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, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 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, 158, 159
}
B grade: { 97, 155, 156, 157 }
C grade: { }
F grade: { 111}
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 60, 61, 62, 63, 64,
65, 66, 67, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 98, 100, 101, 102, 103,
104, 105, 106, 109, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129,
130, 131, 133, 134, 135, 136, 137, 138, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 157, 158,
159 }
B grade: { 54, 97, 99, 107, 108, 110, 111, 155, 156 }
C grade: { 33, 34, 43, 58, 59, 68, 69, 70, 71, 72, 73, 74, 75, 76, 132 }
F grade: { 139, 140, 141, 144}
2.1.3 Maple
A grade: { 1, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 18, 19, 20, 21, 27, 28, 29, 30, 31, 32, 35, 36, 37,
38, 39, 44, 45, 46, 47, 48, 51, 52, 53, 55, 58, 60, 61, 62, 63, 65, 70, 88, 95, 102, 104, 109, 143
}
B grade: { 2, 3, 12, 14, 33, 34, 40, 41, 42, 43, 49, 50, 56, 57, 59, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77,
78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 96, 97, 98, 99, 100, 101, 103, 105, 106, 107, 108,
110, 111, 119, 130, 131, 134, 135 }
C grade: { 22, 23, 24, 25, 26, 54, 64, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159
}
F grade: { 112, 113, 114, 115, 116, 117, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 133,
136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148 }
2.1.4 Maxima
A grade: { 1, 2, 3, 4, 5, 6, 7, 31, 32, 143, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159
B grade: { 155 }
C grade: { }
F grade: { 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 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, 144, 145, 146, 147, 148
}
2.1.5 FriCAS
A grade: { 1, 2, 3, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 143, 149,
150, 151, 152, 153, 154, 155, 156, 157, 158, 159 }
B grade: { 13, 14, 20, 21, 26, 119, 130, 131, 134, 135 }
C grade: { }
F grade: { 4, 5, 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, 120, 121, 122, 123, 124,
125, 126, 127, 128, 129, 132, 133, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148
}
2.1.6 Sympy
A grade: { 1, 2, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 119 }
B grade: { 3, 13, 20 }
C grade: { 22, 23, 24, 25, 26, 27, 28, 29, 30, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159
}
F grade: { 4, 5, 14, 21, 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, 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
}
2.1.7 Giac
A grade: { 1, 2, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 32, 143, 149,
150, 154, 155, 156, 157 }
B grade: { 27, 28, 29, 30, 119, 158, 159 }
C grade: { }
F grade: { 3, 4, 5, 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, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131,
132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148, 151, 152, 153
}
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 | 112 | 112 | 112 | 109 | 146 | 379 | 148 | 203 |
normalized size | 1 | 1. | 1. | 0.97 | 1.3 | 3.38 | 1.32 | 1.81 |
time (sec) |
N/A |
0.158 |
0.049 |
0.002 |
1.144 |
1.08 |
0.074 |
1.41 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 126 | 123 | 246 | 219 | 359 | 141 | 281 |
normalized size | 1 | 1. | 0.98 | 1.95 | 1.74 | 2.85 | 1.12 | 2.23 |
time (sec) |
N/A |
0.211 |
0.089 |
0.004 |
1.15 |
1.212 |
0.972 |
1.304 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
A |
B |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 85 | 196 | 140 | 242 | 507 | 0 |
normalized size |
1 |
1. |
1.01 |
2.33 |
1.67 |
2.88 |
6.04 |
0. |
time (sec) |
N/A |
0.086 |
0.071 |
0.008 |
1.375 |
1.484 |
10.499 |
0. |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 102 | 179 | 181 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.94 |
1.66 |
1.68 |
0. |
0. |
0. |
time (sec) |
N/A |
0.11 |
0.086 |
0.007 |
1.647 |
0. |
0. |
0. |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 163 | 163 | 164 | 164 | 419 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.01 |
1.01 |
2.57 |
0. |
0. |
0. |
time (sec) |
N/A |
0.212 |
0.247 |
0.007 |
1.282 |
0. |
0. |
0. |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 23 | 20 | 26 | 66 | 20 | 30 |
normalized size | 1 | 1. | 1. | 0.87 | 1.13 | 2.87 | 0.87 | 1.3 |
time (sec) |
N/A |
0.011 |
0.006 |
0.006 |
2.159 |
1.685 |
0.115 |
2.225 |
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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 |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 33 | 34 | 46 | 170 | 32 | 42 |
normalized size | 1 | 1. | 0.77 | 0.79 | 1.07 | 3.95 | 0.74 | 0.98 |
time (sec) |
N/A |
0.037 |
0.02 |
0.007 |
1.232 |
1.675 |
0.142 |
2.168 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 227 | 227 | 205 | 301 | 0 | 1419 | 274 | 456 |
normalized size |
1 |
1. |
0.9 |
1.33 |
0. |
6.25 |
1.21 |
2.01 |
time (sec) |
N/A |
0.257 |
0.264 |
0.008 |
0. |
1.83 |
26.773 |
2.38 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 146 | 146 | 145 | 176 | 0 | 914 | 167 | 271 |
normalized size |
1 |
1. |
0.99 |
1.21 |
0. |
6.26 |
1.14 |
1.86 |
time (sec) |
N/A |
0.098 |
0.176 |
0.008 |
0. |
1.838 |
18.801 |
1.734 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 81 | 89 | 0 | 517 | 92 | 142 |
normalized size |
1 |
1. |
1.05 |
1.16 |
0. |
6.71 |
1.19 |
1.84 |
time (sec) |
N/A |
0.024 |
0.15 |
0.006 |
0. |
1.349 |
18.418 |
1.477 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 55 | 46 | 0 | 279 | 54 | 77 |
normalized size |
1 |
1. |
1.02 |
0.85 |
0. |
5.17 |
1. |
1.43 |
time (sec) |
N/A |
0.017 |
0.046 |
0.008 |
0. |
1.324 |
3.872 |
1.531 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 101 | 196 | 0 | 1013 | 97 | 151 |
normalized size |
1 |
1. |
1. |
1.94 |
0. |
10.03 |
0.96 |
1.5 |
time (sec) |
N/A |
0.114 |
0.115 |
0.011 |
0. |
1.693 |
17.092 |
1.436 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 124 | 192 | 0 | 2114 | 1204 | 192 |
normalized size |
1 |
1. |
0.98 |
1.51 |
0. |
16.65 |
9.48 |
1.51 |
time (sec) |
N/A |
0.109 |
0.468 |
0.013 |
0. |
1.91 |
52.541 |
1.673 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 208 | 208 | 260 | 424 | 0 | 4552 | 0 | 405 |
normalized size |
1 |
1. |
1.25 |
2.04 |
0. |
21.88 |
0. |
1.95 |
time (sec) |
N/A |
0.274 |
0.636 |
0.016 |
0. |
4.495 |
0. |
1.745 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 226 | 226 | 204 | 301 | 0 | 1419 | 274 | 456 |
normalized size |
1 |
1. |
0.9 |
1.33 |
0. |
6.28 |
1.21 |
2.02 |
time (sec) |
N/A |
0.252 |
0.273 |
0.008 |
0. |
1.427 |
26.157 |
2.56 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 146 | 176 | 0 | 914 | 167 | 271 |
normalized size |
1 |
1. |
1.01 |
1.21 |
0. |
6.3 |
1.15 |
1.87 |
time (sec) |
N/A |
0.094 |
0.163 |
0.007 |
0. |
1.364 |
18.678 |
1.754 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 87 | 89 | 0 | 517 | 92 | 142 |
normalized size |
1 |
1. |
1.13 |
1.16 |
0. |
6.71 |
1.19 |
1.84 |
time (sec) |
N/A |
0.024 |
0.123 |
0.007 |
0. |
1.226 |
18.186 |
2.756 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 55 | 46 | 0 | 279 | 54 | 77 |
normalized size |
1 |
1. |
1.02 |
0.85 |
0. |
5.17 |
1. |
1.43 |
time (sec) |
N/A |
0.016 |
0.046 |
0.006 |
0. |
1.293 |
3.901 |
2.643 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 100 | 103 | 0 | 1013 | 100 | 151 |
normalized size |
1 |
1. |
0.99 |
1.02 |
0. |
10.03 |
0.99 |
1.5 |
time (sec) |
N/A |
0.119 |
0.218 |
0.013 |
0. |
1.647 |
15.252 |
2.624 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 122 | 137 | 0 | 2118 | 1149 | 192 |
normalized size |
1 |
1. |
0.95 |
1.07 |
0. |
16.55 |
8.98 |
1.5 |
time (sec) |
N/A |
0.116 |
0.191 |
0.016 |
0. |
1.959 |
54.016 |
2.685 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 259 | 221 | 0 | 4551 | 0 | 406 |
normalized size |
1 |
1. |
1.26 |
1.08 |
0. |
22.2 |
0. |
1.98 |
time (sec) |
N/A |
0.279 |
0.55 |
0.014 |
0. |
4.975 |
0. |
1.829 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 89 | 132 | 0 | 165 | 484 | 85 |
normalized size |
1 |
1. |
0.8 |
1.19 |
0. |
1.49 |
4.36 |
0.77 |
time (sec) |
N/A |
0.045 |
0.085 |
0.03 |
0. |
1.263 |
25.737 |
1.779 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 81 | 111 | 0 | 146 | 393 | 72 |
normalized size |
1 |
1. |
0.93 |
1.28 |
0. |
1.68 |
4.52 |
0.83 |
time (sec) |
N/A |
0.034 |
0.031 |
0.013 |
0. |
1.379 |
18.821 |
2.59 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 73 | 90 | 0 | 124 | 269 | 54 |
normalized size |
1 |
1. |
1.16 |
1.43 |
0. |
1.97 |
4.27 |
0.86 |
time (sec) |
N/A |
0.023 |
0.027 |
0.011 |
0. |
1.319 |
14.384 |
2.491 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 61 | 70 | 0 | 100 | 133 | 38 |
normalized size |
1 |
1. |
1.65 |
1.89 |
0. |
2.7 |
3.59 |
1.03 |
time (sec) |
N/A |
0.013 |
0.024 |
0.015 |
0. |
1.303 |
7.767 |
2.546 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
B |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 53 | 69 | 0 | 111 | 71 | 59 |
normalized size |
1 |
1. |
1.83 |
2.38 |
0. |
3.83 |
2.45 |
2.03 |
time (sec) |
N/A |
0.016 |
0.024 |
0.016 |
0. |
1.314 |
10.317 |
2.979 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 29 | 25 | 0 | 69 | 107 | 119 |
normalized size |
1 |
1. |
0.64 |
0.56 |
0. |
1.53 |
2.38 |
2.64 |
time (sec) |
N/A |
0.01 |
0.012 |
0.003 |
0. |
1.452 |
8.864 |
1.572 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 37 | 33 | 0 | 85 | 189 | 176 |
normalized size |
1 |
1. |
0.51 |
0.45 |
0. |
1.16 |
2.59 |
2.41 |
time (sec) |
N/A |
0.019 |
0.015 |
0.004 |
0. |
1.499 |
12.744 |
1.869 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 45 | 41 | 0 | 111 | 274 | 236 |
normalized size |
1 |
1. |
0.46 |
0.42 |
0. |
1.14 |
2.82 |
2.43 |
time (sec) |
N/A |
0.027 |
0.017 |
0.003 |
0. |
1.444 |
18.872 |
2.893 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 121 | 53 | 49 | 0 | 131 | 359 | 293 |
normalized size |
1 |
1. |
0.44 |
0.4 |
0. |
1.08 |
2.97 |
2.42 |
time (sec) |
N/A |
0.038 |
0.019 |
0.005 |
0. |
1.401 |
29.943 |
2.93 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 48 | 44 | 28 | 104 | 0 | 58 |
normalized size |
1 |
1. |
1.23 |
1.13 |
0.72 |
2.67 |
0. |
1.49 |
time (sec) |
N/A |
0.007 |
0.015 |
0.015 |
3.19 |
1.324 |
0. |
1.865 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 48 | 44 | 28 | 104 | 0 | 58 |
normalized size | 1 | 1. | 1.23 | 1.13 | 0.72 | 2.67 | 0. | 1.49 |
time (sec) |
N/A |
0.011 |
0.006 |
0.004 |
1.766 |
1.328 |
0. |
2.334 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 309 | 624 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.13 |
4.3 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.108 |
1.447 |
0.047 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 221 | 312 | 940 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.41 |
4.25 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.199 |
2.175 |
0.039 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 281 | 281 | 135 | 160 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.48 |
0.57 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.389 |
0.416 |
0.047 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 243 | 243 | 130 | 155 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.53 |
0.64 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.3 |
0.268 |
0.011 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 193 | 193 | 125 | 150 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.65 |
0.78 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.077 |
0.232 |
0.012 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
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 | 162 | 162 | 120 | 145 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.74 | 0.9 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.063 |
0.17 |
0.008 |
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 |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 182 | 182 | 141 | 183 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.77 | 1.01 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.213 |
0.766 |
0.02 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 132 | 320 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.7 | 1.69 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.211 |
0.752 |
0.025 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 227 | 227 | 136 | 461 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.6 | 2.03 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.309 |
0.696 |
0.025 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 263 | 263 | 141 | 602 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.54 | 2.29 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.397 |
0.754 |
0.026 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 570 | 570 | 1250 | 3678 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.19 |
6.45 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.286 |
13.841 |
0.059 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 243 | 243 | 130 | 155 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.53 |
0.64 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.297 |
0.368 |
0.02 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 125 | 150 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
0.73 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.213 |
0.3 |
0.012 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
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 | 162 | 162 | 120 | 145 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.74 | 0.9 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.062 |
0.193 |
0.01 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
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 | 131 | 131 | 115 | 140 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.88 | 1.07 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.051 |
0.187 |
0.007 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
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 | 151 | 151 | 97 | 76 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.64 | 0.5 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.121 |
0.404 |
0.013 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 132 | 320 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.7 | 1.69 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.214 |
0.623 |
0.016 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 225 | 225 | 137 | 461 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
2.05 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.301 |
0.562 |
0.016 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 125 | 150 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
0.73 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.212 |
0.35 |
0.023 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 120 | 145 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.72 |
0.87 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.145 |
0.281 |
0.014 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
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 | 131 | 131 | 115 | 140 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.88 | 1.07 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.051 |
0.183 |
0.012 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 111 | 55 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.36 | 1.17 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.015 |
0.34 |
0.011 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
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 | 103 | 103 | 70 | 56 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.68 | 0.54 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.096 |
0.401 |
0.015 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 132 | 320 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.7 |
1.69 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.21 |
0.653 |
0.016 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 225 | 225 | 144 | 461 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.64 |
2.05 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.31 |
0.421 |
0.018 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 293 | 293 | 202 | 382 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.69 |
1.3 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.504 |
1.713 |
0.043 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 449 | 449 | 1195 | 968 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.66 |
2.16 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.672 |
8.35 |
0.024 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
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 | 203 | 203 | 125 | 150 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.62 | 0.74 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.216 |
0.497 |
0.024 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
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 | 165 | 165 | 120 | 145 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.73 | 0.88 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.153 |
0.347 |
0.017 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
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 | 129 | 129 | 115 | 140 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.89 | 1.09 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.063 |
0.239 |
0.017 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
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 | 98 | 98 | 187 | 57 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.91 | 0.58 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.037 |
0.452 |
0.015 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 79 | 36 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.65 | 0.75 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.014 |
0.109 |
0.013 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
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 | 51 | 51 | 99 | 37 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.94 | 0.73 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.07 |
0.468 |
0.016 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 132 | 320 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.7 |
1.69 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.22 |
0.634 |
0.019 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 225 | 225 | 147 | 461 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.65 |
2.05 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.31 |
0.439 |
0.02 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 180 | 552 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.31 | 4.03 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.061 |
0.586 |
0.022 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 284 | 284 | 319 | 559 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.12 | 1.97 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.169 |
1.911 |
0.033 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 225 | 223 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.36 |
1.35 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.374 |
1.365 |
0.026 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 393 | 393 | 321 | 2842 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.82 |
7.23 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.624 |
4.384 |
0.08 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 875 | 875 | 12191 | 17330 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
13.93 |
19.81 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.339 |
17.494 |
0.257 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 203 | 184 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.74 |
2.49 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.16 |
0.868 |
0.097 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 203 | 181 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.74 |
2.45 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.176 |
0.103 |
0.025 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 218 | 212 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.53 |
2.47 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.16 |
0.813 |
0.096 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 218 | 205 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.53 |
2.38 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.175 |
0.107 |
0.024 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 471 | 471 | 350 | 895 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.74 |
1.9 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.665 |
4.381 |
0.074 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 429 | 429 | 345 | 890 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
2.07 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.542 |
4.156 |
0.018 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
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 | 391 | 391 | 340 | 885 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.87 | 2.26 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.429 |
4.066 |
0.02 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
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 | 351 | 351 | 347 | 880 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.99 | 2.51 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.324 |
2.933 |
0.03 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
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 | 349 | 349 | 330 | 875 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.95 | 2.51 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.319 |
2.793 |
0.041 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 391 | 391 | 366 | 1149 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.94 |
2.94 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.429 |
2.974 |
0.04 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 330 | 330 | 251 | 973 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.76 |
2.95 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.395 |
2.258 |
0.042 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 370 | 370 | 259 | 1160 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.7 |
3.14 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.515 |
2.595 |
0.044 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 429 | 429 | 345 | 890 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
2.07 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.526 |
3.661 |
0.031 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 391 | 391 | 340 | 885 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.87 |
2.26 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.412 |
3.596 |
0.02 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
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 | 351 | 351 | 347 | 880 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.99 | 2.51 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.316 |
3.875 |
0.019 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
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 | 365 | 365 | 318 | 875 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.87 | 2.4 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.216 |
1.23 |
0.021 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 279 | 279 | 326 | 870 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.17 |
3.12 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.195 |
2.297 |
0.026 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 290 | 290 | 246 | 786 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.85 |
2.71 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.32 |
1.819 |
0.028 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 330 | 330 | 251 | 973 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.76 |
2.95 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.398 |
1.789 |
0.031 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 370 | 370 | 258 | 1160 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.7 |
3.14 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.521 |
2.196 |
0.031 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 391 | 391 | 340 | 885 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.87 |
2.26 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.421 |
2.445 |
0.036 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 351 | 351 | 349 | 880 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.99 |
2.51 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.322 |
3.148 |
0.024 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
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 | 365 | 365 | 347 | 875 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.95 | 2.4 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.202 |
1.369 |
0.023 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
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 | 101 | 101 | 170 | 172 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.68 | 1.7 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.037 |
0.546 |
0.025 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
B |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 195 | 237 | 330 | 0 | 0 | 0 | 0 |
normalized size |
1 |
3.25 |
3.95 |
5.5 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.131 |
1.729 |
0.025 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 290 | 290 | 248 | 786 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.86 |
2.71 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.296 |
1.805 |
0.029 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 721 | 721 | 6667 | 18077 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
9.25 |
25.07 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.675 |
15.126 |
0.151 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 208 | 206 | 4590 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.29 |
1.28 |
28.51 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.093 |
4.707 |
0.118 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 351 | 351 | 347 | 880 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.99 |
2.51 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.319 |
2.431 |
0.037 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 469 | 469 | 347 | 875 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.74 |
1.87 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.28 |
1.223 |
0.023 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 100 | 95 | 170 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.95 | 1.7 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.038 |
0.158 |
0.021 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
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 | 71 | 71 | 90 | 134 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.27 | 1.89 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.043 |
0.139 |
0.022 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 195 | 270 | 237 | 599 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.38 |
1.22 |
3.07 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.183 |
1.575 |
0.03 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 288 | 288 | 246 | 786 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.85 |
2.73 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.303 |
1.719 |
0.031 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 968 | 968 | 6638 | 16526 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
6.86 |
17.07 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.882 |
14.274 |
0.087 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 228 | 228 | 584 | 2465 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.56 |
10.81 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.15 |
5.571 |
0.053 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
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 | 161 | 198 | 227 | 270 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1.23 | 1.41 | 1.68 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.082 |
1.289 |
0.059 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 429 | 429 | 3247 | 4660 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
7.57 |
10.86 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.256 |
14.337 |
0.095 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
B |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 786 | 0 | 7061 | 21094 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
8.98 |
26.84 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.01 |
17.458 |
0.224 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 319 | 319 | 285 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.89 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.279 |
1.322 |
0.089 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 216 | 216 | 174 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.81 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.154 |
0.496 |
0.077 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 158 | 158 | 153 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.97 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.107 |
0.074 |
0.069 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 116 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.94 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.039 |
0.026 |
0.068 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 116 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.94 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.033 |
0.03 |
0.063 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 170 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.97 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.119 |
0.184 |
0.052 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 222 | 222 | 177 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.151 |
0.267 |
0.082 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 119 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 149 | 726 | 0 | 1847 | 8218 | 2248 |
normalized size |
1 |
1. |
0.89 |
4.35 |
0. |
11.06 |
49.21 |
13.46 |
time (sec) |
N/A |
0.131 |
0.233 |
0.007 |
0. |
1.607 |
7.096 |
2.658 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 134 | 134 | 120 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.9 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.086 |
0.19 |
0.053 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 115 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.82 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.059 |
0.094 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 224 | 224 | 193 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.86 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.195 |
0.395 |
0.101 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 104 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.74 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.123 |
0.217 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 266 | 266 | 195 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.73 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.165 |
0.236 |
0.065 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 245 | 245 | 195 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.155 |
0.261 |
0.061 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 235 | 235 | 189 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.138 |
0.206 |
0.061 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 261 | 261 | 221 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.85 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.186 |
0.186 |
0.056 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 128 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 203 | 205 | 198 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.01 |
0.98 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.107 |
0.249 |
0.054 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 129 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 246 | 246 | 237 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.96 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.16 |
0.331 |
0.052 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 130 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 362 | 362 | 220 | 894 | 0 | 3309 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
2.47 |
0. |
9.14 |
0. |
0. |
time (sec) |
N/A |
0.362 |
0.55 |
0.008 |
0. |
1.46 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 131 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 507 | 507 | 279 | 2343 | 0 | 6969 | 0 | 0 |
normalized size |
1 |
1. |
0.55 |
4.62 |
0. |
13.75 |
0. |
0. |
time (sec) |
N/A |
0.586 |
0.769 |
0.01 |
0. |
1.971 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 815 | 803 | 3579 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.99 |
4.39 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.435 |
48.597 |
0.063 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 133 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 572 | 566 | 422 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.99 |
0.74 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.662 |
1.816 |
0.059 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 134 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 363 | 360 | 227 | 906 | 0 | 3272 | 0 | 0 |
normalized size |
1 |
0.99 |
0.63 |
2.5 |
0. |
9.01 |
0. |
0. |
time (sec) |
N/A |
0.397 |
0.573 |
0.008 |
0. |
1.604 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 135 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 186 | 182 | 509 | 0 | 1805 | 0 | 0 |
normalized size |
1 |
0.99 |
0.97 |
2.71 |
0. |
9.6 |
0. |
0. |
time (sec) |
N/A |
0.098 |
0.119 |
0.008 |
0. |
1.505 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 190 | 199 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.07 |
1.12 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.119 |
0.399 |
0.071 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 137 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 233 | 220 | 174 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.94 |
0.75 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.127 |
0.137 |
0.068 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 138 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 250 | 250 | 184 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.74 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.217 |
0.208 |
0.059 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 139 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 530 | 530 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.179 |
4.524 |
0.25 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 393 | 393 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.493 |
1.486 |
0.173 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 141 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 256 | 256 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.21 |
0.905 |
0.148 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 142 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 121 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.98 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.083 |
0.134 |
0.002 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 143 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.008 |
0.254 |
0.157 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 144 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 268 | 268 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.212 |
0.637 |
0.151 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 145 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 283 | 283 | 208 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.73 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.208 |
0.32 |
0.145 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 146 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 277 | 277 | 215 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.78 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.147 |
0.443 |
0.143 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 147 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 263 | 261 | 223 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.99 |
0.85 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.227 |
0.315 |
0.151 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 148 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 558 | 558 | 508 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.91 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.981 |
1.872 |
0.152 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 149 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 57 | 139 | 134 | 189 | 313 | 123 |
normalized size | 1 | 1. | 0.72 | 1.76 | 1.7 | 2.39 | 3.96 | 1.56 |
time (sec) |
N/A |
0.142 |
0.062 |
0.038 |
3.068 |
1.047 |
46.125 |
2.052 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 150 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 45 | 117 | 105 | 167 | 282 | 97 |
normalized size | 1 | 1. | 0.71 | 1.86 | 1.67 | 2.65 | 4.48 | 1.54 |
time (sec) |
N/A |
0.061 |
0.031 |
0.015 |
4.261 |
1.043 |
21.009 |
2.571 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 151 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 48 | 96 | 89 | 196 | 245 | 0 |
normalized size |
1 |
1. |
1. |
2. |
1.85 |
4.08 |
5.1 |
0. |
time (sec) |
N/A |
0.184 |
0.05 |
0.024 |
3.423 |
1.142 |
27.867 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 152 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 48 | 97 | 89 | 201 | 221 | 0 |
normalized size |
1 |
1. |
1. |
2.02 |
1.85 |
4.19 |
4.6 |
0. |
time (sec) |
N/A |
0.183 |
0.055 |
0.02 |
3.045 |
1.149 |
27.566 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 153 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 56 | 108 | 132 | 154 | 218 | 0 |
normalized size |
1 |
1. |
0.79 |
1.52 |
1.86 |
2.17 |
3.07 |
0. |
time (sec) |
N/A |
0.188 |
0.047 |
0.019 |
2.734 |
1.049 |
34.59 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 154 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 151 | 149 | 137 | 147 | 176 | 308 | 130 |
normalized size | 1 | 1.74 | 1.71 | 1.57 | 1.69 | 2.02 | 3.54 | 1.49 |
time (sec) |
N/A |
0.146 |
0.331 |
0.023 |
1.352 |
1.052 |
44.788 |
2.124 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 155 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
B |
C |
B |
A |
C |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 52 | 135 | 126 | 120 | 142 | 150 | 277 | 104 |
normalized size | 1 | 2.6 | 2.42 | 2.31 | 2.73 | 2.88 | 5.33 | 2. |
time (sec) |
N/A |
0.071 |
0.21 |
0.016 |
1.36 |
1.102 |
20.739 |
2.571 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 156 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
B |
C |
A |
A |
C |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 135 | 128 | 95 | 86 | 184 | 240 | 96 |
normalized size | 1 | 2.45 | 2.33 | 1.73 | 1.56 | 3.35 | 4.36 | 1.75 |
time (sec) |
N/A |
0.184 |
0.399 |
0.019 |
3.912 |
1.086 |
26.248 |
1.986 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 157 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
C |
A |
A |
C |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 135 | 89 | 96 | 86 | 203 | 216 | 112 |
normalized size | 1 | 2.45 | 1.62 | 1.75 | 1.56 | 3.69 | 3.93 | 2.04 |
time (sec) |
N/A |
0.182 |
0.167 |
0.017 |
2.016 |
1.143 |
27.925 |
2.665 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 158 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 129 | 82 | 103 | 88 | 173 | 212 | 196 |
normalized size | 1 | 1.55 | 0.99 | 1.24 | 1.06 | 2.08 | 2.55 | 2.36 |
time (sec) |
N/A |
0.189 |
0.121 |
0.018 |
2.21 |
1.057 |
34.178 |
1.469 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 159 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 171 | 94 | 123 | 119 | 216 | 219 | 266 |
normalized size | 1 | 1.47 | 0.81 | 1.06 | 1.03 | 1.86 | 1.89 | 2.29 |
time (sec) |
N/A |
0.221 |
0.116 |
0.019 |
1.794 |
1.032 |
56.645 |
1.69 |
|
|
|
|
|
|
|
|
|
|
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 [72] had the largest ratio of [ 0.3429
]
|
|
|
|
|
|
|
| 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 |
2 |
1 |
1. |
21 |
0.048 |
|
|
|
|
|
|
|
2 |
A |
2 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
3 |
A |
2 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
4 |
A |
2 |
1 |
1. |
27 |
0.037 |
|
|
|
|
|
|
|
5 |
A |
2 |
1 |
1. |
29 |
0.034 |
|
|
|
|
|
|
|
6 |
A |
2 |
1 |
1. |
17 |
0.059 |
|
|
|
|
|
|
|
7 |
A |
3 |
2 |
1. |
22 |
0.091 |
|
|
|
|
|
|
|
8 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
9 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
10 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
11 |
A |
4 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
12 |
A |
6 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
13 |
A |
6 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
14 |
A |
7 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
15 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
16 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
17 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
18 |
A |
4 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
19 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
20 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
|
21 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
22 |
A |
8 |
6 |
1. |
26 |
0.231 |
|
|
|
|
|
|
|
23 |
A |
7 |
6 |
1. |
26 |
0.231 |
|
|
|
|
|
|
|
24 |
A |
6 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
25 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
26 |
A |
5 |
5 |
1. |
26 |
0.192 |
|
|
|
|
|
|
|
27 |
A |
3 |
3 |
1. |
26 |
0.115 |
|
|
|
|
|
|
|
28 |
A |
4 |
4 |
1. |
26 |
0.154 |
|
|
|
|
|
|
|
29 |
A |
5 |
4 |
1. |
26 |
0.154 |
|
|
|
|
|
|
|
30 |
A |
6 |
4 |
1. |
26 |
0.154 |
|
|
|
|
|
|
|
31 |
A |
4 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
32 |
A |
5 |
5 |
1. |
36 |
0.139 |
|
|
|
|
|
|
|
33 |
A |
3 |
3 |
1. |
45 |
0.067 |
|
|
|
|
|
|
|
34 |
A |
5 |
5 |
1. |
39 |
0.128 |
|
|
|
|
|
|
|
35 |
A |
10 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
36 |
A |
9 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
37 |
A |
8 |
6 |
1. |
33 |
0.182 |
|
|
|
|
|
|
|
38 |
A |
7 |
7 |
1. |
28 |
0.25 |
|
|
|
|
|
|
|
39 |
A |
10 |
10 |
1. |
35 |
0.286 |
|
|
|
|
|
|
|
40 |
A |
10 |
10 |
1. |
35 |
0.286 |
|
|
|
|
|
|
|
|
41 |
A |
11 |
11 |
1. |
35 |
0.314 |
|
|
|
|
|
|
|
42 |
A |
12 |
11 |
1. |
35 |
0.314 |
|
|
|
|
|
|
|
43 |
A |
12 |
10 |
1. |
35 |
0.286 |
|
|
|
|
|
|
|
44 |
A |
9 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
45 |
A |
8 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
46 |
A |
7 |
6 |
1. |
33 |
0.182 |
|
|
|
|
|
|
|
47 |
A |
6 |
6 |
1. |
28 |
0.214 |
|
|
|
|
|
|
|
48 |
A |
9 |
9 |
1. |
35 |
0.257 |
|
|
|
|
|
|
|
49 |
A |
10 |
10 |
1. |
35 |
0.286 |
|
|
|
|
|
|
|
50 |
A |
11 |
11 |
1. |
35 |
0.314 |
|
|
|
|
|
|
|
51 |
A |
8 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
52 |
A |
7 |
7 |
1. |
35 |
0.2 |
|
|
|
|
|
|
|
53 |
A |
6 |
6 |
1. |
33 |
0.182 |
|
|
|
|
|
|
|
54 |
A |
2 |
2 |
1. |
28 |
0.071 |
|
|
|
|
|
|
|
55 |
A |
6 |
6 |
1. |
35 |
0.171 |
|
|
|
|
|
|
|
56 |
A |
10 |
10 |
1. |
35 |
0.286 |
|
|
|
|
|
|
|
57 |
A |
11 |
11 |
1. |
35 |
0.314 |
|
|
|
|
|
|
|
58 |
A |
8 |
6 |
1. |
35 |
0.171 |
|
|
|
|
|
|
|
59 |
A |
11 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
60 |
A |
8 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
|
61 |
A |
7 |
7 |
1. |
35 |
0.2 |
|
|
|
|
|
|
|
62 |
A |
7 |
7 |
1. |
35 |
0.2 |
|
|
|
|
|
|
|
63 |
A |
5 |
5 |
1. |
33 |
0.152 |
|
|
|
|
|
|
|
64 |
A |
2 |
2 |
1. |
28 |
0.071 |
|
|
|
|
|
|
|
65 |
A |
3 |
3 |
1. |
35 |
0.086 |
|
|
|
|
|
|
|
66 |
A |
10 |
10 |
1. |
35 |
0.286 |
|
|
|
|
|
|
|
67 |
A |
11 |
11 |
1. |
35 |
0.314 |
|
|
|
|
|
|
|
68 |
A |
3 |
3 |
1. |
36 |
0.083 |
|
|
|
|
|
|
|
69 |
A |
6 |
5 |
1. |
33 |
0.152 |
|
|
|
|
|
|
|
70 |
A |
4 |
3 |
1. |
35 |
0.086 |
|
|
|
|
|
|
|
71 |
A |
10 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
72 |
A |
18 |
12 |
1. |
35 |
0.343 |
|
|
|
|
|
|
|
73 |
A |
3 |
3 |
1. |
36 |
0.083 |
|
|
|
|
|
|
|
74 |
A |
4 |
4 |
1. |
31 |
0.129 |
|
|
|
|
|
|
|
75 |
A |
3 |
3 |
1. |
40 |
0.075 |
|
|
|
|
|
|
|
76 |
A |
4 |
4 |
1. |
31 |
0.129 |
|
|
|
|
|
|
|
77 |
A |
12 |
10 |
1. |
37 |
0.27 |
|
|
|
|
|
|
|
78 |
A |
11 |
10 |
1. |
37 |
0.27 |
|
|
|
|
|
|
|
79 |
A |
10 |
10 |
1. |
37 |
0.27 |
|
|
|
|
|
|
|
80 |
A |
9 |
9 |
1. |
37 |
0.243 |
|
|
|
|
|
|
|
|
81 |
A |
9 |
9 |
1. |
37 |
0.243 |
|
|
|
|
|
|
|
82 |
A |
10 |
10 |
1. |
37 |
0.27 |
|
|
|
|
|
|
|
83 |
A |
9 |
9 |
1. |
37 |
0.243 |
|
|
|
|
|
|
|
84 |
A |
10 |
9 |
1. |
37 |
0.243 |
|
|
|
|
|
|
|
85 |
A |
11 |
10 |
1. |
37 |
0.27 |
|
|
|
|
|
|
|
86 |
A |
10 |
10 |
1. |
37 |
0.27 |
|
|
|
|
|
|
|
87 |
A |
9 |
9 |
1. |
37 |
0.243 |
|
|
|
|
|
|
|
88 |
A |
9 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
89 |
A |
7 |
7 |
1. |
37 |
0.189 |
|
|
|
|
|
|
|
90 |
A |
8 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
91 |
A |
9 |
9 |
1. |
37 |
0.243 |
|
|
|
|
|
|
|
92 |
A |
10 |
9 |
1. |
37 |
0.243 |
|
|
|
|
|
|
|
93 |
A |
10 |
10 |
1. |
37 |
0.27 |
|
|
|
|
|
|
|
94 |
A |
9 |
9 |
1. |
37 |
0.243 |
|
|
|
|
|
|
|
95 |
A |
9 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
96 |
A |
2 |
2 |
1. |
37 |
0.054 |
|
|
|
|
|
|
|
97 |
B |
5 |
5 |
3.25 |
37 |
0.135 |
|
|
|
|
|
|
|
98 |
A |
8 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
99 |
A |
7 |
7 |
1. |
37 |
0.189 |
|
|
|
|
|
|
|
100 |
A |
2 |
2 |
1.29 |
37 |
0.054 |
|
|
|
|
|
|
|
|
101 |
A |
9 |
9 |
1. |
37 |
0.243 |
|
|
|
|
|
|
|
102 |
A |
12 |
10 |
1. |
37 |
0.27 |
|
|
|
|
|
|
|
103 |
A |
2 |
2 |
1. |
37 |
0.054 |
|
|
|
|
|
|
|
104 |
A |
2 |
2 |
1. |
37 |
0.054 |
|
|
|
|
|
|
|
105 |
A |
8 |
7 |
1.38 |
37 |
0.189 |
|
|
|
|
|
|
|
106 |
A |
8 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
107 |
A |
10 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
108 |
A |
2 |
2 |
1. |
37 |
0.054 |
|
|
|
|
|
|
|
109 |
A |
2 |
2 |
1.23 |
37 |
0.054 |
|
|
|
|
|
|
|
110 |
A |
5 |
5 |
1. |
37 |
0.135 |
|
|
|
|
|
|
|
111 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
112 |
A |
8 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
113 |
A |
6 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
114 |
A |
4 |
2 |
1. |
25 |
0.08 |
|
|
|
|
|
|
|
115 |
A |
3 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
116 |
A |
3 |
2 |
1. |
22 |
0.091 |
|
|
|
|
|
|
|
117 |
A |
5 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
118 |
A |
6 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
119 |
A |
2 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
120 |
A |
2 |
2 |
1. |
25 |
0.08 |
|
|
|
|
|
|
|
|
121 |
A |
3 |
2 |
1. |
27 |
0.074 |
|
|
|
|
|
|
|
122 |
A |
5 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
123 |
A |
6 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
124 |
A |
3 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
125 |
A |
3 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
126 |
A |
3 |
3 |
1. |
27 |
0.111 |
|
|
|
|
|
|
|
127 |
A |
3 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
128 |
A |
3 |
3 |
1.01 |
29 |
0.103 |
|
|
|
|
|
|
|
129 |
A |
3 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
130 |
A |
3 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
131 |
A |
4 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
132 |
A |
10 |
9 |
0.99 |
31 |
0.29 |
|
|
|
|
|
|
|
133 |
A |
9 |
8 |
0.99 |
31 |
0.258 |
|
|
|
|
|
|
|
134 |
A |
3 |
3 |
0.99 |
29 |
0.103 |
|
|
|
|
|
|
|
135 |
A |
3 |
3 |
0.99 |
24 |
0.125 |
|
|
|
|
|
|
|
136 |
A |
5 |
5 |
1.07 |
27 |
0.185 |
|
|
|
|
|
|
|
137 |
A |
7 |
5 |
0.94 |
29 |
0.172 |
|
|
|
|
|
|
|
138 |
A |
7 |
4 |
1. |
29 |
0.138 |
|
|
|
|
|
|
|
139 |
A |
31 |
5 |
1. |
29 |
0.172 |
|
|
|
|
|
|
|
140 |
A |
15 |
5 |
1. |
29 |
0.172 |
|
|
|
|
|
|
|
|
141 |
A |
7 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
142 |
A |
3 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
143 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
144 |
A |
7 |
4 |
1. |
33 |
0.121 |
|
|
|
|
|
|
|
145 |
A |
7 |
4 |
1. |
34 |
0.118 |
|
|
|
|
|
|
|
146 |
A |
5 |
5 |
1. |
34 |
0.147 |
|
|
|
|
|
|
|
147 |
A |
3 |
3 |
0.99 |
34 |
0.088 |
|
|
|
|
|
|
|
148 |
A |
4 |
3 |
1. |
34 |
0.088 |
|
|
|
|
|
|
|
149 |
A |
4 |
4 |
1. |
31 |
0.129 |
|
|
|
|
|
|
|
150 |
A |
4 |
4 |
1. |
30 |
0.133 |
|
|
|
|
|
|
|
151 |
A |
7 |
7 |
1. |
33 |
0.212 |
|
|
|
|
|
|
|
152 |
A |
7 |
7 |
1. |
33 |
0.212 |
|
|
|
|
|
|
|
153 |
A |
6 |
6 |
1. |
33 |
0.182 |
|
|
|
|
|
|
|
154 |
A |
5 |
5 |
1.74 |
30 |
0.167 |
|
|
|
|
|
|
|
155 |
B |
5 |
5 |
2.6 |
29 |
0.172 |
|
|
|
|
|
|
|
156 |
B |
8 |
8 |
2.45 |
32 |
0.25 |
|
|
|
|
|
|
|
157 |
B |
8 |
8 |
2.45 |
32 |
0.25 |
|
|
|
|
|
|
|
158 |
A |
6 |
6 |
1.55 |
32 |
0.188 |
|
|
|
|
|
|
|
159 |
A |
7 |
7 |
1.47 |
32 |
0.219 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|