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
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30,
31, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66,
67, 68, 69, 70, 72, 73, 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, 113, 114, 115, 116, 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, 175, 176, 177, 178, 179, 180, 181, 182, 183
}
B grade: { 28, 52, 54, 60, 62, 71, 173, 174 }
C grade: { 32, 74, 112, 117 }
F grade: { 39, 40}
2.1.3 Maple
A grade: { 4, 5, 6, 12, 13, 19, 20, 21, 25, 29, 30, 33, 34, 35, 39, 40, 68, 69, 70, 75, 79, 80, 102, 103, 107,
108, 109, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 127, 128, 129, 142, 143, 147, 148, 150, 154, 155,
159, 164, 165, 166, 171, 172, 176, 177, 178, 182, 183 }
B grade: { 1, 2, 3, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 22, 23, 24, 28, 31, 32, 38, 99, 100, 101, 104, 105, 106,
110, 111, 112, 116, 156, 157, 158, 161, 163, 167, 170, 175 }
C grade: { 63, 64, 65, 66, 67, 81, 82, 83, 84, 85, 86, 87 }
F grade: { 26, 27, 36, 37, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62,
71, 72, 73, 74, 76, 77, 78, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 124, 125, 126, 130, 131, 132, 133, 134,
135, 136, 137, 138, 139, 140, 141, 144, 145, 146, 149, 151, 152, 153, 160, 162, 168, 169, 173, 174, 179, 180,
181 }
2.1.4 Maxima
A grade: { 5, 6, 7, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 29, 30, 34, 35, 39, 40, 45, 46, 47, 48, 49, 50,
51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 66, 67, 68, 69, 70, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87,
101, 102, 103, 104, 107, 108, 109, 110, 113, 114, 115, 119, 120, 121, 122, 123, 127, 128, 129, 133, 134, 135,
142, 143, 147, 148, 149, 150, 154, 155, 158, 159, 160, 161, 163, 164, 165, 166, 167, 171, 172, 176, 177, 178,
182, 183
B grade: { 1, 2, 3, 4, 8, 9, 16, 17, 18, 19, 31, 33, 41, 42, 43, 44, 63, 64, 65, 99, 100, 105, 106, 111, 116, 118,
156, 157, 162 }
C grade: { }
F grade: { 26, 27, 28, 32, 36, 37, 38, 71, 72, 73, 74, 77, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 112, 117,
124, 125, 126, 130, 131, 132, 136, 137, 138, 139, 140, 141, 144, 145, 146, 151, 152, 153, 168, 169, 170, 173,
174, 175, 179, 180, 181 }
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 5, 9, 10, 11, 12, 18, 19, 20, 23, 24, 25, 29, 30, 34, 35, 39, 40, 44, 51, 59, 65, 68, 69, 75,
76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 99, 100, 101, 102, 103,
105, 106, 107, 108, 114, 115, 119, 120, 142, 143, 147, 148, 150, 151, 152, 153, 154, 155, 156,
157, 158, 159, 160, 162, 163, 164, 165, 166, 171, 172, 176, 177, 178, 179, 180, 181, 182, 183
}
B grade: { 6, 7, 8, 13, 14, 15, 16, 17, 21, 22, 28, 33, 38, 41, 42, 43, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55,
56, 57, 58, 60, 61, 62, 63, 64, 66, 67, 72, 104, 109, 110, 112, 113, 117, 118, 161, 167, 170, 175
}
C grade: { 26, 27, 31, 32, 36, 37, 111, 116, 168, 169, 173, 174 }
F grade: { 70, 71, 73, 74, 95, 96, 97, 98, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133,
134, 135, 136, 137, 138, 139, 140, 141, 144, 145, 146, 149 }
2.1.6 Sympy
A grade: { 1, 2, 3, 4, 8, 9, 10, 11, 16, 17, 18, 19, 23, 24, 25, 29, 30, 34, 35, 39, 68, 69, 75, 79, 80, 99, 100,
101, 105, 106, 107, 113, 114, 115, 118, 119, 142, 143, 149, 154, 155, 156, 157, 158, 162, 163, 164, 182, 183
}
B grade: { }
C grade: { 63, 64, 65, 66 }
F grade: { 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 26, 27, 28, 31, 32, 33, 36, 37, 38, 40, 41, 42, 43, 44,
45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 67, 70, 71, 72, 73, 74, 76,
77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 102, 103, 104, 108,
109, 110, 111, 112, 116, 117, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132,
133, 134, 135, 136, 137, 138, 139, 140, 141, 144, 145, 146, 147, 148, 150, 151, 152, 153, 159,
160, 161, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181
}
2.1.7 Giac
A grade: { 4, 5, 10, 11, 12, 19, 20, 23, 24, 25, 29, 30, 34, 35, 39, 40, 41, 42, 43, 44, 63, 64, 65, 68, 69, 70,
75, 79, 80, 101, 102, 103, 107, 108, 113, 114, 115, 119, 120, 121, 122, 123, 124, 125, 126, 133, 134, 135,
136, 137, 138, 142, 143, 147, 148, 149, 150, 154, 155, 158, 159, 160, 164, 165, 166, 171, 172, 176, 177, 178,
182, 183 }
B grade: { 1, 2, 3, 6, 7, 8, 9, 14, 15, 16, 17, 18, 21, 22, 33, 99, 100, 104, 105, 106, 109, 110, 118, 156, 157,
161, 162, 163, 167 }
C grade: { }
F grade: { 13, 26, 27, 28, 31, 32, 36, 37, 38, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61,
62, 66, 67, 71, 72, 73, 74, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 111,
112, 116, 117, 127, 128, 129, 130, 131, 132, 139, 140, 141, 144, 145, 146, 151, 152, 153, 168, 169, 170, 173,
174, 175, 179, 180, 181 }
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 |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 76 | 547 | 440 | 351 | 311 | 437 |
normalized size | 1 | 1. | 0.84 | 6.01 | 4.84 | 3.86 | 3.42 | 4.8 |
time (sec) |
N/A |
0.119 |
0.303 |
0.013 |
1.241 |
1.72 |
3.25 |
1.456 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 61 | 308 | 300 | 232 | 202 | 275 |
normalized size | 1 | 1. | 0.87 | 4.4 | 4.29 | 3.31 | 2.89 | 3.93 |
time (sec) |
N/A |
0.079 |
0.193 |
0.006 |
1.289 |
1.979 |
1.564 |
1.39 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 44 | 147 | 182 | 140 | 112 | 151 |
normalized size | 1 | 1. | 0.9 | 3. | 3.71 | 2.86 | 2.29 | 3.08 |
time (sec) |
N/A |
0.047 |
0.14 |
0.007 |
1.194 |
1.906 |
0.754 |
1.32 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 27 | 53 | 92 | 73 | 46 | 62 |
normalized size | 1 | 1. | 0.96 | 1.89 | 3.29 | 2.61 | 1.64 | 2.21 |
time (sec) |
N/A |
0.02 |
0.053 |
0.007 |
1.11 |
1.766 |
0.276 |
1.27 |
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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 |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 49 | 82 | 77 | 193 | 0 | 76 |
normalized size | 1 | 1. | 0.96 | 1.61 | 1.51 | 3.78 | 0. | 1.49 |
time (sec) |
N/A |
0.101 |
0.073 |
0.024 |
1.204 |
1.716 |
0. |
1.218 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 65 | 133 | 109 | 316 | 0 | 201 |
normalized size |
1 |
1. |
0.92 |
1.87 |
1.54 |
4.45 |
0. |
2.83 |
time (sec) |
N/A |
0.119 |
0.243 |
0.033 |
1.359 |
1.769 |
0. |
1.231 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 88 | 277 | 128 | 518 | 0 | 402 |
normalized size |
1 |
1. |
0.85 |
2.66 |
1.23 |
4.98 |
0. |
3.87 |
time (sec) |
N/A |
0.163 |
0.525 |
0.039 |
1.215 |
1.849 |
0. |
1.256 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
B |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 162 | 162 | 132 | 910 | 516 | 662 | 660 | 502 |
normalized size | 1 | 1. | 0.81 | 5.62 | 3.19 | 4.09 | 4.07 | 3.1 |
time (sec) |
N/A |
0.101 |
0.616 |
0.01 |
1.125 |
1.876 |
6.526 |
1.178 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 134 | 134 | 104 | 523 | 355 | 458 | 456 | 328 |
normalized size | 1 | 1. | 0.78 | 3.9 | 2.65 | 3.42 | 3.4 | 2.45 |
time (sec) |
N/A |
0.073 |
0.41 |
0.01 |
1.105 |
1.795 |
3.506 |
1.373 |
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Problem 10 |
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 | 95 | 95 | 75 | 262 | 223 | 286 | 264 | 184 |
normalized size | 1 | 1. | 0.79 | 2.76 | 2.35 | 3.01 | 2.78 | 1.94 |
time (sec) |
N/A |
0.053 |
0.278 |
0.008 |
1.143 |
1.81 |
1.625 |
1.333 |
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Problem 11 |
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 | 55 | 55 | 51 | 103 | 119 | 163 | 126 | 85 |
normalized size | 1 | 1. | 0.93 | 1.87 | 2.16 | 2.96 | 2.29 | 1.55 |
time (sec) |
N/A |
0.025 |
0.155 |
0.008 |
1.065 |
1.83 |
0.674 |
1.254 |
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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 |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 64 | 97 | 97 | 232 | 0 | 92 |
normalized size | 1 | 1. | 0.82 | 1.24 | 1.24 | 2.97 | 0. | 1.18 |
time (sec) |
N/A |
0.154 |
0.114 |
0.071 |
1.345 |
1.783 |
0. |
1.294 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 75 | 152 | 119 | 365 | 0 | 0 |
normalized size | 1 | 1. | 0.93 | 1.88 | 1.47 | 4.51 | 0. | 0. |
time (sec) |
N/A |
0.146 |
0.402 |
0.076 |
1.237 |
1.785 |
0. |
0. |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 112 | 112 | 102 | 299 | 134 | 597 | 0 | 446 |
normalized size | 1 | 1. | 0.91 | 2.67 | 1.2 | 5.33 | 0. | 3.98 |
time (sec) |
N/A |
0.187 |
0.88 |
0.081 |
1.288 |
1.85 |
0. |
1.408 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 162 | 162 | 121 | 555 | 149 | 859 | 0 | 725 |
normalized size | 1 | 1. | 0.75 | 3.43 | 0.92 | 5.3 | 0. | 4.48 |
time (sec) |
N/A |
0.181 |
0.834 |
0.092 |
1.298 |
1.892 |
0. |
1.33 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
B |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 225 | 225 | 385 | 1217 | 869 | 1149 | 772 | 883 |
normalized size | 1 | 1. | 1.71 | 5.41 | 3.86 | 5.11 | 3.43 | 3.92 |
time (sec) |
N/A |
0.282 |
0.934 |
0.013 |
1.165 |
2.042 |
11.293 |
1.398 |
|
|
|
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|
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 122 | 676 | 593 | 757 | 495 | 559 |
normalized size | 1 | 1. | 0.7 | 3.86 | 3.39 | 4.33 | 2.83 | 3.19 |
time (sec) |
N/A |
0.176 |
0.926 |
0.01 |
1.101 |
2.111 |
5.883 |
1.368 |
|
|
|
|
|
|
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|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 93 | 320 | 367 | 474 | 284 | 311 |
normalized size | 1 | 1. | 0.76 | 2.6 | 2.98 | 3.85 | 2.31 | 2.53 |
time (sec) |
N/A |
0.103 |
0.536 |
0.01 |
1.104 |
2.018 |
2.934 |
1.329 |
|
|
|
|
|
|
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|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 52 | 115 | 193 | 257 | 126 | 132 |
normalized size | 1 | 1. | 0.69 | 1.53 | 2.57 | 3.43 | 1.68 | 1.76 |
time (sec) |
N/A |
0.044 |
0.227 |
0.009 |
1.072 |
1.961 |
1.334 |
1.304 |
|
|
|
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|
Problem 20 |
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 | 121 | 121 | 102 | 166 | 158 | 398 | 0 | 151 |
normalized size | 1 | 1. | 0.84 | 1.37 | 1.31 | 3.29 | 0. | 1.25 |
time (sec) |
N/A |
0.24 |
0.227 |
0.088 |
1.278 |
1.984 |
0. |
1.332 |
|
|
|
|
|
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|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 196 | 271 | 196 | 680 | 0 | 401 |
normalized size | 1 | 1. | 1.35 | 1.87 | 1.35 | 4.69 | 0. | 2.77 |
time (sec) |
N/A |
0.237 |
0.534 |
0.102 |
1.335 |
1.947 |
0. |
1.395 |
|
|
|
|
|
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|
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|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 218 | 562 | 196 | 1122 | 0 | 813 |
normalized size | 1 | 1. | 1.18 | 3.05 | 1.07 | 6.1 | 0. | 4.42 |
time (sec) |
N/A |
0.34 |
0.9 |
0.106 |
1.356 |
2.041 |
0. |
1.308 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 172 | 172 | 100 | 432 | 238 | 486 | 262 | 203 |
normalized size | 1 | 1. | 0.58 | 2.51 | 1.38 | 2.83 | 1.52 | 1.18 |
time (sec) |
N/A |
0.146 |
0.405 |
0.011 |
1.043 |
2.05 |
8.106 |
1.237 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 134 | 134 | 90 | 253 | 178 | 373 | 209 | 159 |
normalized size | 1 | 1. | 0.67 | 1.89 | 1.33 | 2.78 | 1.56 | 1.19 |
time (sec) |
N/A |
0.107 |
0.157 |
0.007 |
1.048 |
1.986 |
4.356 |
1.302 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
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 | 80 | 80 | 53 | 120 | 130 | 306 | 144 | 116 |
normalized size | 1 | 1. | 0.66 | 1.5 | 1.62 | 3.82 | 1.8 | 1.45 |
time (sec) |
N/A |
0.044 |
0.175 |
0.007 |
1.08 |
2.021 |
2.379 |
1.274 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 179 | 179 | 343 | 0 | 0 | 1300 | 0 | 0 |
normalized size | 1 | 1. | 1.92 | 0. | 0. | 7.26 | 0. | 0. |
time (sec) |
N/A |
0.123 |
2.556 |
0.216 |
0. |
2.251 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 199 | 0 | 0 | 845 | 0 | 0 |
normalized size | 1 | 1. | 1.67 | 0. | 0. | 7.1 | 0. | 0. |
time (sec) |
N/A |
0.081 |
1.459 |
0.128 |
0. |
2.229 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 61 | 61 | 129 | 449 | 0 | 463 | 0 | 0 |
normalized size | 1 | 1. | 2.11 | 7.36 | 0. | 7.59 | 0. | 0. |
time (sec) |
N/A |
0.037 |
0.079 |
0.007 |
0. |
2.146 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
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 |
0.021 |
3.538 |
0.053 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
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 |
0.02 |
7.201 |
0.046 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 145 | 298 | 321 | 3131 | 0 | 0 |
normalized size | 1 | 1. | 1.41 | 2.89 | 3.12 | 30.4 | 0. | 0. |
time (sec) |
N/A |
0.206 |
2.039 |
0.067 |
1.694 |
2.426 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 277 | 159 | 0 | 1777 | 0 | 0 |
normalized size | 1 | 1. | 3.79 | 2.18 | 0. | 24.34 | 0. | 0. |
time (sec) |
N/A |
0.133 |
6.281 |
0.031 |
0. |
2.232 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 51 | 57 | 97 | 429 | 0 | 105 |
normalized size | 1 | 1. | 1.76 | 1.97 | 3.34 | 14.79 | 0. | 3.62 |
time (sec) |
N/A |
0.029 |
0.09 |
0.023 |
1.012 |
2.07 |
0. |
1.315 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.037 |
17.409 |
0.073 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.035 |
17.628 |
0.085 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 296 | 296 | 455 | 0 | 0 | 11732 | 0 | 0 |
normalized size | 1 | 1. | 1.54 | 0. | 0. | 39.64 | 0. | 0. |
time (sec) |
N/A |
0.217 |
27.244 |
0.193 |
0. |
3.435 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 270 | 0 | 0 | 6791 | 0 | 0 |
normalized size | 1 | 1. | 1.54 | 0. | 0. | 38.81 | 0. | 0. |
time (sec) |
N/A |
0.133 |
5.31 |
0.164 |
0. |
2.832 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 180 | 216 | 0 | 3492 | 0 | 0 |
normalized size | 1 | 1. | 1.76 | 2.12 | 0. | 34.24 | 0. | 0. |
time (sec) |
N/A |
0.063 |
2.858 |
0.053 |
0. |
2.521 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
F |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.037 |
180.016 |
0.3 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
F |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.034 |
180.015 |
0.422 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 107 | 0 | 416 | 1177 | 0 | 313 |
normalized size |
1 |
1. |
0.63 |
0. |
2.43 |
6.88 |
0. |
1.83 |
time (sec) |
N/A |
0.33 |
0.052 |
0.046 |
1.083 |
2.128 |
0. |
1.479 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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|
|
|
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|
|
|
grade |
A |
A |
A |
F |
B |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 146 | 146 | 107 | 0 | 362 | 892 | 0 | 273 |
normalized size | 1 | 1. | 0.73 | 0. | 2.48 | 6.11 | 0. | 1.87 |
time (sec) |
N/A |
0.243 |
0.101 |
0.045 |
1.086 |
2.166 |
0. |
1.466 |
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Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
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|
|
grade |
A |
A |
A |
F |
B |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 105 | 0 | 311 | 717 | 0 | 228 |
normalized size | 1 | 1. | 0.85 | 0. | 2.53 | 5.83 | 0. | 1.85 |
time (sec) |
N/A |
0.178 |
0.092 |
0.043 |
1.117 |
2.083 |
0. |
1.442 |
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Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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|
|
grade |
A |
A |
A |
F |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 105 | 0 | 243 | 271 | 0 | 123 |
normalized size | 1 | 1. | 1.01 | 0. | 2.34 | 2.61 | 0. | 1.18 |
time (sec) |
N/A |
0.13 |
0.043 |
0.046 |
1.084 |
2.096 |
0. |
1.396 |
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Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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|
|
grade |
A |
A |
A |
F |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 118 | 0 | 140 | 815 | 0 | 0 |
normalized size | 1 | 1. | 0.99 | 0. | 1.18 | 6.85 | 0. | 0. |
time (sec) |
N/A |
0.183 |
0.35 |
0.044 |
1.051 |
2.101 |
0. |
0. |
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Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
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|
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|
|
|
grade |
A |
A |
A |
F |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 150 | 0 | 155 | 1224 | 0 | 0 |
normalized size | 1 | 1. | 1.01 | 0. | 1.04 | 8.21 | 0. | 0. |
time (sec) |
N/A |
0.248 |
0.709 |
0.043 |
1.206 |
2.157 |
0. |
0. |
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Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
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|
|
|
grade |
A |
A |
A |
F |
A |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 174 | 174 | 191 | 0 | 155 | 1821 | 0 | 0 |
normalized size |
1 |
1. |
1.1 |
0. |
0.89 |
10.47 |
0. |
0. |
time (sec) |
N/A |
0.312 |
0.395 |
0.046 |
1.187 |
2.293 |
0. |
0. |
|
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Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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|
|
|
grade |
A |
A |
A |
F |
A |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 239 | 239 | 189 | 0 | 379 | 2319 | 0 | 0 |
normalized size |
1 |
1. |
0.79 |
0. |
1.59 |
9.7 |
0. |
0. |
time (sec) |
N/A |
0.4 |
1.156 |
0.085 |
1.59 |
2.256 |
0. |
0. |
|
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Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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|
|
grade |
A |
A |
A |
F |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 211 | 211 | 163 | 0 | 323 | 1789 | 0 | 0 |
normalized size | 1 | 1. | 0.77 | 0. | 1.53 | 8.48 | 0. | 0. |
time (sec) |
N/A |
0.303 |
0.583 |
0.08 |
1.57 |
2.218 |
0. |
0. |
|
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Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 129 | 0 | 255 | 1438 | 0 | 0 |
normalized size | 1 | 1. | 0.78 | 0. | 1.54 | 8.66 | 0. | 0. |
time (sec) |
N/A |
0.269 |
0.44 |
0.08 |
1.549 |
2.215 |
0. |
0. |
|
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Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 141 | 0 | 144 | 369 | 0 | 0 |
normalized size | 1 | 1. | 1.02 | 0. | 1.04 | 2.67 | 0. | 0. |
time (sec) |
N/A |
0.214 |
0.118 |
0.088 |
1.568 |
2.211 |
0. |
0. |
|
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Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 142 | 142 | 570 | 0 | 157 | 1442 | 0 | 0 |
normalized size | 1 | 1. | 4.01 | 0. | 1.11 | 10.15 | 0. | 0. |
time (sec) |
N/A |
0.23 |
2.847 |
0.092 |
1.269 |
2.226 |
0. |
0. |
|
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Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 174 | 174 | 156 | 0 | 159 | 2053 | 0 | 0 |
normalized size | 1 | 1. | 0.9 | 0. | 0.91 | 11.8 | 0. | 0. |
time (sec) |
N/A |
0.309 |
1.35 |
0.102 |
1.206 |
2.328 |
0. |
0. |
|
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Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
A |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 220 | 825 | 0 | 157 | 2974 | 0 | 0 |
normalized size |
1 |
1. |
3.75 |
0. |
0.71 |
13.52 |
0. |
0. |
time (sec) |
N/A |
0.311 |
3.034 |
0.095 |
1.201 |
2.388 |
0. |
0. |
|
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Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 251 | 251 | 222 | 0 | 157 | 3951 | 0 | 0 |
normalized size |
1 |
1. |
0.88 |
0. |
0.63 |
15.74 |
0. |
0. |
time (sec) |
N/A |
0.379 |
0.828 |
0.104 |
1.213 |
2.29 |
0. |
0. |
|
|
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Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 381 | 381 | 243 | 0 | 693 | 4815 | 0 | 0 |
normalized size |
1 |
1. |
0.64 |
0. |
1.82 |
12.64 |
0. |
0. |
time (sec) |
N/A |
0.906 |
3.736 |
0.125 |
1.666 |
2.246 |
0. |
0. |
|
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Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 326 | 326 | 243 | 0 | 579 | 3621 | 0 | 0 |
normalized size |
1 |
1. |
0.75 |
0. |
1.78 |
11.11 |
0. |
0. |
time (sec) |
N/A |
0.712 |
1.929 |
0.119 |
1.86 |
2.018 |
0. |
0. |
|
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Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
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|
|
|
grade |
A |
A |
A |
F |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 275 | 275 | 210 | 0 | 451 | 2965 | 0 | 0 |
normalized size | 1 | 1. | 0.76 | 0. | 1.64 | 10.78 | 0. | 0. |
time (sec) |
N/A |
0.484 |
0.287 |
0.122 |
1.704 |
1.872 |
0. |
0. |
|
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Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
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|
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|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 228 | 228 | 192 | 0 | 239 | 594 | 0 | 0 |
normalized size | 1 | 1. | 0.84 | 0. | 1.05 | 2.61 | 0. | 0. |
time (sec) |
N/A |
0.374 |
0.206 |
0.123 |
1.62 |
2.087 |
0. |
0. |
|
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Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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|
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|
|
|
grade |
A |
A |
B |
F |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 246 | 246 | 717 | 0 | 265 | 3313 | 0 | 0 |
normalized size | 1 | 1. | 2.91 | 0. | 1.08 | 13.47 | 0. | 0. |
time (sec) |
N/A |
0.421 |
2.736 |
0.155 |
1.363 |
2.376 |
0. |
0. |
|
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Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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|
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|
|
|
grade |
A |
A |
A |
F |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 277 | 277 | 253 | 0 | 262 | 4825 | 0 | 0 |
normalized size | 1 | 1. | 0.91 | 0. | 0.95 | 17.42 | 0. | 0. |
time (sec) |
N/A |
0.605 |
2.907 |
0.141 |
1.36 |
2.365 |
0. |
0. |
|
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Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
A |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 331 | 331 | 3211 | 0 | 265 | 7121 | 0 | 0 |
normalized size |
1 |
1. |
9.7 |
0. |
0.8 |
21.51 |
0. |
0. |
time (sec) |
N/A |
0.68 |
6.325 |
0.131 |
1.341 |
2.48 |
0. |
0. |
|
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Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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|
|
grade |
A |
A |
A |
C |
B |
B |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 51 | 133 | 235 | 466 | 131 | 194 |
normalized size | 1 | 1. | 0.46 | 1.2 | 2.12 | 4.2 | 1.18 | 1.75 |
time (sec) |
N/A |
0.155 |
0.013 |
0.027 |
1.062 |
1.839 |
142.406 |
1.232 |
|
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Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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|
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|
|
|
grade |
A |
A |
A |
C |
B |
B |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 92 | 92 | 48 | 121 | 200 | 355 | 100 | 138 |
normalized size | 1 | 1. | 0.52 | 1.32 | 2.17 | 3.86 | 1.09 | 1.5 |
time (sec) |
N/A |
0.106 |
0.011 |
0.019 |
1.124 |
1.85 |
3.545 |
1.216 |
|
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Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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|
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|
|
|
grade |
A |
A |
A |
C |
B |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 48 | 72 | 158 | 136 | 66 | 81 |
normalized size | 1 | 1. | 0.62 | 0.94 | 2.05 | 1.77 | 0.86 | 1.05 |
time (sec) |
N/A |
0.077 |
0.008 |
0.022 |
1.057 |
1.833 |
1.643 |
1.292 |
|
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Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
B |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 67 | 115 | 103 | 356 | 99 | 0 |
normalized size | 1 | 1. | 0.76 | 1.31 | 1.17 | 4.05 | 1.12 | 0. |
time (sec) |
N/A |
0.113 |
0.034 |
0.022 |
1.043 |
1.792 |
7.426 |
0. |
|
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Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
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|
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|
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|
|
|
grade |
A |
A |
A |
C |
A |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 114 | 78 | 126 | 78 | 452 | 0 | 0 |
normalized size |
1 |
1. |
0.68 |
1.11 |
0.68 |
3.96 |
0. |
0. |
time (sec) |
N/A |
0.148 |
0.093 |
0.027 |
1.261 |
1.855 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.028 |
11.162 |
0.068 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.03 |
9.845 |
0.064 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
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 | 61 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.085 |
3.849 |
0.026 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 46 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.3 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.048 |
0.372 |
0.074 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 16 | 0 | 0 | 374 | 0 | 0 |
normalized size |
1 |
1. |
0.67 |
0. |
0. |
15.58 |
0. |
0. |
time (sec) |
N/A |
0.05 |
0.074 |
0.079 |
0. |
1.76 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 64 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.36 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.066 |
0.616 |
0.1 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 76 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.11 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.092 |
0.947 |
0.07 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
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 |
0.046 |
2.79 |
0.072 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 237 | 237 | 205 | 0 | 217 | 801 | 0 | 0 |
normalized size |
1 |
1. |
0.86 |
0. |
0.92 |
3.38 |
0. |
0. |
time (sec) |
N/A |
0.284 |
0.188 |
0.135 |
1.28 |
1.948 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 144 | 144 | 132 | 0 | 0 | 597 | 0 | 0 |
normalized size |
1 |
1. |
0.92 |
0. |
0. |
4.15 |
0. |
0. |
time (sec) |
N/A |
0.184 |
0.202 |
0.091 |
0. |
1.796 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 102 | 0 | 107 | 378 | 0 | 0 |
normalized size |
1 |
1. |
0.93 |
0. |
0.97 |
3.44 |
0. |
0. |
time (sec) |
N/A |
0.091 |
0.056 |
0.06 |
1.244 |
1.905 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
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 |
0.02 |
5.654 |
0.046 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.036 |
3.295 |
0.052 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 54 | 73 | 74 | 259 | 0 | 0 |
normalized size |
1 |
1. |
0.92 |
1.24 |
1.25 |
4.39 |
0. |
0. |
time (sec) |
N/A |
0.074 |
0.038 |
0.033 |
1.26 |
1.818 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 54 | 73 | 74 | 259 | 0 | 0 |
normalized size |
1 |
1. |
0.92 |
1.24 |
1.25 |
4.39 |
0. |
0. |
time (sec) |
N/A |
0.072 |
0.019 |
0.055 |
1.144 |
1.898 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 54 | 73 | 74 | 259 | 0 | 0 |
normalized size |
1 |
1. |
0.92 |
1.24 |
1.25 |
4.39 |
0. |
0. |
time (sec) |
N/A |
0.071 |
0.032 |
0.048 |
1.153 |
1.748 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 54 | 73 | 74 | 227 | 0 | 0 |
normalized size |
1 |
1. |
0.92 |
1.24 |
1.25 |
3.85 |
0. |
0. |
time (sec) |
N/A |
0.069 |
0.018 |
0.039 |
1.153 |
1.928 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 49 | 67 | 58 | 238 | 0 | 0 |
normalized size |
1 |
1. |
1. |
1.37 |
1.18 |
4.86 |
0. |
0. |
time (sec) |
N/A |
0.069 |
0.02 |
0.046 |
1.17 |
1.974 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 52 | 67 | 74 | 259 | 0 | 0 |
normalized size |
1 |
1. |
0.95 |
1.22 |
1.35 |
4.71 |
0. |
0. |
time (sec) |
N/A |
0.069 |
0.019 |
0.055 |
1.155 |
1.849 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 55 | 71 | 74 | 259 | 0 | 0 |
normalized size |
1 |
1. |
0.93 |
1.2 |
1.25 |
4.39 |
0. |
0. |
time (sec) |
N/A |
0.07 |
0.022 |
0.032 |
1.161 |
1.891 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 79 | 0 | 0 | 425 | 0 | 0 |
normalized size |
1 |
1. |
0.92 |
0. |
0. |
4.94 |
0. |
0. |
time (sec) |
N/A |
0.15 |
0.106 |
0.048 |
0. |
1.878 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 78 | 0 | 0 | 425 | 0 | 0 |
normalized size |
1 |
1. |
0.92 |
0. |
0. |
5. |
0. |
0. |
time (sec) |
N/A |
0.133 |
0.095 |
0.052 |
0. |
1.803 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 79 | 0 | 0 | 425 | 0 | 0 |
normalized size |
1 |
1. |
0.92 |
0. |
0. |
4.94 |
0. |
0. |
time (sec) |
N/A |
0.133 |
0.106 |
0.08 |
0. |
1.741 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 76 | 0 | 0 | 374 | 0 | 0 |
normalized size |
1 |
1. |
0.89 |
0. |
0. |
4.4 |
0. |
0. |
time (sec) |
N/A |
0.127 |
0.085 |
0.054 |
0. |
1.861 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 64 | 0 | 0 | 363 | 0 | 0 |
normalized size |
1 |
1. |
0.89 |
0. |
0. |
5.04 |
0. |
0. |
time (sec) |
N/A |
0.125 |
0.056 |
0.078 |
0. |
1.981 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 73 | 0 | 0 | 423 | 0 | 0 |
normalized size |
1 |
1. |
0.88 |
0. |
0. |
5.1 |
0. |
0. |
time (sec) |
N/A |
0.13 |
0.098 |
0.049 |
0. |
2.092 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 84 | 0 | 0 | 425 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0. |
0. |
5.06 |
0. |
0. |
time (sec) |
N/A |
0.14 |
0.102 |
0.049 |
0. |
2.198 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 17 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.71 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.091 |
0.087 |
0.079 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 17 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.71 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.088 |
0.139 |
0.077 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 45 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.96 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.104 |
0.104 |
0.082 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 55 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.83 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.169 |
0.101 |
0.074 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 122 | 482 | 320 | 365 | 264 | 351 |
normalized size | 1 | 1. | 1.37 | 5.42 | 3.6 | 4.1 | 2.97 | 3.94 |
time (sec) |
N/A |
0.132 |
0.541 |
0.016 |
1.121 |
2.012 |
2.418 |
1.255 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 80 | 240 | 190 | 231 | 151 | 200 |
normalized size | 1 | 1. | 1.19 | 3.58 | 2.84 | 3.45 | 2.25 | 2.99 |
time (sec) |
N/A |
0.091 |
0.314 |
0.012 |
1.091 |
1.972 |
0.946 |
1.293 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 52 | 91 | 89 | 128 | 68 | 89 |
normalized size | 1 | 1. | 1.16 | 2.02 | 1.98 | 2.84 | 1.51 | 1.98 |
time (sec) |
N/A |
0.045 |
0.218 |
0.012 |
1.06 |
1.983 |
0.402 |
1.253 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
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 | 64 | 64 | 54 | 94 | 95 | 230 | 0 | 93 |
normalized size | 1 | 1. | 0.84 | 1.47 | 1.48 | 3.59 | 0. | 1.45 |
time (sec) |
N/A |
0.138 |
0.108 |
0.042 |
1.262 |
2.046 |
0. |
1.294 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 68 | 149 | 117 | 351 | 0 | 227 |
normalized size |
1 |
1. |
0.78 |
1.71 |
1.34 |
4.03 |
0. |
2.61 |
time (sec) |
N/A |
0.172 |
0.298 |
0.052 |
1.231 |
2.005 |
0. |
1.271 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 90 | 296 | 132 | 572 | 0 | 443 |
normalized size |
1 |
1. |
0.73 |
2.41 |
1.07 |
4.65 |
0. |
3.6 |
time (sec) |
N/A |
0.216 |
0.456 |
0.053 |
1.226 |
2.072 |
0. |
1.197 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 237 | 237 | 217 | 1071 | 711 | 828 | 779 | 784 |
normalized size | 1 | 1. | 0.92 | 4.52 | 3. | 3.49 | 3.29 | 3.31 |
time (sec) |
N/A |
0.265 |
1.408 |
0.016 |
1.281 |
2.158 |
6.985 |
1.256 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 168 | 168 | 192 | 541 | 441 | 491 | 456 | 450 |
normalized size | 1 | 1. | 1.14 | 3.22 | 2.62 | 2.92 | 2.71 | 2.68 |
time (sec) |
N/A |
0.188 |
0.521 |
0.014 |
1.249 |
2.118 |
3.247 |
1.237 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
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 | 118 | 118 | 81 | 211 | 225 | 269 | 219 | 209 |
normalized size | 1 | 1. | 0.69 | 1.79 | 1.91 | 2.28 | 1.86 | 1.77 |
time (sec) |
N/A |
0.099 |
0.478 |
0.013 |
1.08 |
2.023 |
1.398 |
1.33 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
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 | 145 | 145 | 113 | 191 | 201 | 470 | 0 | 188 |
normalized size | 1 | 1. | 0.78 | 1.32 | 1.39 | 3.24 | 0. | 1.3 |
time (sec) |
N/A |
0.342 |
0.197 |
0.105 |
1.303 |
2.141 |
0. |
1.28 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 207 | 308 | 246 | 767 | 0 | 485 |
normalized size | 1 | 1. | 1.32 | 1.96 | 1.57 | 4.89 | 0. | 3.09 |
time (sec) |
N/A |
0.333 |
0.63 |
0.123 |
1.32 |
2.17 |
0. |
2.314 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 207 | 207 | 353 | 618 | 273 | 1223 | 0 | 953 |
normalized size | 1 | 1. | 1.71 | 2.99 | 1.32 | 5.91 | 0. | 4.6 |
time (sec) |
N/A |
0.505 |
1.082 |
0.134 |
1.41 |
2.196 |
0. |
1.276 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 154 | 325 | 308 | 1008 | 0 | 0 |
normalized size | 1 | 1. | 1.32 | 2.78 | 2.63 | 8.62 | 0. | 0. |
time (sec) |
N/A |
0.273 |
2.059 |
0.119 |
1.615 |
2.06 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 472 | 174 | 0 | 590 | 0 | 0 |
normalized size | 1 | 1. | 5.36 | 1.98 | 0. | 6.7 | 0. | 0. |
time (sec) |
N/A |
0.201 |
6.346 |
0.045 |
0. |
2.103 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 70 | 63 | 96 | 251 | 76 | 96 |
normalized size | 1 | 1. | 1.43 | 1.29 | 1.96 | 5.12 | 1.55 | 1.96 |
time (sec) |
N/A |
0.068 |
0.258 |
0.039 |
1.036 |
2.108 |
2.011 |
1.31 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
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 | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.06 |
8.873 |
0.07 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
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 | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.057 |
9.314 |
0.083 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 255 | 255 | 462 | 600 | 824 | 4103 | 0 | 0 |
normalized size | 1 | 1. | 1.81 | 2.35 | 3.23 | 16.09 | 0. | 0. |
time (sec) |
N/A |
0.364 |
3.434 |
0.116 |
1.895 |
2.327 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 200 | 200 | 637 | 313 | 0 | 2267 | 0 | 0 |
normalized size | 1 | 1. | 3.18 | 1.56 | 0. | 11.34 | 0. | 0. |
time (sec) |
N/A |
0.252 |
6.457 |
0.065 |
0. |
2.194 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 114 | 108 | 323 | 1002 | 156 | 279 |
normalized size | 1 | 1. | 0.93 | 0.88 | 2.63 | 8.15 | 1.27 | 2.27 |
time (sec) |
N/A |
0.096 |
0.437 |
0.06 |
1.11 |
2.119 |
2.872 |
1.257 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 119 |
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 | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.054 |
30.104 |
0.347 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 120 |
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 | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.052 |
31.286 |
0.465 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-2) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 53 | 108 | 162 | 0 | 0 | 198 |
normalized size |
1 |
1. |
0.48 |
0.98 |
1.47 |
0. |
0. |
1.8 |
time (sec) |
N/A |
0.148 |
0.197 |
0.106 |
1.71 |
0. |
0. |
1.305 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-2) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 44 | 86 | 122 | 0 | 0 | 144 |
normalized size |
1 |
1. |
0.5 |
0.98 |
1.39 |
0. |
0. |
1.64 |
time (sec) |
N/A |
0.113 |
0.149 |
0.056 |
1.659 |
0. |
0. |
1.333 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-2) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 34 | 64 | 81 | 0 | 0 | 90 |
normalized size |
1 |
1. |
0.64 |
1.21 |
1.53 |
0. |
0. |
1.7 |
time (sec) |
N/A |
0.062 |
0.12 |
0.055 |
1.766 |
0. |
0. |
1.294 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 54 | 0 | 0 | 0 | 0 | 43 |
normalized size |
1 |
1. |
0.65 |
0. |
0. |
0. |
0. |
0.52 |
time (sec) |
N/A |
0.132 |
0.075 |
0.069 |
0. |
0. |
0. |
1.3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 75 | 0 | 0 | 0 | 0 | 92 |
normalized size |
1 |
1. |
0.68 |
0. |
0. |
0. |
0. |
0.84 |
time (sec) |
N/A |
0.14 |
0.136 |
0.052 |
0. |
0. |
0. |
1.216 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 97 | 0 | 0 | 0 | 0 | 144 |
normalized size |
1 |
1. |
0.64 |
0. |
0. |
0. |
0. |
0.95 |
time (sec) |
N/A |
0.17 |
0.205 |
0.053 |
0. |
0. |
0. |
1.198 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 33 | 62 | 119 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.49 |
0.91 |
1.75 |
0. |
0. |
0. |
time (sec) |
N/A |
0.117 |
0.052 |
0.051 |
1.74 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 128 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 31 | 50 | 89 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.58 |
0.94 |
1.68 |
0. |
0. |
0. |
time (sec) |
N/A |
0.097 |
0.044 |
0.038 |
1.695 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 129 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 22 | 38 | 59 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.69 |
1.19 |
1.84 |
0. |
0. |
0. |
time (sec) |
N/A |
0.051 |
0.02 |
0.036 |
1.687 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 130 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 23 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.083 |
0.007 |
0.049 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 131 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 33 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.79 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.09 |
0.053 |
0.039 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 44 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.66 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.106 |
0.07 |
0.043 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 133 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F(-2) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 185 | 185 | 70 | 0 | 243 | 0 | 0 | 240 |
normalized size |
1 |
1. |
0.38 |
0. |
1.31 |
0. |
0. |
1.3 |
time (sec) |
N/A |
0.195 |
0.279 |
0.023 |
1.67 |
0. |
0. |
1.188 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 134 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F(-2) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 54 | 0 | 184 | 0 | 0 | 176 |
normalized size |
1 |
1. |
0.37 |
0. |
1.27 |
0. |
0. |
1.21 |
time (sec) |
N/A |
0.149 |
0.215 |
0.024 |
1.683 |
0. |
0. |
1.202 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 135 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F(-2) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 56 | 0 | 124 | 0 | 0 | 111 |
normalized size |
1 |
1. |
0.63 |
0. |
1.39 |
0. |
0. |
1.25 |
time (sec) |
N/A |
0.075 |
0.084 |
0.023 |
1.743 |
0. |
0. |
1.211 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 36 | 0 | 0 | 0 | 0 | 54 |
normalized size |
1 |
1. |
0.65 |
0. |
0. |
0. |
0. |
0.98 |
time (sec) |
N/A |
0.128 |
0.02 |
0.023 |
0. |
0. |
0. |
1.179 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 137 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 53 | 0 | 0 | 0 | 0 | 115 |
normalized size |
1 |
1. |
0.67 |
0. |
0. |
0. |
0. |
1.46 |
time (sec) |
N/A |
0.131 |
0.084 |
0.023 |
0. |
0. |
0. |
1.268 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 138 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 69 | 0 | 0 | 0 | 0 | 180 |
normalized size |
1 |
1. |
0.63 |
0. |
0. |
0. |
0. |
1.65 |
time (sec) |
N/A |
0.173 |
0.065 |
0.023 |
0. |
0. |
0. |
1.309 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 139 |
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 | 383 | 383 | 213 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.56 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.208 |
1.724 |
0.041 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 140 |
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 | 269 | 269 | 163 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.61 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.163 |
1.707 |
0.039 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 141 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 117 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.75 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.082 |
0.665 |
180. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 142 |
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 |
0.068 |
2.664 |
0.043 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 143 |
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 |
0.066 |
1.646 |
0.042 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 144 |
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 | 402 | 402 | 716 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.78 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.257 |
2.923 |
0.024 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 145 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 248 | 248 | 214 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.86 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.191 |
0.879 |
0.023 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 146 |
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 | 137 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.98 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.101 |
0.102 |
0.026 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 147 |
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 | 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.077 |
8.373 |
0.026 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 148 |
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 | 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.074 |
10.178 |
0.023 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 149 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
F |
A |
F(-2) |
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 |
0.063 |
2.513 |
180. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 150 |
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 | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.045 |
5.875 |
0.082 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 151 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 402 | 402 | 429 | 0 | 0 | 1665 | 0 | 0 |
normalized size |
1 |
1. |
1.07 |
0. |
0. |
4.14 |
0. |
0. |
time (sec) |
N/A |
0.553 |
2.289 |
0.15 |
0. |
2.403 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 152 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 263 | 263 | 302 | 0 | 0 | 1139 | 0 | 0 |
normalized size |
1 |
1. |
1.15 |
0. |
0. |
4.33 |
0. |
0. |
time (sec) |
N/A |
0.342 |
1.045 |
0.113 |
0. |
2.297 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 153 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 189 | 0 | 0 | 586 | 0 | 0 |
normalized size |
1 |
1. |
1.44 |
0. |
0. |
4.47 |
0. |
0. |
time (sec) |
N/A |
0.147 |
0.312 |
0.069 |
0. |
2.214 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 154 |
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 | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.054 |
4.925 |
0.055 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 155 |
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 | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.052 |
8.884 |
0.082 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 156 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 123 | 482 | 320 | 365 | 264 | 351 |
normalized size | 1 | 1. | 1.38 | 5.42 | 3.6 | 4.1 | 2.97 | 3.94 |
time (sec) |
N/A |
0.132 |
0.461 |
0.014 |
1.203 |
2.121 |
2.231 |
1.281 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 157 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 83 | 240 | 190 | 231 | 151 | 200 |
normalized size | 1 | 1. | 1.24 | 3.58 | 2.84 | 3.45 | 2.25 | 2.99 |
time (sec) |
N/A |
0.09 |
0.317 |
0.01 |
1.192 |
2.011 |
1.157 |
1.237 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 158 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 46 | 91 | 89 | 128 | 68 | 89 |
normalized size | 1 | 1. | 1.02 | 2.02 | 1.98 | 2.84 | 1.51 | 1.98 |
time (sec) |
N/A |
0.046 |
0.096 |
0.012 |
1.142 |
2.006 |
0.715 |
1.171 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 159 |
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 | 64 | 64 | 57 | 94 | 95 | 230 | 0 | 93 |
normalized size | 1 | 1. | 0.89 | 1.47 | 1.48 | 3.59 | 0. | 1.45 |
time (sec) |
N/A |
0.121 |
0.137 |
0.028 |
1.307 |
2.169 |
0. |
1.187 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 160 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 71 | 0 | 117 | 351 | 0 | 227 |
normalized size |
1 |
1. |
0.82 |
0. |
1.34 |
4.03 |
0. |
2.61 |
time (sec) |
N/A |
0.152 |
0.4 |
180. |
1.399 |
2.35 |
0. |
1.202 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 161 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 95 | 296 | 132 | 572 | 0 | 443 |
normalized size |
1 |
1. |
0.77 |
2.41 |
1.07 |
4.65 |
0. |
3.6 |
time (sec) |
N/A |
0.197 |
0.602 |
0.029 |
1.331 |
2.368 |
0. |
1.149 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 162 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 250 | 250 | 232 | 0 | 706 | 879 | 779 | 814 |
normalized size | 1 | 1. | 0.93 | 0. | 2.82 | 3.52 | 3.12 | 3.26 |
time (sec) |
N/A |
0.285 |
1.394 |
180. |
1.252 |
2.114 |
5.54 |
1.224 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 163 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 182 | 182 | 252 | 535 | 437 | 541 | 456 | 471 |
normalized size | 1 | 1. | 1.38 | 2.94 | 2.4 | 2.97 | 2.51 | 2.59 |
time (sec) |
N/A |
0.194 |
0.95 |
0.015 |
1.221 |
2.035 |
2.352 |
1.194 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 164 |
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 | 116 | 116 | 96 | 208 | 223 | 294 | 219 | 221 |
normalized size | 1 | 1. | 0.83 | 1.79 | 1.92 | 2.53 | 1.89 | 1.91 |
time (sec) |
N/A |
0.101 |
0.846 |
0.013 |
1.179 |
2.043 |
0.929 |
1.202 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 165 |
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 | 156 | 156 | 133 | 202 | 200 | 483 | 0 | 200 |
normalized size | 1 | 1. | 0.85 | 1.29 | 1.28 | 3.1 | 0. | 1.28 |
time (sec) |
N/A |
0.31 |
0.282 |
0.102 |
1.447 |
2.133 |
0. |
1.254 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 166 |
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 | 183 | 183 | 233 | 319 | 244 | 778 | 0 | 485 |
normalized size | 1 | 1. | 1.27 | 1.74 | 1.33 | 4.25 | 0. | 2.65 |
time (sec) |
N/A |
0.345 |
0.76 |
0.12 |
1.386 |
2.156 |
0. |
1.924 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 167 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 242 | 242 | 394 | 626 | 271 | 1234 | 0 | 948 |
normalized size | 1 | 1. | 1.63 | 2.59 | 1.12 | 5.1 | 0. | 3.92 |
time (sec) |
N/A |
0.428 |
1.234 |
0.133 |
1.49 |
2.242 |
0. |
1.265 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
Problem 168 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 436 | 436 | 384 | 0 | 0 | 2418 | 0 | 0 |
normalized size |
1 |
1. |
0.88 |
0. |
0. |
5.55 |
0. |
0. |
time (sec) |
N/A |
0.821 |
1.469 |
0.226 |
0. |
2.311 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 169 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 320 | 320 | 247 | 0 | 0 | 1736 | 0 | 0 |
normalized size |
1 |
1. |
0.77 |
0. |
0. |
5.42 |
0. |
0. |
time (sec) |
N/A |
0.67 |
0.963 |
0.151 |
0. |
2.261 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 170 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 203 | 203 | 152 | 437 | 0 | 1127 | 0 | 0 |
normalized size |
1 |
1. |
0.75 |
2.15 |
0. |
5.55 |
0. |
0. |
time (sec) |
N/A |
0.376 |
0.887 |
0.063 |
0. |
2.129 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
Problem 171 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.061 |
0.893 |
0.05 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 172 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.059 |
0.961 |
0.05 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 173 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F(-2) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 823 | 823 | 11178 | 0 | 0 | 14923 | 0 | 0 |
normalized size |
1 |
1. |
13.58 |
0. |
0. |
18.13 |
0. |
0. |
time (sec) |
N/A |
1.353 |
26.463 |
0.289 |
0. |
3.715 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 174 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F(-2) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 593 | 593 | 6018 | 0 | 0 | 8911 | 0 | 0 |
normalized size |
1 |
1. |
10.15 |
0. |
0. |
15.03 |
0. |
0. |
time (sec) |
N/A |
1.025 |
22.266 |
0.243 |
0. |
3.01 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 175 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 274 | 274 | 509 | 585 | 0 | 4074 | 0 | 0 |
normalized size |
1 |
1. |
1.86 |
2.14 |
0. |
14.87 |
0. |
0. |
time (sec) |
N/A |
0.457 |
4.978 |
0.096 |
0. |
2.323 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 176 |
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 | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.056 |
49.026 |
0.292 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 177 |
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 | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.054 |
51.967 |
0.461 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 178 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.05 |
4.125 |
0.063 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 179 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 543 | 543 | 447 | 0 | 0 | 1886 | 0 | 0 |
normalized size |
1 |
1. |
0.82 |
0. |
0. |
3.47 |
0. |
0. |
time (sec) |
N/A |
0.743 |
1.68 |
0.138 |
0. |
2.454 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 180 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 282 | 282 | 254 | 0 | 0 | 1191 | 0 | 0 |
normalized size |
1 |
1. |
0.9 |
0. |
0. |
4.22 |
0. |
0. |
time (sec) |
N/A |
0.363 |
0.721 |
0.112 |
0. |
2.302 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 181 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 119 | 0 | 0 | 586 | 0 | 0 |
normalized size |
1 |
1. |
0.91 |
0. |
0. |
4.47 |
0. |
0. |
time (sec) |
N/A |
0.145 |
0.172 |
0.068 |
0. |
2.159 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 182 |
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 | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.056 |
1.122 |
0.049 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 183 |
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 | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.055 |
5.085 |
0.076 |
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 [144] had the largest ratio of [ 0.6429
]
|
|
|
|
|
|
|
| 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 |
5 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
2 |
A |
4 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
3 |
A |
3 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
4 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
5 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
6 |
A |
4 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
7 |
A |
5 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
8 |
A |
6 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
9 |
A |
4 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
10 |
A |
4 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
11 |
A |
2 |
1 |
1. |
14 |
0.071 |
|
|
|
|
|
|
|
12 |
A |
5 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
13 |
A |
5 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
14 |
A |
7 |
6 |
1. |
16 |
0.375 |
|
|
|
|
|
|
|
15 |
A |
7 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
16 |
A |
12 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
17 |
A |
8 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
18 |
A |
6 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
19 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
20 |
A |
8 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
|
21 |
A |
8 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
22 |
A |
12 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
23 |
A |
8 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
24 |
A |
8 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
25 |
A |
3 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
26 |
A |
9 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
27 |
A |
7 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
28 |
A |
5 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
29 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
30 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
31 |
A |
6 |
6 |
1. |
16 |
0.375 |
|
|
|
|
|
|
|
32 |
A |
5 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
33 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
34 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
35 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
36 |
A |
15 |
8 |
1. |
16 |
0.5 |
|
|
|
|
|
|
|
37 |
A |
9 |
6 |
1. |
16 |
0.375 |
|
|
|
|
|
|
|
38 |
A |
6 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
39 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
40 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
41 |
A |
8 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
42 |
A |
7 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
43 |
A |
6 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
44 |
A |
5 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
45 |
A |
6 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
46 |
A |
7 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
47 |
A |
8 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
48 |
A |
10 |
8 |
1. |
18 |
0.444 |
|
|
|
|
|
|
|
49 |
A |
9 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
50 |
A |
8 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
51 |
A |
7 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
52 |
A |
7 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
53 |
A |
9 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
54 |
A |
9 |
8 |
1. |
18 |
0.444 |
|
|
|
|
|
|
|
55 |
A |
11 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
56 |
A |
23 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
57 |
A |
20 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
58 |
A |
14 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
59 |
A |
12 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
60 |
A |
12 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
|
61 |
A |
18 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
62 |
A |
19 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
63 |
A |
7 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
64 |
A |
6 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
65 |
A |
5 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
66 |
A |
6 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
67 |
A |
7 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
68 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
69 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
70 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
71 |
A |
2 |
1 |
1. |
17 |
0.059 |
|
|
|
|
|
|
|
72 |
A |
2 |
1 |
1. |
20 |
0.05 |
|
|
|
|
|
|
|
73 |
A |
3 |
1 |
1. |
20 |
0.05 |
|
|
|
|
|
|
|
74 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
75 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
76 |
A |
8 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
77 |
A |
5 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
78 |
A |
3 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
79 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
80 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
81 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
82 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
83 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
84 |
A |
3 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
85 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
86 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
87 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
88 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
89 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
90 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
91 |
A |
5 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
92 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
93 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
94 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
95 |
A |
4 |
2 |
1. |
20 |
0.1 |
|
|
|
|
|
|
|
96 |
A |
4 |
2 |
1. |
20 |
0.1 |
|
|
|
|
|
|
|
97 |
A |
5 |
2 |
1. |
20 |
0.1 |
|
|
|
|
|
|
|
98 |
A |
7 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
99 |
A |
6 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
100 |
A |
5 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
|
101 |
A |
4 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
102 |
A |
5 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
103 |
A |
6 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
104 |
A |
7 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
105 |
A |
10 |
6 |
1. |
20 |
0.3 |
|
|
|
|
|
|
|
106 |
A |
9 |
7 |
1. |
20 |
0.35 |
|
|
|
|
|
|
|
107 |
A |
6 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
108 |
A |
9 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
109 |
A |
9 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
110 |
A |
15 |
6 |
1. |
20 |
0.3 |
|
|
|
|
|
|
|
111 |
A |
7 |
7 |
1. |
20 |
0.35 |
|
|
|
|
|
|
|
112 |
A |
6 |
6 |
1. |
20 |
0.3 |
|
|
|
|
|
|
|
113 |
A |
3 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
114 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
115 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
116 |
A |
10 |
9 |
1. |
20 |
0.45 |
|
|
|
|
|
|
|
117 |
A |
9 |
9 |
1. |
20 |
0.45 |
|
|
|
|
|
|
|
118 |
A |
4 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
119 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
120 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
121 |
A |
5 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
122 |
A |
4 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
123 |
A |
3 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
124 |
A |
4 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
125 |
A |
5 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
126 |
A |
6 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
127 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
128 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
129 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
130 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
131 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
132 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
133 |
A |
9 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
134 |
A |
7 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
135 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
136 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
137 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
138 |
A |
7 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
139 |
A |
10 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
140 |
A |
8 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
|
141 |
A |
6 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
142 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
143 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
144 |
A |
16 |
9 |
1. |
14 |
0.643 |
|
|
|
|
|
|
|
145 |
A |
10 |
7 |
1. |
14 |
0.5 |
|
|
|
|
|
|
|
146 |
A |
7 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
147 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
148 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
149 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
150 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
151 |
A |
12 |
4 |
1. |
20 |
0.2 |
|
|
|
|
|
|
|
152 |
A |
9 |
4 |
1. |
20 |
0.2 |
|
|
|
|
|
|
|
153 |
A |
5 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
154 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
155 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
156 |
A |
6 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
157 |
A |
5 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
158 |
A |
4 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
159 |
A |
5 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
160 |
A |
6 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
|
161 |
A |
7 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
162 |
A |
10 |
6 |
1. |
20 |
0.3 |
|
|
|
|
|
|
|
163 |
A |
9 |
7 |
1. |
20 |
0.35 |
|
|
|
|
|
|
|
164 |
A |
6 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
165 |
A |
10 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
166 |
A |
11 |
7 |
1. |
20 |
0.35 |
|
|
|
|
|
|
|
167 |
A |
14 |
8 |
1. |
20 |
0.4 |
|
|
|
|
|
|
|
168 |
A |
12 |
7 |
1. |
20 |
0.35 |
|
|
|
|
|
|
|
169 |
A |
10 |
6 |
1. |
20 |
0.3 |
|
|
|
|
|
|
|
170 |
A |
8 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
171 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
172 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
173 |
A |
22 |
9 |
1. |
20 |
0.45 |
|
|
|
|
|
|
|
174 |
A |
18 |
10 |
1. |
20 |
0.5 |
|
|
|
|
|
|
|
175 |
A |
11 |
8 |
1. |
18 |
0.444 |
|
|
|
|
|
|
|
176 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
177 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
178 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
179 |
A |
18 |
4 |
1. |
20 |
0.2 |
|
|
|
|
|
|
|
180 |
A |
10 |
4 |
1. |
20 |
0.2 |
|
|
|
|
|
|
|
|
181 |
A |
5 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
182 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
183 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|