Chapter 2
detailed summary tables of results
2.1 List of integrals sorted by grade for each CAS
2.1.1 Rubi
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57,
58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82,
83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105,
106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124,
125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 36,
39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 64, 65, 66, 67,
68, 69, 70, 71, 72, 73, 74, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95,
96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115,
116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 133, 134, 135, 136, 137, 138, 139, 140, 141
}
B grade: { 35 }
C grade: { 11, 12, 31, 32, 33, 34, 37, 38, 62, 63, 75, 76, 93, 126, 127, 128, 129, 130, 131, 132, 142
}
F grade: { 143 }
2.1.3 Maple
A grade: { 1, 2, 3, 10, 22, 28, 31, 32, 33, 34, 36, 38, 39, 92, 94, 95, 96, 99, 100, 101, 126, 127, 128, 129,
130, 131, 132, 133, 134, 138, 139, 140, 141 }
B grade: { 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 29, 30, 35, 37, 52, 53,
54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79,
80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 93, 97, 98, 102, 103, 104, 105, 106, 107, 108, 109,
110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 135, 136, 137
}
C grade: { 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 }
F grade: { 142, 143 }
2.1.4 Maxima
A grade: { 1, 2, 3, 10, 92, 133, 134, 138, 139 }
B grade: { 25, 26, 27, 28, 29, 30 }
C grade: { }
F grade: { 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 31, 32, 33, 34, 35, 36, 37, 38,
39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67,
68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 93, 94, 95, 96, 97,
98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119,
120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 135, 136, 137, 140, 141, 142, 143
}
2.1.5 FriCAS
A grade: { 1, 2, 3, 10, 13, 14, 33, 36, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 92, 126, 127, 128,
129, 130, 131, 132, 133, 134, 136, 137, 138, 139, 140, 141 }
B grade: { 7, 11, 17, 18, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 37, 55, 66, 67, 81, 82, 93, 97, 98, 99,
116, 117, 135 }
C grade: { }
F grade: { 4, 5, 6, 8, 9, 12, 15, 16, 19, 20, 21, 35, 39, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 68, 69,
70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 83, 84, 85, 86, 87, 88, 89, 90, 91, 94, 95, 96, 100, 101, 102, 103,
104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 121, 122, 123, 124, 125, 142, 143
}
2.1.6 Sympy
A grade: { 33, 139 }
B grade: { 1, 2, 3, 13, 14, 17, 18, 31, 138 }
C grade: { }
F grade: { 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 34, 35, 36, 37,
38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66,
67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95,
96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118,
119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 140, 141, 142,
143 }
2.1.7 Giac
A grade: { 1, 2, 3, 4, 10, 13, 14, 15, 17, 18, 28, 29, 30, 36, 40, 41, 42, 43, 44, 45, 46, 47, 48, 92, 126, 127,
129, 131, 133, 134, 137, 138, 139, 140, 141 }
B grade: { 5, 11, 16, 31, 32, 33, 34, 37, 38, 51, 128, 130, 132, 135, 136 }
C grade: { }
F grade: { 6, 7, 8, 9, 12, 19, 20, 21, 22, 23, 24, 25, 26, 27, 35, 39, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85,
86, 87, 88, 89, 90, 91, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108,
109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 142, 143
}
2.1.8 Mupad
A grade: { }
B grade: { 1, 2, 3, 4, 5, 13, 14, 16, 17, 18, 31, 33, 36, 133, 134, 138, 139, 140, 141 }
C grade: { }
F grade: { 6, 7, 8, 9, 10, 11, 12, 15, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 34, 35, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69,
70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,
99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118,
119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 135, 136, 137, 142, 143
}
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 |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 86 | 133 | 84 | 200 | 333 | 87 | 97 |
normalized size | 1 | 1.00 | 0.91 | 1.41 | 0.89 | 2.13 | 3.54 | 0.93 | 1.03 |
time (sec) |
N/A |
0.113 |
0.072 |
0.031 |
0.968 |
0.860 |
1.854 |
0.151 |
3.436 |
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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 |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 228 | 228 | 204 | 373 | 220 | 500 | 933 | 263 | 253 |
normalized size | 1 | 1.00 | 0.89 | 1.64 | 0.96 | 2.19 | 4.09 | 1.15 | 1.11 |
time (sec) |
N/A |
0.330 |
0.204 |
0.012 |
0.979 |
0.688 |
7.873 |
0.159 |
0.249 |
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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 |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 441 | 441 | 422 | 822 | 471 | 1014 | 1962 | 623 | 552 |
normalized size | 1 | 1.00 | 0.96 | 1.86 | 1.07 | 2.30 | 4.45 | 1.41 | 1.25 |
time (sec) |
N/A |
0.621 |
0.459 |
0.008 |
0.989 |
0.710 |
23.623 |
0.164 |
3.792 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 274 | 274 | 212 | 745 | 0 | 0 | 0 | 266 | 3888 |
normalized size | 1 | 1.00 | 0.77 | 2.72 | 0.00 | 0.00 | 0.00 | 0.97 | 14.19 |
time (sec) |
N/A |
0.282 |
0.368 |
0.016 |
0.000 |
0.000 |
0.000 |
0.168 |
38.323 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 596 | 596 | 523 | 9311 | 0 | 0 | 0 | 1313 | 23006 |
normalized size | 1 | 1.00 | 0.88 | 15.62 | 0.00 | 0.00 | 0.00 | 2.20 | 38.60 |
time (sec) |
N/A |
1.772 |
1.842 |
0.055 |
0.000 |
0.000 |
0.000 |
0.205 |
7.534 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 331 | 331 | 322 | 3358 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 10.15 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.601 |
0.801 |
0.085 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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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(-2) |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 249 | 249 | 249 | 714 | 0 | 6113 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 2.87 | 0.00 | 24.55 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.204 |
0.240 |
0.024 |
0.000 |
147.137 |
0.000 |
0.000 |
0.000 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 381 | 380 | 440 | 2758 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.15 | 7.24 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.798 |
0.650 |
0.026 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 797 | 796 | 674 | 6422 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.85 | 8.06 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.870 |
4.060 |
0.031 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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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 |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 49 | 46 | 65 | 46 | 0 | 48 | -1 |
normalized size | 1 | 1.00 | 1.04 | 0.98 | 1.38 | 0.98 | 0.00 | 1.02 | -0.02 |
time (sec) |
N/A |
0.034 |
0.008 |
0.018 |
0.973 |
1.120 |
0.000 |
0.246 |
0.000 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
F |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 78 | 637 | 0 | 758 | 0 | 457 | -1 |
normalized size | 1 | 1.00 | 0.67 | 5.44 | 0.00 | 6.48 | 0.00 | 3.91 | -0.01 |
time (sec) |
N/A |
0.169 |
0.033 |
0.176 |
0.000 |
1.005 |
0.000 |
0.376 |
0.000 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 484 | 484 | 136 | 6871419 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.28 | 14197.15 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
23.581 |
0.083 |
0.515 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F(-2) |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 182 | 175 | 510 | 0 | 583 | 1260 | 191 | 273 |
normalized size | 1 | 0.99 | 0.95 | 2.77 | 0.00 | 3.17 | 6.85 | 1.04 | 1.48 |
time (sec) |
N/A |
0.346 |
0.211 |
0.008 |
0.000 |
1.387 |
16.651 |
0.169 |
3.852 |
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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(-2) |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 542 | 542 | 535 | 1672 | 0 | 1837 | 4663 | 738 | 893 |
normalized size | 1 | 1.00 | 0.99 | 3.08 | 0.00 | 3.39 | 8.60 | 1.36 | 1.65 |
time (sec) |
N/A |
1.102 |
0.604 |
0.012 |
0.000 |
1.957 |
145.638 |
0.246 |
4.854 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 406 | 398 | 267 | 1698 | 0 | 0 | 0 | 416 | -1 |
normalized size | 1 | 0.98 | 0.66 | 4.18 | 0.00 | 0.00 | 0.00 | 1.02 | -0.00 |
time (sec) |
N/A |
0.478 |
0.462 |
0.013 |
0.000 |
0.000 |
0.000 |
0.169 |
0.000 |
|
|
|
|
|
|
|
|
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|
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|
|
|
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|
|
Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1075 | 1067 | 952 | 51470 | 0 | 0 | 0 | 3226 | 118429 |
normalized size | 1 | 0.99 | 0.89 | 47.88 | 0.00 | 0.00 | 0.00 | 3.00 | 110.17 |
time (sec) |
N/A |
4.177 |
6.700 |
0.054 |
0.000 |
0.000 |
0.000 |
0.451 |
30.314 |
|
|
|
|
|
|
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 131 | 340 | 0 | 1150 | 709 | 219 | 395 |
normalized size | 1 | 1.00 | 0.94 | 2.43 | 0.00 | 8.21 | 5.06 | 1.56 | 2.82 |
time (sec) |
N/A |
0.131 |
0.143 |
0.006 |
0.000 |
1.419 |
2.437 |
0.172 |
0.422 |
|
|
|
|
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|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 131 | 340 | 0 | 1130 | 680 | 207 | 375 |
normalized size | 1 | 1.00 | 0.94 | 2.43 | 0.00 | 8.07 | 4.86 | 1.48 | 2.68 |
time (sec) |
N/A |
0.104 |
0.027 |
0.006 |
0.000 |
0.886 |
2.259 |
0.170 |
4.020 |
|
|
|
|
|
|
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|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 617 | 615 | 517 | 16209 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.84 | 26.27 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
8.998 |
2.086 |
0.051 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1092 | 1092 | 1627 | 59465 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.49 | 54.46 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
18.867 |
6.564 |
0.032 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
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|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 416 | 416 | 393 | 2269 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 5.45 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.702 |
4.175 |
0.044 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 780 | 780 | 254 | 784 | 0 | 6861 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.33 | 1.01 | 0.00 | 8.80 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
5.162 |
0.409 |
0.039 |
0.000 |
134.783 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 302 | 302 | 283 | 1771 | 0 | 8977 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 5.86 | 0.00 | 29.73 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.843 |
0.430 |
0.033 |
0.000 |
124.907 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 154 | 608 | 0 | 1515 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.52 | 6.02 | 0.00 | 15.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.127 |
0.174 |
0.021 |
0.000 |
1.199 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 139 | 140 | 324 | 361 | 322 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 2.33 | 2.60 | 2.32 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.220 |
0.301 |
0.068 |
1.074 |
0.928 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 167 | 760 | 678 | 344 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 4.58 | 4.08 | 2.07 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.221 |
0.378 |
0.027 |
1.112 |
0.899 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 193 | 193 | 185 | 1560 | 1276 | 439 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 8.08 | 6.61 | 2.27 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.266 |
0.596 |
0.020 |
1.263 |
0.990 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
A |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 148 | 186 | 363 | 245 | 0 | 93 | -1 |
normalized size | 1 | 1.00 | 0.98 | 1.23 | 2.40 | 1.62 | 0.00 | 0.62 | -0.01 |
time (sec) |
N/A |
0.229 |
0.356 |
0.051 |
1.069 |
1.228 |
0.000 |
0.477 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 174 | 174 | 172 | 466 | 668 | 365 | 0 | 112 | -1 |
normalized size | 1 | 1.00 | 0.99 | 2.68 | 3.84 | 2.10 | 0.00 | 0.64 | -0.01 |
time (sec) |
N/A |
0.255 |
0.570 |
0.019 |
1.099 |
0.974 |
0.000 |
0.499 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 197 | 197 | 190 | 878 | 1276 | 435 | 0 | 121 | -1 |
normalized size | 1 | 1.00 | 0.96 | 4.46 | 6.48 | 2.21 | 0.00 | 0.61 | -0.01 |
time (sec) |
N/A |
0.303 |
0.710 |
0.017 |
1.241 |
1.018 |
0.000 |
0.541 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
B |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 79 | 14 | 0 | 49 | 36 | 31 | 13 |
normalized size | 1 | 1.00 | 5.27 | 0.93 | 0.00 | 3.27 | 2.40 | 2.07 | 0.87 |
time (sec) |
N/A |
0.017 |
0.045 |
0.020 |
0.000 |
0.870 |
6.999 |
0.347 |
3.763 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 44 | 44 | 101 | 40 | 0 | 106 | 0 | 108 | -1 |
normalized size | 1 | 1.00 | 2.30 | 0.91 | 0.00 | 2.41 | 0.00 | 2.45 | -0.02 |
time (sec) |
N/A |
0.052 |
0.055 |
0.012 |
0.000 |
0.992 |
0.000 |
0.374 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 90 | 20 | 0 | 34 | 68 | 39 | 19 |
normalized size | 1 | 1.00 | 3.75 | 0.83 | 0.00 | 1.42 | 2.83 | 1.62 | 0.79 |
time (sec) |
N/A |
0.019 |
0.063 |
0.018 |
0.000 |
1.097 |
6.813 |
0.355 |
3.781 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 114 | 45 | 0 | 307 | 0 | 133 | -1 |
normalized size | 1 | 1.00 | 2.04 | 0.80 | 0.00 | 5.48 | 0.00 | 2.38 | -0.02 |
time (sec) |
N/A |
0.050 |
0.061 |
0.012 |
0.000 |
1.098 |
0.000 |
0.319 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 249 | 249 | 767 | 3606 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.08 | 14.48 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.910 |
1.489 |
0.053 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 46 | 48 | 0 | 85 | 0 | 81 | 49 |
normalized size | 1 | 1.00 | 0.96 | 1.00 | 0.00 | 1.77 | 0.00 | 1.69 | 1.02 |
time (sec) |
N/A |
0.050 |
0.185 |
0.005 |
0.000 |
1.973 |
0.000 |
0.266 |
3.753 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 165 | 94 | 0 | 56 | 0 | 98 | -1 |
normalized size | 1 | 1.00 | 9.71 | 5.53 | 0.00 | 3.29 | 0.00 | 5.76 | -0.06 |
time (sec) |
N/A |
0.022 |
0.288 |
0.017 |
0.000 |
1.344 |
0.000 |
0.231 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 150 | 123 | 0 | 132 | 0 | 163 | -1 |
normalized size | 1 | 1.00 | 1.74 | 1.43 | 0.00 | 1.53 | 0.00 | 1.90 | -0.01 |
time (sec) |
N/A |
0.185 |
0.109 |
0.013 |
0.000 |
1.022 |
0.000 |
0.275 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 108 | 121 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.79 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.114 |
0.091 |
0.027 |
0.000 |
119.134 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 212 | 212 | 129 | 103 | 0 | 175 | 0 | 117 | -1 |
normalized size | 1 | 1.00 | 0.61 | 0.49 | 0.00 | 0.83 | 0.00 | 0.55 | -0.00 |
time (sec) |
N/A |
0.116 |
0.151 |
0.048 |
0.000 |
0.937 |
0.000 |
0.253 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 117 | 83 | 0 | 157 | 0 | 98 | -1 |
normalized size | 1 | 1.00 | 0.73 | 0.52 | 0.00 | 0.98 | 0.00 | 0.61 | -0.01 |
time (sec) |
N/A |
0.067 |
0.116 |
0.010 |
0.000 |
1.000 |
0.000 |
0.213 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 85 | 65 | 0 | 128 | 0 | 79 | -1 |
normalized size | 1 | 1.00 | 0.57 | 0.44 | 0.00 | 0.86 | 0.00 | 0.53 | -0.01 |
time (sec) |
N/A |
0.057 |
0.063 |
0.008 |
0.000 |
0.785 |
0.000 |
0.271 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 139 | 94 | 0 | 341 | 0 | 102 | -1 |
normalized size | 1 | 1.00 | 0.87 | 0.59 | 0.00 | 2.13 | 0.00 | 0.64 | -0.01 |
time (sec) |
N/A |
0.119 |
0.143 |
0.009 |
0.000 |
0.993 |
0.000 |
0.247 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 156 | 156 | 118 | 118 | 0 | 333 | 0 | 126 | -1 |
normalized size | 1 | 1.00 | 0.76 | 0.76 | 0.00 | 2.13 | 0.00 | 0.81 | -0.01 |
time (sec) |
N/A |
0.113 |
0.281 |
0.013 |
0.000 |
1.047 |
0.000 |
0.260 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 126 | 141 | 0 | 377 | 0 | 199 | -1 |
normalized size | 1 | 1.00 | 0.78 | 0.88 | 0.00 | 2.34 | 0.00 | 1.24 | -0.01 |
time (sec) |
N/A |
0.116 |
0.116 |
0.015 |
0.000 |
0.758 |
0.000 |
0.275 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 317 | 317 | 198 | 530 | 0 | 517 | 0 | 368 | -1 |
normalized size | 1 | 1.00 | 0.62 | 1.67 | 0.00 | 1.63 | 0.00 | 1.16 | -0.00 |
time (sec) |
N/A |
0.333 |
0.275 |
0.018 |
0.000 |
1.033 |
0.000 |
0.311 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 227 | 227 | 147 | 381 | 0 | 391 | 0 | 268 | -1 |
normalized size | 1 | 1.00 | 0.65 | 1.68 | 0.00 | 1.72 | 0.00 | 1.18 | -0.00 |
time (sec) |
N/A |
0.127 |
0.131 |
0.013 |
0.000 |
0.902 |
0.000 |
0.283 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 198 | 198 | 134 | 257 | 0 | 287 | 0 | 185 | -1 |
normalized size | 1 | 1.00 | 0.68 | 1.30 | 0.00 | 1.45 | 0.00 | 0.93 | -0.01 |
time (sec) |
N/A |
0.101 |
0.127 |
0.011 |
0.000 |
0.935 |
0.000 |
0.302 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 211 | 211 | 149 | 214 | 0 | 651 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.71 | 1.01 | 0.00 | 3.09 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.221 |
0.198 |
0.011 |
0.000 |
2.544 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 202 | 202 | 155 | 249 | 0 | 647 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.77 | 1.23 | 0.00 | 3.20 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.194 |
0.189 |
0.013 |
0.000 |
1.402 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 215 | 215 | 161 | 358 | 0 | 693 | 0 | 450 | -1 |
normalized size | 1 | 1.00 | 0.75 | 1.67 | 0.00 | 3.22 | 0.00 | 2.09 | -0.00 |
time (sec) |
N/A |
0.183 |
0.218 |
0.016 |
0.000 |
1.813 |
0.000 |
0.413 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 452 | 452 | 516 | 7739 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.14 | 17.12 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.967 |
2.500 |
0.039 |
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 |
B |
F(-2) |
F(-1) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 395 | 395 | 422 | 5581 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.07 | 14.13 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.931 |
1.524 |
0.015 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 298 | 298 | 282 | 3249 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 10.90 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.376 |
0.363 |
0.013 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 358 | 358 | 314 | 3544 | 0 | 2266 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.88 | 9.90 | 0.00 | 6.33 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.314 |
0.651 |
0.019 |
0.000 |
83.145 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 382 | 382 | 569 | 3703 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.49 | 9.69 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.417 |
3.033 |
0.025 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 507 | 507 | 642 | 3993 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.27 | 7.88 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.880 |
2.607 |
0.019 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 795 | 795 | 793 | 19148 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 24.09 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
4.264 |
3.449 |
0.030 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 553 | 553 | 755 | 14709 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.37 | 26.60 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.431 |
2.011 |
0.015 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 484 | 482 | 603 | 8954 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.25 | 18.50 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
4.240 |
1.073 |
0.014 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 496 | 496 | 746 | 9728 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.50 | 19.61 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.569 |
1.575 |
0.018 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 604 | 604 | 885 | 9912 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.47 | 16.41 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.809 |
4.159 |
0.020 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 668 | 668 | 904 | 10298 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.35 | 15.42 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.465 |
3.223 |
0.019 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 380 | 380 | 378 | 2397 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 6.31 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.170 |
1.333 |
0.029 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 344 | 344 | 334 | 1796 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 5.22 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.541 |
0.701 |
0.015 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 294 | 294 | 275 | 1172 | 0 | 5085 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 3.99 | 0.00 | 17.30 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.235 |
0.320 |
0.013 |
0.000 |
3.458 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 266 | 266 | 247 | 589 | 0 | 5073 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.93 | 2.21 | 0.00 | 19.07 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.151 |
0.291 |
0.013 |
0.000 |
3.446 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 330 | 330 | 319 | 681 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 2.06 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.825 |
0.742 |
0.017 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 367 | 367 | 356 | 736 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 2.01 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.199 |
0.838 |
0.018 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 457 | 457 | 460 | 911 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 1.99 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.863 |
1.569 |
0.018 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 499 | 499 | 577 | 6124 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.16 | 12.27 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.107 |
2.696 |
0.032 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 410 | 410 | 509 | 4752 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.24 | 11.59 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.709 |
2.073 |
0.019 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 411 | 411 | 457 | 3000 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.11 | 7.30 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.826 |
0.806 |
0.015 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 416 | 416 | 320 | 1713 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.77 | 4.12 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.617 |
2.061 |
0.015 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 526 | 526 | 497 | 1945 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 3.70 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.183 |
3.497 |
0.017 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 618 | 618 | 557 | 2046 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 3.31 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.280 |
3.604 |
0.019 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 392 | 392 | 327 | 1817 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.83 | 4.64 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.952 |
0.889 |
0.018 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 316 | 316 | 302 | 1810 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 5.73 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.489 |
0.485 |
0.017 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 282 | 282 | 272 | 1667 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 5.91 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.295 |
0.294 |
0.014 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 266 | 266 | 253 | 1669 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 6.27 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.226 |
0.166 |
0.014 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
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 | 267 | 267 | 255 | 1764 | 0 | 1253 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 6.61 | 0.00 | 4.69 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.778 |
0.295 |
0.018 |
0.000 |
26.876 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 286 | 286 | 275 | 1819 | 0 | 1094 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 6.36 | 0.00 | 3.83 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.706 |
0.431 |
0.020 |
0.000 |
38.759 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 353 | 353 | 316 | 1953 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 5.53 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.879 |
0.522 |
0.017 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 501 | 501 | 447 | 4884 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.89 | 9.75 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.412 |
1.493 |
0.032 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 417 | 417 | 395 | 4900 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 11.75 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.015 |
1.017 |
0.018 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 349 | 349 | 330 | 4567 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 13.09 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.522 |
0.805 |
0.015 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 315 | 315 | 298 | 4574 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 14.52 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.517 |
0.812 |
0.015 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 469 | 469 | 755 | 4765 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.61 | 10.16 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.274 |
0.505 |
0.018 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 463 | 463 | 765 | 4799 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.65 | 10.37 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.201 |
0.638 |
0.018 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 614 | 614 | 303 | 5056 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.49 | 8.23 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.436 |
0.970 |
0.020 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 181 | 1346 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 7.12 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.285 |
0.583 |
0.018 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 75 | 102 | 83 | 70 | 0 | 73 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.36 | 1.11 | 0.93 | 0.00 | 0.97 | -0.01 |
time (sec) |
N/A |
0.058 |
0.038 |
0.015 |
0.975 |
1.386 |
0.000 |
0.195 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 130 | 120 | 789 | 0 | 777 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.92 | 6.07 | 0.00 | 5.98 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.160 |
0.161 |
0.137 |
0.000 |
1.281 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 369 | 369 | 300 | 516 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.81 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.809 |
1.709 |
0.027 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 287 | 287 | 325 | 410 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.13 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.633 |
1.158 |
0.018 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 266 | 266 | 250 | 399 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.216 |
0.425 |
0.015 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 220 | 211 | 354 | 0 | 2753 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 1.61 | 0.00 | 12.51 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.130 |
0.173 |
0.015 |
0.000 |
2.398 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 220 | 209 | 358 | 0 | 2641 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 1.63 | 0.00 | 12.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.118 |
0.096 |
0.015 |
0.000 |
2.147 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 267 | 267 | 252 | 391 | 0 | 5995 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 1.46 | 0.00 | 22.45 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.663 |
0.443 |
0.016 |
0.000 |
149.604 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 291 | 291 | 325 | 427 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.12 | 1.47 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.657 |
1.033 |
0.017 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 376 | 376 | 314 | 519 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.84 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.734 |
2.009 |
0.022 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 466 | 466 | 562 | 1648 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.21 | 3.54 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.347 |
1.405 |
0.022 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 341 | 341 | 414 | 1480 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.21 | 4.34 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.041 |
1.197 |
0.019 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 297 | 297 | 352 | 1427 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.19 | 4.80 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.454 |
0.402 |
0.019 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 299 | 299 | 356 | 1360 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.19 | 4.55 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.400 |
0.353 |
0.016 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 310 | 310 | 360 | 1376 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.16 | 4.44 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.411 |
0.399 |
0.016 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 394 | 394 | 436 | 1518 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.11 | 3.85 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.182 |
0.866 |
0.019 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 454 | 454 | 488 | 1656 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.07 | 3.65 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.193 |
1.193 |
0.019 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 761 | 761 | 552 | 14815 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.73 | 19.47 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.135 |
2.312 |
0.019 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 549 | 549 | 496 | 10138 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 18.47 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
7.028 |
1.776 |
0.015 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 431 | 431 | 417 | 6019 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 13.97 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.650 |
0.738 |
0.015 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 523 | 521 | 454 | 6460 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.87 | 12.35 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.701 |
1.309 |
0.019 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 736 | 736 | 520 | 6765 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.71 | 9.19 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.476 |
1.683 |
0.019 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 545 | 545 | 550 | 3131 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 5.74 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.722 |
2.201 |
0.032 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 463 | 463 | 468 | 2321 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 5.01 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.436 |
0.947 |
0.017 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 402 | 402 | 407 | 1516 | 0 | 11311 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 3.77 | 0.00 | 28.14 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.963 |
0.974 |
0.014 |
0.000 |
11.374 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 374 | 374 | 376 | 761 | 0 | 11287 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 2.03 | 0.00 | 30.18 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.314 |
0.789 |
0.014 |
0.000 |
10.296 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 451 | 451 | 450 | 859 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.632 |
2.414 |
0.019 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 119 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 543 | 543 | 533 | 983 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
4.592 |
1.408 |
0.017 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 679 | 679 | 669 | 1296 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 1.91 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
11.226 |
2.110 |
0.020 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 779 | 779 | 1066 | 14651 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.37 | 18.81 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
14.170 |
2.624 |
0.035 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 609 | 609 | 1097 | 11341 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.80 | 18.62 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
5.842 |
6.585 |
0.021 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 609 | 609 | 770 | 7163 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.26 | 11.76 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
5.643 |
5.684 |
0.017 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 666 | 666 | 700 | 4099 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.05 | 6.15 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.746 |
5.042 |
0.018 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 816 | 814 | 1121 | 4594 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.37 | 5.63 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
15.916 |
6.560 |
0.036 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 210 | 159 | 0 | 178 | 0 | 188 | -1 |
normalized size | 1 | 1.00 | 1.50 | 1.14 | 0.00 | 1.27 | 0.00 | 1.34 | -0.01 |
time (sec) |
N/A |
0.501 |
0.527 |
0.019 |
0.000 |
0.986 |
0.000 |
0.203 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 192 | 144 | 0 | 175 | 0 | 185 | -1 |
normalized size | 1 | 1.00 | 1.67 | 1.25 | 0.00 | 1.52 | 0.00 | 1.61 | -0.01 |
time (sec) |
N/A |
0.420 |
0.438 |
0.015 |
0.000 |
1.504 |
0.000 |
0.247 |
0.000 |
|
|
|
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Problem 128 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 159 | 130 | 0 | 161 | 0 | 171 | -1 |
normalized size | 1 | 1.00 | 1.62 | 1.33 | 0.00 | 1.64 | 0.00 | 1.74 | -0.01 |
time (sec) |
N/A |
0.198 |
0.187 |
0.009 |
0.000 |
0.924 |
0.000 |
0.226 |
0.000 |
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Problem 129 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 69 | 174 | 92 | 0 | 50 | 0 | 68 | -1 |
normalized size | 1 | 1.01 | 2.56 | 1.35 | 0.00 | 0.74 | 0.00 | 1.00 | -0.01 |
time (sec) |
N/A |
0.062 |
0.168 |
0.011 |
0.000 |
0.876 |
0.000 |
0.185 |
0.000 |
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Problem 130 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 150 | 121 | 0 | 132 | 0 | 165 | -1 |
normalized size | 1 | 1.00 | 1.58 | 1.27 | 0.00 | 1.39 | 0.00 | 1.74 | -0.01 |
time (sec) |
N/A |
0.111 |
0.100 |
0.011 |
0.000 |
0.952 |
0.000 |
0.188 |
0.000 |
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Problem 131 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 130 | 200 | 152 | 0 | 170 | 0 | 199 | -1 |
normalized size | 1 | 1.00 | 1.54 | 1.17 | 0.00 | 1.31 | 0.00 | 1.53 | -0.01 |
time (sec) |
N/A |
0.417 |
0.437 |
0.019 |
0.000 |
0.665 |
0.000 |
0.201 |
0.000 |
|
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Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 225 | 169 | 0 | 194 | 0 | 269 | -1 |
normalized size | 1 | 1.00 | 1.49 | 1.12 | 0.00 | 1.28 | 0.00 | 1.78 | -0.01 |
time (sec) |
N/A |
0.454 |
0.405 |
0.020 |
0.000 |
0.731 |
0.000 |
0.483 |
0.000 |
|
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Problem 133 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 87 | 147 | 155 | 88 | 0 | 85 | 187 |
normalized size | 1 | 1.00 | 0.58 | 0.99 | 1.04 | 0.59 | 0.00 | 0.57 | 1.26 |
time (sec) |
N/A |
0.093 |
0.191 |
0.019 |
1.001 |
0.582 |
0.000 |
0.297 |
5.085 |
|
|
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|
Problem 134 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 72 | 96 | 104 | 73 | 0 | 70 | 136 |
normalized size | 1 | 1.00 | 0.70 | 0.93 | 1.01 | 0.71 | 0.00 | 0.68 | 1.32 |
time (sec) |
N/A |
0.042 |
0.033 |
0.006 |
0.981 |
0.587 |
0.000 |
0.204 |
4.690 |
|
|
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|
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|
Problem 135 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 37 | 163 | 0 | 53 | 0 | 63 | -1 |
normalized size | 1 | 1.00 | 1.32 | 5.82 | 0.00 | 1.89 | 0.00 | 2.25 | -0.04 |
time (sec) |
N/A |
0.048 |
0.098 |
0.016 |
0.000 |
0.700 |
0.000 |
0.272 |
0.000 |
|
|
|
|
|
|
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|
|
Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 114 | 245 | 0 | 126 | 0 | 159 | -1 |
normalized size | 1 | 1.00 | 1.36 | 2.92 | 0.00 | 1.50 | 0.00 | 1.89 | -0.01 |
time (sec) |
N/A |
0.078 |
0.238 |
0.023 |
0.000 |
0.721 |
0.000 |
0.272 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 137 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 139 | 131 | 306 | 0 | 186 | 0 | 232 | -1 |
normalized size | 1 | 1.00 | 0.94 | 2.20 | 0.00 | 1.34 | 0.00 | 1.67 | -0.01 |
time (sec) |
N/A |
0.117 |
0.367 |
0.021 |
0.000 |
0.638 |
0.000 |
0.260 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 138 |
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 | 15 | 15 | 13 | 16 | 11 | 11 | 31 | 11 | 15 |
normalized size | 1 | 1.00 | 0.87 | 1.07 | 0.73 | 0.73 | 2.07 | 0.73 | 1.00 |
time (sec) |
N/A |
0.004 |
0.007 |
0.004 |
0.434 |
0.608 |
0.311 |
0.153 |
3.723 |
|
|
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|
|
|
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|
|
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|
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|
|
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 | 16 | 16 | 13 | 14 | 9 | 11 | 10 | 11 | 13 |
normalized size | 1 | 1.00 | 0.81 | 0.88 | 0.56 | 0.69 | 0.62 | 0.69 | 0.81 |
time (sec) |
N/A |
0.006 |
0.003 |
0.003 |
0.428 |
0.561 |
4.252 |
0.150 |
3.664 |
|
|
|
|
|
|
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|
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|
|
Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 13 | 20 | 0 | 11 | 0 | 11 | 15 |
normalized size | 1 | 1.00 | 0.87 | 1.33 | 0.00 | 0.73 | 0.00 | 0.73 | 1.00 |
time (sec) |
N/A |
0.028 |
0.006 |
0.004 |
0.000 |
0.411 |
0.000 |
0.160 |
3.675 |
|
|
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|
|
|
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|
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|
|
Problem 141 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 13 | 18 | 0 | 11 | 0 | 11 | 13 |
normalized size | 1 | 1.00 | 0.87 | 1.20 | 0.00 | 0.73 | 0.00 | 0.73 | 0.87 |
time (sec) |
N/A |
0.058 |
0.004 |
0.004 |
0.000 |
0.424 |
0.000 |
0.201 |
3.607 |
|
|
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|
Problem 142 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 242 | 242 | 268 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.093 |
0.560 |
0.135 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
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|
Problem 143 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 488 | 488 | 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 |
0.360 |
0.535 |
0.449 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
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|
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 [63] had the largest ratio of
[.5556]
|
|
|
|
|
|
|
| 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 |
5 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
2 |
A |
5 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
3 |
A |
5 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
4 |
A |
8 |
8 |
1.00 |
27 |
0.296 |
|
|
|
|
|
|
|
5 |
A |
9 |
9 |
1.00 |
27 |
0.333 |
|
|
|
|
|
|
|
6 |
A |
9 |
6 |
1.00 |
30 |
0.200 |
|
|
|
|
|
|
|
7 |
A |
5 |
3 |
1.00 |
30 |
0.100 |
|
|
|
|
|
|
|
8 |
A |
6 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
9 |
A |
7 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
10 |
A |
5 |
4 |
1.00 |
23 |
0.174 |
|
|
|
|
|
|
|
11 |
A |
5 |
4 |
1.00 |
23 |
0.174 |
|
|
|
|
|
|
|
12 |
A |
5 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
13 |
A |
6 |
5 |
0.99 |
28 |
0.179 |
|
|
|
|
|
|
|
14 |
A |
6 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
15 |
A |
9 |
5 |
0.98 |
30 |
0.167 |
|
|
|
|
|
|
|
16 |
A |
10 |
6 |
0.99 |
30 |
0.200 |
|
|
|
|
|
|
|
17 |
A |
5 |
5 |
1.00 |
34 |
0.147 |
|
|
|
|
|
|
|
18 |
A |
5 |
5 |
1.00 |
34 |
0.147 |
|
|
|
|
|
|
|
19 |
A |
9 |
6 |
1.00 |
32 |
0.188 |
|
|
|
|
|
|
|
20 |
A |
10 |
7 |
1.00 |
32 |
0.219 |
|
|
|
|
|
|
|
21 |
A |
5 |
3 |
1.00 |
32 |
0.094 |
|
|
|
|
|
|
|
22 |
A |
5 |
3 |
1.00 |
29 |
0.103 |
|
|
|
|
|
|
|
23 |
A |
5 |
3 |
1.00 |
29 |
0.103 |
|
|
|
|
|
|
|
24 |
A |
6 |
6 |
1.00 |
26 |
0.231 |
|
|
|
|
|
|
|
25 |
A |
5 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
26 |
A |
7 |
6 |
1.00 |
30 |
0.200 |
|
|
|
|
|
|
|
27 |
A |
7 |
6 |
1.00 |
30 |
0.200 |
|
|
|
|
|
|
|
28 |
A |
5 |
3 |
1.00 |
30 |
0.100 |
|
|
|
|
|
|
|
29 |
A |
6 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
30 |
A |
7 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
31 |
A |
2 |
2 |
1.00 |
26 |
0.077 |
|
|
|
|
|
|
|
32 |
A |
5 |
5 |
1.00 |
26 |
0.192 |
|
|
|
|
|
|
|
33 |
A |
2 |
2 |
1.00 |
24 |
0.083 |
|
|
|
|
|
|
|
34 |
A |
5 |
5 |
1.00 |
20 |
0.250 |
|
|
|
|
|
|
|
35 |
A |
6 |
5 |
1.00 |
36 |
0.139 |
|
|
|
|
|
|
|
36 |
A |
2 |
2 |
1.00 |
36 |
0.056 |
|
|
|
|
|
|
|
37 |
A |
2 |
2 |
1.00 |
32 |
0.062 |
|
|
|
|
|
|
|
38 |
A |
13 |
9 |
1.00 |
32 |
0.281 |
|
|
|
|
|
|
|
39 |
A |
5 |
5 |
1.00 |
38 |
0.132 |
|
|
|
|
|
|
|
40 |
A |
6 |
6 |
1.00 |
35 |
0.171 |
|
|
|
|
|
|
|
41 |
A |
5 |
5 |
1.00 |
33 |
0.152 |
|
|
|
|
|
|
|
42 |
A |
5 |
5 |
1.00 |
32 |
0.156 |
|
|
|
|
|
|
|
43 |
A |
8 |
8 |
1.00 |
35 |
0.229 |
|
|
|
|
|
|
|
44 |
A |
8 |
8 |
1.00 |
35 |
0.229 |
|
|
|
|
|
|
|
45 |
A |
8 |
8 |
1.00 |
35 |
0.229 |
|
|
|
|
|
|
|
46 |
A |
6 |
6 |
1.00 |
38 |
0.158 |
|
|
|
|
|
|
|
47 |
A |
5 |
5 |
1.00 |
36 |
0.139 |
|
|
|
|
|
|
|
48 |
A |
5 |
5 |
1.00 |
35 |
0.143 |
|
|
|
|
|
|
|
49 |
A |
7 |
6 |
1.00 |
38 |
0.158 |
|
|
|
|
|
|
|
50 |
A |
7 |
6 |
1.00 |
38 |
0.158 |
|
|
|
|
|
|
|
51 |
A |
7 |
6 |
1.00 |
38 |
0.158 |
|
|
|
|
|
|
|
52 |
A |
9 |
6 |
1.00 |
27 |
0.222 |
|
|
|
|
|
|
|
53 |
A |
9 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
54 |
A |
8 |
5 |
1.00 |
24 |
0.208 |
|
|
|
|
|
|
|
55 |
A |
12 |
9 |
1.00 |
27 |
0.333 |
|
|
|
|
|
|
|
56 |
A |
18 |
12 |
1.00 |
27 |
0.444 |
|
|
|
|
|
|
|
57 |
A |
22 |
13 |
1.00 |
27 |
0.482 |
|
|
|
|
|
|
|
58 |
A |
10 |
7 |
1.00 |
27 |
0.259 |
|
|
|
|
|
|
|
59 |
A |
10 |
7 |
1.00 |
25 |
0.280 |
|
|
|
|
|
|
|
60 |
A |
9 |
6 |
1.00 |
24 |
0.250 |
|
|
|
|
|
|
|
61 |
A |
17 |
11 |
1.00 |
27 |
0.407 |
|
|
|
|
|
|
|
62 |
A |
21 |
14 |
1.00 |
27 |
0.518 |
|
|
|
|
|
|
|
63 |
A |
26 |
15 |
1.00 |
27 |
0.556 |
|
|
|
|
|
|
|
64 |
A |
10 |
6 |
1.00 |
27 |
0.222 |
|
|
|
|
|
|
|
65 |
A |
8 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
66 |
A |
5 |
3 |
1.00 |
25 |
0.120 |
|
|
|
|
|
|
|
67 |
A |
5 |
3 |
1.00 |
24 |
0.125 |
|
|
|
|
|
|
|
68 |
A |
10 |
7 |
1.00 |
27 |
0.259 |
|
|
|
|
|
|
|
69 |
A |
11 |
8 |
1.00 |
27 |
0.296 |
|
|
|
|
|
|
|
70 |
A |
15 |
9 |
1.00 |
27 |
0.333 |
|
|
|
|
|
|
|
71 |
A |
10 |
7 |
1.00 |
27 |
0.259 |
|
|
|
|
|
|
|
72 |
A |
6 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
73 |
A |
6 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
74 |
A |
6 |
4 |
1.00 |
24 |
0.167 |
|
|
|
|
|
|
|
75 |
A |
12 |
9 |
1.00 |
27 |
0.333 |
|
|
|
|
|
|
|
76 |
A |
14 |
11 |
1.00 |
27 |
0.407 |
|
|
|
|
|
|
|
77 |
A |
15 |
9 |
1.00 |
28 |
0.321 |
|
|
|
|
|
|
|
78 |
A |
9 |
6 |
1.00 |
28 |
0.214 |
|
|
|
|
|
|
|
79 |
A |
9 |
6 |
1.00 |
26 |
0.231 |
|
|
|
|
|
|
|
80 |
A |
8 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
81 |
A |
17 |
9 |
1.00 |
28 |
0.321 |
|
|
|
|
|
|
|
82 |
A |
16 |
8 |
1.00 |
28 |
0.286 |
|
|
|
|
|
|
|
83 |
A |
20 |
10 |
1.00 |
28 |
0.357 |
|
|
|
|
|
|
|
84 |
A |
17 |
10 |
1.00 |
28 |
0.357 |
|
|
|
|
|
|
|
85 |
A |
10 |
7 |
1.00 |
28 |
0.250 |
|
|
|
|
|
|
|
86 |
A |
10 |
7 |
1.00 |
26 |
0.269 |
|
|
|
|
|
|
|
87 |
A |
9 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
88 |
A |
19 |
11 |
1.00 |
28 |
0.393 |
|
|
|
|
|
|
|
89 |
A |
18 |
10 |
1.00 |
28 |
0.357 |
|
|
|
|
|
|
|
90 |
A |
26 |
13 |
1.00 |
28 |
0.464 |
|
|
|
|
|
|
|
91 |
A |
9 |
6 |
1.00 |
24 |
0.250 |
|
|
|
|
|
|
|
92 |
A |
8 |
6 |
1.00 |
22 |
0.273 |
|
|
|
|
|
|
|
93 |
A |
10 |
9 |
1.00 |
17 |
0.529 |
|
|
|
|
|
|
|
94 |
A |
13 |
7 |
1.00 |
28 |
0.250 |
|
|
|
|
|
|
|
95 |
A |
10 |
6 |
1.00 |
28 |
0.214 |
|
|
|
|
|
|
|
96 |
A |
8 |
5 |
1.00 |
28 |
0.179 |
|
|
|
|
|
|
|
97 |
A |
5 |
3 |
1.00 |
26 |
0.115 |
|
|
|
|
|
|
|
98 |
A |
5 |
3 |
1.00 |
25 |
0.120 |
|
|
|
|
|
|
|
99 |
A |
9 |
4 |
1.00 |
28 |
0.143 |
|
|
|
|
|
|
|
100 |
A |
10 |
5 |
1.00 |
28 |
0.179 |
|
|
|
|
|
|
|
101 |
A |
13 |
6 |
1.00 |
28 |
0.214 |
|
|
|
|
|
|
|
102 |
A |
13 |
9 |
1.00 |
28 |
0.321 |
|
|
|
|
|
|
|
103 |
A |
9 |
6 |
1.00 |
28 |
0.214 |
|
|
|
|
|
|
|
104 |
A |
6 |
4 |
1.00 |
28 |
0.143 |
|
|
|
|
|
|
|
105 |
A |
6 |
4 |
1.00 |
26 |
0.154 |
|
|
|
|
|
|
|
106 |
A |
6 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
107 |
A |
12 |
7 |
1.00 |
28 |
0.250 |
|
|
|
|
|
|
|
108 |
A |
12 |
7 |
1.00 |
28 |
0.250 |
|
|
|
|
|
|
|
109 |
A |
9 |
6 |
1.00 |
30 |
0.200 |
|
|
|
|
|
|
|
110 |
A |
9 |
6 |
1.00 |
28 |
0.214 |
|
|
|
|
|
|
|
111 |
A |
8 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
112 |
A |
17 |
9 |
1.00 |
30 |
0.300 |
|
|
|
|
|
|
|
113 |
A |
23 |
10 |
1.00 |
30 |
0.333 |
|
|
|
|
|
|
|
114 |
A |
12 |
6 |
1.00 |
30 |
0.200 |
|
|
|
|
|
|
|
115 |
A |
8 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
116 |
A |
5 |
3 |
1.00 |
28 |
0.107 |
|
|
|
|
|
|
|
117 |
A |
5 |
3 |
1.00 |
27 |
0.111 |
|
|
|
|
|
|
|
118 |
A |
9 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
119 |
A |
12 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
120 |
A |
16 |
7 |
1.00 |
30 |
0.233 |
|
|
|
|
|
|
|
121 |
A |
10 |
7 |
1.00 |
30 |
0.233 |
|
|
|
|
|
|
|
122 |
A |
6 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
123 |
A |
6 |
4 |
1.00 |
28 |
0.143 |
|
|
|
|
|
|
|
124 |
A |
6 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
125 |
A |
12 |
7 |
1.00 |
30 |
0.233 |
|
|
|
|
|
|
|
126 |
A |
24 |
14 |
1.00 |
30 |
0.467 |
|
|
|
|
|
|
|
127 |
A |
20 |
13 |
1.00 |
30 |
0.433 |
|
|
|
|
|
|
|
128 |
A |
16 |
12 |
1.00 |
30 |
0.400 |
|
|
|
|
|
|
|
129 |
A |
6 |
4 |
1.01 |
28 |
0.143 |
|
|
|
|
|
|
|
130 |
A |
10 |
8 |
1.00 |
27 |
0.296 |
|
|
|
|
|
|
|
131 |
A |
17 |
11 |
1.00 |
30 |
0.367 |
|
|
|
|
|
|
|
132 |
A |
20 |
12 |
1.00 |
30 |
0.400 |
|
|
|
|
|
|
|
133 |
A |
8 |
6 |
1.00 |
34 |
0.176 |
|
|
|
|
|
|
|
134 |
A |
6 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
135 |
A |
3 |
3 |
1.00 |
34 |
0.088 |
|
|
|
|
|
|
|
136 |
A |
5 |
5 |
1.00 |
34 |
0.147 |
|
|
|
|
|
|
|
137 |
A |
7 |
7 |
1.00 |
34 |
0.206 |
|
|
|
|
|
|
|
138 |
A |
1 |
1 |
1.00 |
17 |
0.059 |
|
|
|
|
|
|
|
139 |
A |
1 |
1 |
1.00 |
15 |
0.067 |
|
|
|
|
|
|
|
140 |
A |
2 |
2 |
1.00 |
23 |
0.087 |
|
|
|
|
|
|
|
141 |
A |
3 |
3 |
1.00 |
21 |
0.143 |
|
|
|
|
|
|
|
142 |
A |
2 |
2 |
1.00 |
40 |
0.050 |
|
|
|
|
|
|
|
143 |
A |
2 |
2 |
1.00 |
104 |
0.019 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|