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, 78, 81, 82, 83, 84, 85, 88, 91, 92, 93, 94, 95, 96, 97,
98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 117, 124, 127, 128, 129, 130, 131,
132, 133, 134, 135, 136, 137, 138, 139, 144, 151, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165,
166 }
B grade: { 75, 77, 79, 86, 87, 114, 116, 118, 120, 121, 122, 123, 141, 143, 145, 152 }
C grade: { 74, 76, 80, 113, 115, 119, 140, 142, 146 }
F grade: { 89, 90, 125, 126, 147, 148, 149, 150, 153}
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 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, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78,
79, 80, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107,
108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126,
127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145,
146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 160, 161, 162, 163, 164, 165, 166
}
B grade: { 83 }
C grade: { 9, 11, 66, 82, 102, 158, 159 }
F grade: { 81, 84, 85}
2.1.3 Maple
A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 18, 21, 23, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46,
47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 80,
91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 116, 119,
127, 128, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 142, 145, 146, 154, 155, 156, 158, 159, 160, 161,
162, 163, 164 }
B grade: { 7, 14, 16, 20, 22, 24, 26, 28, 29, 32, 34, 87, 123, 136, 141, 143, 147, 149, 152, 153, 157, 166
}
C grade: { 19, 25, 27, 30, 31, 33, 64, 86, 100, 122, 144, 148, 150, 151, 165 }
F grade: { 56, 75, 78, 79, 81, 82, 83, 84, 85, 88, 89, 90, 93, 114, 117, 118, 120, 121, 124, 125, 126, 129
}
2.1.4 Maxima
A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 35, 36, 37, 38, 39, 40, 53, 57, 58, 59, 60, 61, 62,
63, 65, 66, 67, 74, 76, 80, 94, 95, 96, 97, 98, 99, 101, 102, 103, 105, 107, 109, 111, 113, 115, 119, 130, 131,
132, 133, 134, 135, 137, 138, 139, 140, 142, 146, 154, 155, 156, 158, 159, 160, 161, 162, 163,
164
B grade: { 68, 69, 70, 71, 72, 73, 104, 106, 108, 110, 112, 157, 165 }
C grade: { }
F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 41, 42, 43, 44, 45, 46, 47, 48,
49, 50, 51, 52, 54, 55, 56, 64, 75, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 100, 114, 116,
117, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 136, 141, 143, 144, 145, 147, 148, 149, 150, 151,
152, 153, 166 }
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 35, 36, 37, 38, 39, 40, 53, 54, 55, 57, 58, 60, 61,
62, 63, 65, 66, 67, 74, 76, 80, 91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 105, 107, 109, 111, 113, 115, 119,
127, 128, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 142, 146, 154, 155, 156, 158, 159, 160, 161, 162,
163, 164 }
B grade: { 68, 69, 70, 71, 72, 73, 104, 106, 108, 110, 112, 166 }
C grade: { }
F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 41, 42, 43, 44, 45, 46, 47, 48,
49, 50, 51, 52, 56, 59, 64, 75, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 93, 100, 114, 116, 117, 118,
120, 121, 122, 123, 124, 125, 126, 129, 136, 141, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 157, 165
}
2.1.6 Sympy
A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47,
48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 80, 98, 99, 101,
102, 104, 105, 106, 109, 110, 111, 132, 133, 134, 135, 137, 138, 139, 140, 142, 146, 154, 155, 156, 161, 162,
163 }
B grade: { 158, 159, 160, 164 }
C grade: { }
F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 56, 59, 64, 74, 75, 77, 78, 79,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 100, 103, 107, 108, 112, 113, 114, 115, 116,
117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 136, 141, 143, 144, 145, 147, 148,
149, 150, 151, 152, 153, 157, 165, 166 }
2.1.7 Giac
A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49,
50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 67, 68, 69, 70, 71, 72, 73, 74, 76, 91, 92, 94, 95, 96,
97, 98, 99, 101, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 127, 128, 130, 131,
132, 133, 134, 135, 137, 138, 139, 140, 142, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164
}
B grade: { 66, 102 }
C grade: { }
F grade: { 7, 14, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 56, 64, 75, 77, 78, 79,
80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 93, 100, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124,
125, 126, 129, 136, 141, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 157, 165, 166
}
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 \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)
|
|
|
|
|
|
|
|
|
Problem 1 |
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 | 59 | 59 | 64 | 53 | 77 | 131 | 63 | 89 |
normalized size | 1 | 1. | 1.08 | 0.9 | 1.31 | 2.22 | 1.07 | 1.51 |
time (sec) |
N/A |
0.032 |
0.003 |
0.006 |
1.46 |
2.364 |
2.023 |
1.223 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 2 |
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 | 61 | 52 | 76 | 134 | 60 | 80 |
normalized size | 1 | 1. | 1.09 | 0.93 | 1.36 | 2.39 | 1.07 | 1.43 |
time (sec) |
N/A |
0.042 |
0.013 |
0.006 |
0.977 |
2.29 |
1.446 |
1.249 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 3 |
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 | 48 | 48 | 53 | 44 | 65 | 105 | 53 | 66 |
normalized size | 1 | 1. | 1.1 | 0.92 | 1.35 | 2.19 | 1.1 | 1.38 |
time (sec) |
N/A |
0.027 |
0.003 |
0.005 |
1.443 |
2.442 |
1.108 |
1.353 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 4 |
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 | 45 | 45 | 50 | 43 | 62 | 111 | 49 | 66 |
normalized size | 1 | 1. | 1.11 | 0.96 | 1.38 | 2.47 | 1.09 | 1.47 |
time (sec) |
N/A |
0.032 |
0.008 |
0.006 |
0.982 |
2.306 |
0.765 |
1.203 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 5 |
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 | 42 | 35 | 50 | 80 | 42 | 61 |
normalized size | 1 | 1. | 1.14 | 0.95 | 1.35 | 2.16 | 1.14 | 1.65 |
time (sec) |
N/A |
0.016 |
0.002 |
0.004 |
1.484 |
2.22 |
0.561 |
1.194 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 6 |
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 | 29 | 29 | 29 | 28 | 42 | 81 | 26 | 42 |
normalized size | 1 | 1. | 1. | 0.97 | 1.45 | 2.79 | 0.9 | 1.45 |
time (sec) |
N/A |
0.011 |
0.003 |
0.003 |
0.985 |
2.232 |
0.253 |
1.335 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 35 | 74 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1. | 2.11 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.029 |
0.002 |
0.015 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 8 |
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 | 38 | 39 | 53 | 100 | 37 | 50 |
normalized size | 1 | 1. | 1.09 | 1.11 | 1.51 | 2.86 | 1.06 | 1.43 |
time (sec) |
N/A |
0.023 |
0.003 |
0.006 |
0.969 |
2.492 |
0.889 |
1.323 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 46 | 35 | 42 | 70 | 37 | 74 |
normalized size | 1 | 1. | 1.24 | 0.95 | 1.14 | 1.89 | 1. | 2. |
time (sec) |
N/A |
0.02 |
0.003 |
0.007 |
1.468 |
2.565 |
0.744 |
1.298 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 10 |
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 | 53 | 53 | 54 | 51 | 69 | 123 | 61 | 68 |
normalized size | 1 | 1. | 1.02 | 0.96 | 1.3 | 2.32 | 1.15 | 1.28 |
time (sec) |
N/A |
0.033 |
0.016 |
0.007 |
0.969 |
2.481 |
1.536 |
1.807 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 46 | 44 | 62 | 95 | 46 | 88 |
normalized size | 1 | 1. | 0.96 | 0.92 | 1.29 | 1.98 | 0.96 | 1.83 |
time (sec) |
N/A |
0.025 |
0.003 |
0.009 |
1.459 |
2.376 |
1.205 |
1.735 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 12 |
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 | 64 | 64 | 64 | 60 | 84 | 147 | 71 | 80 |
normalized size | 1 | 1. | 1. | 0.94 | 1.31 | 2.3 | 1.11 | 1.25 |
time (sec) |
N/A |
0.038 |
0.017 |
0.01 |
0.975 |
2.528 |
2.591 |
1.406 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 13 |
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 | 144 | 144 | 138 | 171 | 220 | 351 | 199 | 243 |
normalized size | 1 | 1. | 0.96 | 1.19 | 1.53 | 2.44 | 1.38 | 1.69 |
time (sec) |
N/A |
0.31 |
0.13 |
0.013 |
1.509 |
2.543 |
3.607 |
1.203 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 170 | 170 | 169 | 334 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.99 | 1.96 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.289 |
0.485 |
0.044 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 15 |
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 | 112 | 112 | 111 | 135 | 184 | 266 | 155 | 181 |
normalized size | 1 | 1. | 0.99 | 1.21 | 1.64 | 2.38 | 1.38 | 1.62 |
time (sec) |
N/A |
0.209 |
0.079 |
0.016 |
1.52 |
2.407 |
2.089 |
1.187 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 131 | 298 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.95 | 2.16 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.194 |
0.28 |
0.014 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 17 |
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 | 76 | 76 | 75 | 97 | 140 | 189 | 107 | 140 |
normalized size | 1 | 1. | 0.99 | 1.28 | 1.84 | 2.49 | 1.41 | 1.84 |
time (sec) |
N/A |
0.106 |
0.065 |
0.012 |
1.531 |
2.441 |
0.935 |
1.197 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 90 | 128 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.08 | 1.54 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.098 |
0.076 |
0.071 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 144 | 1128 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.09 | 8.55 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.25 |
0.072 |
0.394 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 102 | 323 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.24 |
3.94 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.147 |
0.141 |
0.013 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 90 | 110 | 132 | 221 | 119 | 0 |
normalized size | 1 | 1. | 1.14 | 1.39 | 1.67 | 2.8 | 1.51 | 0. |
time (sec) |
N/A |
0.128 |
0.065 |
0.011 |
1.497 |
2.54 |
1.452 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 153 | 399 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.09 | 2.85 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.23 |
0.364 |
0.014 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 128 | 147 | 205 | 297 | 170 | 0 |
normalized size | 1 | 1. | 1.1 | 1.27 | 1.77 | 2.56 | 1.47 | 0. |
time (sec) |
N/A |
0.219 |
0.088 |
0.017 |
1.538 |
2.75 |
2.615 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 255 | 255 | 291 | 528 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.14 |
2.07 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.948 |
0.764 |
0.017 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 271 | 271 | 396 | 3053 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.46 | 11.27 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.756 |
0.83 |
3.677 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 225 | 445 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.16 |
2.29 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.545 |
0.524 |
0.019 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 206 | 206 | 269 | 2020 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.31 | 9.81 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.434 |
0.566 |
1.106 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 152 | 352 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.16 |
2.69 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.239 |
0.284 |
0.089 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 192 | 270 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.61 | 2.27 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.209 |
0.092 |
0.134 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 206 | 206 | 212 | 2309 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.03 | 11.21 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.427 |
0.136 |
0.301 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 214 | 2159 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.84 |
18.61 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.267 |
0.369 |
0.341 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 176 | 457 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.32 |
3.44 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.285 |
0.323 |
0.043 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 213 | 213 | 321 | 5974 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.51 |
28.05 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.476 |
0.812 |
1.735 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 198 | 198 | 265 | 550 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.34 |
2.78 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.601 |
0.656 |
0.1 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
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 | 10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.008 |
0.611 |
0.189 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
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 | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.003 |
0.011 |
0.148 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
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 | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.015 |
0.425 |
0.12 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
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 | 10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.008 |
0.591 |
0.368 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
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 | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.003 |
0.881 |
0.149 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
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 | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.013 |
1.01 |
0.135 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.007 |
1.959 |
0.246 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.003 |
1.741 |
0.131 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.013 |
1.246 |
0.26 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.007 |
0.948 |
0.206 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.003 |
2.149 |
0.135 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.013 |
1.069 |
0.25 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.007 |
1.232 |
0.225 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.003 |
0.02 |
0.132 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.014 |
1.13 |
0.223 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.007 |
1.477 |
0.239 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.003 |
2.531 |
0.135 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
F(-2) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.013 |
2.72 |
0.183 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
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 | 117 | 117 | 108 | 74 | 116 | 404 | 104 | 116 |
normalized size | 1 | 1. | 0.92 | 0.63 | 0.99 | 3.45 | 0.89 | 0.99 |
time (sec) |
N/A |
0.067 |
0.025 |
0.023 |
1.485 |
2.794 |
8.17 |
1.212 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.022 |
3.731 |
1.937 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.021 |
2.433 |
1.633 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 60 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.82 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.031 |
0.031 |
1.434 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
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 | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
0.253 |
0.824 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
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 | 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.005 |
0.437 |
0.41 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.021 |
0.328 |
0.986 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 54 | 54 | 59 | 50 | 73 | 111 | 58 | 81 |
normalized size | 1 | 1. | 1.09 | 0.93 | 1.35 | 2.06 | 1.07 | 1.5 |
time (sec) |
N/A |
0.035 |
0.008 |
0.024 |
1.458 |
2.628 |
128.876 |
1.097 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 47 | 47 | 52 | 45 | 65 | 115 | 80 | 63 |
normalized size | 1 | 1. | 1.11 | 0.96 | 1.38 | 2.45 | 1.7 | 1.34 |
time (sec) |
N/A |
0.031 |
0.013 |
0.024 |
0.984 |
2.582 |
76.17 |
1.125 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 43 | 43 | 48 | 41 | 58 | 85 | 48 | 58 |
normalized size | 1 | 1. | 1.12 | 0.95 | 1.35 | 1.98 | 1.12 | 1.35 |
time (sec) |
N/A |
0.027 |
0.005 |
0.025 |
1.519 |
2.605 |
40.632 |
1.154 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
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 | 41 | 36 | 51 | 89 | 70 | 54 |
normalized size | 1 | 1. | 1.14 | 1. | 1.42 | 2.47 | 1.94 | 1.5 |
time (sec) |
N/A |
0.014 |
0.006 |
0.019 |
1.027 |
2.932 |
20.899 |
1.154 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 39 | 63 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.62 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.045 |
0.005 |
0.082 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
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 | 39 | 39 | 44 | 39 | 55 | 111 | 593 | 81 |
normalized size | 1 | 1. | 1.13 | 1. | 1.41 | 2.85 | 15.21 | 2.08 |
time (sec) |
N/A |
0.024 |
0.006 |
0.027 |
0.998 |
2.749 |
45.408 |
1.226 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 48 | 39 | 47 | 76 | 42 | 100 |
normalized size | 1 | 1. | 1.17 | 0.95 | 1.15 | 1.85 | 1.02 | 2.44 |
time (sec) |
N/A |
0.025 |
0.007 |
0.024 |
1.501 |
2.681 |
36.268 |
1.201 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
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 | 55 | 55 | 60 | 51 | 72 | 130 | 784 | 93 |
normalized size | 1 | 1. | 1.09 | 0.93 | 1.31 | 2.36 | 14.25 | 1.69 |
time (sec) |
N/A |
0.032 |
0.014 |
0.029 |
1.002 |
2.822 |
140.139 |
1.142 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 179 | 140 | 375 | 894 | 184 | 228 |
normalized size | 1 | 1. | 1.11 | 0.87 | 2.33 | 5.55 | 1.14 | 1.42 |
time (sec) |
N/A |
0.113 |
0.048 |
0.037 |
1.527 |
2.852 |
55.237 |
1.305 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 159 | 159 | 177 | 138 | 354 | 807 | 1207 | 223 |
normalized size | 1 | 1. | 1.11 | 0.87 | 2.23 | 5.08 | 7.59 | 1.4 |
time (sec) |
N/A |
0.101 |
0.033 |
0.026 |
1.532 |
2.803 |
28.332 |
1.239 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 107 | 125 | 348 | 768 | 146 | 201 |
normalized size | 1 | 1. | 0.76 | 0.89 | 2.49 | 5.49 | 1.04 | 1.44 |
time (sec) |
N/A |
0.105 |
0.042 |
0.023 |
1.519 |
2.826 |
15.067 |
1.144 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 158 | 125 | 339 | 790 | 1105 | 186 |
normalized size | 1 | 1. | 1.1 | 0.87 | 2.37 | 5.52 | 7.73 | 1.3 |
time (sec) |
N/A |
0.086 |
0.042 |
0.025 |
1.529 |
2.757 |
32.019 |
1.228 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 159 | 159 | 177 | 132 | 369 | 900 | 704 | 215 |
normalized size | 1 | 1. | 1.11 | 0.83 | 2.32 | 5.66 | 4.43 | 1.35 |
time (sec) |
N/A |
0.104 |
0.052 |
0.029 |
1.525 |
2.858 |
55.576 |
1.268 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 159 | 159 | 177 | 138 | 366 | 873 | 1265 | 203 |
normalized size | 1 | 1. | 1.11 | 0.87 | 2.3 | 5.49 | 7.96 | 1.28 |
time (sec) |
N/A |
0.103 |
0.05 |
0.03 |
1.52 |
2.831 |
107.518 |
1.364 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 731 | 121 | 151 | 228 | 301 | 0 | 196 |
normalized size |
1 |
5.9 |
0.98 |
1.22 |
1.84 |
2.43 |
0. |
1.58 |
time (sec) |
N/A |
1.627 |
0.091 |
0.036 |
1.779 |
2.993 |
0. |
1.196 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 647 | 141 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
4.2 |
0.92 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.366 |
0.289 |
180. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
A |
A |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 612 | 85 | 113 | 170 | 227 | 529 | 135 |
normalized size | 1 | 6.8 | 0.94 | 1.26 | 1.89 | 2.52 | 5.88 | 1.5 |
time (sec) |
N/A |
1.042 |
0.064 |
0.033 |
1.752 |
2.773 |
63.552 |
1.197 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
A |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 255 | 107 | 146 | 0 | 0 | 0 | 0 |
normalized size | 1 | 2.52 | 1.06 | 1.45 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.554 |
0.087 |
0.087 |
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 |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 165 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.09 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.321 |
0.1 |
0.167 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 290 | 127 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
2.99 |
1.31 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.653 |
0.149 |
0.337 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
A |
F |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 419 | 98 | 118 | 149 | 258 | 1187 | 0 |
normalized size | 1 | 4.82 | 1.13 | 1.36 | 1.71 | 2.97 | 13.64 | 0. |
time (sec) |
N/A |
1.136 |
0.077 |
0.037 |
1.837 |
2.732 |
86.816 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1393 | 1393 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.602 |
4.849 |
0.207 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1191 | 1191 | 5466 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
4.59 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.778 |
31.777 |
0.188 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1164 | 1164 | 5434 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
4.67 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.622 |
31.403 |
0.191 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1360 | 1360 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.227 |
2.674 |
0.2 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1444 | 1444 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.427 |
2.7 |
0.208 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
C |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 951 | 170 | 690 | 0 | 0 | 0 | 0 |
normalized size | 1 | 6.38 | 1.14 | 4.63 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
4.736 |
0.311 |
0.733 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
B |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 144 | 545 | 224 | 306 | 0 | 0 | 0 | 0 |
normalized size | 1 | 3.78 | 1.56 | 2.12 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.545 |
0.102 |
0.125 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
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 | 229 | 229 | 245 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.07 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.529 |
0.195 |
0.199 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 0 | 239 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
1.73 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.831 |
0.43 |
0.332 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 0 | 196 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
1.32 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.659 |
0.334 |
0.661 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.023 |
1.788 |
0.237 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
1.175 |
0.213 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 65 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.87 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.041 |
0.059 |
0.209 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.027 |
0.312 |
0.145 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.026 |
0.329 |
0.171 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 59 | 50 | 73 | 113 | 0 | 81 |
normalized size |
1 |
1. |
1.09 |
0.93 |
1.35 |
2.09 |
0. |
1.5 |
time (sec) |
N/A |
0.039 |
0.008 |
0.026 |
1.502 |
2.619 |
0. |
1.117 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 52 | 45 | 65 | 115 | 0 | 63 |
normalized size |
1 |
1. |
1.11 |
0.96 |
1.38 |
2.45 |
0. |
1.34 |
time (sec) |
N/A |
0.036 |
0.013 |
0.023 |
1.052 |
2.656 |
0. |
1.137 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
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 | 43 | 43 | 48 | 41 | 58 | 85 | 48 | 58 |
normalized size | 1 | 1. | 1.12 | 0.95 | 1.35 | 1.98 | 1.12 | 1.35 |
time (sec) |
N/A |
0.029 |
0.005 |
0.023 |
1.483 |
2.587 |
166.108 |
1.105 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
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 | 41 | 36 | 51 | 89 | 808 | 54 |
normalized size | 1 | 1. | 1.14 | 1. | 1.42 | 2.47 | 22.44 | 1.5 |
time (sec) |
N/A |
0.021 |
0.007 |
0.021 |
1.003 |
2.661 |
83.144 |
1.161 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 39 | 63 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.62 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.05 |
0.005 |
0.086 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
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 | 39 | 39 | 44 | 39 | 55 | 111 | 505 | 81 |
normalized size | 1 | 1. | 1.13 | 1. | 1.41 | 2.85 | 12.95 | 2.08 |
time (sec) |
N/A |
0.025 |
0.007 |
0.026 |
0.993 |
3.279 |
155.503 |
1.111 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 48 | 39 | 47 | 76 | 42 | 100 |
normalized size | 1 | 1. | 1.17 | 0.95 | 1.15 | 1.85 | 1.02 | 2.44 |
time (sec) |
N/A |
0.027 |
0.006 |
0.028 |
1.505 |
3.132 |
153.635 |
1.166 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 60 | 51 | 72 | 130 | 0 | 93 |
normalized size |
1 |
1. |
1.09 |
0.93 |
1.31 |
2.36 |
0. |
1.69 |
time (sec) |
N/A |
0.035 |
0.014 |
0.027 |
1.021 |
3.325 |
0. |
1.113 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 174 | 174 | 179 | 165 | 396 | 948 | 1287 | 225 |
normalized size | 1 | 1. | 1.03 | 0.95 | 2.28 | 5.45 | 7.4 | 1.29 |
time (sec) |
N/A |
0.325 |
0.043 |
0.092 |
1.532 |
3.141 |
111.885 |
1.235 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
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 | 101 | 101 | 131 | 98 | 143 | 632 | 1703 | 128 |
normalized size | 1 | 1. | 1.3 | 0.97 | 1.42 | 6.26 | 16.86 | 1.27 |
time (sec) |
N/A |
0.098 |
0.04 |
0.023 |
1.494 |
3.306 |
55.892 |
1.152 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 170 | 148 | 381 | 1224 | 311 | 185 |
normalized size | 1 | 1. | 1.03 | 0.9 | 2.31 | 7.42 | 1.88 | 1.12 |
time (sec) |
N/A |
0.294 |
0.048 |
0.056 |
1.521 |
3.584 |
124.381 |
1.244 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 183 | 105 | 144 | 336 | 0 | 146 |
normalized size |
1 |
1. |
1.59 |
0.91 |
1.25 |
2.92 |
0. |
1.27 |
time (sec) |
N/A |
0.091 |
0.045 |
0.03 |
1.541 |
2.738 |
0. |
1.205 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 176 | 176 | 181 | 170 | 432 | 1069 | 0 | 231 |
normalized size |
1 |
1. |
1.03 |
0.97 |
2.45 |
6.07 |
0. |
1.31 |
time (sec) |
N/A |
0.431 |
0.075 |
0.069 |
1.503 |
3.25 |
0. |
1.394 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
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 | 117 | 117 | 185 | 113 | 162 | 362 | 1640 | 161 |
normalized size | 1 | 1. | 1.58 | 0.97 | 1.38 | 3.09 | 14.02 | 1.38 |
time (sec) |
N/A |
0.096 |
0.027 |
0.028 |
1.521 |
3.246 |
160.661 |
1.22 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 170 | 154 | 412 | 971 | 1620 | 212 |
normalized size | 1 | 1. | 1.03 | 0.93 | 2.5 | 5.88 | 9.82 | 1.28 |
time (sec) |
N/A |
0.393 |
0.025 |
0.056 |
1.557 |
2.54 |
67.111 |
1.307 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
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 | 104 | 104 | 170 | 104 | 151 | 258 | 1975 | 123 |
normalized size | 1 | 1. | 1.63 | 1. | 1.45 | 2.48 | 18.99 | 1.18 |
time (sec) |
N/A |
0.085 |
0.037 |
0.026 |
1.54 |
2.66 |
92.538 |
1.23 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 174 | 174 | 179 | 159 | 425 | 1385 | 0 | 217 |
normalized size |
1 |
1. |
1.03 |
0.91 |
2.44 |
7.96 |
0. |
1.25 |
time (sec) |
N/A |
0.413 |
0.05 |
0.059 |
1.535 |
2.963 |
0. |
1.714 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 731 | 121 | 151 | 228 | 281 | 0 | 196 |
normalized size |
1 |
5.9 |
0.98 |
1.22 |
1.84 |
2.27 |
0. |
1.58 |
time (sec) |
N/A |
1.655 |
0.095 |
0.037 |
1.928 |
2.711 |
0. |
1.14 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 647 | 141 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
4.2 |
0.92 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.394 |
0.293 |
180. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 612 | 85 | 113 | 170 | 200 | 0 | 135 |
normalized size |
1 |
6.8 |
0.94 |
1.26 |
1.89 |
2.22 |
0. |
1.5 |
time (sec) |
N/A |
1.052 |
0.065 |
0.037 |
1.871 |
2.619 |
0. |
1.158 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
A |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 255 | 107 | 148 | 0 | 0 | 0 | 0 |
normalized size | 1 | 2.45 | 1.03 | 1.42 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.644 |
0.071 |
0.09 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 117 |
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 | 154 | 154 | 167 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.08 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.316 |
0.116 |
0.198 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 290 | 125 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
2.9 |
1.25 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.661 |
0.155 |
0.408 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 119 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
F(-1) |
F |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 419 | 98 | 118 | 149 | 232 | 0 | 0 |
normalized size |
1 |
4.82 |
1.13 |
1.36 |
1.71 |
2.67 |
0. |
0. |
time (sec) |
N/A |
1.122 |
0.077 |
0.04 |
1.947 |
2.843 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 536 | 167 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
3.48 |
1.08 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.45 |
0.374 |
0.288 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 240 | 1867 | 346 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
7.78 |
1.44 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
7.034 |
0.505 |
0.279 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
C |
F |
F |
F(-1) |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 951 | 170 | 867 | 0 | 0 | 0 | 0 |
normalized size |
1 |
6.47 |
1.16 |
5.9 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
4.733 |
0.166 |
0.917 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 545 | 224 | 303 | 0 | 0 | 0 | 0 |
normalized size |
1 |
3.92 |
1.61 |
2.18 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.702 |
0.1 |
0.129 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 232 | 232 | 248 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.07 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.523 |
0.195 |
0.194 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 0 | 240 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
1.8 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.86 |
0.397 |
0.381 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 146 | 0 | 196 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
1.34 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.67 |
0.329 |
0.557 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 127 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
1.798 |
0.261 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 128 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
1.192 |
0.23 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 129 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 65 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.87 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.042 |
0.061 |
0.239 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 130 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.027 |
0.314 |
0.158 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 131 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.026 |
0.331 |
0.205 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 132 |
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 | 50 | 50 | 55 | 46 | 61 | 101 | 46 | 81 |
normalized size | 1 | 1. | 1.1 | 0.92 | 1.22 | 2.02 | 0.92 | 1.62 |
time (sec) |
N/A |
0.031 |
0.01 |
0.032 |
1.479 |
2.21 |
0.827 |
1.161 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 133 |
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 | 43 | 43 | 48 | 55 | 58 | 103 | 41 | 54 |
normalized size | 1 | 1. | 1.12 | 1.28 | 1.35 | 2.4 | 0.95 | 1.26 |
time (sec) |
N/A |
0.03 |
0.007 |
0.033 |
0.989 |
2.182 |
0.545 |
1.125 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 134 |
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 | 39 | 39 | 44 | 37 | 49 | 77 | 36 | 69 |
normalized size | 1 | 1. | 1.13 | 0.95 | 1.26 | 1.97 | 0.92 | 1.77 |
time (sec) |
N/A |
0.017 |
0.008 |
0.03 |
1.487 |
2.331 |
0.385 |
1.164 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 135 |
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 | 27 | 27 | 27 | 38 | 36 | 65 | 22 | 36 |
normalized size | 1 | 1. | 1. | 1.41 | 1.33 | 2.41 | 0.81 | 1.33 |
time (sec) |
N/A |
0.012 |
0.003 |
0.029 |
0.987 |
2.126 |
0.22 |
1.121 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 39 | 94 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1. | 2.41 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.045 |
0.006 |
0.036 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 137 |
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 | 37 | 36 | 51 | 103 | 36 | 54 |
normalized size | 1 | 1. | 1.09 | 1.06 | 1.5 | 3.03 | 1.06 | 1.59 |
time (sec) |
N/A |
0.019 |
0.008 |
0.021 |
1.026 |
2.227 |
0.977 |
1.116 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 138 |
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 | 43 | 43 | 48 | 41 | 57 | 84 | 44 | 84 |
normalized size | 1 | 1. | 1.12 | 0.95 | 1.33 | 1.95 | 1.02 | 1.95 |
time (sec) |
N/A |
0.024 |
0.01 |
0.026 |
1.525 |
2.068 |
1.237 |
1.145 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 139 |
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 | 55 | 55 | 60 | 45 | 73 | 132 | 60 | 74 |
normalized size | 1 | 1. | 1.09 | 0.82 | 1.33 | 2.4 | 1.09 | 1.35 |
time (sec) |
N/A |
0.036 |
0.01 |
0.026 |
1.026 |
2.232 |
1.637 |
1.135 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
A |
A |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 862 | 111 | 157 | 177 | 290 | 144 | 228 |
normalized size | 1 | 7.07 | 0.91 | 1.29 | 1.45 | 2.38 | 1.18 | 1.87 |
time (sec) |
N/A |
1.791 |
0.09 |
0.043 |
1.604 |
2.19 |
1.148 |
1.176 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 141 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
B |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 152 | 787 | 152 | 445 | 0 | 0 | 0 | 0 |
normalized size | 1 | 5.18 | 1. | 2.93 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.49 |
0.328 |
0.104 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 142 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
A |
A |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 663 | 73 | 116 | 136 | 201 | 97 | 173 |
normalized size | 1 | 8.09 | 0.89 | 1.41 | 1.66 | 2.45 | 1.18 | 2.11 |
time (sec) |
N/A |
1.126 |
0.054 |
0.04 |
1.54 |
2.282 |
0.587 |
1.175 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 143 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
B |
F |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 478 | 105 | 357 | 0 | 0 | 0 | 0 |
normalized size | 1 | 5.76 | 1.27 | 4.3 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.44 |
0.106 |
0.09 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 144 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 148 | 1249 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1. | 8.44 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.294 |
0.085 |
0.394 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 145 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
A |
F(-1) |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 259 | 107 | 147 | 0 | 0 | 0 | 0 |
normalized size |
1 |
2.7 |
1.11 |
1.53 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.528 |
0.111 |
0.088 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 146 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
A |
F |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 836 | 99 | 110 | 158 | 239 | 117 | 0 |
normalized size | 1 | 9.95 | 1.18 | 1.31 | 1.88 | 2.85 | 1.39 | 0. |
time (sec) |
N/A |
1.294 |
0.074 |
0.034 |
1.62 |
2.312 |
1.438 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 147 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
B |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 0 | 253 | 608 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 1.18 | 2.84 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
4.629 |
0.591 |
0.108 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 148 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
C |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 229 | 0 | 330 | 6441 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 1.44 | 28.13 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
3.52 |
0.678 |
1.027 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 149 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
B |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 0 | 174 | 507 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 1.2 | 3.5 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.352 |
0.274 |
0.104 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 150 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
C |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 0 | 215 | 2363 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 1.81 | 19.86 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.739 |
0.257 |
0.33 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 151 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 230 | 230 | 219 | 2542 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.95 | 11.05 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.494 |
0.207 |
0.276 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 152 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
B |
F(-1) |
F |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 551 | 222 | 306 | 0 | 0 | 0 | 0 |
normalized size |
1 |
4.05 |
1.63 |
2.25 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.359 |
0.119 |
0.125 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 153 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
B |
F(-1) |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 0 | 178 | 396 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
1.21 |
2.69 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.255 |
0.283 |
0.095 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 154 |
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 | 34 | 32 | 42 | 88 | 39 | 42 |
normalized size | 1 | 1. | 0.67 | 0.63 | 0.82 | 1.73 | 0.76 | 0.82 |
time (sec) |
N/A |
0.015 |
0.013 |
0.023 |
1.506 |
2.213 |
4.159 |
1.138 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 155 |
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 | 42 | 42 | 28 | 27 | 35 | 72 | 32 | 35 |
normalized size | 1 | 1. | 0.67 | 0.64 | 0.83 | 1.71 | 0.76 | 0.83 |
time (sec) |
N/A |
0.01 |
0.011 |
0.025 |
1.494 |
2.201 |
2.021 |
1.117 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 156 |
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 | 22 | 22 | 18 | 17 | 22 | 47 | 19 | 22 |
normalized size | 1 | 1. | 0.82 | 0.77 | 1. | 2.14 | 0.86 | 1. |
time (sec) |
N/A |
0.006 |
0.006 |
0.02 |
1.468 |
2.209 |
1.358 |
1.105 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 157 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 31 | 61 | 47 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.97 | 1.52 | 0. | 0. | 0. |
time (sec) |
N/A |
0.035 |
0.004 |
0.036 |
1.534 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 158 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 30 | 22 | 28 | 54 | 94 | 28 |
normalized size | 1 | 1. | 1.11 | 0.81 | 1.04 | 2. | 3.48 | 1.04 |
time (sec) |
N/A |
0.012 |
0.01 |
0.026 |
1.466 |
2.132 |
3.14 |
1.345 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 159 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 34 | 27 | 35 | 80 | 160 | 35 |
normalized size | 1 | 1. | 0.81 | 0.64 | 0.83 | 1.9 | 3.81 | 0.83 |
time (sec) |
N/A |
0.014 |
0.011 |
0.027 |
1.453 |
2.192 |
8.434 |
1.245 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 160 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 30 | 25 | 32 | 88 | 92 | 32 |
normalized size | 1 | 1. | 0.83 | 0.69 | 0.89 | 2.44 | 2.56 | 0.89 |
time (sec) |
N/A |
0.015 |
0.015 |
0.023 |
0.977 |
2.225 |
7.674 |
1.109 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 161 |
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 | 29 | 29 | 25 | 20 | 26 | 73 | 24 | 26 |
normalized size | 1 | 1. | 0.86 | 0.69 | 0.9 | 2.52 | 0.83 | 0.9 |
time (sec) |
N/A |
0.012 |
0.01 |
0.023 |
0.977 |
2.179 |
1.633 |
1.182 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 162 |
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 | 20 | 20 | 20 | 17 | 22 | 54 | 17 | 22 |
normalized size | 1 | 1. | 1. | 0.85 | 1.1 | 2.7 | 0.85 | 1.1 |
time (sec) |
N/A |
0.008 |
0.007 |
0.023 |
0.966 |
2.163 |
0.452 |
1.118 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 163 |
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 | 22 | 22 | 22 | 19 | 24 | 78 | 20 | 24 |
normalized size | 1 | 1. | 1. | 0.86 | 1.09 | 3.55 | 0.91 | 1.09 |
time (sec) |
N/A |
0.009 |
0.011 |
0.026 |
1.15 |
2.185 |
1.919 |
1.11 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 164 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 31 | 26 | 34 | 96 | 143 | 38 |
normalized size | 1 | 1. | 0.84 | 0.7 | 0.92 | 2.59 | 3.86 | 1.03 |
time (sec) |
N/A |
0.014 |
0.018 |
0.029 |
0.996 |
2.192 |
8.499 |
1.158 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 165 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 33 | 57 | 84 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1. |
1.73 |
2.55 |
0. |
0. |
0. |
time (sec) |
N/A |
0.036 |
0.006 |
0.088 |
1.469 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 166 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 32 | 94 | 0 | 181 | 0 | 0 |
normalized size | 1 | 1. | 0.82 | 2.41 | 0. | 4.64 | 0. | 0. |
time (sec) |
N/A |
0.036 |
0.013 |
0.033 |
0. |
2.562 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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 [142] had the largest ratio of [ 2.286
]
|
|
|
|
|
|
|
| Table 2.1Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
2 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
3 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
4 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
5 |
A |
3 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
6 |
A |
3 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
7 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
8 |
A |
5 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
9 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
10 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
11 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
12 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
13 |
A |
16 |
7 |
1. |
14 |
0.5 |
|
|
|
|
|
|
|
14 |
A |
14 |
9 |
1. |
14 |
0.643 |
|
|
|
|
|
|
|
15 |
A |
11 |
7 |
1. |
14 |
0.5 |
|
|
|
|
|
|
|
16 |
A |
9 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
17 |
A |
6 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
18 |
A |
5 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
19 |
A |
6 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
20 |
A |
4 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
|
21 |
A |
8 |
7 |
1. |
14 |
0.5 |
|
|
|
|
|
|
|
22 |
A |
8 |
7 |
1. |
14 |
0.5 |
|
|
|
|
|
|
|
23 |
A |
13 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
24 |
A |
33 |
11 |
1. |
14 |
0.786 |
|
|
|
|
|
|
|
25 |
A |
24 |
11 |
1. |
14 |
0.786 |
|
|
|
|
|
|
|
26 |
A |
18 |
10 |
1. |
14 |
0.714 |
|
|
|
|
|
|
|
27 |
A |
12 |
9 |
1. |
14 |
0.643 |
|
|
|
|
|
|
|
28 |
A |
8 |
8 |
1. |
12 |
0.667 |
|
|
|
|
|
|
|
29 |
A |
5 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
30 |
A |
8 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
31 |
A |
5 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
32 |
A |
7 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
33 |
A |
14 |
11 |
1. |
14 |
0.786 |
|
|
|
|
|
|
|
34 |
A |
16 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
35 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
36 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
37 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
38 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
39 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
40 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
41 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
42 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
43 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
44 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
45 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
46 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
47 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
48 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
49 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
50 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
51 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
52 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
53 |
A |
12 |
9 |
1. |
8 |
1.125 |
|
|
|
|
|
|
|
54 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
55 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
56 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
57 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
58 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
59 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
60 |
A |
5 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
|
61 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
62 |
A |
4 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
63 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
64 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
65 |
A |
5 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
66 |
A |
4 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
67 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
68 |
A |
11 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
69 |
A |
11 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
70 |
A |
11 |
7 |
1. |
10 |
0.7 |
|
|
|
|
|
|
|
71 |
A |
10 |
7 |
1. |
14 |
0.5 |
|
|
|
|
|
|
|
72 |
A |
11 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
73 |
A |
11 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
74 |
C |
62 |
19 |
5.9 |
16 |
1.187 |
|
|
|
|
|
|
|
75 |
B |
53 |
19 |
4.2 |
16 |
1.187 |
|
|
|
|
|
|
|
76 |
C |
44 |
16 |
6.8 |
16 |
1. |
|
|
|
|
|
|
|
77 |
B |
28 |
12 |
2.52 |
14 |
0.857 |
|
|
|
|
|
|
|
78 |
A |
7 |
6 |
1. |
16 |
0.375 |
|
|
|
|
|
|
|
79 |
B |
24 |
13 |
2.99 |
16 |
0.812 |
|
|
|
|
|
|
|
80 |
C |
46 |
23 |
4.82 |
16 |
1.438 |
|
|
|
|
|
|
|
|
81 |
A |
86 |
27 |
1. |
16 |
1.687 |
|
|
|
|
|
|
|
82 |
A |
69 |
23 |
1. |
12 |
1.917 |
|
|
|
|
|
|
|
83 |
A |
47 |
23 |
1. |
16 |
1.438 |
|
|
|
|
|
|
|
84 |
A |
64 |
25 |
1. |
16 |
1.562 |
|
|
|
|
|
|
|
85 |
A |
77 |
25 |
1. |
16 |
1.562 |
|
|
|
|
|
|
|
86 |
B |
155 |
30 |
6.38 |
16 |
1.875 |
|
|
|
|
|
|
|
87 |
B |
82 |
23 |
3.78 |
14 |
1.643 |
|
|
|
|
|
|
|
88 |
A |
9 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
89 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
90 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
91 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
92 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
93 |
A |
3 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
94 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
95 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
96 |
A |
5 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
97 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
98 |
A |
4 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
99 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
100 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
|
101 |
A |
5 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
102 |
A |
4 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
103 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
104 |
A |
12 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
105 |
A |
9 |
8 |
1. |
10 |
0.8 |
|
|
|
|
|
|
|
106 |
A |
11 |
7 |
1. |
14 |
0.5 |
|
|
|
|
|
|
|
107 |
A |
9 |
9 |
1. |
14 |
0.643 |
|
|
|
|
|
|
|
108 |
A |
12 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
109 |
A |
9 |
9 |
1. |
14 |
0.643 |
|
|
|
|
|
|
|
110 |
A |
11 |
7 |
1. |
12 |
0.583 |
|
|
|
|
|
|
|
111 |
A |
8 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
112 |
A |
12 |
8 |
1. |
14 |
0.571 |
|
|
|
|
|
|
|
113 |
C |
62 |
19 |
5.9 |
16 |
1.187 |
|
|
|
|
|
|
|
114 |
B |
53 |
19 |
4.2 |
16 |
1.187 |
|
|
|
|
|
|
|
115 |
C |
44 |
16 |
6.8 |
16 |
1. |
|
|
|
|
|
|
|
116 |
B |
28 |
12 |
2.45 |
16 |
0.75 |
|
|
|
|
|
|
|
117 |
A |
7 |
6 |
1. |
16 |
0.375 |
|
|
|
|
|
|
|
118 |
B |
24 |
13 |
2.9 |
16 |
0.812 |
|
|
|
|
|
|
|
119 |
C |
46 |
23 |
4.82 |
16 |
1.438 |
|
|
|
|
|
|
|
120 |
B |
59 |
24 |
3.48 |
16 |
1.5 |
|
|
|
|
|
|
|
|
121 |
B |
239 |
32 |
7.78 |
16 |
2. |
|
|
|
|
|
|
|
122 |
B |
155 |
30 |
6.47 |
16 |
1.875 |
|
|
|
|
|
|
|
123 |
B |
82 |
23 |
3.92 |
16 |
1.438 |
|
|
|
|
|
|
|
124 |
A |
9 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
125 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
126 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
127 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
128 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
129 |
A |
3 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
130 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
131 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
132 |
A |
5 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
133 |
A |
5 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
134 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
135 |
A |
4 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
136 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
137 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
138 |
A |
4 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
139 |
A |
5 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
140 |
C |
88 |
34 |
7.07 |
16 |
2.125 |
|
|
|
|
|
|
|
|
141 |
B |
73 |
34 |
5.18 |
16 |
2.125 |
|
|
|
|
|
|
|
142 |
C |
58 |
32 |
8.09 |
14 |
2.286 |
|
|
|
|
|
|
|
143 |
B |
31 |
14 |
5.76 |
12 |
1.167 |
|
|
|
|
|
|
|
144 |
A |
7 |
6 |
1. |
16 |
0.375 |
|
|
|
|
|
|
|
145 |
B |
28 |
12 |
2.7 |
16 |
0.75 |
|
|
|
|
|
|
|
146 |
C |
66 |
23 |
9.95 |
16 |
1.438 |
|
|
|
|
|
|
|
147 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
148 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
149 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
150 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
151 |
A |
9 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
152 |
B |
82 |
23 |
4.05 |
16 |
1.438 |
|
|
|
|
|
|
|
153 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
154 |
A |
6 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
155 |
A |
5 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
156 |
A |
4 |
4 |
1. |
6 |
0.667 |
|
|
|
|
|
|
|
157 |
A |
4 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
158 |
A |
4 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
159 |
A |
5 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
160 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
|
161 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
162 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
163 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
164 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
165 |
A |
4 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
166 |
A |
4 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|