Chapter 2
detailed summary tables of results
2.1 List of integrals sorted by grade for each CAS
2.1.1 Rubi
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,
29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,
54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78,
79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102,
103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121,
122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140,
141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159,
160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178
}
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, 26, 28, 29, 30, 31,
32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 54, 55, 61, 62, 67, 68, 73, 74, 76, 77, 78,
79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 119, 120, 121, 122, 123, 124, 125,
129, 130, 131, 132, 133, 134, 135, 138, 139, 140, 141, 142, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153,
154, 156, 157, 158, 159, 160, 161, 162, 163, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178
}
B grade: { 25, 27 }
C grade: { 48, 51, 52, 53, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 75, 98, 99, 100, 101, 102, 103,
104, 105, 107, 108, 109, 110, 111, 112, 113, 115, 116, 117, 118, 126, 127, 128, 136, 137, 146, 155, 164
}
F grade: { 106, 114, 165, 166, 167}
2.1.3 Maple
A grade: { 1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 14, 33, 34, 35, 39, 40, 42, 43, 44, 45, 46, 47, 54, 55, 61, 62, 67, 68,
73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 88, 89, 90, 91, 92, 93, 94, 95, 121, 122, 123, 124, 125, 130, 131,
132, 133, 134, 135, 141, 142, 143, 144, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171, 172, 173,
177, 178 }
B grade: { 9, 10, 49, 50, 105, 112, 113 }
C grade: { 51, 52, 53, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 75 }
F grade: { 8, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 37, 38, 41, 48, 86, 87,
96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 114, 115, 116, 117, 118, 119, 120, 126,
127, 128, 129, 136, 137, 138, 139, 140, 145, 146, 147, 148, 149, 154, 155, 156, 157, 158, 163, 164, 165, 166,
167, 174, 175, 176 }
2.1.4 Maxima
A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 17, 20, 29, 33, 34, 35, 42, 43, 44, 45, 46, 47, 76, 77, 78, 79, 80, 81, 82,
83, 84, 85, 88, 89, 90, 91, 92, 93, 94, 95, 168, 169, 170, 171, 172, 173, 177, 178
B grade: { 10, 12, 14 }
C grade: { }
F grade: { 8, 15, 16, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 36, 37, 38, 39, 40, 41, 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, 86, 87, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113,
114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132,
133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151,
152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 174, 175, 176
}
2.1.5 FriCAS
A grade: { 2, 4, 10, 11, 12, 13, 14, 23, 32, 33, 34, 35, 39, 40, 42, 43, 54, 55, 61, 62, 67, 68, 73, 74, 76, 77,
80, 81, 82, 83, 84, 85, 88, 92, 93, 94, 95, 118, 119, 120, 121, 122, 123, 124, 125, 128, 129, 130, 131, 132,
133, 134, 135, 138, 139, 141, 142, 143, 144, 147, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171,
172, 173, 174, 175, 177, 178 }
B grade: { 1, 3, 5, 6, 7, 9, 15, 17, 20, 21, 22, 29, 30, 31, 44, 45, 46, 47, 49, 50, 78, 79, 89, 90, 91, 105, 112,
113, 140, 148, 149, 156, 157, 158, 176 }
C grade: { }
F grade: { 8, 16, 18, 19, 24, 25, 26, 27, 28, 36, 37, 38, 41, 48, 51, 52, 53, 56, 57, 58, 59, 60, 63, 64,
65, 66, 69, 70, 71, 72, 75, 86, 87, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109,
110, 111, 114, 115, 116, 117, 126, 127, 136, 137, 145, 146, 154, 155, 163, 164, 165, 166, 167
}
2.1.6 Sympy
A grade: { 9, 33, 34, 35, 40, 42, 43, 61, 121, 124, 125, 141, 144, 177 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30,
31, 32, 36, 37, 38, 39, 41, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66,
67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95,
96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115,
116, 117, 118, 119, 120, 122, 123, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137,
138, 139, 140, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158,
159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 178
}
2.1.7 Giac
A grade: { 33, 34, 35, 39, 40, 42, 43, 54, 55, 61, 62, 67, 68, 73, 74, 121, 122, 123, 124, 125, 130, 131, 132,
133, 134, 135, 141, 142, 143, 144, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171, 172, 173, 177,
178 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 36, 37, 38, 41, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71,
72, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101,
102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 126, 127, 128,
129, 136, 137, 138, 139, 140, 145, 146, 147, 148, 149, 154, 155, 156, 157, 158, 163, 164, 165, 166, 167, 174,
175, 176 }
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 |
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grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 107 | 127 | 213 | 473 | 0 | 0 |
normalized size | 1 | 1. | 0.97 | 1.15 | 1.94 | 4.3 | 0. | 0. |
time (sec) |
N/A |
0.061 |
0.137 |
0.205 |
1.037 |
2.437 |
0. |
0. |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 72 | 83 | 104 | 215 | 0 | 0 |
normalized size | 1 | 1. | 0.84 | 0.97 | 1.21 | 2.5 | 0. | 0. |
time (sec) |
N/A |
0.044 |
0.127 |
0.184 |
1.004 |
2.192 |
0. |
0. |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 97 | 108 | 173 | 443 | 0 | 0 |
normalized size | 1 | 1. | 1.13 | 1.26 | 2.01 | 5.15 | 0. | 0. |
time (sec) |
N/A |
0.048 |
0.047 |
0.184 |
1.006 |
2.314 |
0. |
0. |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 62 | 74 | 77 | 190 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.19 | 1.24 | 3.06 | 0. | 0. |
time (sec) |
N/A |
0.027 |
0.094 |
0.194 |
1.01 |
2.266 |
0. |
0. |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 85 | 87 | 130 | 414 | 0 | 0 |
normalized size | 1 | 1. | 1.37 | 1.4 | 2.1 | 6.68 | 0. | 0. |
time (sec) |
N/A |
0.035 |
0.05 |
0.171 |
0.986 |
2.325 |
0. |
0. |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 38 | 50 | 65 | 47 | 154 | 0 | 0 |
normalized size | 1 | 1. | 1.32 | 1.71 | 1.24 | 4.05 | 0. | 0. |
time (sec) |
N/A |
0.013 |
0.023 |
0.197 |
1.007 |
2.208 |
0. |
0. |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 44 | 36 | 66 | 320 | 0 | 0 |
normalized size | 1 | 1. | 1.47 | 1.2 | 2.2 | 10.67 | 0. | 0. |
time (sec) |
N/A |
0.021 |
0.06 |
0.198 |
1.016 |
2.257 |
0. |
0. |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 47 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.84 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.09 |
0.04 |
0.198 |
0. |
0. |
0. |
0. |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
B |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 40 | 62 | 43 | 135 | 36 | 0 |
normalized size | 1 | 1. | 1.33 | 2.07 | 1.43 | 4.5 | 1.2 | 0. |
time (sec) |
N/A |
0.024 |
0.03 |
0.174 |
0.996 |
2.142 |
2.732 |
0. |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 50 | 50 | 66 | 100 | 142 | 167 | 0 | 0 |
normalized size | 1 | 1. | 1.32 | 2. | 2.84 | 3.34 | 0. | 0. |
time (sec) |
N/A |
0.037 |
0.033 |
0.182 |
0.998 |
2.203 |
0. |
0. |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 59 | 75 | 76 | 171 | 0 | 0 |
normalized size | 1 | 1. | 1.02 | 1.29 | 1.31 | 2.95 | 0. | 0. |
time (sec) |
N/A |
0.043 |
0.046 |
0.197 |
0.996 |
2.137 |
0. |
0. |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 78 | 120 | 198 | 196 | 0 | 0 |
normalized size | 1 | 1. | 1.05 | 1.62 | 2.68 | 2.65 | 0. | 0. |
time (sec) |
N/A |
0.048 |
0.042 |
0.195 |
1.015 |
2.126 |
0. |
0. |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 69 | 83 | 99 | 197 | 0 | 0 |
normalized size | 1 | 1. | 0.87 | 1.05 | 1.25 | 2.49 | 0. | 0. |
time (sec) |
N/A |
0.051 |
0.061 |
0.193 |
0.978 |
2.12 |
0. |
0. |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 88 | 139 | 250 | 225 | 0 | 0 |
normalized size | 1 | 1. | 0.9 | 1.42 | 2.55 | 2.3 | 0. | 0. |
time (sec) |
N/A |
0.064 |
0.072 |
0.197 |
1.052 |
2.177 |
0. |
0. |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 122 | 0 | 0 | 603 | 0 | 0 |
normalized size | 1 | 1. | 1.16 | 0. | 0. | 5.74 | 0. | 0. |
time (sec) |
N/A |
0.119 |
0.205 |
0.187 |
0. |
2.356 |
0. |
0. |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 211 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.73 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.132 |
1.366 |
0.184 |
0. |
0. |
0. |
0. |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 87 | 0 | 111 | 524 | 0 | 0 |
normalized size | 1 | 1. | 1.61 | 0. | 2.06 | 9.7 | 0. | 0. |
time (sec) |
N/A |
0.076 |
0.137 |
0.19 |
1.009 |
2.451 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 121 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.78 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.068 |
0.222 |
0.207 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 115 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.42 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.138 |
0.131 |
0.201 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 70 | 0 | 105 | 296 | 0 | 0 |
normalized size | 1 | 1. | 1.43 | 0. | 2.14 | 6.04 | 0. | 0. |
time (sec) |
N/A |
0.07 |
0.162 |
0.18 |
1.012 |
2.057 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 100 | 0 | 0 | 350 | 0 | 0 |
normalized size | 1 | 1. | 1.15 | 0. | 0. | 4.02 | 0. | 0. |
time (sec) |
N/A |
0.082 |
0.137 |
0.187 |
0. |
2.114 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 100 | 106 | 0 | 0 | 385 | 0 | 0 |
normalized size | 1 | 1. | 1.06 | 0. | 0. | 3.85 | 0. | 0. |
time (sec) |
N/A |
0.108 |
0.184 |
0.186 |
0. |
2.203 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 147 | 0 | 0 | 432 | 0 | 0 |
normalized size | 1 | 1. | 1.11 | 0. | 0. | 3.27 | 0. | 0. |
time (sec) |
N/A |
0.117 |
0.174 |
0.204 |
0. |
2.229 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 195 | 195 | 271 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.39 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.232 |
0.975 |
0.178 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 548 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.82 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.208 |
7.484 |
0.199 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 171 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.46 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.16 |
0.457 |
0.191 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 120 | 120 | 246 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.05 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.117 |
0.324 |
0.191 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 198 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.8 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.154 |
0.216 |
0.2 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 132 | 0 | 194 | 477 | 0 | 0 |
normalized size | 1 | 1. | 1.69 | 0. | 2.49 | 6.12 | 0. | 0. |
time (sec) |
N/A |
0.099 |
0.232 |
0.186 |
0.992 |
2.312 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 182 | 0 | 0 | 576 | 0 | 0 |
normalized size | 1 | 1. | 1.48 | 0. | 0. | 4.68 | 0. | 0. |
time (sec) |
N/A |
0.106 |
0.311 |
0.204 |
0. |
2.468 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 200 | 0 | 0 | 640 | 0 | 0 |
normalized size | 1 | 1. | 1.2 | 0. | 0. | 3.86 | 0. | 0. |
time (sec) |
N/A |
0.171 |
0.301 |
0.184 |
0. |
2.566 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 204 | 204 | 277 | 0 | 0 | 747 | 0 | 0 |
normalized size | 1 | 1. | 1.36 | 0. | 0. | 3.66 | 0. | 0. |
time (sec) |
N/A |
0.181 |
0.336 |
0.183 |
0. |
2.472 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.015 |
2.875 |
0.194 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.006 |
2.698 |
0.185 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.026 |
0.286 |
0.21 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 44 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.96 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.104 |
0.072 |
0.177 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 56 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.89 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.141 |
0.072 |
0.19 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 91 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.78 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.24 |
0.157 |
0.179 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
4.832 |
0.183 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.025 |
3.198 |
0.194 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 81 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.21 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.045 |
0.231 |
0.183 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.028 |
0.362 |
0.186 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.027 |
0.719 |
0.196 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 165 | 269 | 352 | 898 | 0 | 0 |
normalized size | 1 | 1. | 0.99 | 1.61 | 2.11 | 5.38 | 0. | 0. |
time (sec) |
N/A |
0.384 |
0.279 |
0.178 |
1.016 |
3.641 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 122 | 204 | 259 | 709 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.67 | 2.12 | 5.81 | 0. | 0. |
time (sec) |
N/A |
0.259 |
0.181 |
0.218 |
1.029 |
3.171 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 99 | 115 | 117 | 479 | 0 | 0 |
normalized size | 1 | 1. | 1.22 | 1.42 | 1.44 | 5.91 | 0. | 0. |
time (sec) |
N/A |
0.161 |
0.195 |
0.22 |
1.002 |
2.65 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 44 | 36 | 66 | 320 | 0 | 0 |
normalized size | 1 | 1. | 1.47 | 1.2 | 2.2 | 10.67 | 0. | 0. |
time (sec) |
N/A |
0.022 |
0.048 |
0.169 |
0.988 |
2.385 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 215 | 215 | 506 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.35 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.39 |
0.729 |
0.566 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 134 | 208 | 0 | 741 | 0 | 0 |
normalized size | 1 | 1. | 1.37 | 2.12 | 0. | 7.56 | 0. | 0. |
time (sec) |
N/A |
0.154 |
0.215 |
0.305 |
0. |
2.683 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 163 | 163 | 204 | 963 | 0 | 1524 | 0 | 0 |
normalized size | 1 | 1. | 1.25 | 5.91 | 0. | 9.35 | 0. | 0. |
time (sec) |
N/A |
0.292 |
0.462 |
0.273 |
0. |
5.631 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 918 | 918 | 1094 | 2515 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.19 |
2.74 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
3.253 |
14.284 |
0.684 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 679 | 679 | 418 | 1964 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.62 |
2.89 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.519 |
1.605 |
0.32 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 429 | 429 | 926 | 840 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.16 |
1.96 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.708 |
13.992 |
0.301 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.076 |
18.568 |
6.829 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.079 |
7.771 |
4.661 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 486 | 486 | 380 | 1939 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.78 |
3.99 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.023 |
1.526 |
0.293 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 939 | 939 | 1098 | 2543 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.17 |
2.71 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.871 |
14.176 |
0.321 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 707 | 707 | 1012 | 1991 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.43 |
2.82 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.142 |
14.325 |
0.305 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 474 | 474 | 343 | 868 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.72 |
1.83 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.751 |
1.279 |
0.299 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 284 | 284 | 307 | 395 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.08 |
1.39 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.414 |
4.957 |
0.281 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.077 |
6.304 |
1.24 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.082 |
8.863 |
5.133 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 731 | 731 | 1042 | 2019 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.43 |
2.76 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.636 |
14.578 |
0.305 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 499 | 499 | 979 | 896 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.96 |
1.8 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.01 |
14.367 |
0.299 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 318 | 318 | 264 | 418 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.83 |
1.31 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.691 |
1.558 |
0.323 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 166 | 328 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.11 |
2.2 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.284 |
0.655 |
0.299 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.09 |
11.462 |
2.531 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.099 |
14.568 |
6.172 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 777 | 777 | 1108 | 2726 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.43 |
3.51 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
3.186 |
14.346 |
0.316 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 569 | 569 | 1076 | 2497 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.89 |
4.39 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.497 |
14.271 |
0.319 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 393 | 393 | 390 | 2107 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.99 |
5.36 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.191 |
2.42 |
0.308 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 369 | 369 | 892 | 2079 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.42 |
5.63 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.567 |
14.064 |
0.316 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.094 |
30.203 |
4.395 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.106 |
29.24 |
7.439 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 648 | 785 | 1217 | 3782 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.21 |
1.88 |
5.84 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.035 |
14.295 |
0.326 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 214 | 138 | 211 | 390 | 680 | 0 | 0 |
normalized size | 1 | 1. | 0.64 | 0.99 | 1.82 | 3.18 | 0. | 0. |
time (sec) |
N/A |
0.132 |
0.233 |
0.196 |
1.022 |
3.32 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 119 | 171 | 306 | 617 | 0 | 0 |
normalized size | 1 | 1. | 0.71 | 1.02 | 1.83 | 3.69 | 0. | 0. |
time (sec) |
N/A |
0.109 |
0.167 |
0.18 |
1.01 |
3.17 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 135 | 126 | 200 | 544 | 0 | 0 |
normalized size | 1 | 1. | 1.17 | 1.1 | 1.74 | 4.73 | 0. | 0. |
time (sec) |
N/A |
0.056 |
0.263 |
0.209 |
1.02 |
2.959 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 89 | 107 | 113 | 493 | 0 | 0 |
normalized size | 1 | 1. | 0.98 | 1.18 | 1.24 | 5.42 | 0. | 0. |
time (sec) |
N/A |
0.068 |
0.13 |
0.194 |
0.975 |
2.762 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 68 | 122 | 123 | 234 | 0 | 0 |
normalized size | 1 | 1. | 0.62 | 1.12 | 1.13 | 2.15 | 0. | 0. |
time (sec) |
N/A |
0.079 |
0.085 |
0.2 |
0.994 |
2.359 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 158 | 158 | 93 | 140 | 178 | 294 | 0 | 0 |
normalized size | 1 | 1. | 0.59 | 0.89 | 1.13 | 1.86 | 0. | 0. |
time (sec) |
N/A |
0.103 |
0.122 |
0.197 |
1.001 |
2.604 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 109 | 158 | 223 | 350 | 0 | 0 |
normalized size | 1 | 1. | 0.53 | 0.77 | 1.09 | 1.71 | 0. | 0. |
time (sec) |
N/A |
0.122 |
0.146 |
0.198 |
1.018 |
2.703 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 204 | 204 | 114 | 152 | 238 | 378 | 0 | 0 |
normalized size | 1 | 1. | 0.56 | 0.75 | 1.17 | 1.85 | 0. | 0. |
time (sec) |
N/A |
0.161 |
0.248 |
0.2 |
1.006 |
3.051 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 159 | 159 | 97 | 134 | 185 | 323 | 0 | 0 |
normalized size | 1 | 1. | 0.61 | 0.84 | 1.16 | 2.03 | 0. | 0. |
time (sec) |
N/A |
0.134 |
0.208 |
0.197 |
1.023 |
3.343 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 146 | 146 | 77 | 115 | 128 | 266 | 0 | 0 |
normalized size | 1 | 1. | 0.53 | 0.79 | 0.88 | 1.82 | 0. | 0. |
time (sec) |
N/A |
0.106 |
0.095 |
0.184 |
1.008 |
2.777 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 93 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.81 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.291 |
0.134 |
0.222 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 138 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.08 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.3 |
0.558 |
0.231 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 260 | 260 | 182 | 286 | 535 | 891 | 0 | 0 |
normalized size | 1 | 1. | 0.7 | 1.1 | 2.06 | 3.43 | 0. | 0. |
time (sec) |
N/A |
0.258 |
0.353 |
0.19 |
1.009 |
4.209 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 197 | 197 | 149 | 217 | 387 | 792 | 0 | 0 |
normalized size | 1 | 1. | 0.76 | 1.1 | 1.96 | 4.02 | 0. | 0. |
time (sec) |
N/A |
0.128 |
0.229 |
0.184 |
1.037 |
3.813 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 170 | 170 | 134 | 189 | 258 | 747 | 0 | 0 |
normalized size | 1 | 1. | 0.79 | 1.11 | 1.52 | 4.39 | 0. | 0. |
time (sec) |
N/A |
0.139 |
0.214 |
0.187 |
1.035 |
3.269 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 164 | 164 | 123 | 191 | 205 | 743 | 0 | 0 |
normalized size | 1 | 1. | 0.75 | 1.16 | 1.25 | 4.53 | 0. | 0. |
time (sec) |
N/A |
0.143 |
0.263 |
0.191 |
1.029 |
3.013 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 126 | 191 | 236 | 382 | 0 | 0 |
normalized size | 1 | 1. | 0.67 | 1.01 | 1.25 | 2.02 | 0. | 0. |
time (sec) |
N/A |
0.16 |
0.217 |
0.191 |
1.01 |
2.454 |
0. |
0. |
|
|
|
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|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 249 | 249 | 152 | 223 | 313 | 481 | 0 | 0 |
normalized size | 1 | 1. | 0.61 | 0.9 | 1.26 | 1.93 | 0. | 0. |
time (sec) |
N/A |
0.197 |
0.259 |
0.207 |
1.04 |
2.55 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 250 | 250 | 159 | 214 | 329 | 506 | 0 | 0 |
normalized size | 1 | 1. | 0.64 | 0.86 | 1.32 | 2.02 | 0. | 0. |
time (sec) |
N/A |
0.235 |
0.403 |
0.19 |
1.055 |
2.787 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 203 | 203 | 123 | 182 | 247 | 410 | 0 | 0 |
normalized size | 1 | 1. | 0.61 | 0.9 | 1.22 | 2.02 | 0. | 0. |
time (sec) |
N/A |
0.156 |
0.302 |
0.173 |
1.026 |
2.725 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 178 | 178 | 148 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.83 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.421 |
0.44 |
0.383 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 178 | 178 | 187 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.05 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.424 |
0.902 |
0.368 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 512 | 512 | 1221 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.38 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.198 |
1.617 |
1.688 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 467 | 449 | 1103 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0.96 | 2.36 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.106 |
0.34 |
0.552 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 477 | 477 | 1055 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.21 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.849 |
0.493 |
1.143 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 425 | 425 | 387 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.91 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.862 |
0.957 |
0.48 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 518 | 518 | 1211 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.34 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.06 |
1.604 |
1.497 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 591 | 571 | 1447 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.97 |
2.45 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.282 |
6.017 |
0.585 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 553 | 535 | 1410 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.97 |
2.55 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.249 |
2.325 |
0.476 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 139 | 271 | 358 | 0 | 1288 | 0 | 0 |
normalized size |
1 |
1. |
1.95 |
2.58 |
0. |
9.27 |
0. |
0. |
time (sec) |
N/A |
0.15 |
0.719 |
0.273 |
0. |
2.732 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 515 | 515 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.153 |
43.207 |
0.586 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 756 | 756 | 1583 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.09 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.468 |
6.235 |
13.253 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 719 | 719 | 1442 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.01 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.242 |
2.58 |
1.7 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 713 | 713 | 1437 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.02 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.187 |
3.487 |
1.997 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 758 | 758 | 1487 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.96 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.246 |
2.876 |
19.474 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 694 | 676 | 2023 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.97 |
2.91 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.408 |
7.625 |
0.595 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 375 | 1914 | 0 | 2850 | 0 | 0 |
normalized size |
1 |
1. |
2.25 |
11.46 |
0. |
17.07 |
0. |
0. |
time (sec) |
N/A |
0.215 |
1.435 |
0.281 |
0. |
4.943 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 368 | 1884 | 0 | 2596 | 0 | 0 |
normalized size |
1 |
1. |
1.8 |
9.19 |
0. |
12.66 |
0. |
0. |
time (sec) |
N/A |
0.205 |
0.883 |
0.279 |
0. |
4.781 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 657 | 657 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.322 |
63.858 |
0.492 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1106 | 1106 | 2045 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.85 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.741 |
6.197 |
1.855 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1106 | 1106 | 2053 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.86 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
3.046 |
6.127 |
3.93 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1096 | 1096 | 2038 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.86 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
3.743 |
6.059 |
2. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 413 | 413 | 345 | 0 | 0 | 4346 | 0 | 0 |
normalized size |
1 |
1. |
0.84 |
0. |
0. |
10.52 |
0. |
0. |
time (sec) |
N/A |
1.412 |
0.678 |
0.457 |
0. |
20.553 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 119 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 302 | 302 | 337 | 0 | 0 | 3614 | 0 | 0 |
normalized size |
1 |
1. |
1.12 |
0. |
0. |
11.97 |
0. |
0. |
time (sec) |
N/A |
0.434 |
0.741 |
0.414 |
0. |
9.544 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 203 | 203 | 278 | 0 | 0 | 2984 | 0 | 0 |
normalized size |
1 |
1. |
1.37 |
0. |
0. |
14.7 |
0. |
0. |
time (sec) |
N/A |
0.206 |
0.507 |
0.466 |
0. |
5.439 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.1 |
5.393 |
0.452 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.106 |
5.632 |
0.453 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.101 |
9.078 |
0.448 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.037 |
2.584 |
0.464 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.09 |
1.701 |
0.449 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 389 | 389 | 237 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.427 |
0.597 |
0.539 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 527 | 527 | 314 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.6 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.638 |
0.666 |
0.451 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 128 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 384 | 384 | 318 | 0 | 0 | 4343 | 0 | 0 |
normalized size |
1 |
1. |
0.83 |
0. |
0. |
11.31 |
0. |
0. |
time (sec) |
N/A |
0.514 |
0.735 |
0.459 |
0. |
19.924 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 129 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 270 | 270 | 314 | 0 | 0 | 3579 | 0 | 0 |
normalized size |
1 |
1. |
1.16 |
0. |
0. |
13.26 |
0. |
0. |
time (sec) |
N/A |
0.281 |
0.728 |
0.447 |
0. |
10.5 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 130 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.117 |
6.294 |
0.449 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 131 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.123 |
5.661 |
0.447 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.12 |
9.293 |
0.448 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 133 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.044 |
3.482 |
0.459 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 134 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.106 |
5.537 |
0.491 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 135 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.108 |
15.47 |
0.458 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 492 | 492 | 291 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.59 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.575 |
0.682 |
0.453 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 137 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 643 | 643 | 372 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.58 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.866 |
0.824 |
0.453 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 138 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 329 | 329 | 339 | 0 | 0 | 3636 | 0 | 0 |
normalized size |
1 |
1. |
1.03 |
0. |
0. |
11.05 |
0. |
0. |
time (sec) |
N/A |
1.179 |
0.775 |
0.452 |
0. |
11.059 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 139 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 229 | 229 | 280 | 0 | 0 | 3011 | 0 | 0 |
normalized size |
1 |
1. |
1.22 |
0. |
0. |
13.15 |
0. |
0. |
time (sec) |
N/A |
0.318 |
0.543 |
0.452 |
0. |
5.885 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 223 | 0 | 0 | 2398 | 0 | 0 |
normalized size | 1 | 1. | 1.65 | 0. | 0. | 17.76 | 0. | 0. |
time (sec) |
N/A |
0.154 |
0.238 |
0.46 |
0. |
3.932 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 141 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.096 |
1.675 |
0.454 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 142 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.108 |
22.798 |
0.455 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
Problem 143 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.092 |
6.254 |
0.451 |
0. |
0. |
0. |
0. |
|
|
|
|
|
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|
|
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|
Problem 144 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.031 |
1.039 |
0.482 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
Problem 145 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 294 | 294 | 139 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.47 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.251 |
0.2 |
0.455 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
Problem 146 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 425 | 425 | 239 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.56 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.486 |
0.626 |
0.491 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 147 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 256 | 256 | 311 | 0 | 0 | 3738 | 0 | 0 |
normalized size |
1 |
1. |
1.21 |
0. |
0. |
14.6 |
0. |
0. |
time (sec) |
N/A |
1.135 |
0.634 |
0.472 |
0. |
6.069 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 148 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 233 | 0 | 0 | 2844 | 0 | 0 |
normalized size |
1 |
1. |
1.46 |
0. |
0. |
17.77 |
0. |
0. |
time (sec) |
N/A |
0.275 |
0.369 |
0.467 |
0. |
4.387 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 149 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 122 | 0 | 0 | 822 | 0 | 0 |
normalized size |
1 |
1. |
1.49 |
0. |
0. |
10.02 |
0. |
0. |
time (sec) |
N/A |
0.111 |
0.159 |
0.463 |
0. |
3.049 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 150 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.121 |
31.647 |
0.453 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 151 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.133 |
37.171 |
0.451 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 152 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.111 |
8.159 |
0.477 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 153 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.107 |
4.444 |
0.448 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 154 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 113 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.02 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.075 |
0.193 |
0.451 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 155 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 321 | 321 | 201 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.63 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.32 |
0.435 |
0.455 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 156 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 251 | 251 | 327 | 0 | 0 | 5065 | 0 | 0 |
normalized size |
1 |
1. |
1.3 |
0. |
0. |
20.18 |
0. |
0. |
time (sec) |
N/A |
1.229 |
0.556 |
0.466 |
0. |
5.798 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 157 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 169 | 169 | 201 | 0 | 0 | 1627 | 0 | 0 |
normalized size |
1 |
1. |
1.19 |
0. |
0. |
9.63 |
0. |
0. |
time (sec) |
N/A |
0.268 |
0.284 |
0.5 |
0. |
4.103 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 158 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 144 | 144 | 185 | 0 | 0 | 1439 | 0 | 0 |
normalized size |
1 |
1. |
1.28 |
0. |
0. |
9.99 |
0. |
0. |
time (sec) |
N/A |
0.144 |
0.236 |
0.496 |
0. |
3.915 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 159 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.124 |
42.622 |
0.456 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 160 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.152 |
55.256 |
0.483 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 161 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.132 |
12.566 |
0.491 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 162 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.11 |
12.23 |
0.489 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 163 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 359 | 359 | 189 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.53 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.308 |
0.281 |
0.484 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 164 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 278 | 278 | 248 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.89 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.177 |
0.532 |
0.483 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 165 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 596 | 577 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.97 |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.575 |
0.212 |
0.362 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 166 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 379 | 360 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.95 |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.491 |
0.14 |
0.374 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 167 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 208 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.95 |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.22 |
0.105 |
0.188 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 168 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.079 |
1.791 |
0.519 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 169 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.076 |
2.717 |
0.501 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 170 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.116 |
1.084 |
0.484 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 171 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.104 |
0.107 |
0.483 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 172 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.103 |
1.448 |
0.486 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 173 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.115 |
1.717 |
0.48 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 174 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 395 | 395 | 214 | 0 | 0 | 846 | 0 | 0 |
normalized size |
1 |
1. |
0.54 |
0. |
0. |
2.14 |
0. |
0. |
time (sec) |
N/A |
2.344 |
0.309 |
0.483 |
0. |
2.68 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 175 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 264 | 264 | 180 | 0 | 0 | 699 | 0 | 0 |
normalized size |
1 |
1. |
0.68 |
0. |
0. |
2.65 |
0. |
0. |
time (sec) |
N/A |
1.916 |
0.407 |
0.423 |
0. |
2.777 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 176 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 133 | 141 | 0 | 0 | 571 | 0 | 0 |
normalized size |
1 |
1.02 |
1.08 |
0. |
0. |
4.39 |
0. |
0. |
time (sec) |
N/A |
0.214 |
0.337 |
0.372 |
0. |
2.858 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 177 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.091 |
0.386 |
0.464 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 178 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.104 |
3.309 |
0.454 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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 [69] had the largest ratio of [ 0.8571
]
|
|
|
|
|
|
|
| Table 2.1Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
7 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
2 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
3 |
A |
6 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
4 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
5 |
A |
5 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
6 |
A |
2 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
7 |
A |
5 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
8 |
A |
6 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
9 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
10 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
11 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
12 |
A |
5 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
13 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
14 |
A |
6 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
15 |
A |
5 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
16 |
A |
8 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
17 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
18 |
A |
7 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
19 |
A |
6 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
20 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
|
21 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
22 |
A |
5 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
23 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
24 |
A |
10 |
10 |
1. |
14 |
0.714 |
|
|
|
|
|
|
|
25 |
A |
11 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
26 |
A |
7 |
7 |
1. |
12 |
0.583 |
|
|
|
|
|
|
|
27 |
A |
9 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
28 |
A |
7 |
7 |
1. |
14 |
0.5 |
|
|
|
|
|
|
|
29 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
30 |
A |
6 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
31 |
A |
8 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
32 |
A |
10 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
33 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
34 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
35 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
36 |
A |
4 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
37 |
A |
6 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
38 |
A |
9 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
39 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
40 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
41 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
42 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
43 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
44 |
A |
11 |
9 |
1. |
16 |
0.562 |
|
|
|
|
|
|
|
45 |
A |
10 |
9 |
1. |
16 |
0.562 |
|
|
|
|
|
|
|
46 |
A |
9 |
9 |
1. |
14 |
0.643 |
|
|
|
|
|
|
|
47 |
A |
5 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
48 |
A |
4 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
49 |
A |
7 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
50 |
A |
8 |
8 |
1. |
16 |
0.5 |
|
|
|
|
|
|
|
51 |
A |
31 |
16 |
1. |
21 |
0.762 |
|
|
|
|
|
|
|
52 |
A |
24 |
15 |
1. |
19 |
0.79 |
|
|
|
|
|
|
|
53 |
A |
15 |
11 |
1. |
18 |
0.611 |
|
|
|
|
|
|
|
54 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
55 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
56 |
A |
22 |
13 |
1. |
18 |
0.722 |
|
|
|
|
|
|
|
57 |
A |
27 |
17 |
1. |
21 |
0.81 |
|
|
|
|
|
|
|
58 |
A |
20 |
15 |
1. |
21 |
0.714 |
|
|
|
|
|
|
|
59 |
A |
14 |
13 |
1. |
19 |
0.684 |
|
|
|
|
|
|
|
60 |
A |
9 |
9 |
1. |
18 |
0.5 |
|
|
|
|
|
|
|
|
61 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
62 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
63 |
A |
23 |
15 |
1. |
21 |
0.714 |
|
|
|
|
|
|
|
64 |
A |
16 |
13 |
1. |
21 |
0.619 |
|
|
|
|
|
|
|
65 |
A |
11 |
11 |
1. |
19 |
0.579 |
|
|
|
|
|
|
|
66 |
A |
6 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
67 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
68 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
69 |
A |
31 |
18 |
1. |
21 |
0.857 |
|
|
|
|
|
|
|
70 |
A |
25 |
17 |
1. |
21 |
0.81 |
|
|
|
|
|
|
|
71 |
A |
19 |
14 |
1. |
19 |
0.737 |
|
|
|
|
|
|
|
72 |
A |
12 |
11 |
1. |
18 |
0.611 |
|
|
|
|
|
|
|
73 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
74 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
75 |
A |
19 |
14 |
1.21 |
18 |
0.778 |
|
|
|
|
|
|
|
76 |
A |
7 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
77 |
A |
6 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
78 |
A |
5 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
79 |
A |
4 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
80 |
A |
4 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
|
81 |
A |
5 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
82 |
A |
6 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
83 |
A |
5 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
84 |
A |
5 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
85 |
A |
6 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
86 |
A |
11 |
11 |
1. |
19 |
0.579 |
|
|
|
|
|
|
|
87 |
A |
13 |
13 |
1. |
19 |
0.684 |
|
|
|
|
|
|
|
88 |
A |
7 |
8 |
1. |
21 |
0.381 |
|
|
|
|
|
|
|
89 |
A |
6 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
90 |
A |
6 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
91 |
A |
6 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
92 |
A |
5 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
93 |
A |
6 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
94 |
A |
5 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
95 |
A |
6 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
96 |
A |
12 |
13 |
1. |
21 |
0.619 |
|
|
|
|
|
|
|
97 |
A |
14 |
15 |
1. |
21 |
0.714 |
|
|
|
|
|
|
|
98 |
A |
25 |
12 |
1. |
21 |
0.571 |
|
|
|
|
|
|
|
99 |
A |
26 |
9 |
0.96 |
19 |
0.474 |
|
|
|
|
|
|
|
100 |
A |
19 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
|
101 |
A |
19 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
102 |
A |
24 |
10 |
1. |
21 |
0.476 |
|
|
|
|
|
|
|
103 |
A |
31 |
14 |
0.97 |
21 |
0.667 |
|
|
|
|
|
|
|
104 |
A |
29 |
12 |
0.97 |
21 |
0.571 |
|
|
|
|
|
|
|
105 |
A |
7 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
106 |
A |
24 |
10 |
1. |
21 |
0.476 |
|
|
|
|
|
|
|
107 |
A |
51 |
15 |
1. |
21 |
0.714 |
|
|
|
|
|
|
|
108 |
A |
27 |
10 |
1. |
21 |
0.476 |
|
|
|
|
|
|
|
109 |
A |
47 |
11 |
1. |
18 |
0.611 |
|
|
|
|
|
|
|
110 |
A |
50 |
13 |
1. |
21 |
0.619 |
|
|
|
|
|
|
|
111 |
A |
33 |
13 |
0.97 |
21 |
0.619 |
|
|
|
|
|
|
|
112 |
A |
6 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
113 |
A |
8 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
114 |
A |
28 |
11 |
1. |
21 |
0.524 |
|
|
|
|
|
|
|
115 |
A |
35 |
11 |
1. |
21 |
0.524 |
|
|
|
|
|
|
|
116 |
A |
63 |
12 |
1. |
21 |
0.571 |
|
|
|
|
|
|
|
117 |
A |
81 |
12 |
1. |
18 |
0.667 |
|
|
|
|
|
|
|
118 |
A |
12 |
12 |
1. |
23 |
0.522 |
|
|
|
|
|
|
|
119 |
A |
11 |
12 |
1. |
23 |
0.522 |
|
|
|
|
|
|
|
120 |
A |
9 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
|
121 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
122 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
123 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
124 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
125 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
126 |
A |
8 |
9 |
1. |
23 |
0.391 |
|
|
|
|
|
|
|
127 |
A |
9 |
10 |
1. |
23 |
0.435 |
|
|
|
|
|
|
|
128 |
A |
12 |
12 |
1. |
23 |
0.522 |
|
|
|
|
|
|
|
129 |
A |
10 |
10 |
1. |
21 |
0.476 |
|
|
|
|
|
|
|
130 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
131 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
132 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
133 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
134 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
135 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
136 |
A |
9 |
10 |
1. |
23 |
0.435 |
|
|
|
|
|
|
|
137 |
A |
10 |
10 |
1. |
23 |
0.435 |
|
|
|
|
|
|
|
138 |
A |
11 |
12 |
1. |
23 |
0.522 |
|
|
|
|
|
|
|
139 |
A |
10 |
12 |
1. |
23 |
0.522 |
|
|
|
|
|
|
|
140 |
A |
8 |
8 |
1. |
21 |
0.381 |
|
|
|
|
|
|
|
|
141 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
142 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
143 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
144 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
145 |
A |
8 |
9 |
1. |
23 |
0.391 |
|
|
|
|
|
|
|
146 |
A |
8 |
10 |
1. |
23 |
0.435 |
|
|
|
|
|
|
|
147 |
A |
10 |
11 |
1. |
23 |
0.478 |
|
|
|
|
|
|
|
148 |
A |
9 |
11 |
1. |
23 |
0.478 |
|
|
|
|
|
|
|
149 |
A |
4 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
150 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
151 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
152 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
153 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
154 |
A |
3 |
4 |
1. |
20 |
0.2 |
|
|
|
|
|
|
|
155 |
A |
7 |
9 |
1. |
23 |
0.391 |
|
|
|
|
|
|
|
156 |
A |
10 |
11 |
1. |
23 |
0.478 |
|
|
|
|
|
|
|
157 |
A |
7 |
8 |
1. |
23 |
0.348 |
|
|
|
|
|
|
|
158 |
A |
5 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
159 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
160 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
161 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
162 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
163 |
A |
7 |
8 |
1. |
23 |
0.348 |
|
|
|
|
|
|
|
164 |
A |
5 |
7 |
1. |
20 |
0.35 |
|
|
|
|
|
|
|
165 |
A |
6 |
7 |
0.97 |
23 |
0.304 |
|
|
|
|
|
|
|
166 |
A |
6 |
7 |
0.95 |
23 |
0.304 |
|
|
|
|
|
|
|
167 |
A |
5 |
6 |
0.95 |
21 |
0.286 |
|
|
|
|
|
|
|
168 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
169 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
170 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
171 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
172 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
173 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
174 |
A |
16 |
11 |
1. |
26 |
0.423 |
|
|
|
|
|
|
|
175 |
A |
13 |
11 |
1. |
26 |
0.423 |
|
|
|
|
|
|
|
176 |
A |
8 |
9 |
1.02 |
26 |
0.346 |
|
|
|
|
|
|
|
177 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
178 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|