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, 3, 4, 5, 6, 7, 8, 9, 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, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 62, 63, 64, 65, 66, 67, 68, 69,
70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 96, 97, 99, 105, 106,
107 }
B grade: { 10 }
C grade: { 2, 46, 52, 82, 83, 98, 100, 101, 102, 113, 114, 116 }
F grade: { 43, 44, 45, 58, 59, 60, 61, 95, 103, 104, 108, 109, 110, 111, 112, 115 }
2.1.2 Mathematica
A grade: { 1, 3, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33,
34, 35, 36, 41, 42, 57, 62, 85, 94, 96, 97, 99, 103, 104, 105, 107 }
B grade: { }
C grade: { 2, 4, 24, 39, 40, 43, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72,
73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 91, 98, 101, 106, 113, 114, 115, 116
}
F grade: { 12, 13, 37, 38, 44, 45, 46, 58, 59, 60, 61, 92, 93, 95, 100, 102, 108, 109, 110, 111, 112
}
2.1.3 Maple
A grade: { 1, 7, 8, 16, 21, 22, 23, 32, 47, 48, 49, 62, 63, 64, 103, 104, 105 }
B grade: { 3, 4, 5, 6, 9, 10, 11, 17, 24, 31, 50, 51, 65, 68 }
C grade: { 2, 15, 28, 33, 34, 35, 36, 37, 39, 40, 52, 55, 56, 57, 58, 59, 66, 67, 73, 74, 75, 76,
77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 97, 99, 100, 101, 102, 106, 107, 116
}
F grade: { 12, 13, 14, 18, 19, 20, 25, 26, 27, 29, 30, 38, 41, 42, 43, 44, 45, 46, 53, 54, 60, 61, 69, 70, 71, 72,
80, 94, 95, 96, 98, 108, 109, 110, 111, 112, 113, 114, 115 }
2.1.4 Maxima
A grade: { 1, 6, 16, 21, 22, 23, 29, 32, 33, 34, 35, 36, 56, 57, 62, 96, 99, 107 }
B grade: { 2, 106 }
C grade: { }
F grade: { 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 24, 25, 26, 27, 28, 30, 31, 37, 38, 39,
40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 58, 59, 60, 61, 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, 97, 98, 100, 101, 102, 103, 104, 105, 108, 109, 110, 111, 112, 113, 114, 115, 116
}
2.1.5 FriCAS
A grade: { 1, 2, 3, 5, 6, 8, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 30, 31, 32, 33, 34, 36, 40, 52,
56, 57, 62, 63, 64, 65, 66, 67, 81, 83, 99, 106, 107, 113, 116 }
B grade: { 4, 7, 9, 10, 12, 13, 14, 24, 35, 37, 39, 41, 42, 43, 47, 48, 49, 50, 51, 55, 59, 68, 73, 74, 75, 76, 77,
78, 79, 80, 85, 86, 87, 88, 89, 90, 91, 93, 96, 97, 98, 100, 101, 102, 110 }
C grade: { 82 }
F grade: { 29, 38, 44, 45, 46, 53, 54, 58, 60, 61, 69, 70, 71, 72, 84, 92, 94, 95, 103, 104, 105, 108, 109, 111,
112, 114, 115 }
2.1.6 Sympy
A grade: { 1, 2, 14, 15, 20, 21, 22, 23, 25, 26, 62, 63, 64 }
B grade: { 8, 16, 17, 19, 30, 31 }
C grade: { 27, 28, 33, 34, 35, 36, 56, 57, 106, 107 }
F grade: { 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 18, 24, 29, 32, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50,
51, 52, 53, 54, 55, 58, 59, 60, 61, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84,
85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 108, 109, 110, 111,
112, 113, 114, 115, 116 }
2.1.7 Giac
A grade: { 1, 6, 8, 16, 21, 22, 23, 25, 26, 33, 34, 36, 41, 48, 49, 57, 62, 63, 64, 96, 99, 107 }
B grade: { 2, 3, 4, 7, 9, 10, 24, 47 }
C grade: { 50 }
F grade: { 5, 11, 12, 13, 14, 15, 17, 18, 19, 20, 27, 28, 29, 30, 31, 32, 35, 37, 38, 39, 40, 42, 43, 44, 45, 46,
51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 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, 97, 98, 100, 101, 102, 103, 104, 105, 106, 108, 109, 110, 111,
112, 113, 114, 115, 116 }
2.1.8 Mupad
A grade: { }
B grade: { 1, 2, 3, 5, 8, 16, 19, 20, 21, 22, 23, 25, 26, 30, 33, 34, 35, 36, 41, 47, 48, 49, 57, 62, 63, 64, 73, 74,
75, 81, 82, 84, 85, 96, 99, 106, 107 }
C grade: { }
F grade: { 4, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 24, 27, 28, 29, 31, 32, 37, 38, 39, 40, 42, 43, 44, 45, 46,
50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 65, 66, 67, 68, 69, 70, 71, 72, 76, 77, 78, 79, 80, 83, 86, 87, 88, 89,
90, 91, 92, 93, 94, 95, 97, 98, 100, 101, 102, 103, 104, 105, 108, 109, 110, 111, 112, 113, 114, 115, 116
}
2.2 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2)
if the failure was due to an exception being raised, which could indicate a bug in the system. If
the failure was due to integral not being evaluated within the time limit, then it is given just an
F.
In this table,the column normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 14 | 13 | 13 | 12 | 13 | 13 |
normalized size | 1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.80 | 0.87 | 0.87 |
time (sec) |
N/A |
0.001 |
0.005 |
0.002 |
0.510 |
0.841 |
0.062 |
0.907 |
0.027 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
C |
C |
C |
B |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 52 | 37 | 34 | 41 | 1 | 42 | 41 | 43 |
normalized size | 1 | 3.47 | 2.47 | 2.27 | 2.73 | 0.07 | 2.80 | 2.73 | 2.87 |
time (sec) |
N/A |
0.056 |
0.034 |
0.004 |
0.466 |
0.853 |
59.577 |
1.057 |
0.515 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F |
A |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 99 | 370 | 0 | 100 | 0 | 177 | 204 |
normalized size | 1 | 1.00 | 1.21 | 4.51 | 0.00 | 1.22 | 0.00 | 2.16 | 2.49 |
time (sec) |
N/A |
0.076 |
0.191 |
0.049 |
0.000 |
1.173 |
0.000 |
0.913 |
0.569 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
F |
B |
F |
B |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 167 | 172 | 0 | 80 | 0 | 94 | -1 |
normalized size | 1 | 1.00 | 3.88 | 4.00 | 0.00 | 1.86 | 0.00 | 2.19 | -0.02 |
time (sec) |
N/A |
0.012 |
3.763 |
0.053 |
0.000 |
1.529 |
0.000 |
0.938 |
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 |
B |
F |
A |
F |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 126 | 115 | 0 | 105 | 0 | 0 | 82 |
normalized size | 1 | 1.00 | 1.70 | 1.55 | 0.00 | 1.42 | 0.00 | 0.00 | 1.11 |
time (sec) |
N/A |
0.056 |
0.166 |
0.017 |
0.000 |
0.904 |
0.000 |
0.000 |
1.707 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 59 | 125 | 53 | 92 | 0 | 84 | -1 |
normalized size | 1 | 1.00 | 0.92 | 1.95 | 0.83 | 1.44 | 0.00 | 1.31 | -0.02 |
time (sec) |
N/A |
0.026 |
0.086 |
0.039 |
1.452 |
0.978 |
0.000 |
1.068 |
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 |
A |
F |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 75 | 45 | 0 | 83 | 0 | 101 | -1 |
normalized size | 1 | 1.00 | 1.56 | 0.94 | 0.00 | 1.73 | 0.00 | 2.10 | -0.02 |
time (sec) |
N/A |
0.013 |
0.130 |
0.021 |
0.000 |
1.011 |
0.000 |
0.961 |
0.000 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
F |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 30 | 21 | 0 | 18 | 53 | 20 | 21 |
normalized size | 1 | 1.00 | 1.00 | 0.70 | 0.00 | 0.60 | 1.77 | 0.67 | 0.70 |
time (sec) |
N/A |
0.082 |
0.058 |
0.004 |
0.000 |
0.886 |
0.753 |
0.949 |
0.381 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F |
B |
F |
B |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 365 | 340 | 902 | 0 | 424 | 0 | 367 | -1 |
normalized size | 1 | 1.66 | 1.55 | 4.10 | 0.00 | 1.93 | 0.00 | 1.67 | -0.00 |
time (sec) |
N/A |
0.506 |
0.855 |
0.138 |
0.000 |
0.780 |
0.000 |
8.762 |
0.000 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
B |
A |
B |
F |
B |
F(-1) |
B |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 541 | 311 | 1542 | 0 | 424 | 0 | 358 | -1 |
normalized size | 1 | 2.46 | 1.41 | 7.01 | 0.00 | 1.93 | 0.00 | 1.63 | -0.00 |
time (sec) |
N/A |
0.751 |
0.713 |
0.023 |
0.000 |
0.612 |
0.000 |
9.218 |
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 |
B |
F(-2) |
A |
F(-2) |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 125 | 278 | 0 | 161 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.91 | 2.01 | 0.00 | 1.17 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.075 |
0.203 |
0.032 |
0.000 |
1.061 |
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 |
F |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 0 | 0 | 0 | 394 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 3.15 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.185 |
0.240 |
0.098 |
0.000 |
4.546 |
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 |
F |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 0 | 0 | 0 | 369 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 4.56 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.162 |
0.173 |
0.088 |
0.000 |
10.157 |
0.000 |
0.000 |
0.000 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 31 | 0 | 0 | 60 | 15 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.94 | 0.48 | 0.00 | -0.03 |
time (sec) |
N/A |
0.054 |
0.009 |
0.080 |
0.000 |
1.215 |
1.225 |
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 |
C |
F |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 33 | 22 | 0 | 29 | 15 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.67 | 0.00 | 0.88 | 0.45 | 0.00 | -0.03 |
time (sec) |
N/A |
0.063 |
0.011 |
0.100 |
0.000 |
1.621 |
0.860 |
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 |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 16 | 15 | 28 | 56 | 15 | 15 |
normalized size | 1 | 1.00 | 1.00 | 0.84 | 0.79 | 1.47 | 2.95 | 0.79 | 0.79 |
time (sec) |
N/A |
0.270 |
0.018 |
0.003 |
0.635 |
0.986 |
6.629 |
1.147 |
0.400 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 52 | 52 | 43 | 120 | 0 | 32 | 2147 | 0 | -1 |
normalized size | 1 | 1.00 | 0.83 | 2.31 | 0.00 | 0.62 | 41.29 | 0.00 | -0.02 |
time (sec) |
N/A |
0.023 |
0.042 |
0.033 |
0.000 |
1.382 |
3.534 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 50 | 0 | 0 | 33 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.59 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.022 |
0.068 |
0.090 |
0.000 |
1.168 |
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 |
F |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 0 | 0 | 15 | 311 | 0 | 15 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.88 | 18.29 | 0.00 | 0.88 |
time (sec) |
N/A |
0.054 |
0.007 |
0.082 |
0.000 |
1.089 |
2.986 |
0.000 |
0.297 |
|
|
|
|
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|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 0 | 0 | 18 | 36 | 0 | 18 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.90 | 1.80 | 0.00 | 0.90 |
time (sec) |
N/A |
0.060 |
0.007 |
0.092 |
0.000 |
0.625 |
1.598 |
0.000 |
0.296 |
|
|
|
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|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 36 | 48 | 40 | 52 | 36 | 47 | 58 |
normalized size | 1 | 1.00 | 0.86 | 1.14 | 0.95 | 1.24 | 0.86 | 1.12 | 1.38 |
time (sec) |
N/A |
0.033 |
0.042 |
0.013 |
0.588 |
1.108 |
0.147 |
0.986 |
0.413 |
|
|
|
|
|
|
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|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 22 | 21 | 20 | 19 | 20 | 19 | 24 |
normalized size | 1 | 1.00 | 1.00 | 0.95 | 0.91 | 0.86 | 0.91 | 0.86 | 1.09 |
time (sec) |
N/A |
0.024 |
0.021 |
0.003 |
0.604 |
1.247 |
0.120 |
0.776 |
0.385 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
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 | 62 | 62 | 49 | 51 | 51 | 58 | 51 | 74 | 47 |
normalized size | 1 | 1.00 | 0.79 | 0.82 | 0.82 | 0.94 | 0.82 | 1.19 | 0.76 |
time (sec) |
N/A |
0.091 |
0.066 |
0.014 |
0.588 |
0.740 |
0.185 |
1.211 |
0.406 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 961 | 455 | 0 | 358 | 0 | 304 | -1 |
normalized size | 1 | 1.00 | 11.17 | 5.29 | 0.00 | 4.16 | 0.00 | 3.53 | -0.01 |
time (sec) |
N/A |
0.084 |
2.520 |
0.043 |
0.000 |
1.013 |
0.000 |
1.061 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 0 | 0 | 15 | 15 | 15 | 15 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.79 | 0.79 | 0.79 | 0.79 |
time (sec) |
N/A |
0.065 |
0.012 |
0.104 |
0.000 |
1.020 |
0.230 |
0.787 |
0.423 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F(-2) |
F |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 26 | 0 | 0 | 22 | 27 | 22 | 22 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.85 | 1.04 | 0.85 | 0.85 |
time (sec) |
N/A |
0.097 |
0.018 |
180.000 |
0.000 |
0.985 |
1.072 |
0.984 |
0.506 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 56 | 0 | 0 | 198 | 46 | 0 | -1 |
normalized size | 1 | 1.00 | 0.89 | 0.00 | 0.00 | 3.14 | 0.73 | 0.00 | -0.02 |
time (sec) |
N/A |
0.219 |
0.203 |
0.085 |
0.000 |
1.087 |
1.469 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 127 | 25 | 0 | 216 | 51 | 0 | -1 |
normalized size | 1 | 1.00 | 1.55 | 0.30 | 0.00 | 2.63 | 0.62 | 0.00 | -0.01 |
time (sec) |
N/A |
0.072 |
0.048 |
0.013 |
0.000 |
0.771 |
1.316 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 606 | 679 | 412 | 0 | 518 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.12 | 0.68 | 0.00 | 0.85 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
4.799 |
0.262 |
0.092 |
0.557 |
1.017 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 0 | 0 | 15 | 311 | 0 | 15 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.88 | 18.29 | 0.00 | 0.88 |
time (sec) |
N/A |
0.055 |
0.011 |
0.091 |
0.000 |
0.884 |
2.577 |
0.000 |
0.314 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 52 | 52 | 46 | 120 | 0 | 32 | 2147 | 0 | -1 |
normalized size | 1 | 1.00 | 0.88 | 2.31 | 0.00 | 0.62 | 41.29 | 0.00 | -0.02 |
time (sec) |
N/A |
0.024 |
0.061 |
0.027 |
0.000 |
1.028 |
2.715 |
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 |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 33 | 44 | 48 | 48 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 1.29 | 1.41 | 1.41 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.044 |
0.126 |
0.048 |
0.902 |
0.943 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 57 | 65 | 62 | 64 | 36 | 64 | 86 |
normalized size | 1 | 1.00 | 0.98 | 1.12 | 1.07 | 1.10 | 0.62 | 1.10 | 1.48 |
time (sec) |
N/A |
0.036 |
0.015 |
0.105 |
1.092 |
0.948 |
0.944 |
0.916 |
0.543 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 81 | 48 | 62 | 64 | 37 | 64 | 76 |
normalized size | 1 | 1.00 | 1.40 | 0.83 | 1.07 | 1.10 | 0.64 | 1.10 | 1.31 |
time (sec) |
N/A |
0.035 |
0.012 |
0.100 |
1.296 |
0.711 |
0.977 |
1.091 |
0.457 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
B |
C |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 86 | 12 | 78 | 82 | 29 | 0 | 10 |
normalized size | 1 | 1.00 | 1.76 | 0.24 | 1.59 | 1.67 | 0.59 | 0.00 | 0.20 |
time (sec) |
N/A |
0.005 |
0.040 |
0.092 |
1.361 |
0.896 |
0.893 |
0.000 |
0.334 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 55 | 65 | 62 | 64 | 32 | 63 | 80 |
normalized size | 1 | 1.00 | 1.00 | 1.18 | 1.13 | 1.16 | 0.58 | 1.15 | 1.45 |
time (sec) |
N/A |
0.033 |
0.013 |
0.103 |
1.211 |
1.114 |
0.919 |
0.824 |
0.514 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 0 | 1143 | 0 | 301 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 11.78 | 0.00 | 3.10 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.044 |
0.080 |
8.055 |
0.000 |
7.448 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 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 |
0.107 |
0.080 |
0.616 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 176 | 59 | 1069 | 0 | 277 | 0 | 0 | -1 |
normalized size | 1 | 1.60 | 0.54 | 9.72 | 0.00 | 2.52 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.025 |
0.023 |
8.325 |
0.000 |
4.940 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 131 | 85 | 653 | 0 | 120 | 0 | 0 | -1 |
normalized size | 1 | 1.62 | 1.05 | 8.06 | 0.00 | 1.48 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.073 |
0.015 |
1.348 |
0.000 |
1.747 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 117 | 127 | 0 | 0 | 415 | 0 | 67 | 37 |
normalized size | 1 | 1.77 | 1.92 | 0.00 | 0.00 | 6.29 | 0.00 | 1.02 | 0.56 |
time (sec) |
N/A |
0.056 |
0.079 |
0.141 |
0.000 |
3.859 |
0.000 |
1.049 |
0.394 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 145 | 140 | 0 | 0 | 665 | 0 | 0 | -1 |
normalized size | 1 | 1.84 | 1.77 | 0.00 | 0.00 | 8.42 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.098 |
0.151 |
0.037 |
0.000 |
3.454 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
C |
F |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
N/A |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 118 | 0 | 55 | 0 | 0 | 1496 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.47 | 0.00 | 0.00 | 12.68 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
21.937 |
0.195 |
0.047 |
0.000 |
52.735 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 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 |
0.611 |
1.638 |
0.126 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 176 | 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 |
0.462 |
0.666 |
0.097 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
F |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 493 | 576 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.846 |
0.396 |
0.276 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 407 | 407 | 198 | 584 | 0 | 957 | 0 | 767 | 343 |
normalized size | 1 | 1.00 | 0.49 | 1.43 | 0.00 | 2.35 | 0.00 | 1.88 | 0.84 |
time (sec) |
N/A |
0.676 |
2.129 |
0.120 |
0.000 |
1.518 |
0.000 |
2.819 |
0.474 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 648 | 648 | 610 | 719 | 0 | 1563 | 0 | 972 | 567 |
normalized size | 1 | 1.00 | 0.94 | 1.11 | 0.00 | 2.41 | 0.00 | 1.50 | 0.88 |
time (sec) |
N/A |
1.158 |
6.092 |
0.069 |
0.000 |
1.716 |
0.000 |
4.186 |
0.561 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1058 | 1058 | 1100 | 989 | 0 | 2763 | 0 | 1382 | 1017 |
normalized size | 1 | 1.00 | 1.04 | 0.93 | 0.00 | 2.61 | 0.00 | 1.31 | 0.96 |
time (sec) |
N/A |
2.490 |
6.175 |
0.105 |
0.000 |
151.296 |
0.000 |
6.839 |
0.972 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 378 | 378 | 342 | 21028 | 0 | 1873 | 0 | 2509 | -1 |
normalized size | 1 | 1.00 | 0.90 | 55.63 | 0.00 | 4.96 | 0.00 | 6.64 | -0.00 |
time (sec) |
N/A |
0.774 |
6.135 |
0.648 |
0.000 |
1.029 |
0.000 |
93.770 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 638 | 638 | 1431 | 86793 | 0 | 2775 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.24 | 136.04 | 0.00 | 4.35 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.397 |
11.601 |
5.033 |
0.000 |
1.554 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
C |
F |
A |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 204 | 213 | 1275 | 0 | 546 | 0 | 0 | -1 |
normalized size | 1 | 3.09 | 3.23 | 19.32 | 0.00 | 8.27 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
1.234 |
1.150 |
0.119 |
0.000 |
1.128 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 198 | 198 | 145 | 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 |
0.097 |
0.234 |
0.122 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 198 | 198 | 153 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.091 |
0.238 |
0.114 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 111 | 2378 | 0 | 171 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.14 | 24.52 | 0.00 | 1.76 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.013 |
0.055 |
14.133 |
0.000 |
4.153 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
A |
A |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 107 | 20 | 69 | 105 | 96 | 32 | 0 | -1 |
normalized size | 1 | 1.47 | 0.27 | 0.95 | 1.44 | 1.32 | 0.44 | 0.00 | -0.01 |
time (sec) |
N/A |
0.044 |
0.003 |
0.104 |
1.252 |
1.033 |
1.022 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 90 | 49 | 71 | 73 | 37 | 72 | 83 |
normalized size | 1 | 1.00 | 1.34 | 0.73 | 1.06 | 1.09 | 0.55 | 1.07 | 1.24 |
time (sec) |
N/A |
0.037 |
0.021 |
0.107 |
1.297 |
0.877 |
0.986 |
1.116 |
0.366 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
C |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 482 | 0 | 0 | 2972 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 6.17 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.052 |
0.353 |
19.957 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
C |
F |
B |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 280 | 0 | 0 | 1404 | 0 | 3085 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 5.01 | 0.00 | 11.02 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.235 |
0.105 |
33.314 |
0.000 |
16.511 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 232 | 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 | -0.00 |
time (sec) |
N/A |
0.050 |
0.344 |
0.850 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 168 | 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 |
0.204 |
0.138 |
4.236 |
0.000 |
18.875 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 24 | 23 | 23 | 22 | 23 | 23 |
normalized size | 1 | 1.00 | 1.00 | 0.96 | 0.92 | 0.92 | 0.88 | 0.92 | 0.92 |
time (sec) |
N/A |
0.023 |
0.007 |
0.004 |
0.540 |
0.921 |
0.106 |
0.989 |
0.074 |
|
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Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 86 | 52 | 0 | 43 | 73 | 40 | 53 |
normalized size | 1 | 1.00 | 1.46 | 0.88 | 0.00 | 0.73 | 1.24 | 0.68 | 0.90 |
time (sec) |
N/A |
0.032 |
0.018 |
0.031 |
0.000 |
0.847 |
0.172 |
0.848 |
0.335 |
|
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Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 99 | 75 | 0 | 66 | 100 | 64 | 76 |
normalized size | 1 | 1.00 | 1.27 | 0.96 | 0.00 | 0.85 | 1.28 | 0.82 | 0.97 |
time (sec) |
N/A |
0.077 |
0.021 |
0.026 |
0.000 |
0.883 |
0.184 |
0.969 |
0.090 |
|
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Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 110 | 100 | 0 | 56 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.24 | 2.04 | 0.00 | 1.14 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.007 |
0.095 |
0.026 |
0.000 |
0.676 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 108 | 365 | 0 | 61 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.04 | 6.89 | 0.00 | 1.15 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.015 |
0.091 |
0.038 |
0.000 |
0.908 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 5727 | 1512 | 0 | 359 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 76.36 | 20.16 | 0.00 | 4.79 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.094 |
7.076 |
0.092 |
0.000 |
0.750 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 322 | 456 | 0 | 2667 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.88 | 2.67 | 0.00 | 15.60 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.080 |
0.421 |
0.111 |
0.000 |
5.831 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 157 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.040 |
0.256 |
0.135 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
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|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 162 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.048 |
0.264 |
0.120 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
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|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 144 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.045 |
0.215 |
0.139 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
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|
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|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 152 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.036 |
0.186 |
0.119 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 73 |
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 | 127 | 127 | 28 | 164 | 0 | 1191 | 0 | 0 | 653 |
normalized size | 1 | 1.00 | 0.22 | 1.29 | 0.00 | 9.38 | 0.00 | 0.00 | 5.14 |
time (sec) |
N/A |
0.019 |
0.021 |
0.186 |
0.000 |
1.260 |
0.000 |
0.000 |
0.449 |
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 74 |
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 | 157 | 157 | 54 | 240 | 0 | 1666 | 0 | 0 | 331 |
normalized size | 1 | 1.00 | 0.34 | 1.53 | 0.00 | 10.61 | 0.00 | 0.00 | 2.11 |
time (sec) |
N/A |
0.033 |
0.030 |
0.219 |
0.000 |
1.815 |
0.000 |
0.000 |
15.034 |
|
|
|
|
|
|
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|
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|
|
|
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|
|
Problem 75 |
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 | 74 | 74 | 48 | 421 | 0 | 547 | 0 | 0 | 533 |
normalized size | 1 | 1.00 | 0.65 | 5.69 | 0.00 | 7.39 | 0.00 | 0.00 | 7.20 |
time (sec) |
N/A |
0.156 |
0.021 |
0.200 |
0.000 |
1.101 |
0.000 |
0.000 |
0.211 |
|
|
|
|
|
|
|
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|
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|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 32 | 383 | 0 | 497 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.31 | 3.72 | 0.00 | 4.83 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.305 |
0.028 |
0.352 |
0.000 |
1.428 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
|
|
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|
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|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 126 | 538 | 0 | 1792 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.56 | 6.64 | 0.00 | 22.12 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.011 |
0.098 |
10.056 |
0.000 |
3.816 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
|
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|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 126 | 444 | 0 | 345 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.56 | 5.48 | 0.00 | 4.26 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.011 |
0.095 |
2.458 |
0.000 |
2.760 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 118 | 704 | 0 | 1943 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.04 | 6.23 | 0.00 | 17.19 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.014 |
0.069 |
50.764 |
0.000 |
1.818 |
0.000 |
0.000 |
0.000 |
|
|
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|
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|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F(-1) |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 124 | 0 | 0 | 1685 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.14 | 0.00 | 0.00 | 15.46 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.012 |
0.101 |
180.000 |
0.000 |
1.731 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 159 | 206 | 0 | 85 | 0 | 0 | 217 |
normalized size | 1 | 1.00 | 1.83 | 2.37 | 0.00 | 0.98 | 0.00 | 0.00 | 2.49 |
time (sec) |
N/A |
0.874 |
0.934 |
0.041 |
0.000 |
0.702 |
0.000 |
0.000 |
0.169 |
|
|
|
|
|
|
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|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
C |
F |
C |
F |
F |
B |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1 | 529 | 127 | 317 | 0 | 70 | 0 | 0 | 207 |
normalized size | 1 | 529.00 | 127.00 | 317.00 | 0.00 | 70.00 | 0.00 | 0.00 | 207.00 |
time (sec) |
N/A |
1.669 |
0.602 |
0.049 |
0.000 |
1.209 |
0.000 |
0.000 |
0.478 |
|
|
|
|
|
|
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|
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|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
C |
F |
A |
F |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 180 | 133 | 536 | 0 | 63 | 0 | 0 | -1 |
normalized size | 1 | 3.91 | 2.89 | 11.65 | 0.00 | 1.37 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
1.492 |
1.091 |
0.059 |
0.000 |
0.722 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
|
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|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-2) |
F |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 323 | 258 | 0 | 0 | 0 | 0 | 67 |
normalized size | 1 | 1.00 | 10.09 | 8.06 | 0.00 | 0.00 | 0.00 | 0.00 | 2.09 |
time (sec) |
N/A |
0.096 |
0.463 |
0.122 |
0.000 |
0.000 |
0.000 |
0.000 |
1.686 |
|
|
|
|
|
|
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|
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|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 46 | 240 | 0 | 44 | 0 | 0 | 204 |
normalized size | 1 | 1.00 | 2.00 | 10.43 | 0.00 | 1.91 | 0.00 | 0.00 | 8.87 |
time (sec) |
N/A |
0.054 |
0.008 |
0.110 |
0.000 |
0.550 |
0.000 |
0.000 |
0.219 |
|
|
|
|
|
|
|
|
|
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|
|
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|
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|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 218 | 218 | 47 | 353 | 0 | 7739 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.22 | 1.62 | 0.00 | 35.50 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.041 |
0.060 |
0.285 |
0.000 |
10.636 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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|
|
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|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 210 | 210 | 50 | 350 | 0 | 8237 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.24 | 1.67 | 0.00 | 39.22 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.032 |
0.077 |
0.263 |
0.000 |
10.425 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
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|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 222 | 222 | 65 | 349 | 0 | 7910 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.29 | 1.57 | 0.00 | 35.63 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.030 |
0.073 |
0.271 |
0.000 |
9.991 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
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|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 214 | 68 | 350 | 0 | 8105 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.32 | 1.64 | 0.00 | 37.87 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.029 |
0.057 |
0.259 |
0.000 |
9.371 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 685 | 327 | 0 | 323 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 10.54 | 5.03 | 0.00 | 4.97 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.129 |
3.211 |
0.161 |
0.000 |
0.710 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 876 | 311 | 0 | 112 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 13.90 | 4.94 | 0.00 | 1.78 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.128 |
7.991 |
0.158 |
0.000 |
0.911 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
C |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 0 | 818 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 15.43 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.055 |
0.156 |
2.997 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 0 | 2134 | 0 | 267 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 19.76 | 0.00 | 2.47 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.093 |
0.036 |
5.820 |
0.000 |
2.696 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 135 | 120 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.38 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.093 |
0.087 |
0.134 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 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 |
0.300 |
0.199 |
0.206 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 80 | 0 | 110 | 387 | 0 | 113 | 157 |
normalized size | 1 | 1.00 | 0.83 | 0.00 | 1.15 | 4.03 | 0.00 | 1.18 | 1.64 |
time (sec) |
N/A |
0.078 |
0.040 |
0.120 |
1.474 |
0.932 |
0.000 |
20.990 |
0.590 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 122 | 112 | 614 | 0 | 253 | 0 | 0 | -1 |
normalized size | 1 | 1.39 | 1.27 | 6.98 | 0.00 | 2.88 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.062 |
0.073 |
2.416 |
0.000 |
4.673 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
F |
F |
B |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 233 | 26 | 26 | 0 | 0 | 373 | 0 | 0 | -1 |
normalized size | 1 | 0.11 | 0.11 | 0.00 | 0.00 | 1.60 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.011 |
0.017 |
1.865 |
0.000 |
3.433 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 73 | 655 | 86 | 90 | 0 | 87 | 100 |
normalized size | 1 | 1.00 | 0.89 | 7.99 | 1.05 | 1.10 | 0.00 | 1.06 | 1.22 |
time (sec) |
N/A |
0.058 |
0.028 |
3.427 |
1.512 |
0.663 |
0.000 |
0.884 |
0.548 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
F |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 409 | 0 | 720 | 0 | 318 | 0 | 0 | -1 |
normalized size | 1 | 3.03 | 0.00 | 5.33 | 0.00 | 2.36 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.337 |
0.138 |
7.804 |
0.000 |
12.832 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 409 | 150 | 676 | 0 | 318 | 0 | 0 | -1 |
normalized size | 1 | 3.03 | 1.11 | 5.01 | 0.00 | 2.36 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.301 |
0.308 |
7.503 |
0.000 |
12.883 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
F |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 399 | 0 | 652 | 0 | 268 | 0 | 0 | -1 |
normalized size | 1 | 3.35 | 0.00 | 5.48 | 0.00 | 2.25 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.299 |
0.128 |
7.938 |
0.000 |
13.536 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 0 | 43 | 34 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.425 |
0.154 |
0.096 |
0.000 |
0.578 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 0 | 43 | 34 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.220 |
0.085 |
0.092 |
0.000 |
0.603 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
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 | 39 | 39 | 43 | 34 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.029 |
0.019 |
0.095 |
0.000 |
0.725 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
B |
A |
C |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 101 | 12 | 105 | 94 | 31 | 0 | 10 |
normalized size | 1 | 1.00 | 1.51 | 0.18 | 1.57 | 1.40 | 0.46 | 0.00 | 0.15 |
time (sec) |
N/A |
0.010 |
0.120 |
0.102 |
1.300 |
0.622 |
1.021 |
0.000 |
0.342 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 65 | 66 | 73 | 75 | 41 | 74 | 91 |
normalized size | 1 | 1.00 | 0.93 | 0.94 | 1.04 | 1.07 | 0.59 | 1.06 | 1.30 |
time (sec) |
N/A |
0.038 |
0.027 |
0.104 |
1.410 |
0.871 |
1.017 |
0.889 |
0.403 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 384 | 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 | -0.00 |
time (sec) |
N/A |
0.068 |
0.282 |
0.127 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 234 | 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 | -0.00 |
time (sec) |
N/A |
0.415 |
0.352 |
0.194 |
0.000 |
4.434 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F(-1) |
F |
B |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 199 | 0 | 0 | 0 | 0 | 1827 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 9.18 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.945 |
0.284 |
180.000 |
0.000 |
5.170 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 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 |
0.060 |
0.326 |
0.114 |
0.000 |
5.349 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 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 |
0.071 |
0.153 |
0.017 |
0.000 |
4.596 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
F |
F |
A |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 21 | 111 | 0 | 0 | 191 | 0 | 0 | -1 |
normalized size | 1 | 0.16 | 0.84 | 0.00 | 0.00 | 1.45 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.008 |
0.096 |
0.603 |
0.000 |
0.631 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
F |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 250 | 26 | 26 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.10 | 0.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.012 |
0.014 |
0.116 |
0.000 |
4.310 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
C |
F |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 383 | 0 | 138 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.399 |
0.157 |
0.112 |
0.000 |
11.791 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
C |
F |
A |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 272 | 21 | 109 | 1214 | 0 | 341 | 0 | 0 | -1 |
normalized size | 1 | 0.08 | 0.40 | 4.46 | 0.00 | 1.25 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.008 |
0.093 |
6.549 |
0.000 |
3.530 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
2.3 Detailed conclusion table specific for Rubi results
The following table is specific to Rubi. It gives additional statistics for each integral. the column
steps is the number of steps used by Rubi to obtain the antiderivative. The rules
column is the number of unique rules used. The integrand size column is the leaf
size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder
the integral was to solve. In this test, problem number [29] had the largest ratio of
[2.143]
|
|
|
|
|
|
|
| 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 |
1 |
1 |
1.00 |
10 |
0.100 |
|
|
|
|
|
|
|
2 |
C |
5 |
2 |
3.47 |
37 |
0.054 |
|
|
|
|
|
|
|
3 |
A |
9 |
6 |
1.00 |
15 |
0.400 |
|
|
|
|
|
|
|
4 |
A |
3 |
3 |
1.00 |
19 |
0.158 |
|
|
|
|
|
|
|
5 |
A |
8 |
7 |
1.00 |
17 |
0.412 |
|
|
|
|
|
|
|
6 |
A |
6 |
6 |
1.00 |
17 |
0.353 |
|
|
|
|
|
|
|
7 |
A |
3 |
3 |
1.00 |
17 |
0.176 |
|
|
|
|
|
|
|
8 |
A |
4 |
2 |
1.00 |
23 |
0.087 |
|
|
|
|
|
|
|
9 |
A |
18 |
12 |
1.66 |
27 |
0.444 |
|
|
|
|
|
|
|
10 |
B |
25 |
13 |
2.46 |
39 |
0.333 |
|
|
|
|
|
|
|
11 |
A |
7 |
3 |
1.00 |
45 |
0.067 |
|
|
|
|
|
|
|
12 |
A |
7 |
4 |
1.00 |
32 |
0.125 |
|
|
|
|
|
|
|
13 |
A |
5 |
3 |
1.00 |
32 |
0.094 |
|
|
|
|
|
|
|
14 |
A |
2 |
2 |
1.00 |
27 |
0.074 |
|
|
|
|
|
|
|
15 |
A |
2 |
2 |
1.00 |
29 |
0.069 |
|
|
|
|
|
|
|
16 |
A |
2 |
1 |
1.00 |
30 |
0.033 |
|
|
|
|
|
|
|
17 |
A |
3 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
18 |
A |
3 |
2 |
1.00 |
15 |
0.133 |
|
|
|
|
|
|
|
19 |
A |
2 |
2 |
1.00 |
23 |
0.087 |
|
|
|
|
|
|
|
20 |
A |
2 |
2 |
1.00 |
25 |
0.080 |
|
|
|
|
|
|
|
21 |
A |
3 |
2 |
1.00 |
11 |
0.182 |
|
|
|
|
|
|
|
22 |
A |
2 |
2 |
1.00 |
18 |
0.111 |
|
|
|
|
|
|
|
23 |
A |
6 |
6 |
1.00 |
20 |
0.300 |
|
|
|
|
|
|
|
24 |
A |
6 |
5 |
1.00 |
31 |
0.161 |
|
|
|
|
|
|
|
25 |
A |
2 |
2 |
1.00 |
29 |
0.069 |
|
|
|
|
|
|
|
26 |
A |
2 |
2 |
1.00 |
35 |
0.057 |
|
|
|
|
|
|
|
27 |
A |
5 |
5 |
1.00 |
32 |
0.156 |
|
|
|
|
|
|
|
28 |
A |
6 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
29 |
A |
359 |
30 |
1.12 |
14 |
2.143 |
|
|
|
|
|
|
|
30 |
A |
2 |
2 |
1.00 |
23 |
0.087 |
|
|
|
|
|
|
|
31 |
A |
3 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
32 |
A |
2 |
2 |
1.00 |
33 |
0.061 |
|
|
|
|
|
|
|
33 |
A |
5 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
34 |
A |
5 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
35 |
A |
1 |
1 |
1.00 |
11 |
0.091 |
|
|
|
|
|
|
|
36 |
A |
5 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
37 |
A |
1 |
1 |
1.00 |
17 |
0.059 |
|
|
|
|
|
|
|
38 |
A |
3 |
3 |
1.00 |
18 |
0.167 |
|
|
|
|
|
|
|
39 |
A |
2 |
2 |
1.60 |
16 |
0.125 |
|
|
|
|
|
|
|
40 |
A |
5 |
5 |
1.62 |
17 |
0.294 |
|
|
|
|
|
|
|
41 |
A |
5 |
5 |
1.77 |
13 |
0.385 |
|
|
|
|
|
|
|
42 |
A |
5 |
5 |
1.84 |
16 |
0.312 |
|
|
|
|
|
|
|
43 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
44 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
45 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
46 |
C |
7 |
3 |
1.17 |
32 |
0.094 |
|
|
|
|
|
|
|
47 |
A |
19 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
48 |
A |
29 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
49 |
A |
49 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
50 |
A |
14 |
6 |
1.00 |
23 |
0.261 |
|
|
|
|
|
|
|
51 |
A |
24 |
6 |
1.00 |
23 |
0.261 |
|
|
|
|
|
|
|
52 |
C |
9 |
8 |
3.09 |
48 |
0.167 |
|
|
|
|
|
|
|
53 |
A |
7 |
7 |
1.00 |
24 |
0.292 |
|
|
|
|
|
|
|
54 |
A |
7 |
7 |
1.00 |
24 |
0.292 |
|
|
|
|
|
|
|
55 |
A |
1 |
1 |
1.00 |
18 |
0.056 |
|
|
|
|
|
|
|
56 |
A |
8 |
8 |
1.47 |
13 |
0.615 |
|
|
|
|
|
|
|
57 |
A |
6 |
6 |
1.00 |
15 |
0.400 |
|
|
|
|
|
|
|
58 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
59 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
60 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
61 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
62 |
A |
1 |
1 |
1.00 |
38 |
0.026 |
|
|
|
|
|
|
|
63 |
A |
1 |
1 |
1.00 |
33 |
0.030 |
|
|
|
|
|
|
|
64 |
A |
2 |
2 |
1.00 |
39 |
0.051 |
|
|
|
|
|
|
|
65 |
A |
1 |
1 |
1.00 |
19 |
0.053 |
|
|
|
|
|
|
|
66 |
A |
4 |
4 |
1.00 |
19 |
0.210 |
|
|
|
|
|
|
|
67 |
A |
4 |
4 |
1.00 |
24 |
0.167 |
|
|
|
|
|
|
|
68 |
A |
1 |
1 |
1.00 |
24 |
0.042 |
|
|
|
|
|
|
|
69 |
A |
7 |
7 |
1.00 |
24 |
0.292 |
|
|
|
|
|
|
|
70 |
A |
7 |
7 |
1.00 |
24 |
0.292 |
|
|
|
|
|
|
|
71 |
A |
3 |
3 |
1.00 |
26 |
0.115 |
|
|
|
|
|
|
|
72 |
A |
3 |
3 |
1.00 |
22 |
0.136 |
|
|
|
|
|
|
|
73 |
A |
1 |
1 |
1.00 |
22 |
0.045 |
|
|
|
|
|
|
|
74 |
A |
1 |
1 |
1.00 |
23 |
0.043 |
|
|
|
|
|
|
|
75 |
A |
8 |
8 |
1.00 |
18 |
0.444 |
|
|
|
|
|
|
|
76 |
A |
8 |
7 |
1.00 |
23 |
0.304 |
|
|
|
|
|
|
|
77 |
A |
1 |
1 |
1.00 |
21 |
0.048 |
|
|
|
|
|
|
|
78 |
A |
1 |
1 |
1.00 |
19 |
0.053 |
|
|
|
|
|
|
|
79 |
A |
1 |
1 |
1.00 |
19 |
0.053 |
|
|
|
|
|
|
|
80 |
A |
1 |
1 |
1.00 |
19 |
0.053 |
|
|
|
|
|
|
|
81 |
A |
4 |
4 |
1.00 |
34 |
0.118 |
|
|
|
|
|
|
|
82 |
C |
5 |
5 |
529.00 |
40 |
0.125 |
|
|
|
|
|
|
|
83 |
C |
7 |
7 |
3.91 |
51 |
0.137 |
|
|
|
|
|
|
|
84 |
A |
2 |
2 |
1.00 |
29 |
0.069 |
|
|
|
|
|
|
|
85 |
A |
2 |
2 |
1.00 |
18 |
0.111 |
|
|
|
|
|
|
|
86 |
A |
1 |
1 |
1.00 |
25 |
0.040 |
|
|
|
|
|
|
|
87 |
A |
1 |
1 |
1.00 |
25 |
0.040 |
|
|
|
|
|
|
|
88 |
A |
1 |
1 |
1.00 |
25 |
0.040 |
|
|
|
|
|
|
|
89 |
A |
1 |
1 |
1.00 |
25 |
0.040 |
|
|
|
|
|
|
|
90 |
A |
2 |
2 |
1.00 |
40 |
0.050 |
|
|
|
|
|
|
|
91 |
A |
2 |
2 |
1.00 |
40 |
0.050 |
|
|
|
|
|
|
|
92 |
A |
1 |
1 |
1.00 |
18 |
0.056 |
|
|
|
|
|
|
|
93 |
A |
3 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
94 |
A |
7 |
7 |
1.38 |
21 |
0.333 |
|
|
|
|
|
|
|
95 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
96 |
A |
5 |
5 |
1.00 |
24 |
0.208 |
|
|
|
|
|
|
|
97 |
A |
7 |
7 |
1.39 |
19 |
0.368 |
|
|
|
|
|
|
|
98 |
C |
1 |
1 |
0.11 |
20 |
0.050 |
|
|
|
|
|
|
|
99 |
A |
5 |
5 |
1.00 |
22 |
0.227 |
|
|
|
|
|
|
|
100 |
C |
4 |
2 |
3.03 |
25 |
0.080 |
|
|
|
|
|
|
|
101 |
C |
5 |
3 |
3.03 |
24 |
0.125 |
|
|
|
|
|
|
|
102 |
C |
4 |
2 |
3.35 |
23 |
0.087 |
|
|
|
|
|
|
|
103 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
104 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
105 |
A |
3 |
3 |
1.00 |
19 |
0.158 |
|
|
|
|
|
|
|
106 |
A |
2 |
2 |
1.00 |
11 |
0.182 |
|
|
|
|
|
|
|
107 |
A |
6 |
6 |
1.00 |
15 |
0.400 |
|
|
|
|
|
|
|
108 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
109 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
110 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
111 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
112 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
113 |
C |
1 |
1 |
0.16 |
19 |
0.053 |
|
|
|
|
|
|
|
114 |
C |
1 |
1 |
0.10 |
20 |
0.050 |
|
|
|
|
|
|
|
115 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
116 |
C |
1 |
1 |
0.08 |
19 |
0.053 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|