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
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 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, 75, 76, 78, 81
}
B grade: { 18, 79, 82 }
C grade: { }
F grade: { 74, 77, 80, 83 }
2.1.3 Maple
A grade: { 2, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 24, 26, 27, 28, 29, 30, 34, 35, 39, 40, 44, 45,
49, 50, 53, 54, 55, 58, 59, 60, 63, 64, 65, 68, 69, 70, 71 }
B grade: { }
C grade: { 72, 73, 75, 76, 78, 79, 81, 82 }
F grade: { 1, 3, 8, 10, 16, 18, 23, 25, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 61, 62, 66,
67, 74, 77, 80, 83 }
2.1.4 Maxima
A grade: { 2, 4, 5, 6, 7, 13, 22, 34, 39, 40, 53, 58, 59, 71 }
B grade: { 12, 15, 20, 27, 31, 32, 33, 36, 37, 38, 51, 52, 56, 57 }
C grade: { }
F grade: { 1, 3, 8, 9, 10, 11, 14, 16, 17, 18, 19, 21, 23, 24, 25, 26, 28, 29, 30, 35, 41, 42, 43, 44, 45, 46, 47,
48, 49, 50, 54, 55, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83
}
2.1.5 FriCAS
A grade: { 2, 4, 5, 6, 7, 9, 11, 13, 14, 15, 17, 19, 20, 21, 22, 24, 26, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50,
53, 54, 55, 59, 60, 63, 64, 65, 69, 70, 71, 72, 75, 78, 81 }
B grade: { 3, 10, 12, 18, 25, 27, 58, 68, 73, 76, 79, 82 }
C grade: { 1, 8, 16, 23, 74, 77, 80, 83 }
F grade: { 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 61, 62, 66, 67 }
2.1.6 Sympy
A grade: { 2, 4, 5, 6, 7, 9, 11, 13, 14, 17, 19, 21, 22, 24, 26, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50, 53, 54,
55, 58, 59, 60, 64, 65, 69, 70, 71 }
B grade: { }
C grade: { }
F grade: { 1, 3, 8, 10, 12, 15, 16, 18, 20, 23, 25, 27, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56,
57, 61, 62, 63, 66, 67, 68, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83 }
2.1.7 Giac
A grade: { 2, 4, 6, 7, 9, 11, 13, 14, 15, 17, 19, 21, 22, 24, 26, 27, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50,
54, 55, 59, 60, 64, 65, 68, 69, 70, 71 }
B grade: { 5, 12, 20, 53, 58, 63 }
C grade: { }
F grade: { 1, 3, 8, 10, 16, 18, 23, 25, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 61, 62, 66,
67, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83 }
2.1.8 Mupad
A grade: { 2, 4, 6, 7, 9, 11, 13, 14, 17, 19, 21, 22, 24, 26, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50, 54, 55,
59, 60, 64, 65, 69, 70, 71 }
B grade: { 5, 12, 15, 20, 27, 53, 58, 63, 68, 72, 75, 78, 81 }
C grade: { }
F grade: { 1, 3, 8, 10, 16, 18, 23, 25, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 61, 62, 66,
67, 73, 74, 76, 77, 79, 80, 82, 83 }
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 |
Mupad |
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grade |
A |
A |
A |
F |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 146 | 0 | 0 | 495 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.02 | 0.00 | 0.00 | 3.46 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.162 |
0.048 |
0.744 |
0.000 |
1.189 |
0.000 |
0.000 |
0.000 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.015 |
0.958 |
0.742 |
0.000 |
0.644 |
0.000 |
0.000 |
0.000 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 92 | 92 | 95 | 0 | 0 | 346 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 0.00 | 0.00 | 3.76 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.088 |
0.025 |
0.742 |
0.000 |
0.787 |
0.000 |
0.000 |
0.000 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.015 |
0.771 |
0.752 |
0.000 |
0.792 |
0.000 |
0.000 |
0.000 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 26 | 39 | 31 | 42 | 42 | 50 | 67 |
normalized size | 1 | 1.00 | 1.00 | 1.50 | 1.19 | 1.62 | 1.62 | 1.92 | 2.58 |
time (sec) |
N/A |
0.023 |
0.014 |
0.201 |
0.311 |
0.746 |
2.869 |
0.546 |
0.581 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.016 |
0.766 |
0.758 |
0.000 |
0.697 |
0.000 |
0.000 |
0.000 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.016 |
0.739 |
0.704 |
0.000 |
0.769 |
0.000 |
0.000 |
0.000 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 242 | 242 | 229 | 0 | 0 | 795 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 0.00 | 0.00 | 3.29 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.370 |
0.610 |
1.100 |
0.000 |
0.751 |
0.000 |
0.000 |
0.000 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.023 |
9.611 |
1.134 |
0.000 |
0.572 |
0.000 |
0.000 |
0.000 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F(-1) |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 123 | 0 | 0 | 525 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.92 | 0.00 | 0.00 | 3.95 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.164 |
0.465 |
1.288 |
0.000 |
0.870 |
0.000 |
0.000 |
0.000 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.024 |
7.907 |
0.979 |
0.000 |
0.617 |
0.000 |
0.000 |
0.000 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 44 | 44 | 41 | 59 | 96 | 91 | 0 | 88 | 100 |
normalized size | 1 | 1.00 | 0.93 | 1.34 | 2.18 | 2.07 | 0.00 | 2.00 | 2.27 |
time (sec) |
N/A |
0.052 |
0.213 |
0.524 |
0.820 |
0.664 |
0.000 |
0.859 |
1.497 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.022 |
17.858 |
1.155 |
0.000 |
0.532 |
0.000 |
0.000 |
0.000 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.022 |
9.318 |
1.122 |
0.000 |
1.367 |
0.000 |
0.000 |
0.000 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 62 | 92 | 2838 | 100 | 0 | 85 | 496 |
normalized size | 1 | 1.00 | 0.69 | 1.02 | 31.53 | 1.11 | 0.00 | 0.94 | 5.51 |
time (sec) |
N/A |
0.073 |
0.210 |
0.553 |
1.421 |
0.656 |
0.000 |
0.336 |
12.531 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 382 | 382 | 472 | 0 | 0 | 1457 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.24 | 0.00 | 0.00 | 3.81 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.878 |
1.119 |
0.846 |
0.000 |
0.948 |
0.000 |
0.000 |
0.000 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.026 |
1.404 |
0.798 |
0.000 |
0.576 |
0.000 |
0.000 |
0.000 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
F |
F(-2) |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 261 | 261 | 845 | 0 | 0 | 1063 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.24 | 0.00 | 0.00 | 4.07 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.540 |
1.397 |
0.825 |
0.000 |
1.097 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.025 |
1.169 |
0.831 |
0.000 |
0.668 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 67 | 70 | 7945 | 251 | 0 | 278 | 157 |
normalized size | 1 | 1.00 | 1.02 | 1.06 | 120.38 | 3.80 | 0.00 | 4.21 | 2.38 |
time (sec) |
N/A |
0.109 |
0.179 |
0.543 |
63.895 |
0.754 |
0.000 |
0.500 |
2.239 |
|
|
|
|
|
|
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|
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|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.025 |
0.975 |
0.701 |
0.000 |
0.606 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.014 |
0.151 |
0.030 |
0.000 |
0.586 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1092 | 1092 | 895 | 0 | 0 | 3048 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.82 | 0.00 | 0.00 | 2.79 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.288 |
6.578 |
1.673 |
0.000 |
1.069 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.024 |
6.880 |
1.413 |
0.000 |
0.623 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 596 | 596 | 1069 | 0 | 0 | 1928 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.79 | 0.00 | 0.00 | 3.23 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.204 |
9.033 |
1.535 |
0.000 |
1.011 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.024 |
5.802 |
1.128 |
0.000 |
0.609 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 153 | 214 | 8871 | 525 | 0 | 195 | 340 |
normalized size | 1 | 1.00 | 1.24 | 1.74 | 72.12 | 4.27 | 0.00 | 1.59 | 2.76 |
time (sec) |
N/A |
0.254 |
0.689 |
0.529 |
66.778 |
2.060 |
0.000 |
0.541 |
5.013 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.024 |
11.296 |
1.311 |
0.000 |
0.672 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.024 |
7.373 |
1.465 |
0.000 |
0.994 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.024 |
7.815 |
1.635 |
0.000 |
0.841 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 476 | 476 | 479 | 0 | 1512 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 0.00 | 3.18 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.457 |
0.147 |
1.289 |
1.070 |
2.106 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 348 | 348 | 351 | 0 | 966 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 0.00 | 2.78 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.311 |
0.084 |
1.165 |
1.006 |
0.591 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 220 | 223 | 0 | 540 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 0.00 | 2.45 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.186 |
0.063 |
1.151 |
0.895 |
0.820 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.017 |
2.063 |
1.349 |
0.000 |
0.750 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.018 |
2.199 |
1.337 |
0.000 |
0.477 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 749 | 749 | 739 | 0 | 6373 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 0.00 | 8.51 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.860 |
2.198 |
1.385 |
1.623 |
0.583 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 551 | 551 | 543 | 0 | 3898 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 0.00 | 7.07 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.634 |
1.257 |
1.384 |
1.427 |
0.618 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 355 | 355 | 347 | 0 | 2006 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 0.00 | 5.65 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.451 |
0.708 |
1.378 |
0.920 |
0.903 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.023 |
40.078 |
1.402 |
0.000 |
0.754 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.023 |
21.034 |
1.398 |
0.000 |
0.739 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1041 | 1041 | 1122 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.476 |
2.667 |
1.134 |
0.000 |
1.038 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 781 | 781 | 858 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.180 |
2.129 |
1.128 |
0.000 |
0.847 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 521 | 521 | 632 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.966 |
20.442 |
1.358 |
0.000 |
0.587 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.025 |
2.013 |
1.234 |
0.000 |
0.723 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.015 |
0.390 |
0.026 |
0.000 |
0.539 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 3123 | 3123 | 3702 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
4.118 |
14.878 |
1.374 |
0.000 |
0.838 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2323 | 2323 | 2777 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.228 |
13.262 |
1.296 |
0.000 |
0.755 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1523 | 1523 | 1767 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.504 |
15.938 |
1.306 |
0.000 |
0.626 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.026 |
44.417 |
1.303 |
0.000 |
1.387 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.025 |
31.565 |
1.281 |
0.000 |
0.821 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 284 | 284 | 281 | 0 | 738 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 0.00 | 2.60 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.248 |
0.254 |
1.204 |
0.972 |
0.595 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 158 | 158 | 155 | 0 | 374 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 0.00 | 2.37 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.132 |
0.135 |
1.181 |
0.981 |
0.712 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 26 | 32 | 31 | 41 | 56 | 50 | 71 |
normalized size | 1 | 1.00 | 1.00 | 1.23 | 1.19 | 1.58 | 2.15 | 1.92 | 2.73 |
time (sec) |
N/A |
0.021 |
0.083 |
0.264 |
0.372 |
0.663 |
4.742 |
0.848 |
2.943 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.014 |
2.899 |
1.381 |
0.000 |
0.590 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.014 |
2.833 |
1.456 |
0.000 |
0.553 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 451 | 451 | 443 | 0 | 2876 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 0.00 | 6.38 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.537 |
1.583 |
1.287 |
0.866 |
0.530 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 255 | 255 | 247 | 0 | 1279 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.00 | 5.02 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.325 |
0.823 |
1.289 |
0.998 |
0.736 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 45 | 60 | 50 | 91 | 88 | 88 | 109 |
normalized size | 1 | 1.00 | 0.96 | 1.28 | 1.06 | 1.94 | 1.87 | 1.87 | 2.32 |
time (sec) |
N/A |
0.052 |
0.279 |
0.758 |
0.529 |
0.786 |
9.752 |
0.747 |
2.683 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.022 |
23.126 |
1.290 |
0.000 |
0.518 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.023 |
23.811 |
1.315 |
0.000 |
0.702 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 653 | 653 | 725 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.049 |
2.492 |
1.071 |
0.000 |
0.535 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 393 | 393 | 486 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.826 |
6.700 |
1.011 |
0.000 |
0.617 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 69 | 71 | 0 | 274 | 0 | 278 | 153 |
normalized size | 1 | 1.00 | 1.01 | 1.04 | 0.00 | 4.03 | 0.00 | 4.09 | 2.25 |
time (sec) |
N/A |
0.082 |
0.263 |
0.706 |
0.000 |
0.548 |
0.000 |
0.537 |
2.746 |
|
|
|
|
|
|
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|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.025 |
4.399 |
1.000 |
0.000 |
0.662 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.024 |
3.955 |
0.987 |
0.000 |
0.494 |
0.000 |
0.000 |
0.000 |
|
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Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1925 | 1925 | 2254 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.858 |
13.833 |
1.332 |
0.000 |
0.616 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1125 | 1125 | 1210 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.106 |
9.439 |
1.159 |
0.000 |
0.551 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 163 | 216 | 0 | 574 | 0 | 196 | 330 |
normalized size | 1 | 1.00 | 1.28 | 1.70 | 0.00 | 4.52 | 0.00 | 1.54 | 2.60 |
time (sec) |
N/A |
0.199 |
0.793 |
0.852 |
0.000 |
0.581 |
0.000 |
0.736 |
5.251 |
|
|
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Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.023 |
29.076 |
1.308 |
0.000 |
0.513 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.023 |
29.211 |
1.237 |
0.000 |
0.575 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.048 |
3.087 |
1.509 |
0.000 |
0.745 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 44 | 44 | 38 | 159 | 0 | 60 | 0 | 0 | 104 |
normalized size | 1 | 1.00 | 0.86 | 3.61 | 0.00 | 1.36 | 0.00 | 0.00 | 2.36 |
time (sec) |
N/A |
0.047 |
0.116 |
1.584 |
0.000 |
0.754 |
0.000 |
0.000 |
2.656 |
|
|
|
|
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|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 188 | 873 | 0 | 470 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.26 | 5.86 | 0.00 | 3.15 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.114 |
0.646 |
1.867 |
0.000 |
1.484 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 235 | 235 | 0 | 0 | 0 | 655 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 2.79 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.190 |
1.324 |
2.273 |
0.000 |
0.826 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
|
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|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-1) |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 54 | 276 | 0 | 113 | 0 | 0 | 180 |
normalized size | 1 | 1.00 | 0.68 | 3.49 | 0.00 | 1.43 | 0.00 | 0.00 | 2.28 |
time (sec) |
N/A |
0.090 |
0.417 |
1.191 |
0.000 |
0.581 |
0.000 |
0.000 |
2.710 |
|
|
|
|
|
|
|
|
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|
|
|
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|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 221 | 347 | 1096 | 0 | 656 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.57 | 4.96 | 0.00 | 2.97 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.200 |
5.162 |
1.202 |
0.000 |
0.936 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 390 | 390 | 0 | 0 | 0 | 1028 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 2.64 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.396 |
11.662 |
3.020 |
0.000 |
1.277 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-1) |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 80 | 314 | 0 | 300 | 0 | 0 | 223 |
normalized size | 1 | 1.00 | 0.92 | 3.61 | 0.00 | 3.45 | 0.00 | 0.00 | 2.56 |
time (sec) |
N/A |
0.147 |
0.288 |
1.071 |
0.000 |
0.638 |
0.000 |
0.000 |
2.753 |
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
C |
F(-1) |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 328 | 328 | 861 | 1308 | 0 | 1291 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.62 | 3.99 | 0.00 | 3.94 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.595 |
1.947 |
1.522 |
0.000 |
0.707 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 485 | 485 | 0 | 0 | 0 | 1733 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 3.57 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.923 |
1.837 |
1.951 |
0.000 |
2.327 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-1) |
A |
F(-1) |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 191 | 704 | 0 | 628 | 0 | 0 | 461 |
normalized size | 1 | 1.00 | 1.22 | 4.48 | 0.00 | 4.00 | 0.00 | 0.00 | 2.94 |
time (sec) |
N/A |
0.287 |
0.932 |
1.330 |
0.000 |
0.663 |
0.000 |
0.000 |
5.331 |
|
|
|
|
|
|
|
|
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|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
C |
F(-1) |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 757 | 757 | 2450 | 2817 | 0 | 2531 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.24 | 3.72 | 0.00 | 3.34 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.273 |
10.473 |
1.142 |
0.000 |
1.096 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1384 | 1384 | 0 | 0 | 0 | 3855 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 2.79 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.367 |
11.748 |
2.933 |
0.000 |
1.314 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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 [23] had the largest ratio of
[.6667]
|
|
|
|
|
|
|
| Table 2.1:Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
10 |
6 |
1.00 |
16 |
0.375 |
|
|
|
|
|
|
|
2 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
3 |
A |
8 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
4 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
5 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
6 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
7 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
8 |
A |
15 |
11 |
1.00 |
18 |
0.611 |
|
|
|
|
|
|
|
9 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
10 |
A |
10 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
11 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
12 |
A |
5 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
13 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
14 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
15 |
A |
5 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
16 |
A |
13 |
8 |
1.00 |
18 |
0.444 |
|
|
|
|
|
|
|
17 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
18 |
A |
11 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
19 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
20 |
A |
4 |
4 |
1.00 |
16 |
0.250 |
|
|
|
|
|
|
|
21 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
22 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
23 |
A |
31 |
12 |
1.00 |
18 |
0.667 |
|
|
|
|
|
|
|
24 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
25 |
A |
22 |
10 |
1.00 |
18 |
0.556 |
|
|
|
|
|
|
|
26 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
27 |
A |
6 |
6 |
1.00 |
16 |
0.375 |
|
|
|
|
|
|
|
28 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
29 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
30 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
31 |
A |
20 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
32 |
A |
16 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
33 |
A |
12 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
34 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
35 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
36 |
A |
30 |
10 |
1.00 |
20 |
0.500 |
|
|
|
|
|
|
|
37 |
A |
24 |
10 |
1.00 |
20 |
0.500 |
|
|
|
|
|
|
|
38 |
A |
18 |
10 |
1.00 |
18 |
0.556 |
|
|
|
|
|
|
|
39 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
40 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
41 |
A |
23 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
42 |
A |
19 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
43 |
A |
15 |
9 |
1.00 |
18 |
0.500 |
|
|
|
|
|
|
|
44 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
45 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
46 |
A |
61 |
11 |
1.00 |
20 |
0.550 |
|
|
|
|
|
|
|
47 |
A |
49 |
11 |
1.00 |
20 |
0.550 |
|
|
|
|
|
|
|
48 |
A |
37 |
11 |
1.00 |
18 |
0.611 |
|
|
|
|
|
|
|
49 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
50 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
51 |
A |
14 |
7 |
1.00 |
20 |
0.350 |
|
|
|
|
|
|
|
52 |
A |
10 |
6 |
1.00 |
20 |
0.300 |
|
|
|
|
|
|
|
53 |
A |
4 |
3 |
1.00 |
20 |
0.150 |
|
|
|
|
|
|
|
54 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
55 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
56 |
A |
21 |
10 |
1.00 |
22 |
0.454 |
|
|
|
|
|
|
|
57 |
A |
15 |
11 |
1.00 |
22 |
0.500 |
|
|
|
|
|
|
|
58 |
A |
5 |
5 |
1.00 |
22 |
0.227 |
|
|
|
|
|
|
|
59 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
60 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
61 |
A |
17 |
9 |
1.00 |
22 |
0.409 |
|
|
|
|
|
|
|
62 |
A |
13 |
8 |
1.00 |
22 |
0.364 |
|
|
|
|
|
|
|
63 |
A |
4 |
4 |
1.00 |
22 |
0.182 |
|
|
|
|
|
|
|
64 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
65 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
66 |
A |
43 |
11 |
1.00 |
22 |
0.500 |
|
|
|
|
|
|
|
67 |
A |
31 |
12 |
1.00 |
22 |
0.546 |
|
|
|
|
|
|
|
68 |
A |
6 |
6 |
1.00 |
22 |
0.273 |
|
|
|
|
|
|
|
69 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
70 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
71 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
72 |
A |
5 |
4 |
1.00 |
20 |
0.200 |
|
|
|
|
|
|
|
73 |
A |
9 |
6 |
1.00 |
22 |
0.273 |
|
|
|
|
|
|
|
74 |
A |
11 |
7 |
1.00 |
22 |
0.318 |
|
|
|
|
|
|
|
75 |
A |
6 |
6 |
1.00 |
22 |
0.273 |
|
|
|
|
|
|
|
76 |
A |
11 |
8 |
1.00 |
24 |
0.333 |
|
|
|
|
|
|
|
77 |
A |
16 |
12 |
1.00 |
24 |
0.500 |
|
|
|
|
|
|
|
78 |
A |
5 |
5 |
1.00 |
22 |
0.227 |
|
|
|
|
|
|
|
79 |
A |
12 |
8 |
1.00 |
24 |
0.333 |
|
|
|
|
|
|
|
80 |
A |
14 |
9 |
1.00 |
24 |
0.375 |
|
|
|
|
|
|
|
81 |
A |
7 |
7 |
1.00 |
22 |
0.318 |
|
|
|
|
|
|
|
82 |
A |
23 |
11 |
1.00 |
24 |
0.458 |
|
|
|
|
|
|
|
83 |
A |
32 |
13 |
1.00 |
24 |
0.542 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|