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, 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
}
B grade: { }
C grade: { }
F grade: { 74, 75 }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32,
33, 34, 35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 70, 71,
72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 93, 94, 95, 96, 97, 98, 99, 100,
101, 102, 103, 104, 105 }
B grade: { 16, 17, 24, 40, 41, 42, 51, 56, 57, 58, 67, 68, 69, 92, 106, 107, 108 }
C grade: { }
F grade: { }
2.1.3 Maple
A grade: { 29, 54, 55, 60, 61, 62, 63, 65, 66, 70, 72, 73, 89, 93, 96, 102, 106 }
B grade: { 88, 99, 104, 107 }
C grade: { 64, 74, 75 }
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, 30,
31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 67, 68,
69, 71, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 94, 95, 97, 98, 100, 101, 103, 105, 108
}
2.1.4 Maxima
A grade: { 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38,
40, 41, 47, 48, 53, 54, 55, 59, 60, 61, 62, 63, 65, 66, 70, 71, 72, 73, 74, 75, 79, 93, 94, 96, 97, 99, 100
}
B grade: { 7, 15, 24, 25, 34, 42, 44, 45, 46, 49, 50, 77, 81, 88, 89 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 20, 39, 43, 51, 52, 56, 57, 58, 64, 67, 68, 69, 76, 78, 80, 82, 83, 84, 85, 86, 87, 90,
91, 92, 95, 98, 101, 102, 103, 104, 105, 106, 107, 108 }
2.1.5 FriCAS
A grade: { 10, 12, 28, 29, 43, 46, 47, 48, 49, 50, 54, 55, 60, 61, 62, 63, 65, 66, 70, 71, 72, 73, 74, 75, 89, 93,
96, 99 }
B grade: { 7, 8, 9, 13, 14, 15, 25, 26, 27, 31, 44, 45 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 11, 16, 17, 18, 19, 20, 21, 22, 23, 24, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42,
51, 52, 53, 56, 57, 58, 59, 64, 67, 68, 69, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 94, 95,
97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108 }
2.1.6 Sympy
A grade: { 10, 12, 28, 29, 43, 44, 45, 46, 47, 62, 63, 65, 66, 72, 73, 74, 75, 89, 93, 96, 99 }
B grade: { 50 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33,
34, 35, 36, 37, 38, 39, 40, 41, 42, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 64, 67, 68, 69, 70, 71, 76,
77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 94, 95, 97, 98, 100, 101, 102, 103, 104, 105, 106,
107, 108 }
2.1.7 Giac
A grade: { 10, 12, 13, 27, 29, 31, 47, 48, 54, 55, 60, 61, 62, 63, 65, 66, 70, 71, 72, 73, 96, 99
}
B grade: { 7, 8, 9, 14, 15, 32, 33, 34, 46, 49, 50, 93 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 11, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 30, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 51, 52, 53, 56, 57, 58, 59, 64, 67, 68, 69, 74, 75, 76, 77, 78, 79, 80, 81, 82,
83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95, 97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108
}
2.1.8 Mupad
A grade: { 54, 55, 60, 61, 62, 63, 65, 66, 70, 71, 72, 73 }
B grade: { 7, 8, 9, 10, 12, 13, 14, 15, 25, 26, 27, 28, 29, 31, 32, 33, 34, 74, 75, 89, 93, 96, 99
}
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 11, 16, 17, 18, 19, 20, 21, 22, 23, 24, 30, 35, 36, 37, 38, 39, 40, 41, 42,
43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 64, 67, 68, 69, 76, 77, 78, 79, 80, 81,
82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 94, 95, 97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108
}
2.2 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2)
if the failure was due to an exception being raised, which could indicate a bug in the system. If
the failure was due to integral not being evaluated within the time limit, then it is given just an
F.
In this table,the column normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 404 | 385 | 336 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.95 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.493 |
0.409 |
0.115 |
0.000 |
0.427 |
0.000 |
0.000 |
0.000 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 263 | 242 | 217 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.92 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.337 |
0.214 |
0.070 |
0.000 |
0.423 |
0.000 |
0.000 |
0.000 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 135 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.225 |
0.096 |
0.077 |
0.000 |
0.451 |
0.000 |
0.000 |
0.000 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 217 | 217 | 185 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.332 |
0.155 |
0.218 |
0.000 |
0.425 |
0.000 |
0.000 |
0.000 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 322 | 352 | 295 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.09 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.494 |
0.478 |
0.069 |
0.000 |
0.430 |
0.000 |
0.000 |
0.000 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 531 | 562 | 470 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.06 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.797 |
1.225 |
0.072 |
0.000 |
0.419 |
0.000 |
0.000 |
0.000 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
B |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 201 | 201 | 185 | 0 | 395 | 624 | 0 | 560 | 886 |
normalized size | 1 | 1.00 | 0.92 | 0.00 | 1.97 | 3.10 | 0.00 | 2.79 | 4.41 |
time (sec) |
N/A |
0.095 |
0.308 |
1.076 |
0.739 |
0.434 |
0.000 |
34.441 |
0.697 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
A |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 172 | 172 | 154 | 0 | 285 | 469 | 0 | 407 | 501 |
normalized size | 1 | 1.00 | 0.90 | 0.00 | 1.66 | 2.73 | 0.00 | 2.37 | 2.91 |
time (sec) |
N/A |
0.072 |
0.215 |
0.305 |
0.907 |
0.441 |
0.000 |
8.961 |
0.533 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
A |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 127 | 0 | 194 | 325 | 0 | 269 | 255 |
normalized size | 1 | 1.00 | 0.89 | 0.00 | 1.36 | 2.27 | 0.00 | 1.88 | 1.78 |
time (sec) |
N/A |
0.061 |
0.138 |
0.293 |
0.654 |
0.433 |
0.000 |
2.355 |
0.469 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 105 | 0 | 118 | 197 | 427 | 148 | 128 |
normalized size | 1 | 1.00 | 0.91 | 0.00 | 1.02 | 1.70 | 3.68 | 1.28 | 1.10 |
time (sec) |
N/A |
0.043 |
0.200 |
0.156 |
0.682 |
0.420 |
60.278 |
0.713 |
0.401 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 93 | 0 | 164 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.87 | 0.00 | 1.53 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.083 |
0.108 |
0.327 |
0.801 |
0.425 |
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 |
F |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 89 | 0 | 99 | 120 | 1931 | 112 | 99 |
normalized size | 1 | 1.00 | 0.94 | 0.00 | 1.04 | 1.26 | 20.33 | 1.18 | 1.04 |
time (sec) |
N/A |
0.037 |
0.055 |
0.305 |
0.710 |
0.427 |
139.980 |
0.192 |
2.160 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
A |
B |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 116 | 0 | 165 | 323 | 0 | 246 | 182 |
normalized size | 1 | 1.00 | 0.86 | 0.00 | 1.22 | 2.39 | 0.00 | 1.82 | 1.35 |
time (sec) |
N/A |
0.056 |
0.243 |
0.313 |
0.748 |
0.440 |
0.000 |
0.225 |
2.389 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
A |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 164 | 164 | 141 | 0 | 289 | 580 | 0 | 469 | 346 |
normalized size | 1 | 1.00 | 0.86 | 0.00 | 1.76 | 3.54 | 0.00 | 2.86 | 2.11 |
time (sec) |
N/A |
0.069 |
0.358 |
0.307 |
0.735 |
0.438 |
0.000 |
0.231 |
2.869 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
B |
B |
F(-2) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 193 | 193 | 164 | 0 | 459 | 861 | 0 | 748 | 526 |
normalized size | 1 | 1.00 | 0.85 | 0.00 | 2.38 | 4.46 | 0.00 | 3.88 | 2.73 |
time (sec) |
N/A |
0.085 |
0.357 |
0.306 |
0.848 |
0.441 |
0.000 |
0.206 |
3.712 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
F |
A |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 920 | 920 | 2508 | 0 | 1421 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.73 | 0.00 | 1.54 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.845 |
2.867 |
0.316 |
1.099 |
0.500 |
0.000 |
0.000 |
0.000 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
F |
A |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 805 | 805 | 1853 | 0 | 1071 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.30 | 0.00 | 1.33 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.665 |
2.086 |
0.307 |
1.192 |
0.481 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 686 | 686 | 1211 | 0 | 769 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.77 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.533 |
1.287 |
0.300 |
0.879 |
0.457 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 540 | 540 | 781 | 0 | 504 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.45 | 0.00 | 0.93 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.391 |
0.677 |
0.151 |
1.130 |
0.426 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
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|
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 | 431 | 431 | 460 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.492 |
0.203 |
0.311 |
0.000 |
0.410 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 465 | 465 | 411 | 0 | 392 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.88 | 0.00 | 0.84 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.387 |
0.710 |
0.310 |
0.895 |
0.455 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 632 | 632 | 872 | 0 | 755 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.38 | 0.00 | 1.19 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.490 |
1.329 |
0.312 |
1.098 |
0.471 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 764 | 764 | 1407 | 0 | 1252 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.84 | 0.00 | 1.64 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.606 |
1.945 |
0.309 |
1.727 |
0.536 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 884 | 884 | 2003 | 0 | 1816 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.27 | 0.00 | 2.05 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.738 |
3.001 |
0.305 |
1.675 |
0.718 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
B |
F(-1) |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 334 | 334 | 275 | 0 | 624 | 945 | 0 | 0 | 1128 |
normalized size | 1 | 1.00 | 0.82 | 0.00 | 1.87 | 2.83 | 0.00 | 0.00 | 3.38 |
time (sec) |
N/A |
0.186 |
0.332 |
0.294 |
0.792 |
0.417 |
0.000 |
0.000 |
1.034 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F(-1) |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 276 | 276 | 231 | 0 | 431 | 679 | 0 | 0 | 641 |
normalized size | 1 | 1.00 | 0.84 | 0.00 | 1.56 | 2.46 | 0.00 | 0.00 | 2.32 |
time (sec) |
N/A |
0.127 |
0.292 |
0.304 |
0.789 |
0.431 |
0.000 |
0.000 |
0.829 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 218 | 218 | 209 | 0 | 269 | 441 | 0 | 357 | 328 |
normalized size | 1 | 1.00 | 0.96 | 0.00 | 1.23 | 2.02 | 0.00 | 1.64 | 1.50 |
time (sec) |
N/A |
0.099 |
0.244 |
0.291 |
0.920 |
0.444 |
0.000 |
100.515 |
0.652 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 120 | 0 | 143 | 242 | 632 | 0 | 153 |
normalized size | 1 | 1.00 | 0.75 | 0.00 | 0.89 | 1.51 | 3.95 | 0.00 | 0.96 |
time (sec) |
N/A |
0.069 |
0.206 |
0.157 |
0.574 |
0.408 |
75.965 |
0.000 |
0.507 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 61 | 61 | 57 | 61 | 75 | 72 | 187 | 66 | 60 |
normalized size | 1 | 1.00 | 0.93 | 1.00 | 1.23 | 1.18 | 3.07 | 1.08 | 0.98 |
time (sec) |
N/A |
0.015 |
0.070 |
0.053 |
0.618 |
0.412 |
17.644 |
0.204 |
0.218 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 163 | 0 | 186 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 0.00 | 1.26 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.120 |
0.096 |
0.324 |
0.929 |
0.428 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 93 | 0 | 123 | 280 | 0 | 190 | 152 |
normalized size | 1 | 1.00 | 0.73 | 0.00 | 0.96 | 2.19 | 0.00 | 1.48 | 1.19 |
time (sec) |
N/A |
0.052 |
0.189 |
0.309 |
0.721 |
109.509 |
0.000 |
0.371 |
1.199 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F(-1) |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 202 | 202 | 206 | 0 | 232 | 0 | 0 | 595 | 384 |
normalized size | 1 | 1.00 | 1.02 | 0.00 | 1.15 | 0.00 | 0.00 | 2.95 | 1.90 |
time (sec) |
N/A |
0.112 |
0.530 |
0.308 |
0.783 |
0.000 |
0.000 |
0.570 |
2.709 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F(-1) |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 260 | 260 | 254 | 0 | 456 | 0 | 0 | 1765 | 977 |
normalized size | 1 | 1.00 | 0.98 | 0.00 | 1.75 | 0.00 | 0.00 | 6.79 | 3.76 |
time (sec) |
N/A |
0.152 |
0.763 |
0.310 |
0.765 |
0.000 |
0.000 |
0.851 |
5.479 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F(-1) |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 318 | 318 | 480 | 0 | 776 | 0 | 0 | 3911 | 2215 |
normalized size | 1 | 1.00 | 1.51 | 0.00 | 2.44 | 0.00 | 0.00 | 12.30 | 6.97 |
time (sec) |
N/A |
0.195 |
1.493 |
0.316 |
1.034 |
0.000 |
0.000 |
1.173 |
10.154 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2240 | 2220 | 1386 | 0 | 1799 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 0.62 | 0.00 | 0.80 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.436 |
3.394 |
0.299 |
1.308 |
1.386 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1645 | 1657 | 899 | 0 | 1123 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.01 | 0.55 | 0.00 | 0.68 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.758 |
2.033 |
0.300 |
1.181 |
1.585 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1063 | 1097 | 480 | 0 | 623 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.03 | 0.45 | 0.00 | 0.59 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.163 |
0.928 |
0.155 |
1.095 |
0.872 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 269 | 269 | 389 | 0 | 298 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.45 | 0.00 | 1.11 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.153 |
0.235 |
0.114 |
0.877 |
1.546 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 1471 | 2096 | 1370 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.42 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.931 |
0.294 |
0.323 |
0.000 |
0.735 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
A |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 832 | 878 | 2930 | 0 | 745 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.06 | 3.52 | 0.00 | 0.90 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.932 |
1.344 |
0.311 |
1.795 |
0.617 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
A |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1304 | 1362 | 15960 | 0 | 1857 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.04 | 12.24 | 0.00 | 1.42 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.408 |
6.312 |
0.326 |
3.862 |
1.753 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1957 | 2013 | 47127 | 0 | 4732 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.03 | 24.08 | 0.00 | 2.42 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.102 |
6.529 |
0.323 |
8.912 |
1.249 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 42 | 0 | 0 | 56 | 94 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.33 | 2.24 | 0.00 | -0.02 |
time (sec) |
N/A |
0.080 |
0.032 |
0.356 |
0.000 |
0.785 |
133.766 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 37 | 0 | 526 | 101 | 65 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 14.22 | 2.73 | 1.76 | 0.00 | -0.03 |
time (sec) |
N/A |
0.061 |
0.009 |
0.314 |
1.529 |
0.950 |
12.571 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 37 | 0 | 268 | 74 | 65 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 7.24 | 2.00 | 1.76 | 0.00 | -0.03 |
time (sec) |
N/A |
0.063 |
0.011 |
0.316 |
1.250 |
0.833 |
9.966 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 37 | 0 | 105 | 47 | 61 | 86 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 2.84 | 1.27 | 1.65 | 2.32 | -0.03 |
time (sec) |
N/A |
0.038 |
0.007 |
0.324 |
1.018 |
0.885 |
9.304 |
0.214 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 34 | 0 | 36 | 30 | 53 | 31 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 1.06 | 0.88 | 1.56 | 0.91 | -0.03 |
time (sec) |
N/A |
0.068 |
0.037 |
0.313 |
1.758 |
0.644 |
23.959 |
0.241 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F(-1) |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 34 | 0 | 34 | 29 | 0 | 34 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 1.00 | 0.85 | 0.00 | 1.00 | -0.03 |
time (sec) |
N/A |
0.065 |
0.010 |
0.308 |
1.843 |
0.652 |
0.000 |
0.218 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
F(-1) |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 37 | 0 | 80 | 59 | 0 | 85 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 2.16 | 1.59 | 0.00 | 2.30 | -0.03 |
time (sec) |
N/A |
0.065 |
0.011 |
0.311 |
2.164 |
1.099 |
0.000 |
0.327 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
B |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 30 | 0 | 83 | 24 | 65 | 58 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 2.77 | 0.80 | 2.17 | 1.93 | -0.03 |
time (sec) |
N/A |
0.023 |
0.009 |
0.321 |
2.531 |
0.608 |
6.276 |
0.276 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 410 | 410 | 22595 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 55.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.471 |
7.488 |
0.642 |
0.000 |
0.767 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 306 | 306 | 436 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.288 |
1.541 |
0.512 |
0.000 |
0.625 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 172 | 172 | 166 | 0 | 204 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.00 | 1.19 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.136 |
0.090 |
0.324 |
1.197 |
0.689 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.053 |
0.386 |
0.519 |
0.000 |
0.635 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.053 |
2.872 |
0.528 |
0.000 |
0.508 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 328 | 328 | 1241 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.252 |
1.842 |
2.920 |
0.000 |
0.999 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 262 | 262 | 839 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.910 |
0.883 |
1.728 |
0.000 |
0.643 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 451 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.603 |
0.433 |
1.707 |
0.000 |
1.144 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 78 | 0 | 126 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 0.00 | 1.56 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.066 |
0.075 |
0.115 |
1.140 |
1.218 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.545 |
0.487 |
1.691 |
0.000 |
0.669 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.425 |
2.546 |
1.725 |
0.000 |
0.967 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.021 |
5.095 |
0.423 |
0.000 |
1.495 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.021 |
5.088 |
0.319 |
0.000 |
0.721 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 66 | 450 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.80 | 5.49 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.177 |
5.033 |
0.183 |
0.000 |
0.635 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.022 |
5.100 |
0.145 |
0.000 |
0.589 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.022 |
33.658 |
0.353 |
0.000 |
1.094 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 620 | 649 | 18164 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.05 | 29.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.133 |
22.153 |
12.089 |
0.000 |
0.682 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 496 | 517 | 9211 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.04 | 18.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.819 |
10.211 |
9.230 |
0.000 |
0.717 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 371 | 384 | 1408 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.04 | 3.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.558 |
3.166 |
6.677 |
0.000 |
1.269 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.500 |
2.014 |
52.396 |
0.000 |
0.606 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
F(-1) |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 93 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.128 |
1.325 |
180.000 |
0.000 |
1.987 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.519 |
0.650 |
0.920 |
0.000 |
1.387 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.484 |
0.639 |
0.858 |
0.000 |
1.713 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
C |
A |
A |
A |
F |
B |
verified |
N/A |
N/A |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 0 | 44 | 662 | 59 | 50 | 44 | 0 | 44 |
normalized size | 1 | 0.00 | 0.98 | 14.71 | 1.31 | 1.11 | 0.98 | 0.00 | 0.98 |
time (sec) |
N/A |
0.516 |
0.319 |
1.160 |
1.022 |
0.536 |
2.170 |
0.000 |
0.701 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
C |
A |
A |
A |
F |
B |
verified |
N/A |
N/A |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 0 | 45 | 503 | 58 | 49 | 44 | 0 | 44 |
normalized size | 1 | 0.00 | 1.00 | 11.18 | 1.29 | 1.09 | 0.98 | 0.00 | 0.98 |
time (sec) |
N/A |
0.512 |
0.089 |
1.059 |
1.308 |
1.465 |
2.146 |
0.000 |
0.537 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 560 | 560 | 461 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.735 |
0.386 |
0.327 |
0.000 |
0.715 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 550 | 550 | 467 | 0 | 1047 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.85 | 0.00 | 1.90 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.565 |
0.255 |
0.310 |
2.214 |
0.559 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 403 | 403 | 413 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.352 |
0.130 |
0.313 |
0.000 |
1.800 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 291 | 468 | 421 | 0 | 349 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.61 | 1.45 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.317 |
0.109 |
0.307 |
1.843 |
0.584 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 518 | 518 | 487 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.602 |
0.196 |
0.311 |
0.000 |
1.483 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 596 | 596 | 479 | 0 | 969 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.80 | 0.00 | 1.63 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.583 |
0.402 |
0.314 |
2.375 |
0.648 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1046 | 1046 | 1240 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.717 |
1.479 |
0.946 |
0.000 |
0.577 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 831 | 831 | 1105 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.068 |
4.107 |
0.828 |
0.000 |
0.832 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 685 | 685 | 539 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.636 |
0.730 |
0.858 |
0.000 |
0.710 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 401 | 545 | 515 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.36 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.518 |
0.353 |
0.855 |
0.000 |
1.474 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 800 | 800 | 625 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.980 |
0.937 |
0.832 |
0.000 |
0.592 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 995 | 995 | 721 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.291 |
0.883 |
0.858 |
0.000 |
0.635 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 84 | 97 | 95 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.83 | 2.11 | 2.07 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.159 |
0.016 |
0.076 |
0.684 |
0.654 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 29 | 141 | 18 | 14 | 0 | 18 |
normalized size | 1 | 1.00 | 1.00 | 1.45 | 7.05 | 0.90 | 0.70 | 0.00 | 0.90 |
time (sec) |
N/A |
0.058 |
0.102 |
0.045 |
0.613 |
0.677 |
0.291 |
0.000 |
0.257 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
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 | 82 | 82 | 76 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.168 |
0.014 |
0.624 |
0.000 |
0.946 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
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 | 150 | 150 | 110 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.248 |
0.038 |
1.093 |
0.000 |
0.671 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 559 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.250 |
0.454 |
10.225 |
0.000 |
0.710 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 28 | 44 | 25 | 29 | 20 | 153 | 25 |
normalized size | 1 | 1.00 | 1.12 | 1.76 | 1.00 | 1.16 | 0.80 | 6.12 | 1.00 |
time (sec) |
N/A |
0.012 |
0.005 |
0.123 |
0.631 |
0.711 |
0.268 |
0.180 |
0.081 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 63 | 0 | 113 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 0.00 | 1.69 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.074 |
0.016 |
0.620 |
0.661 |
0.729 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
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 | 97 | 97 | 91 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.110 |
0.026 |
0.522 |
0.000 |
0.642 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 28 | 40 | 28 | 42 | 26 | 29 | 28 |
normalized size | 1 | 1.00 | 1.00 | 1.43 | 1.00 | 1.50 | 0.93 | 1.04 | 1.00 |
time (sec) |
N/A |
0.007 |
0.003 |
0.058 |
0.989 |
0.710 |
0.277 |
0.182 |
0.148 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 106 | 0 | 118 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.58 | 0.00 | 1.76 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.157 |
0.016 |
0.363 |
1.050 |
0.776 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
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 | 102 | 102 | 98 | 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 |
0.132 |
0.025 |
0.302 |
0.000 |
0.693 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 28 | 79 | 28 | 41 | 26 | 29 | 28 |
normalized size | 1 | 1.00 | 1.00 | 2.82 | 1.00 | 1.46 | 0.93 | 1.04 | 1.00 |
time (sec) |
N/A |
0.007 |
0.003 |
0.123 |
0.893 |
0.624 |
0.296 |
0.252 |
0.149 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 106 | 0 | 118 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.58 | 0.00 | 1.76 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.155 |
0.014 |
0.570 |
1.117 |
0.799 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
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 | 98 | 102 | 98 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.04 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.127 |
0.026 |
0.558 |
0.000 |
0.811 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
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 | 35 | 35 | 30 | 36 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.86 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.064 |
0.012 |
0.050 |
0.000 |
0.635 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
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 | 85 | 85 | 68 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.134 |
0.025 |
1.302 |
0.000 |
0.775 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 149 | 135 | 879 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.06 | 0.96 | 6.28 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.180 |
0.043 |
0.049 |
0.000 |
0.668 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
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 | 109 | 109 | 96 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.164 |
0.027 |
2.766 |
0.000 |
0.667 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F(-2) |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 204 | 206 | 1636 | 357 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.01 | 8.02 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.254 |
0.521 |
0.051 |
0.000 |
0.708 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 322 | 334 | 1080 | 4733 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.04 | 3.35 | 14.70 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.507 |
0.283 |
0.059 |
0.000 |
1.342 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
F |
F(-2) |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 433 | 445 | 908 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.03 | 2.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.594 |
0.815 |
3.091 |
0.000 |
0.604 |
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 [42] had the largest ratio of
[.5484]
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| Table 2.1:Rubi specific breakdown of results for each
integral
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# |
grade |
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normalized | antiderivative |
leaf size | |
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\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) |
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1 |
A |
20 |
10 |
0.95 |
32 |
0.312 |
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2 |
A |
16 |
10 |
0.92 |
32 |
0.312 |
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3 |
A |
12 |
7 |
1.00 |
30 |
0.233 |
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4 |
A |
14 |
8 |
1.00 |
32 |
0.250 |
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5 |
A |
18 |
11 |
1.09 |
32 |
0.344 |
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6 |
A |
22 |
11 |
1.06 |
32 |
0.344 |
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7 |
A |
4 |
3 |
1.00 |
29 |
0.103 |
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8 |
A |
4 |
3 |
1.00 |
29 |
0.103 |
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9 |
A |
4 |
3 |
1.00 |
29 |
0.103 |
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10 |
A |
4 |
2 |
1.00 |
27 |
0.074 |
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11 |
A |
6 |
6 |
1.00 |
29 |
0.207 |
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12 |
A |
5 |
4 |
1.00 |
29 |
0.138 |
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13 |
A |
4 |
3 |
1.00 |
29 |
0.103 |
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14 |
A |
4 |
3 |
1.00 |
29 |
0.103 |
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15 |
A |
4 |
3 |
1.00 |
29 |
0.103 |
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16 |
A |
32 |
14 |
1.00 |
31 |
0.452 |
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17 |
A |
28 |
14 |
1.00 |
31 |
0.452 |
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18 |
A |
24 |
14 |
1.00 |
31 |
0.452 |
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19 |
A |
20 |
13 |
1.00 |
29 |
0.448 |
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20 |
A |
19 |
15 |
1.00 |
31 |
0.484 |
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21 |
A |
20 |
12 |
1.00 |
31 |
0.387 |
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22 |
A |
24 |
13 |
1.00 |
31 |
0.419 |
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23 |
A |
28 |
13 |
1.00 |
31 |
0.419 |
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24 |
A |
32 |
13 |
1.00 |
31 |
0.419 |
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25 |
A |
5 |
2 |
1.00 |
29 |
0.069 |
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26 |
A |
5 |
2 |
1.00 |
29 |
0.069 |
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27 |
A |
5 |
2 |
1.00 |
29 |
0.069 |
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28 |
A |
5 |
2 |
1.00 |
27 |
0.074 |
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29 |
A |
3 |
3 |
1.00 |
21 |
0.143 |
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30 |
A |
7 |
4 |
1.00 |
29 |
0.138 |
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31 |
A |
7 |
3 |
1.00 |
29 |
0.103 |
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32 |
A |
5 |
2 |
1.00 |
29 |
0.069 |
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33 |
A |
5 |
2 |
1.00 |
29 |
0.069 |
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34 |
A |
5 |
2 |
1.00 |
29 |
0.069 |
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35 |
A |
49 |
14 |
0.99 |
31 |
0.452 |
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36 |
A |
47 |
15 |
1.01 |
31 |
0.484 |
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37 |
A |
39 |
15 |
1.03 |
29 |
0.517 |
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38 |
A |
10 |
9 |
1.00 |
23 |
0.391 |
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39 |
A |
29 |
14 |
1.42 |
31 |
0.452 |
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40 |
A |
35 |
12 |
1.06 |
31 |
0.387 |
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41 |
A |
47 |
16 |
1.04 |
31 |
0.516 |
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42 |
A |
61 |
17 |
1.03 |
31 |
0.548 |
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43 |
A |
3 |
3 |
1.00 |
40 |
0.075 |
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44 |
A |
3 |
3 |
1.00 |
40 |
0.075 |
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45 |
A |
3 |
3 |
1.00 |
40 |
0.075 |
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46 |
A |
2 |
2 |
1.00 |
38 |
0.053 |
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47 |
A |
3 |
3 |
1.00 |
40 |
0.075 |
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48 |
A |
3 |
3 |
1.00 |
40 |
0.075 |
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49 |
A |
3 |
3 |
1.00 |
40 |
0.075 |
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50 |
A |
1 |
1 |
1.00 |
34 |
0.029 |
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51 |
A |
11 |
6 |
1.00 |
48 |
0.125 |
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52 |
A |
9 |
5 |
1.00 |
46 |
0.109 |
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53 |
A |
7 |
4 |
1.00 |
32 |
0.125 |
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54 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
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55 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
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56 |
A |
13 |
6 |
1.00 |
39 |
0.154 |
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57 |
A |
11 |
6 |
1.00 |
39 |
0.154 |
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58 |
A |
9 |
5 |
1.00 |
37 |
0.135 |
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59 |
A |
5 |
3 |
1.00 |
25 |
0.120 |
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60 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
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61 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
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62 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
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63 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
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64 |
A |
5 |
5 |
1.00 |
26 |
0.192 |
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65 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
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66 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
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67 |
A |
12 |
7 |
1.05 |
45 |
0.156 |
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68 |
A |
10 |
7 |
1.04 |
45 |
0.156 |
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69 |
A |
8 |
6 |
1.04 |
43 |
0.140 |
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70 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
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71 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
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72 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
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73 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
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74 |
F |
0 |
0 |
N/A |
0 |
N/A |
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75 |
F |
0 |
0 |
N/A |
0 |
N/A |
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76 |
A |
30 |
9 |
1.00 |
32 |
0.281 |
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77 |
A |
27 |
10 |
1.00 |
32 |
0.312 |
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78 |
A |
18 |
6 |
1.00 |
30 |
0.200 |
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79 |
A |
18 |
6 |
1.61 |
29 |
0.207 |
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80 |
A |
29 |
11 |
1.00 |
32 |
0.344 |
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81 |
A |
31 |
12 |
1.00 |
32 |
0.375 |
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82 |
A |
37 |
14 |
1.00 |
34 |
0.412 |
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83 |
A |
30 |
12 |
1.00 |
34 |
0.353 |
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84 |
A |
21 |
9 |
1.00 |
32 |
0.281 |
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85 |
A |
19 |
7 |
1.36 |
31 |
0.226 |
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86 |
A |
31 |
12 |
1.00 |
34 |
0.353 |
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87 |
A |
40 |
16 |
1.00 |
34 |
0.471 |
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88 |
A |
5 |
5 |
1.00 |
19 |
0.263 |
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89 |
A |
1 |
1 |
1.00 |
24 |
0.042 |
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90 |
A |
3 |
3 |
1.00 |
34 |
0.088 |
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91 |
A |
3 |
3 |
1.00 |
55 |
0.055 |
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92 |
A |
3 |
3 |
1.00 |
58 |
0.052 |
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93 |
A |
4 |
4 |
1.00 |
11 |
0.364 |
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94 |
A |
5 |
5 |
1.00 |
13 |
0.385 |
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95 |
A |
7 |
7 |
1.00 |
13 |
0.538 |
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96 |
A |
2 |
2 |
1.00 |
13 |
0.154 |
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97 |
A |
6 |
6 |
1.00 |
15 |
0.400 |
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98 |
A |
4 |
4 |
1.00 |
15 |
0.267 |
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99 |
A |
2 |
2 |
1.00 |
13 |
0.154 |
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100 |
A |
6 |
6 |
1.00 |
15 |
0.400 |
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101 |
A |
4 |
4 |
1.04 |
15 |
0.267 |
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102 |
A |
1 |
1 |
1.00 |
38 |
0.026 |
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103 |
A |
2 |
2 |
1.00 |
50 |
0.040 |
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104 |
A |
3 |
3 |
1.06 |
42 |
0.071 |
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105 |
A |
2 |
2 |
1.00 |
62 |
0.032 |
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106 |
A |
3 |
3 |
1.01 |
49 |
0.061 |
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107 |
A |
7 |
5 |
1.04 |
42 |
0.119 |
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108 |
A |
8 |
6 |
1.03 |
65 |
0.092 |
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