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, 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
}
B grade: { }
C grade: { }
F grade: { 74, 75}
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32,
33, 34, 35, 36, 37, 38, 39, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 59, 60, 61, 62, 63, 64, 65, 66, 70, 71,
72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 93, 94, 95, 96, 97, 98, 99, 100,
101, 102, 103, 104, 105 }
B grade: { 16, 17, 24, 40, 41, 42, 51, 56, 57, 58, 67, 68, 69, 92, 106, 107, 108 }
C grade: { }
F grade: { }
2.1.3 Maple
A grade: { 29, 54, 55, 60, 61, 62, 63, 65, 66, 70, 71, 72, 73, 89, 93, 96, 102, 106 }
B grade: { 88, 99, 104, 107 }
C grade: { 64, 74, 75 }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30,
31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 67, 68,
69, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 94, 95, 97, 98, 100, 101, 103, 105, 108
}
2.1.4 Maxima
A grade: { 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38,
40, 41, 47, 48, 53, 54, 55, 59, 60, 61, 62, 63, 65, 66, 70, 71, 72, 73, 74, 75, 93, 94, 96, 97, 99,
100
B grade: { 7, 15, 24, 25, 34, 42, 44, 45, 46, 49, 50, 88, 89 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 20, 39, 43, 51, 52, 56, 57, 58, 64, 67, 68, 69, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85,
86, 87, 90, 91, 92, 95, 98, 101, 102, 103, 104, 105, 106, 107, 108 }
2.1.5 FriCAS
A grade: { 10, 12, 28, 29, 43, 46, 47, 48, 49, 50, 54, 55, 60, 61, 62, 63, 65, 66, 70, 71, 72, 73, 74, 75, 89, 93,
96, 99 }
B grade: { 7, 8, 9, 13, 14, 15, 25, 26, 27, 44, 45 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 11, 16, 17, 18, 19, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41,
42, 51, 52, 53, 56, 57, 58, 59, 64, 67, 68, 69, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 94,
95, 97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108 }
2.1.6 Sympy
A grade: { 44, 45, 46, 47, 62, 63, 65, 66, 74, 75, 89, 93, 96, 99 }
B grade: { 50 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 64, 67,
68, 69, 70, 71, 72, 73, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 94, 95, 97, 98, 100, 101,
102, 103, 104, 105, 106, 107, 108 }
2.1.7 Giac
A grade: { 12, 13, 31, 47, 48, 54, 55, 60, 61, 62, 63, 65, 66, 70, 71, 72, 73, 89, 93, 96, 99 }
B grade: { 7, 8, 9, 10, 14, 15, 25, 26, 27, 28, 29, 32, 33, 34, 46, 49, 50 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 11, 16, 17, 18, 19, 20, 21, 22, 23, 24, 30, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45,
51, 52, 53, 56, 57, 58, 59, 64, 67, 68, 69, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92,
94, 95, 97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108 }
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 |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 404 | 385 | 336 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.95 |
0.83 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.493 |
0.413 |
0.154 |
0. |
0. |
0. |
0. |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 263 | 242 | 217 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.92 |
0.83 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.337 |
0.23 |
0.086 |
0. |
0. |
0. |
0. |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 135 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.94 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.225 |
0.096 |
0.089 |
0. |
0. |
0. |
0. |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 217 | 217 | 185 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.85 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.332 |
0.148 |
0.199 |
0. |
0. |
0. |
0. |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 322 | 352 | 295 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.09 |
0.92 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.494 |
0.594 |
0.084 |
0. |
0. |
0. |
0. |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 531 | 562 | 470 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.06 |
0.89 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.797 |
1.653 |
0.084 |
0. |
0. |
0. |
0. |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
B |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 201 | 201 | 185 | 0 | 533 | 1315 | 0 | 1002 |
normalized size |
1 |
1. |
0.92 |
0. |
2.65 |
6.54 |
0. |
4.99 |
time (sec) |
N/A |
0.095 |
0.308 |
0.734 |
1.307 |
0.864 |
0. |
1.26 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
A |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 172 | 172 | 154 | 0 | 385 | 980 | 0 | 774 |
normalized size |
1 |
1. |
0.9 |
0. |
2.24 |
5.7 |
0. |
4.5 |
time (sec) |
N/A |
0.072 |
0.211 |
0.422 |
1.336 |
0.957 |
0. |
1.406 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
A |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 127 | 0 | 262 | 693 | 0 | 566 |
normalized size |
1 |
1. |
0.89 |
0. |
1.83 |
4.85 |
0. |
3.96 |
time (sec) |
N/A |
0.061 |
0.135 |
0.386 |
1.288 |
0.88 |
0. |
1.308 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 105 | 0 | 159 | 435 | 0 | 381 |
normalized size |
1 |
1. |
0.91 |
0. |
1.37 |
3.75 |
0. |
3.28 |
time (sec) |
N/A |
0.043 |
0.193 |
0.174 |
1.354 |
0.82 |
0. |
1.35 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 93 | 0 | 221 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.87 |
0. |
2.07 |
0. |
0. |
0. |
time (sec) |
N/A |
0.083 |
0.109 |
0.436 |
3.137 |
0. |
0. |
0. |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 89 | 0 | 134 | 267 | 0 | 151 |
normalized size |
1 |
1. |
0.94 |
0. |
1.41 |
2.81 |
0. |
1.59 |
time (sec) |
N/A |
0.037 |
0.058 |
0.421 |
1.265 |
0.902 |
0. |
1.197 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 116 | 0 | 223 | 689 | 0 | 332 |
normalized size |
1 |
1. |
0.86 |
0. |
1.65 |
5.1 |
0. |
2.46 |
time (sec) |
N/A |
0.056 |
0.273 |
0.424 |
1.238 |
0.871 |
0. |
1.192 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
A |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 164 | 164 | 141 | 0 | 390 | 1177 | 0 | 633 |
normalized size |
1 |
1. |
0.86 |
0. |
2.38 |
7.18 |
0. |
3.86 |
time (sec) |
N/A |
0.069 |
0.392 |
0.425 |
1.278 |
0.854 |
0. |
1.211 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
B |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 193 | 193 | 164 | 0 | 620 | 1758 | 0 | 1010 |
normalized size |
1 |
1. |
0.85 |
0. |
3.21 |
9.11 |
0. |
5.23 |
time (sec) |
N/A |
0.085 |
0.407 |
0.424 |
1.279 |
0.849 |
0. |
1.35 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 920 | 920 | 2508 | 0 | 1918 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.73 |
0. |
2.08 |
0. |
0. |
0. |
time (sec) |
N/A |
0.845 |
2.686 |
0.414 |
1.579 |
0. |
0. |
0. |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 805 | 805 | 1853 | 0 | 1446 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.3 |
0. |
1.8 |
0. |
0. |
0. |
time (sec) |
N/A |
0.665 |
1.859 |
0.402 |
1.471 |
0. |
0. |
0. |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 686 | 686 | 1211 | 0 | 1038 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.77 |
0. |
1.51 |
0. |
0. |
0. |
time (sec) |
N/A |
0.533 |
1.127 |
0.404 |
1.428 |
0. |
0. |
0. |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 540 | 540 | 781 | 0 | 680 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.45 |
0. |
1.26 |
0. |
0. |
0. |
time (sec) |
N/A |
0.391 |
0.57 |
0.166 |
1.504 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 431 | 431 | 460 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.07 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.492 |
0.171 |
0.416 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 465 | 465 | 411 | 0 | 529 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.88 |
0. |
1.14 |
0. |
0. |
0. |
time (sec) |
N/A |
0.387 |
0.836 |
0.41 |
1.342 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 632 | 632 | 872 | 0 | 1019 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.38 |
0. |
1.61 |
0. |
0. |
0. |
time (sec) |
N/A |
0.49 |
1.605 |
0.412 |
1.481 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 764 | 764 | 1407 | 0 | 1690 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.84 |
0. |
2.21 |
0. |
0. |
0. |
time (sec) |
N/A |
0.606 |
2.731 |
0.414 |
1.761 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 884 | 884 | 14573 | 0 | 2452 | 0 | 0 | 0 |
normalized size |
1 |
1. |
16.49 |
0. |
2.77 |
0. |
0. |
0. |
time (sec) |
N/A |
0.738 |
7.025 |
0.418 |
2.175 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 334 | 334 | 275 | 0 | 842 | 1932 | 0 | 1715 |
normalized size |
1 |
1. |
0.82 |
0. |
2.52 |
5.78 |
0. |
5.13 |
time (sec) |
N/A |
0.186 |
0.352 |
0.393 |
1.203 |
1.542 |
0. |
1.522 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 276 | 276 | 231 | 0 | 582 | 1377 | 0 | 1254 |
normalized size |
1 |
1. |
0.84 |
0. |
2.11 |
4.99 |
0. |
4.54 |
time (sec) |
N/A |
0.127 |
0.31 |
0.397 |
1.216 |
1.249 |
0. |
1.328 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 218 | 218 | 209 | 0 | 363 | 917 | 0 | 837 |
normalized size |
1 |
1. |
0.96 |
0. |
1.67 |
4.21 |
0. |
3.84 |
time (sec) |
N/A |
0.099 |
0.254 |
0.431 |
1.258 |
1.161 |
0. |
1.305 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 120 | 0 | 193 | 524 | 0 | 479 |
normalized size |
1 |
1. |
0.75 |
0. |
1.21 |
3.28 |
0. |
2.99 |
time (sec) |
N/A |
0.069 |
0.196 |
0.174 |
1.202 |
1.208 |
0. |
1.31 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 61 | 61 | 57 | 61 | 101 | 182 | 0 | 242 |
normalized size |
1 |
1. |
0.93 |
1. |
1.66 |
2.98 |
0. |
3.97 |
time (sec) |
N/A |
0.015 |
0.063 |
0.071 |
1.157 |
1.089 |
0. |
1.238 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 163 | 0 | 251 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.1 |
0. |
1.7 |
0. |
0. |
0. |
time (sec) |
N/A |
0.12 |
0.083 |
0.622 |
1.22 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F(-1) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 93 | 0 | 166 | 0 | 0 | 257 |
normalized size |
1 |
1. |
0.73 |
0. |
1.3 |
0. |
0. |
2.01 |
time (sec) |
N/A |
0.052 |
0.233 |
0.493 |
1.253 |
0. |
0. |
1.469 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F(-1) |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 202 | 202 | 206 | 0 | 313 | 0 | 0 | 1413 |
normalized size |
1 |
1. |
1.02 |
0. |
1.55 |
0. |
0. |
7. |
time (sec) |
N/A |
0.112 |
0.55 |
0.496 |
1.259 |
0. |
0. |
1.579 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F(-1) |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 260 | 260 | 254 | 0 | 616 | 0 | 0 | 2383 |
normalized size |
1 |
1. |
0.98 |
0. |
2.37 |
0. |
0. |
9.17 |
time (sec) |
N/A |
0.152 |
0.96 |
0.519 |
1.298 |
0. |
0. |
1.864 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F(-1) |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 318 | 318 | 480 | 0 | 1048 | 0 | 0 | 6884 |
normalized size |
1 |
1. |
1.51 |
0. |
3.3 |
0. |
0. |
21.65 |
time (sec) |
N/A |
0.195 |
1.822 |
0.509 |
1.412 |
0. |
0. |
2.777 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2240 | 2220 | 1386 | 0 | 2429 | 0 | 0 | 0 |
normalized size |
1 |
0.99 |
0.62 |
0. |
1.08 |
0. |
0. |
0. |
time (sec) |
N/A |
2.436 |
3.013 |
0.392 |
1.452 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1645 | 1657 | 899 | 0 | 1516 | 0 | 0 | 0 |
normalized size |
1 |
1.01 |
0.55 |
0. |
0.92 |
0. |
0. |
0. |
time (sec) |
N/A |
1.758 |
1.89 |
0.385 |
1.379 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1063 | 1097 | 480 | 0 | 841 | 0 | 0 | 0 |
normalized size |
1 |
1.03 |
0.45 |
0. |
0.79 |
0. |
0. |
0. |
time (sec) |
N/A |
1.163 |
1.127 |
0.176 |
1.376 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 269 | 269 | 437 | 0 | 402 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.62 |
0. |
1.49 |
0. |
0. |
0. |
time (sec) |
N/A |
0.153 |
0.216 |
0.131 |
1.366 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1471 | 2096 | 1370 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.42 |
0.93 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.931 |
0.281 |
0.578 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 832 | 878 | 2930 | 0 | 1006 | 0 | 0 | 0 |
normalized size |
1 |
1.06 |
3.52 |
0. |
1.21 |
0. |
0. |
0. |
time (sec) |
N/A |
0.932 |
2.671 |
0.498 |
1.577 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
A |
F |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1304 | 1362 | 15976 | 0 | 2507 | 0 | 0 | 0 |
normalized size |
1 |
1.04 |
12.25 |
0. |
1.92 |
0. |
0. |
0. |
time (sec) |
N/A |
1.408 |
6.322 |
0.5 |
2.45 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1957 | 2013 | 47110 | 0 | 6388 | 0 | 0 | 0 |
normalized size |
1 |
1.03 |
24.07 |
0. |
3.26 |
0. |
0. |
0. |
time (sec) |
N/A |
2.102 |
6.541 |
0.52 |
5.212 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 42 | 0 | 0 | 138 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0. |
0. |
3.29 |
0. |
0. |
time (sec) |
N/A |
0.08 |
0.029 |
0.485 |
0. |
2.193 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
B |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 37 | 0 | 710 | 248 | 65 | 0 |
normalized size | 1 | 1. | 1. | 0. | 19.19 | 6.7 | 1.76 | 0. |
time (sec) |
N/A |
0.061 |
0.009 |
0.411 |
1.352 |
2.012 |
47.02 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
B |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 37 | 0 | 362 | 184 | 65 | 0 |
normalized size | 1 | 1. | 1. | 0. | 9.78 | 4.97 | 1.76 | 0. |
time (sec) |
N/A |
0.063 |
0.01 |
0.342 |
1.277 |
2.129 |
23.341 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
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 | 37 | 37 | 37 | 0 | 142 | 119 | 61 | 116 |
normalized size | 1 | 1. | 1. | 0. | 3.84 | 3.22 | 1.65 | 3.14 |
time (sec) |
N/A |
0.038 |
0.006 |
0.364 |
1.207 |
1.995 |
30.809 |
1.263 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 34 | 0 | 49 | 72 | 53 | 42 |
normalized size | 1 | 1. | 1. | 0. | 1.44 | 2.12 | 1.56 | 1.24 |
time (sec) |
N/A |
0.068 |
0.036 |
0.351 |
1.482 |
2.005 |
164.757 |
1.161 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
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 | 34 | 34 | 34 | 0 | 46 | 72 | 0 | 46 |
normalized size |
1 |
1. |
1. |
0. |
1.35 |
2.12 |
0. |
1.35 |
time (sec) |
N/A |
0.065 |
0.01 |
0.356 |
1.583 |
1.991 |
0. |
1.259 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 37 | 0 | 108 | 142 | 0 | 115 |
normalized size |
1 |
1. |
1. |
0. |
2.92 |
3.84 |
0. |
3.11 |
time (sec) |
N/A |
0.065 |
0.011 |
0.349 |
1.609 |
1.847 |
0. |
1.304 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 30 | 0 | 112 | 59 | 65 | 78 |
normalized size | 1 | 1. | 1. | 0. | 3.73 | 1.97 | 2.17 | 2.6 |
time (sec) |
N/A |
0.023 |
0.009 |
0.389 |
1.924 |
1.947 |
13.519 |
1.298 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 410 | 410 | 22595 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
55.11 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.471 |
7.545 |
0.982 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 306 | 306 | 436 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.42 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.288 |
2.552 |
0.75 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 172 | 172 | 166 | 0 | 275 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.97 |
0. |
1.6 |
0. |
0. |
0. |
time (sec) |
N/A |
0.136 |
0.089 |
0.491 |
1.262 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
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 | 50 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.053 |
0.362 |
0.723 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
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 | 50 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.053 |
2.743 |
0.739 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 328 | 328 | 1241 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
3.78 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.252 |
1.827 |
2.213 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 262 | 262 | 839 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
3.2 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.91 |
0.913 |
1.8 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 451 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.32 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.603 |
0.448 |
1.784 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 78 | 0 | 170 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.96 |
0. |
2.1 |
0. |
0. |
0. |
time (sec) |
N/A |
0.066 |
0.063 |
0.123 |
1.208 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
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 | 41 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.545 |
0.445 |
1.772 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
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 | 41 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.425 |
2.462 |
1.78 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
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 | 30 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.021 |
5.094 |
0.385 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
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 | 30 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.021 |
5.084 |
0.209 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 66 | 450 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
5.49 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.177 |
5.027 |
0.121 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.022 |
5.098 |
0.089 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.022 |
33.103 |
0.327 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 620 | 649 | 18164 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.05 |
29.3 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.133 |
21.544 |
7.167 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 496 | 517 | 9211 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.04 |
18.57 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.819 |
10.071 |
5.039 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 371 | 384 | 1408 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.04 |
3.8 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.558 |
6.028 |
4.115 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
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 | 106 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.5 |
1.908 |
38.288 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
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 | 92 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.128 |
1.287 |
48.165 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
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 | 112 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.519 |
0.632 |
1.07 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
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 | 112 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.484 |
0.575 |
1.008 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
C |
A |
A |
A |
F |
verified |
N/A |
N/A |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 0 | 44 | 662 | 80 | 104 | 44 | 0 |
normalized size | 1 | 0. | 0.98 | 14.71 | 1.78 | 2.31 | 0.98 | 0. |
time (sec) |
N/A |
0.516 |
0.312 |
1.322 |
1.497 |
2.068 |
3.06 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
C |
A |
A |
A |
F |
verified |
N/A |
N/A |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 0 | 45 | 503 | 78 | 103 | 44 | 0 |
normalized size | 1 | 0. | 1. | 11.18 | 1.73 | 2.29 | 0.98 | 0. |
time (sec) |
N/A |
0.512 |
0.085 |
1.214 |
1.68 |
1.992 |
3.329 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 560 | 560 | 461 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.82 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.735 |
0.387 |
0.493 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 550 | 550 | 467 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.85 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.565 |
0.24 |
0.418 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 403 | 403 | 413 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.02 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.352 |
0.121 |
0.44 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 291 | 468 | 421 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.61 |
1.45 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.317 |
0.102 |
0.474 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 518 | 518 | 487 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.94 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.602 |
0.187 |
0.457 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 596 | 596 | 479 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.583 |
0.309 |
0.455 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1046 | 1046 | 1240 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.19 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.717 |
1.377 |
1.511 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 831 | 831 | 1105 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.33 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.068 |
5.472 |
1.393 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 685 | 685 | 539 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.79 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.636 |
0.685 |
1.349 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 401 | 545 | 515 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.36 |
1.28 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.518 |
0.308 |
1.362 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 800 | 800 | 625 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.78 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.98 |
0.94 |
1.414 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 995 | 995 | 721 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.72 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.291 |
0.825 |
1.398 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 84 | 97 | 128 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.83 | 2.11 | 2.78 | 0. | 0. | 0. |
time (sec) |
N/A |
0.159 |
0.017 |
0.098 |
1.129 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
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 | 20 | 20 | 20 | 29 | 190 | 38 | 14 | 24 |
normalized size | 1 | 1. | 1. | 1.45 | 9.5 | 1.9 | 0.7 | 1.2 |
time (sec) |
N/A |
0.058 |
0.096 |
0.059 |
1.195 |
1.982 |
0.391 |
1.154 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
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 | 82 | 82 | 76 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.93 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.168 |
0.014 |
0.531 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 110 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.73 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.248 |
0.038 |
1.102 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 559 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
3.49 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.25 |
0.456 |
5.443 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
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 | 25 | 25 | 28 | 44 | 34 | 63 | 20 | 35 |
normalized size | 1 | 1. | 1.12 | 1.76 | 1.36 | 2.52 | 0.8 | 1.4 |
time (sec) |
N/A |
0.012 |
0.005 |
0.188 |
1.177 |
1.937 |
0.342 |
1.257 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 63 | 0 | 153 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.94 | 0. | 2.28 | 0. | 0. | 0. |
time (sec) |
N/A |
0.074 |
0.014 |
0.655 |
1.179 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
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 | 97 | 97 | 91 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.94 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.11 |
0.025 |
0.549 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
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 | 28 | 28 | 28 | 40 | 38 | 93 | 26 | 39 |
normalized size | 1 | 1. | 1. | 1.43 | 1.36 | 3.32 | 0.93 | 1.39 |
time (sec) |
N/A |
0.007 |
0.003 |
0.125 |
1.192 |
1.877 |
0.312 |
1.147 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 106 | 0 | 159 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.58 | 0. | 2.37 | 0. | 0. | 0. |
time (sec) |
N/A |
0.157 |
0.016 |
0.526 |
1.224 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
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 | 102 | 102 | 98 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.96 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.132 |
0.025 |
0.504 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
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 | 28 | 28 | 28 | 79 | 38 | 88 | 26 | 39 |
normalized size | 1 | 1. | 1. | 2.82 | 1.36 | 3.14 | 0.93 | 1.39 |
time (sec) |
N/A |
0.007 |
0.003 |
0.224 |
1.241 |
1.962 |
0.364 |
1.263 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 106 | 0 | 159 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.58 | 0. | 2.37 | 0. | 0. | 0. |
time (sec) |
N/A |
0.155 |
0.014 |
0.94 |
1.145 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
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 | 98 | 102 | 98 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1.04 | 1. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.127 |
0.025 |
0.786 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 30 | 36 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.86 |
1.03 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.064 |
0.012 |
0.062 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 68 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.134 |
0.024 |
1.318 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 149 | 135 | 879 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.06 |
0.96 |
6.28 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.18 |
0.042 |
0.065 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 96 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.88 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.164 |
0.027 |
2.268 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 204 | 206 | 1636 | 357 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.01 |
8.02 |
1.75 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.254 |
0.469 |
0.063 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 322 | 334 | 1080 | 4733 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.04 |
3.35 |
14.7 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.507 |
0.234 |
0.072 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 433 | 445 | 908 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.03 |
2.1 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.594 |
0.799 |
2.336 |
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 [42] had the largest ratio of [ 0.5484
]
|
|
|
|
|
|
|
| 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 |
20 |
10 |
0.95 |
32 |
0.312 |
|
|
|
|
|
|
|
2 |
A |
16 |
10 |
0.92 |
32 |
0.312 |
|
|
|
|
|
|
|
3 |
A |
12 |
7 |
1. |
30 |
0.233 |
|
|
|
|
|
|
|
4 |
A |
14 |
8 |
1. |
32 |
0.25 |
|
|
|
|
|
|
|
5 |
A |
18 |
11 |
1.09 |
32 |
0.344 |
|
|
|
|
|
|
|
6 |
A |
22 |
11 |
1.06 |
32 |
0.344 |
|
|
|
|
|
|
|
7 |
A |
4 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
8 |
A |
4 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
9 |
A |
4 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
10 |
A |
4 |
2 |
1. |
27 |
0.074 |
|
|
|
|
|
|
|
11 |
A |
6 |
6 |
1. |
29 |
0.207 |
|
|
|
|
|
|
|
12 |
A |
5 |
4 |
1. |
29 |
0.138 |
|
|
|
|
|
|
|
13 |
A |
4 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
14 |
A |
4 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
15 |
A |
4 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
16 |
A |
32 |
14 |
1. |
31 |
0.452 |
|
|
|
|
|
|
|
17 |
A |
28 |
14 |
1. |
31 |
0.452 |
|
|
|
|
|
|
|
18 |
A |
24 |
14 |
1. |
31 |
0.452 |
|
|
|
|
|
|
|
19 |
A |
20 |
13 |
1. |
29 |
0.448 |
|
|
|
|
|
|
|
20 |
A |
19 |
15 |
1. |
31 |
0.484 |
|
|
|
|
|
|
|
|
21 |
A |
20 |
12 |
1. |
31 |
0.387 |
|
|
|
|
|
|
|
22 |
A |
24 |
13 |
1. |
31 |
0.419 |
|
|
|
|
|
|
|
23 |
A |
28 |
13 |
1. |
31 |
0.419 |
|
|
|
|
|
|
|
24 |
A |
32 |
13 |
1. |
31 |
0.419 |
|
|
|
|
|
|
|
25 |
A |
5 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
26 |
A |
5 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
27 |
A |
5 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
28 |
A |
5 |
2 |
1. |
27 |
0.074 |
|
|
|
|
|
|
|
29 |
A |
3 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
30 |
A |
7 |
4 |
1. |
29 |
0.138 |
|
|
|
|
|
|
|
31 |
A |
7 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
32 |
A |
5 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
33 |
A |
5 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
34 |
A |
5 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
35 |
A |
49 |
14 |
0.99 |
31 |
0.452 |
|
|
|
|
|
|
|
36 |
A |
47 |
15 |
1.01 |
31 |
0.484 |
|
|
|
|
|
|
|
37 |
A |
39 |
15 |
1.03 |
29 |
0.517 |
|
|
|
|
|
|
|
38 |
A |
10 |
9 |
1. |
23 |
0.391 |
|
|
|
|
|
|
|
39 |
A |
29 |
14 |
1.42 |
31 |
0.452 |
|
|
|
|
|
|
|
40 |
A |
35 |
12 |
1.06 |
31 |
0.387 |
|
|
|
|
|
|
|
|
41 |
A |
47 |
16 |
1.04 |
31 |
0.516 |
|
|
|
|
|
|
|
42 |
A |
61 |
17 |
1.03 |
31 |
0.548 |
|
|
|
|
|
|
|
43 |
A |
3 |
3 |
1. |
40 |
0.075 |
|
|
|
|
|
|
|
44 |
A |
3 |
3 |
1. |
40 |
0.075 |
|
|
|
|
|
|
|
45 |
A |
3 |
3 |
1. |
40 |
0.075 |
|
|
|
|
|
|
|
46 |
A |
2 |
2 |
1. |
38 |
0.053 |
|
|
|
|
|
|
|
47 |
A |
3 |
3 |
1. |
40 |
0.075 |
|
|
|
|
|
|
|
48 |
A |
3 |
3 |
1. |
40 |
0.075 |
|
|
|
|
|
|
|
49 |
A |
3 |
3 |
1. |
40 |
0.075 |
|
|
|
|
|
|
|
50 |
A |
1 |
1 |
1. |
34 |
0.029 |
|
|
|
|
|
|
|
51 |
A |
11 |
6 |
1. |
48 |
0.125 |
|
|
|
|
|
|
|
52 |
A |
9 |
5 |
1. |
46 |
0.109 |
|
|
|
|
|
|
|
53 |
A |
7 |
4 |
1. |
32 |
0.125 |
|
|
|
|
|
|
|
54 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
55 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
56 |
A |
13 |
6 |
1. |
39 |
0.154 |
|
|
|
|
|
|
|
57 |
A |
11 |
6 |
1. |
39 |
0.154 |
|
|
|
|
|
|
|
58 |
A |
9 |
5 |
1. |
37 |
0.135 |
|
|
|
|
|
|
|
59 |
A |
5 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
60 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
61 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
62 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
63 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
64 |
A |
5 |
5 |
1. |
26 |
0.192 |
|
|
|
|
|
|
|
65 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
66 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
67 |
A |
12 |
7 |
1.05 |
45 |
0.156 |
|
|
|
|
|
|
|
68 |
A |
10 |
7 |
1.04 |
45 |
0.156 |
|
|
|
|
|
|
|
69 |
A |
8 |
6 |
1.04 |
43 |
0.14 |
|
|
|
|
|
|
|
70 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
71 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
72 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
73 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
74 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
75 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
76 |
A |
30 |
9 |
1. |
32 |
0.281 |
|
|
|
|
|
|
|
77 |
A |
27 |
10 |
1. |
32 |
0.312 |
|
|
|
|
|
|
|
78 |
A |
18 |
6 |
1. |
30 |
0.2 |
|
|
|
|
|
|
|
79 |
A |
18 |
6 |
1.61 |
29 |
0.207 |
|
|
|
|
|
|
|
80 |
A |
29 |
11 |
1. |
32 |
0.344 |
|
|
|
|
|
|
|
|
81 |
A |
31 |
12 |
1. |
32 |
0.375 |
|
|
|
|
|
|
|
82 |
A |
37 |
14 |
1. |
34 |
0.412 |
|
|
|
|
|
|
|
83 |
A |
30 |
12 |
1. |
34 |
0.353 |
|
|
|
|
|
|
|
84 |
A |
21 |
9 |
1. |
32 |
0.281 |
|
|
|
|
|
|
|
85 |
A |
19 |
7 |
1.36 |
31 |
0.226 |
|
|
|
|
|
|
|
86 |
A |
31 |
12 |
1. |
34 |
0.353 |
|
|
|
|
|
|
|
87 |
A |
40 |
16 |
1. |
34 |
0.471 |
|
|
|
|
|
|
|
88 |
A |
5 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
89 |
A |
1 |
1 |
1. |
24 |
0.042 |
|
|
|
|
|
|
|
90 |
A |
3 |
3 |
1. |
34 |
0.088 |
|
|
|
|
|
|
|
91 |
A |
3 |
3 |
1. |
55 |
0.055 |
|
|
|
|
|
|
|
92 |
A |
3 |
3 |
1. |
58 |
0.052 |
|
|
|
|
|
|
|
93 |
A |
4 |
4 |
1. |
11 |
0.364 |
|
|
|
|
|
|
|
94 |
A |
5 |
5 |
1. |
13 |
0.385 |
|
|
|
|
|
|
|
95 |
A |
7 |
7 |
1. |
13 |
0.538 |
|
|
|
|
|
|
|
96 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
97 |
A |
6 |
6 |
1. |
15 |
0.4 |
|
|
|
|
|
|
|
98 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
99 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
100 |
A |
6 |
6 |
1. |
15 |
0.4 |
|
|
|
|
|
|
|
|
101 |
A |
4 |
4 |
1.04 |
15 |
0.267 |
|
|
|
|
|
|
|
102 |
A |
1 |
1 |
1. |
38 |
0.026 |
|
|
|
|
|
|
|
103 |
A |
2 |
2 |
1. |
50 |
0.04 |
|
|
|
|
|
|
|
104 |
A |
3 |
3 |
1.06 |
42 |
0.071 |
|
|
|
|
|
|
|
105 |
A |
2 |
2 |
1. |
62 |
0.032 |
|
|
|
|
|
|
|
106 |
A |
3 |
3 |
1.01 |
49 |
0.061 |
|
|
|
|
|
|
|
107 |
A |
7 |
5 |
1.04 |
42 |
0.119 |
|
|
|
|
|
|
|
108 |
A |
8 |
6 |
1.03 |
65 |
0.092 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|