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, 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
}
B grade: { 10, 11 }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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
}
B grade: { }
C grade: { 15, 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 }
F grade: { }
2.1.3 Maple
A grade: { 2, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 31,
32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 66
}
B grade: { 1, 3, 11, 24, 26, 44, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78,
79, 80, 81, 82, 83, 84, 85, 86, 87, 88 }
C grade: { }
F grade: { }
2.1.4 Maxima
A grade: { 2, 4, 5, 6, 8, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 27, 29, 31
B grade: { 1, 3, 7, 9, 11 }
C grade: { }
F grade: { 24, 26, 28, 30, 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 }
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30
}
B grade: { 10, 11, 31, 32 }
C grade: { }
F grade: { 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 }
2.1.6 Sympy
A grade: { 4, 5, 10, 12, 13, 14, 15, 18, 19, 20, 21, 27, 28 }
B grade: { 1, 2, 3, 11, 16, 17, 22, 23 }
C grade: { }
F grade: { 6, 7, 8, 9, 24, 25, 26, 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 }
2.1.7 Giac
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31
}
B grade: { 11, 24, 32 }
C grade: { }
F grade: { 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 }
2.2 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2)
if the failure was due to an exception being raised, which could indicate a bug in the system. If
the failure was due to integral not being evaluated within the time limit, then it is given just an
F.
In this table,the column normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
B |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 25 | 68 | 127 | 68 | 294 | 61 |
normalized size | 1 | 1. | 0.81 | 2.19 | 4.1 | 2.19 | 9.48 | 1.97 |
time (sec) |
N/A |
0.043 |
0.04 |
0.046 |
1.767 |
1.581 |
2.067 |
1.1 |
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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 |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 13 | 16 | 19 | 39 | 88 | 19 |
normalized size | 1 | 1. | 0.68 | 0.84 | 1. | 2.05 | 4.63 | 1. |
time (sec) |
N/A |
0.04 |
0.012 |
0.039 |
1.083 |
1.545 |
0.977 |
1.142 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
B |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 17 | 31 | 57 | 22 | 46 | 34 |
normalized size | 1 | 1. | 1.31 | 2.38 | 4.38 | 1.69 | 3.54 | 2.62 |
time (sec) |
N/A |
0.038 |
0.008 |
0.047 |
1.637 |
1.571 |
0.502 |
1.107 |
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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 | 10 | 10 | 12 | 13 | 16 | 35 | 8 | 14 |
normalized size | 1 | 1. | 1.2 | 1.3 | 1.6 | 3.5 | 0.8 | 1.4 |
time (sec) |
N/A |
0.024 |
0.006 |
0.031 |
1.113 |
1.62 |
0.146 |
1.106 |
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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 | 11 | 11 | 10 | 9 | 16 | 31 | 5 | 11 |
normalized size | 1 | 1. | 0.91 | 0.82 | 1.45 | 2.82 | 0.45 | 1. |
time (sec) |
N/A |
0.01 |
0.005 |
0.025 |
1.105 |
1.511 |
0.221 |
1.158 |
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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 |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 42 | 33 | 42 | 135 | 0 | 46 |
normalized size | 1 | 1. | 1.83 | 1.43 | 1.83 | 5.87 | 0. | 2. |
time (sec) |
N/A |
0.05 |
0.031 |
0.046 |
1.135 |
1.667 |
0. |
1.115 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 30 | 29 | 55 | 78 | 0 | 50 |
normalized size | 1 | 1. | 1.25 | 1.21 | 2.29 | 3.25 | 0. | 2.08 |
time (sec) |
N/A |
0.046 |
0.048 |
0.043 |
1.124 |
1.572 |
0. |
1.132 |
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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 |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 60 | 55 | 78 | 267 | 0 | 70 |
normalized size | 1 | 1. | 1.22 | 1.12 | 1.59 | 5.45 | 0. | 1.43 |
time (sec) |
N/A |
0.074 |
0.102 |
0.052 |
1.186 |
1.629 |
0. |
1.127 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 38 | 45 | 95 | 153 | 0 | 80 |
normalized size | 1 | 1. | 1.03 | 1.22 | 2.57 | 4.14 | 0. | 2.16 |
time (sec) |
N/A |
0.048 |
0.057 |
0.051 |
1.076 |
1.542 |
0. |
1.143 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
B |
A |
A |
A |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 5 | 11 | 5 | 10 | 12 | 41 | 10 | 12 |
normalized size | 1 | 2.2 | 1. | 2. | 2.4 | 8.2 | 2. | 2.4 |
time (sec) |
N/A |
0.021 |
0.003 |
0.03 |
1.142 |
1.59 |
0.127 |
1.158 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
B |
A |
B |
B |
B |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 3 | 13 | 3 | 12 | 12 | 41 | 8 | 15 |
normalized size | 1 | 4.33 | 1. | 4. | 4. | 13.67 | 2.67 | 5. |
time (sec) |
N/A |
0.022 |
0.004 |
0.033 |
1.125 |
1.603 |
0.144 |
1.169 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 6 | 6 | 12 | 7 | 8 | 22 | 8 | 8 |
normalized size | 1 | 1. | 2. | 1.17 | 1.33 | 3.67 | 1.33 | 1.33 |
time (sec) |
N/A |
0.019 |
0.009 |
0.031 |
1.14 |
1.549 |
0.439 |
1.152 |
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Problem 13 |
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 | 10 | 10 | 12 | 11 | 8 | 22 | 7 | 8 |
normalized size | 1 | 1. | 1.2 | 1.1 | 0.8 | 2.2 | 0.7 | 0.8 |
time (sec) |
N/A |
0.019 |
0.009 |
0.037 |
1.139 |
1.536 |
0.468 |
1.131 |
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Problem 14 |
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 | 14 | 14 | 18 | 11 | 31 | 55 | 7 | 14 |
normalized size | 1 | 1. | 1.29 | 0.79 | 2.21 | 3.93 | 0.5 | 1. |
time (sec) |
N/A |
0.031 |
0.006 |
0.043 |
1.73 |
1.581 |
0.677 |
1.146 |
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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 |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 26 | 13 | 31 | 47 | 8 | 16 |
normalized size | 1 | 1. | 1.62 | 0.81 | 1.94 | 2.94 | 0.5 | 1. |
time (sec) |
N/A |
0.031 |
0.008 |
0.061 |
1.688 |
1.604 |
1.401 |
1.201 |
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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 | 10 | 10 | 13 | 11 | 14 | 46 | 61 | 14 |
normalized size | 1 | 1. | 1.3 | 1.1 | 1.4 | 4.6 | 6.1 | 1.4 |
time (sec) |
N/A |
0.036 |
0.019 |
0.042 |
1.3 |
1.658 |
0.693 |
1.178 |
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Problem 17 |
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 | 12 | 12 | 13 | 11 | 14 | 47 | 61 | 16 |
normalized size | 1 | 1. | 1.08 | 0.92 | 1.17 | 3.92 | 5.08 | 1.33 |
time (sec) |
N/A |
0.036 |
0.016 |
0.05 |
2.097 |
1.593 |
0.645 |
1.186 |
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Problem 18 |
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 | 10 | 10 | 12 | 9 | 11 | 42 | 14 | 11 |
normalized size | 1 | 1. | 1.2 | 0.9 | 1.1 | 4.2 | 1.4 | 1.1 |
time (sec) |
N/A |
0.019 |
0.008 |
0.029 |
1.253 |
1.584 |
0.946 |
1.141 |
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Problem 19 |
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 | 12 | 12 | 12 | 11 | 11 | 43 | 15 | 11 |
normalized size | 1 | 1. | 1. | 0.92 | 0.92 | 3.58 | 1.25 | 0.92 |
time (sec) |
N/A |
0.019 |
0.01 |
0.039 |
1.402 |
1.56 |
0.817 |
1.141 |
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Problem 20 |
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 | 14 | 14 | 12 | 9 | 16 | 70 | 7 | 11 |
normalized size | 1 | 1. | 0.86 | 0.64 | 1.14 | 5. | 0.5 | 0.79 |
time (sec) |
N/A |
0.031 |
0.028 |
0.046 |
1.601 |
1.537 |
1.607 |
1.163 |
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Problem 21 |
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 | 16 | 16 | 12 | 9 | 16 | 72 | 10 | 11 |
normalized size | 1 | 1. | 0.75 | 0.56 | 1. | 4.5 | 0.62 | 0.69 |
time (sec) |
N/A |
0.031 |
0.029 |
0.06 |
1.399 |
1.565 |
2.274 |
1.156 |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 22 |
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 | 14 | 14 | 18 | 15 | 19 | 74 | 126 | 19 |
normalized size | 1 | 1. | 1.29 | 1.07 | 1.36 | 5.29 | 9. | 1.36 |
time (sec) |
N/A |
0.038 |
0.009 |
0.046 |
1.324 |
1.634 |
0.785 |
1.172 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
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|
|
Problem 23 |
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 | 20 | 20 | 29 | 17 | 22 | 77 | 126 | 24 |
normalized size | 1 | 1. | 1.45 | 0.85 | 1.1 | 3.85 | 6.3 | 1.2 |
time (sec) |
N/A |
0.037 |
0.011 |
0.064 |
1.512 |
1.613 |
0.891 |
1.146 |
|
|
|
|
|
|
|
|
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|
|
|
|
|
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|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 96 | 315 | 0 | 587 | 0 | 262 |
normalized size |
1 |
1. |
0.92 |
3.03 |
0. |
5.64 |
0. |
2.52 |
time (sec) |
N/A |
0.256 |
0.206 |
0.093 |
0. |
1.862 |
0. |
1.184 |
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 25 |
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 | 40 | 40 | 40 | 45 | 51 | 100 | 0 | 53 |
normalized size |
1 |
1. |
1. |
1.12 |
1.27 |
2.5 |
0. |
1.32 |
time (sec) |
N/A |
0.061 |
0.057 |
0.031 |
1.521 |
1.691 |
0. |
1.176 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 54 | 108 | 0 | 378 | 0 | 122 |
normalized size |
1 |
1. |
0.92 |
1.83 |
0. |
6.41 |
0. |
2.07 |
time (sec) |
N/A |
0.109 |
0.079 |
0.076 |
0. |
1.764 |
0. |
1.157 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
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 | 12 | 12 | 12 | 13 | 16 | 31 | 17 | 18 |
normalized size | 1 | 1. | 1. | 1.08 | 1.33 | 2.58 | 1.42 | 1.5 |
time (sec) |
N/A |
0.025 |
0.014 |
0.025 |
1.362 |
1.629 |
0.367 |
1.262 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 41 | 36 | 0 | 328 | 144 | 82 |
normalized size |
1 |
1. |
0.98 |
0.86 |
0. |
7.81 |
3.43 |
1.95 |
time (sec) |
N/A |
0.026 |
0.023 |
0.062 |
0. |
1.746 |
7.143 |
1.294 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 50 | 54 | 63 | 144 | 0 | 73 |
normalized size | 1 | 1. | 0.94 | 1.02 | 1.19 | 2.72 | 0. | 1.38 |
time (sec) |
N/A |
0.072 |
0.041 |
0.04 |
1.53 |
1.745 |
0. |
1.156 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 66 | 78 | 0 | 544 | 0 | 123 |
normalized size |
1 |
1. |
0.99 |
1.16 |
0. |
8.12 |
0. |
1.84 |
time (sec) |
N/A |
0.095 |
0.311 |
0.08 |
0. |
1.773 |
0. |
1.158 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 92 | 92 | 99 | 114 | 155 | 429 | 0 | 184 |
normalized size | 1 | 1. | 1.08 | 1.24 | 1.68 | 4.66 | 0. | 2. |
time (sec) |
N/A |
0.154 |
0.429 |
0.052 |
1.502 |
2.027 |
0. |
1.169 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 112 | 153 | 0 | 1027 | 0 | 278 |
normalized size |
1 |
1. |
1.02 |
1.39 |
0. |
9.34 |
0. |
2.53 |
time (sec) |
N/A |
0.271 |
0.627 |
0.088 |
0. |
1.893 |
0. |
1.201 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 108 | 127 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.84 |
0.98 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.097 |
0.869 |
1.659 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 100 | 80 | 171 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
1.71 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.07 |
0.508 |
1.651 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
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 | 100 | 100 | 80 | 116 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.8 | 1.16 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.071 |
0.459 |
1.426 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
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 | 68 | 68 | 60 | 117 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.88 | 1.72 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.049 |
0.097 |
1.609 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
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 | 66 | 66 | 54 | 92 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.82 | 1.39 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.051 |
0.202 |
1.162 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 58 | 153 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.6 | 1.59 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.073 |
0.115 |
1.76 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 59 | 124 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.58 |
1.22 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.071 |
0.151 |
1.694 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 74 | 187 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.56 |
1.43 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.091 |
0.255 |
1.826 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 193 | 193 | 157 | 228 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.81 |
1.18 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.19 |
1.767 |
1.855 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 154 | 116 | 332 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.75 |
2.16 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.161 |
0.801 |
1.938 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 154 | 117 | 229 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.76 |
1.49 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.168 |
0.812 |
1.75 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 114 | 83 | 294 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.73 |
2.58 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.131 |
0.271 |
1.878 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
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 | 114 | 114 | 79 | 170 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.69 | 1.49 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.129 |
0.379 |
1.77 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 118 | 118 | 75 | 277 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.64 |
2.35 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.138 |
0.239 |
1.618 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 76 | 190 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
1.53 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.139 |
0.265 |
1.883 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 109 | 327 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.66 |
1.98 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.171 |
0.489 |
1.971 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 242 | 242 | 205 | 252 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.85 |
1.04 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.32 |
2.5 |
2.711 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 202 | 202 | 149 | 356 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.74 |
1.76 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.293 |
1.411 |
2.378 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 202 | 202 | 147 | 226 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.73 |
1.12 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.298 |
1.307 |
2.476 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 105 | 315 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.65 |
1.96 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.25 |
0.554 |
2.518 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 98 | 210 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.62 |
1.34 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.243 |
0.711 |
2.188 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 101 | 313 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
1.9 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.253 |
0.322 |
2.81 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 169 | 169 | 102 | 214 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.6 |
1.27 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.26 |
0.826 |
2.434 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 192 | 192 | 130 | 351 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.68 |
1.83 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.271 |
0.612 |
2.664 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 193 | 193 | 144 | 241 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.75 |
1.25 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.274 |
0.608 |
2.634 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 544 | 544 | 2035 | 2930 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
3.74 |
5.39 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.899 |
17.239 |
8.839 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 461 | 461 | 834 | 2051 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.81 |
4.45 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.336 |
15.008 |
8.355 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 474 | 474 | 1955 | 2087 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
4.12 |
4.4 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.337 |
17.059 |
7.774 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 399 | 399 | 757 | 1247 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.9 |
3.13 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.898 |
14.473 |
6.6 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 410 | 410 | 434 | 1314 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.06 |
3.2 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.904 |
5.831 |
5.977 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 302 | 302 | 361 | 815 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.2 |
2.7 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.607 |
1.855 |
4.738 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 307 | 307 | 265 | 855 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.86 |
2.79 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.588 |
2.029 |
5.006 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 426 | 426 | 791 | 1248 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.86 |
2.93 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.964 |
14.656 |
5.633 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 447 | 447 | 1192 | 845 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.67 |
1.89 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.013 |
12.069 |
7.659 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 501 | 501 | 881 | 1795 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.76 |
3.58 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.355 |
6.731 |
6.188 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 557 | 557 | 2029 | 4706 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
3.64 |
8.45 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.557 |
17.351 |
12.187 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 473 | 473 | 835 | 3595 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.77 |
7.6 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.157 |
14.792 |
10.988 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 487 | 487 | 1956 | 3396 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
4.02 |
6.97 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.151 |
16.519 |
10.518 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 404 | 404 | 366 | 3174 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.91 |
7.86 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.842 |
20.199 |
6.118 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 418 | 418 | 614 | 2148 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.47 |
5.14 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.907 |
9.649 |
8.499 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 438 | 438 | 786 | 1384 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.79 |
3.16 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.905 |
14.061 |
8.185 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 445 | 445 | 1182 | 1351 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.66 |
3.04 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.933 |
11.121 |
7.964 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 507 | 507 | 865 | 4318 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.71 |
8.52 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.271 |
6.68 |
6.776 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 530 | 530 | 1257 | 2143 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.37 |
4.04 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.367 |
14.79 |
11.063 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 590 | 590 | 950 | 2888 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.61 |
4.89 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.68 |
6.848 |
13.2 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 590 | 590 | 930 | 7803 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.58 |
13.23 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.473 |
15.135 |
16.654 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 604 | 604 | 2024 | 7238 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
3.35 |
11.98 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.582 |
16.697 |
15.757 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 498 | 498 | 837 | 5791 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.68 |
11.63 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.115 |
14.617 |
13.824 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 512 | 512 | 1954 | 5404 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
3.82 |
10.55 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.138 |
16.69 |
14.263 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 520 | 520 | 831 | 4303 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.6 |
8.28 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.12 |
14.609 |
12.88 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 534 | 534 | 1211 | 4116 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.27 |
7.71 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.21 |
11.422 |
13.042 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 529 | 529 | 837 | 2986 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.58 |
5.64 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.212 |
14.56 |
11.102 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 535 | 535 | 1226 | 2918 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.29 |
5.45 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.229 |
12.838 |
12.183 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 611 | 611 | 922 | 4913 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.51 |
8.04 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.647 |
6.797 |
15.789 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 629 | 629 | 1308 | 4661 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.08 |
7.41 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.775 |
15.533 |
16.93 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 700 | 700 | 1014 | 5638 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.45 |
8.05 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.118 |
6.96 |
18.155 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
2.3 Detailed conclusion table specific for Rubi results
The following table is specific to Rubi. It gives additional statistics for each integral. the column
steps is the number of steps used by Rubi to obtain the antiderivative. The rules
column is the number of unique rules used. The integrand size column is the leaf size
of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the
integral was to solve. In this test, problem number [78] had the largest ratio of [ 0.52
]
|
|
|
|
|
|
|
| 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 |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
2 |
A |
2 |
1 |
1. |
13 |
0.077 |
|
|
|
|
|
|
|
3 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
4 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
5 |
A |
1 |
1 |
1. |
8 |
0.125 |
|
|
|
|
|
|
|
6 |
A |
4 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
7 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
8 |
A |
4 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
9 |
A |
3 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
10 |
B |
2 |
2 |
2.2 |
13 |
0.154 |
|
|
|
|
|
|
|
11 |
B |
2 |
2 |
4.33 |
15 |
0.133 |
|
|
|
|
|
|
|
12 |
A |
2 |
2 |
1. |
9 |
0.222 |
|
|
|
|
|
|
|
13 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
14 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
15 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
16 |
A |
3 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
17 |
A |
3 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
18 |
A |
2 |
2 |
1. |
9 |
0.222 |
|
|
|
|
|
|
|
19 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
20 |
A |
1 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
|
21 |
A |
1 |
1 |
1. |
13 |
0.077 |
|
|
|
|
|
|
|
22 |
A |
3 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
23 |
A |
3 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
24 |
A |
5 |
5 |
1. |
13 |
0.385 |
|
|
|
|
|
|
|
25 |
A |
3 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
26 |
A |
4 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
27 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
28 |
A |
2 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
29 |
A |
6 |
4 |
1. |
11 |
0.364 |
|
|
|
|
|
|
|
30 |
A |
4 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
31 |
A |
4 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
32 |
A |
5 |
5 |
1. |
13 |
0.385 |
|
|
|
|
|
|
|
33 |
A |
5 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
34 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
35 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
36 |
A |
3 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
37 |
A |
3 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
38 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
39 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
40 |
A |
5 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
|
41 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
42 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
43 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
44 |
A |
4 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
45 |
A |
4 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
46 |
A |
4 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
47 |
A |
4 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
48 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
49 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
50 |
A |
6 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
51 |
A |
6 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
52 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
53 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
54 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
55 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
56 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
57 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
58 |
A |
15 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
59 |
A |
14 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
60 |
A |
14 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
|
61 |
A |
13 |
11 |
1. |
25 |
0.44 |
|
|
|
|
|
|
|
62 |
A |
13 |
11 |
1. |
25 |
0.44 |
|
|
|
|
|
|
|
63 |
A |
9 |
7 |
1. |
25 |
0.28 |
|
|
|
|
|
|
|
64 |
A |
9 |
7 |
1. |
25 |
0.28 |
|
|
|
|
|
|
|
65 |
A |
13 |
11 |
1. |
25 |
0.44 |
|
|
|
|
|
|
|
66 |
A |
13 |
11 |
1. |
25 |
0.44 |
|
|
|
|
|
|
|
67 |
A |
14 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
68 |
A |
15 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
69 |
A |
14 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
70 |
A |
14 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
71 |
A |
13 |
11 |
1. |
25 |
0.44 |
|
|
|
|
|
|
|
72 |
A |
13 |
11 |
1. |
25 |
0.44 |
|
|
|
|
|
|
|
73 |
A |
13 |
11 |
1. |
25 |
0.44 |
|
|
|
|
|
|
|
74 |
A |
13 |
11 |
1. |
25 |
0.44 |
|
|
|
|
|
|
|
75 |
A |
14 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
76 |
A |
14 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
77 |
A |
15 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
78 |
A |
15 |
13 |
1. |
25 |
0.52 |
|
|
|
|
|
|
|
79 |
A |
15 |
13 |
1. |
25 |
0.52 |
|
|
|
|
|
|
|
80 |
A |
14 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
|
81 |
A |
14 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
82 |
A |
14 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
83 |
A |
14 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
84 |
A |
14 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
85 |
A |
14 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
86 |
A |
15 |
13 |
1. |
25 |
0.52 |
|
|
|
|
|
|
|
87 |
A |
15 |
13 |
1. |
25 |
0.52 |
|
|
|
|
|
|
|
88 |
A |
16 |
13 |
1. |
25 |
0.52 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|