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
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31,
32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 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 }
B grade: { 3, 24, 53 }
C grade: { 101, 102 }
F grade: { 37}
2.1.3 Maple
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, 27, 28, 29, 30, 31, 32,
33, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 56, 57, 61, 67, 72, 74, 75, 77, 79, 83, 84, 85, 86, 87,
91, 92, 95, 100 }
B grade: { 35, 36, 93, 94, 98, 99 }
C grade: { 26, 39, 55, 58, 59, 60, 62, 63, 82, 88, 89, 90 }
F grade: { 24, 25, 37, 38, 53, 54, 64, 65, 66, 68, 69, 70, 71, 73, 76, 78, 80, 81, 96, 97, 101, 102
}
2.1.4 Maxima
A grade: { 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 23, 27, 28, 29, 30, 31, 32, 33, 40, 41, 42,
43, 44, 45, 46, 47, 48, 49, 51, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77,
79, 83, 84, 86, 87, 91, 92, 93, 94, 98, 99, 100
B grade: { 1, 2, 4, 17, 22, 88, 89, 90, 95 }
C grade: { 34, 35, 36, 50, 52 }
F grade: { 24, 25, 26, 37, 38, 39, 53, 54, 55, 76, 78, 80, 81, 82, 85, 96, 97, 101, 102 }
2.1.5 FriCAS
A grade: { 1, 3, 4, 5, 7, 8, 10, 11, 12, 14, 15, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 40, 42, 44, 46, 47, 48, 50, 52, 56, 57, 67, 72, 74, 75, 77, 79, 83, 87, 88, 90, 91, 92, 93, 94, 95, 98, 99, 100
}
B grade: { 2, 6, 9, 13, 16, 20, 22, 41, 43, 45, 49, 51, 61, 84, 85, 86, 89, 96, 97, 101, 102 }
C grade: { }
F grade: { 37, 38, 39, 53, 54, 55, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 73, 76, 78, 80, 81, 82
}
2.1.6 Sympy
A grade: { 1, 3, 8, 10, 15, 17, 22, 23, 27, 28, 32, 33, 34, 35, 36, 40, 48, 50, 52, 56, 57, 74, 83, 91, 92, 93, 94,
95, 100 }
B grade: { }
C grade: { }
F grade: { 2, 4, 5, 6, 7, 9, 11, 12, 13, 14, 16, 18, 19, 20, 21, 24, 25, 26, 29, 30, 31, 37, 38, 39, 41, 42, 43, 44,
45, 46, 47, 49, 51, 53, 54, 55, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79,
80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 96, 97, 98, 99, 101, 102 }
2.1.7 Giac
A grade: { 1, 2, 3, 4, 5, 9, 11, 12, 16, 17, 18, 19, 22, 23, 27, 28, 33, 40, 48, 56, 57, 74, 75, 77, 79, 83, 91, 92,
100 }
B grade: { 7, 8, 10, 14, 15, 21, 93, 94, 95, 98, 99 }
C grade: { 88, 89, 90 }
F grade: { 6, 13, 20, 24, 25, 26, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51,
52, 53, 54, 55, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 78, 80, 81, 82, 84, 85, 86, 87,
96, 97, 101, 102 }
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 |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 31 | 45 | 109 | 69 | 36 | 63 |
normalized size | 1 | 1. | 0.91 | 1.32 | 3.21 | 2.03 | 1.06 | 1.85 |
time (sec) |
N/A |
0.036 |
0.034 |
0.013 |
1.035 |
1.985 |
1.127 |
1.391 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 67 | 74 | 149 | 539 | 0 | 101 |
normalized size | 1 | 1. | 0.97 | 1.07 | 2.16 | 7.81 | 0. | 1.46 |
time (sec) |
N/A |
0.041 |
0.068 |
0.048 |
0.993 |
2.114 |
0. |
1.307 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 31 | 14 | 18 | 31 | 19 | 34 |
normalized size | 1 | 1. | 2.07 | 0.93 | 1.2 | 2.07 | 1.27 | 2.27 |
time (sec) |
N/A |
0.016 |
0.01 |
0.002 |
1.136 |
1.996 |
0.259 |
1.252 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 45 | 40 | 116 | 159 | 0 | 55 |
normalized size | 1 | 1. | 0.85 | 0.75 | 2.19 | 3. | 0. | 1.04 |
time (sec) |
N/A |
0.018 |
0.038 |
0.017 |
1.143 |
1.912 |
0. |
1.205 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 23 | 27 | 32 | 104 | 0 | 32 |
normalized size | 1 | 1. | 0.92 | 1.08 | 1.28 | 4.16 | 0. | 1.28 |
time (sec) |
N/A |
0.035 |
0.014 |
0.012 |
1.252 |
1.586 |
0. |
1.117 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 70 | 70 | 73 | 529 | 0 | 0 |
normalized size | 1 | 1. | 1.06 | 1.06 | 1.11 | 8.02 | 0. | 0. |
time (sec) |
N/A |
0.035 |
0.064 |
0.023 |
1.117 |
1.811 |
0. |
0. |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 38 | 58 | 53 | 166 | 0 | 147 |
normalized size | 1 | 1. | 0.9 | 1.38 | 1.26 | 3.95 | 0. | 3.5 |
time (sec) |
N/A |
0.092 |
0.04 |
0.017 |
1.274 |
1.685 |
0. |
1.155 |
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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 |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 42 | 55 | 80 | 142 | 78 | 158 |
normalized size | 1 | 1. | 0.82 | 1.08 | 1.57 | 2.78 | 1.53 | 3.1 |
time (sec) |
N/A |
0.05 |
0.102 |
0.029 |
1.09 |
1.671 |
2.555 |
1.176 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 101 | 90 | 128 | 1126 | 0 | 131 |
normalized size | 1 | 1. | 1.02 | 0.91 | 1.29 | 11.37 | 0. | 1.32 |
time (sec) |
N/A |
0.096 |
0.224 |
0.056 |
1.727 |
1.762 |
0. |
1.17 |
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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 |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 27 | 34 | 51 | 68 | 60 | 76 |
normalized size | 1 | 1. | 0.87 | 1.1 | 1.65 | 2.19 | 1.94 | 2.45 |
time (sec) |
N/A |
0.027 |
0.024 |
0.006 |
1.134 |
1.738 |
0.636 |
1.147 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 86 | 51 | 76 | 225 | 0 | 78 |
normalized size | 1 | 1. | 1.1 | 0.65 | 0.97 | 2.88 | 0. | 1. |
time (sec) |
N/A |
0.046 |
0.076 |
0.029 |
1.649 |
1.795 |
0. |
1.168 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 33 | 34 | 42 | 138 | 0 | 47 |
normalized size | 1 | 1. | 0.89 | 0.92 | 1.14 | 3.73 | 0. | 1.27 |
time (sec) |
N/A |
0.059 |
0.02 |
0.033 |
1.352 |
1.86 |
0. |
1.185 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 94 | 86 | 82 | 1058 | 0 | 0 |
normalized size | 1 | 1. | 1.07 | 0.98 | 0.93 | 12.02 | 0. | 0. |
time (sec) |
N/A |
0.068 |
0.226 |
0.038 |
1.17 |
1.862 |
0. |
0. |
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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 |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 46 | 69 | 49 | 216 | 0 | 170 |
normalized size | 1 | 1. | 0.81 | 1.21 | 0.86 | 3.79 | 0. | 2.98 |
time (sec) |
N/A |
0.121 |
0.091 |
0.034 |
1.387 |
1.759 |
0. |
1.138 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 58 | 93 | 135 | 234 | 92 | 247 |
normalized size | 1 | 1. | 0.73 | 1.18 | 1.71 | 2.96 | 1.16 | 3.13 |
time (sec) |
N/A |
0.083 |
0.128 |
0.041 |
1.094 |
1.779 |
4.684 |
1.192 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 184 | 157 | 219 | 2429 | 0 | 224 |
normalized size | 1 | 1. | 1.15 | 0.98 | 1.37 | 15.18 | 0. | 1.4 |
time (sec) |
N/A |
0.138 |
0.305 |
0.07 |
1.828 |
1.895 |
0. |
1.239 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 33 | 28 | 84 | 116 | 44 | 76 |
normalized size | 1 | 1. | 1. | 0.85 | 2.55 | 3.52 | 1.33 | 2.3 |
time (sec) |
N/A |
0.033 |
0.014 |
0.006 |
1.055 |
1.783 |
1.409 |
1.226 |
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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 |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 136 | 86 | 123 | 369 | 0 | 128 |
normalized size | 1 | 1. | 1.09 | 0.69 | 0.98 | 2.95 | 0. | 1.02 |
time (sec) |
N/A |
0.072 |
0.137 |
0.036 |
1.641 |
1.8 |
0. |
1.264 |
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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 |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 49 | 55 | 68 | 231 | 0 | 68 |
normalized size | 1 | 1. | 0.89 | 1. | 1.24 | 4.2 | 0. | 1.24 |
time (sec) |
N/A |
0.094 |
0.034 |
0.038 |
1.322 |
1.643 |
0. |
1.279 |
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 204 | 149 | 138 | 2395 | 0 | 0 |
normalized size | 1 | 1. | 1.5 | 1.1 | 1.01 | 17.61 | 0. | 0. |
time (sec) |
N/A |
0.11 |
0.329 |
0.052 |
1.372 |
1.869 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 90 | 120 | 78 | 385 | 0 | 301 |
normalized size | 1 | 1. | 0.99 | 1.32 | 0.86 | 4.23 | 0. | 3.31 |
time (sec) |
N/A |
0.214 |
0.117 |
0.041 |
1.208 |
1.74 |
0. |
1.284 |
|
|
|
|
|
|
|
|
|
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|
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|
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|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 67 | 52 | 170 | 398 | 94 | 146 |
normalized size | 1 | 1. | 1. | 0.78 | 2.54 | 5.94 | 1.4 | 2.18 |
time (sec) |
N/A |
0.047 |
0.025 |
0.045 |
1.03 |
1.688 |
13.321 |
1.311 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.02 |
2.379 |
0.039 |
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 |
B |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 214 | 735 | 0 | 0 | 745 | 0 | 0 |
normalized size | 1 | 1. | 3.43 | 0. | 0. | 3.48 | 0. | 0. |
time (sec) |
N/A |
0.201 |
12.765 |
0.135 |
0. |
1.929 |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 152 | 0 | 0 | 512 | 0 | 0 |
normalized size |
1 |
1. |
1.13 |
0. |
0. |
3.79 |
0. |
0. |
time (sec) |
N/A |
0.148 |
0.615 |
0.092 |
0. |
1.833 |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 98 | 77 | 0 | 355 | 0 | 0 |
normalized size | 1 | 1. | 1.03 | 0.81 | 0. | 3.74 | 0. | 0. |
time (sec) |
N/A |
0.068 |
0.153 |
0.069 |
0. |
1.779 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.025 |
2.711 |
0.041 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
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 | 15 | 15 | 15 | 14 | 18 | 31 | 19 | 34 |
normalized size | 1 | 1. | 1. | 0.93 | 1.2 | 2.07 | 1.27 | 2.27 |
time (sec) |
N/A |
0.02 |
0.008 |
0.002 |
1.033 |
1.734 |
1.143 |
1.233 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 70 | 130 | 63 | 212 | 0 | 0 |
normalized size | 1 | 1. | 0.9 | 1.67 | 0.81 | 2.72 | 0. | 0. |
time (sec) |
N/A |
0.143 |
0.065 |
0.036 |
1.166 |
1.72 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 54 | 93 | 59 | 190 | 0 | 0 |
normalized size | 1 | 1. | 0.9 | 1.55 | 0.98 | 3.17 | 0. | 0. |
time (sec) |
N/A |
0.107 |
0.044 |
0.03 |
1.159 |
1.722 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 33 | 56 | 49 | 135 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.7 | 1.48 | 4.09 | 0. | 0. |
time (sec) |
N/A |
0.076 |
0.02 |
0.029 |
1.158 |
1.7 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 21 | 27 | 32 | 95 | 17 | 0 |
normalized size | 1 | 1. | 1. | 1.29 | 1.52 | 4.52 | 0.81 | 0. |
time (sec) |
N/A |
0.032 |
0.015 |
0.022 |
1.214 |
1.71 |
1.672 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
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 | 13 | 13 | 13 | 14 | 18 | 30 | 15 | 34 |
normalized size | 1 | 1. | 1. | 1.08 | 1.38 | 2.31 | 1.15 | 2.62 |
time (sec) |
N/A |
0.017 |
0.005 |
0.004 |
1.052 |
1.624 |
1.564 |
1.257 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 44 | 65 | 73 | 29 | 0 |
normalized size | 1 | 1. | 1. | 1.52 | 2.24 | 2.52 | 1. | 0. |
time (sec) |
N/A |
0.03 |
0.026 |
0.009 |
1.184 |
1.635 |
3.088 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 39 | 94 | 63 | 96 | 46 | 0 |
normalized size | 1 | 1. | 0.85 | 2.04 | 1.37 | 2.09 | 1. | 0. |
time (sec) |
N/A |
0.054 |
0.044 |
0.007 |
1.251 |
1.715 |
5.233 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 48 | 165 | 65 | 116 | 61 | 0 |
normalized size | 1 | 1. | 0.77 | 2.66 | 1.05 | 1.87 | 0.98 | 0. |
time (sec) |
N/A |
0.08 |
0.058 |
0.009 |
1.238 |
1.785 |
9.017 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 146 | 146 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.251 |
180.001 |
0.075 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 88 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.98 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.158 |
0.252 |
0.058 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 63 | 70 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.94 | 1.04 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.088 |
0.075 |
0.034 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
3.085 |
0.032 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 102 | 138 | 84 | 795 | 0 | 0 |
normalized size | 1 | 1. | 0.98 | 1.33 | 0.81 | 7.64 | 0. | 0. |
time (sec) |
N/A |
0.09 |
0.11 |
0.059 |
1.248 |
1.805 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 56 | 93 | 59 | 215 | 0 | 0 |
normalized size | 1 | 1. | 0.9 | 1.5 | 0.95 | 3.47 | 0. | 0. |
time (sec) |
N/A |
0.113 |
0.042 |
0.031 |
1.241 |
1.773 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 84 | 103 | 78 | 697 | 0 | 0 |
normalized size | 1 | 1. | 0.98 | 1.2 | 0.91 | 8.1 | 0. | 0. |
time (sec) |
N/A |
0.066 |
0.088 |
0.036 |
1.18 |
1.781 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 39 | 58 | 53 | 158 | 0 | 0 |
normalized size | 1 | 1. | 0.93 | 1.38 | 1.26 | 3.76 | 0. | 0. |
time (sec) |
N/A |
0.082 |
0.025 |
0.023 |
1.219 |
1.713 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 70 | 70 | 96 | 606 | 0 | 0 |
normalized size | 1 | 1. | 1.04 | 1.04 | 1.43 | 9.04 | 0. | 0. |
time (sec) |
N/A |
0.044 |
0.067 |
0.031 |
1.221 |
1.787 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 27 | 32 | 105 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.08 | 1.28 | 4.2 | 0. | 0. |
time (sec) |
N/A |
0.033 |
0.014 |
0.023 |
1.383 |
1.702 |
0. |
0. |
|
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Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 50 | 44 | 84 | 158 | 0 | 0 |
normalized size | 1 | 1. | 0.88 | 0.77 | 1.47 | 2.77 | 0. | 0. |
time (sec) |
N/A |
0.031 |
0.034 |
0.027 |
1.173 |
1.823 |
0. |
0. |
|
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Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
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|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 14 | 18 | 41 | 22 | 34 |
normalized size | 1 | 1. | 1. | 0.93 | 1.2 | 2.73 | 1.47 | 2.27 |
time (sec) |
N/A |
0.019 |
0.005 |
0.003 |
1.14 |
1.615 |
4.689 |
1.238 |
|
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Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 74 | 82 | 84 | 653 | 0 | 0 |
normalized size | 1 | 1. | 0.99 | 1.09 | 1.12 | 8.71 | 0. | 0. |
time (sec) |
N/A |
0.048 |
0.071 |
0.035 |
1.265 |
1.779 |
0. |
0. |
|
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Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 34 | 55 | 65 | 93 | 37 | 0 |
normalized size | 1 | 1. | 1. | 1.62 | 1.91 | 2.74 | 1.09 | 0. |
time (sec) |
N/A |
0.034 |
0.027 |
0.025 |
1.311 |
1.711 |
15.067 |
0. |
|
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Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 93 | 93 | 97 | 117 | 84 | 768 | 0 | 0 |
normalized size | 1 | 1. | 1.04 | 1.26 | 0.9 | 8.26 | 0. | 0. |
time (sec) |
N/A |
0.068 |
0.125 |
0.043 |
1.273 |
1.868 |
0. |
0. |
|
|
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Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 44 | 73 | 63 | 115 | 51 | 0 |
normalized size | 1 | 1. | 0.94 | 1.55 | 1.34 | 2.45 | 1.09 | 0. |
time (sec) |
N/A |
0.059 |
0.043 |
0.035 |
1.184 |
1.651 |
48.208 |
0. |
|
|
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Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 1039 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
5.36 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.221 |
24.272 |
0.074 |
0. |
0. |
0. |
0. |
|
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Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 122 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.04 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.166 |
0.8 |
0.059 |
0. |
0. |
0. |
0. |
|
|
|
|
|
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Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 84 | 77 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.97 | 0.89 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.087 |
0.139 |
0.034 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
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Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
3.133 |
0.034 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
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|
Problem 57 |
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 | 8 | 8 | 8 | 7 | 8 | 23 | 7 | 15 |
normalized size | 1 | 1. | 1. | 0.88 | 1. | 2.88 | 0.88 | 1.88 |
time (sec) |
N/A |
0.012 |
0.003 |
0.004 |
1.046 |
1.844 |
0.389 |
1.165 |
|
|
|
|
|
|
|
|
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|
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|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 88 | 77 | 99 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.17 | 1.03 | 1.32 | 0. | 0. | 0. |
time (sec) |
N/A |
0.074 |
0.095 |
0.09 |
1.21 |
0. |
0. |
0. |
|
|
|
|
|
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Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 88 | 69 | 99 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.17 | 0.92 | 1.32 | 0. | 0. | 0. |
time (sec) |
N/A |
0.041 |
0.081 |
0.065 |
1.215 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 79 | 74 | 82 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.18 | 1.1 | 1.22 | 0. | 0. | 0. |
time (sec) |
N/A |
0.017 |
0.08 |
0.052 |
1.172 |
0. |
0. |
0. |
|
|
|
|
|
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Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 23 | 33 | 41 | 178 | 0 | 0 |
normalized size | 1 | 1. | 0.92 | 1.32 | 1.64 | 7.12 | 0. | 0. |
time (sec) |
N/A |
0.037 |
0.021 |
0.014 |
1.235 |
1.878 |
0. |
0. |
|
|
|
|
|
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|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 68 | 77 | 88 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.96 | 1.08 | 1.24 | 0. | 0. | 0. |
time (sec) |
N/A |
0.063 |
0.067 |
0.077 |
1.198 |
0. |
0. |
0. |
|
|
|
|
|
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|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 72 | 77 | 93 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.96 | 1.03 | 1.24 | 0. | 0. | 0. |
time (sec) |
N/A |
0.062 |
0.072 |
0.039 |
1.199 |
0. |
0. |
0. |
|
|
|
|
|
|
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|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 89 | 0 | 111 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.9 | 0. | 1.12 | 0. | 0. | 0. |
time (sec) |
N/A |
0.137 |
1.435 |
0.07 |
1.224 |
0. |
0. |
0. |
|
|
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|
|
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|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 85 | 0 | 111 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.86 | 0. | 1.12 | 0. | 0. | 0. |
time (sec) |
N/A |
0.107 |
1.245 |
0.098 |
1.186 |
0. |
0. |
0. |
|
|
|
|
|
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|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 81 | 0 | 92 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.91 | 0. | 1.03 | 0. | 0. | 0. |
time (sec) |
N/A |
0.065 |
1.075 |
0.066 |
1.163 |
0. |
0. |
0. |
|
|
|
|
|
|
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|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 39 | 40 | 50 | 217 | 0 | 0 |
normalized size | 1 | 1. | 0.91 | 0.93 | 1.16 | 5.05 | 0. | 0. |
time (sec) |
N/A |
0.064 |
0.03 |
0.079 |
1.18 |
1.871 |
0. |
0. |
|
|
|
|
|
|
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|
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|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 79 | 0 | 100 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.87 | 0. | 1.1 | 0. | 0. | 0. |
time (sec) |
N/A |
0.128 |
1.375 |
0.062 |
1.218 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 161 | 0 | 201 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.97 | 0. | 1.21 | 0. | 0. | 0. |
time (sec) |
N/A |
0.195 |
1.534 |
0.083 |
1.341 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 161 | 0 | 201 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.97 | 0. | 1.21 | 0. | 0. | 0. |
time (sec) |
N/A |
0.133 |
1.556 |
0.072 |
1.271 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 140 | 0 | 169 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.93 | 0. | 1.13 | 0. | 0. | 0. |
time (sec) |
N/A |
0.076 |
1.203 |
0.088 |
1.252 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 52 | 67 | 84 | 374 | 0 | 0 |
normalized size | 1 | 1. | 0.78 | 1. | 1.25 | 5.58 | 0. | 0. |
time (sec) |
N/A |
0.1 |
0.05 |
0.109 |
1.25 |
1.88 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 154 | 126 | 0 | 180 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.82 | 0. | 1.17 | 0. | 0. | 0. |
time (sec) |
N/A |
0.182 |
1.33 |
0.074 |
1.302 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.021 |
5.239 |
0.778 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.025 |
8.061 |
0.661 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 93 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.99 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.104 |
0.138 |
0.838 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.051 |
5.787 |
0.753 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 167 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.11 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.199 |
0.409 |
0.701 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.06 |
8.352 |
0.674 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 220 | 185 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.84 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.234 |
2.047 |
0.24 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 117 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.82 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.174 |
1.907 |
0.207 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 102 | 115 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.03 | 1.16 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.071 |
0.17 |
0.22 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.038 |
24.333 |
0.13 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 46 | 74 | 46 | 462 | 0 | 0 |
normalized size |
1 |
1. |
1.02 |
1.64 |
1.02 |
10.27 |
0. |
0. |
time (sec) |
N/A |
0.093 |
0.059 |
0.036 |
1.335 |
1.89 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 54 | 90 | 0 | 567 | 0 | 0 |
normalized size |
1 |
1. |
0.81 |
1.34 |
0. |
8.46 |
0. |
0. |
time (sec) |
N/A |
0.123 |
0.131 |
0.073 |
0. |
1.894 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 95 | 152 | 95 | 986 | 0 | 0 |
normalized size |
1 |
1. |
0.84 |
1.35 |
0.84 |
8.73 |
0. |
0. |
time (sec) |
N/A |
0.217 |
0.201 |
0.087 |
1.336 |
1.893 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 60 | 54 | 93 | 333 | 0 | 0 |
normalized size | 1 | 1. | 0.85 | 0.76 | 1.31 | 4.69 | 0. | 0. |
time (sec) |
N/A |
0.045 |
1.502 |
0.057 |
1.315 |
1.95 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 63 | 136 | 1192 | 383 | 0 | 185 |
normalized size | 1 | 1. | 0.56 | 1.2 | 10.55 | 3.39 | 0. | 1.64 |
time (sec) |
N/A |
0.096 |
0.128 |
0.049 |
1.817 |
1.892 |
0. |
1.283 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
B |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 44 | 66 | 948 | 317 | 0 | 134 |
normalized size | 1 | 1. | 0.81 | 1.22 | 17.56 | 5.87 | 0. | 2.48 |
time (sec) |
N/A |
0.053 |
0.027 |
0.029 |
1.675 |
1.887 |
0. |
1.155 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 27 | 36 | 695 | 144 | 0 | 53 |
normalized size | 1 | 1. | 0.73 | 0.97 | 18.78 | 3.89 | 0. | 1.43 |
time (sec) |
N/A |
0.017 |
0.005 |
0.028 |
1.611 |
1.801 |
0. |
1.255 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.036 |
9.856 |
0.036 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.039 |
13.156 |
0.044 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 346 | 346 | 104 | 831 | 656 | 251 | 269 | 2072 |
normalized size | 1 | 1. | 0.3 | 2.4 | 1.9 | 0.73 | 0.78 | 5.99 |
time (sec) |
N/A |
0.418 |
1.296 |
0.01 |
1.095 |
2.091 |
2.444 |
1.906 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 72 | 303 | 396 | 169 | 151 | 780 |
normalized size | 1 | 1. | 0.43 | 1.81 | 2.37 | 1.01 | 0.9 | 4.67 |
time (sec) |
N/A |
0.186 |
0.199 |
0.01 |
1.22 |
2.036 |
0.771 |
1.575 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 50 | 63 | 150 | 112 | 65 | 281 |
normalized size | 1 | 1. | 0.93 | 1.17 | 2.78 | 2.07 | 1.2 | 5.2 |
time (sec) |
N/A |
0.046 |
0.063 |
0.007 |
1.148 |
2.037 |
0.628 |
1.324 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 130 | 0 | 0 | 547 | 0 | 0 |
normalized size | 1 | 1. | 1.05 | 0. | 0. | 4.41 | 0. | 0. |
time (sec) |
N/A |
0.287 |
0.964 |
0.016 |
0. |
2.156 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 182 | 182 | 199 | 0 | 0 | 757 | 0 | 0 |
normalized size |
1 |
1. |
1.09 |
0. |
0. |
4.16 |
0. |
0. |
time (sec) |
N/A |
0.361 |
3.042 |
0.016 |
0. |
2.147 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 537 | 537 | 378 | 1815 | 867 | 467 | 0 | 2919 |
normalized size | 1 | 1. | 0.7 | 3.38 | 1.61 | 0.87 | 0. | 5.44 |
time (sec) |
N/A |
0.697 |
2.874 |
0.01 |
1.183 |
2.058 |
0. |
3.707 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 261 | 261 | 118 | 659 | 501 | 294 | 0 | 953 |
normalized size | 1 | 1. | 0.45 | 2.52 | 1.92 | 1.13 | 0. | 3.65 |
time (sec) |
N/A |
0.315 |
0.344 |
0.007 |
1.23 |
2.09 |
0. |
2.256 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
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 | 85 | 85 | 65 | 133 | 185 | 159 | 94 | 173 |
normalized size | 1 | 1. | 0.76 | 1.56 | 2.18 | 1.87 | 1.11 | 2.04 |
time (sec) |
N/A |
0.079 |
0.082 |
0.007 |
1.156 |
2.055 |
1.738 |
1.687 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 232 | 232 | 233 | 0 | 0 | 1539 | 0 | 0 |
normalized size | 1 | 1. | 1. | 0. | 0. | 6.63 | 0. | 0. |
time (sec) |
N/A |
0.519 |
0.068 |
0.016 |
0. |
2.422 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 329 | 329 | 210 | 0 | 0 | 2032 | 0 | 0 |
normalized size |
1 |
1. |
0.64 |
0. |
0. |
6.18 |
0. |
0. |
time (sec) |
N/A |
0.724 |
1.836 |
0.015 |
0. |
2.5 |
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 [88] had the largest ratio of [ 0.75
]
|
|
|
|
|
|
|
| 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. |
12 |
0.25 |
|
|
|
|
|
|
|
2 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
3 |
A |
2 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
4 |
A |
3 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
5 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
6 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
7 |
A |
5 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
8 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
9 |
A |
6 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
10 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
11 |
A |
5 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
12 |
A |
5 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
13 |
A |
6 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
14 |
A |
7 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
15 |
A |
4 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
16 |
A |
10 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
17 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
18 |
A |
8 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
19 |
A |
8 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
20 |
A |
9 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
|
21 |
A |
12 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
22 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
23 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
24 |
A |
8 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
25 |
A |
5 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
26 |
A |
3 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
27 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
28 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
29 |
A |
7 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
30 |
A |
6 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
31 |
A |
5 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
32 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
33 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
34 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
35 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
36 |
A |
5 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
37 |
A |
9 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
38 |
A |
6 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
39 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
40 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
41 |
A |
7 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
42 |
A |
6 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
43 |
A |
6 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
44 |
A |
5 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
45 |
A |
5 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
46 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
47 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
48 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
49 |
A |
5 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
50 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
51 |
A |
6 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
52 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
53 |
A |
9 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
54 |
A |
6 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
55 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
56 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
57 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
58 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
59 |
A |
3 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
60 |
A |
3 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
|
61 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
62 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
63 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
64 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
65 |
A |
5 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
66 |
A |
5 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
67 |
A |
5 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
68 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
69 |
A |
8 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
70 |
A |
8 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
71 |
A |
8 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
72 |
A |
8 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
73 |
A |
8 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
74 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
75 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
76 |
A |
3 |
3 |
1. |
20 |
0.15 |
|
|
|
|
|
|
|
77 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
78 |
A |
5 |
5 |
1. |
22 |
0.227 |
|
|
|
|
|
|
|
79 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
80 |
A |
8 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
|
81 |
A |
5 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
82 |
A |
3 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
83 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
84 |
A |
5 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
85 |
A |
7 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
86 |
A |
12 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
87 |
A |
4 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
88 |
A |
12 |
9 |
1. |
12 |
0.75 |
|
|
|
|
|
|
|
89 |
A |
8 |
7 |
1. |
10 |
0.7 |
|
|
|
|
|
|
|
90 |
A |
4 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
91 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
92 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
93 |
A |
16 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
94 |
A |
10 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
95 |
A |
4 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
96 |
A |
10 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
97 |
A |
11 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
98 |
A |
23 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
99 |
A |
13 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
100 |
A |
5 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
|
101 |
A |
13 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
102 |
A |
14 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|