Chapter 2
detailed summary tables of results
2.1 List of integrals sorted by grade for each CAS
2.1.1 Rubi
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83,
84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 8, 10, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 90, 91, 92, 96, 97, 98,
101, 102, 103, 104, 105, 106 }
B grade: { 1, 95 }
C grade: { 2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 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, 93, 94, 99, 100 }
F grade: { 89 }
2.1.3 Maple
A grade: { 8, 9, 10, 11, 12, 13, 14, 29, 30, 31, 32, 33, 34, 51, 52, 54, 55, 69, 70, 71, 72, 73, 74
}
B grade: { 2, 3, 4, 5, 6, 7, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 35, 36, 37, 38, 39, 40, 41, 42,
43, 44, 45, 46, 47, 48, 49, 50, 53, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 75, 76, 77, 78, 79, 80, 81,
82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
}
C grade: { }
F grade: { 1, 88, 89 }
2.1.4 Maxima
A grade: { 2, 3, 4, 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, 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, 92, 93, 94
}
B grade: { 5 }
C grade: { }
F grade: { 1, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 88, 89, 90, 91, 95, 96, 97, 98, 99, 100, 101, 102, 103,
104, 105, 106 }
2.1.5 FriCAS
A grade: { 2, 4, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 35, 36, 37, 38, 40, 92 }
B grade: { 3, 5, 6, 7, 27, 39, 90, 91, 93, 94 }
C grade: { }
F grade: { 1, 8, 9, 10, 11, 12, 13, 14, 29, 30, 31, 32, 33, 34, 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, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
}
2.1.6 Sympy
A grade: { 92, 93 }
B grade: { }
C grade: { }
F 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, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
}
2.1.7 Giac
A grade: { 92 }
B grade: { 93, 94 }
C grade: { }
F 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, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
}
2.1.8 Mupad
A grade: { }
B grade: { 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, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
}
C grade: { }
F grade: { 1, 88, 89 }
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 |
B |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 117 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.028 |
0.322 |
2.502 |
0.000 |
0.861 |
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 |
A |
A |
C |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 68 | 388 | 149 | 377 | 0 | 0 | 144 |
normalized size | 1 | 1.00 | 0.59 | 3.34 | 1.28 | 3.25 | 0.00 | 0.00 | 1.24 |
time (sec) |
N/A |
0.157 |
0.187 |
0.495 |
0.760 |
0.902 |
0.000 |
0.000 |
1.978 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
A |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 67 | 363 | 124 | 334 | 0 | 0 | 98 |
normalized size | 1 | 1.00 | 0.71 | 3.86 | 1.32 | 3.55 | 0.00 | 0.00 | 1.04 |
time (sec) |
N/A |
0.116 |
0.112 |
0.427 |
0.616 |
0.750 |
0.000 |
0.000 |
1.161 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 154 | 337 | 108 | 236 | 0 | 0 | 128 |
normalized size | 1 | 1.00 | 2.17 | 4.75 | 1.52 | 3.32 | 0.00 | 0.00 | 1.80 |
time (sec) |
N/A |
0.078 |
0.289 |
0.431 |
0.896 |
0.650 |
0.000 |
0.000 |
0.777 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
B |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 165 | 327 | 83 | 172 | 0 | 0 | 65 |
normalized size | 1 | 1.00 | 3.37 | 6.67 | 1.69 | 3.51 | 0.00 | 0.00 | 1.33 |
time (sec) |
N/A |
0.044 |
0.217 |
0.430 |
0.692 |
0.601 |
0.000 |
0.000 |
0.728 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
A |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 191 | 355 | 111 | 321 | 0 | 0 | 84 |
normalized size | 1 | 1.00 | 2.55 | 4.73 | 1.48 | 4.28 | 0.00 | 0.00 | 1.12 |
time (sec) |
N/A |
0.086 |
0.259 |
0.359 |
0.719 |
0.533 |
0.000 |
0.000 |
0.960 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
A |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 203 | 374 | 123 | 358 | 0 | 0 | 103 |
normalized size | 1 | 1.00 | 2.05 | 3.78 | 1.24 | 3.62 | 0.00 | 0.00 | 1.04 |
time (sec) |
N/A |
0.135 |
0.419 |
0.356 |
0.599 |
0.815 |
0.000 |
0.000 |
1.483 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
F(-2) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 269 | 269 | 187 | 234 | 232 | 0 | 0 | 0 | 125 |
normalized size | 1 | 1.00 | 0.70 | 0.87 | 0.86 | 0.00 | 0.00 | 0.00 | 0.46 |
time (sec) |
N/A |
0.288 |
1.188 |
0.606 |
0.595 |
0.000 |
0.000 |
0.000 |
1.728 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
A |
A |
F(-2) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 246 | 246 | 52 | 213 | 213 | 0 | 0 | 0 | 104 |
normalized size | 1 | 1.00 | 0.21 | 0.87 | 0.87 | 0.00 | 0.00 | 0.00 | 0.42 |
time (sec) |
N/A |
0.235 |
0.386 |
0.613 |
0.601 |
0.000 |
0.000 |
0.000 |
0.948 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
F(-2) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 244 | 244 | 175 | 204 | 211 | 0 | 0 | 0 | 104 |
normalized size | 1 | 1.00 | 0.72 | 0.84 | 0.86 | 0.00 | 0.00 | 0.00 | 0.43 |
time (sec) |
N/A |
0.227 |
0.432 |
0.592 |
0.705 |
0.000 |
0.000 |
0.000 |
0.697 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
A |
A |
F(-2) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 222 | 222 | 53 | 186 | 193 | 0 | 0 | 0 | 86 |
normalized size | 1 | 1.00 | 0.24 | 0.84 | 0.87 | 0.00 | 0.00 | 0.00 | 0.39 |
time (sec) |
N/A |
0.200 |
0.257 |
0.535 |
0.787 |
0.000 |
0.000 |
0.000 |
0.445 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
A |
A |
F(-2) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 222 | 222 | 236 | 195 | 202 | 0 | 0 | 0 | 86 |
normalized size | 1 | 1.00 | 1.06 | 0.88 | 0.91 | 0.00 | 0.00 | 0.00 | 0.39 |
time (sec) |
N/A |
0.208 |
1.808 |
0.484 |
0.461 |
0.000 |
0.000 |
0.000 |
0.593 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
A |
A |
F(-2) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 247 | 247 | 233 | 216 | 211 | 0 | 0 | 0 | 99 |
normalized size | 1 | 1.00 | 0.94 | 0.87 | 0.85 | 0.00 | 0.00 | 0.00 | 0.40 |
time (sec) |
N/A |
0.237 |
1.262 |
0.467 |
0.540 |
0.000 |
0.000 |
0.000 |
0.701 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
A |
A |
F(-2) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 249 | 249 | 141 | 216 | 221 | 0 | 0 | 0 | 99 |
normalized size | 1 | 1.00 | 0.57 | 0.87 | 0.89 | 0.00 | 0.00 | 0.00 | 0.40 |
time (sec) |
N/A |
0.237 |
0.414 |
0.460 |
0.690 |
0.000 |
0.000 |
0.000 |
1.292 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 186 | 186 | 729 | 446 | 193 | 535 | 0 | 0 | 177 |
normalized size | 1 | 1.00 | 3.92 | 2.40 | 1.04 | 2.88 | 0.00 | 0.00 | 0.95 |
time (sec) |
N/A |
0.300 |
6.104 |
0.791 |
0.500 |
0.951 |
0.000 |
0.000 |
2.440 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 332 | 419 | 175 | 487 | 0 | 0 | 143 |
normalized size | 1 | 1.00 | 2.08 | 2.62 | 1.09 | 3.04 | 0.00 | 0.00 | 0.89 |
time (sec) |
N/A |
0.259 |
2.810 |
0.869 |
0.466 |
0.723 |
0.000 |
0.000 |
1.617 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 315 | 391 | 149 | 366 | 0 | 0 | 136 |
normalized size | 1 | 1.00 | 2.28 | 2.83 | 1.08 | 2.65 | 0.00 | 0.00 | 0.99 |
time (sec) |
N/A |
0.203 |
1.553 |
0.960 |
0.760 |
0.718 |
0.000 |
0.000 |
0.990 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 292 | 379 | 136 | 349 | 0 | 0 | 100 |
normalized size | 1 | 1.00 | 2.50 | 3.24 | 1.16 | 2.98 | 0.00 | 0.00 | 0.85 |
time (sec) |
N/A |
0.169 |
5.171 |
0.568 |
0.551 |
0.841 |
0.000 |
0.000 |
0.621 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 114 | 311 | 388 | 130 | 372 | 0 | 0 | 119 |
normalized size | 1 | 1.00 | 2.73 | 3.40 | 1.14 | 3.26 | 0.00 | 0.00 | 1.04 |
time (sec) |
N/A |
0.175 |
2.894 |
0.479 |
0.680 |
0.665 |
0.000 |
0.000 |
0.576 |
|
|
|
|
|
|
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|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 417 | 388 | 133 | 378 | 0 | 0 | 101 |
normalized size | 1 | 1.00 | 3.56 | 3.32 | 1.14 | 3.23 | 0.00 | 0.00 | 0.86 |
time (sec) |
N/A |
0.188 |
6.109 |
0.498 |
0.791 |
1.540 |
0.000 |
0.000 |
0.705 |
|
|
|
|
|
|
|
|
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|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 269 | 409 | 148 | 485 | 0 | 0 | 126 |
normalized size | 1 | 1.00 | 1.91 | 2.90 | 1.05 | 3.44 | 0.00 | 0.00 | 0.89 |
time (sec) |
N/A |
0.229 |
3.345 |
0.526 |
0.773 |
0.454 |
0.000 |
0.000 |
1.261 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 174 | 430 | 170 | 514 | 0 | 0 | 129 |
normalized size | 1 | 1.00 | 1.05 | 2.61 | 1.03 | 3.12 | 0.00 | 0.00 | 0.78 |
time (sec) |
N/A |
0.296 |
1.998 |
0.536 |
0.855 |
0.865 |
0.000 |
0.000 |
1.924 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 110 | 394 | 134 | 400 | 0 | 0 | 123 |
normalized size | 1 | 1.00 | 0.99 | 3.55 | 1.21 | 3.60 | 0.00 | 0.00 | 1.11 |
time (sec) |
N/A |
0.451 |
0.884 |
0.730 |
1.567 |
0.899 |
0.000 |
0.000 |
0.682 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 107 | 368 | 118 | 333 | 0 | 0 | 79 |
normalized size | 1 | 1.00 | 1.23 | 4.23 | 1.36 | 3.83 | 0.00 | 0.00 | 0.91 |
time (sec) |
N/A |
0.239 |
4.052 |
0.732 |
0.703 |
0.792 |
0.000 |
0.000 |
0.492 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 98 | 358 | 113 | 331 | 0 | 0 | 102 |
normalized size | 1 | 1.00 | 1.13 | 4.11 | 1.30 | 3.80 | 0.00 | 0.00 | 1.17 |
time (sec) |
N/A |
0.218 |
0.251 |
0.812 |
0.809 |
0.841 |
0.000 |
0.000 |
0.368 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 107 | 365 | 120 | 321 | 0 | 0 | 79 |
normalized size | 1 | 1.00 | 1.29 | 4.40 | 1.45 | 3.87 | 0.00 | 0.00 | 0.95 |
time (sec) |
N/A |
0.219 |
0.516 |
0.877 |
0.632 |
0.624 |
0.000 |
0.000 |
0.523 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 176 | 394 | 136 | 472 | 0 | 0 | 123 |
normalized size | 1 | 1.00 | 1.59 | 3.55 | 1.23 | 4.25 | 0.00 | 0.00 | 1.11 |
time (sec) |
N/A |
0.452 |
2.034 |
0.810 |
1.645 |
1.134 |
0.000 |
0.000 |
0.644 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 131 | 416 | 154 | 500 | 0 | 0 | 132 |
normalized size | 1 | 1.00 | 0.97 | 3.08 | 1.14 | 3.70 | 0.00 | 0.00 | 0.98 |
time (sec) |
N/A |
0.538 |
1.333 |
0.758 |
0.444 |
0.935 |
0.000 |
0.000 |
0.929 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-2) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 281 | 281 | 224 | 234 | 233 | 0 | 0 | 0 | 375 |
normalized size | 1 | 1.00 | 0.80 | 0.83 | 0.83 | 0.00 | 0.00 | 0.00 | 1.33 |
time (sec) |
N/A |
0.544 |
2.019 |
0.829 |
0.438 |
0.000 |
0.000 |
0.000 |
0.898 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-2) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 279 | 279 | 312 | 234 | 232 | 0 | 0 | 0 | 376 |
normalized size | 1 | 1.00 | 1.12 | 0.84 | 0.83 | 0.00 | 0.00 | 0.00 | 1.35 |
time (sec) |
N/A |
0.564 |
2.829 |
0.745 |
0.491 |
0.000 |
0.000 |
0.000 |
0.823 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-2) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 278 | 278 | 207 | 223 | 231 | 0 | 0 | 0 | 366 |
normalized size | 1 | 1.00 | 0.74 | 0.80 | 0.83 | 0.00 | 0.00 | 0.00 | 1.32 |
time (sec) |
N/A |
0.531 |
1.299 |
0.792 |
0.585 |
0.000 |
0.000 |
0.000 |
0.722 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-2) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 281 | 281 | 337 | 222 | 238 | 0 | 0 | 0 | 366 |
normalized size | 1 | 1.00 | 1.20 | 0.79 | 0.85 | 0.00 | 0.00 | 0.00 | 1.30 |
time (sec) |
N/A |
0.566 |
0.839 |
0.714 |
0.545 |
0.000 |
0.000 |
0.000 |
0.813 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-2) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 306 | 306 | 203 | 255 | 256 | 0 | 0 | 0 | 414 |
normalized size | 1 | 1.00 | 0.66 | 0.83 | 0.84 | 0.00 | 0.00 | 0.00 | 1.35 |
time (sec) |
N/A |
0.796 |
1.327 |
0.654 |
0.870 |
0.000 |
0.000 |
0.000 |
0.923 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-2) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 331 | 331 | 467 | 276 | 274 | 0 | 0 | 0 | 425 |
normalized size | 1 | 1.00 | 1.41 | 0.83 | 0.83 | 0.00 | 0.00 | 0.00 | 1.28 |
time (sec) |
N/A |
1.075 |
6.341 |
0.666 |
1.013 |
0.000 |
0.000 |
0.000 |
1.226 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 164 | 164 | 192 | 440 | 197 | 567 | 0 | 0 | 154 |
normalized size | 1 | 1.00 | 1.17 | 2.68 | 1.20 | 3.46 | 0.00 | 0.00 | 0.94 |
time (sec) |
N/A |
0.617 |
2.134 |
0.831 |
0.456 |
0.465 |
0.000 |
0.000 |
1.037 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 164 | 164 | 131 | 434 | 189 | 533 | 0 | 0 | 178 |
normalized size | 1 | 1.00 | 0.80 | 2.65 | 1.15 | 3.25 | 0.00 | 0.00 | 1.09 |
time (sec) |
N/A |
0.663 |
2.023 |
0.845 |
0.918 |
0.543 |
0.000 |
0.000 |
0.938 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 181 | 423 | 190 | 518 | 0 | 0 | 151 |
normalized size | 1 | 1.00 | 1.12 | 2.63 | 1.18 | 3.22 | 0.00 | 0.00 | 0.94 |
time (sec) |
N/A |
0.592 |
0.818 |
0.856 |
0.601 |
0.534 |
0.000 |
0.000 |
0.898 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 217 | 426 | 189 | 504 | 0 | 0 | 173 |
normalized size | 1 | 1.00 | 1.32 | 2.58 | 1.15 | 3.05 | 0.00 | 0.00 | 1.05 |
time (sec) |
N/A |
0.648 |
1.271 |
0.833 |
0.512 |
0.451 |
0.000 |
0.000 |
0.944 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 156 | 458 | 214 | 697 | 0 | 0 | 175 |
normalized size | 1 | 1.00 | 0.83 | 2.42 | 1.13 | 3.69 | 0.00 | 0.00 | 0.93 |
time (sec) |
N/A |
0.863 |
1.211 |
0.795 |
0.713 |
0.662 |
0.000 |
0.000 |
1.141 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 215 | 215 | 167 | 482 | 224 | 718 | 0 | 0 | 193 |
normalized size | 1 | 1.00 | 0.78 | 2.24 | 1.04 | 3.34 | 0.00 | 0.00 | 0.90 |
time (sec) |
N/A |
1.105 |
3.190 |
0.855 |
0.778 |
0.480 |
0.000 |
0.000 |
1.385 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 223 | 223 | 69 | 356 | 0 | 0 | 0 | 0 | 119 |
normalized size | 1 | 1.00 | 0.31 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 |
time (sec) |
N/A |
0.266 |
0.166 |
0.269 |
0.000 |
0.000 |
0.000 |
0.000 |
0.631 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 61 | 249 | 0 | 0 | 0 | 0 | 210 |
normalized size | 1 | 1.00 | 0.45 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 1.56 |
time (sec) |
N/A |
0.240 |
0.091 |
0.132 |
0.000 |
0.000 |
0.000 |
0.000 |
0.483 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
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|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 139 | 96 | 265 | 0 | 0 | 0 | 0 | 254 |
normalized size | 1 | 1.00 | 0.69 | 1.91 | 0.00 | 0.00 | 0.00 | 0.00 | 1.83 |
time (sec) |
N/A |
0.235 |
0.318 |
0.175 |
0.000 |
0.000 |
0.000 |
0.000 |
0.996 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 221 | 98 | 452 | 0 | 0 | 0 | 0 | 254 |
normalized size | 1 | 1.00 | 0.44 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | 1.15 |
time (sec) |
N/A |
0.209 |
0.260 |
0.117 |
0.000 |
0.000 |
0.000 |
0.000 |
0.674 |
|
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 214 | 67 | 442 | 0 | 0 | 0 | 0 | 238 |
normalized size | 1 | 1.00 | 0.31 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | 1.11 |
time (sec) |
N/A |
0.185 |
0.168 |
0.224 |
0.000 |
0.000 |
0.000 |
0.000 |
0.438 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 121 | 51 | 249 | 0 | 0 | 0 | 0 | 230 |
normalized size | 1 | 1.00 | 0.42 | 2.06 | 0.00 | 0.00 | 0.00 | 0.00 | 1.90 |
time (sec) |
N/A |
0.127 |
0.076 |
0.161 |
0.000 |
0.000 |
0.000 |
0.000 |
0.410 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 139 | 65 | 249 | 0 | 0 | 0 | 0 | 208 |
normalized size | 1 | 1.00 | 0.47 | 1.79 | 0.00 | 0.00 | 0.00 | 0.00 | 1.50 |
time (sec) |
N/A |
0.193 |
0.132 |
0.186 |
0.000 |
0.000 |
0.000 |
0.000 |
0.501 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 226 | 226 | 71 | 356 | 0 | 0 | 0 | 0 | 121 |
normalized size | 1 | 1.00 | 0.31 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 |
time (sec) |
N/A |
0.193 |
0.143 |
0.126 |
0.000 |
0.000 |
0.000 |
0.000 |
0.400 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 75 | 265 | 0 | 0 | 0 | 0 | 242 |
normalized size | 1 | 1.00 | 0.52 | 1.85 | 0.00 | 0.00 | 0.00 | 0.00 | 1.69 |
time (sec) |
N/A |
0.205 |
0.406 |
0.193 |
0.000 |
0.000 |
0.000 |
0.000 |
0.800 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 216 | 216 | 69 | 444 | 0 | 0 | 0 | 0 | 238 |
normalized size | 1 | 1.00 | 0.32 | 2.06 | 0.00 | 0.00 | 0.00 | 0.00 | 1.10 |
time (sec) |
N/A |
0.176 |
0.242 |
0.134 |
0.000 |
0.000 |
0.000 |
0.000 |
0.709 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 247 | 247 | 68 | 363 | 221 | 0 | 0 | 0 | 153 |
normalized size | 1 | 1.00 | 0.28 | 1.47 | 0.89 | 0.00 | 0.00 | 0.00 | 0.62 |
time (sec) |
N/A |
0.207 |
0.131 |
0.367 |
0.852 |
0.000 |
0.000 |
0.000 |
1.397 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 226 | 226 | 155 | 337 | 199 | 0 | 0 | 0 | 128 |
normalized size | 1 | 1.00 | 0.69 | 1.49 | 0.88 | 0.00 | 0.00 | 0.00 | 0.57 |
time (sec) |
N/A |
0.172 |
0.282 |
0.355 |
0.728 |
0.000 |
0.000 |
0.000 |
0.726 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 208 | 208 | 166 | 327 | 180 | 0 | 0 | 0 | 118 |
normalized size | 1 | 1.00 | 0.80 | 1.57 | 0.87 | 0.00 | 0.00 | 0.00 | 0.57 |
time (sec) |
N/A |
0.142 |
0.216 |
0.406 |
0.750 |
0.000 |
0.000 |
0.000 |
0.647 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 229 | 229 | 196 | 355 | 204 | 0 | 0 | 0 | 137 |
normalized size | 1 | 1.00 | 0.86 | 1.55 | 0.89 | 0.00 | 0.00 | 0.00 | 0.60 |
time (sec) |
N/A |
0.194 |
0.359 |
0.372 |
0.692 |
0.000 |
0.000 |
0.000 |
0.805 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 252 | 252 | 196 | 374 | 220 | 0 | 0 | 0 | 158 |
normalized size | 1 | 1.00 | 0.78 | 1.48 | 0.87 | 0.00 | 0.00 | 0.00 | 0.63 |
time (sec) |
N/A |
0.258 |
0.758 |
0.482 |
0.704 |
0.000 |
0.000 |
0.000 |
1.245 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 317 | 317 | 224 | 581 | 287 | 0 | 0 | 0 | 1274 |
normalized size | 1 | 1.00 | 0.71 | 1.83 | 0.91 | 0.00 | 0.00 | 0.00 | 4.02 |
time (sec) |
N/A |
0.334 |
1.982 |
0.650 |
0.585 |
0.000 |
0.000 |
0.000 |
2.471 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 288 | 288 | 220 | 534 | 257 | 0 | 0 | 0 | 1157 |
normalized size | 1 | 1.00 | 0.76 | 1.85 | 0.89 | 0.00 | 0.00 | 0.00 | 4.02 |
time (sec) |
N/A |
0.275 |
0.569 |
0.539 |
0.451 |
0.000 |
0.000 |
0.000 |
1.212 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 267 | 267 | 192 | 529 | 242 | 0 | 0 | 0 | 1234 |
normalized size | 1 | 1.00 | 0.72 | 1.98 | 0.91 | 0.00 | 0.00 | 0.00 | 4.62 |
time (sec) |
N/A |
0.249 |
0.890 |
0.520 |
0.797 |
0.000 |
0.000 |
0.000 |
1.013 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 267 | 267 | 218 | 538 | 242 | 0 | 0 | 0 | 1196 |
normalized size | 1 | 1.00 | 0.82 | 2.01 | 0.91 | 0.00 | 0.00 | 0.00 | 4.48 |
time (sec) |
N/A |
0.258 |
0.330 |
0.456 |
0.900 |
0.000 |
0.000 |
0.000 |
0.936 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 291 | 291 | 82 | 558 | 259 | 0 | 0 | 0 | 1214 |
normalized size | 1 | 1.00 | 0.28 | 1.92 | 0.89 | 0.00 | 0.00 | 0.00 | 4.17 |
time (sec) |
N/A |
0.334 |
0.301 |
0.466 |
0.626 |
0.000 |
0.000 |
0.000 |
1.512 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 322 | 322 | 85 | 600 | 286 | 0 | 0 | 0 | 1227 |
normalized size | 1 | 1.00 | 0.26 | 1.86 | 0.89 | 0.00 | 0.00 | 0.00 | 3.81 |
time (sec) |
N/A |
0.428 |
0.358 |
0.449 |
0.530 |
0.000 |
0.000 |
0.000 |
2.320 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 372 | 372 | 251 | 807 | 347 | 0 | 0 | 0 | 2317 |
normalized size | 1 | 1.00 | 0.67 | 2.17 | 0.93 | 0.00 | 0.00 | 0.00 | 6.23 |
time (sec) |
N/A |
0.564 |
3.061 |
0.753 |
0.440 |
0.000 |
0.000 |
0.000 |
5.474 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 342 | 342 | 247 | 750 | 316 | 0 | 0 | 0 | 2071 |
normalized size | 1 | 1.00 | 0.72 | 2.19 | 0.92 | 0.00 | 0.00 | 0.00 | 6.06 |
time (sec) |
N/A |
0.477 |
2.593 |
0.722 |
0.437 |
0.000 |
0.000 |
0.000 |
2.546 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 313 | 313 | 216 | 725 | 292 | 0 | 0 | 0 | 1896 |
normalized size | 1 | 1.00 | 0.69 | 2.32 | 0.93 | 0.00 | 0.00 | 0.00 | 6.06 |
time (sec) |
N/A |
0.425 |
1.034 |
0.607 |
0.517 |
0.000 |
0.000 |
0.000 |
1.413 |
|
|
|
|
|
|
|
|
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|
|
|
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|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 313 | 313 | 193 | 742 | 290 | 0 | 0 | 0 | 1951 |
normalized size | 1 | 1.00 | 0.62 | 2.37 | 0.93 | 0.00 | 0.00 | 0.00 | 6.23 |
time (sec) |
N/A |
0.420 |
3.390 |
0.467 |
0.653 |
0.000 |
0.000 |
0.000 |
1.204 |
|
|
|
|
|
|
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|
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|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 313 | 313 | 104 | 743 | 289 | 0 | 0 | 0 | 1946 |
normalized size | 1 | 1.00 | 0.33 | 2.37 | 0.92 | 0.00 | 0.00 | 0.00 | 6.22 |
time (sec) |
N/A |
0.458 |
0.376 |
0.459 |
0.693 |
0.000 |
0.000 |
0.000 |
1.671 |
|
|
|
|
|
|
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|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 343 | 343 | 108 | 786 | 316 | 0 | 0 | 0 | 1969 |
normalized size | 1 | 1.00 | 0.31 | 2.29 | 0.92 | 0.00 | 0.00 | 0.00 | 5.74 |
time (sec) |
N/A |
0.561 |
0.612 |
0.463 |
0.711 |
0.000 |
0.000 |
0.000 |
3.063 |
|
|
|
|
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|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 377 | 377 | 116 | 829 | 342 | 0 | 0 | 0 | 1992 |
normalized size | 1 | 1.00 | 0.31 | 2.20 | 0.91 | 0.00 | 0.00 | 0.00 | 5.28 |
time (sec) |
N/A |
0.662 |
0.677 |
0.451 |
0.766 |
0.000 |
0.000 |
0.000 |
5.257 |
|
|
|
|
|
|
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|
|
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|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 325 | 325 | 286 | 459 | 259 | 0 | 0 | 0 | 5579 |
normalized size | 1 | 1.00 | 0.88 | 1.41 | 0.80 | 0.00 | 0.00 | 0.00 | 17.17 |
time (sec) |
N/A |
0.660 |
0.874 |
0.673 |
0.538 |
0.000 |
0.000 |
0.000 |
1.973 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 302 | 302 | 249 | 429 | 236 | 0 | 0 | 0 | 5129 |
normalized size | 1 | 1.00 | 0.82 | 1.42 | 0.78 | 0.00 | 0.00 | 0.00 | 16.98 |
time (sec) |
N/A |
0.379 |
0.567 |
0.687 |
0.494 |
0.000 |
0.000 |
0.000 |
1.627 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 302 | 302 | 226 | 417 | 233 | 0 | 0 | 0 | 4808 |
normalized size | 1 | 1.00 | 0.75 | 1.38 | 0.77 | 0.00 | 0.00 | 0.00 | 15.92 |
time (sec) |
N/A |
0.376 |
0.283 |
0.790 |
0.484 |
0.000 |
0.000 |
0.000 |
1.386 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 302 | 302 | 248 | 423 | 239 | 0 | 0 | 0 | 4871 |
normalized size | 1 | 1.00 | 0.82 | 1.40 | 0.79 | 0.00 | 0.00 | 0.00 | 16.13 |
time (sec) |
N/A |
0.370 |
0.254 |
0.712 |
0.526 |
0.000 |
0.000 |
0.000 |
1.768 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 325 | 325 | 198 | 459 | 261 | 0 | 0 | 0 | 4899 |
normalized size | 1 | 1.00 | 0.61 | 1.41 | 0.80 | 0.00 | 0.00 | 0.00 | 15.07 |
time (sec) |
N/A |
0.660 |
0.446 |
0.614 |
0.910 |
0.000 |
0.000 |
0.000 |
1.860 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 351 | 351 | 109 | 481 | 280 | 0 | 0 | 0 | 6042 |
normalized size | 1 | 1.00 | 0.31 | 1.37 | 0.80 | 0.00 | 0.00 | 0.00 | 17.21 |
time (sec) |
N/A |
0.962 |
0.283 |
0.629 |
0.662 |
0.000 |
0.000 |
0.000 |
2.807 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F(-1) |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 437 | 437 | 445 | 805 | 385 | 0 | 0 | 0 | 13244 |
normalized size | 1 | 1.00 | 1.02 | 1.84 | 0.88 | 0.00 | 0.00 | 0.00 | 30.31 |
time (sec) |
N/A |
1.108 |
6.158 |
0.831 |
0.462 |
0.000 |
0.000 |
0.000 |
3.970 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F(-1) |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 393 | 393 | 390 | 784 | 359 | 0 | 0 | 0 | 12617 |
normalized size | 1 | 1.00 | 0.99 | 1.99 | 0.91 | 0.00 | 0.00 | 0.00 | 32.10 |
time (sec) |
N/A |
0.740 |
2.795 |
0.781 |
0.449 |
0.000 |
0.000 |
0.000 |
3.121 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 387 | 387 | 322 | 768 | 344 | 0 | 0 | 0 | 11953 |
normalized size | 1 | 1.00 | 0.83 | 1.98 | 0.89 | 0.00 | 0.00 | 0.00 | 30.89 |
time (sec) |
N/A |
0.677 |
3.326 |
0.757 |
0.592 |
0.000 |
0.000 |
0.000 |
3.366 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 386 | 386 | 401 | 749 | 343 | 0 | 0 | 0 | 11731 |
normalized size | 1 | 1.00 | 1.04 | 1.94 | 0.89 | 0.00 | 0.00 | 0.00 | 30.39 |
time (sec) |
N/A |
0.646 |
6.099 |
0.823 |
0.668 |
0.000 |
0.000 |
0.000 |
3.084 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 394 | 394 | 300 | 765 | 360 | 0 | 0 | 0 | 9400 |
normalized size | 1 | 1.00 | 0.76 | 1.94 | 0.91 | 0.00 | 0.00 | 0.00 | 23.86 |
time (sec) |
N/A |
0.738 |
2.865 |
0.846 |
0.535 |
0.000 |
0.000 |
0.000 |
8.163 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 437 | 437 | 244 | 803 | 402 | 0 | 0 | 0 | 15251 |
normalized size | 1 | 1.00 | 0.56 | 1.84 | 0.92 | 0.00 | 0.00 | 0.00 | 34.90 |
time (sec) |
N/A |
1.095 |
0.630 |
0.763 |
0.718 |
0.000 |
0.000 |
0.000 |
4.335 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F(-1) |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 529 | 529 | 556 | 1254 | 537 | 0 | 0 | 0 | 20651 |
normalized size | 1 | 1.00 | 1.05 | 2.37 | 1.02 | 0.00 | 0.00 | 0.00 | 39.04 |
time (sec) |
N/A |
1.631 |
6.261 |
0.853 |
0.615 |
0.000 |
0.000 |
0.000 |
10.399 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F(-1) |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 476 | 476 | 525 | 1232 | 516 | 0 | 0 | 0 | 20089 |
normalized size | 1 | 1.00 | 1.10 | 2.59 | 1.08 | 0.00 | 0.00 | 0.00 | 42.20 |
time (sec) |
N/A |
1.230 |
6.189 |
0.880 |
0.755 |
0.000 |
0.000 |
0.000 |
7.262 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 470 | 470 | 488 | 1229 | 505 | 0 | 0 | 0 | 19256 |
normalized size | 1 | 1.00 | 1.04 | 2.61 | 1.07 | 0.00 | 0.00 | 0.00 | 40.97 |
time (sec) |
N/A |
1.295 |
6.199 |
0.995 |
0.558 |
0.000 |
0.000 |
0.000 |
6.515 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 461 | 461 | 518 | 1212 | 492 | 0 | 0 | 0 | 19000 |
normalized size | 1 | 1.00 | 1.12 | 2.63 | 1.07 | 0.00 | 0.00 | 0.00 | 41.21 |
time (sec) |
N/A |
1.234 |
6.156 |
0.870 |
0.778 |
0.000 |
0.000 |
0.000 |
6.213 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 463 | 463 | 483 | 1187 | 496 | 0 | 0 | 0 | 19534 |
normalized size | 1 | 1.00 | 1.04 | 2.56 | 1.07 | 0.00 | 0.00 | 0.00 | 42.19 |
time (sec) |
N/A |
1.147 |
6.186 |
0.972 |
0.842 |
0.000 |
0.000 |
0.000 |
6.127 |
|
|
|
|
|
|
|
|
|
|
|
|
|
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Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 476 | 476 | 411 | 1190 | 510 | 0 | 0 | 0 | 20155 |
normalized size | 1 | 1.00 | 0.86 | 2.50 | 1.07 | 0.00 | 0.00 | 0.00 | 42.34 |
time (sec) |
N/A |
1.242 |
6.134 |
0.845 |
0.475 |
0.000 |
0.000 |
0.000 |
6.789 |
|
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Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 529 | 529 | 303 | 1245 | 565 | 0 | 0 | 0 | 21158 |
normalized size | 1 | 1.00 | 0.57 | 2.35 | 1.07 | 0.00 | 0.00 | 0.00 | 40.00 |
time (sec) |
N/A |
1.658 |
1.792 |
0.795 |
0.453 |
0.000 |
0.000 |
0.000 |
9.999 |
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Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 118 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.243 |
0.302 |
1.235 |
0.000 |
1.000 |
0.000 |
0.000 |
0.000 |
|
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Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 193 | 193 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.272 |
3.252 |
2.421 |
0.000 |
1.218 |
0.000 |
0.000 |
0.000 |
|
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Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 45 | 1622 | 0 | 159 | 0 | 0 | 1410 |
normalized size | 1 | 1.00 | 1.00 | 36.04 | 0.00 | 3.53 | 0.00 | 0.00 | 31.33 |
time (sec) |
N/A |
0.065 |
0.081 |
0.457 |
0.000 |
0.710 |
0.000 |
0.000 |
2.536 |
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Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 70 | 1622 | 0 | 159 | 0 | 0 | 1410 |
normalized size | 1 | 1.00 | 1.56 | 36.04 | 0.00 | 3.53 | 0.00 | 0.00 | 31.33 |
time (sec) |
N/A |
0.059 |
1.721 |
0.538 |
0.000 |
0.590 |
0.000 |
0.000 |
1.403 |
|
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Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 67 | 187 | 89 | 79 | 534 | 95 | 155 |
normalized size | 1 | 1.00 | 1.14 | 3.17 | 1.51 | 1.34 | 9.05 | 1.61 | 2.63 |
time (sec) |
N/A |
0.078 |
0.130 |
0.419 |
1.690 |
0.546 |
1.109 |
0.534 |
0.995 |
|
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Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 144 | 356 | 185 | 340 | 3966 | 241 | 268 |
normalized size | 1 | 1.00 | 1.30 | 3.21 | 1.67 | 3.06 | 35.73 | 2.17 | 2.41 |
time (sec) |
N/A |
0.149 |
1.929 |
0.370 |
0.530 |
0.559 |
4.232 |
0.490 |
1.460 |
|
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Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
B |
F(-2) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 202 | 559 | 337 | 549 | 0 | 412 | 481 |
normalized size | 1 | 1.00 | 1.15 | 3.19 | 1.93 | 3.14 | 0.00 | 2.35 | 2.75 |
time (sec) |
N/A |
0.276 |
5.003 |
0.382 |
0.866 |
0.708 |
0.000 |
0.489 |
2.602 |
|
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Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 188 | 379 | 2405 | 0 | 0 | 0 | 0 | 3864 |
normalized size | 1 | 1.00 | 2.02 | 12.79 | 0.00 | 0.00 | 0.00 | 0.00 | 20.55 |
time (sec) |
N/A |
0.453 |
1.795 |
0.547 |
0.000 |
0.000 |
0.000 |
0.000 |
31.594 |
|
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Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 294 | 1665 | 0 | 0 | 0 | 0 | 2823 |
normalized size | 1 | 1.00 | 1.96 | 11.10 | 0.00 | 0.00 | 0.00 | 0.00 | 18.82 |
time (sec) |
N/A |
0.333 |
0.974 |
0.539 |
0.000 |
0.000 |
0.000 |
0.000 |
13.758 |
|
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|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 212 | 968 | 0 | 0 | 0 | 0 | 843 |
normalized size | 1 | 1.00 | 1.74 | 7.93 | 0.00 | 0.00 | 0.00 | 0.00 | 6.91 |
time (sec) |
N/A |
0.262 |
0.567 |
0.531 |
0.000 |
0.000 |
0.000 |
0.000 |
3.029 |
|
|
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|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 253 | 1375 | 0 | 0 | 0 | 0 | 3442 |
normalized size | 1 | 1.00 | 1.68 | 9.11 | 0.00 | 0.00 | 0.00 | 0.00 | 22.79 |
time (sec) |
N/A |
0.278 |
3.959 |
0.555 |
0.000 |
0.000 |
0.000 |
0.000 |
26.556 |
|
|
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|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 408 | 408 | 178 | 972 | 0 | 0 | 0 | 0 | 2529 |
normalized size | 1 | 1.00 | 0.44 | 2.38 | 0.00 | 0.00 | 0.00 | 0.00 | 6.20 |
time (sec) |
N/A |
0.511 |
1.938 |
0.510 |
0.000 |
0.000 |
0.000 |
0.000 |
11.956 |
|
|
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|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 422 | 422 | 158 | 2285 | 0 | 0 | 0 | 0 | 583 |
normalized size | 1 | 1.00 | 0.37 | 5.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.38 |
time (sec) |
N/A |
0.418 |
1.055 |
0.540 |
0.000 |
0.000 |
0.000 |
0.000 |
2.571 |
|
|
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|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 154 | 3976 | 0 | 0 | 0 | 0 | 2909 |
normalized size | 1 | 1.00 | 1.51 | 38.98 | 0.00 | 0.00 | 0.00 | 0.00 | 28.52 |
time (sec) |
N/A |
0.160 |
0.611 |
0.490 |
0.000 |
0.000 |
0.000 |
0.000 |
2.290 |
|
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|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 226 | 7951 | 0 | 0 | 0 | 0 | 5737 |
normalized size | 1 | 1.00 | 1.64 | 57.62 | 0.00 | 0.00 | 0.00 | 0.00 | 41.57 |
time (sec) |
N/A |
0.263 |
1.674 |
0.459 |
0.000 |
0.000 |
0.000 |
0.000 |
6.466 |
|
|
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|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 185 | 185 | 319 | 12836 | 0 | 0 | 0 | 0 | 9453 |
normalized size | 1 | 1.00 | 1.72 | 69.38 | 0.00 | 0.00 | 0.00 | 0.00 | 51.10 |
time (sec) |
N/A |
0.402 |
3.530 |
0.440 |
0.000 |
0.000 |
0.000 |
0.000 |
17.933 |
|
|
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|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 146 | 1905 | 0 | 0 | 0 | 0 | 2731 |
normalized size | 1 | 1.00 | 1.43 | 18.68 | 0.00 | 0.00 | 0.00 | 0.00 | 26.77 |
time (sec) |
N/A |
0.162 |
0.331 |
0.543 |
0.000 |
0.000 |
0.000 |
0.000 |
2.202 |
|
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|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 216 | 2291 | 0 | 0 | 0 | 0 | 5475 |
normalized size | 1 | 1.00 | 1.64 | 17.36 | 0.00 | 0.00 | 0.00 | 0.00 | 41.48 |
time (sec) |
N/A |
0.248 |
1.473 |
0.563 |
0.000 |
0.000 |
0.000 |
0.000 |
5.961 |
|
|
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|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 174 | 174 | 232 | 3055 | 0 | 0 | 0 | 0 | 8438 |
normalized size | 1 | 1.00 | 1.33 | 17.56 | 0.00 | 0.00 | 0.00 | 0.00 | 48.49 |
time (sec) |
N/A |
0.382 |
5.938 |
0.556 |
0.000 |
0.000 |
0.000 |
0.000 |
16.173 |
|
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|
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 [48] had the largest ratio of
[.9091]
|
|
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|
|
|
|
| Table 2.1:Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
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|
|
|
|
1 |
A |
2 |
2 |
1.00 |
15 |
0.133 |
|
|
|
|
|
|
|
2 |
A |
5 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
3 |
A |
4 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
4 |
A |
3 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
5 |
A |
2 |
2 |
1.00 |
23 |
0.087 |
|
|
|
|
|
|
|
6 |
A |
3 |
3 |
1.00 |
23 |
0.130 |
|
|
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|
|
|
7 |
A |
4 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
8 |
A |
16 |
12 |
1.00 |
25 |
0.480 |
|
|
|
|
|
|
|
9 |
A |
15 |
12 |
1.00 |
25 |
0.480 |
|
|
|
|
|
|
|
10 |
A |
15 |
12 |
1.00 |
25 |
0.480 |
|
|
|
|
|
|
|
11 |
A |
14 |
11 |
1.00 |
25 |
0.440 |
|
|
|
|
|
|
|
12 |
A |
13 |
10 |
1.00 |
25 |
0.400 |
|
|
|
|
|
|
|
13 |
A |
14 |
11 |
1.00 |
25 |
0.440 |
|
|
|
|
|
|
|
14 |
A |
14 |
11 |
1.00 |
25 |
0.440 |
|
|
|
|
|
|
|
15 |
A |
7 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
16 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
17 |
A |
5 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
18 |
A |
4 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
19 |
A |
4 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
20 |
A |
4 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
21 |
A |
5 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
22 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
23 |
A |
7 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
24 |
A |
6 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
25 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
26 |
A |
6 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
27 |
A |
7 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
28 |
A |
10 |
10 |
1.00 |
25 |
0.400 |
|
|
|
|
|
|
|
29 |
A |
17 |
14 |
1.00 |
25 |
0.560 |
|
|
|
|
|
|
|
30 |
A |
18 |
15 |
1.00 |
25 |
0.600 |
|
|
|
|
|
|
|
31 |
A |
17 |
14 |
1.00 |
25 |
0.560 |
|
|
|
|
|
|
|
32 |
A |
18 |
15 |
1.00 |
25 |
0.600 |
|
|
|
|
|
|
|
33 |
A |
18 |
15 |
1.00 |
25 |
0.600 |
|
|
|
|
|
|
|
34 |
A |
20 |
16 |
1.00 |
25 |
0.640 |
|
|
|
|
|
|
|
35 |
A |
8 |
8 |
1.00 |
25 |
0.320 |
|
|
|
|
|
|
|
36 |
A |
8 |
7 |
1.00 |
25 |
0.280 |
|
|
|
|
|
|
|
37 |
A |
8 |
8 |
1.00 |
25 |
0.320 |
|
|
|
|
|
|
|
38 |
A |
8 |
7 |
1.00 |
25 |
0.280 |
|
|
|
|
|
|
|
39 |
A |
9 |
8 |
1.00 |
25 |
0.320 |
|
|
|
|
|
|
|
40 |
A |
10 |
8 |
1.00 |
25 |
0.320 |
|
|
|
|
|
|
|
41 |
A |
12 |
9 |
1.00 |
13 |
0.692 |
|
|
|
|
|
|
|
42 |
A |
6 |
5 |
1.00 |
11 |
0.454 |
|
|
|
|
|
|
|
43 |
A |
8 |
7 |
1.00 |
13 |
0.538 |
|
|
|
|
|
|
|
44 |
A |
14 |
9 |
1.00 |
11 |
0.818 |
|
|
|
|
|
|
|
45 |
A |
12 |
8 |
1.00 |
13 |
0.615 |
|
|
|
|
|
|
|
46 |
A |
5 |
4 |
1.00 |
11 |
0.364 |
|
|
|
|
|
|
|
47 |
A |
6 |
5 |
1.00 |
13 |
0.385 |
|
|
|
|
|
|
|
48 |
A |
13 |
10 |
1.00 |
11 |
0.909 |
|
|
|
|
|
|
|
49 |
A |
8 |
7 |
1.00 |
13 |
0.538 |
|
|
|
|
|
|
|
50 |
A |
13 |
9 |
1.00 |
11 |
0.818 |
|
|
|
|
|
|
|
51 |
A |
12 |
8 |
1.00 |
23 |
0.348 |
|
|
|
|
|
|
|
52 |
A |
11 |
8 |
1.00 |
23 |
0.348 |
|
|
|
|
|
|
|
53 |
A |
10 |
7 |
1.00 |
23 |
0.304 |
|
|
|
|
|
|
|
54 |
A |
11 |
8 |
1.00 |
23 |
0.348 |
|
|
|
|
|
|
|
55 |
A |
12 |
8 |
1.00 |
23 |
0.348 |
|
|
|
|
|
|
|
56 |
A |
13 |
9 |
1.00 |
25 |
0.360 |
|
|
|
|
|
|
|
57 |
A |
12 |
9 |
1.00 |
25 |
0.360 |
|
|
|
|
|
|
|
58 |
A |
11 |
8 |
1.00 |
25 |
0.320 |
|
|
|
|
|
|
|
59 |
A |
11 |
8 |
1.00 |
25 |
0.320 |
|
|
|
|
|
|
|
60 |
A |
12 |
9 |
1.00 |
25 |
0.360 |
|
|
|
|
|
|
|
61 |
A |
13 |
9 |
1.00 |
25 |
0.360 |
|
|
|
|
|
|
|
62 |
A |
14 |
10 |
1.00 |
25 |
0.400 |
|
|
|
|
|
|
|
63 |
A |
13 |
10 |
1.00 |
25 |
0.400 |
|
|
|
|
|
|
|
64 |
A |
12 |
9 |
1.00 |
25 |
0.360 |
|
|
|
|
|
|
|
65 |
A |
12 |
9 |
1.00 |
25 |
0.360 |
|
|
|
|
|
|
|
66 |
A |
12 |
9 |
1.00 |
25 |
0.360 |
|
|
|
|
|
|
|
67 |
A |
13 |
10 |
1.00 |
25 |
0.400 |
|
|
|
|
|
|
|
68 |
A |
14 |
10 |
1.00 |
25 |
0.400 |
|
|
|
|
|
|
|
69 |
A |
15 |
12 |
1.00 |
25 |
0.480 |
|
|
|
|
|
|
|
70 |
A |
14 |
11 |
1.00 |
25 |
0.440 |
|
|
|
|
|
|
|
71 |
A |
14 |
11 |
1.00 |
25 |
0.440 |
|
|
|
|
|
|
|
72 |
A |
14 |
11 |
1.00 |
25 |
0.440 |
|
|
|
|
|
|
|
73 |
A |
15 |
12 |
1.00 |
25 |
0.480 |
|
|
|
|
|
|
|
74 |
A |
16 |
13 |
1.00 |
25 |
0.520 |
|
|
|
|
|
|
|
75 |
A |
16 |
13 |
1.00 |
25 |
0.520 |
|
|
|
|
|
|
|
76 |
A |
15 |
12 |
1.00 |
25 |
0.480 |
|
|
|
|
|
|
|
77 |
A |
15 |
12 |
1.00 |
25 |
0.480 |
|
|
|
|
|
|
|
78 |
A |
15 |
12 |
1.00 |
25 |
0.480 |
|
|
|
|
|
|
|
79 |
A |
15 |
12 |
1.00 |
25 |
0.480 |
|
|
|
|
|
|
|
80 |
A |
16 |
13 |
1.00 |
25 |
0.520 |
|
|
|
|
|
|
|
81 |
A |
17 |
14 |
1.00 |
25 |
0.560 |
|
|
|
|
|
|
|
82 |
A |
16 |
13 |
1.00 |
25 |
0.520 |
|
|
|
|
|
|
|
83 |
A |
16 |
13 |
1.00 |
25 |
0.520 |
|
|
|
|
|
|
|
84 |
A |
16 |
13 |
1.00 |
25 |
0.520 |
|
|
|
|
|
|
|
85 |
A |
16 |
13 |
1.00 |
25 |
0.520 |
|
|
|
|
|
|
|
86 |
A |
16 |
13 |
1.00 |
25 |
0.520 |
|
|
|
|
|
|
|
87 |
A |
17 |
13 |
1.00 |
25 |
0.520 |
|
|
|
|
|
|
|
88 |
A |
5 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
89 |
A |
8 |
5 |
1.00 |
23 |
0.217 |
|
|
|
|
|
|
|
90 |
A |
3 |
3 |
1.00 |
27 |
0.111 |
|
|
|
|
|
|
|
91 |
A |
3 |
3 |
1.00 |
27 |
0.111 |
|
|
|
|
|
|
|
92 |
A |
2 |
2 |
1.00 |
23 |
0.087 |
|
|
|
|
|
|
|
93 |
A |
3 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
94 |
A |
4 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
95 |
A |
10 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
96 |
A |
9 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
97 |
A |
8 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
98 |
A |
10 |
7 |
1.00 |
27 |
0.259 |
|
|
|
|
|
|
|
99 |
A |
13 |
9 |
1.00 |
27 |
0.333 |
|
|
|
|
|
|
|
100 |
A |
13 |
9 |
1.00 |
27 |
0.333 |
|
|
|
|
|
|
|
101 |
A |
7 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
102 |
A |
8 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
103 |
A |
9 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
104 |
A |
7 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
105 |
A |
8 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
106 |
A |
9 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|