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, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189,
190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208,
209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 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, 79, 85, 91, 97, 98, 106, 112, 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, 158, 159, 160, 161, 162, 163, 164,
165, 166, 167, 168, 169, 170, 171, 172, 176, 177, 181, 182, 186, 187, 191, 192, 196, 197, 201,
202, 209, 210, 211, 212, 213, 214, 215, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227
}
B grade: { 157 }
C grade: { 11, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 99, 100, 101,
102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 173, 174, 175, 178, 179,
180, 183, 184, 185, 188, 189, 190, 193, 194, 195, 198, 199, 200, 203, 204, 205, 206, 207, 208
}
F grade: { 216}
2.1.3 Maple
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, 123, 124, 125, 126, 127, 128, 129, 134,
135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154,
155, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175,
176, 177, 179, 181, 182, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 201, 202,
203, 204, 205, 206, 207, 208, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227
}
B grade: { 151, 156, 157, 178, 180, 183, 184, 185, 198, 199, 200 }
C grade: { 132, 133 }
F grade: { 121, 122, 130, 131, 209, 210, 211, 212, 213, 214 }
2.1.4 Maxima
A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 16, 19, 21, 22, 24, 26, 33, 35, 37, 49, 50, 65, 66, 72, 73, 123,
140, 141, 142, 143, 145, 146, 147, 148, 150, 153, 155, 161, 162, 171, 172, 176, 177, 181, 182, 186, 187, 191,
192, 196, 197, 201, 202, 220, 221, 222, 223, 224, 225, 226, 227
B grade: { }
C grade: { }
F grade: { 6, 13, 15, 17, 18, 20, 23, 25, 27, 28, 29, 30, 31, 32, 34, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47,
48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 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, 124, 125, 126, 127, 128, 129, 130, 131,
132, 133, 134, 135, 136, 137, 138, 139, 144, 149, 151, 152, 154, 156, 157, 158, 159, 160, 163, 164, 165, 166,
167, 168, 169, 170, 173, 174, 175, 178, 179, 180, 183, 184, 185, 188, 189, 190, 193, 194, 195, 198,
199, 200, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219
}
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 21, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49,
50, 58, 59, 65, 66, 72, 73, 119, 120, 123, 124, 129, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 145,
146, 147, 148, 149, 150, 153, 154, 155, 161, 162, 166, 167, 171, 172, 215, 216, 217, 218, 219, 220, 221, 222,
223, 224, 225, 226, 227 }
B grade: { }
C grade: { }
F grade: { 6, 17, 18, 20, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55,
56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 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, 121, 122, 125, 126, 127, 128, 130, 131, 132,
133, 144, 151, 152, 156, 157, 158, 159, 160, 163, 164, 165, 168, 169, 170, 173, 174, 175, 176,
177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195,
196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214
}
2.1.6 Sympy
A grade: { 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 58, 59,
65, 66, 72, 73, 79, 85, 97, 98, 106, 112, 119, 120, 123, 124, 126, 127, 128, 129, 134, 135, 137, 138, 140,
141, 142, 143, 145, 146, 147, 148, 149, 150, 153, 154, 155, 161, 162, 166, 167, 171, 172, 176,
177, 181, 182, 191, 192, 196, 197, 201, 204, 205, 216, 220, 221, 222, 223, 224, 225, 226, 227
}
B grade: { }
C grade: { 7, 8 }
F grade: { 6, 17, 18, 19, 20, 21, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54,
55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 91,
92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118,
121, 122, 125, 130, 131, 132, 133, 136, 139, 144, 151, 152, 156, 157, 158, 159, 160, 163, 164, 165,
168, 169, 170, 173, 174, 175, 178, 179, 180, 183, 184, 185, 186, 187, 188, 189, 190, 193, 194,
195, 198, 199, 200, 202, 203, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 217, 218, 219
}
2.1.7 Giac
A grade: { 1, 2, 3, 4, 5, 7, 9, 11, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 42, 43, 44, 45,
46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 79, 85,
91, 97, 98, 106, 112, 118, 119, 120, 123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 139, 140,
141, 142, 143, 150, 155, 158, 159, 160, 161, 162, 166, 167, 171, 172, 176, 177, 181, 182, 186, 187,
191, 192, 196, 197, 201, 202, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227
}
B grade: { 8, 10, 19, 21, 51, 145, 146, 147, 148, 149, 153, 154, 163, 164, 165, 168, 169, 170
}
C grade: { 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 173, 174, 175, 178,
179, 180, 183, 184, 185, 188, 189, 190 }
F grade: { 6, 17, 18, 20, 27, 28, 29, 30, 31, 38, 39, 40, 41, 99, 100, 101, 102, 103, 104, 105, 107,
108, 109, 110, 111, 113, 114, 115, 116, 117, 121, 122, 130, 131, 132, 133, 144, 151, 152, 156,
157, 193, 194, 195, 198, 199, 200, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214
}
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 |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 51 | 72 | 96 | 113 | 70 | 153 |
normalized size | 1 | 1. | 0.68 | 0.96 | 1.28 | 1.51 | 0.93 | 2.04 |
time (sec) |
N/A |
0.049 |
0.032 |
0.032 |
1.686 |
2.134 |
7.083 |
1.222 |
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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 |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 50 | 60 | 99 | 109 | 61 | 113 |
normalized size | 1 | 1. | 0.72 | 0.87 | 1.43 | 1.58 | 0.88 | 1.64 |
time (sec) |
N/A |
0.029 |
0.019 |
0.004 |
1.727 |
2.026 |
1.645 |
1.448 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 41 | 52 | 68 | 92 | 48 | 86 |
normalized size | 1 | 1. | 0.76 | 0.96 | 1.26 | 1.7 | 0.89 | 1.59 |
time (sec) |
N/A |
0.035 |
0.025 |
0.003 |
1.709 |
2.138 |
0.82 |
1.303 |
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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 |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 40 | 40 | 70 | 86 | 37 | 62 |
normalized size | 1 | 1. | 0.89 | 0.89 | 1.56 | 1.91 | 0.82 | 1.38 |
time (sec) |
N/A |
0.016 |
0.011 |
0.004 |
1.671 |
2.2 |
0.346 |
1.239 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 25 | 32 | 57 | 20 | 32 |
normalized size | 1 | 1. | 1. | 1. | 1.28 | 2.28 | 0.8 | 1.28 |
time (sec) |
N/A |
0.008 |
0.008 |
0.001 |
1.689 |
2.106 |
0.619 |
1.331 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 46 | 111 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.9 | 2.18 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.058 |
0.028 |
0.158 |
0. |
0. |
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 |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 28 | 31 | 53 | 124 | 32 | 65 |
normalized size | 1 | 1. | 1. | 1.11 | 1.89 | 4.43 | 1.14 | 2.32 |
time (sec) |
N/A |
0.022 |
0.002 |
0.003 |
1.624 |
2.235 |
4.859 |
1.475 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 29 | 38 | 38 | 66 | 51 | 92 |
normalized size | 1 | 1. | 0.85 | 1.12 | 1.12 | 1.94 | 1.5 | 2.71 |
time (sec) |
N/A |
0.014 |
0.007 |
0.003 |
1.658 |
2.191 |
2.114 |
1.282 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 53 | 53 | 81 | 176 | 109 | 95 |
normalized size | 1 | 1. | 0.95 | 0.95 | 1.45 | 3.14 | 1.95 | 1.7 |
time (sec) |
N/A |
0.033 |
0.014 |
0.003 |
1.731 |
2.743 |
7.035 |
1.315 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 41 | 58 | 68 | 89 | 100 | 176 |
normalized size | 1 | 1. | 0.71 | 1. | 1.17 | 1.53 | 1.72 | 3.03 |
time (sec) |
N/A |
0.022 |
0.019 |
0.003 |
1.656 |
2.535 |
3.911 |
1.354 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 51 | 73 | 111 | 204 | 182 | 120 |
normalized size | 1 | 1. | 0.64 | 0.91 | 1.39 | 2.55 | 2.28 | 1.5 |
time (sec) |
N/A |
0.045 |
0.013 |
0.004 |
1.764 |
2.794 |
24.051 |
1.302 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 120 | 120 | 82 | 76 | 138 | 189 | 114 | 228 |
normalized size | 1 | 1. | 0.68 | 0.63 | 1.15 | 1.58 | 0.95 | 1.9 |
time (sec) |
N/A |
0.194 |
0.034 |
0.126 |
1.67 |
2.428 |
7.614 |
1.344 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 74 | 93 | 0 | 162 | 90 | 180 |
normalized size | 1 | 1. | 0.76 | 0.95 | 0. | 1.65 | 0.92 | 1.84 |
time (sec) |
N/A |
0.163 |
0.029 |
0.063 |
0. |
2.402 |
4.84 |
1.229 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 64 | 59 | 97 | 143 | 76 | 131 |
normalized size | 1 | 1. | 0.78 | 0.72 | 1.18 | 1.74 | 0.93 | 1.6 |
time (sec) |
N/A |
0.121 |
0.028 |
0.059 |
1.735 |
2.415 |
2.594 |
1.312 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 55 | 65 | 0 | 123 | 51 | 99 |
normalized size | 1 | 1. | 0.92 | 1.08 | 0. | 2.05 | 0.85 | 1.65 |
time (sec) |
N/A |
0.093 |
0.017 |
0.025 |
0. |
2.339 |
0.77 |
1.215 |
|
|
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 35 | 37 | 45 | 89 | 32 | 45 |
normalized size | 1 | 1. | 1. | 1.06 | 1.29 | 2.54 | 0.91 | 1.29 |
time (sec) |
N/A |
0.045 |
0.011 |
0.021 |
1.821 |
2.352 |
0.239 |
1.348 |
|
|
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 71 | 169 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1. | 2.38 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.095 |
0.04 |
0.042 |
0. |
0. |
0. |
0. |
|
|
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 87 | 119 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.32 | 1.8 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.103 |
0.162 |
0.092 |
0. |
0. |
0. |
0. |
|
|
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 44 | 44 | 44 | 43 | 54 | 112 | 0 | 116 |
normalized size | 1 | 1. | 1. | 0.98 | 1.23 | 2.55 | 0. | 2.64 |
time (sec) |
N/A |
0.08 |
0.025 |
0.026 |
1.628 |
2.568 |
0. |
1.382 |
|
|
|
|
|
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|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 139 | 157 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.2 | 1.35 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.17 |
0.615 |
0.196 |
0. |
0. |
0. |
0. |
|
|
|
|
|
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|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 69 | 76 | 100 | 149 | 0 | 223 |
normalized size | 1 | 1. | 0.79 | 0.87 | 1.15 | 1.71 | 0. | 2.56 |
time (sec) |
N/A |
0.14 |
0.038 |
0.032 |
1.613 |
2.309 |
0. |
1.457 |
|
|
|
|
|
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|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 201 | 201 | 122 | 159 | 231 | 265 | 196 | 336 |
normalized size | 1 | 1. | 0.61 | 0.79 | 1.15 | 1.32 | 0.98 | 1.67 |
time (sec) |
N/A |
0.385 |
0.07 |
0.059 |
1.692 |
2.2 |
13.62 |
1.386 |
|
|
|
|
|
|
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|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 112 | 154 | 0 | 234 | 160 | 250 |
normalized size | 1 | 1. | 0.67 | 0.92 | 0. | 1.4 | 0.96 | 1.5 |
time (sec) |
N/A |
0.297 |
0.048 |
0.06 |
0. |
2.05 |
6.943 |
1.302 |
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 95 | 106 | 162 | 189 | 128 | 192 |
normalized size | 1 | 1. | 0.7 | 0.78 | 1.19 | 1.39 | 0.94 | 1.41 |
time (sec) |
N/A |
0.225 |
0.045 |
0.045 |
1.726 |
2.169 |
5.895 |
1.3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 82 | 96 | 0 | 170 | 92 | 136 |
normalized size | 1 | 1. | 0.83 | 0.97 | 0. | 1.72 | 0.93 | 1.37 |
time (sec) |
N/A |
0.156 |
0.025 |
0.041 |
0. |
2.035 |
1.609 |
1.305 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 60 | 57 | 77 | 116 | 54 | 76 |
normalized size | 1 | 1. | 1. | 0.95 | 1.28 | 1.93 | 0.9 | 1.27 |
time (sec) |
N/A |
0.08 |
0.011 |
0.024 |
1.681 |
2.047 |
0.832 |
1.36 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 97 | 229 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1. | 2.36 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.109 |
0.056 |
0.046 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 133 | 179 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.23 | 1.66 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.163 |
0.124 |
0.074 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 92 | 163 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.9 | 1.6 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.169 |
0.253 |
0.098 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 179 | 179 | 284 | 250 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.59 | 1.4 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.285 |
2.795 |
0.148 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 169 | 169 | 116 | 225 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.69 | 1.33 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.292 |
0.679 |
0.156 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 282 | 282 | 167 | 320 | 0 | 383 | 269 | 489 |
normalized size | 1 | 1. | 0.59 | 1.13 | 0. | 1.36 | 0.95 | 1.73 |
time (sec) |
N/A |
0.869 |
0.098 |
0.1 |
0. |
2.22 |
33.002 |
1.375 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 250 | 250 | 150 | 197 | 279 | 352 | 241 | 412 |
normalized size | 1 | 1. | 0.6 | 0.79 | 1.12 | 1.41 | 0.96 | 1.65 |
time (sec) |
N/A |
0.663 |
0.075 |
0.059 |
1.853 |
2.149 |
18.648 |
1.29 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 198 | 198 | 135 | 209 | 0 | 292 | 190 | 316 |
normalized size | 1 | 1. | 0.68 | 1.06 | 0. | 1.47 | 0.96 | 1.6 |
time (sec) |
N/A |
0.516 |
0.059 |
0.059 |
0. |
2.209 |
15.126 |
1.414 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 114 | 130 | 198 | 247 | 158 | 238 |
normalized size | 1 | 1. | 0.69 | 0.78 | 1.19 | 1.49 | 0.95 | 1.43 |
time (sec) |
N/A |
0.353 |
0.048 |
0.048 |
1.687 |
2.01 |
5.592 |
1.404 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 96 | 117 | 0 | 205 | 104 | 171 |
normalized size | 1 | 1. | 0.86 | 1.05 | 0. | 1.85 | 0.94 | 1.54 |
time (sec) |
N/A |
0.238 |
0.029 |
0.039 |
0. |
2.211 |
3.343 |
1.404 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 69 | 67 | 101 | 149 | 65 | 88 |
normalized size | 1 | 1. | 1. | 0.97 | 1.46 | 2.16 | 0.94 | 1.28 |
time (sec) |
N/A |
0.118 |
0.016 |
0.026 |
1.768 |
1.926 |
1.988 |
1.39 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 113 | 287 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1. | 2.54 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.122 |
0.044 |
0.046 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 156 | 156 | 198 | 241 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.27 | 1.54 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.194 |
0.267 |
0.077 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 124 | 227 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.04 | 1.91 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.216 |
0.283 |
0.091 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 276 | 276 | 399 | 409 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.45 | 1.48 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.41 |
4.27 |
0.145 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 40 | 40 | 0 | 0 | 0 | 63 |
normalized size | 1 | 1. | 0.73 | 0.73 | 0. | 0. | 0. | 1.15 |
time (sec) |
N/A |
0.097 |
0.016 |
0.039 |
0. |
0. |
0. |
1.318 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 33 | 33 | 0 | 0 | 0 | 50 |
normalized size | 1 | 1. | 0.77 | 0.77 | 0. | 0. | 0. | 1.16 |
time (sec) |
N/A |
0.08 |
0.115 |
0.031 |
0. |
0. |
0. |
1.275 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 31 | 31 | 0 | 0 | 0 | 47 |
normalized size | 1 | 1. | 0.76 | 0.76 | 0. | 0. | 0. | 1.15 |
time (sec) |
N/A |
0.081 |
0.009 |
0.023 |
0. |
0. |
0. |
1.352 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 24 | 24 | 0 | 0 | 0 | 34 |
normalized size | 1 | 1. | 0.83 | 0.83 | 0. | 0. | 0. | 1.17 |
time (sec) |
N/A |
0.062 |
0.079 |
0.022 |
0. |
0. |
0. |
1.339 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 22 | 22 | 0 | 0 | 0 | 31 |
normalized size | 1 | 1. | 0.81 | 0.81 | 0. | 0. | 0. | 1.15 |
time (sec) |
N/A |
0.063 |
0.006 |
0.021 |
0. |
0. |
0. |
1.371 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 14 | 13 | 0 | 0 | 0 | 16 |
normalized size | 1 | 1. | 1. | 0.93 | 0. | 0. | 0. | 1.14 |
time (sec) |
N/A |
0.035 |
0.023 |
0.025 |
0. |
0. |
0. |
1.346 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 9 | 9 | 10 | 0 | 0 | 0 | 12 |
normalized size | 1 | 1. | 1. | 1.11 | 0. | 0. | 0. | 1.33 |
time (sec) |
N/A |
0.017 |
0.009 |
0.017 |
0. |
0. |
0. |
1.356 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
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 |
0.013 |
0.191 |
0.09 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
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 |
0.014 |
1.098 |
0.123 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 86 | 105 | 0 | 0 | 0 | 217 |
normalized size |
1 |
1. |
1.04 |
1.27 |
0. |
0. |
0. |
2.61 |
time (sec) |
N/A |
0.074 |
0.244 |
0.042 |
0. |
0. |
0. |
1.287 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 78 | 78 | 0 | 0 | 0 | 162 |
normalized size |
1 |
1. |
1.1 |
1.1 |
0. |
0. |
0. |
2.28 |
time (sec) |
N/A |
0.063 |
0.045 |
0.033 |
0. |
0. |
0. |
1.311 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 61 | 81 | 0 | 0 | 0 | 155 |
normalized size |
1 |
1. |
0.88 |
1.17 |
0. |
0. |
0. |
2.25 |
time (sec) |
N/A |
0.058 |
0.209 |
0.026 |
0. |
0. |
0. |
1.305 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 56 | 54 | 0 | 0 | 0 | 97 |
normalized size |
1 |
1. |
0.98 |
0.95 |
0. |
0. |
0. |
1.7 |
time (sec) |
N/A |
0.049 |
0.017 |
0.021 |
0. |
0. |
0. |
1.385 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 50 | 57 | 0 | 0 | 0 | 92 |
normalized size |
1 |
1. |
0.91 |
1.04 |
0. |
0. |
0. |
1.67 |
time (sec) |
N/A |
0.044 |
0.165 |
0.023 |
0. |
0. |
0. |
1.36 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 38 | 32 | 28 | 0 | 0 | 0 | 49 |
normalized size |
1 |
1. |
0.84 |
0.74 |
0. |
0. |
0. |
1.29 |
time (sec) |
N/A |
0.025 |
0.003 |
0.024 |
0. |
0. |
0. |
1.374 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 32 | 33 | 0 | 0 | 0 | 46 |
normalized size | 1 | 1. | 0.89 | 0.92 | 0. | 0. | 0. | 1.28 |
time (sec) |
N/A |
0.078 |
0.059 |
0.019 |
0. |
0. |
0. |
1.33 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
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 |
0.012 |
0.904 |
0.078 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
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 |
0.014 |
9.711 |
0.141 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 103 | 121 | 0 | 0 | 0 | 230 |
normalized size | 1 | 1. | 1.05 | 1.23 | 0. | 0. | 0. | 2.35 |
time (sec) |
N/A |
0.343 |
0.185 |
0.042 |
0. |
0. |
0. |
1.328 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 73 | 82 | 0 | 0 | 0 | 169 |
normalized size | 1 | 1. | 0.88 | 0.99 | 0. | 0. | 0. | 2.04 |
time (sec) |
N/A |
0.3 |
0.187 |
0.034 |
0. |
0. |
0. |
1.362 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 68 | 82 | 0 | 0 | 0 | 138 |
normalized size | 1 | 1. | 0.83 | 1. | 0. | 0. | 0. | 1.68 |
time (sec) |
N/A |
0.249 |
0.136 |
0.026 |
0. |
0. |
0. |
1.371 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 61 | 45 | 0 | 0 | 0 | 90 |
normalized size | 1 | 1. | 0.95 | 0.7 | 0. | 0. | 0. | 1.41 |
time (sec) |
N/A |
0.168 |
0.06 |
0.026 |
0. |
0. |
0. |
1.418 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 48 | 43 | 0 | 0 | 0 | 58 |
normalized size | 1 | 1. | 0.94 | 0.84 | 0. | 0. | 0. | 1.14 |
time (sec) |
N/A |
0.085 |
0.022 |
0.021 |
0. |
0. |
0. |
1.339 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
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 |
0.012 |
0.541 |
0.078 |
0. |
0. |
0. |
0. |
|
|
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Problem 66 |
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 |
0.013 |
6.431 |
0.122 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 158 | 158 | 159 | 171 | 0 | 0 | 0 | 338 |
normalized size | 1 | 1. | 1.01 | 1.08 | 0. | 0. | 0. | 2.14 |
time (sec) |
N/A |
0.314 |
0.338 |
0.04 |
0. |
0. |
0. |
1.271 |
|
|
|
|
|
|
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|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 144 | 144 | 107 | 114 | 0 | 0 | 0 | 235 |
normalized size | 1 | 1. | 0.74 | 0.79 | 0. | 0. | 0. | 1.63 |
time (sec) |
N/A |
0.282 |
0.36 |
0.03 |
0. |
0. |
0. |
1.377 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
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|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 102 | 117 | 0 | 0 | 0 | 200 |
normalized size | 1 | 1. | 0.72 | 0.83 | 0. | 0. | 0. | 1.42 |
time (sec) |
N/A |
0.303 |
0.259 |
0.028 |
0. |
0. |
0. |
1.329 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 86 | 60 | 0 | 0 | 0 | 124 |
normalized size | 1 | 1. | 0.89 | 0.62 | 0. | 0. | 0. | 1.28 |
time (sec) |
N/A |
0.164 |
0.138 |
0.027 |
0. |
0. |
0. |
1.257 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 70 | 63 | 0 | 0 | 0 | 89 |
normalized size | 1 | 1. | 0.9 | 0.81 | 0. | 0. | 0. | 1.14 |
time (sec) |
N/A |
0.153 |
0.062 |
0.023 |
0. |
0. |
0. |
1.245 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
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 |
0.012 |
2.34 |
0.075 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
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 |
0.014 |
17.869 |
0.118 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 121 | 204 | 143 | 0 | 0 | 0 | 333 |
normalized size |
1 |
1. |
1.69 |
1.18 |
0. |
0. |
0. |
2.75 |
time (sec) |
N/A |
0.242 |
0.099 |
0.074 |
0. |
0. |
0. |
1.345 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 138 | 91 | 0 | 0 | 0 | 207 |
normalized size |
1 |
1. |
1.45 |
0.96 |
0. |
0. |
0. |
2.18 |
time (sec) |
N/A |
0.189 |
0.061 |
0.049 |
0. |
0. |
0. |
1.432 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 126 | 96 | 0 | 0 | 0 | 223 |
normalized size |
1 |
1. |
1.47 |
1.12 |
0. |
0. |
0. |
2.59 |
time (sec) |
N/A |
0.181 |
0.05 |
0.044 |
0. |
0. |
0. |
1.488 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 81 | 42 | 0 | 0 | 0 | 96 |
normalized size |
1 |
1. |
1.37 |
0.71 |
0. |
0. |
0. |
1.63 |
time (sec) |
N/A |
0.151 |
0.021 |
0.033 |
0. |
0. |
0. |
1.378 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 44 | 44 | 66 | 49 | 0 | 0 | 0 | 112 |
normalized size |
1 |
1. |
1.5 |
1.11 |
0. |
0. |
0. |
2.55 |
time (sec) |
N/A |
0.09 |
0.031 |
0.032 |
0. |
0. |
0. |
1.361 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
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 |
0.013 |
0.399 |
0.078 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F(-1) |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 282 | 202 | 193 | 0 | 0 | 0 | 479 |
normalized size |
1 |
1.32 |
0.94 |
0.9 |
0. |
0. |
0. |
2.24 |
time (sec) |
N/A |
0.533 |
0.065 |
0.079 |
0. |
0. |
0. |
1.401 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 130 | 121 | 0 | 0 | 0 | 304 |
normalized size |
1 |
1. |
0.83 |
0.77 |
0. |
0. |
0. |
1.94 |
time (sec) |
N/A |
0.379 |
0.033 |
0.053 |
0. |
0. |
0. |
1.398 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 136 | 131 | 0 | 0 | 0 | 320 |
normalized size |
1 |
1. |
0.93 |
0.89 |
0. |
0. |
0. |
2.18 |
time (sec) |
N/A |
0.303 |
0.059 |
0.05 |
0. |
0. |
0. |
1.392 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 71 | 64 | 0 | 0 | 0 | 144 |
normalized size |
1 |
1. |
0.8 |
0.72 |
0. |
0. |
0. |
1.62 |
time (sec) |
N/A |
0.183 |
0.015 |
0.036 |
0. |
0. |
0. |
1.342 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 76 | 72 | 0 | 0 | 0 | 161 |
normalized size |
1 |
1. |
1.01 |
0.96 |
0. |
0. |
0. |
2.15 |
time (sec) |
N/A |
0.099 |
0.043 |
0.036 |
0. |
0. |
0. |
1.469 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
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 |
0.013 |
0.372 |
0.063 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F(-1) |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 263 | 298 | 204 | 233 | 0 | 0 | 0 | 625 |
normalized size |
1 |
1.13 |
0.78 |
0.89 |
0. |
0. |
0. |
2.38 |
time (sec) |
N/A |
0.803 |
0.071 |
0.077 |
0. |
0. |
0. |
1.475 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F(-1) |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 140 | 154 | 0 | 0 | 0 | 401 |
normalized size |
1 |
1. |
0.68 |
0.75 |
0. |
0. |
0. |
1.96 |
time (sec) |
N/A |
0.6 |
0.041 |
0.056 |
0. |
0. |
0. |
1.494 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F(-1) |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 178 | 178 | 125 | 156 | 0 | 0 | 0 | 417 |
normalized size |
1 |
1. |
0.7 |
0.88 |
0. |
0. |
0. |
2.34 |
time (sec) |
N/A |
0.469 |
0.047 |
0.055 |
0. |
0. |
0. |
1.436 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F(-1) |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 81 | 79 | 0 | 0 | 0 | 193 |
normalized size |
1 |
1. |
0.68 |
0.66 |
0. |
0. |
0. |
1.62 |
time (sec) |
N/A |
0.313 |
0.02 |
0.036 |
0. |
0. |
0. |
1.463 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F(-1) |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 68 | 88 | 0 | 0 | 0 | 209 |
normalized size |
1 |
1. |
0.77 |
1. |
0. |
0. |
0. |
2.38 |
time (sec) |
N/A |
0.165 |
0.035 |
0.037 |
0. |
0. |
0. |
1.514 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
F(-1) |
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 |
0.013 |
0.373 |
0.063 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 106 | 106 | 193 | 72 | 0 | 0 | 0 | 188 |
normalized size |
1 |
1. |
1.82 |
0.68 |
0. |
0. |
0. |
1.77 |
time (sec) |
N/A |
0.112 |
0.057 |
0.055 |
0. |
0. |
0. |
1.452 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 128 | 44 | 0 | 0 | 0 | 109 |
normalized size |
1 |
1. |
1.97 |
0.68 |
0. |
0. |
0. |
1.68 |
time (sec) |
N/A |
0.083 |
0.032 |
0.039 |
0. |
0. |
0. |
1.476 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 128 | 51 | 0 | 0 | 0 | 126 |
normalized size |
1 |
1. |
1.8 |
0.72 |
0. |
0. |
0. |
1.77 |
time (sec) |
N/A |
0.089 |
0.051 |
0.039 |
0. |
0. |
0. |
1.434 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 71 | 21 | 0 | 0 | 0 | 47 |
normalized size |
1 |
1. |
2.54 |
0.75 |
0. |
0. |
0. |
1.68 |
time (sec) |
N/A |
0.045 |
0.017 |
0.029 |
0. |
0. |
0. |
1.479 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 69 | 25 | 0 | 0 | 0 | 63 |
normalized size |
1 |
1. |
2.3 |
0.83 |
0. |
0. |
0. |
2.1 |
time (sec) |
N/A |
0.024 |
0.026 |
0.028 |
0. |
0. |
0. |
1.369 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
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 |
0.014 |
0.356 |
0.069 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
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 |
0.013 |
2.993 |
0.122 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 427 | 184 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.5 |
1.08 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.144 |
0.234 |
0.077 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 231 | 121 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.82 |
0.95 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.107 |
0.135 |
0.067 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 319 | 138 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.35 |
1.01 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.098 |
0.152 |
0.051 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 154 | 83 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.71 |
0.92 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.07 |
0.046 |
0.042 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 211 | 95 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.2 |
0.99 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.069 |
0.072 |
0.046 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 91 | 43 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.65 |
0.78 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.032 |
0.033 |
0.031 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 87 | 65 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.47 |
1.1 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.09 |
0.095 |
0.035 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
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 |
0.014 |
0.455 |
0.063 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 235 | 418 | 175 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.37 |
2.44 |
1.02 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.434 |
0.329 |
0.07 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 126 | 200 | 109 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.59 |
0.87 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.338 |
0.394 |
0.057 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 277 | 117 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.22 |
0.94 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.301 |
0.208 |
0.055 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 112 | 56 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.26 |
0.63 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.18 |
0.225 |
0.039 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 76 | 76 | 138 | 83 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.82 |
1.09 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.099 |
0.127 |
0.042 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
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 |
0.013 |
0.462 |
0.069 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 264 | 264 | 417 | 225 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.58 |
0.85 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.396 |
0.772 |
0.083 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 190 | 190 | 272 | 139 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.43 |
0.73 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.319 |
1.187 |
0.055 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 191 | 191 | 280 | 154 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.47 |
0.81 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.348 |
0.476 |
0.055 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 146 | 73 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.23 |
0.61 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.172 |
0.412 |
0.038 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 143 | 110 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.36 |
1.05 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.166 |
0.26 |
0.04 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
F(-1) |
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 |
0.013 |
0.462 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 119 |
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 | 64 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.122 |
1.064 |
0.828 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 120 |
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 | 64 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.118 |
0.941 |
0.548 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 121 |
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 | 150 | 150 | 122 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.81 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.114 |
0.043 |
0.525 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 122 |
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 | 69 | 69 | 56 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.81 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.025 |
0.02 |
0.531 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 123 |
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 |
0.017 |
0.561 |
0.434 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
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 |
0.576 |
0.434 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
F(-1) |
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 |
0.016 |
2.626 |
0.07 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
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 |
0.015 |
2.929 |
0.062 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
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 |
0.015 |
2.204 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 128 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
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 |
0.015 |
2.192 |
0.059 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 129 |
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 | 14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.016 |
0.798 |
0.758 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 130 |
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 | 167 | 167 | 132 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.79 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.177 |
0.088 |
0.144 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 131 |
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 | 171 | 171 | 137 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.166 |
0.072 |
0.154 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 75 | 138 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.88 |
1.62 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.082 |
0.019 |
0.117 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 133 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 73 | 240 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.92 |
3.04 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.055 |
0.035 |
0.082 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 134 |
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 | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.015 |
0.278 |
0.102 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 135 |
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 | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.016 |
0.525 |
0.072 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 136 |
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 | 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.021 |
3.571 |
0.089 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 137 |
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 | 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.017 |
4.269 |
0.07 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 138 |
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 | 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.018 |
1.552 |
0.069 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 139 |
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 | 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.021 |
1.9 |
0.069 |
0. |
0. |
0. |
0. |
|
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Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 76 | 76 | 81 | 72 | 111 | 139 | 80 | 163 |
normalized size | 1 | 1. | 1.07 | 0.95 | 1.46 | 1.83 | 1.05 | 2.14 |
time (sec) |
N/A |
0.035 |
0.03 |
0.005 |
1.591 |
1.436 |
2.371 |
1.37 |
|
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Problem 141 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 49 | 64 | 80 | 119 | 65 | 100 |
normalized size | 1 | 1. | 0.82 | 1.07 | 1.33 | 1.98 | 1.08 | 1.67 |
time (sec) |
N/A |
0.039 |
0.039 |
0.003 |
1.686 |
1.53 |
0.922 |
1.347 |
|
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Problem 142 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 56 | 52 | 82 | 111 | 54 | 86 |
normalized size | 1 | 1. | 1.1 | 1.02 | 1.61 | 2.18 | 1.06 | 1.69 |
time (sec) |
N/A |
0.019 |
0.019 |
0.003 |
1.598 |
1.484 |
0.435 |
1.316 |
|
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Problem 143 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 30 | 30 | 39 | 73 | 26 | 39 |
normalized size | 1 | 1. | 1. | 1. | 1.3 | 2.43 | 0.87 | 1.3 |
time (sec) |
N/A |
0.014 |
0.012 |
0.003 |
1.517 |
1.459 |
0.17 |
1.286 |
|
|
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Problem 144 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 52 | 122 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.83 | 1.94 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.07 |
0.032 |
0.03 |
0. |
0. |
0. |
0. |
|
|
|
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|
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Problem 145 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 36 | 43 | 63 | 140 | 39 | 439 |
normalized size | 1 | 1. | 1.09 | 1.3 | 1.91 | 4.24 | 1.18 | 13.3 |
time (sec) |
N/A |
0.027 |
0.003 |
0.004 |
1.505 |
1.552 |
3.323 |
1.583 |
|
|
|
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|
|
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Problem 146 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 44 | 50 | 49 | 88 | 61 | 220 |
normalized size | 1 | 1. | 1.13 | 1.28 | 1.26 | 2.26 | 1.56 | 5.64 |
time (sec) |
N/A |
0.019 |
0.013 |
0.004 |
1.538 |
1.489 |
2.896 |
1.402 |
|
|
|
|
|
|
|
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Problem 147 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 67 | 65 | 93 | 194 | 119 | 383 |
normalized size | 1 | 1. | 1.08 | 1.05 | 1.5 | 3.13 | 1.92 | 6.18 |
time (sec) |
N/A |
0.038 |
0.018 |
0.003 |
1.55 |
1.663 |
5.744 |
2.034 |
|
|
|
|
|
|
|
|
|
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|
|
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|
Problem 148 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 95 | 126 | 192 | 255 | 170 | 262 |
normalized size | 1 | 1. | 0.93 | 1.24 | 1.88 | 2.5 | 1.67 | 2.57 |
time (sec) |
N/A |
0.154 |
0.189 |
0.025 |
1.549 |
1.436 |
2.059 |
1.347 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 149 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 76 | 76 | 73 | 120 | 0 | 221 | 126 | 209 |
normalized size | 1 | 1. | 0.96 | 1.58 | 0. | 2.91 | 1.66 | 2.75 |
time (sec) |
N/A |
0.119 |
0.073 |
0.023 |
0. |
1.482 |
1.174 |
1.3 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 150 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 47 | 72 | 97 | 159 | 82 | 101 |
normalized size | 1 | 1. | 1. | 1.53 | 2.06 | 3.38 | 1.74 | 2.15 |
time (sec) |
N/A |
0.06 |
0.04 |
0.023 |
1.566 |
1.555 |
0.528 |
1.351 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 151 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 143 | 319 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.59 | 3.54 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.123 |
0.156 |
0.03 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 152 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 126 | 171 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.56 | 2.11 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.128 |
0.225 |
0.056 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 153 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 178 | 178 | 163 | 235 | 369 | 441 | 328 | 497 |
normalized size | 1 | 1. | 0.92 | 1.32 | 2.07 | 2.48 | 1.84 | 2.79 |
time (sec) |
N/A |
0.297 |
0.409 |
0.029 |
1.888 |
1.804 |
3.745 |
1.458 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 154 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 114 | 219 | 0 | 378 | 264 | 385 |
normalized size | 1 | 1. | 0.91 | 1.75 | 0. | 3.02 | 2.11 | 3.08 |
time (sec) |
N/A |
0.205 |
0.148 |
0.027 |
0. |
1.681 |
1.893 |
1.478 |
|
|
|
|
|
|
|
|
|
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|
|
|
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|
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|
|
Problem 155 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 77 | 132 | 190 | 262 | 160 | 203 |
normalized size | 1 | 1. | 0.94 | 1.61 | 2.32 | 3.2 | 1.95 | 2.48 |
time (sec) |
N/A |
0.109 |
0.088 |
0.024 |
1.869 |
1.793 |
1.209 |
1.374 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 156 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 244 | 592 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.98 | 4.81 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.147 |
0.239 |
0.026 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 157 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 283 | 378 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.07 | 2.76 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.213 |
0.314 |
0.042 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 158 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 117 | 91 | 102 | 0 | 0 | 0 | 234 |
normalized size | 1 | 0.97 | 0.75 | 0.84 | 0. | 0. | 0. | 1.93 |
time (sec) |
N/A |
0.254 |
0.2 |
0.025 |
0. |
0. |
0. |
1.302 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 159 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 56 | 58 | 0 | 0 | 0 | 116 |
normalized size | 1 | 1. | 0.89 | 0.92 | 0. | 0. | 0. | 1.84 |
time (sec) |
N/A |
0.132 |
0.079 |
0.023 |
0. |
0. |
0. |
1.288 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 160 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 44 | 48 | 0 | 0 | 0 | 66 |
normalized size | 1 | 1. | 0.83 | 0.91 | 0. | 0. | 0. | 1.25 |
time (sec) |
N/A |
0.067 |
0.065 |
0.023 |
0. |
0. |
0. |
1.412 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 161 |
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 |
0.024 |
0.245 |
0.145 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 162 |
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 |
0.025 |
2.167 |
0.243 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 163 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 156 | 152 | 125 | 149 | 0 | 0 | 0 | 872 |
normalized size |
1 |
0.97 |
0.8 |
0.96 |
0. |
0. |
0. |
5.59 |
time (sec) |
N/A |
0.182 |
0.531 |
0.037 |
0. |
0. |
0. |
1.403 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 164 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 79 | 77 | 0 | 0 | 0 | 440 |
normalized size |
1 |
1. |
0.88 |
0.86 |
0. |
0. |
0. |
4.89 |
time (sec) |
N/A |
0.1 |
0.266 |
0.027 |
0. |
0. |
0. |
1.413 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 165 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 82 | 72 | 76 | 0 | 0 | 0 | 259 |
normalized size |
1 |
0.95 |
0.84 |
0.88 |
0. |
0. |
0. |
3.01 |
time (sec) |
N/A |
0.169 |
0.156 |
0.03 |
0. |
0. |
0. |
1.359 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 166 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
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 |
0.023 |
3.985 |
0.184 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 167 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
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 |
0.023 |
33.323 |
0.339 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 168 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 197 | 245 | 168 | 290 | 0 | 0 | 0 | 2078 |
normalized size | 1 | 1.24 | 0.85 | 1.47 | 0. | 0. | 0. | 10.55 |
time (sec) |
N/A |
0.542 |
0.861 |
0.034 |
0. |
0. |
0. |
1.705 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 169 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 130 | 108 | 157 | 0 | 0 | 0 | 1166 |
normalized size | 1 | 1. | 0.83 | 1.21 | 0. | 0. | 0. | 8.97 |
time (sec) |
N/A |
0.323 |
0.33 |
0.027 |
0. |
0. |
0. |
1.687 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 170 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 93 | 138 | 0 | 0 | 0 | 651 |
normalized size | 1 | 1. | 0.84 | 1.24 | 0. | 0. | 0. | 5.86 |
time (sec) |
N/A |
0.172 |
0.418 |
0.03 |
0. |
0. |
0. |
1.426 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 171 |
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 |
0.023 |
2.128 |
0.276 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 172 |
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 |
0.023 |
17.855 |
0.5 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 173 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 242 | 242 | 246 | 356 | 0 | 0 | 0 | 531 |
normalized size |
1 |
1. |
1.02 |
1.47 |
0. |
0. |
0. |
2.19 |
time (sec) |
N/A |
0.756 |
0.304 |
0.083 |
0. |
0. |
0. |
2.105 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 174 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 141 | 173 | 0 | 0 | 0 | 236 |
normalized size |
1 |
1. |
1.03 |
1.26 |
0. |
0. |
0. |
1.72 |
time (sec) |
N/A |
0.453 |
0.072 |
0.052 |
0. |
0. |
0. |
1.805 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 175 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 120 | 120 | 119 | 178 | 0 | 0 | 0 | 266 |
normalized size |
1 |
1. |
0.99 |
1.48 |
0. |
0. |
0. |
2.22 |
time (sec) |
N/A |
0.331 |
0.089 |
0.043 |
0. |
0. |
0. |
1.687 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 176 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.046 |
3.254 |
0.128 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 177 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.037 |
11.4 |
0.165 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 178 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 313 | 313 | 245 | 540 | 0 | 0 | 0 | 1740 |
normalized size |
1 |
1. |
0.78 |
1.73 |
0. |
0. |
0. |
5.56 |
time (sec) |
N/A |
1.046 |
0.285 |
0.105 |
0. |
0. |
0. |
3.5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 179 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 172 | 172 | 126 | 267 | 0 | 0 | 0 | 757 |
normalized size |
1 |
1. |
0.73 |
1.55 |
0. |
0. |
0. |
4.4 |
time (sec) |
N/A |
0.525 |
0.059 |
0.092 |
0. |
0. |
0. |
2.23 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 180 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 159 | 159 | 291 | 270 | 0 | 0 | 0 | 879 |
normalized size |
1 |
1. |
1.83 |
1.7 |
0. |
0. |
0. |
5.53 |
time (sec) |
N/A |
0.281 |
2.796 |
0.056 |
0. |
0. |
0. |
2.469 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 181 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.045 |
2.901 |
0.11 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 182 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.042 |
10.143 |
0.169 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 183 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-2) |
F(-1) |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 358 | 358 | 228 | 792 | 0 | 0 | 0 | 3357 |
normalized size |
1 |
1. |
0.64 |
2.21 |
0. |
0. |
0. |
9.38 |
time (sec) |
N/A |
1.409 |
0.273 |
0.118 |
0. |
0. |
0. |
5.104 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 184 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-2) |
F(-1) |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 216 | 216 | 141 | 394 | 0 | 0 | 0 | 1570 |
normalized size |
1 |
1. |
0.65 |
1.82 |
0. |
0. |
0. |
7.27 |
time (sec) |
N/A |
0.743 |
0.095 |
0.068 |
0. |
0. |
0. |
2.798 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 185 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-2) |
F(-1) |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 179 | 179 | 379 | 393 | 0 | 0 | 0 | 1578 |
normalized size |
1 |
1. |
2.12 |
2.2 |
0. |
0. |
0. |
8.82 |
time (sec) |
N/A |
0.502 |
2.899 |
0.067 |
0. |
0. |
0. |
3.193 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 186 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.044 |
3.06 |
0.101 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 187 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.043 |
10.216 |
0.161 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 188 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 223 | 223 | 228 | 168 | 0 | 0 | 0 | 428 |
normalized size |
1 |
1. |
1.02 |
0.75 |
0. |
0. |
0. |
1.92 |
time (sec) |
N/A |
0.421 |
0.266 |
0.058 |
0. |
0. |
0. |
2.271 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 189 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 123 | 80 | 0 | 0 | 0 | 178 |
normalized size |
1 |
1. |
1.24 |
0.81 |
0. |
0. |
0. |
1.8 |
time (sec) |
N/A |
0.176 |
0.061 |
0.038 |
0. |
0. |
0. |
1.992 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 190 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-2) |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 121 | 83 | 0 | 0 | 0 | 215 |
normalized size |
1 |
1. |
1.2 |
0.82 |
0. |
0. |
0. |
2.13 |
time (sec) |
N/A |
0.091 |
0.087 |
0.029 |
0. |
0. |
0. |
1.912 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 191 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.037 |
2.866 |
0.082 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 192 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.037 |
11.63 |
0.137 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 193 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 250 | 250 | 343 | 295 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.37 |
1.18 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.418 |
0.443 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 194 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 130 | 155 | 143 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.19 |
1.1 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.163 |
0.145 |
0.045 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 195 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 167 | 149 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.22 |
1.09 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.294 |
0.298 |
0.042 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 196 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.044 |
3.458 |
0.079 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 197 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.043 |
11.405 |
0.158 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 198 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 291 | 291 | 370 | 660 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.27 |
2.27 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.007 |
1.855 |
0.088 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 199 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 180 | 180 | 173 | 311 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.96 |
1.73 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.506 |
1.231 |
0.059 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 200 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 163 | 163 | 214 | 325 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.31 |
1.99 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.276 |
0.852 |
0.053 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 201 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.045 |
3.613 |
0.073 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 202 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.045 |
11.448 |
0.161 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 203 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 120 | 120 | 100 | 144 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.83 |
1.2 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.076 |
0.039 |
0.036 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 204 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 66 | 138 | 0 | 0 | 82 | 0 |
normalized size |
1 |
1. |
0.53 |
1.11 |
0. |
0. |
0.66 |
0. |
time (sec) |
N/A |
0.098 |
0.025 |
0.01 |
0. |
0. |
163.098 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 205 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 66 | 119 | 0 | 0 | 76 | 0 |
normalized size |
1 |
1. |
0.75 |
1.35 |
0. |
0. |
0.86 |
0. |
time (sec) |
N/A |
0.045 |
0.017 |
0.008 |
0. |
0. |
4.419 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 206 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 45 | 98 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.51 |
1.1 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.078 |
0.015 |
0.009 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 207 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 40 | 85 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.73 |
1.55 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.038 |
0.013 |
0.009 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 208 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 42 | 129 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.34 |
1.03 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.097 |
0.015 |
0.013 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 209 |
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 | 109 | 109 | 90 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.83 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.141 |
0.061 |
0.158 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 210 |
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 | 109 | 109 | 90 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.83 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.141 |
0.056 |
0.143 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 211 |
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 | 109 | 109 | 90 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.83 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.143 |
0.052 |
0.184 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 212 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 90 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.84 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.13 |
0.049 |
0.358 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 213 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 87 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.83 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.135 |
0.047 |
0.154 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 214 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 87 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.145 |
0.054 |
0.144 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 215 |
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 | 68 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.17 |
36.379 |
0.144 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 216 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
F |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.168 |
180.002 |
0.142 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 217 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-2) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.16 |
8.126 |
0.199 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 218 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-2) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.159 |
7.576 |
0.145 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 219 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-2) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.173 |
13.129 |
0.139 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 220 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.03 |
2.676 |
0.093 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 221 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.026 |
2.565 |
0.092 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 222 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.029 |
0.769 |
0.1 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 223 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.032 |
3.841 |
0.099 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 224 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.029 |
5.683 |
0.098 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 225 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.026 |
4.897 |
0.095 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 226 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.025 |
8.376 |
0.102 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 227 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.028 |
13.561 |
0.092 |
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 [30] had the largest ratio of [ 1.
]
|
|
|
|
|
|
|
| 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 |
4 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
2 |
A |
4 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
3 |
A |
4 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
4 |
A |
3 |
3 |
1. |
6 |
0.5 |
|
|
|
|
|
|
|
5 |
A |
2 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
6 |
A |
5 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
7 |
A |
4 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
8 |
A |
2 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
9 |
A |
5 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
10 |
A |
3 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
11 |
A |
6 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
12 |
A |
7 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
13 |
A |
6 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
14 |
A |
5 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
15 |
A |
4 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
16 |
A |
3 |
3 |
1. |
6 |
0.5 |
|
|
|
|
|
|
|
17 |
A |
6 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
18 |
A |
7 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
19 |
A |
3 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
20 |
A |
9 |
7 |
1. |
10 |
0.7 |
|
|
|
|
|
|
|
|
21 |
A |
5 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
22 |
A |
14 |
7 |
1. |
10 |
0.7 |
|
|
|
|
|
|
|
23 |
A |
11 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
24 |
A |
9 |
7 |
1. |
10 |
0.7 |
|
|
|
|
|
|
|
25 |
A |
6 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
26 |
A |
4 |
3 |
1. |
6 |
0.5 |
|
|
|
|
|
|
|
27 |
A |
7 |
7 |
1. |
10 |
0.7 |
|
|
|
|
|
|
|
28 |
A |
9 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
29 |
A |
7 |
7 |
1. |
10 |
0.7 |
|
|
|
|
|
|
|
30 |
A |
14 |
10 |
1. |
10 |
1. |
|
|
|
|
|
|
|
31 |
A |
10 |
9 |
1. |
10 |
0.9 |
|
|
|
|
|
|
|
32 |
A |
23 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
33 |
A |
19 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
34 |
A |
14 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
35 |
A |
11 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
36 |
A |
7 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
37 |
A |
5 |
3 |
1. |
6 |
0.5 |
|
|
|
|
|
|
|
38 |
A |
8 |
7 |
1. |
10 |
0.7 |
|
|
|
|
|
|
|
39 |
A |
11 |
7 |
1. |
10 |
0.7 |
|
|
|
|
|
|
|
40 |
A |
8 |
8 |
1. |
10 |
0.8 |
|
|
|
|
|
|
|
|
41 |
A |
19 |
10 |
1. |
10 |
1. |
|
|
|
|
|
|
|
42 |
A |
7 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
43 |
A |
6 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
44 |
A |
6 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
45 |
A |
5 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
46 |
A |
5 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
47 |
A |
4 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
48 |
A |
2 |
2 |
1. |
6 |
0.333 |
|
|
|
|
|
|
|
49 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
50 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
51 |
A |
6 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
52 |
A |
5 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
53 |
A |
5 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
54 |
A |
4 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
55 |
A |
4 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
56 |
A |
2 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
57 |
A |
3 |
3 |
1. |
6 |
0.5 |
|
|
|
|
|
|
|
58 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
59 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
60 |
A |
14 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
|
61 |
A |
12 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
62 |
A |
10 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
63 |
A |
7 |
7 |
1. |
8 |
0.875 |
|
|
|
|
|
|
|
64 |
A |
4 |
4 |
1. |
6 |
0.667 |
|
|
|
|
|
|
|
65 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
66 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
67 |
A |
12 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
68 |
A |
9 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
69 |
A |
10 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
70 |
A |
5 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
71 |
A |
5 |
4 |
1. |
6 |
0.667 |
|
|
|
|
|
|
|
72 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
73 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
74 |
A |
10 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
75 |
A |
8 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
76 |
A |
8 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
77 |
A |
6 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
78 |
A |
4 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
79 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
80 |
A |
23 |
8 |
1.32 |
12 |
0.667 |
|
|
|
|
|
|
|
|
81 |
A |
16 |
8 |
1. |
12 |
0.667 |
|
|
|
|
|
|
|
82 |
A |
13 |
8 |
1. |
12 |
0.667 |
|
|
|
|
|
|
|
83 |
A |
8 |
8 |
1. |
10 |
0.8 |
|
|
|
|
|
|
|
84 |
A |
5 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
85 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
86 |
A |
26 |
8 |
1.13 |
12 |
0.667 |
|
|
|
|
|
|
|
87 |
A |
18 |
7 |
1. |
12 |
0.583 |
|
|
|
|
|
|
|
88 |
A |
15 |
8 |
1. |
12 |
0.667 |
|
|
|
|
|
|
|
89 |
A |
9 |
7 |
1. |
10 |
0.7 |
|
|
|
|
|
|
|
90 |
A |
6 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
91 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
92 |
A |
9 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
93 |
A |
7 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
94 |
A |
7 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
95 |
A |
5 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
96 |
A |
3 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
97 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
98 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
99 |
A |
10 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
100 |
A |
8 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
|
101 |
A |
8 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
102 |
A |
6 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
103 |
A |
6 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
104 |
A |
3 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
105 |
A |
4 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
106 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
107 |
A |
19 |
6 |
1.37 |
12 |
0.5 |
|
|
|
|
|
|
|
108 |
A |
15 |
7 |
1. |
12 |
0.583 |
|
|
|
|
|
|
|
109 |
A |
13 |
7 |
1. |
12 |
0.583 |
|
|
|
|
|
|
|
110 |
A |
8 |
8 |
1. |
10 |
0.8 |
|
|
|
|
|
|
|
111 |
A |
5 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
112 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
113 |
A |
17 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
114 |
A |
12 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
115 |
A |
13 |
7 |
1. |
12 |
0.583 |
|
|
|
|
|
|
|
116 |
A |
6 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
117 |
A |
6 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
118 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
119 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
120 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
121 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
122 |
A |
2 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
123 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
124 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
125 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
126 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
127 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
128 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
129 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
130 |
A |
9 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
131 |
A |
9 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
132 |
A |
6 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
133 |
A |
4 |
3 |
1. |
6 |
0.5 |
|
|
|
|
|
|
|
134 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
135 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
136 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
137 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
138 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
139 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
140 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
|
141 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
142 |
A |
3 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
143 |
A |
3 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
144 |
A |
5 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
145 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
146 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
147 |
A |
5 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
148 |
A |
5 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
149 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
150 |
A |
3 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
151 |
A |
6 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
152 |
A |
7 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
153 |
A |
10 |
7 |
1. |
14 |
0.5 |
|
|
|
|
|
|
|
154 |
A |
6 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
155 |
A |
5 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
156 |
A |
7 |
7 |
1. |
14 |
0.5 |
|
|
|
|
|
|
|
157 |
A |
9 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
158 |
A |
9 |
5 |
0.97 |
14 |
0.357 |
|
|
|
|
|
|
|
159 |
A |
6 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
160 |
A |
4 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
|
161 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
162 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
163 |
A |
8 |
4 |
0.97 |
14 |
0.286 |
|
|
|
|
|
|
|
164 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
165 |
A |
5 |
5 |
0.95 |
10 |
0.5 |
|
|
|
|
|
|
|
166 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
167 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
168 |
A |
16 |
8 |
1.24 |
14 |
0.571 |
|
|
|
|
|
|
|
169 |
A |
9 |
9 |
1. |
12 |
0.75 |
|
|
|
|
|
|
|
170 |
A |
6 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
171 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
172 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
173 |
A |
14 |
8 |
1. |
16 |
0.5 |
|
|
|
|
|
|
|
174 |
A |
9 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
175 |
A |
7 |
7 |
1. |
12 |
0.583 |
|
|
|
|
|
|
|
176 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
177 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
178 |
A |
22 |
11 |
1. |
16 |
0.688 |
|
|
|
|
|
|
|
179 |
A |
11 |
11 |
1. |
14 |
0.786 |
|
|
|
|
|
|
|
180 |
A |
8 |
8 |
1. |
12 |
0.667 |
|
|
|
|
|
|
|
|
181 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
182 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
183 |
A |
24 |
11 |
1. |
16 |
0.688 |
|
|
|
|
|
|
|
184 |
A |
12 |
10 |
1. |
14 |
0.714 |
|
|
|
|
|
|
|
185 |
A |
9 |
8 |
1. |
12 |
0.667 |
|
|
|
|
|
|
|
186 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
187 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
188 |
A |
13 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
189 |
A |
8 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
190 |
A |
6 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
191 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
192 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
193 |
A |
12 |
6 |
1. |
16 |
0.375 |
|
|
|
|
|
|
|
194 |
A |
6 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
195 |
A |
7 |
7 |
1. |
12 |
0.583 |
|
|
|
|
|
|
|
196 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
197 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
198 |
A |
22 |
10 |
1. |
16 |
0.625 |
|
|
|
|
|
|
|
199 |
A |
11 |
11 |
1. |
14 |
0.786 |
|
|
|
|
|
|
|
200 |
A |
8 |
8 |
1. |
12 |
0.667 |
|
|
|
|
|
|
|
|
201 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
202 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
203 |
A |
5 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
204 |
A |
7 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
205 |
A |
4 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
206 |
A |
6 |
6 |
1. |
16 |
0.375 |
|
|
|
|
|
|
|
207 |
A |
3 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
208 |
A |
7 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
209 |
A |
2 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
210 |
A |
2 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
211 |
A |
2 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
212 |
A |
2 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
213 |
A |
2 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
214 |
A |
2 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
215 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
216 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
217 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
218 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
219 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
220 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
221 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
222 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
223 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
224 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
225 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
226 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
227 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|