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, 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, 98, 99, 100 }
B grade: { 38, 97 }
C grade: { 39 }
F grade: { }
2.1.2 Mathematica
A grade: { 8, 9, 10, 11, 12, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 32, 34, 39, 40, 41, 42, 43, 44,
47, 51, 53, 55, 56, 57, 58, 59, 60, 61, 62, 64, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 80, 82, 83, 84, 85, 86,
87, 89, 91, 93, 94, 95, 96, 98, 99, 100 }
B grade: { 4, 6, 7, 29, 31, 36, 38, 97 }
C grade: { 1, 2, 3, 5, 13, 14, 18, 33, 35, 37, 45, 46, 48, 49, 50, 52, 54, 63, 65, 67, 77, 79, 81, 90, 92
}
F grade: { 19, 88 }
2.1.3 Maple
A grade: { 1, 2, 3, 4, 9, 10, 11, 13, 14, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 36, 38, 39, 40, 41,
42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 66, 68, 70, 71, 72, 73, 74, 75, 89, 91, 93, 95, 97, 98, 99
}
B grade: { 6, 7, 8, 80 }
C grade: { 5, 33, 35, 37, 51, 55, 63, 65, 67, 69, 76, 78, 90, 92, 94, 96 }
F grade: { 12, 15, 16, 17, 18, 19, 30, 56, 57, 58, 59, 60, 61, 62, 64, 77, 79, 81, 82, 83, 84, 85, 86, 87, 88, 100
}
2.1.4 Maxima
A grade: { 4, 20, 21, 22, 23, 25, 26, 27, 28, 32, 34, 39, 41, 43, 47, 66, 71, 73, 75, 99, 100 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 24, 29, 30, 31, 33, 35, 36, 37, 38, 40,
42, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69,
70, 72, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98
}
2.1.5 FriCAS
A grade: { 1, 20, 21, 22, 23, 25, 26, 27, 28, 32, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 55, 63, 65,
66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 91, 94, 96, 97
}
B grade: { 2, 3, 4, 6, 7, 8, 36, 38, 51, 53, 90, 92, 93, 95, 99, 100 }
C grade: { }
F grade: { 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 24, 29, 30, 31, 46, 48, 50, 52, 54, 56, 57, 58, 59, 60, 61,
62, 64, 88, 98 }
2.1.6 Sympy
A grade: { 93 }
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, 94, 95, 96, 97, 98, 99, 100 }
2.1.7 Giac
A grade: { 82 }
B grade: { 45, 47, 49, 53, 71 }
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, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62,
63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93,
94, 95, 96, 97, 98, 99, 100 }
2.1.8 Mupad
A grade: { }
B grade: { 4, 25, 28, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 49, 51, 53, 55, 65, 66, 67, 68,
69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99,
100 }
C grade: { }
F grade: { 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 29, 30, 31, 46,
48, 50, 52, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 88, 98 }
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 |
C |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 203 | 203 | 225 | 250 | 0 | 345 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.11 | 1.23 | 0.00 | 1.70 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.155 |
0.542 |
0.102 |
0.000 |
0.483 |
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 |
C |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 153 | 153 | 200 | 189 | 0 | 327 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.31 | 1.24 | 0.00 | 2.14 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.099 |
0.284 |
0.070 |
0.000 |
1.921 |
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 |
C |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 176 | 111 | 0 | 308 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.64 | 1.04 | 0.00 | 2.88 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.062 |
0.168 |
0.070 |
0.000 |
1.393 |
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 |
B |
A |
A |
B |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 44 | 44 | 125 | 50 | 31 | 253 | 0 | 0 | 43 |
normalized size | 1 | 1.00 | 2.84 | 1.14 | 0.70 | 5.75 | 0.00 | 0.00 | 0.98 |
time (sec) |
N/A |
0.056 |
0.314 |
0.047 |
0.303 |
0.762 |
0.000 |
0.000 |
2.161 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 170 | 170 | 332 | 886 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.95 | 5.21 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.290 |
0.204 |
0.955 |
0.000 |
0.666 |
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 |
B |
B |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 244 | 542 | 0 | 651 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.49 | 7.74 | 0.00 | 9.30 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.106 |
0.257 |
0.084 |
0.000 |
0.707 |
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 |
B |
B |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 315 | 1233 | 0 | 865 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.37 | 9.27 | 0.00 | 6.50 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.204 |
0.974 |
0.090 |
0.000 |
0.689 |
0.000 |
0.000 |
0.000 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 197 | 197 | 368 | 1946 | 0 | 987 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.87 | 9.88 | 0.00 | 5.01 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.316 |
0.389 |
0.099 |
0.000 |
0.695 |
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 |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 279 | 279 | 305 | 655 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.09 | 2.35 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.242 |
1.995 |
1.678 |
0.000 |
1.288 |
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 |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 172 | 396 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.15 | 2.66 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.138 |
0.430 |
1.310 |
0.000 |
0.621 |
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 |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 105 | 209 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.31 | 2.61 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.068 |
0.227 |
0.339 |
0.000 |
0.786 |
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 |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 274 | 274 | 280 | 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 |
0.463 |
0.305 |
0.801 |
0.000 |
0.966 |
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 |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 224 | 224 | 678 | 367 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.03 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.389 |
2.690 |
0.751 |
0.000 |
0.559 |
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 |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 537 | 537 | 1439 | 1026 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.68 | 1.91 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.750 |
7.576 |
1.292 |
0.000 |
0.513 |
0.000 |
0.000 |
0.000 |
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Problem 15 |
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 |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 260 | 260 | 254 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.257 |
0.542 |
1.885 |
0.000 |
0.606 |
0.000 |
0.000 |
0.000 |
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Problem 16 |
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 |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 153 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.105 |
0.141 |
0.610 |
0.000 |
0.568 |
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 |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 378 | 378 | 384 | 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 |
0.511 |
0.324 |
0.810 |
0.000 |
0.577 |
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 |
C |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 330 | 330 | 1849 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 5.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.575 |
46.916 |
0.896 |
0.000 |
1.036 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
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|
|
|
|
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|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 965 | 965 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.338 |
9.954 |
1.667 |
0.000 |
0.558 |
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 |
A |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 164 | 164 | 84 | 54 | 58 | 57 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.51 | 0.33 | 0.35 | 0.35 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.030 |
0.044 |
0.074 |
0.324 |
0.636 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 126 | 72 | 49 | 46 | 52 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.57 | 0.39 | 0.37 | 0.41 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.027 |
0.031 |
0.069 |
0.338 |
0.519 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 56 | 42 | 34 | 45 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.64 | 0.48 | 0.39 | 0.51 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.018 |
0.026 |
0.062 |
0.376 |
0.630 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 67 | 36 | 19 | 39 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.56 | 0.84 | 0.44 | 0.91 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.007 |
0.096 |
0.059 |
0.388 |
0.562 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 45 | 65 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.095 |
0.039 |
0.101 |
0.000 |
0.570 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
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 | 98 | 98 | 111 | 64 | 65 | 45 | 0 | 0 | 40 |
normalized size | 1 | 1.00 | 1.13 | 0.65 | 0.66 | 0.46 | 0.00 | 0.00 | 0.41 |
time (sec) |
N/A |
0.023 |
0.077 |
0.072 |
0.300 |
0.608 |
0.000 |
0.000 |
2.150 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 125 | 79 | 92 | 54 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.92 | 0.58 | 0.68 | 0.40 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.033 |
0.116 |
0.073 |
0.342 |
1.086 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 172 | 172 | 140 | 91 | 116 | 60 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.81 | 0.53 | 0.67 | 0.35 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.040 |
0.133 |
0.072 |
0.315 |
1.385 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
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 | 21 | 21 | 25 | 29 | 16 | 22 | 0 | 0 | 17 |
normalized size | 1 | 1.00 | 1.19 | 1.38 | 0.76 | 1.05 | 0.00 | 0.00 | 0.81 |
time (sec) |
N/A |
0.007 |
0.025 |
0.061 |
0.318 |
0.635 |
0.000 |
0.000 |
1.349 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 61 | 61 | 219 | 116 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.59 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.105 |
0.983 |
0.150 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
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 | 54 | 54 | 49 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.107 |
0.047 |
0.180 |
0.000 |
0.696 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 249 | 140 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.23 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.101 |
1.173 |
0.148 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F(-2) |
B |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 83 | 65 | 64 | 47 | 65 | 0 | 0 | 75 |
normalized size | 1 | 1.30 | 1.02 | 1.00 | 0.73 | 1.02 | 0.00 | 0.00 | 1.17 |
time (sec) |
N/A |
0.038 |
0.094 |
0.057 |
0.379 |
0.552 |
0.000 |
0.000 |
1.469 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 97 | 118 | 0 | 95 | 0 | 0 | 521 |
normalized size | 1 | 1.00 | 1.15 | 1.40 | 0.00 | 1.13 | 0.00 | 0.00 | 6.20 |
time (sec) |
N/A |
0.032 |
0.133 |
0.058 |
0.000 |
0.512 |
0.000 |
0.000 |
11.925 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-2) |
B |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 52 | 48 | 54 | 38 | 54 | 0 | 0 | 55 |
normalized size | 1 | 1.37 | 1.26 | 1.42 | 1.00 | 1.42 | 0.00 | 0.00 | 1.45 |
time (sec) |
N/A |
0.024 |
0.063 |
0.049 |
0.401 |
0.758 |
0.000 |
0.000 |
1.433 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F(-1) |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 75 | 92 | 0 | 79 | 0 | 0 | 303 |
normalized size | 1 | 1.00 | 1.42 | 1.74 | 0.00 | 1.49 | 0.00 | 0.00 | 5.72 |
time (sec) |
N/A |
0.018 |
0.079 |
0.052 |
0.000 |
0.619 |
0.000 |
0.000 |
6.959 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
B |
F |
F |
B |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 39 | 79 | 80 | 0 | 115 | 0 | 0 | 182 |
normalized size | 1 | 1.62 | 3.29 | 3.33 | 0.00 | 4.79 | 0.00 | 0.00 | 7.58 |
time (sec) |
N/A |
0.137 |
0.044 |
0.056 |
0.000 |
0.696 |
0.000 |
0.000 |
2.983 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
B |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 64 | 75 | 92 | 0 | 77 | 0 | 0 | 184 |
normalized size | 1 | 1.33 | 1.56 | 1.92 | 0.00 | 1.60 | 0.00 | 0.00 | 3.83 |
time (sec) |
N/A |
0.031 |
0.047 |
0.056 |
0.000 |
0.698 |
0.000 |
0.000 |
3.104 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
B |
A |
F |
B |
F |
F |
B |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 99 | 93 | 91 | 0 | 128 | 0 | 0 | 71 |
normalized size | 1 | 2.83 | 2.66 | 2.60 | 0.00 | 3.66 | 0.00 | 0.00 | 2.03 |
time (sec) |
N/A |
0.041 |
0.063 |
0.054 |
0.000 |
0.808 |
0.000 |
0.000 |
1.842 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
F |
F |
B |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 84 | 43 | 53 | 43 | 52 | 0 | 0 | 58 |
normalized size | 1 | 1.53 | 0.78 | 0.96 | 0.78 | 0.95 | 0.00 | 0.00 | 1.05 |
time (sec) |
N/A |
0.037 |
0.043 |
0.053 |
0.368 |
0.663 |
0.000 |
0.000 |
1.473 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 110 | 110 | 0 | 138 | 0 | 0 | 602 |
normalized size | 1 | 1.00 | 0.83 | 0.83 | 0.00 | 1.05 | 0.00 | 0.00 | 4.56 |
time (sec) |
N/A |
0.059 |
0.078 |
0.056 |
0.000 |
0.652 |
0.000 |
0.000 |
13.421 |
|
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Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 60 | 63 | 51 | 60 | 0 | 0 | 76 |
normalized size | 1 | 1.00 | 0.52 | 0.55 | 0.44 | 0.52 | 0.00 | 0.00 | 0.66 |
time (sec) |
N/A |
0.052 |
0.069 |
0.059 |
0.333 |
0.487 |
0.000 |
0.000 |
1.562 |
|
|
|
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Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 163 | 163 | 129 | 132 | 0 | 148 | 0 | 0 | 878 |
normalized size | 1 | 1.00 | 0.79 | 0.81 | 0.00 | 0.91 | 0.00 | 0.00 | 5.39 |
time (sec) |
N/A |
0.077 |
0.105 |
0.065 |
0.000 |
0.860 |
0.000 |
0.000 |
34.076 |
|
|
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Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 146 | 146 | 76 | 71 | 60 | 69 | 0 | 0 | 95 |
normalized size | 1 | 1.00 | 0.52 | 0.49 | 0.41 | 0.47 | 0.00 | 0.00 | 0.65 |
time (sec) |
N/A |
0.071 |
0.089 |
0.075 |
0.341 |
0.495 |
0.000 |
0.000 |
1.675 |
|
|
|
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Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 145 | 152 | 0 | 156 | 0 | 0 | 1155 |
normalized size | 1 | 1.00 | 0.75 | 0.78 | 0.00 | 0.80 | 0.00 | 0.00 | 5.95 |
time (sec) |
N/A |
0.098 |
0.125 |
0.087 |
0.000 |
0.545 |
0.000 |
0.000 |
38.560 |
|
|
|
|
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Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F(-1) |
B |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 111 | 137 | 0 | 116 | 0 | 205 | 521 |
normalized size | 1 | 1.00 | 1.00 | 1.23 | 0.00 | 1.05 | 0.00 | 1.85 | 4.69 |
time (sec) |
N/A |
0.062 |
0.193 |
0.216 |
0.000 |
0.498 |
0.000 |
0.206 |
14.445 |
|
|
|
|
|
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Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 139 | 114 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.21 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.051 |
0.320 |
0.055 |
0.000 |
0.728 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
B |
B |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 71 | 56 | 60 | 42 | 60 | 0 | 190 | 57 |
normalized size | 1 | 1.22 | 0.97 | 1.03 | 0.72 | 1.03 | 0.00 | 3.28 | 0.98 |
time (sec) |
N/A |
0.041 |
0.098 |
0.051 |
0.400 |
0.536 |
0.000 |
0.172 |
1.638 |
|
|
|
|
|
|
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|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 112 | 112 | 140 | 136 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.25 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.067 |
0.445 |
0.057 |
0.000 |
1.734 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F(-1) |
B |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 92 | 112 | 0 | 102 | 0 | 132 | 306 |
normalized size | 1 | 1.00 | 1.46 | 1.78 | 0.00 | 1.62 | 0.00 | 2.10 | 4.86 |
time (sec) |
N/A |
0.037 |
0.105 |
0.154 |
0.000 |
0.756 |
0.000 |
0.173 |
7.139 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 116 | 102 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.73 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.028 |
0.200 |
0.056 |
0.000 |
1.848 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
|
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|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 100 | 127 | 0 | 133 | 0 | 0 | 182 |
normalized size | 1 | 1.00 | 1.47 | 1.87 | 0.00 | 1.96 | 0.00 | 0.00 | 2.68 |
time (sec) |
N/A |
0.043 |
0.066 |
0.188 |
0.000 |
1.592 |
0.000 |
0.000 |
3.202 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 135 | 132 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.92 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.068 |
0.297 |
0.066 |
0.000 |
0.741 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
B |
B |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 93 | 113 | 103 | 0 | 102 | 0 | 252 | 185 |
normalized size | 1 | 1.16 | 1.41 | 1.29 | 0.00 | 1.28 | 0.00 | 3.15 | 2.31 |
time (sec) |
N/A |
0.053 |
0.149 |
0.160 |
0.000 |
0.974 |
0.000 |
3.324 |
3.996 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 123 | 104 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.07 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.051 |
0.198 |
0.066 |
0.000 |
0.773 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F(-2) |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 118 | 118 | 105 | 129 | 0 | 146 | 0 | 0 | 71 |
normalized size | 1 | 1.00 | 0.89 | 1.09 | 0.00 | 1.24 | 0.00 | 0.00 | 0.60 |
time (sec) |
N/A |
0.061 |
0.268 |
0.176 |
0.000 |
0.862 |
0.000 |
0.000 |
2.017 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 159 | 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 |
0.068 |
2.520 |
0.094 |
0.000 |
2.368 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 159 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.056 |
2.391 |
0.070 |
0.000 |
1.634 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
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 | 91 | 91 | 145 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.040 |
0.309 |
0.044 |
0.000 |
0.637 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
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 | 109 | 109 | 139 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.075 |
0.836 |
0.641 |
0.000 |
2.072 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 186 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.083 |
5.171 |
1.085 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 159 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.053 |
0.309 |
1.061 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 139 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.047 |
0.411 |
1.069 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F(-1) |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 106 | 96 | 145 | 0 | 102 | 0 | 0 | -1 |
normalized size | 1 | 1.22 | 1.10 | 1.67 | 0.00 | 1.17 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.069 |
0.157 |
0.147 |
0.000 |
0.700 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
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|
|
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|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 156 | 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 |
0.060 |
0.284 |
1.071 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 203 | 203 | 105 | 123 | 0 | 103 | 0 | 0 | 808 |
normalized size | 1 | 1.00 | 0.52 | 0.61 | 0.00 | 0.51 | 0.00 | 0.00 | 3.98 |
time (sec) |
N/A |
0.700 |
0.156 |
0.064 |
0.000 |
0.888 |
0.000 |
0.000 |
19.727 |
|
|
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Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 52 | 72 | 42 | 62 | 0 | 0 | 63 |
normalized size | 1 | 1.00 | 0.44 | 0.62 | 0.36 | 0.53 | 0.00 | 0.00 | 0.54 |
time (sec) |
N/A |
0.546 |
0.070 |
0.047 |
0.414 |
1.539 |
0.000 |
0.000 |
1.751 |
|
|
|
|
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Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 169 | 169 | 86 | 97 | 0 | 87 | 0 | 0 | 420 |
normalized size | 1 | 1.00 | 0.51 | 0.57 | 0.00 | 0.51 | 0.00 | 0.00 | 2.49 |
time (sec) |
N/A |
0.465 |
0.076 |
0.061 |
0.000 |
1.533 |
0.000 |
0.000 |
8.956 |
|
|
|
|
|
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|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 89 | 89 | 0 | 124 | 0 | 0 | 56 |
normalized size | 1 | 1.00 | 1.05 | 1.05 | 0.00 | 1.46 | 0.00 | 0.00 | 0.66 |
time (sec) |
N/A |
0.434 |
0.062 |
0.055 |
0.000 |
0.502 |
0.000 |
0.000 |
3.692 |
|
|
|
|
|
|
|
|
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|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 75 | 98 | 0 | 85 | 0 | 0 | 162 |
normalized size | 1 | 1.00 | 1.32 | 1.72 | 0.00 | 1.49 | 0.00 | 0.00 | 2.84 |
time (sec) |
N/A |
0.174 |
0.099 |
0.061 |
0.000 |
1.016 |
0.000 |
0.000 |
4.636 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 86 | 97 | 0 | 138 | 0 | 0 | 323 |
normalized size | 1 | 1.00 | 1.00 | 1.13 | 0.00 | 1.60 | 0.00 | 0.00 | 3.76 |
time (sec) |
N/A |
0.446 |
0.060 |
0.061 |
0.000 |
0.850 |
0.000 |
0.000 |
11.205 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 52 | 73 | 46 | 61 | 0 | 122 | 67 |
normalized size | 1 | 1.00 | 0.91 | 1.28 | 0.81 | 1.07 | 0.00 | 2.14 | 1.18 |
time (sec) |
N/A |
0.390 |
0.063 |
0.058 |
0.348 |
1.061 |
0.000 |
0.208 |
1.796 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 121 | 131 | 0 | 146 | 0 | 0 | 885 |
normalized size | 1 | 1.00 | 0.82 | 0.89 | 0.00 | 0.99 | 0.00 | 0.00 | 6.02 |
time (sec) |
N/A |
0.453 |
0.126 |
0.057 |
0.000 |
1.016 |
0.000 |
0.000 |
46.991 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 183 | 183 | 69 | 84 | 56 | 69 | 0 | 0 | 86 |
normalized size | 1 | 1.00 | 0.38 | 0.46 | 0.31 | 0.38 | 0.00 | 0.00 | 0.47 |
time (sec) |
N/A |
0.505 |
0.084 |
0.059 |
0.397 |
0.745 |
0.000 |
0.000 |
1.938 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 267 | 267 | 137 | 153 | 0 | 156 | 0 | 0 | 2480 |
normalized size | 1 | 1.00 | 0.51 | 0.57 | 0.00 | 0.58 | 0.00 | 0.00 | 9.29 |
time (sec) |
N/A |
0.543 |
0.147 |
0.093 |
0.000 |
0.549 |
0.000 |
0.000 |
65.189 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 301 | 301 | 85 | 92 | 65 | 78 | 0 | 0 | 105 |
normalized size | 1 | 1.00 | 0.28 | 0.31 | 0.22 | 0.26 | 0.00 | 0.00 | 0.35 |
time (sec) |
N/A |
0.576 |
0.103 |
0.072 |
0.397 |
0.764 |
0.000 |
0.000 |
2.125 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 65 | 531 | 0 | 65 | 0 | 0 | 73 |
normalized size | 1 | 1.00 | 0.44 | 3.61 | 0.00 | 0.44 | 0.00 | 0.00 | 0.50 |
time (sec) |
N/A |
0.619 |
0.096 |
0.362 |
0.000 |
1.971 |
0.000 |
0.000 |
2.138 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F(-2) |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 163 | 163 | 97 | 0 | 0 | 95 | 0 | 0 | 795 |
normalized size | 1 | 1.00 | 0.60 | 0.00 | 0.00 | 0.58 | 0.00 | 0.00 | 4.88 |
time (sec) |
N/A |
0.569 |
0.129 |
180.000 |
0.000 |
0.782 |
0.000 |
0.000 |
19.825 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 48 | 269 | 0 | 54 | 0 | 0 | 57 |
normalized size | 1 | 1.00 | 0.64 | 3.59 | 0.00 | 0.72 | 0.00 | 0.00 | 0.76 |
time (sec) |
N/A |
0.513 |
0.060 |
0.315 |
0.000 |
0.537 |
0.000 |
0.000 |
2.063 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F(-2) |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 75 | 0 | 0 | 79 | 0 | 0 | 407 |
normalized size | 1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.84 | 0.00 | 0.00 | 4.33 |
time (sec) |
N/A |
0.309 |
0.069 |
180.000 |
0.000 |
0.852 |
0.000 |
0.000 |
9.223 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 72 | 2612 | 0 | 115 | 0 | 0 | 47 |
normalized size | 1 | 1.00 | 1.11 | 40.18 | 0.00 | 1.77 | 0.00 | 0.00 | 0.72 |
time (sec) |
N/A |
0.166 |
0.032 |
0.308 |
0.000 |
0.530 |
0.000 |
0.000 |
4.169 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F(-2) |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 74 | 0 | 0 | 76 | 0 | 0 | 184 |
normalized size | 1 | 1.00 | 1.61 | 0.00 | 0.00 | 1.65 | 0.00 | 0.00 | 4.00 |
time (sec) |
N/A |
0.401 |
0.038 |
180.000 |
0.000 |
1.700 |
0.000 |
0.000 |
3.845 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F(-2) |
F |
A |
F |
A |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 92 | 0 | 0 | 128 | 0 | 110 | 323 |
normalized size | 1 | 1.00 | 1.28 | 0.00 | 0.00 | 1.78 | 0.00 | 1.53 | 4.49 |
time (sec) |
N/A |
0.383 |
0.060 |
180.000 |
0.000 |
0.514 |
0.000 |
0.171 |
12.053 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F(-2) |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 43 | 0 | 0 | 52 | 0 | 0 | 58 |
normalized size | 1 | 1.00 | 0.37 | 0.00 | 0.00 | 0.45 | 0.00 | 0.00 | 0.50 |
time (sec) |
N/A |
0.424 |
0.056 |
180.000 |
0.000 |
0.785 |
0.000 |
0.000 |
2.137 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F(-2) |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 200 | 200 | 110 | 0 | 0 | 138 | 0 | 0 | 1511 |
normalized size | 1 | 1.00 | 0.55 | 0.00 | 0.00 | 0.69 | 0.00 | 0.00 | 7.56 |
time (sec) |
N/A |
0.500 |
0.109 |
180.000 |
0.000 |
0.629 |
0.000 |
0.000 |
43.714 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F(-2) |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 233 | 233 | 60 | 0 | 0 | 60 | 0 | 0 | 75 |
normalized size | 1 | 1.00 | 0.26 | 0.00 | 0.00 | 0.26 | 0.00 | 0.00 | 0.32 |
time (sec) |
N/A |
0.500 |
0.074 |
180.000 |
0.000 |
0.743 |
0.000 |
0.000 |
2.366 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F(-2) |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 320 | 320 | 129 | 0 | 0 | 148 | 0 | 0 | 2479 |
normalized size | 1 | 1.00 | 0.40 | 0.00 | 0.00 | 0.46 | 0.00 | 0.00 | 7.75 |
time (sec) |
N/A |
0.567 |
0.141 |
180.000 |
0.000 |
0.831 |
0.000 |
0.000 |
65.404 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F(-2) |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 353 | 353 | 76 | 0 | 0 | 69 | 0 | 0 | 91 |
normalized size | 1 | 1.00 | 0.22 | 0.00 | 0.00 | 0.20 | 0.00 | 0.00 | 0.26 |
time (sec) |
N/A |
0.605 |
0.101 |
180.000 |
0.000 |
0.805 |
0.000 |
0.000 |
2.593 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.272 |
0.674 |
0.439 |
0.000 |
1.415 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 69 | 69 | 0 | 69 | 0 | 0 | 76 |
normalized size | 1 | 1.00 | 0.78 | 0.78 | 0.00 | 0.78 | 0.00 | 0.00 | 0.86 |
time (sec) |
N/A |
0.181 |
0.201 |
0.102 |
0.000 |
1.264 |
0.000 |
0.000 |
2.603 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 110 | 117 | 0 | 91 | 0 | 0 | 340 |
normalized size | 1 | 1.00 | 1.47 | 1.56 | 0.00 | 1.21 | 0.00 | 0.00 | 4.53 |
time (sec) |
N/A |
0.165 |
0.161 |
0.080 |
0.000 |
1.567 |
0.000 |
0.000 |
8.085 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 44 | 52 | 0 | 49 | 0 | 0 | 44 |
normalized size | 1 | 1.00 | 0.98 | 1.16 | 0.00 | 1.09 | 0.00 | 0.00 | 0.98 |
time (sec) |
N/A |
0.125 |
0.092 |
0.070 |
0.000 |
0.496 |
0.000 |
0.000 |
2.700 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 68 | 92 | 0 | 53 | 0 | 0 | 84 |
normalized size | 1 | 1.00 | 1.84 | 2.49 | 0.00 | 1.43 | 0.00 | 0.00 | 2.27 |
time (sec) |
N/A |
0.114 |
0.050 |
0.076 |
0.000 |
0.825 |
0.000 |
0.000 |
3.567 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
A |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 73 | 87 | 0 | 92 | 48 | 0 | 59 |
normalized size | 1 | 1.00 | 1.03 | 1.23 | 0.00 | 1.30 | 0.68 | 0.00 | 0.83 |
time (sec) |
N/A |
0.119 |
0.043 |
0.077 |
0.000 |
1.914 |
16.429 |
0.000 |
2.918 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 59 | 61 | 0 | 62 | 0 | 0 | 37 |
normalized size | 1 | 1.00 | 1.40 | 1.45 | 0.00 | 1.48 | 0.00 | 0.00 | 0.88 |
time (sec) |
N/A |
0.143 |
0.167 |
0.083 |
0.000 |
0.916 |
0.000 |
0.000 |
2.528 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 108 | 111 | 0 | 156 | 0 | 0 | 331 |
normalized size | 1 | 1.00 | 1.00 | 1.03 | 0.00 | 1.44 | 0.00 | 0.00 | 3.06 |
time (sec) |
N/A |
0.176 |
0.159 |
0.090 |
0.000 |
0.854 |
0.000 |
0.000 |
14.525 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 90 | 86 | 0 | 89 | 0 | 0 | 75 |
normalized size | 1 | 1.00 | 1.06 | 1.01 | 0.00 | 1.05 | 0.00 | 0.00 | 0.88 |
time (sec) |
N/A |
0.165 |
0.264 |
0.099 |
0.000 |
0.863 |
0.000 |
0.000 |
2.505 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
B |
A |
F |
A |
F |
F |
B |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 26 | 28 | 36 | 0 | 35 | 0 | 0 | 76 |
normalized size | 1 | 2.17 | 2.33 | 3.00 | 0.00 | 2.92 | 0.00 | 0.00 | 6.33 |
time (sec) |
N/A |
1.052 |
0.275 |
0.048 |
0.000 |
0.629 |
0.000 |
0.000 |
2.962 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 61 | 61 | 52 | 104 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.85 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.098 |
0.061 |
0.341 |
0.000 |
0.885 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 84 | 62 | 38 | 283 | 0 | 0 | 56 |
normalized size | 1 | 1.00 | 1.47 | 1.09 | 0.67 | 4.96 | 0.00 | 0.00 | 0.98 |
time (sec) |
N/A |
0.115 |
0.213 |
0.103 |
0.363 |
1.754 |
0.000 |
0.000 |
2.992 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F(-1) |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 84 | 0 | 40 | 385 | 0 | 0 | 54 |
normalized size | 1 | 1.00 | 1.45 | 0.00 | 0.69 | 6.64 | 0.00 | 0.00 | 0.93 |
time (sec) |
N/A |
0.113 |
0.264 |
0.247 |
0.381 |
0.915 |
0.000 |
0.000 |
2.349 |
|
|
|
|
|
|
|
|
|
|
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 [15] had the largest ratio of
[1.200]
|
|
|
|
|
|
|
| Table 2.1:Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
8 |
7 |
1.00 |
10 |
0.700 |
|
|
|
|
|
|
|
2 |
A |
7 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
3 |
A |
6 |
6 |
1.00 |
8 |
0.750 |
|
|
|
|
|
|
|
4 |
A |
4 |
4 |
1.00 |
6 |
0.667 |
|
|
|
|
|
|
|
5 |
A |
14 |
8 |
1.00 |
10 |
0.800 |
|
|
|
|
|
|
|
6 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
7 |
A |
7 |
7 |
1.00 |
10 |
0.700 |
|
|
|
|
|
|
|
8 |
A |
8 |
8 |
1.00 |
10 |
0.800 |
|
|
|
|
|
|
|
9 |
A |
17 |
9 |
1.00 |
12 |
0.750 |
|
|
|
|
|
|
|
10 |
A |
11 |
8 |
1.00 |
10 |
0.800 |
|
|
|
|
|
|
|
11 |
A |
8 |
6 |
1.00 |
8 |
0.750 |
|
|
|
|
|
|
|
12 |
A |
17 |
9 |
1.00 |
12 |
0.750 |
|
|
|
|
|
|
|
13 |
A |
12 |
8 |
1.00 |
12 |
0.667 |
|
|
|
|
|
|
|
14 |
A |
23 |
11 |
1.00 |
12 |
0.917 |
|
|
|
|
|
|
|
15 |
A |
16 |
12 |
1.00 |
10 |
1.200 |
|
|
|
|
|
|
|
16 |
A |
10 |
7 |
1.00 |
8 |
0.875 |
|
|
|
|
|
|
|
17 |
A |
20 |
10 |
1.00 |
12 |
0.833 |
|
|
|
|
|
|
|
18 |
A |
14 |
9 |
1.00 |
12 |
0.750 |
|
|
|
|
|
|
|
19 |
A |
32 |
13 |
1.00 |
12 |
1.083 |
|
|
|
|
|
|
|
20 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
21 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
22 |
A |
4 |
3 |
1.00 |
8 |
0.375 |
|
|
|
|
|
|
|
23 |
A |
3 |
3 |
1.00 |
6 |
0.500 |
|
|
|
|
|
|
|
24 |
A |
7 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
25 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
26 |
A |
6 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
27 |
A |
7 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
28 |
A |
3 |
3 |
1.00 |
4 |
0.750 |
|
|
|
|
|
|
|
29 |
A |
7 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
30 |
A |
7 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
31 |
A |
7 |
7 |
1.00 |
10 |
0.700 |
|
|
|
|
|
|
|
32 |
A |
5 |
5 |
1.30 |
10 |
0.500 |
|
|
|
|
|
|
|
33 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
34 |
A |
3 |
3 |
1.37 |
10 |
0.300 |
|
|
|
|
|
|
|
35 |
A |
4 |
4 |
1.00 |
8 |
0.500 |
|
|
|
|
|
|
|
36 |
A |
3 |
3 |
1.62 |
6 |
0.500 |
|
|
|
|
|
|
|
37 |
A |
5 |
5 |
1.33 |
10 |
0.500 |
|
|
|
|
|
|
|
38 |
B |
6 |
6 |
2.83 |
10 |
0.600 |
|
|
|
|
|
|
|
39 |
C |
5 |
5 |
1.53 |
10 |
0.500 |
|
|
|
|
|
|
|
40 |
A |
8 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
41 |
A |
7 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
42 |
A |
10 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
43 |
A |
9 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
44 |
A |
12 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
45 |
A |
6 |
6 |
1.00 |
12 |
0.500 |
|
|
|
|
|
|
|
46 |
A |
5 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
47 |
A |
4 |
4 |
1.22 |
12 |
0.333 |
|
|
|
|
|
|
|
48 |
A |
7 |
7 |
1.00 |
12 |
0.583 |
|
|
|
|
|
|
|
49 |
A |
5 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
50 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
51 |
A |
6 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
52 |
A |
8 |
8 |
1.00 |
8 |
1.000 |
|
|
|
|
|
|
|
53 |
A |
5 |
5 |
1.16 |
12 |
0.417 |
|
|
|
|
|
|
|
54 |
A |
5 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
55 |
A |
7 |
7 |
1.00 |
12 |
0.583 |
|
|
|
|
|
|
|
56 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
57 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
58 |
A |
4 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
59 |
A |
5 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
60 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
61 |
A |
4 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
62 |
A |
4 |
4 |
1.00 |
8 |
0.500 |
|
|
|
|
|
|
|
63 |
A |
6 |
6 |
1.22 |
12 |
0.500 |
|
|
|
|
|
|
|
64 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
65 |
A |
9 |
6 |
1.00 |
12 |
0.500 |
|
|
|
|
|
|
|
66 |
A |
8 |
6 |
1.00 |
12 |
0.500 |
|
|
|
|
|
|
|
67 |
A |
7 |
6 |
1.00 |
12 |
0.500 |
|
|
|
|
|
|
|
68 |
A |
8 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
69 |
A |
7 |
5 |
1.00 |
8 |
0.625 |
|
|
|
|
|
|
|
70 |
A |
5 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
71 |
A |
4 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
72 |
A |
5 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
73 |
A |
4 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
74 |
A |
5 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
75 |
A |
4 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
76 |
A |
8 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
77 |
A |
7 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
78 |
A |
6 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
79 |
A |
5 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
80 |
A |
6 |
4 |
1.00 |
8 |
0.500 |
|
|
|
|
|
|
|
81 |
A |
5 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
82 |
A |
5 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
83 |
A |
4 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
84 |
A |
5 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
85 |
A |
4 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
86 |
A |
5 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
87 |
A |
4 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
88 |
A |
5 |
4 |
1.00 |
24 |
0.167 |
|
|
|
|
|
|
|
89 |
A |
8 |
7 |
1.00 |
22 |
0.318 |
|
|
|
|
|
|
|
90 |
A |
7 |
7 |
1.00 |
22 |
0.318 |
|
|
|
|
|
|
|
91 |
A |
4 |
4 |
1.00 |
22 |
0.182 |
|
|
|
|
|
|
|
92 |
A |
5 |
5 |
1.00 |
20 |
0.250 |
|
|
|
|
|
|
|
93 |
A |
8 |
8 |
1.00 |
19 |
0.421 |
|
|
|
|
|
|
|
94 |
A |
5 |
5 |
1.00 |
22 |
0.227 |
|
|
|
|
|
|
|
95 |
A |
9 |
8 |
1.00 |
22 |
0.364 |
|
|
|
|
|
|
|
96 |
A |
8 |
7 |
1.00 |
22 |
0.318 |
|
|
|
|
|
|
|
97 |
B |
7 |
5 |
2.17 |
25 |
0.200 |
|
|
|
|
|
|
|
98 |
A |
8 |
8 |
1.00 |
19 |
0.421 |
|
|
|
|
|
|
|
99 |
A |
5 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
100 |
A |
5 |
5 |
1.00 |
14 |
0.357 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|