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 }
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 11, 13, 15, 16, 19, 22, 24, 26, 27, 30, 34, 35, 36, 37, 38, 40, 42, 43, 44, 45, 46, 47, 48,
49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 66, 67, 68, 69, 70, 71, 72, 73, 74, 77, 85, 87, 88, 90, 91, 92,
93, 94, 95, 96 }
B grade: { 75, 76, 78, 79, 80, 81, 82, 83, 84, 86, 89 }
C grade: { 5, 6, 7, 8, 9, 10, 12, 14, 17, 18, 20, 21, 23, 25, 28, 29, 31, 32, 33, 39, 41 }
F grade: { 58, 63, 64, 65 }
2.1.3 Maple
A grade: { 1, 2, 11, 12, 15, 16, 19, 22, 23, 26, 27, 30, 34, 35, 36, 38, 59, 66, 67, 68, 90, 94, 95, 96
}
B grade: { 37 }
C grade: { 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 17, 18, 20, 21, 24, 25, 28, 29, 31, 32, 33, 39, 40, 41 }
F grade: { 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 69, 70, 71,
72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93 }
2.1.4 Maxima
A grade: { 1, 2, 11, 15, 22, 26, 34, 36, 38, 59, 66, 67, 68, 90, 94, 95, 96 }
B grade: { }
C grade: { }
F grade: { 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 35,
37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63,
64, 65, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93
}
2.1.5 FriCAS
A grade: { 11, 12, 14, 22, 23, 26, 31, 32, 33, 34, 35, 59, 90, 94, 95, 96 }
B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 15, 16, 17, 18, 19, 20, 21, 24, 25, 27, 28, 29, 30, 36, 37, 38, 40, 66,
67, 68 }
C grade: { }
F grade: { 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63,
64, 65, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93
}
2.1.6 Sympy
A grade: { 1, 2, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 27, 28, 29, 30, 31, 36, 38,
66, 67, 68 }
B grade: { 26, 34, 35 }
C grade: { 12, 23, 42, 43, 44, 47 }
F grade: { 3, 4, 32, 33, 37, 39, 40, 41, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64,
65, 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
}
2.1.7 Giac
A grade: { 1, 2, 3, 10, 11, 12, 13, 14, 15, 16, 19, 21, 22, 23, 24, 25, 27, 30, 31, 32, 33, 34, 35, 36, 38, 40, 59,
90, 94, 95, 96 }
B grade: { 4, 26, 37, 66, 67, 68 }
C grade: { }
F grade: { 5, 6, 7, 8, 9, 17, 18, 20, 28, 29, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57,
58, 60, 61, 62, 63, 64, 65, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91,
92, 93 }
2.1.8 Mupad
A grade: { 59, 90, 94, 95, 96 }
B 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, 66, 67, 68 }
C grade: { }
F grade: { 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 69, 70, 71,
72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93 }
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 |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 305 | 305 | 334 | 329 | 282 | 3224 | 165 | 288 | 1331 |
normalized size | 1 | 1.00 | 1.10 | 1.08 | 0.92 | 10.57 | 0.54 | 0.94 | 4.36 |
time (sec) |
N/A |
0.249 |
0.100 |
0.115 |
1.494 |
1.315 |
3.111 |
0.429 |
1.542 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 323 | 323 | 337 | 386 | 313 | 3178 | 168 | 308 | 1293 |
normalized size | 1 | 1.00 | 1.04 | 1.20 | 0.97 | 9.84 | 0.52 | 0.95 | 4.00 |
time (sec) |
N/A |
0.189 |
0.116 |
0.110 |
1.341 |
1.321 |
3.123 |
0.379 |
2.973 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F |
B |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 754 | 754 | 534 | 34 | 0 | 3406 | 0 | 601 | 2510 |
normalized size | 1 | 1.00 | 0.71 | 0.05 | 0.00 | 4.52 | 0.00 | 0.80 | 3.33 |
time (sec) |
N/A |
1.247 |
0.628 |
0.018 |
0.000 |
1.710 |
0.000 |
0.737 |
2.780 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 329 | 329 | 425 | 39 | 0 | 3385 | 0 | 633 | 2438 |
normalized size | 1 | 1.00 | 1.29 | 0.12 | 0.00 | 10.29 | 0.00 | 1.92 | 7.41 |
time (sec) |
N/A |
0.209 |
0.134 |
0.013 |
0.000 |
1.776 |
0.000 |
0.753 |
2.719 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
C |
F |
B |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 791 | 791 | 67 | 53 | 0 | 3059 | 136 | 0 | 10409 |
normalized size | 1 | 1.00 | 0.08 | 0.07 | 0.00 | 3.87 | 0.17 | 0.00 | 13.16 |
time (sec) |
N/A |
0.863 |
0.045 |
0.049 |
0.000 |
1.328 |
8.503 |
0.000 |
3.825 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
C |
F |
B |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 791 | 791 | 67 | 53 | 0 | 3059 | 136 | 0 | 10411 |
normalized size | 1 | 1.00 | 0.08 | 0.07 | 0.00 | 3.87 | 0.17 | 0.00 | 13.16 |
time (sec) |
N/A |
0.805 |
0.035 |
0.049 |
0.000 |
1.367 |
7.139 |
0.000 |
4.030 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
C |
F |
B |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 349 | 349 | 69 | 55 | 0 | 3048 | 136 | 0 | 10337 |
normalized size | 1 | 1.00 | 0.20 | 0.16 | 0.00 | 8.73 | 0.39 | 0.00 | 29.62 |
time (sec) |
N/A |
0.422 |
0.045 |
0.033 |
0.000 |
1.152 |
8.251 |
0.000 |
4.035 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
C |
F |
B |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 751 | 751 | 69 | 55 | 0 | 3051 | 136 | 0 | 10343 |
normalized size | 1 | 1.00 | 0.09 | 0.07 | 0.00 | 4.06 | 0.18 | 0.00 | 13.77 |
time (sec) |
N/A |
0.925 |
0.039 |
0.034 |
0.000 |
1.239 |
7.255 |
0.000 |
4.204 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
C |
F |
B |
A |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 411 | 411 | 55 | 42 | 0 | 1443 | 75 | 0 | 5341 |
normalized size | 1 | 1.00 | 0.13 | 0.10 | 0.00 | 3.51 | 0.18 | 0.00 | 13.00 |
time (sec) |
N/A |
0.292 |
0.026 |
0.056 |
0.000 |
1.179 |
3.669 |
0.000 |
3.683 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
C |
F |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 451 | 451 | 55 | 42 | 0 | 951 | 24 | 239 | 459 |
normalized size | 1 | 1.00 | 0.12 | 0.09 | 0.00 | 2.11 | 0.05 | 0.53 | 1.02 |
time (sec) |
N/A |
0.407 |
0.015 |
0.010 |
0.000 |
1.051 |
1.475 |
0.931 |
0.176 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 64 | 58 | 72 | 95 | 73 | 72 | 33 |
normalized size | 1 | 1.00 | 0.75 | 0.68 | 0.85 | 1.12 | 0.86 | 0.85 | 0.39 |
time (sec) |
N/A |
0.045 |
0.020 |
0.003 |
1.587 |
0.909 |
0.154 |
0.388 |
1.562 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
A |
F |
A |
C |
A |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 135 | 109 | 0 | 211 | 190 | 108 | 95 |
normalized size | 1 | 1.00 | 0.96 | 0.78 | 0.00 | 1.51 | 1.36 | 0.77 | 0.68 |
time (sec) |
N/A |
0.095 |
0.174 |
0.018 |
0.000 |
0.898 |
0.702 |
0.420 |
0.144 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 347 | 347 | 258 | 27 | 0 | 991 | 19 | 247 | 311 |
normalized size | 1 | 1.00 | 0.74 | 0.08 | 0.00 | 2.86 | 0.05 | 0.71 | 0.90 |
time (sec) |
N/A |
0.247 |
0.188 |
0.008 |
0.000 |
0.866 |
2.784 |
0.875 |
2.284 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
C |
F |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 331 | 331 | 55 | 42 | 0 | 377 | 20 | 245 | 145 |
normalized size | 1 | 1.00 | 0.17 | 0.13 | 0.00 | 1.14 | 0.06 | 0.74 | 0.44 |
time (sec) |
N/A |
0.235 |
0.016 |
0.013 |
0.000 |
0.931 |
3.100 |
0.498 |
0.225 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 31 | 42 | 27 | 43 | 26 | 29 | 21 |
normalized size | 1 | 1.00 | 1.15 | 1.56 | 1.00 | 1.59 | 0.96 | 1.07 | 0.78 |
time (sec) |
N/A |
0.008 |
0.013 |
0.012 |
1.326 |
0.613 |
0.147 |
0.518 |
0.047 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
F |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 131 | 96 | 0 | 247 | 49 | 147 | 269 |
normalized size | 1 | 1.00 | 1.00 | 0.73 | 0.00 | 1.89 | 0.37 | 1.12 | 2.05 |
time (sec) |
N/A |
0.086 |
0.077 |
0.040 |
0.000 |
0.950 |
1.189 |
0.960 |
0.200 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
C |
F |
B |
A |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 53 | 40 | 0 | 331 | 24 | 0 | 399 |
normalized size | 1 | 1.00 | 0.34 | 0.25 | 0.00 | 2.11 | 0.15 | 0.00 | 2.54 |
time (sec) |
N/A |
0.087 |
0.013 |
0.013 |
0.000 |
0.826 |
0.192 |
0.000 |
1.721 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
A |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 55 | 42 | 0 | 574 | 24 | 0 | 483 |
normalized size | 1 | 1.00 | 0.32 | 0.25 | 0.00 | 3.36 | 0.14 | 0.00 | 2.82 |
time (sec) |
N/A |
0.151 |
0.013 |
0.013 |
0.000 |
0.939 |
0.195 |
0.000 |
1.758 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 111 | 78 | 0 | 181 | 49 | 123 | 233 |
normalized size | 1 | 1.00 | 0.95 | 0.67 | 0.00 | 1.55 | 0.42 | 1.05 | 1.99 |
time (sec) |
N/A |
0.057 |
0.054 |
0.062 |
0.000 |
0.756 |
1.157 |
0.907 |
0.190 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
A |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 511 | 511 | 57 | 44 | 0 | 1443 | 76 | 0 | 5341 |
normalized size | 1 | 1.00 | 0.11 | 0.09 | 0.00 | 2.82 | 0.15 | 0.00 | 10.45 |
time (sec) |
N/A |
0.359 |
0.025 |
0.003 |
0.000 |
0.850 |
3.632 |
0.000 |
3.743 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 411 | 411 | 57 | 44 | 0 | 894 | 26 | 223 | 447 |
normalized size | 1 | 1.00 | 0.14 | 0.11 | 0.00 | 2.18 | 0.06 | 0.54 | 1.09 |
time (sec) |
N/A |
0.321 |
0.015 |
0.012 |
0.000 |
0.973 |
1.455 |
0.685 |
1.677 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 90 | 68 | 82 | 126 | 82 | 82 | 44 |
normalized size | 1 | 1.00 | 0.93 | 0.70 | 0.85 | 1.30 | 0.85 | 0.85 | 0.45 |
time (sec) |
N/A |
0.052 |
0.065 |
0.007 |
1.557 |
0.826 |
0.176 |
0.300 |
1.616 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
C |
A |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 129 | 109 | 0 | 137 | 148 | 108 | 109 |
normalized size | 1 | 1.00 | 0.92 | 0.78 | 0.00 | 0.98 | 1.06 | 0.77 | 0.78 |
time (sec) |
N/A |
0.099 |
0.173 |
0.013 |
0.000 |
0.841 |
0.621 |
0.371 |
0.185 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 347 | 347 | 257 | 29 | 0 | 991 | 20 | 247 | 312 |
normalized size | 1 | 1.00 | 0.74 | 0.08 | 0.00 | 2.86 | 0.06 | 0.71 | 0.90 |
time (sec) |
N/A |
0.270 |
0.164 |
0.008 |
0.000 |
0.974 |
2.746 |
0.719 |
1.956 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 355 | 355 | 57 | 44 | 0 | 715 | 26 | 253 | 208 |
normalized size | 1 | 1.00 | 0.16 | 0.12 | 0.00 | 2.01 | 0.07 | 0.71 | 0.59 |
time (sec) |
N/A |
0.277 |
0.016 |
0.009 |
0.000 |
1.016 |
3.103 |
0.462 |
1.666 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 25 | 10 | 17 | 17 | 17 | 19 | 9 |
normalized size | 1 | 1.00 | 1.92 | 0.77 | 1.31 | 1.31 | 1.31 | 1.46 | 0.69 |
time (sec) |
N/A |
0.005 |
0.005 |
0.001 |
1.596 |
0.828 |
0.130 |
0.449 |
0.025 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 129 | 110 | 0 | 255 | 51 | 147 | 269 |
normalized size | 1 | 1.00 | 1.00 | 0.85 | 0.00 | 1.98 | 0.40 | 1.14 | 2.09 |
time (sec) |
N/A |
0.118 |
0.077 |
0.026 |
0.000 |
0.907 |
1.172 |
0.746 |
1.709 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
A |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 55 | 42 | 0 | 302 | 26 | 0 | 399 |
normalized size | 1 | 1.00 | 0.33 | 0.25 | 0.00 | 1.83 | 0.16 | 0.00 | 2.42 |
time (sec) |
N/A |
0.104 |
0.013 |
0.010 |
0.000 |
0.897 |
0.198 |
0.000 |
0.181 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
A |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 169 | 169 | 57 | 44 | 0 | 546 | 26 | 0 | 483 |
normalized size | 1 | 1.00 | 0.34 | 0.26 | 0.00 | 3.23 | 0.15 | 0.00 | 2.86 |
time (sec) |
N/A |
0.142 |
0.014 |
0.012 |
0.000 |
0.941 |
0.194 |
0.000 |
1.787 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 114 | 90 | 0 | 199 | 51 | 135 | 245 |
normalized size | 1 | 1.00 | 0.91 | 0.72 | 0.00 | 1.59 | 0.41 | 1.08 | 1.96 |
time (sec) |
N/A |
0.067 |
0.054 |
0.031 |
0.000 |
0.889 |
1.165 |
0.633 |
0.199 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 71 | 47 | 0 | 104 | 163 | 107 | 133 |
normalized size | 1 | 1.00 | 0.53 | 0.35 | 0.00 | 0.77 | 1.21 | 0.79 | 0.99 |
time (sec) |
N/A |
0.124 |
0.034 |
0.056 |
0.000 |
0.885 |
0.904 |
0.494 |
2.235 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F(-2) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 164 | 164 | 72 | 62 | 0 | 111 | 0 | 123 | 1 |
normalized size | 1 | 1.00 | 0.44 | 0.38 | 0.00 | 0.68 | 0.00 | 0.75 | 0.01 |
time (sec) |
N/A |
0.095 |
0.038 |
0.045 |
0.000 |
0.911 |
0.000 |
0.432 |
2.190 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F(-2) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 180 | 180 | 89 | 62 | 0 | 141 | 0 | 131 | 1 |
normalized size | 1 | 1.00 | 0.49 | 0.34 | 0.00 | 0.78 | 0.00 | 0.73 | 0.01 |
time (sec) |
N/A |
0.122 |
0.046 |
0.014 |
0.000 |
0.877 |
0.000 |
0.448 |
2.230 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 49 | 43 | 42 | 108 | 112 | 43 | 39 |
normalized size | 1 | 1.00 | 1.00 | 0.88 | 0.86 | 2.20 | 2.29 | 0.88 | 0.80 |
time (sec) |
N/A |
0.030 |
0.024 |
0.006 |
1.619 |
0.876 |
0.283 |
0.268 |
1.594 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 86 | 161 | 0 | 291 | 423 | 85 | 127 |
normalized size | 1 | 1.00 | 1.00 | 1.87 | 0.00 | 3.38 | 4.92 | 0.99 | 1.48 |
time (sec) |
N/A |
0.081 |
0.090 |
0.003 |
0.000 |
0.835 |
1.372 |
0.324 |
1.772 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 253 | 253 | 293 | 266 | 240 | 754 | 109 | 247 | 555 |
normalized size | 1 | 1.00 | 1.16 | 1.05 | 0.95 | 2.98 | 0.43 | 0.98 | 2.19 |
time (sec) |
N/A |
0.211 |
0.096 |
0.006 |
1.298 |
0.881 |
0.704 |
0.352 |
0.313 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 208 | 208 | 251 | 560 | 0 | 2540 | 0 | 3183 | 6366 |
normalized size | 1 | 1.00 | 1.21 | 2.69 | 0.00 | 12.21 | 0.00 | 15.30 | 30.61 |
time (sec) |
N/A |
0.543 |
0.173 |
0.027 |
0.000 |
1.051 |
0.000 |
3.756 |
2.854 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 311 | 311 | 346 | 334 | 295 | 3169 | 167 | 295 | 1308 |
normalized size | 1 | 1.00 | 1.11 | 1.07 | 0.95 | 10.19 | 0.54 | 0.95 | 4.21 |
time (sec) |
N/A |
0.290 |
0.112 |
0.084 |
1.525 |
1.296 |
2.981 |
0.534 |
3.100 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 716 | 716 | 88 | 67 | 0 | 0 | 0 | 0 | 11453 |
normalized size | 1 | 1.00 | 0.12 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 16.00 |
time (sec) |
N/A |
1.634 |
0.054 |
0.016 |
0.000 |
0.000 |
0.000 |
0.000 |
29.420 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 753 | 753 | 551 | 45 | 0 | 3378 | 0 | 647 | 2520 |
normalized size | 1 | 1.00 | 0.73 | 0.06 | 0.00 | 4.49 | 0.00 | 0.86 | 3.35 |
time (sec) |
N/A |
1.436 |
0.903 |
0.004 |
0.000 |
1.945 |
0.000 |
0.808 |
1.220 |
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 433 | 433 | 88 | 67 | 0 | 0 | 0 | 0 | 50213 |
normalized size | 1 | 1.00 | 0.20 | 0.15 | 0.00 | 0.00 | 0.00 | 0.00 | 115.97 |
time (sec) |
N/A |
0.989 |
0.075 |
0.007 |
0.000 |
0.000 |
0.000 |
0.000 |
9.242 |
|
|
|
|
|
|
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|
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|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 127 | 0 | 0 | 0 | 337 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 2.39 | 0.00 | -0.01 |
time (sec) |
N/A |
0.145 |
0.242 |
0.105 |
0.000 |
0.923 |
10.965 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
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|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 107 | 0 | 0 | 0 | 207 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.93 | 0.00 | -0.01 |
time (sec) |
N/A |
0.097 |
0.150 |
0.089 |
0.000 |
0.968 |
7.651 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 83 | 0 | 0 | 0 | 153 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.84 | 0.00 | -0.01 |
time (sec) |
N/A |
0.027 |
0.039 |
0.084 |
0.000 |
1.019 |
5.543 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 152 | 152 | 131 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.111 |
0.137 |
0.104 |
0.000 |
1.175 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 186 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.174 |
0.255 |
0.167 |
0.000 |
1.158 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 81 | 0 | 0 | 0 | 158 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.95 | 0.00 | -0.01 |
time (sec) |
N/A |
0.028 |
0.059 |
0.083 |
0.000 |
1.039 |
5.703 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 288 | 288 | 188 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.252 |
0.271 |
0.087 |
0.000 |
1.108 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 203 | 203 | 136 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.167 |
0.157 |
0.086 |
0.000 |
0.590 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 134 | 134 | 83 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.054 |
0.042 |
0.089 |
0.000 |
1.007 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 333 | 333 | 227 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.224 |
0.267 |
0.156 |
0.000 |
1.068 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 410 | 410 | 298 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.379 |
0.475 |
0.178 |
0.000 |
1.362 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 424 | 424 | 188 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.383 |
0.291 |
0.103 |
0.000 |
1.068 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 272 | 272 | 136 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.247 |
0.165 |
0.102 |
0.000 |
1.114 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 83 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.101 |
0.044 |
0.098 |
0.000 |
1.054 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 582 | 582 | 346 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.416 |
0.429 |
0.202 |
0.000 |
1.624 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 701 | 701 | 426 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.692 |
0.704 |
0.234 |
0.000 |
2.909 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
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 | 171 | 171 | 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 |
0.166 |
0.152 |
0.099 |
0.000 |
1.051 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
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 |
0.008 |
0.155 |
0.155 |
0.000 |
0.886 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 299 | 299 | 213 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.160 |
0.198 |
0.127 |
0.000 |
0.982 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 217 | 217 | 171 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.101 |
0.104 |
0.108 |
0.000 |
0.990 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 110 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.060 |
0.047 |
0.111 |
0.000 |
1.190 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 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 |
0.142 |
0.070 |
0.112 |
0.000 |
1.145 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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|
|
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|
|
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|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 261 | 261 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.235 |
0.101 |
0.103 |
0.000 |
1.387 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 357 | 357 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.338 |
0.316 |
0.102 |
0.000 |
1.490 |
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 |
A |
A |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 57 | 66 | 82 | 137 | 656 | 207 | 59 |
normalized size | 1 | 1.00 | 0.92 | 1.06 | 1.32 | 2.21 | 10.58 | 3.34 | 0.95 |
time (sec) |
N/A |
0.039 |
0.152 |
0.013 |
0.550 |
1.099 |
1.320 |
0.351 |
1.662 |
|
|
|
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|
Problem 67 |
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 | 132 | 132 | 123 | 138 | 208 | 495 | 3128 | 828 | 131 |
normalized size | 1 | 1.00 | 0.93 | 1.05 | 1.58 | 3.75 | 23.70 | 6.27 | 0.99 |
time (sec) |
N/A |
0.102 |
0.248 |
0.015 |
0.695 |
0.921 |
10.968 |
0.453 |
1.711 |
|
|
|
|
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|
Problem 68 |
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 | 218 | 218 | 205 | 226 | 386 | 1209 | 9190 | 2134 | 227 |
normalized size | 1 | 1.00 | 0.94 | 1.04 | 1.77 | 5.55 | 42.16 | 9.79 | 1.04 |
time (sec) |
N/A |
0.201 |
0.426 |
0.020 |
0.882 |
0.798 |
89.545 |
0.779 |
1.850 |
|
|
|
|
|
|
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|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 308 | 308 | 295 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.699 |
0.843 |
0.067 |
0.000 |
1.065 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 224 | 224 | 216 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.476 |
0.524 |
0.043 |
0.000 |
0.890 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 154 | 134 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.120 |
0.074 |
0.026 |
0.000 |
0.796 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 243 | 243 | 200 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.469 |
0.438 |
0.092 |
0.000 |
0.915 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 368 | 368 | 327 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.707 |
0.893 |
0.174 |
0.000 |
1.239 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 552 | 552 | 509 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.023 |
1.744 |
0.200 |
0.000 |
4.528 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 750 | 750 | 5537 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 7.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.938 |
6.957 |
0.075 |
0.000 |
1.097 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 543 | 543 | 2980 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 5.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.818 |
4.517 |
0.072 |
0.000 |
1.047 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 362 | 328 | 603 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.91 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.630 |
5.690 |
0.065 |
0.000 |
1.156 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 726 | 726 | 11767 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 16.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.927 |
7.223 |
0.197 |
0.000 |
2.021 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1129 | 1129 | 16855 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 14.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.341 |
8.022 |
0.256 |
0.000 |
6.746 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1707 | 1707 | 13018 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 7.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
5.253 |
7.791 |
0.127 |
0.000 |
1.202 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1191 | 1191 | 10910 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 9.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
4.010 |
6.869 |
0.122 |
0.000 |
1.053 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 713 | 713 | 8593 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 12.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.663 |
6.596 |
0.112 |
0.000 |
0.806 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1708 | 1708 | 43535 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 25.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
5.074 |
8.532 |
0.394 |
0.000 |
20.854 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2446 | 2446 | 56566 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 23.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
8.935 |
9.930 |
0.531 |
0.000 |
71.248 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 292 | 292 | 424 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.355 |
1.610 |
0.066 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 294 | 294 | 690 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.348 |
4.525 |
0.066 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 292 | 292 | 245 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.338 |
0.330 |
0.025 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 298 | 298 | 414 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.346 |
1.479 |
0.014 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 298 | 298 | 6752 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 22.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.347 |
6.566 |
0.013 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 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 |
0.010 |
0.286 |
0.137 |
0.000 |
0.856 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 606 | 606 | 438 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.622 |
1.069 |
0.128 |
0.000 |
1.156 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 447 | 447 | 338 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.461 |
0.745 |
0.099 |
0.000 |
1.036 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 288 | 288 | 243 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.287 |
0.458 |
0.109 |
0.000 |
0.891 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 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 |
0.011 |
0.151 |
0.105 |
0.000 |
0.912 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 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 |
0.011 |
0.189 |
0.088 |
0.000 |
1.001 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 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 |
0.012 |
0.728 |
0.083 |
0.000 |
1.148 |
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 [38] had the largest ratio of
[.5882]
|
|
|
|
|
|
|
| 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 |
12 |
8 |
1.00 |
17 |
0.471 |
|
|
|
|
|
|
|
2 |
A |
13 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
3 |
A |
19 |
6 |
1.00 |
17 |
0.353 |
|
|
|
|
|
|
|
4 |
A |
13 |
10 |
1.00 |
18 |
0.556 |
|
|
|
|
|
|
|
5 |
A |
19 |
6 |
1.00 |
26 |
0.231 |
|
|
|
|
|
|
|
6 |
A |
19 |
6 |
1.00 |
26 |
0.231 |
|
|
|
|
|
|
|
7 |
A |
7 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
8 |
A |
19 |
6 |
1.00 |
27 |
0.222 |
|
|
|
|
|
|
|
9 |
A |
19 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
10 |
A |
19 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
11 |
A |
10 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
12 |
A |
19 |
6 |
1.00 |
16 |
0.375 |
|
|
|
|
|
|
|
13 |
A |
19 |
6 |
1.00 |
13 |
0.462 |
|
|
|
|
|
|
|
14 |
A |
19 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
15 |
A |
5 |
5 |
1.00 |
18 |
0.278 |
|
|
|
|
|
|
|
16 |
A |
7 |
4 |
1.00 |
18 |
0.222 |
|
|
|
|
|
|
|
17 |
A |
7 |
4 |
1.00 |
18 |
0.222 |
|
|
|
|
|
|
|
18 |
A |
7 |
4 |
1.00 |
18 |
0.222 |
|
|
|
|
|
|
|
19 |
A |
7 |
4 |
1.00 |
18 |
0.222 |
|
|
|
|
|
|
|
20 |
A |
19 |
6 |
1.00 |
20 |
0.300 |
|
|
|
|
|
|
|
21 |
A |
19 |
7 |
1.00 |
20 |
0.350 |
|
|
|
|
|
|
|
22 |
A |
11 |
8 |
1.00 |
20 |
0.400 |
|
|
|
|
|
|
|
23 |
A |
19 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
24 |
A |
19 |
6 |
1.00 |
15 |
0.400 |
|
|
|
|
|
|
|
25 |
A |
19 |
6 |
1.00 |
20 |
0.300 |
|
|
|
|
|
|
|
26 |
A |
5 |
5 |
1.00 |
20 |
0.250 |
|
|
|
|
|
|
|
27 |
A |
7 |
4 |
1.00 |
20 |
0.200 |
|
|
|
|
|
|
|
28 |
A |
7 |
4 |
1.00 |
20 |
0.200 |
|
|
|
|
|
|
|
29 |
A |
7 |
4 |
1.00 |
20 |
0.200 |
|
|
|
|
|
|
|
30 |
A |
7 |
4 |
1.00 |
20 |
0.200 |
|
|
|
|
|
|
|
31 |
A |
9 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
32 |
A |
9 |
6 |
1.00 |
26 |
0.231 |
|
|
|
|
|
|
|
33 |
A |
9 |
6 |
1.00 |
33 |
0.182 |
|
|
|
|
|
|
|
34 |
A |
5 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
35 |
A |
6 |
6 |
1.00 |
22 |
0.273 |
|
|
|
|
|
|
|
36 |
A |
11 |
8 |
1.00 |
17 |
0.471 |
|
|
|
|
|
|
|
37 |
A |
5 |
4 |
1.00 |
22 |
0.182 |
|
|
|
|
|
|
|
38 |
A |
14 |
10 |
1.00 |
17 |
0.588 |
|
|
|
|
|
|
|
39 |
A |
15 |
9 |
1.00 |
22 |
0.409 |
|
|
|
|
|
|
|
40 |
A |
21 |
8 |
1.00 |
17 |
0.471 |
|
|
|
|
|
|
|
41 |
A |
9 |
6 |
1.00 |
22 |
0.273 |
|
|
|
|
|
|
|
42 |
A |
5 |
4 |
1.00 |
21 |
0.190 |
|
|
|
|
|
|
|
43 |
A |
5 |
4 |
1.00 |
21 |
0.190 |
|
|
|
|
|
|
|
44 |
A |
3 |
3 |
1.00 |
19 |
0.158 |
|
|
|
|
|
|
|
45 |
A |
6 |
4 |
1.00 |
21 |
0.190 |
|
|
|
|
|
|
|
46 |
A |
7 |
4 |
1.00 |
21 |
0.190 |
|
|
|
|
|
|
|
47 |
A |
3 |
3 |
1.00 |
20 |
0.150 |
|
|
|
|
|
|
|
48 |
A |
9 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
49 |
A |
7 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
50 |
A |
4 |
4 |
1.00 |
19 |
0.210 |
|
|
|
|
|
|
|
51 |
A |
10 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
52 |
A |
11 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
53 |
A |
11 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
54 |
A |
8 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
55 |
A |
5 |
4 |
1.00 |
19 |
0.210 |
|
|
|
|
|
|
|
56 |
A |
15 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
57 |
A |
16 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
58 |
A |
6 |
5 |
1.00 |
23 |
0.217 |
|
|
|
|
|
|
|
59 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
60 |
A |
10 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
61 |
A |
8 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
62 |
A |
6 |
5 |
1.00 |
19 |
0.263 |
|
|
|
|
|
|
|
63 |
A |
6 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
64 |
A |
8 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
65 |
A |
10 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
66 |
A |
2 |
1 |
1.00 |
22 |
0.045 |
|
|
|
|
|
|
|
67 |
A |
2 |
1 |
1.00 |
24 |
0.042 |
|
|
|
|
|
|
|
68 |
A |
2 |
1 |
1.00 |
24 |
0.042 |
|
|
|
|
|
|
|
69 |
A |
5 |
3 |
1.00 |
26 |
0.115 |
|
|
|
|
|
|
|
70 |
A |
5 |
3 |
1.00 |
26 |
0.115 |
|
|
|
|
|
|
|
71 |
A |
3 |
2 |
1.00 |
24 |
0.083 |
|
|
|
|
|
|
|
72 |
A |
6 |
3 |
1.00 |
26 |
0.115 |
|
|
|
|
|
|
|
73 |
A |
7 |
3 |
1.00 |
26 |
0.115 |
|
|
|
|
|
|
|
74 |
A |
8 |
3 |
1.00 |
26 |
0.115 |
|
|
|
|
|
|
|
75 |
A |
9 |
4 |
1.00 |
26 |
0.154 |
|
|
|
|
|
|
|
76 |
A |
9 |
5 |
1.00 |
26 |
0.192 |
|
|
|
|
|
|
|
77 |
A |
4 |
3 |
0.91 |
24 |
0.125 |
|
|
|
|
|
|
|
78 |
A |
10 |
4 |
1.00 |
26 |
0.154 |
|
|
|
|
|
|
|
79 |
A |
11 |
4 |
1.00 |
26 |
0.154 |
|
|
|
|
|
|
|
80 |
A |
11 |
4 |
1.00 |
26 |
0.154 |
|
|
|
|
|
|
|
81 |
A |
11 |
5 |
1.00 |
26 |
0.192 |
|
|
|
|
|
|
|
82 |
A |
5 |
3 |
1.00 |
24 |
0.125 |
|
|
|
|
|
|
|
83 |
A |
15 |
4 |
1.00 |
26 |
0.154 |
|
|
|
|
|
|
|
84 |
A |
16 |
4 |
1.00 |
26 |
0.154 |
|
|
|
|
|
|
|
85 |
A |
6 |
5 |
1.00 |
26 |
0.192 |
|
|
|
|
|
|
|
86 |
A |
6 |
5 |
1.00 |
26 |
0.192 |
|
|
|
|
|
|
|
87 |
A |
6 |
5 |
1.00 |
26 |
0.192 |
|
|
|
|
|
|
|
88 |
A |
6 |
5 |
1.00 |
26 |
0.192 |
|
|
|
|
|
|
|
89 |
A |
6 |
5 |
1.00 |
26 |
0.192 |
|
|
|
|
|
|
|
90 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
91 |
A |
10 |
5 |
1.00 |
26 |
0.192 |
|
|
|
|
|
|
|
92 |
A |
8 |
5 |
1.00 |
26 |
0.192 |
|
|
|
|
|
|
|
93 |
A |
6 |
5 |
1.00 |
24 |
0.208 |
|
|
|
|
|
|
|
94 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
95 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
96 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|