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, 107, 108, 109, 110, 111, 112,
113, 114, 115, 116, 117, 118 }
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 45, 46, 47, 49, 51, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 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, 105, 106, 108,
109, 110, 111, 112, 113, 116, 117, 118 }
B grade: { 9, 13, 17, 18, 21, 55, 69, 114 }
C grade: { 37, 38, 39, 40, 41, 42, 43, 44, 48, 50, 52, 115 }
F grade: { 20, 102, 103, 104, 107 }
2.1.3 Maple
A grade: { 4, 17, 19, 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, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 76, 83, 101, 103, 104,
105, 106, 107, 114, 115, 116 }
B grade: { 1, 2, 3, 9, 13, 14, 15, 16, 18, 52, 102 }
C grade: { 5, 6, 7, 8, 10, 11, 12 }
F grade: { 20, 21, 22, 51, 70, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94,
95, 96, 97, 98, 99, 100, 108, 109, 110, 111, 112, 113, 117, 118 }
2.1.4 Maxima
A grade: { 16, 19, 23, 27, 46, 47, 49, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 71, 72, 76, 83,
101, 105, 106 }
B grade: { 24, 25, 26 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 20, 21, 22, 28, 29, 30, 31, 32, 33, 34, 35, 36,
37, 38, 39, 40, 41, 42, 43, 44, 45, 48, 50, 51, 52, 56, 63, 69, 70, 73, 74, 75, 77, 78, 79, 80, 81, 82, 84, 85, 86,
87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 102, 103, 104, 107, 108, 109, 110, 111, 112, 113, 114,
115, 116, 117, 118 }
2.1.5 FriCAS
A grade: { 19, 23, 24, 25, 26, 27, 32, 33, 46, 47, 49, 53, 54, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 71, 72,
73, 74, 75, 76, 80, 81, 82, 83, 101, 105, 106, 108, 109, 110, 111, 117, 118 }
B grade: { 29, 30, 31, 55, 114 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 28, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 48, 50, 51, 52, 56, 63, 69, 70, 77, 78, 79, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96,
97, 98, 99, 100, 102, 103, 104, 107, 112, 113, 115, 116 }
2.1.6 Sympy
A grade: { 23, 24, 25, 26, 27, 32, 33, 46, 47, 48, 49, 50, 52, 54, 55, 57, 59, 60, 61, 62, 65, 66, 67, 68, 71, 72,
108, 109, 110, 111 }
B grade: { }
C grade: { 53, 58, 64 }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 28, 29, 30, 31, 34, 35, 36,
37, 38, 39, 40, 41, 42, 43, 44, 45, 51, 56, 63, 69, 70, 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, 107, 112, 113, 114, 115, 116,
117, 118 }
2.1.7 Giac
A grade: { 19, 23, 25, 26, 27, 29, 32, 33, 34, 35, 36, 43, 44, 46, 47, 49, 53, 57, 58, 59, 60, 61, 62, 64, 68, 71,
72, 76, 83, 101, 105, 106, 108, 109, 110, 111, 116 }
B grade: { 24, 30, 31, 37, 38, 39, 40, 54, 55, 65, 66, 67, 114, 115 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 28, 41, 42, 45, 48, 50, 51, 52,
56, 63, 69, 70, 73, 74, 75, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,
100, 102, 103, 104, 107, 112, 113, 117, 118 }
2.1.8 Mupad
A grade: { 19, 23, 101, 105, 106 }
B grade: { 27, 32, 33, 47, 49, 54, 55, 57, 58, 62, 68, 71, 72, 76, 83, 114, 118 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28,
29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 50, 51, 52, 53, 56, 59, 60, 61,
63, 64, 65, 66, 67, 69, 70, 73, 74, 75, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92,
93, 94, 95, 96, 97, 98, 99, 100, 102, 103, 104, 107, 108, 109, 110, 111, 112, 113, 115, 116, 117
}
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 |
B |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 670 | 670 | 442 | 1285 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.66 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.705 |
1.329 |
2.063 |
0.000 |
0.453 |
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 |
A |
B |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 450 | 450 | 320 | 912 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.71 | 2.03 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.530 |
1.401 |
1.323 |
0.000 |
0.454 |
0.000 |
0.000 |
0.000 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 238 | 238 | 219 | 491 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.92 | 2.06 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.251 |
1.594 |
1.059 |
0.000 |
0.446 |
0.000 |
0.000 |
0.000 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
F(-2) |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 725 | 725 | 1095 | 1209 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.51 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.859 |
3.693 |
0.956 |
0.000 |
0.478 |
0.000 |
0.000 |
0.000 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F(-2) |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 851 | 851 | 1130 | 1573 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.33 | 1.85 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.694 |
9.737 |
1.242 |
0.000 |
0.456 |
0.000 |
0.000 |
0.000 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 959 | 959 | 910 | 3314 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 3.46 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.962 |
4.840 |
1.940 |
0.000 |
0.484 |
0.000 |
0.000 |
0.000 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 680 | 680 | 591 | 3643 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.87 | 5.36 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.735 |
2.269 |
1.345 |
0.000 |
0.446 |
0.000 |
0.000 |
0.000 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 370 | 370 | 337 | 2320 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.91 | 6.27 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.335 |
1.617 |
1.032 |
0.000 |
0.474 |
0.000 |
0.000 |
0.000 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
B |
F(-2) |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1064 | 1064 | 3034 | 2132 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.85 | 2.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.280 |
12.659 |
1.011 |
0.000 |
0.457 |
0.000 |
0.000 |
0.000 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F |
F |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1281 | 1281 | 1144 | 4046 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.89 | 3.16 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.177 |
7.986 |
2.028 |
0.000 |
0.488 |
0.000 |
0.000 |
0.000 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F |
F |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 940 | 940 | 794 | 5035 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.84 | 5.36 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.959 |
4.694 |
1.429 |
0.000 |
0.507 |
0.000 |
0.000 |
0.000 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F |
F |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 517 | 517 | 526 | 4030 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.02 | 7.79 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.403 |
3.028 |
1.099 |
0.000 |
0.484 |
0.000 |
0.000 |
0.000 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
B |
F(-2) |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1637 | 1637 | 6216 | 4692 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.80 | 2.87 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.730 |
20.288 |
1.566 |
0.000 |
0.471 |
0.000 |
0.000 |
0.000 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 450 | 450 | 342 | 843 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.76 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.585 |
1.347 |
1.737 |
0.000 |
0.449 |
0.000 |
0.000 |
0.000 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 270 | 270 | 266 | 548 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 2.03 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.436 |
0.844 |
1.319 |
0.000 |
0.471 |
0.000 |
0.000 |
0.000 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
A |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 172 | 235 | 108 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.35 | 1.85 | 0.85 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.223 |
0.452 |
1.005 |
0.435 |
0.450 |
0.000 |
0.000 |
0.000 |
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|
|
|
|
|
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|
|
Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 370 | 370 | 930 | 487 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.51 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.606 |
2.099 |
0.651 |
0.000 |
0.438 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
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|
|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 496 | 496 | 1108 | 1622 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.23 | 3.27 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.722 |
5.504 |
1.070 |
0.000 |
0.440 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
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|
|
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|
Problem 19 |
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 | 38 | 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 |
0.192 |
0.164 |
12.110 |
0.000 |
0.522 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 20 |
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 | 496 | 496 | 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 |
0.791 |
27.447 |
9.971 |
0.000 |
0.483 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
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|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 374 | 374 | 1248 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.611 |
5.589 |
8.306 |
0.000 |
0.457 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
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 | 237 | 237 | 246 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.338 |
0.022 |
0.020 |
0.000 |
0.505 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 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 |
0.200 |
0.204 |
7.587 |
0.000 |
0.572 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 104 | 235 | 333 | 94 | 255 | 242 | -1 |
normalized size | 1 | 1.00 | 0.76 | 1.72 | 2.43 | 0.69 | 1.86 | 1.77 | -0.01 |
time (sec) |
N/A |
0.194 |
0.122 |
0.023 |
0.416 |
0.468 |
1.350 |
0.715 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 83 | 161 | 220 | 75 | 170 | 156 | -1 |
normalized size | 1 | 1.00 | 0.88 | 1.71 | 2.34 | 0.80 | 1.81 | 1.66 | -0.01 |
time (sec) |
N/A |
0.115 |
0.089 |
0.006 |
0.419 |
0.478 |
0.639 |
1.935 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 69 | 78 | 153 | 59 | 104 | 88 | -1 |
normalized size | 1 | 1.00 | 0.86 | 0.98 | 1.91 | 0.74 | 1.30 | 1.10 | -0.01 |
time (sec) |
N/A |
0.073 |
0.050 |
0.006 |
0.418 |
0.457 |
0.288 |
0.944 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
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 | 36 | 36 | 47 | 33 | 32 | 41 | 46 | 32 | 88 |
normalized size | 1 | 1.00 | 1.31 | 0.92 | 0.89 | 1.14 | 1.28 | 0.89 | 2.44 |
time (sec) |
N/A |
0.017 |
0.040 |
0.003 |
0.419 |
0.465 |
0.151 |
1.976 |
0.543 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 177 | 228 | 199 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.29 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.276 |
0.206 |
0.215 |
0.000 |
0.446 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 79 | 77 | 0 | 360 | 0 | 79 | -1 |
normalized size | 1 | 1.00 | 1.25 | 1.22 | 0.00 | 5.71 | 0.00 | 1.25 | -0.02 |
time (sec) |
N/A |
0.076 |
0.060 |
0.006 |
0.000 |
0.525 |
0.000 |
2.989 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 126 | 118 | 0 | 482 | 0 | 242 | -1 |
normalized size | 1 | 1.00 | 1.22 | 1.15 | 0.00 | 4.68 | 0.00 | 2.35 | -0.01 |
time (sec) |
N/A |
0.111 |
0.185 |
0.008 |
0.000 |
0.537 |
0.000 |
0.299 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 144 | 144 | 168 | 227 | 0 | 580 | 0 | 557 | -1 |
normalized size | 1 | 1.00 | 1.17 | 1.58 | 0.00 | 4.03 | 0.00 | 3.87 | -0.01 |
time (sec) |
N/A |
0.179 |
0.197 |
0.008 |
0.000 |
0.560 |
0.000 |
0.280 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 74 | 71 | 0 | 66 | 109 | 78 | 60 |
normalized size | 1 | 1.00 | 0.90 | 0.87 | 0.00 | 0.80 | 1.33 | 0.95 | 0.73 |
time (sec) |
N/A |
0.082 |
0.038 |
0.065 |
0.000 |
0.475 |
0.525 |
0.184 |
0.281 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 49 | 48 | 0 | 53 | 63 | 52 | 44 |
normalized size | 1 | 1.00 | 1.04 | 1.02 | 0.00 | 1.13 | 1.34 | 1.11 | 0.94 |
time (sec) |
N/A |
0.054 |
0.023 |
0.057 |
0.000 |
0.475 |
0.243 |
2.141 |
0.253 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 12 | 13 | 0 | 0 | 0 | 12 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 1.00 | -0.08 |
time (sec) |
N/A |
0.022 |
0.027 |
0.072 |
0.000 |
0.420 |
0.000 |
0.196 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 40 | 40 | 37 | 0 | 0 | 0 | 38 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.95 | -0.02 |
time (sec) |
N/A |
0.078 |
0.054 |
0.073 |
0.000 |
0.421 |
0.000 |
2.782 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 65 | 53 | 0 | 0 | 0 | 57 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.88 | -0.02 |
time (sec) |
N/A |
0.081 |
0.054 |
0.079 |
0.000 |
0.426 |
0.000 |
0.203 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
B |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 90 | 140 | 0 | 0 | 0 | 209 | -1 |
normalized size | 1 | 1.00 | 0.81 | 1.26 | 0.00 | 0.00 | 0.00 | 1.88 | -0.01 |
time (sec) |
N/A |
0.147 |
0.053 |
0.153 |
0.000 |
0.000 |
0.000 |
0.456 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
B |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 76 | 105 | 0 | 0 | 0 | 164 | -1 |
normalized size | 1 | 1.00 | 0.85 | 1.18 | 0.00 | 0.00 | 0.00 | 1.84 | -0.01 |
time (sec) |
N/A |
0.092 |
0.039 |
0.138 |
0.000 |
0.000 |
0.000 |
0.389 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
B |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 90 | 66 | 0 | 0 | 0 | 117 | -1 |
normalized size | 1 | 1.00 | 1.64 | 1.20 | 0.00 | 0.00 | 0.00 | 2.13 | -0.02 |
time (sec) |
N/A |
0.081 |
0.041 |
0.152 |
0.000 |
0.000 |
0.000 |
0.271 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
B |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 78 | 28 | 0 | 0 | 0 | 72 | -1 |
normalized size | 1 | 1.00 | 2.36 | 0.85 | 0.00 | 0.00 | 0.00 | 2.18 | -0.03 |
time (sec) |
N/A |
0.030 |
0.034 |
0.069 |
0.000 |
0.000 |
0.000 |
0.418 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 97 | 84 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.52 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.086 |
0.053 |
0.144 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 139 | 120 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.54 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.092 |
0.307 |
0.148 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-2) |
F |
A |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 106 | 106 | 128 | 89 | 0 | 0 | 0 | 171 | -1 |
normalized size | 1 | 1.00 | 1.21 | 0.84 | 0.00 | 0.00 | 0.00 | 1.61 | -0.01 |
time (sec) |
N/A |
0.130 |
0.052 |
0.096 |
0.000 |
0.000 |
0.000 |
1.673 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-2) |
F |
A |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 133 | 91 | 0 | 0 | 0 | 175 | -1 |
normalized size | 1 | 1.00 | 1.23 | 0.84 | 0.00 | 0.00 | 0.00 | 1.62 | -0.01 |
time (sec) |
N/A |
0.116 |
0.107 |
0.092 |
0.000 |
0.000 |
0.000 |
1.996 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 59 | 85 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.87 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.081 |
0.044 |
0.164 |
0.000 |
0.447 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 30 | 33 | 30 | 26 | 48 | 27 | -1 |
normalized size | 1 | 1.00 | 0.88 | 0.97 | 0.88 | 0.76 | 1.41 | 0.79 | -0.03 |
time (sec) |
N/A |
0.030 |
0.016 |
0.208 |
0.409 |
0.455 |
20.180 |
0.851 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
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 | 51 | 51 | 48 | 65 | 79 | 41 | 48 | 46 | 42 |
normalized size | 1 | 1.00 | 0.94 | 1.27 | 1.55 | 0.80 | 0.94 | 0.90 | 0.82 |
time (sec) |
N/A |
0.039 |
0.029 |
0.073 |
0.410 |
0.451 |
0.753 |
1.022 |
0.302 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 63 | 79 | 0 | 0 | 48 | 0 | -1 |
normalized size | 1 | 1.00 | 1.15 | 1.44 | 0.00 | 0.00 | 0.87 | 0.00 | -0.02 |
time (sec) |
N/A |
0.028 |
0.163 |
0.008 |
0.000 |
0.421 |
1.226 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
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 | 35 | 35 | 35 | 32 | 31 | 31 | 32 | 31 | 29 |
normalized size | 1 | 1.00 | 1.00 | 0.91 | 0.89 | 0.89 | 0.91 | 0.89 | 0.83 |
time (sec) |
N/A |
0.024 |
0.015 |
0.004 |
0.405 |
0.416 |
0.186 |
0.177 |
0.328 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 34 | 65 | 0 | 0 | 44 | 0 | -1 |
normalized size | 1 | 1.00 | 0.79 | 1.51 | 0.00 | 0.00 | 1.02 | 0.00 | -0.02 |
time (sec) |
N/A |
0.032 |
0.005 |
0.007 |
0.000 |
0.446 |
1.002 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
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 | 62 | 62 | 56 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.058 |
0.032 |
0.076 |
0.000 |
0.431 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 40 | 57 | 0 | 0 | 44 | 0 | -1 |
normalized size | 1 | 1.00 | 1.38 | 1.97 | 0.00 | 0.00 | 1.52 | 0.00 | -0.03 |
time (sec) |
N/A |
0.014 |
0.042 |
0.008 |
0.000 |
0.493 |
1.073 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
C |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 61 | 56 | 72 | 93 | 97 | 77 | -1 |
normalized size | 1 | 1.00 | 1.05 | 0.97 | 1.24 | 1.60 | 1.67 | 1.33 | -0.02 |
time (sec) |
N/A |
0.036 |
0.057 |
0.018 |
0.406 |
0.447 |
2.865 |
0.191 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 33 | 39 | 28 | 32 | 48 | 64 | 28 |
normalized size | 1 | 1.00 | 0.97 | 1.15 | 0.82 | 0.94 | 1.41 | 1.88 | 0.82 |
time (sec) |
N/A |
0.017 |
0.023 |
0.007 |
0.402 |
0.435 |
1.540 |
0.209 |
0.239 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 84 | 30 | 45 | 65 | 27 | 55 | 28 |
normalized size | 1 | 1.00 | 3.11 | 1.11 | 1.67 | 2.41 | 1.00 | 2.04 | 1.04 |
time (sec) |
N/A |
0.017 |
0.109 |
0.009 |
0.406 |
0.480 |
1.714 |
0.243 |
0.567 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 60 | 77 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.055 |
0.021 |
0.043 |
0.000 |
0.435 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
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 | 30 | 30 | 30 | 32 | 31 | 36 | 26 | 31 | 28 |
normalized size | 1 | 1.00 | 1.00 | 1.07 | 1.03 | 1.20 | 0.87 | 1.03 | 0.93 |
time (sec) |
N/A |
0.022 |
0.018 |
0.004 |
0.404 |
0.423 |
1.720 |
0.165 |
0.028 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
C |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 50 | 47 | 77 | 47 | 100 | 44 | 42 |
normalized size | 1 | 1.00 | 0.98 | 0.92 | 1.51 | 0.92 | 1.96 | 0.86 | 0.82 |
time (sec) |
N/A |
0.033 |
0.027 |
0.007 |
0.406 |
0.437 |
3.101 |
1.814 |
0.285 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 47 | 55 | 49 | 49 | 100 | 52 | -1 |
normalized size | 1 | 1.00 | 0.84 | 0.98 | 0.88 | 0.88 | 1.79 | 0.93 | -0.02 |
time (sec) |
N/A |
0.038 |
0.033 |
0.007 |
0.405 |
0.426 |
3.029 |
3.985 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 46 | 53 | 52 | 36 | 73 | 52 | -1 |
normalized size | 1 | 1.00 | 0.59 | 0.68 | 0.67 | 0.46 | 0.94 | 0.67 | -0.01 |
time (sec) |
N/A |
0.028 |
0.039 |
0.005 |
0.406 |
0.435 |
8.091 |
3.963 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 41 | 41 | 40 | 31 | 58 | 40 | -1 |
normalized size | 1 | 1.00 | 0.68 | 0.68 | 0.67 | 0.52 | 0.97 | 0.67 | -0.02 |
time (sec) |
N/A |
0.019 |
0.031 |
0.004 |
0.404 |
0.434 |
3.862 |
0.188 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
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 | 37 | 37 | 38 | 26 | 25 | 24 | 29 | 25 | 35 |
normalized size | 1 | 1.00 | 1.03 | 0.70 | 0.68 | 0.65 | 0.78 | 0.68 | 0.95 |
time (sec) |
N/A |
0.011 |
0.017 |
0.003 |
0.404 |
0.442 |
0.257 |
1.730 |
0.640 |
|
|
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Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 54 | 59 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.056 |
0.028 |
0.003 |
0.000 |
0.459 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
C |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 24 | 22 | 21 | 22 | 44 | 40 | -1 |
normalized size | 1 | 1.00 | 0.89 | 0.81 | 0.78 | 0.81 | 1.63 | 1.48 | -0.04 |
time (sec) |
N/A |
0.012 |
0.017 |
0.002 |
0.415 |
0.461 |
3.107 |
2.991 |
0.000 |
|
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Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 50 | 50 | 43 | 35 | 34 | 28 | 44 | 74 | -1 |
normalized size | 1 | 1.00 | 0.86 | 0.70 | 0.68 | 0.56 | 0.88 | 1.48 | -0.02 |
time (sec) |
N/A |
0.018 |
0.023 |
0.005 |
0.412 |
0.423 |
7.247 |
3.990 |
0.000 |
|
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Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 37 | 47 | 46 | 33 | 60 | 106 | -1 |
normalized size | 1 | 1.00 | 0.54 | 0.69 | 0.68 | 0.49 | 0.88 | 1.56 | -0.01 |
time (sec) |
N/A |
0.022 |
0.041 |
0.007 |
0.405 |
0.434 |
15.864 |
1.042 |
0.000 |
|
|
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Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 42 | 59 | 58 | 38 | 71 | 138 | -1 |
normalized size | 1 | 1.00 | 0.49 | 0.69 | 0.67 | 0.44 | 0.83 | 1.60 | -0.01 |
time (sec) |
N/A |
0.028 |
0.047 |
0.004 |
0.404 |
0.431 |
36.692 |
0.215 |
0.000 |
|
|
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Problem 68 |
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 | 25 | 25 | 25 | 20 | 19 | 19 | 20 | 19 | 19 |
normalized size | 1 | 1.00 | 1.00 | 0.80 | 0.76 | 0.76 | 0.80 | 0.76 | 0.76 |
time (sec) |
N/A |
0.019 |
0.008 |
0.005 |
0.403 |
0.424 |
0.278 |
1.675 |
0.396 |
|
|
|
|
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|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 141 | 89 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.07 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.061 |
0.146 |
0.040 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
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|
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 | 62 | 62 | 56 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.057 |
0.033 |
0.075 |
0.000 |
0.426 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
|
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|
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|
Problem 71 |
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 | 47 | 47 | 43 | 40 | 39 | 48 | 61 | 39 | 99 |
normalized size | 1 | 1.00 | 0.91 | 0.85 | 0.83 | 1.02 | 1.30 | 0.83 | 2.11 |
time (sec) |
N/A |
0.051 |
0.029 |
0.003 |
0.402 |
0.434 |
0.755 |
0.160 |
0.646 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 43 | 0 | 41 | 59 | 76 | 41 | 111 |
normalized size | 1 | 1.00 | 0.90 | 0.00 | 0.85 | 1.23 | 1.58 | 0.85 | 2.31 |
time (sec) |
N/A |
0.054 |
0.043 |
0.049 |
0.407 |
0.438 |
54.922 |
0.839 |
0.354 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 249 | 0 | 0 | 207 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.96 | 0.00 | 0.00 | 1.63 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.029 |
0.245 |
0.151 |
0.000 |
0.449 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
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|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 162 | 0 | 0 | 144 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.47 | 0.00 | 0.00 | 1.31 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.057 |
0.135 |
0.276 |
0.000 |
0.434 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 98 | 0 | 0 | 91 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.56 | 0.00 | 0.00 | 1.44 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.012 |
0.070 |
0.280 |
0.000 |
0.455 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 41 | 45 | 45 | 48 | 0 | 55 | 39 |
normalized size | 1 | 1.00 | 0.95 | 1.05 | 1.05 | 1.12 | 0.00 | 1.28 | 0.91 |
time (sec) |
N/A |
0.037 |
0.031 |
0.010 |
0.420 |
0.420 |
0.000 |
1.966 |
0.465 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 85 | 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 |
0.031 |
0.113 |
0.079 |
0.000 |
0.418 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 133 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.020 |
0.350 |
0.078 |
0.000 |
0.421 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 173 | 173 | 147 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.036 |
0.259 |
0.085 |
0.000 |
0.423 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 249 | 0 | 0 | 207 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.96 | 0.00 | 0.00 | 1.63 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.028 |
0.370 |
0.147 |
0.000 |
0.433 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 162 | 0 | 0 | 144 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.47 | 0.00 | 0.00 | 1.31 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.055 |
0.197 |
0.144 |
0.000 |
0.432 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 98 | 0 | 0 | 91 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.56 | 0.00 | 0.00 | 1.44 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.012 |
0.076 |
0.137 |
0.000 |
0.427 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 41 | 45 | 45 | 48 | 0 | 50 | 39 |
normalized size | 1 | 1.00 | 0.95 | 1.05 | 1.05 | 1.12 | 0.00 | 1.16 | 0.91 |
time (sec) |
N/A |
0.036 |
0.034 |
0.006 |
0.424 |
0.434 |
0.000 |
0.162 |
0.435 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 85 | 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 |
0.013 |
0.112 |
0.081 |
0.000 |
0.450 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 131 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.018 |
0.400 |
0.084 |
0.000 |
0.422 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 149 | 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 |
0.033 |
0.219 |
0.079 |
0.000 |
0.423 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 249 | 249 | 256 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.095 |
2.751 |
0.092 |
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(-2) |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 207 | 207 | 200 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.066 |
0.568 |
0.082 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 157 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.022 |
0.080 |
0.078 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 114 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.018 |
0.171 |
0.087 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 190 | 190 | 177 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.029 |
0.417 |
0.079 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 221 | 234 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.050 |
0.763 |
0.076 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 269 | 269 | 308 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.060 |
0.568 |
0.081 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 249 | 249 | 256 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.055 |
2.244 |
0.081 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 207 | 207 | 200 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.044 |
0.558 |
0.078 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 157 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.020 |
0.113 |
0.075 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 115 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.017 |
0.164 |
0.082 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 190 | 190 | 161 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.024 |
0.343 |
0.077 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 221 | 233 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.043 |
0.623 |
0.079 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 269 | 269 | 309 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.050 |
0.572 |
0.075 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
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 | 43 | 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 | -0.02 |
time (sec) |
N/A |
0.044 |
0.107 |
0.965 |
0.000 |
0.532 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 279 | 279 | 0 | 707 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 2.53 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.207 |
0.307 |
0.922 |
0.000 |
0.454 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
A |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 207 | 207 | 0 | 401 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 1.94 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.174 |
0.730 |
0.009 |
0.000 |
0.465 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
A |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 0 | 171 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.104 |
0.393 |
0.007 |
0.000 |
0.439 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
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 | 43 | 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 | -0.02 |
time (sec) |
N/A |
0.042 |
0.107 |
0.375 |
0.000 |
0.435 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
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 | 43 | 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 | -0.02 |
time (sec) |
N/A |
0.041 |
1.788 |
0.367 |
0.000 |
0.465 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
A |
F(-1) |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 0 | 107 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.066 |
0.991 |
0.005 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 50 | 0 | 0 | 55 | 105 | 82 | -1 |
normalized size | 1 | 1.00 | 0.62 | 0.00 | 0.00 | 0.68 | 1.30 | 1.01 | -0.01 |
time (sec) |
N/A |
0.064 |
0.145 |
0.010 |
0.000 |
0.472 |
2.931 |
0.212 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 50 | 0 | 0 | 46 | 85 | 69 | -1 |
normalized size | 1 | 1.00 | 0.61 | 0.00 | 0.00 | 0.56 | 1.04 | 0.84 | -0.01 |
time (sec) |
N/A |
0.061 |
0.113 |
0.012 |
0.000 |
0.463 |
1.190 |
0.213 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 30 | 0 | 0 | 36 | 58 | 44 | -1 |
normalized size | 1 | 1.00 | 0.73 | 0.00 | 0.00 | 0.88 | 1.41 | 1.07 | -0.02 |
time (sec) |
N/A |
0.034 |
0.040 |
0.010 |
0.000 |
0.454 |
0.393 |
0.204 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 32 | 0 | 0 | 28 | 37 | 31 | -1 |
normalized size | 1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.72 | 0.95 | 0.79 | -0.03 |
time (sec) |
N/A |
0.014 |
0.034 |
0.006 |
0.000 |
0.471 |
0.166 |
0.187 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 79 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.054 |
0.060 |
0.011 |
0.000 |
0.480 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 55 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.106 |
0.066 |
0.008 |
0.000 |
0.480 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 141 | 45 | 0 | 140 | 0 | 95 | 43 |
normalized size | 1 | 1.00 | 2.94 | 0.94 | 0.00 | 2.92 | 0.00 | 1.98 | 0.90 |
time (sec) |
N/A |
0.033 |
0.171 |
0.014 |
0.000 |
0.484 |
0.000 |
0.220 |
0.629 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
B |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 56 | 21 | 0 | 0 | 0 | 58 | -1 |
normalized size | 1 | 1.00 | 2.15 | 0.81 | 0.00 | 0.00 | 0.00 | 2.23 | -0.04 |
time (sec) |
N/A |
0.071 |
0.094 |
0.336 |
0.000 |
0.000 |
0.000 |
0.279 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 5 | 5 | 5 | 6 | 0 | 0 | 0 | 5 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.20 | 0.00 | 0.00 | 0.00 | 1.00 | -0.20 |
time (sec) |
N/A |
0.061 |
0.042 |
0.189 |
0.000 |
0.455 |
0.000 |
0.196 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 39 | 0 | 0 | 42 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.08 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.065 |
0.051 |
0.352 |
0.000 |
0.475 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 25 | 0 | 0 | 27 | 0 | 0 | 25 |
normalized size | 1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.87 | 0.00 | 0.00 | 0.81 |
time (sec) |
N/A |
0.061 |
0.026 |
0.295 |
0.000 |
0.437 |
0.000 |
0.000 |
0.298 |
|
|
|
|
|
|
|
|
|
|
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 [50] had the largest ratio of
[1.000]
|
|
|
|
|
|
|
| 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 |
16 |
12 |
1.00 |
31 |
0.387 |
|
|
|
|
|
|
|
2 |
A |
13 |
8 |
1.00 |
31 |
0.258 |
|
|
|
|
|
|
|
3 |
A |
8 |
6 |
1.00 |
29 |
0.207 |
|
|
|
|
|
|
|
4 |
A |
22 |
19 |
1.00 |
31 |
0.613 |
|
|
|
|
|
|
|
5 |
A |
35 |
22 |
1.00 |
31 |
0.710 |
|
|
|
|
|
|
|
6 |
A |
24 |
17 |
1.00 |
31 |
0.548 |
|
|
|
|
|
|
|
7 |
A |
20 |
12 |
1.00 |
31 |
0.387 |
|
|
|
|
|
|
|
8 |
A |
12 |
9 |
1.00 |
29 |
0.310 |
|
|
|
|
|
|
|
9 |
A |
29 |
23 |
1.00 |
31 |
0.742 |
|
|
|
|
|
|
|
10 |
A |
30 |
18 |
1.00 |
31 |
0.581 |
|
|
|
|
|
|
|
11 |
A |
26 |
15 |
1.00 |
31 |
0.484 |
|
|
|
|
|
|
|
12 |
A |
14 |
10 |
1.00 |
29 |
0.345 |
|
|
|
|
|
|
|
13 |
A |
37 |
28 |
1.00 |
31 |
0.903 |
|
|
|
|
|
|
|
14 |
A |
13 |
7 |
1.00 |
31 |
0.226 |
|
|
|
|
|
|
|
15 |
A |
9 |
7 |
1.00 |
31 |
0.226 |
|
|
|
|
|
|
|
16 |
A |
6 |
5 |
1.00 |
29 |
0.172 |
|
|
|
|
|
|
|
17 |
A |
10 |
7 |
1.00 |
31 |
0.226 |
|
|
|
|
|
|
|
18 |
A |
13 |
10 |
1.00 |
31 |
0.323 |
|
|
|
|
|
|
|
19 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
20 |
A |
13 |
9 |
1.00 |
35 |
0.257 |
|
|
|
|
|
|
|
21 |
A |
11 |
8 |
1.00 |
33 |
0.242 |
|
|
|
|
|
|
|
22 |
A |
9 |
7 |
1.00 |
25 |
0.280 |
|
|
|
|
|
|
|
23 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
24 |
A |
6 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
25 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
26 |
A |
5 |
5 |
1.00 |
8 |
0.625 |
|
|
|
|
|
|
|
27 |
A |
3 |
3 |
1.00 |
6 |
0.500 |
|
|
|
|
|
|
|
28 |
A |
9 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
29 |
A |
4 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
30 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
31 |
A |
6 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
32 |
A |
5 |
4 |
1.00 |
8 |
0.500 |
|
|
|
|
|
|
|
33 |
A |
4 |
4 |
1.00 |
8 |
0.500 |
|
|
|
|
|
|
|
34 |
A |
3 |
3 |
1.00 |
8 |
0.375 |
|
|
|
|
|
|
|
35 |
A |
4 |
4 |
1.00 |
8 |
0.500 |
|
|
|
|
|
|
|
36 |
A |
5 |
5 |
1.00 |
8 |
0.625 |
|
|
|
|
|
|
|
37 |
A |
7 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
38 |
A |
6 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
39 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
40 |
A |
4 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
41 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
42 |
A |
6 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
43 |
A |
7 |
7 |
1.00 |
14 |
0.500 |
|
|
|
|
|
|
|
44 |
A |
7 |
7 |
1.00 |
15 |
0.467 |
|
|
|
|
|
|
|
45 |
A |
7 |
7 |
1.00 |
19 |
0.368 |
|
|
|
|
|
|
|
46 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
47 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
48 |
A |
4 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
49 |
A |
3 |
3 |
1.00 |
8 |
0.375 |
|
|
|
|
|
|
|
50 |
A |
6 |
6 |
1.00 |
6 |
1.000 |
|
|
|
|
|
|
|
51 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
52 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
53 |
A |
6 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
54 |
A |
3 |
3 |
1.00 |
8 |
0.375 |
|
|
|
|
|
|
|
55 |
A |
5 |
5 |
1.00 |
6 |
0.833 |
|
|
|
|
|
|
|
56 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
57 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
58 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
59 |
A |
5 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
60 |
A |
8 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
61 |
A |
7 |
6 |
1.00 |
8 |
0.750 |
|
|
|
|
|
|
|
62 |
A |
6 |
6 |
1.00 |
6 |
1.000 |
|
|
|
|
|
|
|
63 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
64 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
65 |
A |
4 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
66 |
A |
5 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
67 |
A |
6 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
68 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
69 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
70 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
71 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
72 |
A |
4 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
73 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
74 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
75 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
76 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
77 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
|
|
|
|
|
|
|
78 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
|
|
|
|
|
|
|
79 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
80 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
81 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
82 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
83 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
84 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
|
|
|
|
|
|
|
85 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
|
|
|
|
|
|
|
86 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
87 |
A |
2 |
2 |
1.00 |
16 |
0.125 |
|
|
|
|
|
|
|
88 |
A |
2 |
2 |
1.00 |
16 |
0.125 |
|
|
|
|
|
|
|
89 |
A |
1 |
1 |
1.00 |
16 |
0.062 |
|
|
|
|
|
|
|
90 |
A |
1 |
1 |
1.00 |
16 |
0.062 |
|
|
|
|
|
|
|
91 |
A |
1 |
1 |
1.00 |
16 |
0.062 |
|
|
|
|
|
|
|
92 |
A |
2 |
2 |
1.00 |
16 |
0.125 |
|
|
|
|
|
|
|
93 |
A |
2 |
2 |
1.00 |
16 |
0.125 |
|
|
|
|
|
|
|
94 |
A |
2 |
2 |
1.00 |
16 |
0.125 |
|
|
|
|
|
|
|
95 |
A |
2 |
2 |
1.00 |
16 |
0.125 |
|
|
|
|
|
|
|
96 |
A |
1 |
1 |
1.00 |
16 |
0.062 |
|
|
|
|
|
|
|
97 |
A |
1 |
1 |
1.00 |
16 |
0.062 |
|
|
|
|
|
|
|
98 |
A |
1 |
1 |
1.00 |
16 |
0.062 |
|
|
|
|
|
|
|
99 |
A |
2 |
2 |
1.00 |
16 |
0.125 |
|
|
|
|
|
|
|
100 |
A |
2 |
2 |
1.00 |
16 |
0.125 |
|
|
|
|
|
|
|
101 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
102 |
A |
8 |
8 |
1.00 |
40 |
0.200 |
|
|
|
|
|
|
|
103 |
A |
7 |
7 |
1.00 |
40 |
0.175 |
|
|
|
|
|
|
|
104 |
A |
6 |
7 |
1.00 |
38 |
0.184 |
|
|
|
|
|
|
|
105 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
106 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
107 |
A |
6 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
108 |
A |
6 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
109 |
A |
6 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
110 |
A |
5 |
4 |
1.00 |
8 |
0.500 |
|
|
|
|
|
|
|
111 |
A |
2 |
2 |
1.00 |
6 |
0.333 |
|
|
|
|
|
|
|
112 |
A |
6 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
113 |
A |
6 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
114 |
A |
6 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
115 |
A |
3 |
3 |
1.00 |
19 |
0.158 |
|
|
|
|
|
|
|
116 |
A |
2 |
2 |
1.00 |
17 |
0.118 |
|
|
|
|
|
|
|
117 |
A |
2 |
2 |
1.00 |
26 |
0.077 |
|
|
|
|
|
|
|
118 |
A |
2 |
2 |
1.00 |
26 |
0.077 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|