Chapter 2
detailed summary tables of results
2.1 List of integrals sorted by grade for each CAS
2.1.1 Rubi
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87,
88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 36, 37, 38, 39,
40, 41, 42, 43, 44, 45, 46, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73,
74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101,
102 }
B grade: { }
C grade: { 15, 16, 17, 18, 19, 31, 32, 33, 34, 35, 47, 48, 49, 50, 51, 105 }
F grade: { 103, 104, 106, 107, 108, 109, 110, 111}
2.1.3 Maple
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 16, 17, 20, 26, 27, 28, 31, 32, 33, 34, 42, 43, 44, 47,
48, 49, 50, 51, 61, 62, 63, 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, 105, 108, 109, 110, 111
}
B grade: { 11, 12, 13, 14, 18, 19, 21, 22, 23, 24, 25, 29, 30, 35, 36, 37, 38, 39, 40, 41, 45, 46, 52, 53, 54, 55,
56, 57, 58, 59, 60, 64, 65, 66, 103, 104, 106, 107 }
C grade: { }
F grade: { }
2.1.4 Maxima
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 60, 61, 62, 63, 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, 108, 109, 110,
111
B grade: { }
C grade: { }
F grade: { 20, 21, 22, 23, 24, 25, 36, 37, 38, 39, 40, 41, 52, 53, 54, 55, 56, 57, 58, 59, 64, 65, 66, 103, 104,
105, 106, 107 }
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 31, 32, 33, 34, 35, 47, 48, 49, 60, 61,
62, 63, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 108,
109, 110, 111 }
B grade: { 26, 27, 28, 29, 30, 42, 43, 44, 45, 46, 50, 51, 93, 94, 95, 97, 98, 99, 100, 101 }
C grade: { }
F grade: { 20, 21, 22, 23, 24, 25, 36, 37, 38, 39, 40, 41, 52, 53, 54, 55, 56, 57, 58, 59, 64, 65, 66, 90, 96,
102, 103, 104, 105, 106, 107 }
2.1.6 Sympy
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 60, 61, 62, 63, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 91, 97
}
B grade: { 10, 11, 20, 26, 27, 42, 43, 80, 81, 82, 83, 86, 87, 92, 93, 98, 99 }
C grade: { 15, 16, 31, 32, 47, 48 }
F grade: { 12, 13, 14, 17, 18, 19, 21, 22, 23, 24, 25, 28, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 44, 45, 46,
49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 64, 65, 66, 84, 88, 89, 90, 94, 95, 96, 100, 101, 102, 103, 104, 105,
106, 107, 108, 109, 110, 111 }
2.1.7 Giac
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 60, 61, 62, 63, 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
}
B grade: { 40, 56, 108, 109, 110, 111 }
C grade: { 20, 21, 64 }
F grade: { 22, 23, 24, 25, 36, 37, 38, 39, 41, 52, 53, 54, 55, 57, 58, 59, 65, 66, 103, 104, 105, 106, 107
}
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 | 50 | 50 | 50 | 41 | 54 | 104 | 46 | 58 |
normalized size | 1 | 1. | 1. | 0.82 | 1.08 | 2.08 | 0.92 | 1.16 |
time (sec) |
N/A |
0.041 |
0.002 |
0.007 |
1.33 |
1.462 |
0.064 |
1.079 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 69 | 58 | 77 | 161 | 65 | 86 |
normalized size | 1 | 1. | 1. | 0.84 | 1.12 | 2.33 | 0.94 | 1.25 |
time (sec) |
N/A |
0.045 |
0.021 |
0.001 |
1.311 |
1.472 |
0.07 |
1.083 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 88 | 75 | 100 | 217 | 83 | 115 |
normalized size | 1 | 1. | 1. | 0.85 | 1.14 | 2.47 | 0.94 | 1.31 |
time (sec) |
N/A |
0.073 |
0.019 |
0. |
0.979 |
1.53 |
0.072 |
1.077 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 105 | 90 | 120 | 274 | 102 | 143 |
normalized size | 1 | 1. | 1. | 0.86 | 1.14 | 2.61 | 0.97 | 1.36 |
time (sec) |
N/A |
0.095 |
0.035 |
0. |
0.958 |
1.437 |
0.077 |
1.093 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 122 | 105 | 140 | 333 | 121 | 171 |
normalized size | 1 | 1. | 1. | 0.86 | 1.15 | 2.73 | 0.99 | 1.4 |
time (sec) |
N/A |
0.111 |
0.039 |
0.002 |
0.978 |
1.474 |
0.08 |
1.094 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 112 | 112 | 97 | 95 | 127 | 252 | 116 | 143 |
normalized size | 1 | 1. | 0.87 | 0.85 | 1.13 | 2.25 | 1.04 | 1.28 |
time (sec) |
N/A |
0.126 |
0.051 |
0.001 |
0.952 |
1.48 |
0.083 |
1.094 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 154 | 154 | 139 | 186 | 385 | 165 | 212 |
normalized size | 1 | 1. | 1. | 0.9 | 1.21 | 2.5 | 1.07 | 1.38 |
time (sec) |
N/A |
0.13 |
0.046 |
0.002 |
0.96 |
1.704 |
0.093 |
1.09 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 196 | 196 | 196 | 183 | 246 | 518 | 209 | 281 |
normalized size | 1 | 1. | 1. | 0.93 | 1.26 | 2.64 | 1.07 | 1.43 |
time (sec) |
N/A |
0.168 |
0.059 |
0. |
0.949 |
1.731 |
0.099 |
1.097 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 234 | 234 | 234 | 219 | 294 | 653 | 258 | 350 |
normalized size | 1 | 1. | 1. | 0.94 | 1.26 | 2.79 | 1.1 | 1.5 |
time (sec) |
N/A |
0.238 |
0.088 |
0.002 |
0.937 |
1.732 |
0.104 |
1.086 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 50 | 58 | 58 | 143 | 515 | 69 |
normalized size | 1 | 1. | 1.11 | 1.29 | 1.29 | 3.18 | 11.44 | 1.53 |
time (sec) |
N/A |
0.032 |
0.018 |
0.039 |
0.958 |
1.905 |
2.175 |
1.094 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 58 | 86 | 69 | 170 | 2195 | 80 |
normalized size | 1 | 1. | 1.14 | 1.69 | 1.35 | 3.33 | 43.04 | 1.57 |
time (sec) |
N/A |
0.057 |
0.026 |
0.007 |
0.963 |
2.069 |
33.058 |
1.103 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 68 | 114 | 82 | 197 | 0 | 93 |
normalized size |
1 |
1. |
1.19 |
2. |
1.44 |
3.46 |
0. |
1.63 |
time (sec) |
N/A |
0.072 |
0.032 |
0.01 |
0.966 |
3.661 |
0. |
1.144 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 81 | 145 | 97 | 234 | 0 | 108 |
normalized size |
1 |
1. |
1.27 |
2.27 |
1.52 |
3.66 |
0. |
1.69 |
time (sec) |
N/A |
0.147 |
0.046 |
0.01 |
0.96 |
12.735 |
0. |
1.07 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 76 | 76 | 98 | 179 | 119 | 279 | 0 | 130 |
normalized size |
1 |
1. |
1.29 |
2.36 |
1.57 |
3.67 |
0. |
1.71 |
time (sec) |
N/A |
0.192 |
0.065 |
0.01 |
0.954 |
55.14 |
0. |
1.104 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
A |
A |
C |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 92 | 92 | 98 | 92 | 88 | 212 | 923 | 90 |
normalized size | 1 | 1. | 1.07 | 1. | 0.96 | 2.3 | 10.03 | 0.98 |
time (sec) |
N/A |
0.077 |
0.178 |
0.011 |
1.431 |
1.52 |
1.918 |
1.1 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
A |
A |
C |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 121 | 148 | 101 | 239 | 3589 | 104 |
normalized size | 1 | 1. | 1.16 | 1.42 | 0.97 | 2.3 | 34.51 | 1. |
time (sec) |
N/A |
0.085 |
0.139 |
0.006 |
1.437 |
1.775 |
26.542 |
1.097 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 150 | 204 | 112 | 261 | 0 | 115 |
normalized size |
1 |
1. |
1.18 |
1.61 |
0.88 |
2.06 |
0. |
0.91 |
time (sec) |
N/A |
0.101 |
0.485 |
0.004 |
1.473 |
2.986 |
0. |
1.111 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
B |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 165 | 241 | 124 | 285 | 0 | 127 |
normalized size |
1 |
1. |
1.21 |
1.77 |
0.91 |
2.1 |
0. |
0.93 |
time (sec) |
N/A |
0.14 |
0.601 |
0.004 |
1.49 |
11.104 |
0. |
1.102 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
B |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 187 | 303 | 143 | 323 | 0 | 146 |
normalized size |
1 |
1. |
1.24 |
2.01 |
0.95 |
2.14 |
0. |
0.97 |
time (sec) |
N/A |
0.176 |
0.642 |
0.007 |
1.464 |
39.42 |
0. |
1.104 |
|
|
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|
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F(-1) |
B |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 194 | 231 | 0 | 0 | 471 | 3996 |
normalized size |
1 |
1. |
1.03 |
1.22 |
0. |
0. |
2.49 |
21.14 |
time (sec) |
N/A |
0.211 |
0.273 |
0.089 |
0. |
0. |
93.814 |
1.972 |
|
|
|
|
|
|
|
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|
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|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 211 | 211 | 234 | 616 | 0 | 0 | 0 | 9104 |
normalized size |
1 |
1. |
1.11 |
2.92 |
0. |
0. |
0. |
43.15 |
time (sec) |
N/A |
0.24 |
0.226 |
0.024 |
0. |
0. |
0. |
2.929 |
|
|
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|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 245 | 245 | 280 | 866 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.14 |
3.53 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.159 |
0.31 |
0.019 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
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|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 290 | 290 | 383 | 1132 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.32 |
3.9 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.725 |
0.559 |
0.03 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 321 | 321 | 441 | 1435 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.37 |
4.47 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.534 |
0.798 |
0.029 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 545 | 545 | 816 | 3835 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.5 |
7.04 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
4.213 |
1.614 |
0.046 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 90 | 122 | 112 | 446 | 604 | 126 |
normalized size | 1 | 1. | 0.96 | 1.3 | 1.19 | 4.74 | 6.43 | 1.34 |
time (sec) |
N/A |
0.052 |
0.055 |
0.017 |
0.937 |
2.493 |
2.651 |
1.1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 112 | 182 | 143 | 585 | 2689 | 155 |
normalized size | 1 | 1. | 0.97 | 1.58 | 1.24 | 5.09 | 23.38 | 1.35 |
time (sec) |
N/A |
0.14 |
0.081 |
0.018 |
0.942 |
3.002 |
38.346 |
1.087 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 134 | 242 | 171 | 725 | 0 | 184 |
normalized size |
1 |
1. |
0.97 |
1.75 |
1.24 |
5.25 |
0. |
1.33 |
time (sec) |
N/A |
0.154 |
0.054 |
0.018 |
0.941 |
4.617 |
0. |
1.086 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 159 | 302 | 196 | 865 | 0 | 213 |
normalized size |
1 |
1. |
1.06 |
2.01 |
1.31 |
5.77 |
0. |
1.42 |
time (sec) |
N/A |
0.214 |
0.077 |
0.019 |
0.972 |
13.663 |
0. |
1.113 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 162 | 162 | 185 | 362 | 220 | 1007 | 0 | 242 |
normalized size |
1 |
1. |
1.14 |
2.23 |
1.36 |
6.22 |
0. |
1.49 |
time (sec) |
N/A |
0.232 |
0.094 |
0.019 |
1.001 |
65.679 |
0. |
1.083 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
C |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 146 | 146 | 130 | 416 | 952 | 135 |
normalized size | 1 | 1. | 1.04 | 1.04 | 0.93 | 2.97 | 6.8 | 0.96 |
time (sec) |
N/A |
0.098 |
0.494 |
0.02 |
1.434 |
1.582 |
2.771 |
1.091 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
C |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 186 | 214 | 162 | 547 | 4107 | 173 |
normalized size | 1 | 1. | 1.13 | 1.3 | 0.98 | 3.32 | 24.89 | 1.05 |
time (sec) |
N/A |
0.129 |
0.424 |
0.014 |
1.43 |
1.903 |
33.286 |
1.093 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 179 | 179 | 200 | 260 | 182 | 616 | 0 | 192 |
normalized size |
1 |
1. |
1.12 |
1.45 |
1.02 |
3.44 |
0. |
1.07 |
time (sec) |
N/A |
0.141 |
0.434 |
0.013 |
1.457 |
3.159 |
0. |
1.083 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 187 | 187 | 234 | 328 | 193 | 694 | 0 | 209 |
normalized size |
1 |
1. |
1.25 |
1.75 |
1.03 |
3.71 |
0. |
1.12 |
time (sec) |
N/A |
0.167 |
0.629 |
0.014 |
1.504 |
10.495 |
0. |
1.078 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 243 | 374 | 209 | 757 | 0 | 228 |
normalized size |
1 |
1. |
1.25 |
1.93 |
1.08 |
3.9 |
0. |
1.18 |
time (sec) |
N/A |
0.197 |
0.669 |
0.015 |
1.467 |
48.782 |
0. |
1.091 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
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|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 330 | 330 | 341 | 1237 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.03 |
3.75 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.745 |
0.875 |
0.122 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 368 | 368 | 398 | 1813 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.08 |
4.93 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.87 |
1.352 |
0.118 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 386 | 386 | 421 | 2310 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.09 |
5.98 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.49 |
1.559 |
0.122 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 439 | 439 | 489 | 1801 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.11 |
4.1 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.894 |
2.241 |
0.049 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 468 | 468 | 524 | 1917 | 0 | 0 | 0 | 8384 |
normalized size |
1 |
1. |
1.12 |
4.1 |
0. |
0. |
0. |
17.91 |
time (sec) |
N/A |
1.118 |
2.556 |
0.034 |
0. |
0. |
0. |
22.393 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 770 | 770 | 935 | 4570 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.21 |
5.94 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
7.835 |
6.566 |
0.07 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 128 | 186 | 163 | 869 | 668 | 166 |
normalized size | 1 | 1. | 0.9 | 1.3 | 1.14 | 6.08 | 4.67 | 1.16 |
time (sec) |
N/A |
0.076 |
0.098 |
0.019 |
0.941 |
2.077 |
2.794 |
1.132 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 161 | 278 | 209 | 1134 | 2822 | 212 |
normalized size | 1 | 1. | 0.92 | 1.59 | 1.19 | 6.48 | 16.13 | 1.21 |
time (sec) |
N/A |
0.224 |
0.129 |
0.018 |
0.954 |
2.323 |
43.34 |
1.093 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 204 | 204 | 193 | 370 | 254 | 1407 | 0 | 257 |
normalized size |
1 |
1. |
0.95 |
1.81 |
1.25 |
6.9 |
0. |
1.26 |
time (sec) |
N/A |
0.252 |
0.091 |
0.022 |
0.946 |
4.319 |
0. |
1.124 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 224 | 224 | 231 | 462 | 289 | 1671 | 0 | 302 |
normalized size |
1 |
1. |
1.03 |
2.06 |
1.29 |
7.46 |
0. |
1.35 |
time (sec) |
N/A |
0.307 |
0.125 |
0.02 |
0.95 |
12.975 |
0. |
1.136 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 239 | 239 | 261 | 554 | 321 | 1939 | 0 | 347 |
normalized size |
1 |
1. |
1.09 |
2.32 |
1.34 |
8.11 |
0. |
1.45 |
time (sec) |
N/A |
0.345 |
0.142 |
0.021 |
0.988 |
59.828 |
0. |
1.127 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
C |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 185 | 185 | 186 | 180 | 185 | 726 | 1103 | 177 |
normalized size | 1 | 1. | 1.01 | 0.97 | 1. | 3.92 | 5.96 | 0.96 |
time (sec) |
N/A |
0.117 |
0.754 |
0.017 |
1.454 |
1.673 |
2.631 |
1.099 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
C |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 223 | 223 | 235 | 264 | 234 | 977 | 4498 | 231 |
normalized size | 1 | 1. | 1.05 | 1.18 | 1.05 | 4.38 | 20.17 | 1.04 |
time (sec) |
N/A |
0.215 |
0.59 |
0.018 |
1.431 |
2.213 |
36.753 |
1.114 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 243 | 243 | 259 | 322 | 270 | 1111 | 0 | 267 |
normalized size |
1 |
1. |
1.07 |
1.33 |
1.11 |
4.57 |
0. |
1.1 |
time (sec) |
N/A |
0.227 |
0.749 |
0.016 |
1.427 |
4.001 |
0. |
1.097 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 263 | 263 | 303 | 396 | 293 | 1278 | 0 | 308 |
normalized size |
1 |
1. |
1.15 |
1.51 |
1.11 |
4.86 |
0. |
1.17 |
time (sec) |
N/A |
0.263 |
0.942 |
0.017 |
1.441 |
13.062 |
0. |
1.128 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 269 | 269 | 325 | 454 | 309 | 1401 | 0 | 344 |
normalized size |
1 |
1. |
1.21 |
1.69 |
1.15 |
5.21 |
0. |
1.28 |
time (sec) |
N/A |
0.286 |
1.099 |
0.017 |
1.47 |
59.004 |
0. |
1.084 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 474 | 474 | 488 | 3725 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.03 |
7.86 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.193 |
2.301 |
0.24 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 621 | 621 | 625 | 7858 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.01 |
12.65 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
4.512 |
4.463 |
0.28 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 646 | 646 | 661 | 10222 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.02 |
15.82 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
3.299 |
5.195 |
0.285 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 679 | 679 | 845 | 3492 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.24 |
5.14 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
4.182 |
6.645 |
0.067 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 728 | 728 | 980 | 3824 | 0 | 0 | 0 | 16458 |
normalized size |
1 |
1. |
1.35 |
5.25 |
0. |
0. |
0. |
22.61 |
time (sec) |
N/A |
2.733 |
6.851 |
0.046 |
0. |
0. |
0. |
29.755 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1150 | 1144 | 1590 | 6026 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.99 |
1.38 |
5.24 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
8.164 |
7.849 |
0.086 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 645 | 645 | 775 | 3107 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.2 |
4.82 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
3.367 |
6.14 |
0.061 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1177 | 1179 | 1649 | 6130 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.4 |
5.21 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
7.926 |
7.631 |
0.089 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
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 | 416 | 416 | 416 | 829 | 564 | 1152 | 503 | 645 |
normalized size | 1 | 1. | 1. | 1.99 | 1.36 | 2.77 | 1.21 | 1.55 |
time (sec) |
N/A |
0.629 |
0.133 |
0.001 |
0.982 |
1.541 |
0.146 |
1.149 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
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 | 259 | 259 | 259 | 354 | 339 | 716 | 309 | 398 |
normalized size | 1 | 1. | 1. | 1.37 | 1.31 | 2.76 | 1.19 | 1.54 |
time (sec) |
N/A |
0.332 |
0.054 |
0.002 |
0.966 |
1.574 |
0.113 |
1.118 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 154 | 154 | 154 | 161 | 186 | 385 | 165 | 212 |
normalized size | 1 | 1. | 1. | 1.05 | 1.21 | 2.5 | 1.07 | 1.38 |
time (sec) |
N/A |
0.152 |
0.035 |
0.002 |
0.963 |
1.525 |
0.088 |
1.1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
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 | 20 | 20 | 20 | 17 | 22 | 39 | 15 | 23 |
normalized size | 1 | 1. | 1. | 0.85 | 1.1 | 1.95 | 0.75 | 1.15 |
time (sec) |
N/A |
0.033 |
0.002 |
0. |
0.951 |
1.688 |
0.08 |
1.187 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 211 | 211 | 234 | 616 | 0 | 0 | 0 | 9103 |
normalized size |
1 |
1. |
1.11 |
2.92 |
0. |
0. |
0. |
43.14 |
time (sec) |
N/A |
0.318 |
0.254 |
0.014 |
0. |
0. |
0. |
22.35 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 368 | 368 | 398 | 1813 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.08 |
4.93 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.923 |
1.427 |
0.095 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 621 | 621 | 625 | 7858 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.01 |
12.65 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
4.594 |
4.538 |
0.229 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
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 | 4 | 4 | 4 | 5 | 5 | 16 | 3 | 7 |
normalized size | 1 | 1. | 1. | 1.25 | 1.25 | 4. | 0.75 | 1.75 |
time (sec) |
N/A |
0.011 |
0.001 |
0.002 |
0.968 |
1.983 |
0.062 |
1.069 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
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 | 14 | 14 | 16 | 18 | 19 | 38 | 12 | 23 |
normalized size | 1 | 1. | 1.14 | 1.29 | 1.36 | 2.71 | 0.86 | 1.64 |
time (sec) |
N/A |
0.024 |
0.004 |
0.002 |
0.949 |
1.733 |
0.263 |
1.081 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
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 | 31 | 31 | 30 | 35 | 36 | 73 | 26 | 41 |
normalized size | 1 | 1. | 0.97 | 1.13 | 1.16 | 2.35 | 0.84 | 1.32 |
time (sec) |
N/A |
0.052 |
0.012 |
0.002 |
1.035 |
1.463 |
0.287 |
1.096 |
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 45 | 58 | 58 | 116 | 41 | 66 |
normalized size | 1 | 1. | 0.88 | 1.14 | 1.14 | 2.27 | 0.8 | 1.29 |
time (sec) |
N/A |
0.085 |
0.027 |
0.004 |
1.156 |
1.468 |
0.318 |
1.084 |
|
|
|
|
|
|
|
|
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|
|
Problem 71 |
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 | 68 | 68 | 68 | 87 | 84 | 169 | 63 | 100 |
normalized size | 1 | 1. | 1. | 1.28 | 1.24 | 2.49 | 0.93 | 1.47 |
time (sec) |
N/A |
0.117 |
0.023 |
0.003 |
1.032 |
1.517 |
0.342 |
1.072 |
|
|
|
|
|
|
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|
Problem 72 |
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 | 92 | 92 | 92 | 122 | 113 | 231 | 88 | 142 |
normalized size | 1 | 1. | 1. | 1.33 | 1.23 | 2.51 | 0.96 | 1.54 |
time (sec) |
N/A |
0.149 |
0.035 |
0.003 |
0.967 |
1.525 |
0.376 |
1.061 |
|
|
|
|
|
|
|
|
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|
Problem 73 |
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 | 11 | 11 | 11 | 12 | 15 | 35 | 8 | 18 |
normalized size | 1 | 1. | 1. | 1.09 | 1.36 | 3.18 | 0.73 | 1.64 |
time (sec) |
N/A |
0.01 |
0.003 |
0.004 |
0.964 |
1.516 |
0.097 |
1.086 |
|
|
|
|
|
|
|
|
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|
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|
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|
|
Problem 74 |
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 | 23 | 29 | 30 | 59 | 29 | 35 |
normalized size | 1 | 1. | 1.05 | 1.32 | 1.36 | 2.68 | 1.32 | 1.59 |
time (sec) |
N/A |
0.021 |
0.007 |
0.004 |
0.972 |
1.529 |
0.252 |
1.07 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 75 |
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 | 29 | 29 | 30 | 45 | 39 | 80 | 44 | 45 |
normalized size | 1 | 1. | 1.03 | 1.55 | 1.34 | 2.76 | 1.52 | 1.55 |
time (sec) |
N/A |
0.05 |
0.013 |
0.005 |
0.969 |
1.485 |
0.594 |
1.065 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 44 | 69 | 61 | 120 | 66 | 66 |
normalized size | 1 | 1. | 0.94 | 1.47 | 1.3 | 2.55 | 1.4 | 1.4 |
time (sec) |
N/A |
0.068 |
0.02 |
0.006 |
0.963 |
1.509 |
0.885 |
1.11 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
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 | 66 | 66 | 67 | 98 | 84 | 170 | 94 | 93 |
normalized size | 1 | 1. | 1.02 | 1.48 | 1.27 | 2.58 | 1.42 | 1.41 |
time (sec) |
N/A |
0.085 |
0.024 |
0.006 |
0.973 |
1.519 |
1.506 |
1.081 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
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 | 90 | 90 | 91 | 134 | 113 | 230 | 122 | 131 |
normalized size | 1 | 1. | 1.01 | 1.49 | 1.26 | 2.56 | 1.36 | 1.46 |
time (sec) |
N/A |
0.107 |
0.041 |
0.006 |
0.977 |
1.48 |
2.535 |
1.079 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
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 | 29 | 29 | 29 | 20 | 26 | 68 | 19 | 30 |
normalized size | 1 | 1. | 1. | 0.69 | 0.9 | 2.34 | 0.66 | 1.03 |
time (sec) |
N/A |
0.021 |
0.007 |
0.006 |
0.975 |
1.502 |
0.124 |
1.082 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 39 | 44 | 43 | 103 | 304 | 51 |
normalized size | 1 | 1. | 0.93 | 1.05 | 1.02 | 2.45 | 7.24 | 1.21 |
time (sec) |
N/A |
0.052 |
0.019 |
0.007 |
0.969 |
1.509 |
1.148 |
1.074 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 44 | 65 | 50 | 122 | 716 | 58 |
normalized size | 1 | 1. | 0.94 | 1.38 | 1.06 | 2.6 | 15.23 | 1.23 |
time (sec) |
N/A |
0.064 |
0.02 |
0.007 |
0.945 |
1.621 |
5.156 |
1.082 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 55 | 89 | 63 | 149 | 1389 | 72 |
normalized size | 1 | 1. | 0.96 | 1.56 | 1.11 | 2.61 | 24.37 | 1.26 |
time (sec) |
N/A |
0.079 |
0.026 |
0.007 |
0.959 |
1.608 |
26.093 |
1.09 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 71 | 120 | 84 | 196 | 2388 | 92 |
normalized size | 1 | 1. | 0.96 | 1.62 | 1.14 | 2.65 | 32.27 | 1.24 |
time (sec) |
N/A |
0.107 |
0.036 |
0.007 |
0.961 |
1.872 |
137.208 |
1.077 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 91 | 156 | 111 | 251 | 0 | 122 |
normalized size |
1 |
1. |
0.95 |
1.62 |
1.16 |
2.61 |
0. |
1.27 |
time (sec) |
N/A |
0.137 |
0.049 |
0.009 |
0.978 |
2.151 |
0. |
1.099 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
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 | 46 | 46 | 42 | 33 | 43 | 155 | 34 | 49 |
normalized size | 1 | 1. | 0.91 | 0.72 | 0.93 | 3.37 | 0.74 | 1.07 |
time (sec) |
N/A |
0.051 |
0.022 |
0.009 |
0.963 |
1.512 |
0.235 |
1.081 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 66 | 74 | 77 | 263 | 1188 | 89 |
normalized size | 1 | 1. | 0.93 | 1.04 | 1.08 | 3.7 | 16.73 | 1.25 |
time (sec) |
N/A |
0.174 |
0.039 |
0.01 |
0.986 |
1.683 |
5.553 |
1.097 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 77 | 110 | 92 | 335 | 4767 | 104 |
normalized size | 1 | 1. | 0.94 | 1.34 | 1.12 | 4.09 | 58.13 | 1.27 |
time (sec) |
N/A |
0.199 |
0.052 |
0.01 |
0.984 |
2.18 |
105.348 |
1.089 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 90 | 146 | 109 | 406 | 0 | 122 |
normalized size |
1 |
1. |
0.95 |
1.54 |
1.15 |
4.27 |
0. |
1.28 |
time (sec) |
N/A |
0.221 |
0.047 |
0.011 |
0.988 |
6.179 |
0. |
1.082 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 106 | 106 | 102 | 182 | 124 | 483 | 0 | 136 |
normalized size |
1 |
1. |
0.96 |
1.72 |
1.17 |
4.56 |
0. |
1.28 |
time (sec) |
N/A |
0.266 |
0.064 |
0.012 |
0.98 |
37.171 |
0. |
1.088 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-1) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 118 | 221 | 146 | 0 | 0 | 158 |
normalized size |
1 |
1. |
0.97 |
1.81 |
1.2 |
0. |
0. |
1.3 |
time (sec) |
N/A |
0.315 |
0.07 |
0.011 |
0.952 |
0. |
0. |
1.084 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
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 | 56 | 56 | 48 | 40 | 57 | 215 | 44 | 62 |
normalized size | 1 | 1. | 0.86 | 0.71 | 1.02 | 3.84 | 0.79 | 1.11 |
time (sec) |
N/A |
0.057 |
0.025 |
0.013 |
0.95 |
1.826 |
0.267 |
1.081 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 80 | 90 | 101 | 410 | 1255 | 115 |
normalized size | 1 | 1. | 0.9 | 1.01 | 1.13 | 4.61 | 14.1 | 1.29 |
time (sec) |
N/A |
0.26 |
0.051 |
0.011 |
0.959 |
1.948 |
5.75 |
1.078 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 97 | 134 | 123 | 529 | 5015 | 136 |
normalized size | 1 | 1. | 0.92 | 1.28 | 1.17 | 5.04 | 47.76 | 1.3 |
time (sec) |
N/A |
0.32 |
0.074 |
0.013 |
0.977 |
2.568 |
117.971 |
1.094 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 114 | 178 | 144 | 655 | 0 | 158 |
normalized size |
1 |
1. |
0.97 |
1.52 |
1.23 |
5.6 |
0. |
1.35 |
time (sec) |
N/A |
0.246 |
0.06 |
0.013 |
0.945 |
7.256 |
0. |
1.101 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 136 | 222 | 166 | 783 | 0 | 180 |
normalized size |
1 |
1. |
1.04 |
1.69 |
1.27 |
5.98 |
0. |
1.37 |
time (sec) |
N/A |
0.28 |
0.069 |
0.015 |
0.958 |
34.496 |
0. |
1.086 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-1) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 153 | 266 | 188 | 0 | 0 | 201 |
normalized size |
1 |
1. |
1.04 |
1.81 |
1.28 |
0. |
0. |
1.37 |
time (sec) |
N/A |
0.33 |
0.092 |
0.013 |
0.969 |
0. |
0. |
1.127 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 60 | 47 | 70 | 271 | 53 | 76 |
normalized size | 1 | 1. | 0.88 | 0.69 | 1.03 | 3.99 | 0.78 | 1.12 |
time (sec) |
N/A |
0.058 |
0.029 |
0.013 |
0.958 |
1.739 |
0.279 |
1.1 |
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 97 | 106 | 119 | 535 | 1032 | 132 |
normalized size | 1 | 1. | 0.92 | 1.01 | 1.13 | 5.1 | 9.83 | 1.26 |
time (sec) |
N/A |
0.196 |
0.087 |
0.014 |
0.957 |
1.848 |
5.594 |
1.101 |
|
|
|
|
|
|
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|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 121 | 158 | 146 | 698 | 5192 | 159 |
normalized size | 1 | 1. | 0.99 | 1.3 | 1.2 | 5.72 | 42.56 | 1.3 |
time (sec) |
N/A |
0.222 |
0.054 |
0.015 |
0.966 |
2.156 |
104.122 |
1.076 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 144 | 210 | 170 | 867 | 0 | 184 |
normalized size |
1 |
1. |
1.02 |
1.49 |
1.21 |
6.15 |
0. |
1.3 |
time (sec) |
N/A |
0.253 |
0.079 |
0.014 |
0.97 |
6.231 |
0. |
1.093 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 158 | 158 | 169 | 262 | 196 | 1049 | 0 | 209 |
normalized size |
1 |
1. |
1.07 |
1.66 |
1.24 |
6.64 |
0. |
1.32 |
time (sec) |
N/A |
0.289 |
0.1 |
0.018 |
0.976 |
34.309 |
0. |
1.085 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-1) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 177 | 195 | 314 | 220 | 0 | 0 | 234 |
normalized size |
1 |
1. |
1.1 |
1.77 |
1.24 |
0. |
0. |
1.32 |
time (sec) |
N/A |
0.343 |
0.119 |
0.016 |
0.985 |
0. |
0. |
1.084 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 717 | 717 | 0 | 3038 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 4.24 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.596 |
0. |
0.095 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 505 | 505 | 0 | 1585 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 3.14 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.279 |
0. |
0.026 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 359 | 359 | 526 | 453 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.47 | 1.26 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.159 |
1.422 |
0.023 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 447 | 447 | 0 | 1005 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
2.25 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.273 |
0. |
0.039 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 680 | 680 | 0 | 1395 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
2.05 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.515 |
0. |
0.051 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 0 | 18 | 23 | 39 | 0 | 95 |
normalized size |
1 |
1. |
0. |
0.95 |
1.21 |
2.05 |
0. |
5. |
time (sec) |
N/A |
0.018 |
0. |
0.006 |
1.126 |
1.217 |
0. |
1.217 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 0 | 52 | 69 | 173 | 0 | 228 |
normalized size |
1 |
1. |
0. |
0.91 |
1.21 |
3.04 |
0. |
4. |
time (sec) |
N/A |
0.067 |
0. |
0.005 |
1.236 |
1.337 |
0. |
1.17 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 0 | 53 | 66 | 171 | 0 | 221 |
normalized size |
1 |
1. |
0. |
0.93 |
1.16 |
3. |
0. |
3.88 |
time (sec) |
N/A |
0.08 |
0. |
0.004 |
1.133 |
1.31 |
0. |
1.177 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 0 | 63 | 127 | 193 | 0 | 262 |
normalized size |
1 |
1. |
0. |
0.91 |
1.84 |
2.8 |
0. |
3.8 |
time (sec) |
N/A |
0.091 |
0. |
0.004 |
1.155 |
1.306 |
0. |
1.185 |
|
|
|
|
|
|
|
|
|
|
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 [47] had the largest ratio of [ 0.6875
]
|
|
|
|
|
|
|
| Table 2.1Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
2 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
2 |
A |
2 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
3 |
A |
2 |
1 |
1. |
28 |
0.036 |
|
|
|
|
|
|
|
4 |
A |
2 |
1 |
1. |
33 |
0.03 |
|
|
|
|
|
|
|
5 |
A |
2 |
1 |
1. |
38 |
0.026 |
|
|
|
|
|
|
|
6 |
A |
2 |
1 |
1. |
20 |
0.05 |
|
|
|
|
|
|
|
7 |
A |
2 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
8 |
A |
2 |
1 |
1. |
30 |
0.033 |
|
|
|
|
|
|
|
9 |
A |
2 |
1 |
1. |
35 |
0.029 |
|
|
|
|
|
|
|
10 |
A |
10 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
11 |
A |
9 |
7 |
1. |
23 |
0.304 |
|
|
|
|
|
|
|
12 |
A |
8 |
6 |
1. |
28 |
0.214 |
|
|
|
|
|
|
|
13 |
A |
10 |
7 |
1. |
33 |
0.212 |
|
|
|
|
|
|
|
14 |
A |
12 |
8 |
1. |
38 |
0.21 |
|
|
|
|
|
|
|
15 |
A |
15 |
8 |
1. |
16 |
0.5 |
|
|
|
|
|
|
|
16 |
A |
14 |
8 |
1. |
21 |
0.381 |
|
|
|
|
|
|
|
17 |
A |
15 |
7 |
1. |
26 |
0.269 |
|
|
|
|
|
|
|
18 |
A |
17 |
8 |
1. |
31 |
0.258 |
|
|
|
|
|
|
|
19 |
A |
19 |
9 |
1. |
36 |
0.25 |
|
|
|
|
|
|
|
20 |
A |
9 |
7 |
1. |
20 |
0.35 |
|
|
|
|
|
|
|
|
21 |
A |
8 |
7 |
1. |
25 |
0.28 |
|
|
|
|
|
|
|
22 |
A |
9 |
8 |
1. |
30 |
0.267 |
|
|
|
|
|
|
|
23 |
A |
11 |
9 |
1. |
35 |
0.257 |
|
|
|
|
|
|
|
24 |
A |
13 |
10 |
1. |
40 |
0.25 |
|
|
|
|
|
|
|
25 |
A |
13 |
10 |
1. |
55 |
0.182 |
|
|
|
|
|
|
|
26 |
A |
12 |
9 |
1. |
18 |
0.5 |
|
|
|
|
|
|
|
27 |
A |
11 |
9 |
1. |
23 |
0.391 |
|
|
|
|
|
|
|
28 |
A |
10 |
8 |
1. |
28 |
0.286 |
|
|
|
|
|
|
|
29 |
A |
10 |
8 |
1. |
33 |
0.242 |
|
|
|
|
|
|
|
30 |
A |
11 |
9 |
1. |
38 |
0.237 |
|
|
|
|
|
|
|
31 |
A |
17 |
10 |
1. |
16 |
0.625 |
|
|
|
|
|
|
|
32 |
A |
16 |
10 |
1. |
21 |
0.476 |
|
|
|
|
|
|
|
33 |
A |
15 |
9 |
1. |
26 |
0.346 |
|
|
|
|
|
|
|
34 |
A |
15 |
9 |
1. |
31 |
0.29 |
|
|
|
|
|
|
|
35 |
A |
16 |
10 |
1. |
36 |
0.278 |
|
|
|
|
|
|
|
36 |
A |
11 |
9 |
1. |
20 |
0.45 |
|
|
|
|
|
|
|
37 |
A |
10 |
9 |
1. |
25 |
0.36 |
|
|
|
|
|
|
|
38 |
A |
9 |
8 |
1. |
30 |
0.267 |
|
|
|
|
|
|
|
39 |
A |
9 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
40 |
A |
10 |
9 |
1. |
40 |
0.225 |
|
|
|
|
|
|
|
|
41 |
A |
13 |
11 |
1. |
55 |
0.2 |
|
|
|
|
|
|
|
42 |
A |
14 |
10 |
1. |
18 |
0.556 |
|
|
|
|
|
|
|
43 |
A |
13 |
9 |
1. |
23 |
0.391 |
|
|
|
|
|
|
|
44 |
A |
12 |
9 |
1. |
28 |
0.321 |
|
|
|
|
|
|
|
45 |
A |
12 |
10 |
1. |
33 |
0.303 |
|
|
|
|
|
|
|
46 |
A |
13 |
11 |
1. |
38 |
0.29 |
|
|
|
|
|
|
|
47 |
A |
19 |
11 |
1. |
16 |
0.688 |
|
|
|
|
|
|
|
48 |
A |
18 |
10 |
1. |
21 |
0.476 |
|
|
|
|
|
|
|
49 |
A |
17 |
10 |
1. |
26 |
0.385 |
|
|
|
|
|
|
|
50 |
A |
17 |
11 |
1. |
31 |
0.355 |
|
|
|
|
|
|
|
51 |
A |
18 |
12 |
1. |
36 |
0.333 |
|
|
|
|
|
|
|
52 |
A |
13 |
10 |
1. |
20 |
0.5 |
|
|
|
|
|
|
|
53 |
A |
12 |
9 |
1. |
25 |
0.36 |
|
|
|
|
|
|
|
54 |
A |
11 |
9 |
1. |
30 |
0.3 |
|
|
|
|
|
|
|
55 |
A |
11 |
10 |
1. |
35 |
0.286 |
|
|
|
|
|
|
|
56 |
A |
12 |
11 |
1. |
40 |
0.275 |
|
|
|
|
|
|
|
57 |
A |
11 |
9 |
0.99 |
55 |
0.164 |
|
|
|
|
|
|
|
58 |
A |
11 |
10 |
1. |
50 |
0.2 |
|
|
|
|
|
|
|
59 |
A |
13 |
10 |
1. |
50 |
0.2 |
|
|
|
|
|
|
|
60 |
A |
2 |
1 |
1. |
63 |
0.016 |
|
|
|
|
|
|
|
|
61 |
A |
2 |
1 |
1. |
63 |
0.016 |
|
|
|
|
|
|
|
62 |
A |
2 |
1 |
1. |
61 |
0.016 |
|
|
|
|
|
|
|
63 |
A |
2 |
1 |
1. |
63 |
0.016 |
|
|
|
|
|
|
|
64 |
A |
9 |
8 |
1. |
63 |
0.127 |
|
|
|
|
|
|
|
65 |
A |
11 |
10 |
1. |
63 |
0.159 |
|
|
|
|
|
|
|
66 |
A |
13 |
10 |
1. |
63 |
0.159 |
|
|
|
|
|
|
|
67 |
A |
2 |
2 |
1. |
26 |
0.077 |
|
|
|
|
|
|
|
68 |
A |
3 |
2 |
1. |
31 |
0.065 |
|
|
|
|
|
|
|
69 |
A |
3 |
2 |
1. |
36 |
0.056 |
|
|
|
|
|
|
|
70 |
A |
3 |
2 |
1. |
41 |
0.049 |
|
|
|
|
|
|
|
71 |
A |
3 |
2 |
1. |
46 |
0.043 |
|
|
|
|
|
|
|
72 |
A |
3 |
2 |
1. |
51 |
0.039 |
|
|
|
|
|
|
|
73 |
A |
4 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
74 |
A |
4 |
3 |
1. |
26 |
0.115 |
|
|
|
|
|
|
|
75 |
A |
6 |
4 |
1. |
31 |
0.129 |
|
|
|
|
|
|
|
76 |
A |
6 |
4 |
1. |
36 |
0.111 |
|
|
|
|
|
|
|
77 |
A |
6 |
4 |
1. |
41 |
0.098 |
|
|
|
|
|
|
|
78 |
A |
6 |
4 |
1. |
46 |
0.087 |
|
|
|
|
|
|
|
79 |
A |
3 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
80 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
|
81 |
A |
3 |
2 |
1. |
26 |
0.077 |
|
|
|
|
|
|
|
82 |
A |
3 |
2 |
1. |
31 |
0.065 |
|
|
|
|
|
|
|
83 |
A |
3 |
2 |
1. |
36 |
0.056 |
|
|
|
|
|
|
|
84 |
A |
3 |
2 |
1. |
41 |
0.049 |
|
|
|
|
|
|
|
85 |
A |
3 |
2 |
1. |
26 |
0.077 |
|
|
|
|
|
|
|
86 |
A |
3 |
2 |
1. |
31 |
0.065 |
|
|
|
|
|
|
|
87 |
A |
3 |
2 |
1. |
36 |
0.056 |
|
|
|
|
|
|
|
88 |
A |
3 |
2 |
1. |
41 |
0.049 |
|
|
|
|
|
|
|
89 |
A |
3 |
2 |
1. |
46 |
0.043 |
|
|
|
|
|
|
|
90 |
A |
3 |
2 |
1. |
51 |
0.039 |
|
|
|
|
|
|
|
91 |
A |
9 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
92 |
A |
9 |
5 |
1. |
26 |
0.192 |
|
|
|
|
|
|
|
93 |
A |
9 |
5 |
1. |
31 |
0.161 |
|
|
|
|
|
|
|
94 |
A |
3 |
2 |
1. |
36 |
0.056 |
|
|
|
|
|
|
|
95 |
A |
3 |
2 |
1. |
41 |
0.049 |
|
|
|
|
|
|
|
96 |
A |
3 |
2 |
1. |
46 |
0.043 |
|
|
|
|
|
|
|
97 |
A |
3 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
98 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
99 |
A |
3 |
2 |
1. |
26 |
0.077 |
|
|
|
|
|
|
|
100 |
A |
3 |
2 |
1. |
31 |
0.065 |
|
|
|
|
|
|
|
|
101 |
A |
3 |
2 |
1. |
36 |
0.056 |
|
|
|
|
|
|
|
102 |
A |
3 |
2 |
1. |
41 |
0.049 |
|
|
|
|
|
|
|
103 |
A |
12 |
10 |
1. |
32 |
0.312 |
|
|
|
|
|
|
|
104 |
A |
10 |
10 |
1. |
32 |
0.312 |
|
|
|
|
|
|
|
105 |
A |
8 |
8 |
1. |
32 |
0.25 |
|
|
|
|
|
|
|
106 |
A |
7 |
7 |
1. |
32 |
0.219 |
|
|
|
|
|
|
|
107 |
A |
9 |
8 |
1. |
32 |
0.25 |
|
|
|
|
|
|
|
108 |
A |
1 |
1 |
1. |
28 |
0.036 |
|
|
|
|
|
|
|
109 |
A |
5 |
5 |
1. |
31 |
0.161 |
|
|
|
|
|
|
|
110 |
A |
5 |
5 |
1. |
33 |
0.152 |
|
|
|
|
|
|
|
111 |
A |
4 |
4 |
1. |
36 |
0.111 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|