Chapter 2
detailed summary tables of results
2.1 List of integrals sorted by grade for each CAS
2.1.1 Rubi
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87,
88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99 }
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87,
88, 89, 91, 92, 96, 97 }
B grade: { }
C grade: { 90, 93, 94, 95, 98, 99 }
F grade: { }
2.1.3 Maple
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 18, 20, 22, 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, 66, 68, 69, 70, 71, 72, 79, 80, 81, 82,
83, 84, 85, 86, 87, 88, 89, 91, 92, 97 }
B grade: { 90, 93, 94, 95, 96 }
C grade: { 12, 14, 19, 21, 23, 24, 25, 26, 27, 28, 73, 76, 98, 99 }
F grade: { 29, 30, 31, 32, 33, 34, 65, 67, 74, 75, 77, 78 }
2.1.4 Maxima
A grade: { 1, 3, 8, 10, 15, 17, 22, 29, 33, 34, 37, 43, 45, 46, 47, 48, 61, 62, 63, 64, 66, 68, 88, 89, 91, 92, 97
}
B grade: { 23, 24, 25, 26, 27, 28, 30, 31, 32, 90, 95, 96 }
C grade: { 2, 4, 5, 6, 7, 9, 11, 12, 13, 14, 16, 18, 19, 20, 21, 35, 36, 38, 39, 40, 41, 42, 44, 49, 50, 51, 52, 53,
54, 55, 56, 57, 58, 59, 60, 69, 70, 71, 72, 85, 86, 87 }
F grade: { 65, 67, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 93, 94, 98, 99 }
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 62, 63, 64, 66, 68, 69, 70, 71, 72, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 95, 96, 97
}
B grade: { }
C grade: { 93, 94, 98, 99 }
F grade: { 65, 67, 73, 74, 75, 76, 77, 78 }
2.1.6 Sympy
A grade: { 1, 3, 4, 8, 10, 11, 15, 17, 18, 22, 36, 37, 38, 39, 43, 46, 47, 48, 62, 63, 64, 66, 88, 89, 90, 91, 92,
97 }
B grade: { 2, 9, 16, 45, 61 }
C grade: { }
F grade: { 5, 6, 7, 12, 13, 14, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 40, 41, 42, 44, 49,
50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83,
84, 85, 86, 87, 93, 94, 95, 96, 98, 99 }
2.1.7 Giac
A grade: { 1, 3, 5, 8, 10, 12, 15, 17, 19, 22, 37, 38, 45, 46, 47, 48, 61, 62, 63, 64, 66, 68, 88, 89, 90, 91, 92,
96, 97 }
B grade: { 7, 14, 21, 35, 36, 39, 95 }
C grade: { 2, 4, 9, 11, 16, 18, 49, 50, 51, 55, 56, 57, 85, 86, 87 }
F grade: { 6, 13, 20, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44, 52, 53,
54, 58, 59, 60, 65, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 93, 94, 98, 99
}
2.1.8 Mupad
A grade: { 63, 64, 66, 68, 88, 89 }
B grade: { 1, 3, 4, 8, 10, 15, 17, 22, 37, 38, 39, 42, 43, 45, 46, 47, 48, 61, 62, 85, 86, 87, 92, 97
}
C grade: { }
F grade: { 2, 5, 6, 7, 9, 11, 12, 13, 14, 16, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36,
40, 41, 44, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 65, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 90, 91, 93, 94, 95, 96, 98, 99 }
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 | 34 | 34 | 29 | 31 | 27 | 27 | 36 | 27 | 27 |
normalized size | 1 | 1.00 | 0.85 | 0.91 | 0.79 | 0.79 | 1.06 | 0.79 | 0.79 |
time (sec) |
N/A |
0.032 |
0.049 |
0.023 |
1.111 |
0.569 |
0.769 |
0.376 |
0.101 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
C |
A |
B |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 82 | 58 | 67 | 72 | 209 | 135 | -1 |
normalized size | 1 | 1.00 | 0.90 | 0.64 | 0.74 | 0.79 | 2.30 | 1.48 | -0.01 |
time (sec) |
N/A |
0.069 |
0.149 |
0.020 |
2.053 |
0.639 |
1.944 |
0.540 |
0.000 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 14 | 13 | 13 | 19 | 13 | 13 |
normalized size | 1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 1.27 | 0.87 | 0.87 |
time (sec) |
N/A |
0.014 |
0.003 |
0.020 |
0.428 |
0.855 |
0.170 |
0.380 |
0.060 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
C |
A |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 57 | 44 | 48 | 61 | 61 | 95 | 51 |
normalized size | 1 | 1.00 | 0.81 | 0.63 | 0.69 | 0.87 | 0.87 | 1.36 | 0.73 |
time (sec) |
N/A |
0.021 |
0.091 |
0.019 |
0.806 |
0.822 |
0.442 |
0.394 |
0.357 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
C |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 24 | 22 | 43 | 29 | 0 | 21 | -1 |
normalized size | 1 | 1.00 | 0.96 | 0.88 | 1.72 | 1.16 | 0.00 | 0.84 | -0.04 |
time (sec) |
N/A |
0.029 |
0.050 |
0.024 |
1.142 |
0.882 |
0.000 |
0.418 |
0.000 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 81 | 57 | 73 | 70 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 0.71 | 0.91 | 0.88 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.045 |
0.181 |
0.026 |
1.577 |
0.872 |
0.000 |
0.000 |
0.000 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
C |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 42 | 39 | 48 | 57 | 0 | 87 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.93 | 1.14 | 1.36 | 0.00 | 2.07 | -0.02 |
time (sec) |
N/A |
0.089 |
0.071 |
0.022 |
1.075 |
0.930 |
0.000 |
0.487 |
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 |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 40 | 42 | 42 | 45 | 78 | 55 | 41 |
normalized size | 1 | 1.00 | 0.78 | 0.82 | 0.82 | 0.88 | 1.53 | 1.08 | 0.80 |
time (sec) |
N/A |
0.052 |
0.114 |
0.040 |
0.898 |
0.940 |
1.548 |
0.429 |
0.148 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
C |
A |
B |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 87 | 63 | 89 | 84 | 201 | 118 | -1 |
normalized size | 1 | 1.00 | 0.96 | 0.69 | 0.98 | 0.92 | 2.21 | 1.30 | -0.01 |
time (sec) |
N/A |
0.097 |
0.171 |
0.035 |
1.226 |
0.750 |
2.598 |
0.824 |
0.000 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 27 | 34 | 23 | 28 | 60 | 26 | 22 |
normalized size | 1 | 1.00 | 0.87 | 1.10 | 0.74 | 0.90 | 1.94 | 0.84 | 0.71 |
time (sec) |
N/A |
0.029 |
0.043 |
0.028 |
0.591 |
1.326 |
0.407 |
0.400 |
0.272 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
C |
A |
A |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 67 | 45 | 70 | 59 | 56 | 82 | -1 |
normalized size | 1 | 1.00 | 0.96 | 0.64 | 1.00 | 0.84 | 0.80 | 1.17 | -0.01 |
time (sec) |
N/A |
0.044 |
0.054 |
0.046 |
1.455 |
0.950 |
0.800 |
0.315 |
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 |
C |
C |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 34 | 68 | 51 | 39 | 0 | 35 | -1 |
normalized size | 1 | 1.00 | 0.92 | 1.84 | 1.38 | 1.05 | 0.00 | 0.95 | -0.03 |
time (sec) |
N/A |
0.052 |
0.062 |
0.146 |
1.306 |
0.898 |
0.000 |
0.410 |
0.000 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 76 | 76 | 76 | 62 | 83 | 66 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.82 | 1.09 | 0.87 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.067 |
0.161 |
0.037 |
1.544 |
0.889 |
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 |
C |
C |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 50 | 89 | 61 | 65 | 0 | 107 | -1 |
normalized size | 1 | 1.00 | 0.88 | 1.56 | 1.07 | 1.14 | 0.00 | 1.88 | -0.02 |
time (sec) |
N/A |
0.118 |
0.119 |
0.165 |
1.738 |
0.671 |
0.000 |
0.398 |
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 |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 55 | 66 | 58 | 58 | 92 | 58 | 66 |
normalized size | 1 | 1.00 | 0.70 | 0.84 | 0.73 | 0.73 | 1.16 | 0.73 | 0.84 |
time (sec) |
N/A |
0.074 |
0.138 |
0.040 |
1.047 |
0.865 |
2.775 |
0.366 |
0.410 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
C |
A |
B |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 188 | 160 | 130 | 143 | 148 | 439 | 259 | -1 |
normalized size | 1 | 1.00 | 0.85 | 0.69 | 0.76 | 0.79 | 2.34 | 1.38 | -0.01 |
time (sec) |
N/A |
0.182 |
0.425 |
0.036 |
0.963 |
0.661 |
4.380 |
0.522 |
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 |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 33 | 26 | 27 | 25 | 44 | 26 | 28 |
normalized size | 1 | 1.00 | 1.00 | 0.79 | 0.82 | 0.76 | 1.33 | 0.79 | 0.85 |
time (sec) |
N/A |
0.028 |
0.016 |
0.028 |
0.473 |
0.717 |
0.768 |
0.369 |
0.289 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 153 | 153 | 116 | 101 | 112 | 121 | 129 | 185 | -1 |
normalized size | 1 | 1.00 | 0.76 | 0.66 | 0.73 | 0.79 | 0.84 | 1.21 | -0.01 |
time (sec) |
N/A |
0.089 |
0.231 |
0.035 |
1.292 |
1.372 |
1.139 |
0.600 |
0.000 |
|
|
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
C |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 50 | 125 | 89 | 63 | 0 | 47 | -1 |
normalized size | 1 | 1.00 | 0.91 | 2.27 | 1.62 | 1.15 | 0.00 | 0.85 | -0.02 |
time (sec) |
N/A |
0.083 |
0.094 |
0.171 |
1.509 |
1.524 |
0.000 |
0.608 |
0.000 |
|
|
|
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 168 | 168 | 166 | 128 | 151 | 136 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 0.76 | 0.90 | 0.81 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.144 |
0.640 |
0.043 |
3.088 |
0.861 |
0.000 |
0.000 |
0.000 |
|
|
|
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Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
C |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 90 | 162 | 98 | 108 | 0 | 185 | -1 |
normalized size | 1 | 1.00 | 0.99 | 1.78 | 1.08 | 1.19 | 0.00 | 2.03 | -0.01 |
time (sec) |
N/A |
0.201 |
0.175 |
0.196 |
1.061 |
0.682 |
0.000 |
0.463 |
0.000 |
|
|
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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 | 67 | 67 | 54 | 50 | 55 | 51 | 94 | 52 | 55 |
normalized size | 1 | 1.00 | 0.81 | 0.75 | 0.82 | 0.76 | 1.40 | 0.78 | 0.82 |
time (sec) |
N/A |
0.054 |
0.086 |
0.030 |
1.098 |
0.937 |
7.818 |
0.373 |
0.745 |
|
|
|
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Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 113 | 229 | 156 | 58 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.02 | 2.06 | 1.41 | 0.52 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.081 |
0.195 |
0.109 |
2.188 |
0.880 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
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|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 111 | 290 | 158 | 56 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 2.61 | 1.42 | 0.50 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.079 |
0.152 |
0.077 |
1.335 |
0.603 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 89 | 290 | 138 | 44 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 3.58 | 1.70 | 0.54 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.063 |
0.084 |
0.059 |
1.159 |
0.988 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 89 | 338 | 135 | 44 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 4.17 | 1.67 | 0.54 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.065 |
0.066 |
0.079 |
2.843 |
0.953 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 114 | 338 | 133 | 56 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.16 | 3.45 | 1.36 | 0.57 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.076 |
0.173 |
0.071 |
1.336 |
0.796 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 117 | 358 | 133 | 61 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.12 | 3.44 | 1.28 | 0.59 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.075 |
0.154 |
0.061 |
1.802 |
0.915 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 142 | 0 | 174 | 78 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.08 | 0.00 | 1.32 | 0.59 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.175 |
0.404 |
0.197 |
1.753 |
1.054 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 142 | 0 | 182 | 77 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.08 | 0.00 | 1.38 | 0.58 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.124 |
0.328 |
0.164 |
1.971 |
0.872 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 100 | 122 | 0 | 156 | 50 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.22 | 0.00 | 1.56 | 0.50 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.130 |
0.218 |
0.154 |
2.598 |
0.727 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 120 | 0 | 159 | 50 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.25 | 0.00 | 1.66 | 0.52 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.068 |
0.221 |
0.183 |
2.447 |
0.892 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 137 | 0 | 143 | 59 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.17 | 0.00 | 1.22 | 0.50 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.163 |
0.337 |
0.136 |
1.869 |
0.975 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 137 | 0 | 145 | 63 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.18 | 0.00 | 1.25 | 0.54 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.100 |
0.343 |
0.147 |
0.910 |
0.659 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 31 | 39 | 57 | 45 | 0 | 132 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.26 | 1.84 | 1.45 | 0.00 | 4.26 | -0.03 |
time (sec) |
N/A |
0.072 |
0.032 |
0.051 |
1.902 |
1.153 |
0.000 |
0.345 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 21 | 43 | 28 | 15 | 41 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.05 | 2.15 | 1.40 | 0.75 | 2.05 | -0.05 |
time (sec) |
N/A |
0.027 |
0.042 |
0.041 |
2.010 |
1.433 |
0.966 |
0.413 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
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 | 13 | 13 | 13 | 14 | 13 | 15 | 15 | 15 | 13 |
normalized size | 1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.15 | 1.15 | 1.15 | 1.00 |
time (sec) |
N/A |
0.014 |
0.003 |
0.021 |
2.000 |
0.925 |
0.975 |
0.356 |
0.264 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 29 | 42 | 51 | 33 | 31 | 49 | 30 |
normalized size | 1 | 1.00 | 0.97 | 1.40 | 1.70 | 1.10 | 1.03 | 1.63 | 1.00 |
time (sec) |
N/A |
0.025 |
0.051 |
0.039 |
1.695 |
0.746 |
1.803 |
0.393 |
0.279 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 46 | 92 | 50 | 43 | 46 | 107 | 47 |
normalized size | 1 | 1.00 | 1.00 | 2.00 | 1.09 | 0.93 | 1.00 | 2.33 | 1.02 |
time (sec) |
N/A |
0.047 |
0.005 |
0.043 |
1.227 |
0.713 |
3.041 |
0.428 |
0.372 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 80 | 57 | 127 | 73 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 0.72 | 1.61 | 0.92 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.050 |
0.133 |
0.025 |
2.371 |
0.802 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 24 | 22 | 43 | 29 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 0.88 | 1.72 | 1.16 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.028 |
0.042 |
0.025 |
1.336 |
0.568 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
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Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 62 | 48 | 98 | 65 | 0 | 0 | 55 |
normalized size | 1 | 1.00 | 0.84 | 0.65 | 1.32 | 0.88 | 0.00 | 0.00 | 0.74 |
time (sec) |
N/A |
0.032 |
0.107 |
0.023 |
1.242 |
0.694 |
0.000 |
0.000 |
0.406 |
|
|
|
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Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 14 | 13 | 17 | 22 | 0 | 13 |
normalized size | 1 | 1.00 | 1.00 | 0.93 | 0.87 | 1.13 | 1.47 | 0.00 | 0.87 |
time (sec) |
N/A |
0.015 |
0.003 |
0.022 |
0.665 |
0.993 |
2.816 |
0.000 |
0.268 |
|
|
|
|
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Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 88 | 64 | 74 | 84 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.91 | 0.66 | 0.76 | 0.87 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.053 |
0.157 |
0.023 |
1.288 |
0.680 |
0.000 |
0.000 |
0.000 |
|
|
|
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Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 18 | 14 | 12 | 13 | 39 | 12 | 12 |
normalized size | 1 | 1.00 | 0.95 | 0.74 | 0.63 | 0.68 | 2.05 | 0.63 | 0.63 |
time (sec) |
N/A |
0.021 |
0.029 |
0.044 |
0.300 |
0.534 |
0.263 |
0.379 |
0.367 |
|
|
|
|
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|
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Problem 46 |
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 | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 6 |
normalized size | 1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 |
time (sec) |
N/A |
0.009 |
0.002 |
0.023 |
0.904 |
0.778 |
0.249 |
0.382 |
0.033 |
|
|
|
|
|
|
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|
Problem 47 |
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 | 17 | 16 | 16 | 20 | 16 | 16 |
normalized size | 1 | 1.00 | 1.00 | 0.77 | 0.73 | 0.73 | 0.91 | 0.73 | 0.73 |
time (sec) |
N/A |
0.011 |
0.015 |
0.026 |
0.849 |
0.623 |
0.239 |
0.489 |
0.278 |
|
|
|
|
|
|
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|
Problem 48 |
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 | 36 | 36 | 31 | 34 | 23 | 24 | 51 | 23 | 23 |
normalized size | 1 | 1.00 | 0.86 | 0.94 | 0.64 | 0.67 | 1.42 | 0.64 | 0.64 |
time (sec) |
N/A |
0.021 |
0.024 |
0.025 |
0.656 |
1.261 |
0.254 |
0.406 |
0.345 |
|
|
|
|
|
|
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|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 235 | 235 | 165 | 196 | 135 | 145 | 0 | 241 | -1 |
normalized size | 1 | 1.00 | 0.70 | 0.83 | 0.57 | 0.62 | 0.00 | 1.03 | -0.00 |
time (sec) |
N/A |
0.348 |
0.578 |
0.035 |
0.808 |
0.597 |
0.000 |
2.210 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 169 | 169 | 141 | 131 | 111 | 118 | 0 | 193 | -1 |
normalized size | 1 | 1.00 | 0.83 | 0.78 | 0.66 | 0.70 | 0.00 | 1.14 | -0.01 |
time (sec) |
N/A |
0.196 |
0.354 |
0.029 |
1.238 |
0.768 |
0.000 |
0.496 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 94 | 64 | 73 | 78 | 0 | 143 | -1 |
normalized size | 1 | 1.00 | 0.95 | 0.65 | 0.74 | 0.79 | 0.00 | 1.44 | -0.01 |
time (sec) |
N/A |
0.113 |
0.154 |
0.022 |
1.027 |
0.894 |
0.000 |
0.517 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 110 | 78 | 74 | 96 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.71 | 0.67 | 0.87 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.143 |
0.253 |
0.030 |
1.961 |
1.262 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 180 | 129 | 76 | 134 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 0.70 | 0.41 | 0.73 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.238 |
0.249 |
0.035 |
1.622 |
0.809 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 250 | 250 | 238 | 180 | 76 | 164 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 0.72 | 0.30 | 0.66 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.337 |
0.336 |
0.030 |
1.288 |
0.650 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 310 | 310 | 174 | 219 | 161 | 184 | 0 | 224 | -1 |
normalized size | 1 | 1.00 | 0.56 | 0.71 | 0.52 | 0.59 | 0.00 | 0.72 | -0.00 |
time (sec) |
N/A |
0.360 |
0.645 |
0.062 |
1.237 |
0.979 |
0.000 |
1.249 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 218 | 218 | 148 | 145 | 137 | 144 | 0 | 176 | -1 |
normalized size | 1 | 1.00 | 0.68 | 0.67 | 0.63 | 0.66 | 0.00 | 0.81 | -0.00 |
time (sec) |
N/A |
0.251 |
0.438 |
0.060 |
1.237 |
0.732 |
0.000 |
0.451 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 103 | 67 | 95 | 90 | 0 | 124 | -1 |
normalized size | 1 | 1.00 | 1.01 | 0.66 | 0.93 | 0.88 | 0.00 | 1.22 | -0.01 |
time (sec) |
N/A |
0.170 |
0.184 |
0.057 |
1.266 |
1.469 |
0.000 |
0.532 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 116 | 87 | 87 | 100 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.75 | 0.75 | 0.86 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.187 |
0.246 |
0.056 |
1.297 |
0.872 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 228 | 228 | 185 | 146 | 89 | 154 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.81 | 0.64 | 0.39 | 0.68 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.250 |
0.274 |
0.059 |
1.715 |
0.856 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 328 | 328 | 249 | 207 | 89 | 192 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.76 | 0.63 | 0.27 | 0.59 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.351 |
0.384 |
0.064 |
1.829 |
1.237 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 66 | 58 | 47 | 48 | 513 | 47 | 62 |
normalized size | 1 | 1.00 | 0.77 | 0.67 | 0.55 | 0.56 | 5.97 | 0.55 | 0.72 |
time (sec) |
N/A |
0.068 |
0.098 |
0.037 |
0.851 |
1.042 |
2.605 |
0.386 |
0.496 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 6 |
normalized size | 1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 |
time (sec) |
N/A |
0.010 |
0.002 |
0.022 |
0.985 |
0.977 |
75.626 |
0.357 |
0.427 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 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 | -0.05 |
time (sec) |
N/A |
0.020 |
1.010 |
0.985 |
0.000 |
0.657 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 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 | -0.04 |
time (sec) |
N/A |
0.022 |
1.286 |
0.895 |
0.000 |
1.537 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 93 | 93 | 89 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.102 |
0.174 |
1.051 |
0.000 |
1.702 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.049 |
0.933 |
0.914 |
0.000 |
0.935 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 149 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.167 |
0.428 |
1.000 |
0.000 |
0.910 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.054 |
1.142 |
0.943 |
0.000 |
1.004 |
0.000 |
0.000 |
0.000 |
|
|
|
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Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 24 | 25 | 90 | 35 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.92 | 0.96 | 3.46 | 1.35 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.034 |
0.066 |
0.027 |
1.741 |
1.311 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
|
|
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|
|
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|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 37 | 45 | 99 | 48 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.86 | 1.05 | 2.30 | 1.12 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.058 |
0.094 |
0.054 |
2.361 |
0.652 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
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|
|
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|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 53 | 52 | 179 | 74 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.79 | 0.78 | 2.67 | 1.10 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.086 |
0.127 |
0.053 |
1.863 |
0.820 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 66 | 77 | 188 | 87 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.84 | 0.97 | 2.38 | 1.10 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.094 |
0.137 |
0.054 |
2.619 |
0.900 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 92 | 75 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.11 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.022 |
0.082 |
0.119 |
0.000 |
1.136 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 94 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.069 |
0.246 |
0.231 |
0.000 |
0.934 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 179 | 179 | 173 | 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 |
0.079 |
0.242 |
0.284 |
0.000 |
0.815 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 115 | 111 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.075 |
0.205 |
0.160 |
0.000 |
0.993 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 129 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.160 |
0.520 |
0.188 |
0.000 |
0.942 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 229 | 229 | 221 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.212 |
0.559 |
0.253 |
0.000 |
0.681 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 45 | 45 | 0 | 62 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 0.96 | 0.00 | 1.32 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.086 |
0.096 |
0.041 |
0.000 |
0.838 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 53 | 65 | 0 | 72 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.77 | 0.94 | 0.00 | 1.04 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.121 |
0.192 |
0.059 |
0.000 |
0.962 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 95 | 101 | 0 | 117 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.84 | 0.89 | 0.00 | 1.04 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.200 |
0.238 |
0.058 |
0.000 |
1.038 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 70 | 65 | 0 | 90 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 0.83 | 0.00 | 1.15 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.111 |
0.137 |
0.043 |
0.000 |
0.923 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 82 | 89 | 0 | 106 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.86 | 0.94 | 0.00 | 1.12 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.147 |
0.224 |
0.059 |
0.000 |
0.702 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 141 | 144 | 0 | 167 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.85 | 0.87 | 0.00 | 1.01 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.253 |
0.360 |
0.067 |
0.000 |
0.924 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 76 | 131 | 256 | 112 | 0 | 159 | 80 |
normalized size | 1 | 1.00 | 0.77 | 1.32 | 2.59 | 1.13 | 0.00 | 1.61 | 0.81 |
time (sec) |
N/A |
0.068 |
0.285 |
0.027 |
3.190 |
0.815 |
0.000 |
0.457 |
0.146 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 42 | 63 | 197 | 63 | 0 | 119 | 39 |
normalized size | 1 | 1.00 | 0.89 | 1.34 | 4.19 | 1.34 | 0.00 | 2.53 | 0.83 |
time (sec) |
N/A |
0.032 |
0.049 |
0.026 |
1.870 |
0.990 |
0.000 |
0.550 |
0.071 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 36 | 84 | 40 | 0 | 55 | 32 |
normalized size | 1 | 1.00 | 1.00 | 1.24 | 2.90 | 1.38 | 0.00 | 1.90 | 1.10 |
time (sec) |
N/A |
0.006 |
0.008 |
0.020 |
0.823 |
0.951 |
0.000 |
0.400 |
0.062 |
|
|
|
|
|
|
|
|
|
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|
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|
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|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 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 | -0.07 |
time (sec) |
N/A |
0.008 |
2.647 |
0.150 |
0.000 |
0.921 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 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 | -0.07 |
time (sec) |
N/A |
0.009 |
5.219 |
0.133 |
0.000 |
0.655 |
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 |
B |
B |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 346 | 346 | 224 | 825 | 672 | 103 | 269 | 480 | -1 |
normalized size | 1 | 1.00 | 0.65 | 2.38 | 1.94 | 0.30 | 0.78 | 1.39 | -0.00 |
time (sec) |
N/A |
0.305 |
0.831 |
0.050 |
0.645 |
1.750 |
1.647 |
0.454 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 71 | 299 | 263 | 67 | 151 | 166 | -1 |
normalized size | 1 | 1.00 | 0.43 | 1.79 | 1.57 | 0.40 | 0.90 | 0.99 | -0.01 |
time (sec) |
N/A |
0.136 |
0.283 |
0.043 |
0.365 |
0.796 |
0.517 |
0.474 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
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 | 54 | 54 | 48 | 61 | 60 | 42 | 66 | 42 | 42 |
normalized size | 1 | 1.00 | 0.89 | 1.13 | 1.11 | 0.78 | 1.22 | 0.78 | 0.78 |
time (sec) |
N/A |
0.027 |
0.074 |
0.021 |
0.300 |
0.916 |
0.403 |
0.329 |
0.344 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 126 | 145 | 271 | 0 | 149 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.15 | 2.15 | 0.00 | 1.18 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.239 |
0.671 |
0.058 |
0.000 |
0.924 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 240 | 714 | 0 | 210 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.30 | 3.88 | 0.00 | 1.14 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.349 |
1.205 |
0.081 |
0.000 |
0.975 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
B |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 537 | 537 | 382 | 1809 | 1349 | 182 | 0 | 1104 | -1 |
normalized size | 1 | 1.00 | 0.71 | 3.37 | 2.51 | 0.34 | 0.00 | 2.06 | -0.00 |
time (sec) |
N/A |
0.511 |
1.098 |
0.050 |
0.750 |
0.951 |
0.000 |
0.496 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 261 | 261 | 117 | 655 | 523 | 110 | 0 | 370 | -1 |
normalized size | 1 | 1.00 | 0.45 | 2.51 | 2.00 | 0.42 | 0.00 | 1.42 | -0.00 |
time (sec) |
N/A |
0.231 |
0.425 |
0.045 |
0.696 |
0.773 |
0.000 |
1.259 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
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 | 85 | 85 | 65 | 131 | 118 | 57 | 94 | 81 | 68 |
normalized size | 1 | 1.00 | 0.76 | 1.54 | 1.39 | 0.67 | 1.11 | 0.95 | 0.80 |
time (sec) |
N/A |
0.055 |
0.113 |
0.034 |
0.436 |
1.093 |
1.161 |
0.429 |
0.382 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 234 | 234 | 243 | 279 | 0 | 287 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.04 | 1.19 | 0.00 | 1.23 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.468 |
0.428 |
0.067 |
0.000 |
1.089 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 332 | 332 | 138 | 933 | 0 | 406 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.42 | 2.81 | 0.00 | 1.22 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.741 |
0.602 |
0.097 |
0.000 |
0.791 |
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 [35] had the largest ratio of
[.6250]
|
|
|
|
|
|
|
| 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 |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
2 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
3 |
A |
2 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
4 |
A |
3 |
3 |
1.00 |
8 |
0.375 |
|
|
|
|
|
|
|
5 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
6 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
7 |
A |
5 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
8 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
9 |
A |
6 |
5 |
1.00 |
14 |
0.357 |
|
|
|
|
|
|
|
10 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
11 |
A |
5 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
12 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
13 |
A |
6 |
6 |
1.00 |
14 |
0.429 |
|
|
|
|
|
|
|
14 |
A |
7 |
6 |
1.00 |
14 |
0.429 |
|
|
|
|
|
|
|
15 |
A |
4 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
16 |
A |
10 |
5 |
1.00 |
14 |
0.357 |
|
|
|
|
|
|
|
17 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
18 |
A |
8 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
19 |
A |
8 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
20 |
A |
9 |
5 |
1.00 |
14 |
0.357 |
|
|
|
|
|
|
|
21 |
A |
12 |
6 |
1.00 |
14 |
0.429 |
|
|
|
|
|
|
|
22 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
23 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
24 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
25 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
26 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
27 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
28 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
29 |
A |
7 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
30 |
A |
7 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
31 |
A |
6 |
4 |
1.00 |
16 |
0.250 |
|
|
|
|
|
|
|
32 |
A |
6 |
4 |
1.00 |
16 |
0.250 |
|
|
|
|
|
|
|
33 |
A |
7 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
34 |
A |
7 |
6 |
1.00 |
16 |
0.375 |
|
|
|
|
|
|
|
35 |
A |
5 |
5 |
1.00 |
8 |
0.625 |
|
|
|
|
|
|
|
36 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
37 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
38 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
39 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
40 |
A |
5 |
5 |
1.00 |
8 |
0.625 |
|
|
|
|
|
|
|
41 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
42 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
43 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
44 |
A |
5 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
45 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
46 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
47 |
A |
3 |
3 |
1.00 |
6 |
0.500 |
|
|
|
|
|
|
|
48 |
A |
3 |
3 |
1.00 |
8 |
0.375 |
|
|
|
|
|
|
|
49 |
A |
13 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
50 |
A |
10 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
51 |
A |
7 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
52 |
A |
8 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
53 |
A |
11 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
54 |
A |
14 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
55 |
A |
15 |
10 |
1.00 |
18 |
0.556 |
|
|
|
|
|
|
|
56 |
A |
12 |
9 |
1.00 |
18 |
0.500 |
|
|
|
|
|
|
|
57 |
A |
9 |
8 |
1.00 |
18 |
0.444 |
|
|
|
|
|
|
|
58 |
A |
10 |
9 |
1.00 |
18 |
0.500 |
|
|
|
|
|
|
|
59 |
A |
12 |
10 |
1.00 |
18 |
0.556 |
|
|
|
|
|
|
|
60 |
A |
16 |
9 |
1.00 |
18 |
0.500 |
|
|
|
|
|
|
|
61 |
A |
7 |
5 |
1.00 |
8 |
0.625 |
|
|
|
|
|
|
|
62 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
63 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
64 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
65 |
A |
3 |
3 |
1.00 |
20 |
0.150 |
|
|
|
|
|
|
|
66 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
67 |
A |
5 |
5 |
1.00 |
22 |
0.227 |
|
|
|
|
|
|
|
68 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
69 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
70 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
71 |
A |
8 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
72 |
A |
8 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
73 |
A |
3 |
2 |
1.00 |
8 |
0.250 |
|
|
|
|
|
|
|
74 |
A |
5 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
75 |
A |
8 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
76 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
77 |
A |
5 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
78 |
A |
8 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
79 |
A |
5 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
80 |
A |
7 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
81 |
A |
12 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
82 |
A |
6 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
83 |
A |
8 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
84 |
A |
14 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
85 |
A |
7 |
6 |
1.00 |
12 |
0.500 |
|
|
|
|
|
|
|
86 |
A |
5 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
87 |
A |
1 |
1 |
1.00 |
8 |
0.125 |
|
|
|
|
|
|
|
88 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
89 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
90 |
A |
14 |
3 |
1.00 |
18 |
0.167 |
|
|
|
|
|
|
|
91 |
A |
8 |
3 |
1.00 |
16 |
0.188 |
|
|
|
|
|
|
|
92 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
93 |
A |
8 |
4 |
1.00 |
18 |
0.222 |
|
|
|
|
|
|
|
94 |
A |
10 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
95 |
A |
20 |
4 |
1.00 |
18 |
0.222 |
|
|
|
|
|
|
|
96 |
A |
11 |
4 |
1.00 |
16 |
0.250 |
|
|
|
|
|
|
|
97 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
98 |
A |
11 |
4 |
1.00 |
18 |
0.222 |
|
|
|
|
|
|
|
99 |
A |
13 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|