 70, 71, 72, 73, 104, 106, 108, 110, 112, 166 }
C grade: { }
F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 41, 42, 43, 44, 45, 46, 47, 48,
49, 50, 51, 52, 56, 64, 75, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 93, 100, 114, 116, 117, 118, 120,
121, 122, 123, 124, 125, 126, 129, 136, 141, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 157, 165
}
2.1.6 Sympy
A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47,
48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 80, 97, 98, 99,
101, 102, 104, 105, 106, 107, 108, 109, 110, 111, 112, 115, 119, 132, 133, 134, 135, 137, 138, 139, 140, 142,
146, 154, 155, 156, 161, 162, 163 }
B grade: { 158, 159, 160, 164 }
C grade: { }
F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 56, 59, 64, 75, 77, 78, 79, 81,
82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 100, 103, 113, 114, 116, 117, 118, 120, 121, 122,
123, 124, 125, 126, 127, 128, 129, 130, 131, 136, 141, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 157,
165, 166 }
2.1.7 Giac
A grade: { 6, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 47, 48, 49, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 67,
68, 69, 70, 71, 72, 73, 74, 76, 91, 92, 94, 95, 96, 97, 98, 99, 101, 103, 104, 105, 106, 107, 108, 109, 110, 111,
112, 113, 115, 127, 128, 130, 131, 132, 133, 135, 137, 138, 139, 146, 154, 155, 156, 158, 159, 160, 161, 162,
163, 164 }
B grade: { 66, 102, 134, 136 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 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, 43, 46, 50, 51, 52, 56, 64, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 93, 100,
114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 129, 140, 141, 142, 143, 144, 145, 147, 148, 149,
150, 151, 152, 153, 157, 165, 166 }
2.1.8 Mupad
A grade: { 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 57, 58, 59, 91, 92, 94,
95, 127, 128, 130, 131 }
B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 53, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
71, 72, 73, 74, 76, 80, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113,
115, 119, 132, 133, 134, 135, 136, 137, 138, 139, 140, 142, 146, 154, 155, 156, 157, 158, 159, 160, 162, 163,
164, 165 }
C grade: { }
F grade: { 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 56, 75, 77, 78, 79, 81, 82, 83, 84,
85, 86, 87, 88, 89, 90, 93, 114, 116, 117, 118, 120, 121, 122, 123, 124, 125, 126, 129, 141, 143, 144, 145,
147, 148, 149, 150, 151, 152, 153, 161, 166 }
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 |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 64 | 53 | 57 | 54 | 63 | 0 | 52 |
normalized size | 1 | 1.00 | 1.08 | 0.90 | 0.97 | 0.92 | 1.07 | 0.00 | 0.88 |
time (sec) |
N/A |
0.032 |
0.003 |
0.008 |
0.431 |
0.455 |
1.425 |
0.000 |
0.442 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 61 | 52 | 56 | 59 | 60 | 0 | 54 |
normalized size | 1 | 1.00 | 1.09 | 0.93 | 1.00 | 1.05 | 1.07 | 0.00 | 0.96 |
time (sec) |
N/A |
0.042 |
0.014 |
0.007 |
0.330 |
0.448 |
1.042 |
0.000 |
0.417 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 53 | 44 | 48 | 47 | 53 | 0 | 44 |
normalized size | 1 | 1.00 | 1.10 | 0.92 | 1.00 | 0.98 | 1.10 | 0.00 | 0.92 |
time (sec) |
N/A |
0.027 |
0.003 |
0.006 |
0.470 |
0.467 |
0.817 |
0.000 |
0.210 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 50 | 43 | 46 | 49 | 49 | 0 | 42 |
normalized size | 1 | 1.00 | 1.11 | 0.96 | 1.02 | 1.09 | 1.09 | 0.00 | 0.93 |
time (sec) |
N/A |
0.032 |
0.009 |
0.006 |
0.321 |
0.435 |
0.577 |
0.000 |
0.370 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 42 | 35 | 37 | 34 | 42 | 0 | 34 |
normalized size | 1 | 1.00 | 1.14 | 0.95 | 1.00 | 0.92 | 1.14 | 0.00 | 0.92 |
time (sec) |
N/A |
0.016 |
0.002 |
0.006 |
0.469 |
0.420 |
0.423 |
0.000 |
0.123 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 28 | 31 | 33 | 26 | 31 | 27 |
normalized size | 1 | 1.00 | 1.00 | 0.97 | 1.07 | 1.14 | 0.90 | 1.07 | 0.93 |
time (sec) |
N/A |
0.011 |
0.003 |
0.004 |
0.324 |
0.422 |
0.205 |
2.958 |
0.098 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F |
F |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 35 | 74 | 0 | 0 | 0 | 0 | 28 |
normalized size | 1 | 1.00 | 1.00 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.80 |
time (sec) |
N/A |
0.029 |
0.003 |
0.029 |
0.000 |
0.414 |
0.000 |
0.000 |
0.287 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 38 | 39 | 39 | 37 | 37 | 0 | 36 |
normalized size | 1 | 1.00 | 1.09 | 1.11 | 1.11 | 1.06 | 1.06 | 0.00 | 1.03 |
time (sec) |
N/A |
0.023 |
0.003 |
0.011 |
0.327 |
0.425 |
0.631 |
0.000 |
0.319 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 46 | 35 | 31 | 26 | 37 | 0 | 42 |
normalized size | 1 | 1.00 | 1.24 | 0.95 | 0.84 | 0.70 | 1.00 | 0.00 | 1.14 |
time (sec) |
N/A |
0.020 |
0.003 |
0.009 |
0.435 |
0.441 |
0.528 |
0.000 |
0.332 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 54 | 51 | 51 | 50 | 61 | 0 | 46 |
normalized size | 1 | 1.00 | 1.02 | 0.96 | 0.96 | 0.94 | 1.15 | 0.00 | 0.87 |
time (sec) |
N/A |
0.033 |
0.016 |
0.013 |
0.340 |
0.434 |
1.059 |
0.000 |
0.119 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 46 | 44 | 46 | 41 | 46 | 0 | 42 |
normalized size | 1 | 1.00 | 0.96 | 0.92 | 0.96 | 0.85 | 0.96 | 0.00 | 0.88 |
time (sec) |
N/A |
0.025 |
0.003 |
0.009 |
0.427 |
0.423 |
0.827 |
0.000 |
0.363 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 64 | 60 | 62 | 59 | 71 | 0 | 56 |
normalized size | 1 | 1.00 | 1.00 | 0.94 | 0.97 | 0.92 | 1.11 | 0.00 | 0.88 |
time (sec) |
N/A |
0.038 |
0.018 |
0.011 |
0.335 |
0.426 |
1.673 |
0.000 |
0.371 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 144 | 144 | 138 | 171 | 163 | 152 | 199 | 0 | 171 |
normalized size | 1 | 1.00 | 0.96 | 1.19 | 1.13 | 1.06 | 1.38 | 0.00 | 1.19 |
time (sec) |
N/A |
0.310 |
0.139 |
0.015 |
0.458 |
0.428 |
2.393 |
0.000 |
0.667 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 170 | 170 | 169 | 334 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.289 |
0.514 |
0.095 |
0.000 |
0.422 |
0.000 |
0.000 |
0.000 |
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|
|
|
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|
|
Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 112 | 112 | 111 | 135 | 136 | 121 | 155 | 0 | 134 |
normalized size | 1 | 1.00 | 0.99 | 1.21 | 1.21 | 1.08 | 1.38 | 0.00 | 1.20 |
time (sec) |
N/A |
0.209 |
0.085 |
0.014 |
0.432 |
0.432 |
1.444 |
0.000 |
0.316 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 131 | 298 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 2.16 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.194 |
0.295 |
0.016 |
0.000 |
0.437 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 76 | 76 | 75 | 97 | 104 | 83 | 107 | 0 | 88 |
normalized size | 1 | 1.00 | 0.99 | 1.28 | 1.37 | 1.09 | 1.41 | 0.00 | 1.16 |
time (sec) |
N/A |
0.106 |
0.069 |
0.022 |
0.474 |
0.430 |
0.734 |
0.000 |
0.410 |
|
|
|
|
|
|
|
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|
|
|
|
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|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 90 | 128 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.08 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.098 |
0.081 |
0.192 |
0.000 |
0.429 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 144 | 1128 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.09 | 8.55 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.250 |
0.078 |
0.513 |
0.000 |
0.436 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 102 | 323 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.24 | 3.94 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.147 |
0.149 |
0.018 |
0.000 |
0.452 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 90 | 110 | 98 | 94 | 119 | 0 | 140 |
normalized size | 1 | 1.00 | 1.14 | 1.39 | 1.24 | 1.19 | 1.51 | 0.00 | 1.77 |
time (sec) |
N/A |
0.128 |
0.066 |
0.013 |
0.442 |
0.511 |
1.015 |
0.000 |
2.310 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 153 | 399 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.09 | 2.85 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.230 |
0.389 |
0.019 |
0.000 |
0.459 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 128 | 147 | 152 | 135 | 170 | 0 | 171 |
normalized size | 1 | 1.00 | 1.10 | 1.27 | 1.31 | 1.16 | 1.47 | 0.00 | 1.47 |
time (sec) |
N/A |
0.219 |
0.093 |
0.018 |
0.419 |
0.453 |
1.778 |
0.000 |
2.257 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 255 | 255 | 291 | 528 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.14 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.948 |
0.829 |
0.023 |
0.000 |
0.427 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 271 | 271 | 396 | 3053 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.46 | 11.27 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.756 |
0.900 |
5.524 |
0.000 |
0.425 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 225 | 445 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.16 | 2.29 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.545 |
0.559 |
0.019 |
0.000 |
0.469 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 206 | 206 | 269 | 2020 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.31 | 9.81 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.434 |
0.618 |
2.526 |
0.000 |
0.416 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 152 | 352 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.16 | 2.69 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.239 |
0.303 |
0.018 |
0.000 |
0.425 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 192 | 270 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.61 | 2.27 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.209 |
0.098 |
0.227 |
0.000 |
0.428 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 206 | 206 | 212 | 2309 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 11.21 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.427 |
0.151 |
0.243 |
0.000 |
0.420 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-1) |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 214 | 2159 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.84 | 18.61 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.267 |
0.399 |
0.291 |
0.000 |
0.422 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 176 | 457 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.32 | 3.44 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.285 |
0.341 |
0.021 |
0.000 |
0.444 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-1) |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 213 | 213 | 321 | 5974 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.51 | 28.05 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.476 |
0.881 |
3.190 |
0.000 |
0.421 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 198 | 198 | 265 | 550 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.34 | 2.78 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.601 |
0.724 |
0.024 |
0.000 |
0.429 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.09 |
time (sec) |
N/A |
0.008 |
0.652 |
0.466 |
0.000 |
0.418 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.11 |
time (sec) |
N/A |
0.003 |
0.012 |
0.269 |
0.000 |
0.416 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A |
0.015 |
0.448 |
0.321 |
0.000 |
0.420 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.09 |
time (sec) |
N/A |
0.008 |
0.619 |
0.708 |
0.000 |
0.403 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.11 |
time (sec) |
N/A |
0.003 |
0.914 |
0.264 |
0.000 |
0.417 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A |
0.013 |
1.063 |
0.382 |
0.000 |
0.404 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A |
0.007 |
2.107 |
0.966 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.09 |
time (sec) |
N/A |
0.003 |
1.928 |
0.488 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.07 |
time (sec) |
N/A |
0.013 |
1.349 |
0.999 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A |
0.007 |
1.022 |
0.952 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.09 |
time (sec) |
N/A |
0.003 |
2.371 |
0.448 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.07 |
time (sec) |
N/A |
0.013 |
1.172 |
1.136 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A |
0.007 |
1.340 |
0.977 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.09 |
time (sec) |
N/A |
0.003 |
0.019 |
0.452 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.07 |
time (sec) |
N/A |
0.014 |
1.218 |
0.716 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A |
0.007 |
1.582 |
0.977 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.09 |
time (sec) |
N/A |
0.003 |
2.717 |
0.508 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.07 |
time (sec) |
N/A |
0.013 |
2.951 |
1.138 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 108 | 74 | 86 | 118 | 104 | 86 | 49 |
normalized size | 1 | 1.00 | 0.92 | 0.63 | 0.74 | 1.01 | 0.89 | 0.74 | 0.42 |
time (sec) |
N/A |
0.067 |
0.028 |
0.025 |
0.411 |
0.476 |
3.224 |
0.995 |
0.321 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.022 |
4.115 |
3.371 |
0.000 |
0.451 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.021 |
2.655 |
2.928 |
0.000 |
0.430 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 60 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.031 |
0.033 |
2.771 |
0.000 |
0.426 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.024 |
0.280 |
1.127 |
0.000 |
0.430 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A |
0.005 |
0.461 |
0.696 |
0.000 |
0.435 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.021 |
0.360 |
1.359 |
0.000 |
0.444 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
|
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Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 59 | 50 | 54 | 51 | 58 | 60 | 49 |
normalized size | 1 | 1.00 | 1.09 | 0.93 | 1.00 | 0.94 | 1.07 | 1.11 | 0.91 |
time (sec) |
N/A |
0.035 |
0.008 |
0.031 |
0.413 |
0.426 |
65.098 |
0.164 |
0.357 |
|
|
|
|
|
|
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Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 52 | 45 | 48 | 51 | 80 | 47 | 44 |
normalized size | 1 | 1.00 | 1.11 | 0.96 | 1.02 | 1.09 | 1.70 | 1.00 | 0.94 |
time (sec) |
N/A |
0.031 |
0.013 |
0.035 |
0.307 |
0.434 |
46.372 |
0.171 |
0.349 |
|
|
|
|
|
|
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|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 48 | 41 | 43 | 38 | 48 | 43 | 40 |
normalized size | 1 | 1.00 | 1.12 | 0.95 | 1.00 | 0.88 | 1.12 | 1.00 | 0.93 |
time (sec) |
N/A |
0.027 |
0.006 |
0.029 |
0.411 |
0.429 |
23.237 |
0.200 |
0.327 |
|
|
|
|
|
|
|
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Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 41 | 36 | 38 | 39 | 66 | 40 | 35 |
normalized size | 1 | 1.00 | 1.14 | 1.00 | 1.06 | 1.08 | 1.83 | 1.11 | 0.97 |
time (sec) |
N/A |
0.014 |
0.007 |
0.023 |
0.308 |
0.417 |
13.502 |
0.151 |
0.314 |
|
|
|
|
|
|
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Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 39 | 63 | 0 | 0 | 0 | 0 | 32 |
normalized size | 1 | 1.00 | 1.00 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A |
0.045 |
0.005 |
0.109 |
0.000 |
0.409 |
0.000 |
0.000 |
0.327 |
|
|
|
|
|
|
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|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 44 | 39 | 41 | 43 | 75 | 60 | 38 |
normalized size | 1 | 1.00 | 1.13 | 1.00 | 1.05 | 1.10 | 1.92 | 1.54 | 0.97 |
time (sec) |
N/A |
0.024 |
0.007 |
0.030 |
0.317 |
0.437 |
30.285 |
0.174 |
0.343 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 48 | 39 | 35 | 30 | 42 | 74 | 41 |
normalized size | 1 | 1.00 | 1.17 | 0.95 | 0.85 | 0.73 | 1.02 | 1.80 | 1.00 |
time (sec) |
N/A |
0.025 |
0.007 |
0.032 |
0.418 |
0.403 |
24.120 |
2.810 |
0.356 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 60 | 51 | 53 | 54 | 92 | 69 | 50 |
normalized size | 1 | 1.00 | 1.09 | 0.93 | 0.96 | 0.98 | 1.67 | 1.25 | 0.91 |
time (sec) |
N/A |
0.032 |
0.013 |
0.033 |
0.324 |
0.438 |
81.386 |
0.142 |
0.365 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 179 | 140 | 147 | 372 | 184 | 169 | 64 |
normalized size | 1 | 1.00 | 1.11 | 0.87 | 0.91 | 2.31 | 1.14 | 1.05 | 0.40 |
time (sec) |
N/A |
0.113 |
0.064 |
0.039 |
0.445 |
0.462 |
33.026 |
2.852 |
0.363 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 159 | 159 | 177 | 138 | 145 | 337 | 173 | 165 | 62 |
normalized size | 1 | 1.00 | 1.11 | 0.87 | 0.91 | 2.12 | 1.09 | 1.04 | 0.39 |
time (sec) |
N/A |
0.101 |
0.037 |
0.027 |
0.433 |
0.442 |
17.684 |
3.075 |
0.392 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 107 | 125 | 127 | 319 | 930 | 149 | 49 |
normalized size | 1 | 1.00 | 0.76 | 0.89 | 0.91 | 2.28 | 6.64 | 1.06 | 0.35 |
time (sec) |
N/A |
0.105 |
0.046 |
0.029 |
0.428 |
0.443 |
10.228 |
0.180 |
0.390 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 158 | 125 | 132 | 322 | 151 | 138 | 55 |
normalized size | 1 | 1.00 | 1.10 | 0.87 | 0.92 | 2.25 | 1.06 | 0.97 | 0.38 |
time (sec) |
N/A |
0.086 |
0.046 |
0.026 |
0.421 |
0.448 |
20.443 |
0.209 |
0.201 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 159 | 159 | 177 | 132 | 142 | 389 | 590 | 159 | 63 |
normalized size | 1 | 1.00 | 1.11 | 0.83 | 0.89 | 2.45 | 3.71 | 1.00 | 0.40 |
time (sec) |
N/A |
0.104 |
0.057 |
0.033 |
0.413 |
0.449 |
38.521 |
5.357 |
0.428 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 159 | 159 | 177 | 138 | 138 | 350 | 185 | 150 | 63 |
normalized size | 1 | 1.00 | 1.11 | 0.87 | 0.87 | 2.20 | 1.16 | 0.94 | 0.40 |
time (sec) |
N/A |
0.103 |
0.054 |
0.032 |
0.414 |
0.467 |
63.234 |
0.245 |
0.452 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 731 | 121 | 151 | 169 | 137 | 199 | 145 | 150 |
normalized size | 1 | 5.90 | 0.98 | 1.22 | 1.36 | 1.10 | 1.60 | 1.17 | 1.21 |
time (sec) |
N/A |
1.627 |
0.125 |
0.051 |
0.490 |
0.449 |
98.996 |
0.177 |
1.016 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
F(-2) |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 647 | 141 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 4.20 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
1.366 |
0.335 |
180.000 |
0.000 |
0.422 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 612 | 85 | 113 | 126 | 100 | 155 | 100 | 112 |
normalized size | 1 | 6.80 | 0.94 | 1.26 | 1.40 | 1.11 | 1.72 | 1.11 | 1.24 |
time (sec) |
N/A |
1.042 |
0.070 |
0.035 |
0.488 |
0.445 |
34.914 |
1.333 |
0.683 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 255 | 107 | 146 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 2.52 | 1.06 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.554 |
0.074 |
0.206 |
0.000 |
0.429 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 165 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.321 |
0.112 |
0.356 |
0.000 |
0.424 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 290 | 127 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 2.99 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.653 |
0.157 |
0.595 |
0.000 |
0.427 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 419 | 98 | 118 | 110 | 115 | 167 | 0 | 152 |
normalized size | 1 | 4.82 | 1.13 | 1.36 | 1.26 | 1.32 | 1.92 | 0.00 | 1.75 |
time (sec) |
N/A |
1.136 |
0.083 |
0.056 |
0.519 |
0.440 |
52.408 |
0.000 |
0.613 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1393 | 1393 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.602 |
5.175 |
0.357 |
0.000 |
0.438 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1191 | 1191 | 5504 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 4.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.778 |
31.540 |
0.307 |
0.000 |
0.425 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1164 | 1164 | 5535 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 4.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.622 |
30.755 |
0.326 |
0.000 |
0.439 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1360 | 1360 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.227 |
2.942 |
0.333 |
0.000 |
0.417 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1444 | 1444 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.427 |
2.891 |
0.346 |
0.000 |
0.430 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 951 | 170 | 690 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 6.38 | 1.14 | 4.63 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
4.736 |
0.172 |
1.560 |
0.000 |
0.416 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 144 | 545 | 224 | 306 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 3.78 | 1.56 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
2.545 |
0.126 |
0.243 |
0.000 |
0.421 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 229 | 229 | 245 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.529 |
0.207 |
0.403 |
0.000 |
0.417 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 0 | 239 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.831 |
0.461 |
0.559 |
0.000 |
0.431 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 0 | 196 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
1.659 |
0.349 |
1.182 |
0.000 |
0.423 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.023 |
1.962 |
0.265 |
0.000 |
0.434 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.024 |
1.284 |
0.250 |
0.000 |
0.424 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 65 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.041 |
0.066 |
0.241 |
0.000 |
0.435 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.027 |
0.335 |
0.145 |
0.000 |
0.408 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.026 |
0.357 |
0.189 |
0.000 |
0.430 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 59 | 50 | 54 | 51 | 0 | 60 | 49 |
normalized size | 1 | 1.00 | 1.09 | 0.93 | 1.00 | 0.94 | 0.00 | 1.11 | 0.91 |
time (sec) |
N/A |
0.039 |
0.009 |
0.031 |
0.417 |
0.414 |
0.000 |
0.163 |
0.454 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 52 | 45 | 48 | 51 | 133 | 47 | 44 |
normalized size | 1 | 1.00 | 1.11 | 0.96 | 1.02 | 1.09 | 2.83 | 1.00 | 0.94 |
time (sec) |
N/A |
0.036 |
0.014 |
0.033 |
0.315 |
0.417 |
177.260 |
0.807 |
0.379 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 48 | 41 | 43 | 38 | 48 | 43 | 40 |
normalized size | 1 | 1.00 | 1.12 | 0.95 | 1.00 | 0.88 | 1.12 | 1.00 | 0.93 |
time (sec) |
N/A |
0.029 |
0.006 |
0.028 |
0.413 |
0.424 |
89.853 |
0.169 |
0.405 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 41 | 36 | 38 | 39 | 117 | 40 | 35 |
normalized size | 1 | 1.00 | 1.14 | 1.00 | 1.06 | 1.08 | 3.25 | 1.11 | 0.97 |
time (sec) |
N/A |
0.021 |
0.007 |
0.026 |
0.313 |
0.416 |
47.589 |
0.709 |
0.100 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 39 | 63 | 0 | 0 | 0 | 0 | 32 |
normalized size | 1 | 1.00 | 1.00 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A |
0.050 |
0.005 |
0.103 |
0.000 |
0.426 |
0.000 |
0.000 |
0.351 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 44 | 39 | 41 | 43 | 126 | 60 | 38 |
normalized size | 1 | 1.00 | 1.13 | 1.00 | 1.05 | 1.10 | 3.23 | 1.54 | 0.97 |
time (sec) |
N/A |
0.025 |
0.007 |
0.031 |
0.318 |
0.469 |
96.086 |
2.010 |
0.377 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 48 | 39 | 35 | 30 | 42 | 74 | 41 |
normalized size | 1 | 1.00 | 1.17 | 0.95 | 0.85 | 0.73 | 1.02 | 1.80 | 1.00 |
time (sec) |
N/A |
0.027 |
0.007 |
0.037 |
0.424 |
0.410 |
88.005 |
0.170 |
0.386 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 60 | 51 | 53 | 54 | 0 | 69 | 50 |
normalized size | 1 | 1.00 | 1.09 | 0.93 | 0.96 | 0.98 | 0.00 | 1.25 | 0.91 |
time (sec) |
N/A |
0.035 |
0.014 |
0.034 |
0.326 |
0.444 |
0.000 |
0.156 |
0.401 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 174 | 174 | 179 | 165 | 148 | 399 | 311 | 167 | 114 |
normalized size | 1 | 1.00 | 1.03 | 0.95 | 0.85 | 2.29 | 1.79 | 0.96 | 0.66 |
time (sec) |
N/A |
0.325 |
0.057 |
0.156 |
0.428 |
0.459 |
58.103 |
3.785 |
1.164 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 131 | 98 | 92 | 234 | 898 | 95 | 91 |
normalized size | 1 | 1.00 | 1.30 | 0.97 | 0.91 | 2.32 | 8.89 | 0.94 | 0.90 |
time (sec) |
N/A |
0.098 |
0.045 |
0.026 |
0.421 |
0.459 |
31.243 |
0.160 |
2.295 |
|
|
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Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 170 | 148 | 137 | 505 | 301 | 137 | 107 |
normalized size | 1 | 1.00 | 1.03 | 0.90 | 0.83 | 3.06 | 1.82 | 0.83 | 0.65 |
time (sec) |
N/A |
0.294 |
0.052 |
0.108 |
0.416 |
0.480 |
73.747 |
0.179 |
0.909 |
|
|
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Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 183 | 105 | 102 | 121 | 352 | 108 | 118 |
normalized size | 1 | 1.00 | 1.59 | 0.91 | 0.89 | 1.05 | 3.06 | 0.94 | 1.03 |
time (sec) |
N/A |
0.091 |
0.052 |
0.038 |
0.413 |
0.430 |
144.506 |
4.327 |
2.567 |
|
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Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 176 | 176 | 181 | 167 | 152 | 439 | 320 | 171 | 122 |
normalized size | 1 | 1.00 | 1.03 | 0.95 | 0.86 | 2.49 | 1.82 | 0.97 | 0.69 |
time (sec) |
N/A |
0.431 |
0.086 |
0.108 |
0.423 |
0.455 |
149.056 |
2.989 |
1.002 |
|
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Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 185 | 113 | 106 | 137 | 359 | 119 | 106 |
normalized size | 1 | 1.00 | 1.58 | 0.97 | 0.91 | 1.17 | 3.07 | 1.02 | 0.91 |
time (sec) |
N/A |
0.096 |
0.029 |
0.030 |
0.424 |
0.448 |
71.605 |
3.953 |
1.936 |
|
|
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Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 170 | 154 | 137 | 408 | 303 | 157 | 113 |
normalized size | 1 | 1.00 | 1.03 | 0.93 | 0.83 | 2.47 | 1.84 | 0.95 | 0.68 |
time (sec) |
N/A |
0.393 |
0.028 |
0.108 |
0.431 |
0.467 |
39.660 |
2.110 |
0.689 |
|
|
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Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 170 | 104 | 98 | 90 | 328 | 91 | 99 |
normalized size | 1 | 1.00 | 1.63 | 1.00 | 0.94 | 0.87 | 3.15 | 0.88 | 0.95 |
time (sec) |
N/A |
0.085 |
0.040 |
0.026 |
0.421 |
0.439 |
58.274 |
3.822 |
1.828 |
|
|
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Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 174 | 174 | 179 | 159 | 147 | 595 | 320 | 161 | 120 |
normalized size | 1 | 1.00 | 1.03 | 0.91 | 0.84 | 3.42 | 1.84 | 0.93 | 0.69 |
time (sec) |
N/A |
0.413 |
0.054 |
0.105 |
0.420 |
0.516 |
109.838 |
2.985 |
0.706 |
|
|
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Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
F(-1) |
A |
B |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 731 | 121 | 151 | 169 | 129 | 0 | 145 | 150 |
normalized size | 1 | 5.90 | 0.98 | 1.22 | 1.36 | 1.04 | 0.00 | 1.17 | 1.21 |
time (sec) |
N/A |
1.655 |
0.102 |
0.047 |
0.518 |
0.471 |
0.000 |
0.189 |
1.140 |
|
|
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|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
F(-2) |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 647 | 141 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 4.20 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
1.394 |
0.314 |
180.000 |
0.000 |
0.427 |
0.000 |
0.000 |
0.000 |
|
|
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|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 612 | 85 | 113 | 126 | 91 | 209 | 100 | 112 |
normalized size | 1 | 6.80 | 0.94 | 1.26 | 1.40 | 1.01 | 2.32 | 1.11 | 1.24 |
time (sec) |
N/A |
1.052 |
0.068 |
0.043 |
0.515 |
0.445 |
122.135 |
1.601 |
0.724 |
|
|
|
|
|
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|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 255 | 107 | 148 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 2.45 | 1.03 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.644 |
0.074 |
0.234 |
0.000 |
0.419 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 154 | 167 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.316 |
0.124 |
0.400 |
0.000 |
0.416 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 290 | 125 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 2.90 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.661 |
0.168 |
0.592 |
0.000 |
0.442 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 119 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 419 | 98 | 118 | 110 | 102 | 223 | 0 | 152 |
normalized size | 1 | 4.82 | 1.13 | 1.36 | 1.26 | 1.17 | 2.56 | 0.00 | 1.75 |
time (sec) |
N/A |
1.122 |
0.083 |
0.045 |
0.540 |
0.461 |
173.366 |
0.000 |
0.691 |
|
|
|
|
|
|
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|
Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 536 | 167 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 3.48 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
1.450 |
0.412 |
0.418 |
0.000 |
0.433 |
0.000 |
0.000 |
0.000 |
|
|
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|
Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 240 | 1867 | 346 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 7.78 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
7.034 |
0.562 |
0.411 |
0.000 |
0.426 |
0.000 |
0.000 |
0.000 |
|
|
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|
Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 951 | 170 | 867 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 6.47 | 1.16 | 5.90 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
4.733 |
0.176 |
1.776 |
0.000 |
0.445 |
0.000 |
0.000 |
0.000 |
|
|
|
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|
Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 545 | 224 | 303 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 3.92 | 1.61 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
2.702 |
0.100 |
0.244 |
0.000 |
0.428 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
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|
Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 232 | 232 | 248 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.523 |
0.217 |
0.394 |
0.000 |
0.418 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 0 | 240 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.860 |
0.424 |
0.570 |
0.000 |
0.451 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 146 | 0 | 196 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
1.670 |
0.352 |
0.885 |
0.000 |
0.445 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.024 |
1.982 |
0.268 |
0.000 |
0.436 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 128 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.024 |
1.298 |
0.243 |
0.000 |
0.438 |
0.000 |
0.000 |
0.000 |
|
|
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|
Problem 129 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 65 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.042 |
0.067 |
0.227 |
0.000 |
0.435 |
0.000 |
0.000 |
0.000 |
|
|
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|
Problem 130 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.027 |
0.341 |
0.151 |
0.000 |
0.408 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 131 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.026 |
0.363 |
0.181 |
0.000 |
0.420 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 50 | 50 | 55 | 46 | 45 | 41 | 46 | 84 | 45 |
normalized size | 1 | 1.00 | 1.10 | 0.92 | 0.90 | 0.82 | 0.92 | 1.68 | 0.90 |
time (sec) |
N/A |
0.031 |
0.011 |
0.042 |
0.416 |
0.401 |
0.495 |
4.012 |
0.411 |
|
|
|
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Problem 133 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 48 | 55 | 43 | 40 | 41 | 69 | 40 |
normalized size | 1 | 1.00 | 1.12 | 1.28 | 1.00 | 0.93 | 0.95 | 1.60 | 0.93 |
time (sec) |
N/A |
0.030 |
0.008 |
0.047 |
0.435 |
0.416 |
0.368 |
1.998 |
0.352 |
|
|
|
|
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|
Problem 134 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 44 | 37 | 36 | 31 | 36 | 74 | 36 |
normalized size | 1 | 1.00 | 1.13 | 0.95 | 0.92 | 0.79 | 0.92 | 1.90 | 0.92 |
time (sec) |
N/A |
0.017 |
0.008 |
0.037 |
0.416 |
0.416 |
0.289 |
0.182 |
0.344 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 135 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 27 | 38 | 27 | 25 | 22 | 46 | 25 |
normalized size | 1 | 1.00 | 1.00 | 1.41 | 1.00 | 0.93 | 0.81 | 1.70 | 0.93 |
time (sec) |
N/A |
0.012 |
0.003 |
0.036 |
0.318 |
0.420 |
0.178 |
1.759 |
0.303 |
|
|
|
|
|
|
|
|
|
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|
|
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|
Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 39 | 94 | 0 | 0 | 0 | 74 | 32 |
normalized size | 1 | 1.00 | 1.00 | 2.41 | 0.00 | 0.00 | 0.00 | 1.90 | 0.82 |
time (sec) |
N/A |
0.045 |
0.006 |
0.052 |
0.000 |
0.433 |
0.000 |
3.960 |
0.338 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 137 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 37 | 36 | 38 | 41 | 36 | 39 | 43 |
normalized size | 1 | 1.00 | 1.09 | 1.06 | 1.12 | 1.21 | 1.06 | 1.15 | 1.26 |
time (sec) |
N/A |
0.019 |
0.012 |
0.024 |
0.322 |
0.429 |
0.646 |
0.167 |
0.344 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 138 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 48 | 41 | 42 | 37 | 44 | 67 | 50 |
normalized size | 1 | 1.00 | 1.12 | 0.95 | 0.98 | 0.86 | 1.02 | 1.56 | 1.16 |
time (sec) |
N/A |
0.024 |
0.011 |
0.033 |
0.415 |
0.440 |
0.851 |
1.796 |
0.384 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 139 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 60 | 45 | 54 | 55 | 60 | 51 | 56 |
normalized size | 1 | 1.00 | 1.09 | 0.82 | 0.98 | 1.00 | 1.09 | 0.93 | 1.02 |
time (sec) |
N/A |
0.036 |
0.010 |
0.033 |
0.314 |
0.433 |
1.095 |
0.204 |
0.369 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 862 | 111 | 157 | 134 | 125 | 144 | 0 | 140 |
normalized size | 1 | 7.07 | 0.91 | 1.29 | 1.10 | 1.02 | 1.18 | 0.00 | 1.15 |
time (sec) |
N/A |
1.791 |
0.101 |
0.056 |
0.431 |
0.434 |
0.814 |
0.000 |
0.473 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 141 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 152 | 787 | 152 | 445 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 5.18 | 1.00 | 2.93 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
1.490 |
0.355 |
0.128 |
0.000 |
0.426 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 142 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 663 | 73 | 116 | 104 | 88 | 97 | 0 | 98 |
normalized size | 1 | 8.09 | 0.89 | 1.41 | 1.27 | 1.07 | 1.18 | 0.00 | 1.20 |
time (sec) |
N/A |
1.126 |
0.058 |
0.051 |
0.425 |
0.422 |
0.445 |
0.000 |
0.404 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 143 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 478 | 105 | 357 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 5.76 | 1.27 | 4.30 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.440 |
0.115 |
0.104 |
0.000 |
1.103 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 144 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 148 | 1249 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 8.44 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.294 |
0.092 |
0.340 |
0.000 |
0.559 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 145 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
A |
F(-1) |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 259 | 107 | 147 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 2.70 | 1.11 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.528 |
0.120 |
0.207 |
0.000 |
0.435 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 146 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 836 | 99 | 110 | 120 | 109 | 117 | 140 | 143 |
normalized size | 1 | 9.95 | 1.18 | 1.31 | 1.43 | 1.30 | 1.39 | 1.67 | 1.70 |
time (sec) |
N/A |
1.294 |
0.076 |
0.046 |
0.429 |
0.468 |
1.044 |
0.232 |
2.749 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 147 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 0 | 253 | 608 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 1.18 | 2.84 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
4.629 |
0.653 |
0.127 |
0.000 |
0.434 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 148 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 229 | 0 | 330 | 6441 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 1.44 | 28.13 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.520 |
0.731 |
1.376 |
0.000 |
1.467 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 149 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 0 | 174 | 507 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 1.20 | 3.50 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
2.352 |
0.289 |
0.125 |
0.000 |
0.419 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 150 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 0 | 215 | 2363 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 1.81 | 19.86 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.739 |
0.271 |
0.352 |
0.000 |
0.408 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 151 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 230 | 230 | 219 | 2542 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 11.05 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.494 |
0.220 |
0.236 |
0.000 |
0.413 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 152 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
B |
F(-1) |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 551 | 189 | 306 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 4.05 | 1.39 | 2.25 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
2.359 |
0.189 |
0.253 |
0.000 |
0.521 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 153 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
B |
F(-1) |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 0 | 178 | 396 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 1.21 | 2.69 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
2.255 |
0.293 |
0.102 |
0.000 |
0.469 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 154 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 34 | 32 | 31 | 27 | 39 | 31 | 31 |
normalized size | 1 | 1.00 | 0.67 | 0.63 | 0.61 | 0.53 | 0.76 | 0.61 | 0.61 |
time (sec) |
N/A |
0.015 |
0.015 |
0.029 |
0.413 |
0.469 |
1.969 |
0.138 |
0.349 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 155 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 28 | 27 | 26 | 20 | 32 | 26 | 26 |
normalized size | 1 | 1.00 | 0.67 | 0.64 | 0.62 | 0.48 | 0.76 | 0.62 | 0.62 |
time (sec) |
N/A |
0.010 |
0.011 |
0.025 |
0.413 |
0.484 |
1.261 |
0.161 |
0.365 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 156 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 18 | 17 | 16 | 14 | 19 | 16 | 16 |
normalized size | 1 | 1.00 | 0.82 | 0.77 | 0.73 | 0.64 | 0.86 | 0.73 | 0.73 |
time (sec) |
N/A |
0.006 |
0.007 |
0.023 |
0.414 |
0.412 |
1.147 |
0.350 |
0.074 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 157 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
F |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 31 | 61 | 35 | 0 | 0 | 0 | 24 |
normalized size | 1 | 1.00 | 1.00 | 1.97 | 1.13 | 0.00 | 0.00 | 0.00 | 0.77 |
time (sec) |
N/A |
0.035 |
0.005 |
0.040 |
0.418 |
0.528 |
0.000 |
0.000 |
0.302 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 158 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 30 | 22 | 21 | 17 | 94 | 21 | 21 |
normalized size | 1 | 1.00 | 1.11 | 0.81 | 0.78 | 0.63 | 3.48 | 0.78 | 0.78 |
time (sec) |
N/A |
0.012 |
0.010 |
0.031 |
0.411 |
0.434 |
1.917 |
0.303 |
0.348 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 159 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 34 | 27 | 26 | 26 | 160 | 26 | 24 |
normalized size | 1 | 1.00 | 0.81 | 0.64 | 0.62 | 0.62 | 3.81 | 0.62 | 0.57 |
time (sec) |
N/A |
0.014 |
0.012 |
0.030 |
0.408 |
0.459 |
4.919 |
0.165 |
0.353 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 160 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 30 | 25 | 24 | 24 | 85 | 24 | 24 |
normalized size | 1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.67 | 2.36 | 0.67 | 0.67 |
time (sec) |
N/A |
0.015 |
0.016 |
0.025 |
0.306 |
0.481 |
4.793 |
0.175 |
0.351 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 161 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 25 | 20 | 19 | 19 | 24 | 19 | -1 |
normalized size | 1 | 1.00 | 0.86 | 0.69 | 0.66 | 0.66 | 0.83 | 0.66 | -0.03 |
time (sec) |
N/A |
0.012 |
0.011 |
0.031 |
0.308 |
0.468 |
1.239 |
0.177 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 162 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 17 | 16 | 16 | 17 | 16 | 16 |
normalized size | 1 | 1.00 | 1.00 | 0.85 | 0.80 | 0.80 | 0.85 | 0.80 | 0.80 |
time (sec) |
N/A |
0.008 |
0.008 |
0.025 |
0.307 |
0.437 |
0.325 |
0.179 |
0.346 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 163 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 22 | 19 | 18 | 26 | 20 | 18 | 22 |
normalized size | 1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.18 | 0.91 | 0.82 | 1.00 |
time (sec) |
N/A |
0.009 |
0.012 |
0.036 |
0.313 |
0.431 |
1.155 |
0.174 |
0.358 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 164 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 31 | 26 | 25 | 33 | 143 | 28 | 27 |
normalized size | 1 | 1.00 | 0.84 | 0.70 | 0.68 | 0.89 | 3.86 | 0.76 | 0.73 |
time (sec) |
N/A |
0.014 |
0.020 |
0.033 |
0.310 |
0.479 |
4.897 |
0.169 |
0.354 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 165 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
F |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 33 | 57 | 50 | 0 | 0 | 0 | 25 |
normalized size | 1 | 1.00 | 1.00 | 1.73 | 1.52 | 0.00 | 0.00 | 0.00 | 0.76 |
time (sec) |
N/A |
0.036 |
0.007 |
0.091 |
0.424 |
0.451 |
0.000 |
0.000 |
0.336 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 166 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 32 | 94 | 0 | 63 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.82 | 2.41 | 0.00 | 1.62 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.036 |
0.014 |
0.046 |
0.000 |
0.473 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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 [142] had the largest ratio of
[2.286]
|
|
|
|
|
|
|
| Table 2.1:Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
2 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
3 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
4 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
5 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
6 |
A |
3 |
2 |
1.00 |
8 |
0.250 |
|
|
|
|
|
|
|
7 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
8 |
A |
5 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
9 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
10 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
11 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
12 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
13 |
A |
16 |
7 |
1.00 |
14 |
0.500 |
|
|
|
|
|
|
|
14 |
A |
14 |
9 |
1.00 |
14 |
0.643 |
|
|
|
|
|
|
|
15 |
A |
11 |
7 |
1.00 |
14 |
0.500 |
|
|
|
|
|
|
|
16 |
A |
9 |
8 |
1.00 |
14 |
0.571 |
|
|
|
|
|
|
|
17 |
A |
6 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
18 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
19 |
A |
6 |
5 |
1.00 |
14 |
0.357 |
|
|
|
|
|
|
|
20 |
A |
4 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
21 |
A |
8 |
7 |
1.00 |
14 |
0.500 |
|
|
|
|
|
|
|
22 |
A |
8 |
7 |
1.00 |
14 |
0.500 |
|
|
|
|
|
|
|
23 |
A |
13 |
8 |
1.00 |
14 |
0.571 |
|
|
|
|
|
|
|
24 |
A |
33 |
11 |
1.00 |
14 |
0.786 |
|
|
|
|
|
|
|
25 |
A |
24 |
11 |
1.00 |
14 |
0.786 |
|
|
|
|
|
|
|
26 |
A |
18 |
10 |
1.00 |
14 |
0.714 |
|
|
|
|
|
|
|
27 |
A |
12 |
9 |
1.00 |
14 |
0.643 |
|
|
|
|
|
|
|
28 |
A |
8 |
8 |
1.00 |
12 |
0.667 |
|
|
|
|
|
|
|
29 |
A |
5 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
30 |
A |
8 |
6 |
1.00 |
14 |
0.429 |
|
|
|
|
|
|
|
31 |
A |
5 |
6 |
1.00 |
14 |
0.429 |
|
|
|
|
|
|
|
32 |
A |
7 |
6 |
1.00 |
14 |
0.429 |
|
|
|
|
|
|
|
33 |
A |
14 |
11 |
1.00 |
14 |
0.786 |
|
|
|
|
|
|
|
34 |
A |
16 |
8 |
1.00 |
14 |
0.571 |
|
|
|
|
|
|
|
35 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
36 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
37 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
38 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
39 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
40 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
41 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
42 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
43 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
44 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
45 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
46 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
47 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
48 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
49 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
50 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
51 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
52 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
53 |
A |
12 |
9 |
1.00 |
8 |
1.125 |
|
|
|
|
|
|
|
54 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
55 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
56 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
57 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
58 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
59 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
60 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
61 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
62 |
A |
4 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
63 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
64 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
65 |
A |
5 |
5 |
1.00 |
14 |
0.357 |
|
|
|
|
|
|
|
66 |
A |
4 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
67 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
68 |
A |
11 |
8 |
1.00 |
14 |
0.571 |
|
|
|
|
|
|
|
69 |
A |
11 |
8 |
1.00 |
14 |
0.571 |
|
|
|
|
|
|
|
70 |
A |
11 |
7 |
1.00 |
10 |
0.700 |
|
|
|
|
|
|
|
71 |
A |
10 |
7 |
1.00 |
14 |
0.500 |
|
|
|
|
|
|
|
72 |
A |
11 |
8 |
1.00 |
14 |
0.571 |
|
|
|
|
|
|
|
73 |
A |
11 |
8 |
1.00 |
14 |
0.571 |
|
|
|
|
|
|
|
74 |
C |
62 |
19 |
5.90 |
16 |
1.187 |
|
|
|
|
|
|
|
75 |
B |
53 |
19 |
4.20 |
16 |
1.187 |
|
|
|
|
|
|
|
76 |
C |
44 |
16 |
6.80 |
16 |
1.000 |
|
|
|
|
|
|
|
77 |
B |
28 |
12 |
2.52 |
14 |
0.857 |
|
|
|
|
|
|
|
78 |
A |
7 |
6 |
1.00 |
16 |
0.375 |
|
|
|
|
|
|
|
79 |
B |
24 |
13 |
2.99 |
16 |
0.812 |
|
|
|
|
|
|
|
80 |
C |
46 |
23 |
4.82 |
16 |
1.438 |
|
|
|
|
|
|
|
81 |
A |
86 |
27 |
1.00 |
16 |
1.687 |
|
|
|
|
|
|
|
82 |
A |
69 |
23 |
1.00 |
12 |
1.917 |
|
|
|
|
|
|
|
83 |
A |
47 |
23 |
1.00 |
16 |
1.438 |
|
|
|
|
|
|
|
84 |
A |
64 |
25 |
1.00 |
16 |
1.562 |
|
|
|
|
|
|
|
85 |
A |
77 |
25 |
1.00 |
16 |
1.562 |
|
|
|
|
|
|
|
86 |
B |
155 |
30 |
6.38 |
16 |
1.875 |
|
|
|
|
|
|
|
87 |
B |
82 |
23 |
3.78 |
14 |
1.643 |
|
|
|
|
|
|
|
88 |
A |
9 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
89 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
90 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
91 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
92 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
93 |
A |
3 |
3 |
1.00 |
16 |
0.188 |
|
|
|
|
|
|
|
94 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
95 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
96 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
97 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
98 |
A |
4 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
99 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
100 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
101 |
A |
5 |
5 |
1.00 |
14 |
0.357 |
|
|
|
|
|
|
|
102 |
A |
4 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
103 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
104 |
A |
12 |
8 |
1.00 |
14 |
0.571 |
|
|
|
|
|
|
|
105 |
A |
9 |
8 |
1.00 |
10 |
0.800 |
|
|
|
|
|
|
|
106 |
A |
11 |
7 |
1.00 |
14 |
0.500 |
|
|
|
|
|
|
|
107 |
A |
9 |
9 |
1.00 |
14 |
0.643 |
|
|
|
|
|
|
|
108 |
A |
12 |
8 |
1.00 |
14 |
0.571 |
|
|
|
|
|
|
|
109 |
A |
9 |
9 |
1.00 |
14 |
0.643 |
|
|
|
|
|
|
|
110 |
A |
11 |
7 |
1.00 |
12 |
0.583 |
|
|
|
|
|
|
|
111 |
A |
8 |
8 |
1.00 |
14 |
0.571 |
|
|
|
|
|
|
|
112 |
A |
12 |
8 |
1.00 |
14 |
0.571 |
|
|
|
|
|
|
|
113 |
C |
62 |
19 |
5.90 |
16 |
1.187 |
|
|
|
|
|
|
|
114 |
B |
53 |
19 |
4.20 |
16 |
1.187 |
|
|
|
|
|
|
|
115 |
C |
44 |
16 |
6.80 |
16 |
1.000 |
|
|
|
|
|
|
|
116 |
B |
28 |
12 |
2.45 |
16 |
0.750 |
|
|
|
|
|
|
|
117 |
A |
7 |
6 |
1.00 |
16 |
0.375 |
|
|
|
|
|
|
|
118 |
B |
24 |
13 |
2.90 |
16 |
0.812 |
|
|
|
|
|
|
|
119 |
C |
46 |
23 |
4.82 |
16 |
1.438 |
|
|
|
|
|
|
|
120 |
B |
59 |
24 |
3.48 |
16 |
1.500 |
|
|
|
|
|
|
|
121 |
B |
239 |
32 |
7.78 |
16 |
2.000 |
|
|
|
|
|
|
|
122 |
B |
155 |
30 |
6.47 |
16 |
1.875 |
|
|
|
|
|
|
|
123 |
B |
82 |
23 |
3.92 |
16 |
1.438 |
|
|
|
|
|
|
|
124 |
A |
9 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
125 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
126 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
127 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
128 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
129 |
A |
3 |
3 |
1.00 |
16 |
0.188 |
|
|
|
|
|
|
|
130 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
131 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
132 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
133 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
134 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
135 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
136 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
137 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
138 |
A |
4 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
139 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
140 |
C |
88 |
34 |
7.07 |
16 |
2.125 |
|
|
|
|
|
|
|
141 |
B |
73 |
34 |
5.18 |
16 |
2.125 |
|
|
|
|
|
|
|
142 |
C |
58 |
32 |
8.09 |
14 |
2.286 |
|
|
|
|
|
|
|
143 |
B |
31 |
14 |
5.76 |
12 |
1.167 |
|
|
|
|
|
|
|
144 |
A |
7 |
6 |
1.00 |
16 |
0.375 |
|
|
|
|
|
|
|
145 |
B |
28 |
12 |
2.70 |
16 |
0.750 |
|
|
|
|
|
|
|
146 |
C |
66 |
23 |
9.95 |
16 |
1.438 |
|
|
|
|
|
|
|
147 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
148 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
149 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
150 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
151 |
A |
9 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
152 |
B |
82 |
23 |
4.05 |
16 |
1.438 |
|
|
|
|
|
|
|
153 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
154 |
A |
6 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
155 |
A |
5 |
4 |
1.00 |
8 |
0.500 |
|
|
|
|
|
|
|
156 |
A |
4 |
4 |
1.00 |
6 |
0.667 |
|
|
|
|
|
|
|
157 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
158 |
A |
4 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
159 |
A |
5 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
160 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
161 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
162 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
163 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
164 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
165 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
166 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|