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, 10, 11, 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, 6, 7, 8, 9, 12, 13, 14, 15, 16, 18, 52, 102 }
C grade: { 5 }
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: { 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: { }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 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, 68, 71, 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, 67, 69, 70, 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, 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, 54, 55, 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, 65, 66, 67, 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, 114, 117, 118 }
2.2 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2)
if the failure was due to an exception being raised, which could indicate a bug in the system. If
the failure was due to integral not being evaluated within the time limit, then it is given just an
F.
In this table,the column normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 670 | 670 | 442 | 1285 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.66 |
1.92 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.705 |
1.204 |
0.848 |
0. |
0. |
0. |
0. |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 450 | 450 | 320 | 912 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.71 |
2.03 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.53 |
1.314 |
0.533 |
0. |
0. |
0. |
0. |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 238 | 238 | 219 | 491 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.92 |
2.06 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.251 |
1.474 |
0.481 |
0. |
0. |
0. |
0. |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 725 | 725 | 1095 | 1209 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.51 |
1.67 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.859 |
3.38 |
0.437 |
0. |
0. |
0. |
0. |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
C |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 851 | 851 | 1130 | 1573 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.33 |
1.85 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.694 |
9.482 |
0.476 |
0. |
0. |
0. |
0. |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 959 | 959 | 910 | 1734 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.95 |
1.81 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.962 |
4.572 |
0.811 |
0. |
0. |
0. |
0. |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 680 | 680 | 591 | 1252 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.87 |
1.84 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.735 |
2.143 |
0.579 |
0. |
0. |
0. |
0. |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 370 | 370 | 337 | 698 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.91 |
1.89 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.335 |
1.566 |
0.49 |
0. |
0. |
0. |
0. |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
B |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1064 | 1064 | 3034 | 2132 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.85 |
2. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.28 |
12.504 |
0.398 |
0. |
0. |
0. |
0. |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1281 | 1281 | 1144 | 2236 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.89 |
1.75 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.177 |
7.462 |
0.959 |
0. |
0. |
0. |
0. |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 940 | 940 | 794 | 1633 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.84 |
1.74 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.959 |
4.516 |
0.702 |
0. |
0. |
0. |
0. |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 517 | 517 | 526 | 931 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.02 |
1.8 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.403 |
2.901 |
0.602 |
0. |
0. |
0. |
0. |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
B |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1637 | 1637 | 6216 | 4692 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
3.8 |
2.87 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.73 |
19.605 |
0.531 |
0. |
0. |
0. |
0. |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 450 | 450 | 342 | 845 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.76 |
1.88 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.585 |
1.182 |
0.605 |
0. |
0. |
0. |
0. |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 270 | 270 | 266 | 549 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.99 |
2.03 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.436 |
0.757 |
0.356 |
0. |
0. |
0. |
0. |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 172 | 235 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.35 |
1.85 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.223 |
0.413 |
0.299 |
0. |
0. |
0. |
0. |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 370 | 370 | 930 | 487 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.51 | 1.32 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.606 |
2.056 |
0.196 |
0. |
0. |
0. |
0. |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
B |
F |
F |
F |
F(-2) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 496 | 496 | 1108 | 1622 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.23 |
3.27 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.722 |
4.987 |
0.305 |
0. |
0. |
0. |
0. |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.192 |
0.158 |
5.372 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 496 | 496 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.791 |
26.654 |
4.708 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 374 | 374 | 1248 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
3.34 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.611 |
5.566 |
3.134 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 237 | 237 | 246 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.04 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.338 |
0.022 |
0.015 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.2 |
0.199 |
2.447 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 104 | 235 | 0 | 219 | 255 | 327 |
normalized size |
1 |
1. |
0.76 |
1.72 |
0. |
1.6 |
1.86 |
2.39 |
time (sec) |
N/A |
0.194 |
0.1 |
0.02 |
0. |
2.479 |
1.757 |
1.316 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 83 | 161 | 0 | 173 | 170 | 211 |
normalized size |
1 |
1. |
0.88 |
1.71 |
0. |
1.84 |
1.81 |
2.24 |
time (sec) |
N/A |
0.115 |
0.083 |
0.003 |
0. |
2.421 |
0.82 |
1.306 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 69 | 78 | 0 | 135 | 104 | 119 |
normalized size |
1 |
1. |
0.86 |
0.98 |
0. |
1.69 |
1.3 |
1.49 |
time (sec) |
N/A |
0.073 |
0.049 |
0.004 |
0. |
2.551 |
0.361 |
1.322 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 47 | 33 | 43 | 92 | 46 | 43 |
normalized size | 1 | 1. | 1.31 | 0.92 | 1.19 | 2.56 | 1.28 | 1.19 |
time (sec) |
N/A |
0.017 |
0.037 |
0.002 |
1.41 |
2.507 |
0.174 |
1.281 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 177 | 228 | 199 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.29 |
1.12 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.276 |
0.192 |
0.104 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 79 | 77 | 0 | 857 | 0 | 107 |
normalized size |
1 |
1. |
1.25 |
1.22 |
0. |
13.6 |
0. |
1.7 |
time (sec) |
N/A |
0.076 |
0.055 |
0.003 |
0. |
3.011 |
0. |
1.316 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 126 | 118 | 0 | 1121 | 0 | 327 |
normalized size |
1 |
1. |
1.22 |
1.15 |
0. |
10.88 |
0. |
3.17 |
time (sec) |
N/A |
0.111 |
0.175 |
0.004 |
0. |
2.947 |
0. |
1.336 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 144 | 144 | 168 | 227 | 0 | 1328 | 0 | 752 |
normalized size |
1 |
1. |
1.17 |
1.58 |
0. |
9.22 |
0. |
5.22 |
time (sec) |
N/A |
0.179 |
0.184 |
0.005 |
0. |
3.544 |
0. |
1.356 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 74 | 71 | 0 | 170 | 109 | 105 |
normalized size |
1 |
1. |
0.9 |
0.87 |
0. |
2.07 |
1.33 |
1.28 |
time (sec) |
N/A |
0.082 |
0.036 |
0.054 |
0. |
2.559 |
0.693 |
1.43 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 49 | 48 | 0 | 130 | 63 | 70 |
normalized size |
1 |
1. |
1.04 |
1.02 |
0. |
2.77 |
1.34 |
1.49 |
time (sec) |
N/A |
0.054 |
0.023 |
0.049 |
0. |
2.336 |
0.283 |
1.342 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 12 | 13 | 0 | 0 | 0 | 16 |
normalized size | 1 | 1. | 1. | 1.08 | 0. | 0. | 0. | 1.33 |
time (sec) |
N/A |
0.022 |
0.026 |
0.046 |
0. |
0. |
0. |
1.343 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 40 | 40 | 37 | 0 | 0 | 0 | 51 |
normalized size |
1 |
1. |
1. |
0.92 |
0. |
0. |
0. |
1.27 |
time (sec) |
N/A |
0.078 |
0.051 |
0.049 |
0. |
0. |
0. |
1.33 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 65 | 53 | 0 | 0 | 0 | 77 |
normalized size |
1 |
1. |
1. |
0.82 |
0. |
0. |
0. |
1.18 |
time (sec) |
N/A |
0.081 |
0.05 |
0.051 |
0. |
0. |
0. |
1.298 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F(-1) |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 90 | 140 | 0 | 0 | 0 | 282 |
normalized size |
1 |
1. |
0.81 |
1.26 |
0. |
0. |
0. |
2.54 |
time (sec) |
N/A |
0.147 |
0.049 |
0.092 |
0. |
0. |
0. |
1.57 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 76 | 105 | 0 | 0 | 0 | 221 |
normalized size |
1 |
1. |
0.85 |
1.18 |
0. |
0. |
0. |
2.48 |
time (sec) |
N/A |
0.092 |
0.035 |
0.082 |
0. |
0. |
0. |
1.624 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 90 | 66 | 0 | 0 | 0 | 158 |
normalized size |
1 |
1. |
1.64 |
1.2 |
0. |
0. |
0. |
2.87 |
time (sec) |
N/A |
0.081 |
0.039 |
0.073 |
0. |
0. |
0. |
1.378 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 78 | 28 | 0 | 0 | 0 | 97 |
normalized size |
1 |
1. |
2.36 |
0.85 |
0. |
0. |
0. |
2.94 |
time (sec) |
N/A |
0.03 |
0.032 |
0.055 |
0. |
0. |
0. |
1.575 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 97 | 84 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.52 |
1.31 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.086 |
0.054 |
0.075 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 139 | 120 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.54 |
1.33 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.092 |
0.291 |
0.079 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-2) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 106 | 106 | 128 | 89 | 0 | 0 | 0 | 231 |
normalized size |
1 |
1. |
1.21 |
0.84 |
0. |
0. |
0. |
2.18 |
time (sec) |
N/A |
0.13 |
0.105 |
0.071 |
0. |
0. |
0. |
2.344 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-2) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 133 | 90 | 0 | 0 | 0 | 236 |
normalized size |
1 |
1. |
1.23 |
0.83 |
0. |
0. |
0. |
2.19 |
time (sec) |
N/A |
0.116 |
0.102 |
0.064 |
0. |
0. |
0. |
2.944 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 59 | 85 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.87 |
1.25 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.081 |
0.041 |
0.089 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 30 | 33 | 41 | 81 | 48 | 36 |
normalized size | 1 | 1. | 0.88 | 0.97 | 1.21 | 2.38 | 1.41 | 1.06 |
time (sec) |
N/A |
0.03 |
0.016 |
0.083 |
1.49 |
2.381 |
21.528 |
1.323 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 48 | 65 | 107 | 93 | 48 | 62 |
normalized size | 1 | 1. | 0.94 | 1.27 | 2.1 | 1.82 | 0.94 | 1.22 |
time (sec) |
N/A |
0.039 |
0.028 |
0.053 |
1.476 |
2.53 |
1.032 |
1.343 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 63 | 79 | 0 | 0 | 48 | 0 |
normalized size |
1 |
1. |
1.15 |
1.44 |
0. |
0. |
0.87 |
0. |
time (sec) |
N/A |
0.028 |
0.155 |
0.007 |
0. |
0. |
1.427 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 35 | 32 | 42 | 68 | 32 | 42 |
normalized size | 1 | 1. | 1. | 0.91 | 1.2 | 1.94 | 0.91 | 1.2 |
time (sec) |
N/A |
0.024 |
0.016 |
0.002 |
1.448 |
2.378 |
0.23 |
1.328 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 34 | 65 | 0 | 0 | 44 | 0 |
normalized size |
1 |
1. |
0.79 |
1.51 |
0. |
0. |
1.02 |
0. |
time (sec) |
N/A |
0.032 |
0.005 |
0.007 |
0. |
0. |
1.111 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 56 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.9 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.058 |
0.031 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 40 | 57 | 0 | 0 | 44 | 0 |
normalized size |
1 |
1. |
1.38 |
1.97 |
0. |
0. |
1.52 |
0. |
time (sec) |
N/A |
0.014 |
0.039 |
0.006 |
0. |
0. |
1.211 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 61 | 56 | 97 | 207 | 99 | 95 |
normalized size | 1 | 1. | 1.05 | 0.97 | 1.67 | 3.57 | 1.71 | 1.64 |
time (sec) |
N/A |
0.036 |
0.051 |
0.01 |
1.462 |
2.539 |
5.296 |
1.29 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 33 | 39 | 38 | 73 | 49 | 58 |
normalized size | 1 | 1. | 0.97 | 1.15 | 1.12 | 2.15 | 1.44 | 1.71 |
time (sec) |
N/A |
0.017 |
0.021 |
0.004 |
1.442 |
2.563 |
2.684 |
1.248 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 84 | 30 | 61 | 140 | 29 | 58 |
normalized size | 1 | 1. | 3.11 | 1.11 | 2.26 | 5.19 | 1.07 | 2.15 |
time (sec) |
N/A |
0.017 |
0.101 |
0.006 |
1.454 |
2.521 |
2.271 |
1.262 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 60 | 77 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.28 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.055 |
0.021 |
0.055 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 30 | 32 | 42 | 69 | 26 | 42 |
normalized size | 1 | 1. | 1. | 1.07 | 1.4 | 2.3 | 0.87 | 1.4 |
time (sec) |
N/A |
0.022 |
0.019 |
0.001 |
1.438 |
2.394 |
2.34 |
1.228 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 50 | 47 | 104 | 97 | 102 | 84 |
normalized size | 1 | 1. | 0.98 | 0.92 | 2.04 | 1.9 | 2. | 1.65 |
time (sec) |
N/A |
0.033 |
0.024 |
0.006 |
1.465 |
2.47 |
5.305 |
1.28 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 47 | 55 | 66 | 104 | 102 | 88 |
normalized size | 1 | 1. | 0.84 | 0.98 | 1.18 | 1.86 | 1.82 | 1.57 |
time (sec) |
N/A |
0.038 |
0.031 |
0.006 |
1.445 |
2.462 |
6.366 |
1.314 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 46 | 53 | 70 | 115 | 73 | 70 |
normalized size | 1 | 1. | 0.59 | 0.68 | 0.9 | 1.47 | 0.94 | 0.9 |
time (sec) |
N/A |
0.028 |
0.038 |
0.004 |
1.436 |
2.632 |
10.162 |
1.128 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 41 | 41 | 54 | 99 | 58 | 54 |
normalized size | 1 | 1. | 0.68 | 0.68 | 0.9 | 1.65 | 0.97 | 0.9 |
time (sec) |
N/A |
0.019 |
0.029 |
0.003 |
1.465 |
2.585 |
3.901 |
1.277 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 38 | 26 | 34 | 78 | 29 | 34 |
normalized size | 1 | 1. | 1.03 | 0.7 | 0.92 | 2.11 | 0.78 | 0.92 |
time (sec) |
N/A |
0.011 |
0.015 |
0.002 |
1.524 |
2.612 |
0.337 |
1.193 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 54 | 59 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.96 | 1.05 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.056 |
0.026 |
0.002 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
C |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 24 | 22 | 28 | 59 | 44 | 54 |
normalized size | 1 | 1. | 0.89 | 0.81 | 1.04 | 2.19 | 1.63 | 2. |
time (sec) |
N/A |
0.012 |
0.016 |
0.001 |
1.499 |
2.561 |
4.222 |
1.179 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 50 | 50 | 43 | 35 | 46 | 84 | 44 | 100 |
normalized size | 1 | 1. | 0.86 | 0.7 | 0.92 | 1.68 | 0.88 | 2. |
time (sec) |
N/A |
0.018 |
0.021 |
0.004 |
1.473 |
2.628 |
24.914 |
1.281 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 37 | 47 | 62 | 97 | 60 | 143 |
normalized size | 1 | 1. | 0.54 | 0.69 | 0.91 | 1.43 | 0.88 | 2.1 |
time (sec) |
N/A |
0.022 |
0.038 |
0.003 |
1.476 |
2.631 |
150.038 |
1.312 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 42 | 59 | 78 | 111 | 0 | 186 |
normalized size |
1 |
1. |
0.49 |
0.69 |
0.91 |
1.29 |
0. |
2.16 |
time (sec) |
N/A |
0.028 |
0.044 |
0.003 |
1.493 |
2.326 |
0. |
1.285 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 20 | 26 | 59 | 20 | 26 |
normalized size | 1 | 1. | 1. | 0.8 | 1.04 | 2.36 | 0.8 | 1.04 |
time (sec) |
N/A |
0.019 |
0.008 |
0.003 |
1.482 |
2.533 |
0.365 |
1.274 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 141 | 89 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.07 |
1.31 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.061 |
0.137 |
0.04 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 56 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.9 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.057 |
0.031 |
0.058 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 43 | 40 | 53 | 105 | 61 | 53 |
normalized size | 1 | 1. | 0.91 | 0.85 | 1.13 | 2.23 | 1.3 | 1.13 |
time (sec) |
N/A |
0.051 |
0.028 |
0.003 |
1.612 |
2.439 |
1.143 |
1.261 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 43 | 0 | 55 | 132 | 0 | 55 |
normalized size |
1 |
1. |
0.9 |
0. |
1.15 |
2.75 |
0. |
1.15 |
time (sec) |
N/A |
0.054 |
0.041 |
0.03 |
1.606 |
2.646 |
0. |
1.312 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 249 | 0 | 0 | 474 | 0 | 0 |
normalized size |
1 |
1. |
1.96 |
0. |
0. |
3.73 |
0. |
0. |
time (sec) |
N/A |
0.029 |
0.233 |
0.121 |
0. |
2.605 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 162 | 0 | 0 | 328 | 0 | 0 |
normalized size |
1 |
1. |
1.47 |
0. |
0. |
2.98 |
0. |
0. |
time (sec) |
N/A |
0.057 |
0.126 |
0.116 |
0. |
2.362 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 98 | 0 | 0 | 205 | 0 | 0 |
normalized size |
1 |
1. |
1.56 |
0. |
0. |
3.25 |
0. |
0. |
time (sec) |
N/A |
0.012 |
0.066 |
0.117 |
0. |
2.5 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 41 | 45 | 61 | 103 | 0 | 78 |
normalized size | 1 | 1. | 0.95 | 1.05 | 1.42 | 2.4 | 0. | 1.81 |
time (sec) |
N/A |
0.037 |
0.027 |
0.005 |
1.566 |
2.303 |
0. |
1.349 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 85 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.86 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.031 |
0.104 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 133 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.88 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.02 |
0.332 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 173 | 173 | 147 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.85 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.036 |
0.246 |
0.067 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 249 | 0 | 0 | 474 | 0 | 0 |
normalized size |
1 |
1. |
1.96 |
0. |
0. |
3.73 |
0. |
0. |
time (sec) |
N/A |
0.028 |
0.239 |
0.117 |
0. |
2.657 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 162 | 0 | 0 | 328 | 0 | 0 |
normalized size |
1 |
1. |
1.47 |
0. |
0. |
2.98 |
0. |
0. |
time (sec) |
N/A |
0.055 |
0.135 |
0.119 |
0. |
2.573 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 98 | 0 | 0 | 205 | 0 | 0 |
normalized size |
1 |
1. |
1.56 |
0. |
0. |
3.25 |
0. |
0. |
time (sec) |
N/A |
0.012 |
0.066 |
0.118 |
0. |
2.505 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 41 | 45 | 61 | 103 | 0 | 72 |
normalized size | 1 | 1. | 0.95 | 1.05 | 1.42 | 2.4 | 0. | 1.67 |
time (sec) |
N/A |
0.036 |
0.029 |
0.004 |
1.527 |
2.682 |
0. |
1.3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 85 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.87 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.013 |
0.1 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 131 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.88 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.018 |
0.335 |
0.065 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 149 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.87 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.033 |
0.213 |
0.068 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 249 | 249 | 256 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.03 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.095 |
2.617 |
0.076 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 207 | 207 | 200 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.97 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.066 |
0.713 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 157 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.85 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.022 |
0.085 |
0.063 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 114 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.79 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.018 |
0.162 |
0.069 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 190 | 190 | 177 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.93 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.029 |
0.389 |
0.067 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 221 | 234 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.06 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.05 |
0.721 |
0.067 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 269 | 269 | 308 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.14 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.06 |
0.547 |
0.068 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 249 | 249 | 256 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.03 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.055 |
2.146 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 207 | 207 | 200 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.97 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.044 |
0.603 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 157 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.85 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.02 |
0.113 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 115 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.79 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.017 |
0.158 |
0.07 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 190 | 190 | 161 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.85 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
0.321 |
0.064 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 221 | 233 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.05 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.043 |
0.585 |
0.065 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 269 | 269 | 309 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.15 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.05 |
0.553 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.044 |
0.097 |
0.647 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
F |
F |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 279 | 279 | 0 | 707 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
2.53 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.207 |
0.296 |
0.974 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
A |
F |
F |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 207 | 207 | 0 | 401 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
1.94 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.174 |
0.695 |
0.007 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
A |
F |
F |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 0 | 171 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
1.21 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.104 |
0.372 |
0.005 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.042 |
0.101 |
0.344 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.041 |
1.693 |
0.342 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
A |
F(-1) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 0 | 107 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
1.27 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.066 |
0.947 |
0.004 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 50 | 0 | 0 | 130 | 105 | 111 |
normalized size | 1 | 1. | 0.62 | 0. | 0. | 1.6 | 1.3 | 1.37 |
time (sec) |
N/A |
0.064 |
0.139 |
0.01 |
0. |
2.619 |
4.836 |
1.325 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 50 | 0 | 0 | 107 | 85 | 93 |
normalized size | 1 | 1. | 0.61 | 0. | 0. | 1.3 | 1.04 | 1.13 |
time (sec) |
N/A |
0.061 |
0.107 |
0.009 |
0. |
2.566 |
1.716 |
1.376 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 30 | 0 | 0 | 89 | 58 | 59 |
normalized size | 1 | 1. | 0.73 | 0. | 0. | 2.17 | 1.41 | 1.44 |
time (sec) |
N/A |
0.034 |
0.037 |
0.007 |
0. |
2.637 |
0.539 |
1.238 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 32 | 0 | 0 | 68 | 37 | 42 |
normalized size | 1 | 1. | 0.82 | 0. | 0. | 1.74 | 0.95 | 1.08 |
time (sec) |
N/A |
0.014 |
0.033 |
0.004 |
0. |
2.6 |
0.201 |
1.277 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 79 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.76 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.054 |
0.056 |
0.007 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 55 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.63 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.106 |
0.062 |
0.007 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 141 | 45 | 0 | 305 | 0 | 0 |
normalized size | 1 | 1. | 2.94 | 0.94 | 0. | 6.35 | 0. | 0. |
time (sec) |
N/A |
0.033 |
0.163 |
0.008 |
0. |
2.529 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-2) |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 56 | 21 | 0 | 0 | 0 | 78 |
normalized size |
1 |
1. |
2.15 |
0.81 |
0. |
0. |
0. |
3. |
time (sec) |
N/A |
0.071 |
0.085 |
0.106 |
0. |
0. |
0. |
1.398 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 5 | 5 | 5 | 6 | 0 | 0 | 0 | 7 |
normalized size | 1 | 1. | 1. | 1.2 | 0. | 0. | 0. | 1.4 |
time (sec) |
N/A |
0.061 |
0.04 |
0.067 |
0. |
0. |
0. |
1.378 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
A |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 39 | 0 | 0 | 107 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0. |
0. |
2.74 |
0. |
0. |
time (sec) |
N/A |
0.065 |
0.046 |
0.193 |
0. |
2.995 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 25 | 0 | 0 | 68 | 0 | 0 |
normalized size | 1 | 1. | 0.81 | 0. | 0. | 2.19 | 0. | 0. |
time (sec) |
N/A |
0.061 |
0.024 |
0.184 |
0. |
2.571 |
0. |
0. |
|
|
|
|
|
|
|
|
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2.3 Detailed conclusion table specific for Rubi results
The following table is specific to Rubi. It gives additional statistics for each integral. the column
steps is the number of steps used by Rubi to obtain the antiderivative. The rules
column is the number of unique rules used. The integrand size column is the leaf size
of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the
integral was to solve. In this test, problem number [50] had the largest ratio of [ 1.
]
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| Table 2.1Rubi specific breakdown of results for each
integral
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# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
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1 |
A |
16 |
12 |
1. |
31 |
0.387 |
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2 |
A |
13 |
8 |
1. |
31 |
0.258 |
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3 |
A |
8 |
6 |
1. |
29 |
0.207 |
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4 |
A |
22 |
19 |
1. |
31 |
0.613 |
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5 |
A |
35 |
22 |
1. |
31 |
0.71 |
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6 |
A |
24 |
17 |
1. |
31 |
0.548 |
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7 |
A |
20 |
12 |
1. |
31 |
0.387 |
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8 |
A |
12 |
9 |
1. |
29 |
0.31 |
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9 |
A |
29 |
23 |
1. |
31 |
0.742 |
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|
10 |
A |
30 |
18 |
1. |
31 |
0.581 |
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11 |
A |
26 |
15 |
1. |
31 |
0.484 |
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12 |
A |
14 |
10 |
1. |
29 |
0.345 |
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|
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13 |
A |
37 |
28 |
1. |
31 |
0.903 |
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|
|
14 |
A |
13 |
7 |
1. |
31 |
0.226 |
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15 |
A |
9 |
7 |
1. |
31 |
0.226 |
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16 |
A |
6 |
5 |
1. |
29 |
0.172 |
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17 |
A |
10 |
7 |
1. |
31 |
0.226 |
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18 |
A |
13 |
10 |
1. |
31 |
0.323 |
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19 |
A |
0 |
0 |
0. |
0 |
0. |
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20 |
A |
13 |
9 |
1. |
35 |
0.257 |
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21 |
A |
11 |
8 |
1. |
33 |
0.242 |
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22 |
A |
9 |
7 |
1. |
25 |
0.28 |
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23 |
A |
0 |
0 |
0. |
0 |
0. |
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24 |
A |
6 |
6 |
1. |
10 |
0.6 |
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25 |
A |
5 |
5 |
1. |
10 |
0.5 |
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26 |
A |
5 |
5 |
1. |
8 |
0.625 |
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27 |
A |
3 |
3 |
1. |
6 |
0.5 |
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28 |
A |
9 |
6 |
1. |
10 |
0.6 |
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29 |
A |
4 |
4 |
1. |
10 |
0.4 |
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30 |
A |
5 |
5 |
1. |
10 |
0.5 |
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31 |
A |
6 |
6 |
1. |
10 |
0.6 |
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32 |
A |
5 |
4 |
1. |
8 |
0.5 |
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33 |
A |
4 |
4 |
1. |
8 |
0.5 |
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|
34 |
A |
3 |
3 |
1. |
8 |
0.375 |
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35 |
A |
4 |
4 |
1. |
8 |
0.5 |
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36 |
A |
5 |
5 |
1. |
8 |
0.625 |
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37 |
A |
7 |
6 |
1. |
10 |
0.6 |
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38 |
A |
6 |
6 |
1. |
10 |
0.6 |
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|
39 |
A |
5 |
5 |
1. |
10 |
0.5 |
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|
40 |
A |
4 |
4 |
1. |
10 |
0.4 |
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|
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|
41 |
A |
5 |
5 |
1. |
10 |
0.5 |
|
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|
42 |
A |
6 |
6 |
1. |
10 |
0.6 |
|
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|
43 |
A |
7 |
7 |
1. |
14 |
0.5 |
|
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|
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|
44 |
A |
7 |
7 |
1. |
15 |
0.467 |
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45 |
A |
7 |
7 |
1. |
19 |
0.368 |
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46 |
A |
3 |
3 |
1. |
14 |
0.214 |
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47 |
A |
5 |
5 |
1. |
10 |
0.5 |
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48 |
A |
4 |
4 |
1. |
10 |
0.4 |
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|
49 |
A |
3 |
3 |
1. |
8 |
0.375 |
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|
50 |
A |
6 |
6 |
1. |
6 |
1. |
|
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51 |
A |
5 |
5 |
1. |
10 |
0.5 |
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52 |
A |
3 |
3 |
1. |
10 |
0.3 |
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53 |
A |
6 |
6 |
1. |
10 |
0.6 |
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54 |
A |
3 |
3 |
1. |
8 |
0.375 |
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55 |
A |
5 |
5 |
1. |
6 |
0.833 |
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56 |
A |
5 |
5 |
1. |
10 |
0.5 |
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57 |
A |
3 |
3 |
1. |
10 |
0.3 |
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58 |
A |
5 |
5 |
1. |
10 |
0.5 |
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59 |
A |
5 |
4 |
1. |
10 |
0.4 |
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|
60 |
A |
8 |
6 |
1. |
10 |
0.6 |
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|
61 |
A |
7 |
6 |
1. |
8 |
0.75 |
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|
62 |
A |
6 |
6 |
1. |
6 |
1. |
|
|
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|
63 |
A |
5 |
5 |
1. |
10 |
0.5 |
|
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|
64 |
A |
3 |
3 |
1. |
10 |
0.3 |
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|
65 |
A |
4 |
4 |
1. |
10 |
0.4 |
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|
66 |
A |
5 |
4 |
1. |
10 |
0.4 |
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|
67 |
A |
6 |
4 |
1. |
10 |
0.4 |
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|
68 |
A |
3 |
3 |
1. |
12 |
0.25 |
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69 |
A |
5 |
5 |
1. |
10 |
0.5 |
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|
70 |
A |
5 |
5 |
1. |
10 |
0.5 |
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71 |
A |
4 |
4 |
1. |
12 |
0.333 |
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|
72 |
A |
4 |
4 |
1. |
14 |
0.286 |
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|
73 |
A |
3 |
2 |
1. |
14 |
0.143 |
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|
74 |
A |
5 |
4 |
1. |
14 |
0.286 |
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|
75 |
A |
2 |
2 |
1. |
14 |
0.143 |
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|
76 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
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|
77 |
A |
1 |
1 |
1. |
14 |
0.071 |
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|
78 |
A |
1 |
1 |
1. |
14 |
0.071 |
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|
79 |
A |
2 |
2 |
1. |
14 |
0.143 |
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|
80 |
A |
3 |
2 |
1. |
14 |
0.143 |
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|
81 |
A |
5 |
4 |
1. |
14 |
0.286 |
|
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|
82 |
A |
2 |
2 |
1. |
14 |
0.143 |
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|
83 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
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|
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|
84 |
A |
1 |
1 |
1. |
14 |
0.071 |
|
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|
|
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|
85 |
A |
1 |
1 |
1. |
14 |
0.071 |
|
|
|
|
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|
86 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
87 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
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|
|
|
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|
88 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
89 |
A |
1 |
1 |
1. |
16 |
0.062 |
|
|
|
|
|
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|
90 |
A |
1 |
1 |
1. |
16 |
0.062 |
|
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|
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|
91 |
A |
1 |
1 |
1. |
16 |
0.062 |
|
|
|
|
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|
92 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
|
|
|
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|
93 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
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|
|
|
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|
94 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
95 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
96 |
A |
1 |
1 |
1. |
16 |
0.062 |
|
|
|
|
|
|
|
97 |
A |
1 |
1 |
1. |
16 |
0.062 |
|
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|
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|
98 |
A |
1 |
1 |
1. |
16 |
0.062 |
|
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|
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|
99 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
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|
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|
100 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
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|
|
|
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|
101 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
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|
102 |
A |
8 |
8 |
1. |
40 |
0.2 |
|
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|
|
|
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|
103 |
A |
7 |
7 |
1. |
40 |
0.175 |
|
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|
|
|
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|
104 |
A |
6 |
7 |
1. |
38 |
0.184 |
|
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|
|
|
|
|
105 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
106 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
107 |
A |
6 |
6 |
1. |
10 |
0.6 |
|
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|
|
|
|
|
108 |
A |
6 |
4 |
1. |
10 |
0.4 |
|
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|
|
|
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|
109 |
A |
6 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
110 |
A |
5 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
111 |
A |
2 |
2 |
1. |
6 |
0.333 |
|
|
|
|
|
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|
112 |
A |
6 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
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|
113 |
A |
6 |
4 |
1. |
10 |
0.4 |
|
|
|
|
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|
114 |
A |
6 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
115 |
A |
3 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
116 |
A |
2 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
117 |
A |
2 |
2 |
1. |
26 |
0.077 |
|
|
|
|
|
|
|
118 |
A |
2 |
2 |
1. |
26 |
0.077 |
|
|
|
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