Chapter 2
detailed summary tables of results
2.1 List of integrals sorted by grade for each CAS
2.1.1 Rubi
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87,
88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112,
113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134,
135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155,
156, 157, 158, 159, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175
}
B grade: { }
C grade: { 160 }
F grade: { }
2.1.2 Mathematica
A grade: { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 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, 56, 57, 58, 59, 60, 61,
62, 63, 64, 65, 66, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 92, 93, 94, 95,
96, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 111, 114, 116, 118, 119, 120, 121,
122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 135, 137, 138, 139, 141, 143, 145, 147,
149, 152, 153, 156, 157, 158, 160, 163, 164, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175
}
B grade: { 1, 24, 55, 67, 68, 69, 70, 73, 89, 91, 103, 110, 112, 159, 161, 162, 165 }
C grade: { 113, 115, 117, 132, 134, 136, 140, 142, 144, 146, 148, 150, 151, 154, 155 }
F grade: { }
2.1.3 Maple
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 42, 43, 44, 45, 49, 50, 66, 67, 68, 69, 70, 71, 72, 73, 74, 79, 80,
81, 82, 83, 85, 87, 96, 97, 98, 100, 102, 104, 106, 107, 109, 114, 116, 117, 118, 125, 126, 127, 128, 129, 130,
131, 132, 133, 134, 135, 136, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 165, 166, 167,
168, 169, 170, 171, 172, 173, 174, 175 }
B grade: { 17, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 46, 47, 48, 62, 63, 64, 65, 75, 76, 77, 78,
84, 86, 88, 89, 90, 91, 92, 93, 94, 95, 99, 101, 103, 105, 108, 110, 111, 112, 113, 115, 119, 120, 121, 122,
123, 124 }
C grade: { 160 }
F grade: { 13, 14, 15, 16, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61,
137, 139, 149, 153, 154, 155, 156, 157, 158, 159, 161, 162, 163, 164 }
2.1.4 Maxima
A grade: { 1, 2, 29, 30, 31, 32, 33, 34, 35, 45, 46, 47, 48, 49, 50, 62, 63, 64, 65, 66, 67, 71, 72, 73, 74, 75,
77, 78, 79, 80, 81, 82, 84, 87, 93, 95, 97, 98, 105, 106, 107, 114, 115, 116, 117, 118, 119, 123, 126, 127, 128,
129, 130, 131, 133, 145, 162, 165, 166 }
B grade: { 3, 4, 5, 6, 42, 43, 44, 68, 69, 70, 76, 83, 85, 86, 88, 89, 90, 91, 92, 94, 96, 99, 100, 101, 102, 103,
104, 108, 109, 110, 111, 112, 113, 120, 121, 122, 124, 125, 141, 153, 160, 161, 167, 168, 169
}
C grade: { 22, 23, 24, 25, 26, 27, 28 }
F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 51, 52, 53,
54, 55, 56, 57, 58, 59, 60, 61, 132, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 146, 147,
148, 149, 150, 151, 152, 154, 155, 156, 157, 158, 159, 163, 164, 170, 171, 172, 173, 174, 175
}
2.1.5 FriCAS
A grade: { 49, 50, 62, 63, 66, 84, 97, 107, 108, 117, 118, 128, 129, 130, 131, 133, 135, 137, 139, 141, 143,
147, 149, 151, 153, 155, 161, 162 }
B grade: { 1, 2, 3, 4, 5, 6, 29, 30, 31, 32, 33, 34, 35, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91,
92, 93, 94, 95, 96, 98, 99, 100, 101, 102, 103, 104, 105, 106, 109, 110, 111, 112, 113, 114, 115,
116, 119, 120, 121, 122, 123, 124, 125, 126, 127, 145, 160, 163, 164, 165, 166, 167, 168, 169
}
C grade: { 22, 23, 24, 25, 26, 27, 28 }
F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 132, 134, 136,
138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 157, 158, 159, 170, 171, 172, 173, 174, 175
}
2.1.6 Sympy
A grade: { }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87,
88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112,
113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134,
135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156,
157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175
}
2.1.7 Giac
A grade: { 2, 4, 6, 29, 30, 31, 33, 34, 35, 42, 43, 44, 45, 46, 47, 48, 49, 50, 62, 63, 64, 65, 66, 67, 69, 70,
71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 93, 94, 95, 96, 97, 98, 100, 102, 103, 105,
107, 108, 114, 116, 117, 118, 119, 123, 125, 126, 127, 128, 129, 130, 131, 161, 162, 166, 168
}
B grade: { 1, 3, 5, 32, 68, 85, 86, 87, 88, 89, 90, 91, 92, 99, 101, 104, 106, 109, 110, 111, 112, 113, 115,
120, 121, 122, 124, 160, 165, 167, 169 }
C grade: { 22, 23, 24, 25, 26, 27, 28 }
F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 51, 52, 53, 54, 55, 56,
57, 58, 59, 60, 61, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148,
149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 163, 164, 170, 171, 172, 173, 174, 175
}
2.1.8 Mupad
A grade: { }
B grade: { 1, 2, 3, 4, 5, 6, 25, 32, 42, 43, 44, 45, 49, 50, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75,
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, 133, 141, 145, 153, 160, 161, 162, 165, 166, 167, 168, 169
}
C grade: { }
F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35,
36, 37, 38, 39, 40, 41, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 76, 128, 129, 130, 131, 132, 134,
135, 136, 137, 138, 139, 140, 142, 143, 144, 146, 147, 148, 149, 150, 151, 152, 154, 155, 156, 157, 158, 159,
163, 164, 170, 171, 172, 173, 174, 175 }
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 |
B |
A |
A |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 38 | 15 | 14 | 38 | 0 | 27 | 27 |
normalized size | 1 | 1.00 | 3.17 | 1.25 | 1.17 | 3.17 | 0.00 | 2.25 | 2.25 |
time (sec) |
N/A |
0.006 |
0.016 |
0.017 |
0.309 |
0.505 |
0.000 |
0.128 |
0.111 |
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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 |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 11 | 12 | 18 | 43 | 0 | 18 | 18 |
normalized size | 1 | 1.00 | 1.00 | 1.09 | 1.64 | 3.91 | 0.00 | 1.64 | 1.64 |
time (sec) |
N/A |
0.010 |
0.011 |
0.313 |
0.361 |
0.644 |
0.000 |
0.131 |
0.073 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 57 | 27 | 84 | 387 | 0 | 84 | 86 |
normalized size | 1 | 1.00 | 1.68 | 0.79 | 2.47 | 11.38 | 0.00 | 2.47 | 2.53 |
time (sec) |
N/A |
0.022 |
0.013 |
0.322 |
0.332 |
0.585 |
0.000 |
0.120 |
1.403 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 35 | 23 | 90 | 164 | 0 | 31 | 31 |
normalized size | 1 | 1.00 | 1.35 | 0.88 | 3.46 | 6.31 | 0.00 | 1.19 | 1.19 |
time (sec) |
N/A |
0.012 |
0.013 |
0.323 |
0.463 |
0.570 |
0.000 |
0.120 |
1.455 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 95 | 41 | 133 | 1114 | 0 | 110 | 193 |
normalized size | 1 | 1.00 | 1.73 | 0.75 | 2.42 | 20.25 | 0.00 | 2.00 | 3.51 |
time (sec) |
N/A |
0.043 |
0.016 |
0.313 |
0.425 |
0.622 |
0.000 |
0.135 |
0.062 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 56 | 33 | 205 | 344 | 0 | 42 | 42 |
normalized size | 1 | 1.00 | 1.33 | 0.79 | 4.88 | 8.19 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A |
0.015 |
0.017 |
0.291 |
0.319 |
1.200 |
0.000 |
0.142 |
0.077 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 61 | 101 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.76 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.037 |
0.126 |
0.418 |
0.000 |
0.521 |
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 |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 76 | 76 | 57 | 154 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.75 | 2.03 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.030 |
0.222 |
0.375 |
0.000 |
1.105 |
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 |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 48 | 87 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.89 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.020 |
0.193 |
0.239 |
0.000 |
1.093 |
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 |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 50 | 108 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.93 | 2.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.020 |
0.037 |
0.362 |
0.000 |
1.604 |
0.000 |
0.000 |
0.000 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 63 | 100 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.79 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.032 |
0.068 |
0.407 |
0.000 |
0.941 |
0.000 |
0.000 |
0.000 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 67 | 164 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.84 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.032 |
0.130 |
0.389 |
0.000 |
0.470 |
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 |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 79 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.061 |
0.160 |
0.299 |
0.000 |
0.565 |
0.000 |
0.000 |
0.000 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 66 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.039 |
0.112 |
0.291 |
0.000 |
0.934 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 15 |
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 | 84 | 84 | 60 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.038 |
0.061 |
0.245 |
0.000 |
2.145 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 16 |
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 | 56 | 56 | 54 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.022 |
0.036 |
0.351 |
0.000 |
0.505 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
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|
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|
|
Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 52 | 227 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.93 | 4.05 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.023 |
0.046 |
0.329 |
0.000 |
1.400 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
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|
|
|
Problem 18 |
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 | 90 | 90 | 73 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.039 |
0.091 |
0.208 |
0.000 |
0.613 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
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 | 90 | 90 | 68 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.038 |
0.136 |
0.211 |
0.000 |
0.447 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
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 | 118 | 118 | 80 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.056 |
0.162 |
0.208 |
0.000 |
0.591 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
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 | 74 | 74 | 67 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.035 |
0.104 |
0.447 |
0.000 |
0.731 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
C |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 40 | 41 | 114 | 74 | 115 | 0 | 72 | -1 |
normalized size | 1 | 1.00 | 1.02 | 2.85 | 1.85 | 2.88 | 0.00 | 1.80 | -0.02 |
time (sec) |
N/A |
0.017 |
0.124 |
0.220 |
0.523 |
0.502 |
0.000 |
0.143 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
C |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 41 | 99 | 49 | 67 | 0 | 57 | -1 |
normalized size | 1 | 1.00 | 1.71 | 4.12 | 2.04 | 2.79 | 0.00 | 2.38 | -0.04 |
time (sec) |
N/A |
0.012 |
0.063 |
0.189 |
0.633 |
0.563 |
0.000 |
0.140 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
C |
C |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 3 | 3 | 20 | 67 | 19 | 15 | 0 | 27 | -1 |
normalized size | 1 | 1.00 | 6.67 | 22.33 | 6.33 | 5.00 | 0.00 | 9.00 | -0.33 |
time (sec) |
N/A |
0.008 |
0.005 |
0.205 |
0.564 |
0.977 |
0.000 |
0.139 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
C |
F |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 58 | 11 | 14 | 0 | 25 | 31 |
normalized size | 1 | 1.00 | 1.00 | 4.46 | 0.85 | 1.08 | 0.00 | 1.92 | 2.38 |
time (sec) |
N/A |
0.010 |
0.005 |
0.195 |
0.495 |
1.047 |
0.000 |
0.126 |
1.715 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
C |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 27 | 118 | 23 | 26 | 0 | 50 | -1 |
normalized size | 1 | 1.00 | 0.82 | 3.58 | 0.70 | 0.79 | 0.00 | 1.52 | -0.03 |
time (sec) |
N/A |
0.015 |
0.015 |
0.185 |
0.436 |
2.466 |
0.000 |
0.159 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
C |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 33 | 178 | 35 | 38 | 0 | 64 | -1 |
normalized size | 1 | 1.00 | 0.67 | 3.63 | 0.71 | 0.78 | 0.00 | 1.31 | -0.02 |
time (sec) |
N/A |
0.020 |
0.025 |
0.184 |
0.459 |
1.452 |
0.000 |
0.168 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
C |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 39 | 238 | 47 | 50 | 0 | 76 | -1 |
normalized size | 1 | 1.00 | 0.60 | 3.66 | 0.72 | 0.77 | 0.00 | 1.17 | -0.02 |
time (sec) |
N/A |
0.024 |
0.037 |
0.206 |
1.032 |
1.130 |
0.000 |
0.167 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 41 | 123 | 92 | 1128 | 0 | 75 | -1 |
normalized size | 1 | 1.00 | 0.63 | 1.89 | 1.42 | 17.35 | 0.00 | 1.15 | -0.02 |
time (sec) |
N/A |
0.034 |
0.100 |
0.250 |
0.539 |
0.631 |
0.000 |
0.122 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 30 | 103 | 60 | 340 | 0 | 58 | -1 |
normalized size | 1 | 1.00 | 0.65 | 2.24 | 1.30 | 7.39 | 0.00 | 1.26 | -0.02 |
time (sec) |
N/A |
0.025 |
0.068 |
0.206 |
0.474 |
0.567 |
0.000 |
0.118 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 20 | 67 | 24 | 97 | 0 | 29 | -1 |
normalized size | 1 | 1.00 | 0.77 | 2.58 | 0.92 | 3.73 | 0.00 | 1.12 | -0.04 |
time (sec) |
N/A |
0.018 |
0.005 |
0.230 |
0.454 |
1.133 |
0.000 |
0.129 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 58 | 17 | 83 | 0 | 24 | 33 |
normalized size | 1 | 1.00 | 1.00 | 4.46 | 1.31 | 6.38 | 0.00 | 1.85 | 2.54 |
time (sec) |
N/A |
0.014 |
0.006 |
0.213 |
0.446 |
2.481 |
0.000 |
0.131 |
1.603 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 27 | 130 | 35 | 285 | 0 | 54 | -1 |
normalized size | 1 | 1.00 | 0.75 | 3.61 | 0.97 | 7.92 | 0.00 | 1.50 | -0.03 |
time (sec) |
N/A |
0.022 |
0.023 |
0.194 |
0.688 |
1.308 |
0.000 |
0.146 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 36 | 196 | 53 | 590 | 0 | 67 | -1 |
normalized size | 1 | 1.00 | 0.65 | 3.56 | 0.96 | 10.73 | 0.00 | 1.22 | -0.02 |
time (sec) |
N/A |
0.030 |
0.028 |
0.202 |
0.534 |
0.598 |
0.000 |
0.163 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 42 | 262 | 71 | 984 | 0 | 80 | -1 |
normalized size | 1 | 1.00 | 0.57 | 3.54 | 0.96 | 13.30 | 0.00 | 1.08 | -0.01 |
time (sec) |
N/A |
0.040 |
0.056 |
0.207 |
0.496 |
1.287 |
0.000 |
0.170 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
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 | 135 | 135 | 68 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.070 |
0.177 |
0.241 |
0.000 |
0.611 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
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 | 81 | 81 | 56 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.045 |
0.121 |
0.206 |
0.000 |
0.475 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
Problem 38 |
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 | 56 | 60 | 42 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.07 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.034 |
0.031 |
0.225 |
0.000 |
0.515 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 39 |
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 | 62 | 62 | 43 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.034 |
0.077 |
0.227 |
0.000 |
0.591 |
0.000 |
0.000 |
0.000 |
|
|
|
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|
Problem 40 |
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 | 89 | 89 | 57 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.048 |
0.078 |
0.202 |
0.000 |
0.597 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
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|
Problem 41 |
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 | 135 | 135 | 71 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.071 |
0.128 |
0.199 |
0.000 |
1.529 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 164 | 164 | 59 | 72 | 620 | 2825 | 0 | 51 | 498 |
normalized size | 1 | 1.00 | 0.36 | 0.44 | 3.78 | 17.23 | 0.00 | 0.31 | 3.04 |
time (sec) |
N/A |
0.042 |
0.052 |
0.276 |
0.434 |
0.652 |
0.000 |
0.135 |
1.485 |
|
|
|
|
|
|
|
|
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|
|
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|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 118 | 118 | 47 | 60 | 322 | 1493 | 0 | 39 | 356 |
normalized size | 1 | 1.00 | 0.40 | 0.51 | 2.73 | 12.65 | 0.00 | 0.33 | 3.02 |
time (sec) |
N/A |
0.032 |
0.032 |
0.221 |
0.487 |
0.779 |
0.000 |
0.116 |
1.440 |
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 33 | 46 | 120 | 529 | 0 | 27 | 46 |
normalized size | 1 | 1.00 | 0.53 | 0.74 | 1.94 | 8.53 | 0.00 | 0.44 | 0.74 |
time (sec) |
N/A |
0.023 |
0.019 |
0.204 |
0.511 |
1.571 |
0.000 |
0.130 |
1.457 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 16 | 29 | 13 | 81 | 0 | 13 | 71 |
normalized size | 1 | 1.00 | 1.00 | 1.81 | 0.81 | 5.06 | 0.00 | 0.81 | 4.44 |
time (sec) |
N/A |
0.017 |
0.006 |
0.228 |
0.499 |
0.669 |
0.000 |
0.109 |
1.456 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 24 | 89 | 22 | 253 | 0 | 26 | -1 |
normalized size | 1 | 1.00 | 0.67 | 2.47 | 0.61 | 7.03 | 0.00 | 0.72 | -0.03 |
time (sec) |
N/A |
0.016 |
0.025 |
0.249 |
0.440 |
0.651 |
0.000 |
0.111 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 38 | 230 | 46 | 1141 | 0 | 50 | -1 |
normalized size | 1 | 1.00 | 0.44 | 2.67 | 0.53 | 13.27 | 0.00 | 0.58 | -0.01 |
time (sec) |
N/A |
0.033 |
0.040 |
0.209 |
0.465 |
0.811 |
0.000 |
0.110 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 55 | 362 | 72 | 2600 | 0 | 76 | -1 |
normalized size | 1 | 1.00 | 0.42 | 2.74 | 0.55 | 19.70 | 0.00 | 0.58 | -0.01 |
time (sec) |
N/A |
0.051 |
0.116 |
0.219 |
0.581 |
0.742 |
0.000 |
0.131 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
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 | 32 | 32 | 54 | 63 | 35 | 32 | 0 | 29 | 26 |
normalized size | 1 | 1.00 | 1.69 | 1.97 | 1.09 | 1.00 | 0.00 | 0.91 | 0.81 |
time (sec) |
N/A |
0.015 |
0.122 |
0.254 |
0.362 |
1.426 |
0.000 |
0.131 |
1.553 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
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 | 32 | 32 | 54 | 63 | 35 | 32 | 0 | 29 | 26 |
normalized size | 1 | 1.00 | 1.69 | 1.97 | 1.09 | 1.00 | 0.00 | 0.91 | 0.81 |
time (sec) |
N/A |
0.015 |
0.108 |
0.260 |
0.343 |
0.753 |
0.000 |
0.140 |
1.501 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 136 | 0 | 0 | 569 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.27 | 0.00 | 0.00 | 5.32 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.127 |
1.481 |
0.949 |
0.000 |
0.616 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 100 | 0 | 0 | 467 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.39 | 0.00 | 0.00 | 6.49 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.042 |
1.247 |
0.698 |
0.000 |
0.579 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 40 | 80 | 0 | 0 | 386 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.00 | 0.00 | 0.00 | 9.65 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.020 |
0.935 |
2.389 |
0.000 |
0.945 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 118 | 0 | 0 | 561 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.30 | 0.00 | 0.00 | 6.16 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.087 |
1.120 |
0.821 |
0.000 |
1.497 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 327 | 0 | 0 | 886 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.66 | 0.00 | 0.00 | 7.20 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.146 |
2.450 |
0.630 |
0.000 |
2.454 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 40 | 80 | 0 | 0 | 386 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.00 | 0.00 | 0.00 | 9.65 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.023 |
1.009 |
2.784 |
0.000 |
0.582 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 117 | 0 | 0 | 561 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.29 | 0.00 | 0.00 | 6.16 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.084 |
1.098 |
0.876 |
0.000 |
1.281 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 46 | 0 | 0 | 218 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.00 | 0.00 | 0.00 | 9.48 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.017 |
0.736 |
0.829 |
0.000 |
0.460 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 46 | 0 | 0 | 218 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.00 | 0.00 | 0.00 | 9.48 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.018 |
0.716 |
1.010 |
0.000 |
0.464 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 46 | 0 | 0 | 215 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.00 | 0.00 | 0.00 | 9.35 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.016 |
0.689 |
0.565 |
0.000 |
0.432 |
0.000 |
0.000 |
0.000 |
|
|
|
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Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 46 | 0 | 0 | 215 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.00 | 0.00 | 0.00 | 9.35 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.017 |
0.685 |
0.484 |
0.000 |
0.436 |
0.000 |
0.000 |
0.000 |
|
|
|
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Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 63 | 182 | 71 | 79 | 0 | 66 | 64 |
normalized size | 1 | 1.00 | 1.09 | 3.14 | 1.22 | 1.36 | 0.00 | 1.14 | 1.10 |
time (sec) |
N/A |
0.071 |
0.150 |
0.210 |
0.313 |
0.468 |
0.000 |
0.143 |
1.589 |
|
|
|
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Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 56 | 137 | 59 | 67 | 0 | 50 | 52 |
normalized size | 1 | 1.00 | 1.22 | 2.98 | 1.28 | 1.46 | 0.00 | 1.09 | 1.13 |
time (sec) |
N/A |
0.071 |
0.135 |
0.206 |
0.315 |
0.442 |
0.000 |
0.141 |
0.176 |
|
|
|
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Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 46 | 96 | 47 | 55 | 0 | 40 | 38 |
normalized size | 1 | 1.00 | 1.28 | 2.67 | 1.31 | 1.53 | 0.00 | 1.11 | 1.06 |
time (sec) |
N/A |
0.060 |
0.127 |
0.212 |
0.309 |
0.411 |
0.000 |
0.126 |
1.474 |
|
|
|
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Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 35 | 51 | 31 | 40 | 0 | 26 | 24 |
normalized size | 1 | 1.00 | 1.75 | 2.55 | 1.55 | 2.00 | 0.00 | 1.30 | 1.20 |
time (sec) |
N/A |
0.047 |
0.053 |
0.201 |
0.316 |
0.409 |
0.000 |
0.127 |
1.460 |
|
|
|
|
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|
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|
Problem 66 |
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 | 14 | 14 | 27 | 12 | 12 | 8 | 0 | 8 | 10 |
normalized size | 1 | 1.00 | 1.93 | 0.86 | 0.86 | 0.57 | 0.00 | 0.57 | 0.71 |
time (sec) |
N/A |
0.021 |
0.019 |
0.116 |
0.312 |
0.394 |
0.000 |
0.129 |
0.066 |
|
|
|
|
|
|
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|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 37 | 19 | 29 | 31 | 0 | 22 | 26 |
normalized size | 1 | 1.00 | 2.18 | 1.12 | 1.71 | 1.82 | 0.00 | 1.29 | 1.53 |
time (sec) |
N/A |
0.054 |
0.035 |
0.098 |
0.312 |
0.473 |
0.000 |
0.120 |
0.219 |
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 70 | 35 | 55 | 77 | 0 | 46 | 60 |
normalized size | 1 | 1.00 | 2.69 | 1.35 | 2.12 | 2.96 | 0.00 | 1.77 | 2.31 |
time (sec) |
N/A |
0.084 |
0.115 |
0.110 |
0.316 |
0.420 |
0.000 |
0.122 |
1.645 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 81 | 53 | 81 | 130 | 0 | 50 | 63 |
normalized size | 1 | 1.00 | 2.19 | 1.43 | 2.19 | 3.51 | 0.00 | 1.35 | 1.70 |
time (sec) |
N/A |
0.064 |
0.328 |
0.128 |
0.320 |
0.417 |
0.000 |
0.125 |
1.685 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 508 | 92 | 234 | 1440 | 0 | 169 | 239 |
normalized size | 1 | 1.00 | 4.66 | 0.84 | 2.15 | 13.21 | 0.00 | 1.55 | 2.19 |
time (sec) |
N/A |
0.128 |
6.244 |
0.493 |
0.325 |
0.436 |
0.000 |
0.125 |
0.210 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 118 | 66 | 136 | 769 | 0 | 122 | 170 |
normalized size | 1 | 1.00 | 1.57 | 0.88 | 1.81 | 10.25 | 0.00 | 1.63 | 2.27 |
time (sec) |
N/A |
0.051 |
0.872 |
0.414 |
0.327 |
0.422 |
0.000 |
0.139 |
0.150 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 61 | 37 | 44 | 222 | 0 | 59 | 74 |
normalized size | 1 | 1.00 | 1.79 | 1.09 | 1.29 | 6.53 | 0.00 | 1.74 | 2.18 |
time (sec) |
N/A |
0.031 |
0.222 |
0.317 |
0.315 |
0.418 |
0.000 |
0.121 |
1.480 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 43 | 20 | 19 | 44 | 0 | 32 | 42 |
normalized size | 1 | 1.00 | 2.53 | 1.18 | 1.12 | 2.59 | 0.00 | 1.88 | 2.47 |
time (sec) |
N/A |
0.010 |
0.011 |
0.023 |
0.312 |
0.406 |
0.000 |
0.112 |
0.066 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 64 | 87 | 85 | 186 | 0 | 84 | 121 |
normalized size | 1 | 1.00 | 1.19 | 1.61 | 1.57 | 3.44 | 0.00 | 1.56 | 2.24 |
time (sec) |
N/A |
0.059 |
0.109 |
0.202 |
0.415 |
0.415 |
0.000 |
0.144 |
0.328 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 142 | 238 | 187 | 645 | 0 | 161 | 269 |
normalized size | 1 | 1.00 | 1.41 | 2.36 | 1.85 | 6.39 | 0.00 | 1.59 | 2.66 |
time (sec) |
N/A |
0.158 |
0.394 |
0.321 |
0.408 |
0.422 |
0.000 |
0.155 |
1.948 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 76 |
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 | 163 | 163 | 213 | 822 | 373 | 2094 | 0 | 293 | -1 |
normalized size | 1 | 1.00 | 1.31 | 5.04 | 2.29 | 12.85 | 0.00 | 1.80 | -0.01 |
time (sec) |
N/A |
0.316 |
0.930 |
0.342 |
0.419 |
0.459 |
0.000 |
0.161 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 104 | 262 | 157 | 807 | 0 | 155 | 199 |
normalized size | 1 | 1.00 | 0.97 | 2.45 | 1.47 | 7.54 | 0.00 | 1.45 | 1.86 |
time (sec) |
N/A |
0.458 |
0.430 |
0.161 |
0.408 |
0.427 |
0.000 |
0.139 |
1.826 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 82 | 174 | 116 | 456 | 0 | 115 | 157 |
normalized size | 1 | 1.00 | 1.02 | 2.18 | 1.45 | 5.70 | 0.00 | 1.44 | 1.96 |
time (sec) |
N/A |
0.288 |
0.132 |
0.171 |
0.405 |
0.422 |
0.000 |
0.135 |
1.668 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 61 | 92 | 84 | 238 | 0 | 86 | 129 |
normalized size | 1 | 1.00 | 1.07 | 1.61 | 1.47 | 4.18 | 0.00 | 1.51 | 2.26 |
time (sec) |
N/A |
0.107 |
0.106 |
0.165 |
0.401 |
0.420 |
0.000 |
0.133 |
1.579 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 45 | 35 | 54 | 111 | 0 | 56 | 49 |
normalized size | 1 | 1.00 | 1.22 | 0.95 | 1.46 | 3.00 | 0.00 | 1.51 | 1.32 |
time (sec) |
N/A |
0.066 |
0.026 |
0.084 |
0.403 |
0.396 |
0.000 |
0.136 |
1.516 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 50 | 50 | 58 | 49 | 83 | 156 | 0 | 82 | 287 |
normalized size | 1 | 1.00 | 1.16 | 0.98 | 1.66 | 3.12 | 0.00 | 1.64 | 5.74 |
time (sec) |
N/A |
0.115 |
0.051 |
0.094 |
0.406 |
0.440 |
0.000 |
0.147 |
1.685 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 71 | 73 | 100 | 345 | 0 | 98 | 292 |
normalized size | 1 | 1.00 | 1.20 | 1.24 | 1.69 | 5.85 | 0.00 | 1.66 | 4.95 |
time (sec) |
N/A |
0.160 |
0.289 |
0.098 |
0.422 |
0.434 |
0.000 |
0.150 |
1.728 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 124 | 108 | 158 | 947 | 0 | 141 | 617 |
normalized size | 1 | 1.00 | 1.49 | 1.30 | 1.90 | 11.41 | 0.00 | 1.70 | 7.43 |
time (sec) |
N/A |
0.292 |
0.481 |
0.105 |
0.415 |
0.526 |
0.000 |
0.156 |
2.094 |
|
|
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Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 38 | 32 | 170 | 42 | 43 | 0 | 38 | 41 |
normalized size | 1 | 1.00 | 0.84 | 4.47 | 1.11 | 1.13 | 0.00 | 1.00 | 1.08 |
time (sec) |
N/A |
0.128 |
0.034 |
0.165 |
0.304 |
0.410 |
0.000 |
0.138 |
1.551 |
|
|
|
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Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 15 | 39 | 36 | 0 | 35 | 39 |
normalized size | 1 | 1.00 | 1.00 | 0.79 | 2.05 | 1.89 | 0.00 | 1.84 | 2.05 |
time (sec) |
N/A |
0.106 |
0.010 |
0.107 |
0.302 |
0.404 |
0.000 |
0.140 |
0.142 |
|
|
|
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Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 84 | 30 | 31 | 0 | 26 | 29 |
normalized size | 1 | 1.00 | 1.00 | 4.20 | 1.50 | 1.55 | 0.00 | 1.30 | 1.45 |
time (sec) |
N/A |
0.092 |
0.031 |
0.120 |
0.301 |
0.464 |
0.000 |
0.142 |
1.463 |
|
|
|
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Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 16 | 20 | 21 | 28 | 0 | 25 | 12 |
normalized size | 1 | 1.00 | 1.00 | 1.25 | 1.31 | 1.75 | 0.00 | 1.56 | 0.75 |
time (sec) |
N/A |
0.058 |
0.010 |
0.120 |
0.302 |
0.596 |
0.000 |
0.119 |
0.093 |
|
|
|
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|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 20 | 43 | 41 | 53 | 0 | 53 | 46 |
normalized size | 1 | 1.00 | 0.71 | 1.54 | 1.46 | 1.89 | 0.00 | 1.89 | 1.64 |
time (sec) |
N/A |
0.080 |
0.029 |
0.182 |
0.303 |
0.405 |
0.000 |
0.137 |
0.229 |
|
|
|
|
|
|
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|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 64 | 49 | 81 | 33 | 0 | 27 | 31 |
normalized size | 1 | 1.00 | 3.37 | 2.58 | 4.26 | 1.74 | 0.00 | 1.42 | 1.63 |
time (sec) |
N/A |
0.111 |
0.056 |
0.202 |
0.308 |
0.392 |
0.000 |
0.139 |
1.573 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 40 | 32 | 89 | 92 | 145 | 0 | 94 | 122 |
normalized size | 1 | 1.00 | 0.80 | 2.22 | 2.30 | 3.62 | 0.00 | 2.35 | 3.05 |
time (sec) |
N/A |
0.130 |
0.062 |
0.205 |
0.307 |
0.412 |
0.000 |
0.125 |
1.950 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 96 | 93 | 257 | 69 | 0 | 55 | 207 |
normalized size | 1 | 1.00 | 3.31 | 3.21 | 8.86 | 2.38 | 0.00 | 1.90 | 7.14 |
time (sec) |
N/A |
0.121 |
0.111 |
0.203 |
0.307 |
0.524 |
0.000 |
0.130 |
1.924 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 97 | 600 | 242 | 1398 | 0 | 194 | 228 |
normalized size | 1 | 1.00 | 0.95 | 5.88 | 2.37 | 13.71 | 0.00 | 1.90 | 2.24 |
time (sec) |
N/A |
0.198 |
0.287 |
0.141 |
0.317 |
0.555 |
0.000 |
0.129 |
2.067 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 180 | 486 | 217 | 924 | 0 | 221 | 247 |
normalized size | 1 | 1.00 | 1.44 | 3.89 | 1.74 | 7.39 | 0.00 | 1.77 | 1.98 |
time (sec) |
N/A |
0.378 |
1.207 |
0.149 |
0.409 |
0.590 |
0.000 |
0.136 |
2.024 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 56 | 274 | 127 | 476 | 0 | 97 | 121 |
normalized size | 1 | 1.00 | 0.98 | 4.81 | 2.23 | 8.35 | 0.00 | 1.70 | 2.12 |
time (sec) |
N/A |
0.160 |
0.111 |
0.144 |
0.316 |
0.665 |
0.000 |
0.125 |
1.684 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 80 | 172 | 122 | 304 | 0 | 121 | 159 |
normalized size | 1 | 1.00 | 1.04 | 2.23 | 1.58 | 3.95 | 0.00 | 1.57 | 2.06 |
time (sec) |
N/A |
0.206 |
0.223 |
0.136 |
0.403 |
0.764 |
0.000 |
0.135 |
1.693 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 19 | 31 | 48 | 80 | 0 | 39 | 20 |
normalized size | 1 | 1.00 | 0.95 | 1.55 | 2.40 | 4.00 | 0.00 | 1.95 | 1.00 |
time (sec) |
N/A |
0.080 |
0.013 |
0.124 |
0.308 |
0.634 |
0.000 |
0.141 |
0.084 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 97 |
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 | 64 | 64 | 36 | 84 | 66 | 57 | 0 | 89 | 93 |
normalized size | 1 | 1.00 | 0.56 | 1.31 | 1.03 | 0.89 | 0.00 | 1.39 | 1.45 |
time (sec) |
N/A |
0.111 |
0.059 |
0.149 |
0.404 |
0.565 |
0.000 |
0.145 |
2.357 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 67 | 81 | 91 | 256 | 0 | 85 | 133 |
normalized size | 1 | 1.00 | 1.12 | 1.35 | 1.52 | 4.27 | 0.00 | 1.42 | 2.22 |
time (sec) |
N/A |
0.142 |
0.184 |
0.171 |
0.408 |
1.331 |
0.000 |
0.154 |
1.659 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 78 | 275 | 161 | 675 | 0 | 218 | 256 |
normalized size | 1 | 1.00 | 0.82 | 2.89 | 1.69 | 7.11 | 0.00 | 2.29 | 2.69 |
time (sec) |
N/A |
0.220 |
0.156 |
0.194 |
0.411 |
0.640 |
0.000 |
0.138 |
2.994 |
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 114 | 170 | 226 | 1155 | 0 | 174 | 269 |
normalized size | 1 | 1.00 | 1.10 | 1.63 | 2.17 | 11.11 | 0.00 | 1.67 | 2.59 |
time (sec) |
N/A |
0.270 |
0.629 |
0.180 |
0.418 |
1.555 |
0.000 |
0.176 |
1.793 |
|
|
|
|
|
|
|
|
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|
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|
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|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 138 | 1168 | 348 | 2778 | 0 | 374 | 513 |
normalized size | 1 | 1.00 | 0.93 | 7.84 | 2.34 | 18.64 | 0.00 | 2.51 | 3.44 |
time (sec) |
N/A |
0.341 |
0.284 |
0.195 |
0.428 |
1.578 |
0.000 |
0.141 |
5.507 |
|
|
|
|
|
|
|
|
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|
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|
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|
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|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 75 | 155 | 144 | 299 | 0 | 120 | 274 |
normalized size | 1 | 1.00 | 0.69 | 1.42 | 1.32 | 2.74 | 0.00 | 1.10 | 2.51 |
time (sec) |
N/A |
0.086 |
0.203 |
0.251 |
0.328 |
1.372 |
0.000 |
0.148 |
4.105 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 52 | 52 | 126 | 99 | 96 | 123 | 0 | 62 | 237 |
normalized size | 1 | 1.00 | 2.42 | 1.90 | 1.85 | 2.37 | 0.00 | 1.19 | 4.56 |
time (sec) |
N/A |
0.093 |
0.135 |
0.253 |
0.317 |
1.017 |
0.000 |
0.128 |
2.218 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 61 | 109 | 96 | 185 | 0 | 98 | 140 |
normalized size | 1 | 1.00 | 0.79 | 1.42 | 1.25 | 2.40 | 0.00 | 1.27 | 1.82 |
time (sec) |
N/A |
0.067 |
0.124 |
0.250 |
0.317 |
1.974 |
0.000 |
0.124 |
0.577 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 71 | 67 | 42 | 51 | 0 | 38 | 85 |
normalized size | 1 | 1.00 | 1.97 | 1.86 | 1.17 | 1.42 | 0.00 | 1.06 | 2.36 |
time (sec) |
N/A |
0.073 |
0.087 |
0.211 |
0.314 |
1.458 |
0.000 |
0.126 |
1.634 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 39 | 65 | 45 | 71 | 0 | 55 | 50 |
normalized size | 1 | 1.00 | 0.87 | 1.44 | 1.00 | 1.58 | 0.00 | 1.22 | 1.11 |
time (sec) |
N/A |
0.048 |
0.040 |
0.209 |
0.311 |
1.217 |
0.000 |
0.123 |
0.225 |
|
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Problem 107 |
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 | 13 | 13 | 13 | 17 | 15 | 11 | 0 | 13 | 14 |
normalized size | 1 | 1.00 | 1.00 | 1.31 | 1.15 | 0.85 | 0.00 | 1.00 | 1.08 |
time (sec) |
N/A |
0.023 |
0.008 |
0.118 |
0.303 |
1.307 |
0.000 |
0.144 |
1.463 |
|
|
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Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 13 | 27 | 20 | 16 | 0 | 17 | 21 |
normalized size | 1 | 1.00 | 1.18 | 2.45 | 1.82 | 1.45 | 0.00 | 1.55 | 1.91 |
time (sec) |
N/A |
0.038 |
0.036 |
0.116 |
0.310 |
1.970 |
0.000 |
0.122 |
0.178 |
|
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Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 12 | 12 | 36 | 40 | 0 | 38 | 27 |
normalized size | 1 | 1.00 | 1.00 | 1.00 | 3.00 | 3.33 | 0.00 | 3.17 | 2.25 |
time (sec) |
N/A |
0.039 |
0.011 |
0.092 |
0.307 |
0.732 |
0.000 |
0.128 |
1.571 |
|
|
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Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 65 | 61 | 55 | 85 | 0 | 48 | 56 |
normalized size | 1 | 1.00 | 2.41 | 2.26 | 2.04 | 3.15 | 0.00 | 1.78 | 2.07 |
time (sec) |
N/A |
0.056 |
0.037 |
0.182 |
0.309 |
1.062 |
0.000 |
0.130 |
1.640 |
|
|
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Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 30 | 78 | 75 | 97 | 0 | 68 | 81 |
normalized size | 1 | 1.00 | 1.00 | 2.60 | 2.50 | 3.23 | 0.00 | 2.27 | 2.70 |
time (sec) |
N/A |
0.046 |
0.015 |
0.233 |
0.310 |
2.108 |
0.000 |
0.144 |
1.682 |
|
|
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Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 129 | 95 | 96 | 154 | 0 | 77 | 106 |
normalized size | 1 | 1.00 | 3.00 | 2.21 | 2.23 | 3.58 | 0.00 | 1.79 | 2.47 |
time (sec) |
N/A |
0.075 |
0.042 |
0.247 |
0.309 |
0.572 |
0.000 |
0.126 |
1.862 |
|
|
|
|
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|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 253 | 1323 | 383 | 4025 | 0 | 432 | 611 |
normalized size | 1 | 1.00 | 1.30 | 6.82 | 1.97 | 20.75 | 0.00 | 2.23 | 3.15 |
time (sec) |
N/A |
0.255 |
0.506 |
0.227 |
0.432 |
3.045 |
0.000 |
0.163 |
7.041 |
|
|
|
|
|
|
|
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|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 183 | 183 | 141 | 207 | 261 | 1746 | 0 | 215 | 707 |
normalized size | 1 | 1.00 | 0.77 | 1.13 | 1.43 | 9.54 | 0.00 | 1.17 | 3.86 |
time (sec) |
N/A |
0.384 |
0.744 |
0.203 |
0.409 |
0.637 |
0.000 |
0.149 |
3.429 |
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 191 | 324 | 172 | 965 | 0 | 234 | 335 |
normalized size | 1 | 1.00 | 1.69 | 2.87 | 1.52 | 8.54 | 0.00 | 2.07 | 2.96 |
time (sec) |
N/A |
0.163 |
0.201 |
0.189 |
0.419 |
0.867 |
0.000 |
0.130 |
4.011 |
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 100 | 82 | 95 | 108 | 349 | 0 | 102 | 376 |
normalized size | 1 | 1.00 | 0.82 | 0.95 | 1.08 | 3.49 | 0.00 | 1.02 | 3.76 |
time (sec) |
N/A |
0.221 |
0.332 |
0.178 |
0.416 |
0.688 |
0.000 |
0.162 |
2.471 |
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 61 | 61 | 63 | 108 | 74 | 75 | 0 | 89 | 132 |
normalized size | 1 | 1.00 | 1.03 | 1.77 | 1.21 | 1.23 | 0.00 | 1.46 | 2.16 |
time (sec) |
N/A |
0.099 |
0.062 |
0.180 |
0.409 |
1.261 |
0.000 |
0.128 |
2.526 |
|
|
|
|
|
|
|
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|
Problem 118 |
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 | 19 | 19 | 11 | 21 | 28 | 27 | 0 | 22 | 25 |
normalized size | 1 | 1.00 | 0.58 | 1.11 | 1.47 | 1.42 | 0.00 | 1.16 | 1.32 |
time (sec) |
N/A |
0.032 |
0.008 |
0.114 |
0.317 |
0.602 |
0.000 |
0.126 |
0.099 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 119 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 65 | 110 | 90 | 141 | 0 | 89 | 316 |
normalized size | 1 | 1.00 | 1.14 | 1.93 | 1.58 | 2.47 | 0.00 | 1.56 | 5.54 |
time (sec) |
N/A |
0.178 |
0.085 |
0.126 |
0.415 |
0.629 |
0.000 |
0.158 |
0.344 |
|
|
|
|
|
|
|
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|
Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 37 | 106 | 82 | 199 | 0 | 80 | 261 |
normalized size | 1 | 1.00 | 1.16 | 3.31 | 2.56 | 6.22 | 0.00 | 2.50 | 8.16 |
time (sec) |
N/A |
0.072 |
0.053 |
0.144 |
0.316 |
0.614 |
0.000 |
0.126 |
1.840 |
|
|
|
|
|
|
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|
Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 151 | 207 | 178 | 831 | 0 | 161 | 378 |
normalized size | 1 | 1.00 | 1.72 | 2.35 | 2.02 | 9.44 | 0.00 | 1.83 | 4.30 |
time (sec) |
N/A |
0.332 |
0.588 |
0.148 |
0.428 |
1.719 |
0.000 |
0.151 |
2.623 |
|
|
|
|
|
|
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|
Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 83 | 219 | 190 | 1288 | 0 | 170 | 155 |
normalized size | 1 | 1.00 | 1.19 | 3.13 | 2.71 | 18.40 | 0.00 | 2.43 | 2.21 |
time (sec) |
N/A |
0.094 |
0.135 |
0.153 |
0.327 |
0.887 |
0.000 |
0.128 |
1.975 |
|
|
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|
|
|
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|
Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 183 | 183 | 269 | 360 | 330 | 3160 | 0 | 305 | 543 |
normalized size | 1 | 1.00 | 1.47 | 1.97 | 1.80 | 17.27 | 0.00 | 1.67 | 2.97 |
time (sec) |
N/A |
0.337 |
1.579 |
0.167 |
0.418 |
2.180 |
0.000 |
0.142 |
2.898 |
|
|
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|
Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 130 | 388 | 364 | 4024 | 0 | 295 | 317 |
normalized size | 1 | 1.00 | 1.09 | 3.26 | 3.06 | 33.82 | 0.00 | 2.48 | 2.66 |
time (sec) |
N/A |
0.141 |
0.259 |
0.161 |
0.334 |
0.714 |
0.000 |
0.153 |
2.182 |
|
|
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|
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|
Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 199 | 199 | 84 | 91 | 386 | 592 | 0 | 90 | 413 |
normalized size | 1 | 1.00 | 0.42 | 0.46 | 1.94 | 2.97 | 0.00 | 0.45 | 2.08 |
time (sec) |
N/A |
0.303 |
0.082 |
0.636 |
0.420 |
0.635 |
0.000 |
0.154 |
1.595 |
|
|
|
|
|
|
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|
Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 72 | 80 | 209 | 315 | 0 | 77 | 91 |
normalized size | 1 | 1.00 | 0.49 | 0.54 | 1.42 | 2.14 | 0.00 | 0.52 | 0.62 |
time (sec) |
N/A |
0.171 |
0.067 |
0.607 |
0.416 |
1.977 |
0.000 |
0.149 |
1.530 |
|
|
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|
|
|
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|
Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 56 | 69 | 84 | 121 | 0 | 64 | 78 |
normalized size | 1 | 1.00 | 0.97 | 1.19 | 1.45 | 2.09 | 0.00 | 1.10 | 1.34 |
time (sec) |
N/A |
0.118 |
0.045 |
0.601 |
0.422 |
1.060 |
0.000 |
0.130 |
1.549 |
|
|
|
|
|
|
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|
Problem 128 |
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 | 46 | 46 | 44 | 68 | 39 | 42 | 0 | 48 | -1 |
normalized size | 1 | 1.00 | 0.96 | 1.48 | 0.85 | 0.91 | 0.00 | 1.04 | -0.02 |
time (sec) |
N/A |
0.091 |
0.037 |
0.704 |
0.415 |
0.451 |
0.000 |
0.156 |
0.000 |
|
|
|
|
|
|
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Problem 129 |
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 | 74 | 74 | 48 | 106 | 36 | 66 | 0 | 71 | -1 |
normalized size | 1 | 1.00 | 0.65 | 1.43 | 0.49 | 0.89 | 0.00 | 0.96 | -0.01 |
time (sec) |
N/A |
0.115 |
0.051 |
0.542 |
0.415 |
0.594 |
0.000 |
0.127 |
0.000 |
|
|
|
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|
Problem 130 |
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 | 162 | 162 | 76 | 216 | 62 | 126 | 0 | 204 | -1 |
normalized size | 1 | 1.00 | 0.47 | 1.33 | 0.38 | 0.78 | 0.00 | 1.26 | -0.01 |
time (sec) |
N/A |
0.153 |
0.066 |
0.540 |
0.419 |
0.609 |
0.000 |
0.146 |
0.000 |
|
|
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Problem 131 |
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 | 250 | 250 | 106 | 326 | 90 | 218 | 0 | 278 | -1 |
normalized size | 1 | 1.00 | 0.42 | 1.30 | 0.36 | 0.87 | 0.00 | 1.11 | -0.00 |
time (sec) |
N/A |
0.200 |
0.104 |
0.544 |
0.423 |
2.046 |
0.000 |
0.174 |
0.000 |
|
|
|
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Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 80 | 125 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.068 |
0.179 |
0.209 |
0.000 |
2.017 |
0.000 |
0.000 |
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 |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 44 | 39 | 46 | 48 | 0 | 0 | 42 |
normalized size | 1 | 1.00 | 1.47 | 1.30 | 1.53 | 1.60 | 0.00 | 0.00 | 1.40 |
time (sec) |
N/A |
0.045 |
0.050 |
0.145 |
0.475 |
1.213 |
0.000 |
0.000 |
2.153 |
|
|
|
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Problem 134 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 60 | 127 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.50 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.086 |
0.116 |
0.158 |
0.000 |
1.990 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
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|
Problem 135 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 74 | 97 | 0 | 92 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.07 | 1.41 | 0.00 | 1.33 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.058 |
0.144 |
0.186 |
0.000 |
1.664 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
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|
|
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|
Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 57 | 109 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.041 |
0.109 |
0.147 |
0.000 |
0.971 |
0.000 |
0.000 |
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 |
F |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 77 | 0 | 0 | 86 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.28 | 0.00 | 0.00 | 1.43 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.035 |
0.090 |
0.143 |
0.000 |
0.709 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 138 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 43 | 90 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.93 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.032 |
0.075 |
0.287 |
0.000 |
0.607 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 139 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 54 | 0 | 0 | 43 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.32 | 0.00 | 0.00 | 1.05 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.046 |
0.118 |
0.140 |
0.000 |
0.465 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 58 | 126 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.78 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.066 |
0.096 |
0.161 |
0.000 |
0.457 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 141 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 33 | 38 | 89 | 37 | 0 | 0 | 58 |
normalized size | 1 | 1.00 | 1.32 | 1.52 | 3.56 | 1.48 | 0.00 | 0.00 | 2.32 |
time (sec) |
N/A |
0.041 |
0.040 |
0.136 |
0.428 |
0.461 |
0.000 |
0.000 |
1.471 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 142 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 60 | 112 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.055 |
0.099 |
0.137 |
0.000 |
0.593 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 143 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 95 | 121 | 0 | 110 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.74 | 0.95 | 0.00 | 0.86 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.080 |
0.208 |
0.214 |
0.000 |
0.426 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 144 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 118 | 118 | 80 | 133 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.68 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.078 |
0.176 |
0.155 |
0.000 |
0.459 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 145 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 44 | 47 | 46 | 56 | 0 | 0 | 42 |
normalized size | 1 | 1.00 | 1.47 | 1.57 | 1.53 | 1.87 | 0.00 | 0.00 | 1.40 |
time (sec) |
N/A |
0.041 |
0.052 |
0.136 |
0.467 |
1.028 |
0.000 |
0.000 |
1.555 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 146 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 162 | 162 | 63 | 140 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.39 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.100 |
0.127 |
0.150 |
0.000 |
0.539 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 147 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 87 | 113 | 0 | 102 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.91 | 1.18 | 0.00 | 1.06 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.067 |
0.184 |
0.186 |
0.000 |
0.622 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 148 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 65 | 124 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.76 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.063 |
0.128 |
0.148 |
0.000 |
0.565 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 149 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 88 | 0 | 0 | 94 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.00 | 0.00 | 1.03 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.073 |
0.162 |
0.149 |
0.000 |
0.658 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 150 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 130 | 60 | 152 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.46 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.073 |
0.115 |
0.159 |
0.000 |
0.429 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 151 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 63 | 130 | 0 | 106 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.66 | 1.35 | 0.00 | 1.10 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.046 |
0.096 |
0.191 |
0.000 |
0.492 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 152 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 54 | 163 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.81 | 2.43 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.037 |
0.098 |
0.414 |
0.000 |
1.306 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 153 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
F |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 33 | 0 | 87 | 29 | 0 | 0 | 29 |
normalized size | 1 | 1.00 | 1.22 | 0.00 | 3.22 | 1.07 | 0.00 | 0.00 | 1.07 |
time (sec) |
N/A |
0.039 |
0.035 |
0.152 |
0.464 |
0.473 |
0.000 |
0.000 |
1.474 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 154 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 66 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.054 |
0.108 |
0.138 |
0.000 |
0.491 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 155 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 53 | 0 | 0 | 78 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.77 | 0.00 | 0.00 | 1.13 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.061 |
0.107 |
0.147 |
0.000 |
0.730 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 156 |
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 | 62 | 62 | 62 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.055 |
1.201 |
0.369 |
0.000 |
0.463 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 157 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 126 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.065 |
4.320 |
1.782 |
0.000 |
0.493 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 158 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 101 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.069 |
5.097 |
2.109 |
0.000 |
0.716 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 159 |
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 | 68 | 68 | 200 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.069 |
9.024 |
1.813 |
0.000 |
0.478 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 160 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
C |
B |
B |
F |
B |
B |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 137 | 30 | 509 | 95 | 187 | 0 | 215 | 65 |
normalized size | 1 | 3.26 | 0.71 | 12.12 | 2.26 | 4.45 | 0.00 | 5.12 | 1.55 |
time (sec) |
N/A |
0.135 |
0.424 |
1.109 |
0.706 |
1.576 |
0.000 |
0.548 |
1.520 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 161 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
B |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 62 | 0 | 76 | 48 | 0 | 38 | 48 |
normalized size | 1 | 1.00 | 2.38 | 0.00 | 2.92 | 1.85 | 0.00 | 1.46 | 1.85 |
time (sec) |
N/A |
0.039 |
0.127 |
0.529 |
0.315 |
0.585 |
0.000 |
0.145 |
1.647 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 162 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 65 | 0 | 49 | 49 | 0 | 39 | 36 |
normalized size | 1 | 1.00 | 2.50 | 0.00 | 1.88 | 1.88 | 0.00 | 1.50 | 1.38 |
time (sec) |
N/A |
0.046 |
0.112 |
0.728 |
0.354 |
0.409 |
0.000 |
0.111 |
1.592 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 163 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 115 | 0 | 0 | 475 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.28 | 0.00 | 0.00 | 5.28 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.087 |
6.756 |
0.513 |
0.000 |
0.487 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 164 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 64 | 0 | 0 | 539 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.00 | 0.00 | 8.17 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.075 |
0.918 |
0.513 |
0.000 |
1.133 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 165 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 54 | 23 | 22 | 65 | 0 | 145 | 43 |
normalized size | 1 | 1.00 | 2.70 | 1.15 | 1.10 | 3.25 | 0.00 | 7.25 | 2.15 |
time (sec) |
N/A |
0.018 |
0.062 |
0.087 |
0.307 |
0.603 |
0.000 |
0.579 |
1.620 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 166 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 20 | 29 | 71 | 0 | 28 | 25 |
normalized size | 1 | 1.00 | 1.00 | 1.05 | 1.53 | 3.74 | 0.00 | 1.47 | 1.32 |
time (sec) |
N/A |
0.027 |
0.072 |
0.327 |
0.326 |
0.677 |
0.000 |
0.155 |
1.438 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 167 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 81 | 51 | 150 | 643 | 0 | 210 | 140 |
normalized size | 1 | 1.00 | 1.47 | 0.93 | 2.73 | 11.69 | 0.00 | 3.82 | 2.55 |
time (sec) |
N/A |
0.045 |
0.063 |
0.329 |
0.362 |
1.349 |
0.000 |
0.190 |
1.489 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 168 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 56 | 36 | 92 | 272 | 0 | 47 | 55 |
normalized size | 1 | 1.00 | 1.33 | 0.86 | 2.19 | 6.48 | 0.00 | 1.12 | 1.31 |
time (sec) |
N/A |
0.033 |
0.068 |
0.302 |
0.335 |
0.441 |
0.000 |
0.161 |
1.454 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 169 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 135 | 84 | 232 | 1806 | 0 | 248 | 318 |
normalized size | 1 | 1.00 | 1.52 | 0.94 | 2.61 | 20.29 | 0.00 | 2.79 | 3.57 |
time (sec) |
N/A |
0.070 |
0.063 |
0.313 |
0.353 |
0.513 |
0.000 |
0.223 |
1.477 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 170 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 84 | 144 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.76 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.068 |
0.223 |
0.485 |
0.000 |
0.408 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 171 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 80 | 212 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.75 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.063 |
0.115 |
0.550 |
0.000 |
0.478 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 172 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 66 | 120 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.92 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.043 |
0.097 |
0.344 |
0.000 |
0.432 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 173 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 68 | 146 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 2.03 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.044 |
0.082 |
0.587 |
0.000 |
0.460 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 174 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 86 | 143 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.77 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.060 |
0.135 |
0.452 |
0.000 |
0.448 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 175 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 95 | 227 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.86 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.061 |
0.190 |
0.688 |
0.000 |
0.453 |
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 [114] had the largest ratio of
[.6923]
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|
| Table 2.1:Rubi specific breakdown of results for each
integral
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|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
1 |
1 |
1.00 |
6 |
0.167 |
|
|
|
|
|
|
|
2 |
A |
2 |
2 |
1.00 |
8 |
0.250 |
|
|
|
|
|
|
|
3 |
A |
2 |
2 |
1.00 |
8 |
0.250 |
|
|
|
|
|
|
|
4 |
A |
2 |
1 |
1.00 |
8 |
0.125 |
|
|
|
|
|
|
|
5 |
A |
3 |
2 |
1.00 |
8 |
0.250 |
|
|
|
|
|
|
|
6 |
A |
2 |
1 |
1.00 |
8 |
0.125 |
|
|
|
|
|
|
|
7 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
8 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
9 |
A |
2 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
10 |
A |
2 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
11 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
12 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
13 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
14 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
15 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
16 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
17 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
18 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
19 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
20 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
21 |
A |
2 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
22 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
23 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
24 |
A |
2 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
25 |
A |
2 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
26 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
27 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
28 |
A |
5 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
29 |
A |
5 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
30 |
A |
4 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
31 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
32 |
A |
2 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
33 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
34 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
35 |
A |
5 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
36 |
A |
7 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
37 |
A |
5 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
38 |
A |
4 |
4 |
1.07 |
10 |
0.400 |
|
|
|
|
|
|
|
39 |
A |
4 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
40 |
A |
5 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
41 |
A |
7 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
42 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
43 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
44 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
45 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
46 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
47 |
A |
5 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
48 |
A |
7 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
49 |
A |
2 |
2 |
1.00 |
15 |
0.133 |
|
|
|
|
|
|
|
50 |
A |
2 |
2 |
1.00 |
15 |
0.133 |
|
|
|
|
|
|
|
51 |
A |
5 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
52 |
A |
4 |
4 |
1.00 |
17 |
0.235 |
|
|
|
|
|
|
|
53 |
A |
2 |
2 |
1.00 |
17 |
0.118 |
|
|
|
|
|
|
|
54 |
A |
5 |
4 |
1.00 |
17 |
0.235 |
|
|
|
|
|
|
|
55 |
A |
6 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
56 |
A |
2 |
2 |
1.00 |
17 |
0.118 |
|
|
|
|
|
|
|
57 |
A |
5 |
4 |
1.00 |
17 |
0.235 |
|
|
|
|
|
|
|
58 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
59 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
60 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
61 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
62 |
A |
7 |
5 |
1.00 |
13 |
0.385 |
|
|
|
|
|
|
|
63 |
A |
6 |
5 |
1.00 |
13 |
0.385 |
|
|
|
|
|
|
|
64 |
A |
5 |
5 |
1.00 |
13 |
0.385 |
|
|
|
|
|
|
|
65 |
A |
4 |
4 |
1.00 |
11 |
0.364 |
|
|
|
|
|
|
|
66 |
A |
1 |
1 |
1.00 |
11 |
0.091 |
|
|
|
|
|
|
|
67 |
A |
3 |
3 |
1.00 |
13 |
0.231 |
|
|
|
|
|
|
|
68 |
A |
4 |
4 |
1.00 |
13 |
0.308 |
|
|
|
|
|
|
|
69 |
A |
6 |
6 |
1.00 |
13 |
0.462 |
|
|
|
|
|
|
|
70 |
A |
6 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
71 |
A |
5 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
72 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
73 |
A |
2 |
1 |
1.00 |
10 |
0.100 |
|
|
|
|
|
|
|
74 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
75 |
A |
6 |
6 |
1.00 |
12 |
0.500 |
|
|
|
|
|
|
|
76 |
A |
7 |
7 |
1.00 |
12 |
0.583 |
|
|
|
|
|
|
|
77 |
A |
8 |
7 |
1.00 |
13 |
0.538 |
|
|
|
|
|
|
|
78 |
A |
7 |
7 |
1.00 |
13 |
0.538 |
|
|
|
|
|
|
|
79 |
A |
6 |
6 |
1.00 |
11 |
0.546 |
|
|
|
|
|
|
|
80 |
A |
4 |
4 |
1.00 |
11 |
0.364 |
|
|
|
|
|
|
|
81 |
A |
6 |
6 |
1.00 |
13 |
0.462 |
|
|
|
|
|
|
|
82 |
A |
7 |
7 |
1.00 |
13 |
0.538 |
|
|
|
|
|
|
|
83 |
A |
8 |
8 |
1.00 |
13 |
0.615 |
|
|
|
|
|
|
|
84 |
A |
7 |
7 |
1.00 |
13 |
0.538 |
|
|
|
|
|
|
|
85 |
A |
6 |
4 |
1.00 |
13 |
0.308 |
|
|
|
|
|
|
|
86 |
A |
5 |
5 |
1.00 |
13 |
0.385 |
|
|
|
|
|
|
|
87 |
A |
4 |
3 |
1.00 |
11 |
0.273 |
|
|
|
|
|
|
|
88 |
A |
6 |
6 |
1.00 |
11 |
0.546 |
|
|
|
|
|
|
|
89 |
A |
6 |
5 |
1.00 |
13 |
0.385 |
|
|
|
|
|
|
|
90 |
A |
7 |
7 |
1.00 |
13 |
0.538 |
|
|
|
|
|
|
|
91 |
A |
7 |
6 |
1.00 |
13 |
0.462 |
|
|
|
|
|
|
|
92 |
A |
5 |
4 |
1.00 |
13 |
0.308 |
|
|
|
|
|
|
|
93 |
A |
7 |
6 |
1.00 |
13 |
0.462 |
|
|
|
|
|
|
|
94 |
A |
5 |
4 |
1.00 |
13 |
0.308 |
|
|
|
|
|
|
|
95 |
A |
6 |
6 |
1.00 |
13 |
0.462 |
|
|
|
|
|
|
|
96 |
A |
5 |
4 |
1.00 |
11 |
0.364 |
|
|
|
|
|
|
|
97 |
A |
4 |
3 |
1.00 |
11 |
0.273 |
|
|
|
|
|
|
|
98 |
A |
6 |
6 |
1.00 |
13 |
0.462 |
|
|
|
|
|
|
|
99 |
A |
6 |
5 |
1.00 |
13 |
0.385 |
|
|
|
|
|
|
|
100 |
A |
7 |
6 |
1.00 |
13 |
0.462 |
|
|
|
|
|
|
|
101 |
A |
7 |
5 |
1.00 |
13 |
0.385 |
|
|
|
|
|
|
|
102 |
A |
3 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
103 |
A |
5 |
3 |
1.00 |
13 |
0.231 |
|
|
|
|
|
|
|
104 |
A |
3 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
105 |
A |
4 |
3 |
1.00 |
13 |
0.231 |
|
|
|
|
|
|
|
106 |
A |
3 |
2 |
1.00 |
11 |
0.182 |
|
|
|
|
|
|
|
107 |
A |
2 |
2 |
1.00 |
11 |
0.182 |
|
|
|
|
|
|
|
108 |
A |
3 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
109 |
A |
3 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
110 |
A |
4 |
3 |
1.00 |
13 |
0.231 |
|
|
|
|
|
|
|
111 |
A |
3 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
112 |
A |
5 |
3 |
1.00 |
13 |
0.231 |
|
|
|
|
|
|
|
113 |
A |
11 |
7 |
1.00 |
13 |
0.538 |
|
|
|
|
|
|
|
114 |
A |
16 |
9 |
1.00 |
13 |
0.692 |
|
|
|
|
|
|
|
115 |
A |
8 |
6 |
1.00 |
13 |
0.462 |
|
|
|
|
|
|
|
116 |
A |
10 |
9 |
1.00 |
13 |
0.692 |
|
|
|
|
|
|
|
117 |
A |
6 |
5 |
1.00 |
11 |
0.454 |
|
|
|
|
|
|
|
118 |
A |
4 |
4 |
1.00 |
11 |
0.364 |
|
|
|
|
|
|
|
119 |
A |
8 |
8 |
1.00 |
13 |
0.615 |
|
|
|
|
|
|
|
120 |
A |
3 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
121 |
A |
7 |
7 |
1.00 |
13 |
0.538 |
|
|
|
|
|
|
|
122 |
A |
3 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
123 |
A |
16 |
9 |
1.00 |
13 |
0.692 |
|
|
|
|
|
|
|
124 |
A |
3 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
125 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
126 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
127 |
A |
4 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
128 |
A |
4 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
129 |
A |
5 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
130 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
131 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
132 |
A |
6 |
6 |
1.00 |
15 |
0.400 |
|
|
|
|
|
|
|
133 |
A |
3 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
134 |
A |
9 |
9 |
1.00 |
15 |
0.600 |
|
|
|
|
|
|
|
135 |
A |
6 |
6 |
1.00 |
15 |
0.400 |
|
|
|
|
|
|
|
136 |
A |
5 |
5 |
1.00 |
13 |
0.385 |
|
|
|
|
|
|
|
137 |
A |
6 |
6 |
1.00 |
11 |
0.546 |
|
|
|
|
|
|
|
138 |
A |
3 |
2 |
1.00 |
15 |
0.133 |
|
|
|
|
|
|
|
139 |
A |
5 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
140 |
A |
7 |
7 |
1.00 |
15 |
0.467 |
|
|
|
|
|
|
|
141 |
A |
3 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
142 |
A |
5 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
143 |
A |
8 |
7 |
1.00 |
15 |
0.467 |
|
|
|
|
|
|
|
144 |
A |
7 |
6 |
1.00 |
15 |
0.400 |
|
|
|
|
|
|
|
145 |
A |
3 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
146 |
A |
10 |
9 |
1.00 |
15 |
0.600 |
|
|
|
|
|
|
|
147 |
A |
7 |
6 |
1.00 |
15 |
0.400 |
|
|
|
|
|
|
|
148 |
A |
6 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
149 |
A |
7 |
6 |
1.00 |
15 |
0.400 |
|
|
|
|
|
|
|
150 |
A |
9 |
8 |
1.00 |
13 |
0.615 |
|
|
|
|
|
|
|
151 |
A |
7 |
7 |
1.00 |
11 |
0.636 |
|
|
|
|
|
|
|
152 |
A |
4 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
153 |
A |
3 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
154 |
A |
5 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
155 |
A |
6 |
6 |
1.00 |
15 |
0.400 |
|
|
|
|
|
|
|
156 |
A |
4 |
4 |
1.00 |
11 |
0.364 |
|
|
|
|
|
|
|
157 |
A |
4 |
4 |
1.00 |
13 |
0.308 |
|
|
|
|
|
|
|
158 |
A |
4 |
4 |
1.00 |
13 |
0.308 |
|
|
|
|
|
|
|
159 |
A |
4 |
4 |
1.00 |
13 |
0.308 |
|
|
|
|
|
|
|
160 |
C |
9 |
4 |
3.26 |
45 |
0.089 |
|
|
|
|
|
|
|
161 |
A |
3 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
162 |
A |
4 |
4 |
1.00 |
15 |
0.267 |
|
|
|
|
|
|
|
163 |
A |
3 |
3 |
1.00 |
20 |
0.150 |
|
|
|
|
|
|
|
164 |
A |
3 |
3 |
1.00 |
21 |
0.143 |
|
|
|
|
|
|
|
165 |
A |
2 |
1 |
1.00 |
15 |
0.067 |
|
|
|
|
|
|
|
166 |
A |
3 |
2 |
1.00 |
17 |
0.118 |
|
|
|
|
|
|
|
167 |
A |
3 |
2 |
1.00 |
17 |
0.118 |
|
|
|
|
|
|
|
168 |
A |
3 |
1 |
1.00 |
17 |
0.059 |
|
|
|
|
|
|
|
169 |
A |
4 |
2 |
1.00 |
17 |
0.118 |
|
|
|
|
|
|
|
170 |
A |
4 |
3 |
1.00 |
19 |
0.158 |
|
|
|
|
|
|
|
171 |
A |
4 |
3 |
1.00 |
19 |
0.158 |
|
|
|
|
|
|
|
172 |
A |
3 |
2 |
1.00 |
19 |
0.105 |
|
|
|
|
|
|
|
173 |
A |
3 |
2 |
1.00 |
19 |
0.105 |
|
|
|
|
|
|
|
174 |
A |
4 |
3 |
1.00 |
19 |
0.158 |
|
|
|
|
|
|
|
175 |
A |
4 |
3 |
1.00 |
19 |
0.158 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|