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, 3, 4, 5, 6, 7, 8, 9, 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, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 62, 63, 64, 65, 66, 67, 68, 69,
70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 96, 97, 99, 105, 106,
107 }
B grade: { 10 }
C grade: { 2, 46, 52, 82, 83, 98, 100, 101, 102, 113, 114, 116 }
F grade: { 43, 44, 45, 58, 59, 60, 61, 95, 103, 104, 108, 109, 110, 111, 112, 115}
2.1.2 Mathematica
A grade: { 1, 3, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33,
34, 35, 36, 41, 42, 57, 62, 85, 94, 96, 97, 99, 103, 104, 105, 107 }
B grade: { }
C grade: { 2, 4, 24, 39, 40, 43, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72,
73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 91, 98, 101, 106, 113, 114, 115, 116
}
F grade: { 12, 13, 37, 38, 44, 45, 46, 58, 59, 60, 61, 92, 93, 95, 100, 102, 108, 109, 110, 111,
112}
2.1.3 Maple
A grade: { 1, 7, 8, 16, 21, 22, 23, 32, 47, 48, 49, 62, 63, 64, 103, 104, 105 }
B grade: { 3, 4, 5, 6, 9, 10, 11, 17, 24, 31, 50, 51, 65, 68 }
C grade: { 2, 15, 28, 33, 34, 35, 36, 52, 56, 57, 66, 67, 73, 74, 75, 76, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90,
91, 106, 107 }
F grade: { 12, 13, 14, 18, 19, 20, 25, 26, 27, 29, 30, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 53, 54, 55, 58, 59,
60, 61, 69, 70, 71, 72, 77, 78, 79, 80, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 108, 109, 110, 111, 112,
113, 114, 115, 116 }
2.1.4 Maxima
A grade: { 1, 6, 16, 21, 22, 23, 29, 32, 33, 34, 35, 36, 56, 57, 62, 99, 107
B grade: { 2, 106 }
C grade: { }
F grade: { 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 24, 25, 26, 27, 28, 30, 31, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 58, 59, 60, 61, 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, 100, 101, 102, 103, 104, 105, 108, 109, 110, 111, 112, 113, 114, 115, 116
}
2.1.5 FriCAS
A grade: { 1, 2, 3, 5, 6, 8, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 30, 31, 32, 33, 34, 36, 40, 52,
56, 57, 62, 63, 64, 65, 66, 67, 81, 83, 99, 106, 107, 113, 116 }
B grade: { 4, 7, 9, 10, 12, 13, 14, 24, 35, 37, 39, 41, 42, 43, 47, 48, 50, 51, 55, 59, 68, 73, 74, 75, 76, 77, 78,
79, 80, 85, 86, 87, 88, 89, 90, 91, 93, 96, 97, 98, 100, 101, 102, 110 }
C grade: { 82 }
F grade: { 29, 38, 44, 45, 46, 49, 53, 54, 58, 60, 61, 69, 70, 71, 72, 84, 92, 94, 95, 103, 104, 105, 108, 109,
111, 112, 114, 115 }
2.1.6 Sympy
A grade: { 1, 2, 14, 15, 20, 21, 22, 23, 25, 26, 62, 63, 64 }
B grade: { 8, 16, 17, 19, 30, 31 }
C grade: { 27, 28, 33, 34, 35, 36, 56, 57, 106, 107 }
F grade: { 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 18, 24, 29, 32, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50,
51, 52, 53, 54, 55, 58, 59, 60, 61, 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, 108, 109, 110, 111,
112, 113, 114, 115, 116 }
2.1.7 Giac
A grade: { 1, 8, 16, 21, 22, 23, 33, 34, 36, 57, 62, 107 }
B grade: { 2, 3, 4, 7 }
C grade: { 24 }
F grade: { 5, 6, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 25, 26, 27, 28, 29, 30, 31, 32, 35, 37, 38, 39, 40, 41,
42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 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, 108, 109, 110, 111, 112, 113, 114, 115, 116
}
2.2 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2)
if the failure was due to an exception being raised, which could indicate a bug in the system. If
the failure was due to integral not being evaluated within the time limit, then it is given just an
F.
In this table,the column normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 14 | 18 | 28 | 12 | 18 |
normalized size | 1 | 1. | 1. | 0.93 | 1.2 | 1.87 | 0.8 | 1.2 |
time (sec) |
N/A |
0.001 |
0.004 |
0.002 |
0.925 |
2.09 |
0.055 |
1.072 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
C |
C |
C |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 52 | 37 | 34 | 55 | 4 | 42 | 55 |
normalized size | 1 | 3.47 | 2.47 | 2.27 | 3.67 | 0.27 | 2.8 | 3.67 |
time (sec) |
N/A |
0.056 |
0.026 |
0.003 |
0.948 |
2.141 |
57.851 |
1.071 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 69 | 370 | 0 | 251 | 0 | 239 |
normalized size | 1 | 1. | 0.84 | 4.51 | 0. | 3.06 | 0. | 2.91 |
time (sec) |
N/A |
0.076 |
0.108 |
0.041 |
0. |
2.081 |
0. |
1.111 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
B |
F |
B |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 167 | 172 | 0 | 205 | 0 | 127 |
normalized size | 1 | 1. | 3.88 | 4. | 0. | 4.77 | 0. | 2.95 |
time (sec) |
N/A |
0.012 |
3.397 |
0.047 |
0. |
2.048 |
0. |
1.087 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 126 | 115 | 0 | 309 | 0 | 0 |
normalized size |
1 |
1. |
1.7 |
1.55 |
0. |
4.18 |
0. |
0. |
time (sec) |
N/A |
0.056 |
0.132 |
0.014 |
0. |
2.128 |
0. |
0. |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 59 | 125 | 72 | 267 | 0 | 0 |
normalized size | 1 | 1. | 0.92 | 1.95 | 1.12 | 4.17 | 0. | 0. |
time (sec) |
N/A |
0.026 |
0.059 |
0.025 |
1.429 |
2.192 |
0. |
0. |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
B |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 75 | 45 | 0 | 215 | 0 | 136 |
normalized size |
1 |
1. |
1.56 |
0.94 |
0. |
4.48 |
0. |
2.83 |
time (sec) |
N/A |
0.013 |
0.107 |
0.017 |
0. |
2.017 |
0. |
1.088 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 30 | 21 | 0 | 55 | 53 | 27 |
normalized size | 1 | 1. | 1. | 0.7 | 0. | 1.83 | 1.77 | 0.9 |
time (sec) |
N/A |
0.082 |
0.041 |
0.003 |
0. |
2.008 |
0.818 |
1.071 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F |
B |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 365 | 340 | 902 | 0 | 1287 | 0 | 0 |
normalized size | 1 | 1.66 | 1.55 | 4.1 | 0. | 5.85 | 0. | 0. |
time (sec) |
N/A |
0.506 |
0.688 |
0.123 |
0. |
2.291 |
0. |
0. |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
B |
A |
B |
F |
B |
F(-1) |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 541 | 311 | 1542 | 0 | 1287 | 0 | 0 |
normalized size |
1 |
2.46 |
1.41 |
7.01 |
0. |
5.85 |
0. |
0. |
time (sec) |
N/A |
0.751 |
0.649 |
0.021 |
0. |
2.36 |
0. |
0. |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
A |
F(-2) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 125 | 278 | 0 | 678 | 0 | 0 |
normalized size |
1 |
1. |
0.91 |
2.01 |
0. |
4.91 |
0. |
0. |
time (sec) |
N/A |
0.075 |
0.199 |
0.02 |
0. |
2.281 |
0. |
0. |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
F |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 0 | 0 | 0 | 1068 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 8.54 | 0. | 0. |
time (sec) |
N/A |
0.185 |
0.239 |
0.026 |
0. |
19.344 |
0. |
0. |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
F |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 0 | 0 | 0 | 998 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 12.32 | 0. | 0. |
time (sec) |
N/A |
0.162 |
0.176 |
0.022 |
0. |
38.964 |
0. |
0. |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
B |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 31 | 0 | 0 | 162 | 15 | 0 |
normalized size | 1 | 1. | 1. | 0. | 0. | 5.23 | 0.48 | 0. |
time (sec) |
N/A |
0.054 |
0.008 |
0.014 |
0. |
4.026 |
1.281 |
0. |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
C |
F |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 33 | 22 | 0 | 85 | 15 | 0 |
normalized size | 1 | 1. | 1. | 0.67 | 0. | 2.58 | 0.45 | 0. |
time (sec) |
N/A |
0.063 |
0.011 |
0.033 |
0. |
4.074 |
0.706 |
0. |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 16 | 20 | 78 | 56 | 20 |
normalized size | 1 | 1. | 1. | 0.84 | 1.05 | 4.11 | 2.95 | 1.05 |
time (sec) |
N/A |
0.27 |
0.017 |
0.002 |
0.934 |
1.972 |
6.489 |
1.097 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 52 | 52 | 43 | 120 | 0 | 74 | 2149 | 0 |
normalized size | 1 | 1. | 0.83 | 2.31 | 0. | 1.42 | 41.33 | 0. |
time (sec) |
N/A |
0.023 |
0.039 |
0.026 |
0. |
2.204 |
2.733 |
0. |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 50 | 0 | 0 | 76 | 0 | 0 |
normalized size | 1 | 1. | 0.89 | 0. | 0. | 1.36 | 0. | 0. |
time (sec) |
N/A |
0.022 |
0.063 |
0.023 |
0. |
2.155 |
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 |
F |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 0 | 0 | 34 | 313 | 0 |
normalized size | 1 | 1. | 1. | 0. | 0. | 2. | 18.41 | 0. |
time (sec) |
N/A |
0.054 |
0.007 |
0.019 |
0. |
1.992 |
3.679 |
0. |
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 0 | 0 | 35 | 36 | 0 |
normalized size | 1 | 1. | 1. | 0. | 0. | 1.75 | 1.8 | 0. |
time (sec) |
N/A |
0.06 |
0.006 |
0.028 |
0. |
1.985 |
2.868 |
0. |
|
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Problem 21 |
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 | 42 | 42 | 36 | 48 | 54 | 124 | 36 | 55 |
normalized size | 1 | 1. | 0.86 | 1.14 | 1.29 | 2.95 | 0.86 | 1.31 |
time (sec) |
N/A |
0.033 |
0.042 |
0.01 |
0.947 |
2.076 |
0.132 |
1.08 |
|
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Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 22 | 21 | 27 | 43 | 20 | 26 |
normalized size | 1 | 1. | 1. | 0.95 | 1.23 | 1.95 | 0.91 | 1.18 |
time (sec) |
N/A |
0.024 |
0.02 |
0.002 |
0.935 |
1.956 |
0.103 |
1.075 |
|
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Problem 23 |
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 | 62 | 62 | 49 | 51 | 69 | 135 | 51 | 100 |
normalized size | 1 | 1. | 0.79 | 0.82 | 1.11 | 2.18 | 0.82 | 1.61 |
time (sec) |
N/A |
0.091 |
0.065 |
0.012 |
0.955 |
2.189 |
0.158 |
1.079 |
|
|
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Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 961 | 454 | 0 | 1095 | 0 | 424 |
normalized size | 1 | 1. | 11.17 | 5.28 | 0. | 12.73 | 0. | 4.93 |
time (sec) |
N/A |
0.084 |
2.38 |
0.034 |
0. |
2.264 |
0. |
1.137 |
|
|
|
|
|
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Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 0 | 0 | 39 | 15 | 0 |
normalized size | 1 | 1. | 1. | 0. | 0. | 2.05 | 0.79 | 0. |
time (sec) |
N/A |
0.065 |
0.01 |
0.027 |
0. |
2.025 |
0.206 |
0. |
|
|
|
|
|
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Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 26 | 0 | 0 | 47 | 27 | 0 |
normalized size | 1 | 1. | 1. | 0. | 0. | 1.81 | 1.04 | 0. |
time (sec) |
N/A |
0.097 |
0.017 |
0.015 |
0. |
1.975 |
0.879 |
0. |
|
|
|
|
|
|
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|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 56 | 0 | 0 | 487 | 46 | 0 |
normalized size | 1 | 1. | 0.89 | 0. | 0. | 7.73 | 0.73 | 0. |
time (sec) |
N/A |
0.219 |
0.192 |
0.019 |
0. |
2.422 |
1.593 |
0. |
|
|
|
|
|
|
|
|
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|
|
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|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 127 | 25 | 0 | 552 | 51 | 0 |
normalized size | 1 | 1. | 1.55 | 0.3 | 0. | 6.73 | 0.62 | 0. |
time (sec) |
N/A |
0.072 |
0.057 |
0.008 |
0. |
2.562 |
1.438 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
|
|
Problem 29 |
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 | 606 | 679 | 412 | 0 | 699 | 0 | 0 | 0 |
normalized size |
1 |
1.12 |
0.68 |
0. |
1.15 |
0. |
0. |
0. |
time (sec) |
N/A |
4.799 |
0.244 |
0.072 |
1.019 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
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|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 0 | 0 | 34 | 313 | 0 |
normalized size | 1 | 1. | 1. | 0. | 0. | 2. | 18.41 | 0. |
time (sec) |
N/A |
0.055 |
0.009 |
0.026 |
0. |
2.1 |
2.814 |
0. |
|
|
|
|
|
|
|
|
|
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|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 52 | 52 | 46 | 120 | 0 | 74 | 2149 | 0 |
normalized size | 1 | 1. | 0.88 | 2.31 | 0. | 1.42 | 41.33 | 0. |
time (sec) |
N/A |
0.024 |
0.06 |
0.022 |
0. |
2.249 |
2.653 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 33 | 44 | 65 | 109 | 0 | 0 |
normalized size |
1 |
1. |
0.97 |
1.29 |
1.91 |
3.21 |
0. |
0. |
time (sec) |
N/A |
0.044 |
0.118 |
0.039 |
1.138 |
2.183 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 57 | 65 | 84 | 198 | 36 | 86 |
normalized size | 1 | 1. | 0.98 | 1.12 | 1.45 | 3.41 | 0.62 | 1.48 |
time (sec) |
N/A |
0.036 |
0.015 |
0.036 |
1.417 |
1.964 |
0.928 |
1.074 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 81 | 48 | 84 | 200 | 37 | 86 |
normalized size | 1 | 1. | 1.4 | 0.83 | 1.45 | 3.45 | 0.64 | 1.48 |
time (sec) |
N/A |
0.035 |
0.012 |
0.041 |
1.419 |
2.159 |
0.95 |
1.066 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
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 | 49 | 49 | 86 | 12 | 105 | 225 | 29 | 0 |
normalized size | 1 | 1. | 1.76 | 0.24 | 2.14 | 4.59 | 0.59 | 0. |
time (sec) |
N/A |
0.005 |
0.04 |
0.023 |
1.44 |
2.032 |
0.894 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 55 | 65 | 84 | 198 | 32 | 85 |
normalized size | 1 | 1. | 1. | 1.18 | 1.53 | 3.6 | 0.58 | 1.55 |
time (sec) |
N/A |
0.033 |
0.012 |
0.037 |
1.434 |
2.026 |
0.915 |
1.085 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 0 | 0 | 0 | 788 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 8.12 | 0. | 0. |
time (sec) |
N/A |
0.044 |
0.076 |
0.033 |
0. |
37.366 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.107 |
0.078 |
0.033 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 176 | 59 | 0 | 0 | 828 | 0 | 0 |
normalized size | 1 | 1.6 | 0.54 | 0. | 0. | 7.53 | 0. | 0. |
time (sec) |
N/A |
0.025 |
0.025 |
0.074 |
0. |
18.574 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 131 | 85 | 0 | 0 | 410 | 0 | 0 |
normalized size | 1 | 1.62 | 1.05 | 0. | 0. | 5.06 | 0. | 0. |
time (sec) |
N/A |
0.073 |
0.014 |
0.011 |
0. |
4.684 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 117 | 127 | 0 | 0 | 1153 | 0 | 0 |
normalized size | 1 | 1.77 | 1.92 | 0. | 0. | 17.47 | 0. | 0. |
time (sec) |
N/A |
0.056 |
0.082 |
0.042 |
0. |
13.516 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
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 | 79 | 145 | 140 | 0 | 0 | 1866 | 0 | 0 |
normalized size |
1 |
1.84 |
1.77 |
0. |
0. |
23.62 |
0. |
0. |
time (sec) |
N/A |
0.098 |
0.167 |
0.012 |
0. |
12.361 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
C |
F |
F |
B |
F(-1) |
F |
verified |
N/A |
N/A |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 118 | 0 | 55 | 0 | 0 | 3509 | 0 | 0 |
normalized size |
1 |
0. |
0.47 |
0. |
0. |
29.74 |
0. |
0. |
time (sec) |
N/A |
21.937 |
0.193 |
0.014 |
0. |
167.475 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.611 |
1.635 |
0.038 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 176 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.462 |
0.669 |
0.039 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
F |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 493 | 576 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.17 |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.846 |
0.382 |
0.177 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 407 | 407 | 198 | 584 | 0 | 5156 | 0 | 0 |
normalized size |
1 |
1. |
0.49 |
1.43 |
0. |
12.67 |
0. |
0. |
time (sec) |
N/A |
0.676 |
2.075 |
0.089 |
0. |
3.179 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 648 | 648 | 610 | 719 | 0 | 11992 | 0 | 0 |
normalized size |
1 |
1. |
0.94 |
1.11 |
0. |
18.51 |
0. |
0. |
time (sec) |
N/A |
1.158 |
6.087 |
0.053 |
0. |
3.69 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1058 | 1058 | 1100 | 989 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.04 |
0.93 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.49 |
6.17 |
0.08 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 378 | 378 | 342 | 21028 | 0 | 11537 | 0 | 0 |
normalized size |
1 |
1. |
0.9 |
55.63 |
0. |
30.52 |
0. |
0. |
time (sec) |
N/A |
0.774 |
6.027 |
0.533 |
0. |
4.008 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 638 | 638 | 1431 | 86793 | 0 | 30714 | 0 | 0 |
normalized size |
1 |
1. |
2.24 |
136.04 |
0. |
48.14 |
0. |
0. |
time (sec) |
N/A |
1.397 |
11.52 |
3.525 |
0. |
6.015 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
C |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 204 | 213 | 1275 | 0 | 1272 | 0 | 0 |
normalized size |
1 |
3.09 |
3.23 |
19.32 |
0. |
19.27 |
0. |
0. |
time (sec) |
N/A |
1.234 |
1.148 |
0.094 |
0. |
3.062 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 198 | 198 | 145 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.73 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.097 |
0.234 |
0.033 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 198 | 198 | 153 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.77 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.091 |
0.245 |
0.046 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 111 | 0 | 0 | 495 | 0 | 0 |
normalized size | 1 | 1. | 1.14 | 0. | 0. | 5.1 | 0. | 0. |
time (sec) |
N/A |
0.013 |
0.06 |
0.166 |
0. |
20.738 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
A |
A |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 107 | 20 | 69 | 142 | 262 | 32 | 0 |
normalized size | 1 | 1.47 | 0.27 | 0.95 | 1.95 | 3.59 | 0.44 | 0. |
time (sec) |
N/A |
0.044 |
0.003 |
0.046 |
1.428 |
2.053 |
1.106 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 90 | 49 | 96 | 225 | 37 | 97 |
normalized size | 1 | 1. | 1.34 | 0.73 | 1.43 | 3.36 | 0.55 | 1.45 |
time (sec) |
N/A |
0.037 |
0.024 |
0.033 |
1.465 |
1.953 |
0.945 |
1.146 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 482 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.052 |
0.355 |
0.048 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
B |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 280 | 0 | 0 | 0 | 0 | 10386 | 0 | 0 |
normalized size | 1 | 0. | 0. | 0. | 0. | 37.09 | 0. | 0. |
time (sec) |
N/A |
0.235 |
0.107 |
0.086 |
0. |
51.38 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 232 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.05 |
0.343 |
0.048 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 168 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.204 |
0.138 |
0.115 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
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 | 25 | 24 | 31 | 63 | 22 | 31 |
normalized size | 1 | 1. | 1. | 0.96 | 1.24 | 2.52 | 0.88 | 1.24 |
time (sec) |
N/A |
0.023 |
0.008 |
0.001 |
0.937 |
2.302 |
0.097 |
1.078 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 86 | 52 | 0 | 158 | 73 | 0 |
normalized size | 1 | 1. | 1.46 | 0.88 | 0. | 2.68 | 1.24 | 0. |
time (sec) |
N/A |
0.032 |
0.018 |
0.024 |
0. |
1.979 |
0.16 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 99 | 75 | 0 | 213 | 100 | 0 |
normalized size | 1 | 1. | 1.27 | 0.96 | 0. | 2.73 | 1.28 | 0. |
time (sec) |
N/A |
0.077 |
0.02 |
0.018 |
0. |
1.942 |
0.167 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 110 | 100 | 0 | 138 | 0 | 0 |
normalized size | 1 | 1. | 2.24 | 2.04 | 0. | 2.82 | 0. | 0. |
time (sec) |
N/A |
0.007 |
0.097 |
0.013 |
0. |
2.516 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 108 | 365 | 0 | 173 | 0 | 0 |
normalized size | 1 | 1. | 2.04 | 6.89 | 0. | 3.26 | 0. | 0. |
time (sec) |
N/A |
0.015 |
0.091 |
0.024 |
0. |
2.422 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 5727 | 1512 | 0 | 957 | 0 | 0 |
normalized size | 1 | 1. | 76.36 | 20.16 | 0. | 12.76 | 0. | 0. |
time (sec) |
N/A |
0.094 |
7.084 |
0.071 |
0. |
2.568 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 322 | 456 | 0 | 6283 | 0 | 0 |
normalized size | 1 | 1. | 1.88 | 2.67 | 0. | 36.74 | 0. | 0. |
time (sec) |
N/A |
0.08 |
0.432 |
0.072 |
0. |
25.347 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 157 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.96 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.04 |
0.261 |
0.058 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 162 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.84 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.048 |
0.251 |
0.029 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 144 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.97 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.045 |
0.203 |
0.048 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 152 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.13 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.036 |
0.175 |
0.026 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 28 | 164 | 0 | 3299 | 0 | 0 |
normalized size | 1 | 1. | 0.22 | 1.29 | 0. | 25.98 | 0. | 0. |
time (sec) |
N/A |
0.019 |
0.022 |
0.099 |
0. |
5.567 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 54 | 240 | 0 | 4625 | 0 | 0 |
normalized size | 1 | 1. | 0.34 | 1.53 | 0. | 29.46 | 0. | 0. |
time (sec) |
N/A |
0.033 |
0.029 |
0.106 |
0. |
5.796 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 48 | 286 | 0 | 1447 | 0 | 0 |
normalized size | 1 | 1. | 0.65 | 3.86 | 0. | 19.55 | 0. | 0. |
time (sec) |
N/A |
0.156 |
0.019 |
0.115 |
0. |
3.586 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 32 | 383 | 0 | 1214 | 0 | 0 |
normalized size | 1 | 1. | 0.31 | 3.72 | 0. | 11.79 | 0. | 0. |
time (sec) |
N/A |
0.305 |
0.029 |
0.16 |
0. |
4.282 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 126 | 0 | 0 | 5180 | 0 | 0 |
normalized size | 1 | 1. | 1.56 | 0. | 0. | 63.95 | 0. | 0. |
time (sec) |
N/A |
0.011 |
0.1 |
0.048 |
0. |
19.52 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 126 | 0 | 0 | 921 | 0 | 0 |
normalized size | 1 | 1. | 1.56 | 0. | 0. | 11.37 | 0. | 0. |
time (sec) |
N/A |
0.011 |
0.095 |
0.026 |
0. |
15.508 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 118 | 0 | 0 | 5544 | 0 | 0 |
normalized size | 1 | 1. | 1.04 | 0. | 0. | 49.06 | 0. | 0. |
time (sec) |
N/A |
0.014 |
0.072 |
0.033 |
0. |
11.962 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 124 | 0 | 0 | 4852 | 0 | 0 |
normalized size | 1 | 1. | 1.14 | 0. | 0. | 44.51 | 0. | 0. |
time (sec) |
N/A |
0.012 |
0.063 |
0.036 |
0. |
9.774 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 159 | 206 | 0 | 193 | 0 | 0 |
normalized size | 1 | 1. | 1.83 | 2.37 | 0. | 2.22 | 0. | 0. |
time (sec) |
N/A |
0.874 |
0.916 |
0.034 |
0. |
2.36 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
C |
F |
C |
F |
F |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1 | 529 | 127 | 317 | 0 | 150 | 0 | 0 |
normalized size | 1 | 529. | 127. | 317. | 0. | 150. | 0. | 0. |
time (sec) |
N/A |
1.669 |
0.586 |
0.041 |
0. |
2.283 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
C |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 180 | 133 | 536 | 0 | 144 | 0 | 0 |
normalized size | 1 | 3.91 | 2.89 | 11.65 | 0. | 3.13 | 0. | 0. |
time (sec) |
N/A |
1.492 |
1.072 |
0.047 |
0. |
2.315 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 323 | 258 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
10.09 |
8.06 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.096 |
0.449 |
0.059 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 46 | 240 | 0 | 117 | 0 | 0 |
normalized size | 1 | 1. | 2. | 10.43 | 0. | 5.09 | 0. | 0. |
time (sec) |
N/A |
0.054 |
0.007 |
0.021 |
0. |
2.202 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 218 | 218 | 47 | 353 | 0 | 27647 | 0 | 0 |
normalized size | 1 | 1. | 0.22 | 1.62 | 0. | 126.82 | 0. | 0. |
time (sec) |
N/A |
0.041 |
0.056 |
0.195 |
0. |
49.077 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 210 | 210 | 50 | 350 | 0 | 28331 | 0 | 0 |
normalized size | 1 | 1. | 0.24 | 1.67 | 0. | 134.91 | 0. | 0. |
time (sec) |
N/A |
0.032 |
0.07 |
0.173 |
0. |
49.042 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 222 | 222 | 65 | 349 | 0 | 28004 | 0 | 0 |
normalized size | 1 | 1. | 0.29 | 1.57 | 0. | 126.14 | 0. | 0. |
time (sec) |
N/A |
0.03 |
0.066 |
0.173 |
0. |
44.341 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 214 | 68 | 350 | 0 | 28069 | 0 | 0 |
normalized size | 1 | 1. | 0.32 | 1.64 | 0. | 131.16 | 0. | 0. |
time (sec) |
N/A |
0.029 |
0.053 |
0.169 |
0. |
41.119 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 685 | 327 | 0 | 953 | 0 | 0 |
normalized size | 1 | 1. | 10.54 | 5.03 | 0. | 14.66 | 0. | 0. |
time (sec) |
N/A |
0.129 |
3.205 |
0.132 |
0. |
3.467 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 876 | 311 | 0 | 301 | 0 | 0 |
normalized size | 1 | 1. | 13.9 | 4.94 | 0. | 4.78 | 0. | 0. |
time (sec) |
N/A |
0.128 |
7.546 |
0.129 |
0. |
2.834 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.055 |
0.243 |
0.029 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 0 | 0 | 0 | 1422 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 13.17 | 0. | 0. |
time (sec) |
N/A |
0.093 |
0.057 |
0.023 |
0. |
9.281 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 135 | 120 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1.38 |
1.22 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.093 |
0.155 |
0.046 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.3 |
0.288 |
0.088 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
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Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 80 | 0 | 0 | 983 | 0 | 0 |
normalized size |
1 |
1. |
0.83 |
0. |
0. |
10.24 |
0. |
0. |
time (sec) |
N/A |
0.078 |
0.081 |
0.044 |
0. |
2.351 |
0. |
0. |
|
|
|
|
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Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 122 | 112 | 0 | 0 | 660 | 0 | 0 |
normalized size | 1 | 1.39 | 1.27 | 0. | 0. | 7.5 | 0. | 0. |
time (sec) |
N/A |
0.062 |
0.143 |
0.037 |
0. |
26.951 |
0. |
0. |
|
|
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Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
F |
F |
B |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 233 | 26 | 26 | 0 | 0 | 1049 | 0 | 0 |
normalized size | 1 | 0.11 | 0.11 | 0. | 0. | 4.5 | 0. | 0. |
time (sec) |
N/A |
0.011 |
0.027 |
0.036 |
0. |
23.868 |
0. |
0. |
|
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Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 73 | 0 | 116 | 282 | 0 | 0 |
normalized size |
1 |
1. |
0.89 |
0. |
1.41 |
3.44 |
0. |
0. |
time (sec) |
N/A |
0.058 |
0.06 |
0.039 |
1.4 |
2.12 |
0. |
0. |
|
|
|
|
|
|
|
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Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
F |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 409 | 0 | 0 | 0 | 882 | 0 | 0 |
normalized size | 1 | 3.03 | 0. | 0. | 0. | 6.53 | 0. | 0. |
time (sec) |
N/A |
0.337 |
0.19 |
0.079 |
0. |
111.657 |
0. |
0. |
|
|
|
|
|
|
|
|
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|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 409 | 150 | 0 | 0 | 882 | 0 | 0 |
normalized size | 1 | 3.03 | 1.11 | 0. | 0. | 6.53 | 0. | 0. |
time (sec) |
N/A |
0.301 |
0.441 |
0.036 |
0. |
99.462 |
0. |
0. |
|
|
|
|
|
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Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
F |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 399 | 0 | 0 | 0 | 737 | 0 | 0 |
normalized size | 1 | 3.35 | 0. | 0. | 0. | 6.19 | 0. | 0. |
time (sec) |
N/A |
0.299 |
0.163 |
0.069 |
0. |
93.427 |
0. |
0. |
|
|
|
|
|
|
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Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
A |
F |
F |
F |
F |
verified |
N/A |
N/A |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 0 | 43 | 34 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 1. | 0.79 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.425 |
0.151 |
0.036 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
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|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
A |
F |
F |
F |
F |
verified |
N/A |
N/A |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 0 | 43 | 34 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 1. | 0.79 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.22 |
0.075 |
0.027 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
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|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 43 | 34 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.1 | 0.87 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.029 |
0.018 |
0.013 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
B |
A |
C |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 101 | 12 | 142 | 258 | 31 | 0 |
normalized size | 1 | 1. | 1.51 | 0.18 | 2.12 | 3.85 | 0.46 | 0. |
time (sec) |
N/A |
0.01 |
0.103 |
0.025 |
1.397 |
1.599 |
1.16 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 65 | 66 | 99 | 230 | 41 | 100 |
normalized size | 1 | 1. | 0.93 | 0.94 | 1.41 | 3.29 | 0.59 | 1.43 |
time (sec) |
N/A |
0.038 |
0.038 |
0.035 |
1.396 |
1.559 |
1.026 |
1.097 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 384 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.068 |
0.345 |
0.053 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 234 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.415 |
0.452 |
0.091 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
B |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 199 | 0 | 0 | 0 | 0 | 5191 | 0 | 0 |
normalized size | 1 | 0. | 0. | 0. | 0. | 26.09 | 0. | 0. |
time (sec) |
N/A |
0.945 |
0.348 |
0.088 |
0. |
14.505 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.06 |
0.39 |
0.041 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.071 |
0.15 |
0.011 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
F |
F |
A |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 21 | 111 | 0 | 0 | 532 | 0 | 0 |
normalized size | 1 | 0.16 | 0.84 | 0. | 0. | 4.03 | 0. | 0. |
time (sec) |
N/A |
0.008 |
0.094 |
0.038 |
0. |
1.677 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
F |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 250 | 26 | 26 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0.1 | 0.1 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.012 |
0.014 |
0.037 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
C |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 383 | 0 | 138 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 0.36 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.399 |
0.153 |
0.039 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
F |
F |
A |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 272 | 21 | 109 | 0 | 0 | 902 | 0 | 0 |
normalized size | 1 | 0.08 | 0.4 | 0. | 0. | 3.32 | 0. | 0. |
time (sec) |
N/A |
0.008 |
0.088 |
0.038 |
0. |
21.83 |
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 [29] had the largest ratio of [ 2.143
]
|
|
|
|
|
|
|
| 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 |
1 |
1 |
1. |
10 |
0.1 |
|
|
|
|
|
|
|
2 |
C |
5 |
2 |
3.47 |
37 |
0.054 |
|
|
|
|
|
|
|
3 |
A |
9 |
6 |
1. |
15 |
0.4 |
|
|
|
|
|
|
|
4 |
A |
3 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
5 |
A |
8 |
7 |
1. |
17 |
0.412 |
|
|
|
|
|
|
|
6 |
A |
6 |
6 |
1. |
17 |
0.353 |
|
|
|
|
|
|
|
7 |
A |
3 |
3 |
1. |
17 |
0.176 |
|
|
|
|
|
|
|
8 |
A |
4 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
9 |
A |
18 |
12 |
1.66 |
27 |
0.444 |
|
|
|
|
|
|
|
10 |
B |
25 |
13 |
2.46 |
39 |
0.333 |
|
|
|
|
|
|
|
11 |
A |
7 |
3 |
1. |
45 |
0.067 |
|
|
|
|
|
|
|
12 |
A |
7 |
4 |
1. |
32 |
0.125 |
|
|
|
|
|
|
|
13 |
A |
5 |
3 |
1. |
32 |
0.094 |
|
|
|
|
|
|
|
14 |
A |
2 |
2 |
1. |
27 |
0.074 |
|
|
|
|
|
|
|
15 |
A |
2 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
16 |
A |
2 |
1 |
1. |
30 |
0.033 |
|
|
|
|
|
|
|
17 |
A |
3 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
18 |
A |
3 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
19 |
A |
2 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
20 |
A |
2 |
2 |
1. |
25 |
0.08 |
|
|
|
|
|
|
|
|
21 |
A |
3 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
22 |
A |
2 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
23 |
A |
6 |
6 |
1. |
20 |
0.3 |
|
|
|
|
|
|
|
24 |
A |
6 |
5 |
1. |
31 |
0.161 |
|
|
|
|
|
|
|
25 |
A |
2 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
26 |
A |
2 |
2 |
1. |
35 |
0.057 |
|
|
|
|
|
|
|
27 |
A |
5 |
5 |
1. |
32 |
0.156 |
|
|
|
|
|
|
|
28 |
A |
6 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
29 |
A |
359 |
30 |
1.12 |
14 |
2.143 |
|
|
|
|
|
|
|
30 |
A |
2 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
31 |
A |
3 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
32 |
A |
2 |
2 |
1. |
33 |
0.061 |
|
|
|
|
|
|
|
33 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
34 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
35 |
A |
1 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
36 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
37 |
A |
1 |
1 |
1. |
17 |
0.059 |
|
|
|
|
|
|
|
38 |
A |
3 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
39 |
A |
2 |
2 |
1.6 |
16 |
0.125 |
|
|
|
|
|
|
|
40 |
A |
5 |
5 |
1.62 |
17 |
0.294 |
|
|
|
|
|
|
|
|
41 |
A |
5 |
5 |
1.77 |
13 |
0.385 |
|
|
|
|
|
|
|
42 |
A |
5 |
5 |
1.84 |
16 |
0.312 |
|
|
|
|
|
|
|
43 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
44 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
45 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
46 |
C |
7 |
3 |
1.17 |
32 |
0.094 |
|
|
|
|
|
|
|
47 |
A |
19 |
9 |
1. |
20 |
0.45 |
|
|
|
|
|
|
|
48 |
A |
29 |
9 |
1. |
20 |
0.45 |
|
|
|
|
|
|
|
49 |
A |
49 |
9 |
1. |
20 |
0.45 |
|
|
|
|
|
|
|
50 |
A |
14 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
51 |
A |
24 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
52 |
C |
9 |
8 |
3.09 |
48 |
0.167 |
|
|
|
|
|
|
|
53 |
A |
7 |
7 |
1. |
24 |
0.292 |
|
|
|
|
|
|
|
54 |
A |
7 |
7 |
1. |
24 |
0.292 |
|
|
|
|
|
|
|
55 |
A |
1 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
56 |
A |
8 |
8 |
1.47 |
13 |
0.615 |
|
|
|
|
|
|
|
57 |
A |
6 |
6 |
1. |
15 |
0.4 |
|
|
|
|
|
|
|
58 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
59 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
60 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
|
61 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
62 |
A |
1 |
1 |
1. |
38 |
0.026 |
|
|
|
|
|
|
|
63 |
A |
1 |
1 |
1. |
33 |
0.03 |
|
|
|
|
|
|
|
64 |
A |
2 |
2 |
1. |
39 |
0.051 |
|
|
|
|
|
|
|
65 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
66 |
A |
4 |
4 |
1. |
19 |
0.21 |
|
|
|
|
|
|
|
67 |
A |
4 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
68 |
A |
1 |
1 |
1. |
24 |
0.042 |
|
|
|
|
|
|
|
69 |
A |
7 |
7 |
1. |
24 |
0.292 |
|
|
|
|
|
|
|
70 |
A |
7 |
7 |
1. |
24 |
0.292 |
|
|
|
|
|
|
|
71 |
A |
3 |
3 |
1. |
26 |
0.115 |
|
|
|
|
|
|
|
72 |
A |
3 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
73 |
A |
1 |
1 |
1. |
22 |
0.045 |
|
|
|
|
|
|
|
74 |
A |
1 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
75 |
A |
8 |
8 |
1. |
18 |
0.444 |
|
|
|
|
|
|
|
76 |
A |
8 |
7 |
1. |
23 |
0.304 |
|
|
|
|
|
|
|
77 |
A |
1 |
1 |
1. |
21 |
0.048 |
|
|
|
|
|
|
|
78 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
79 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
80 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
|
81 |
A |
4 |
4 |
1. |
34 |
0.118 |
|
|
|
|
|
|
|
82 |
C |
5 |
5 |
529. |
40 |
0.125 |
|
|
|
|
|
|
|
83 |
C |
7 |
7 |
3.91 |
51 |
0.137 |
|
|
|
|
|
|
|
84 |
A |
2 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
85 |
A |
2 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
86 |
A |
1 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
87 |
A |
1 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
88 |
A |
1 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
89 |
A |
1 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
90 |
A |
2 |
2 |
1. |
40 |
0.05 |
|
|
|
|
|
|
|
91 |
A |
2 |
2 |
1. |
40 |
0.05 |
|
|
|
|
|
|
|
92 |
A |
1 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
93 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
94 |
A |
7 |
7 |
1.38 |
21 |
0.333 |
|
|
|
|
|
|
|
95 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
96 |
A |
5 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
97 |
A |
7 |
7 |
1.39 |
19 |
0.368 |
|
|
|
|
|
|
|
98 |
C |
1 |
1 |
0.11 |
20 |
0.05 |
|
|
|
|
|
|
|
99 |
A |
5 |
5 |
1. |
22 |
0.227 |
|
|
|
|
|
|
|
100 |
C |
4 |
2 |
3.03 |
25 |
0.08 |
|
|
|
|
|
|
|
|
101 |
C |
5 |
3 |
3.03 |
24 |
0.125 |
|
|
|
|
|
|
|
102 |
C |
4 |
2 |
3.35 |
23 |
0.087 |
|
|
|
|
|
|
|
103 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
104 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
105 |
A |
3 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
106 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
107 |
A |
6 |
6 |
1. |
15 |
0.4 |
|
|
|
|
|
|
|
108 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
109 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
110 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
111 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
112 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
113 |
C |
1 |
1 |
0.16 |
19 |
0.053 |
|
|
|
|
|
|
|
114 |
C |
1 |
1 |
0.1 |
20 |
0.05 |
|
|
|
|
|
|
|
115 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
116 |
C |
1 |
1 |
0.08 |
19 |
0.053 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|