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, 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, 98, 99, 100 }
B grade: { 38, 97 }
C grade: { 39 }
F grade: { }
2.1.2 Mathematica
A grade: { 8, 9, 10, 11, 12, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 32, 34, 39, 40, 41, 42, 43, 44,
47, 51, 53, 55, 56, 57, 58, 59, 60, 61, 62, 64, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 80, 82, 83, 84, 85, 86,
87, 89, 91, 93, 94, 95, 96, 98, 99, 100 }
B grade: { 4, 6, 7, 29, 31, 36, 38, 97 }
C grade: { 1, 2, 3, 5, 13, 14, 18, 33, 35, 37, 45, 46, 48, 49, 50, 52, 54, 63, 65, 67, 77, 79, 81, 90, 92
}
F grade: { 19, 88}
2.1.3 Maple
A grade: { 1, 2, 3, 4, 9, 10, 11, 13, 14, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 36, 38, 39, 40, 41,
42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 66, 68, 70, 71, 72, 73, 74, 75, 89, 91, 93, 95, 97, 98, 99
}
B grade: { 6, 7, 8, 80 }
C grade: { 5, 33, 35, 37, 51, 55, 63, 65, 67, 69, 76, 78, 90, 92, 94, 96 }
F grade: { 12, 15, 16, 17, 18, 19, 30, 56, 57, 58, 59, 60, 61, 62, 64, 77, 79, 81, 82, 83, 84, 85, 86, 87, 88, 100
}
2.1.4 Maxima
A grade: { 4, 20, 21, 22, 23, 25, 26, 27, 28, 32, 34, 39, 41, 43, 47, 66, 71, 73, 75, 99, 100
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 24, 29, 30, 31, 33, 35, 36, 37, 38, 40,
42, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69,
70, 72, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98
}
2.1.5 FriCAS
A grade: { 1, 20, 21, 22, 23, 25, 26, 27, 28, 32, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 45, 47, 49, 55, 63, 65,
66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 91, 94, 96, 97
}
B grade: { 2, 3, 4, 6, 7, 8, 36, 38, 51, 53, 90, 92, 93, 95, 99, 100 }
C grade: { }
F grade: { 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 24, 29, 30, 31, 46, 48, 50, 52, 54, 56, 57, 58, 59, 60, 61,
62, 64, 88, 98 }
2.1.6 Sympy
A grade: { 93 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87,
88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100 }
2.1.7 Giac
A grade: { 49, 71 }
B grade: { 45, 47 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61,
62, 63, 64, 65, 66, 67, 68, 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 }
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 |
C |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 203 | 203 | 225 | 250 | 0 | 772 | 0 | 0 |
normalized size | 1 | 1. | 1.11 | 1.23 | 0. | 3.8 | 0. | 0. |
time (sec) |
N/A |
0.155 |
0.494 |
0.292 |
0. |
2.526 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 153 | 153 | 200 | 189 | 0 | 720 | 0 | 0 |
normalized size | 1 | 1. | 1.31 | 1.24 | 0. | 4.71 | 0. | 0. |
time (sec) |
N/A |
0.099 |
0.258 |
0.244 |
0. |
2.351 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 176 | 111 | 0 | 687 | 0 | 0 |
normalized size | 1 | 1. | 1.64 | 1.04 | 0. | 6.42 | 0. | 0. |
time (sec) |
N/A |
0.062 |
0.161 |
0.234 |
0. |
2.263 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 44 | 44 | 95 | 50 | 42 | 567 | 0 | 0 |
normalized size | 1 | 1. | 2.16 | 1.14 | 0.95 | 12.89 | 0. | 0. |
time (sec) |
N/A |
0.056 |
0.196 |
0.213 |
0.978 |
2.147 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 170 | 170 | 332 | 886 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.95 | 5.21 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.29 |
0.192 |
0.352 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 244 | 542 | 0 | 1462 | 0 | 0 |
normalized size | 1 | 1. | 3.49 | 7.74 | 0. | 20.89 | 0. | 0. |
time (sec) |
N/A |
0.106 |
0.215 |
0.252 |
0. |
2.199 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 315 | 1233 | 0 | 1912 | 0 | 0 |
normalized size | 1 | 1. | 2.37 | 9.27 | 0. | 14.38 | 0. | 0. |
time (sec) |
N/A |
0.204 |
0.907 |
0.259 |
0. |
2.481 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 8 |
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 | 197 | 197 | 368 | 1946 | 0 | 2163 | 0 | 0 |
normalized size | 1 | 1. | 1.87 | 9.88 | 0. | 10.98 | 0. | 0. |
time (sec) |
N/A |
0.316 |
0.402 |
0.256 |
0. |
2.668 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 9 |
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 | 279 | 279 | 305 | 655 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.09 | 2.35 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.242 |
1.915 |
0.483 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 10 |
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 | 149 | 149 | 172 | 396 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.15 | 2.66 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.138 |
0.418 |
0.392 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 11 |
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 | 80 | 80 | 105 | 209 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.31 | 2.61 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.068 |
0.21 |
0.285 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 12 |
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 | 274 | 274 | 280 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.02 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.463 |
0.295 |
0.392 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 224 | 224 | 678 | 367 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 3.03 | 1.64 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.389 |
2.625 |
0.357 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 537 | 537 | 1439 | 1026 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.68 | 1.91 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.75 |
7.763 |
0.563 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 15 |
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 | 260 | 260 | 254 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.98 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.257 |
0.552 |
0.559 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 16 |
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 | 136 | 136 | 153 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.12 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.105 |
0.14 |
0.353 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 17 |
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 | 378 | 378 | 384 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.02 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.511 |
0.319 |
0.373 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 330 | 330 | 1849 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 5.6 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.575 |
45.653 |
0.458 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 965 | 965 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.338 |
9.65 |
0.694 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 164 | 164 | 84 | 54 | 78 | 144 | 0 | 0 |
normalized size |
1 |
1. |
0.51 |
0.33 |
0.48 |
0.88 |
0. |
0. |
time (sec) |
N/A |
0.03 |
0.041 |
0.139 |
0.982 |
1.838 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 126 | 72 | 49 | 62 | 131 | 0 | 0 |
normalized size | 1 | 1. | 0.57 | 0.39 | 0.49 | 1.04 | 0. | 0. |
time (sec) |
N/A |
0.027 |
0.04 |
0.126 |
0.983 |
1.872 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 56 | 42 | 46 | 116 | 0 | 0 |
normalized size | 1 | 1. | 0.64 | 0.48 | 0.52 | 1.32 | 0. | 0. |
time (sec) |
N/A |
0.018 |
0.026 |
0.13 |
0.987 |
1.865 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 67 | 36 | 26 | 92 | 0 | 0 |
normalized size | 1 | 1. | 1.56 | 0.84 | 0.6 | 2.14 | 0. | 0. |
time (sec) |
N/A |
0.007 |
0.096 |
0.123 |
0.972 |
1.806 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
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 | 46 | 46 | 45 | 65 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.98 | 1.41 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.095 |
0.036 |
0.16 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 111 | 64 | 88 | 111 | 0 | 0 |
normalized size | 1 | 1. | 1.13 | 0.65 | 0.9 | 1.13 | 0. | 0. |
time (sec) |
N/A |
0.023 |
0.077 |
0.134 |
0.98 |
1.878 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 125 | 79 | 124 | 134 | 0 | 0 |
normalized size | 1 | 1. | 0.92 | 0.58 | 0.91 | 0.99 | 0. | 0. |
time (sec) |
N/A |
0.033 |
0.112 |
0.133 |
0.993 |
1.885 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 172 | 172 | 140 | 91 | 157 | 153 | 0 | 0 |
normalized size |
1 |
1. |
0.81 |
0.53 |
0.91 |
0.89 |
0. |
0. |
time (sec) |
N/A |
0.04 |
0.128 |
0.141 |
0.99 |
1.93 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 25 | 29 | 22 | 57 | 0 | 0 |
normalized size | 1 | 1. | 1.19 | 1.38 | 1.05 | 2.71 | 0. | 0. |
time (sec) |
N/A |
0.007 |
0.024 |
0.101 |
1.024 |
1.811 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 61 | 61 | 219 | 116 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
3.59 |
1.9 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.105 |
0.957 |
0.333 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
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 | 54 | 54 | 49 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.91 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.107 |
0.046 |
0.284 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 249 | 140 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
3.23 |
1.82 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.101 |
1.171 |
0.361 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 83 | 65 | 64 | 63 | 135 | 0 | 0 |
normalized size | 1 | 1.3 | 1.02 | 1. | 0.98 | 2.11 | 0. | 0. |
time (sec) |
N/A |
0.038 |
0.09 |
0.189 |
1.078 |
1.714 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 97 | 118 | 0 | 203 | 0 | 0 |
normalized size | 1 | 1. | 1.15 | 1.4 | 0. | 2.42 | 0. | 0. |
time (sec) |
N/A |
0.032 |
0.127 |
0.179 |
0. |
1.778 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 52 | 48 | 54 | 51 | 111 | 0 | 0 |
normalized size | 1 | 1.37 | 1.26 | 1.42 | 1.34 | 2.92 | 0. | 0. |
time (sec) |
N/A |
0.024 |
0.059 |
0.173 |
1.07 |
1.821 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 75 | 92 | 0 | 171 | 0 | 0 |
normalized size | 1 | 1. | 1.42 | 1.74 | 0. | 3.23 | 0. | 0. |
time (sec) |
N/A |
0.018 |
0.076 |
0.184 |
0. |
1.808 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
B |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 39 | 79 | 79 | 0 | 258 | 0 | 0 |
normalized size | 1 | 1.62 | 3.29 | 3.29 | 0. | 10.75 | 0. | 0. |
time (sec) |
N/A |
0.137 |
0.04 |
0.184 |
0. |
1.832 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 64 | 75 | 92 | 0 | 165 | 0 | 0 |
normalized size | 1 | 1.33 | 1.56 | 1.92 | 0. | 3.44 | 0. | 0. |
time (sec) |
N/A |
0.031 |
0.05 |
0.189 |
0. |
2.024 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
B |
A |
F |
B |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 99 | 93 | 90 | 0 | 278 | 0 | 0 |
normalized size | 1 | 2.83 | 2.66 | 2.57 | 0. | 7.94 | 0. | 0. |
time (sec) |
N/A |
0.041 |
0.06 |
0.204 |
0. |
1.81 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
A |
A |
A |
F |
F |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 84 | 43 | 53 | 58 | 108 | 0 | 0 |
normalized size | 1 | 1.53 | 0.78 | 0.96 | 1.05 | 1.96 | 0. | 0. |
time (sec) |
N/A |
0.037 |
0.043 |
0.178 |
1.045 |
1.835 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 110 | 110 | 0 | 298 | 0 | 0 |
normalized size | 1 | 1. | 0.83 | 0.83 | 0. | 2.26 | 0. | 0. |
time (sec) |
N/A |
0.059 |
0.073 |
0.184 |
0. |
1.809 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 60 | 63 | 69 | 128 | 0 | 0 |
normalized size | 1 | 1. | 0.52 | 0.55 | 0.6 | 1.11 | 0. | 0. |
time (sec) |
N/A |
0.052 |
0.067 |
0.179 |
1.04 |
1.922 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 163 | 163 | 129 | 132 | 0 | 324 | 0 | 0 |
normalized size | 1 | 1. | 0.79 | 0.81 | 0. | 1.99 | 0. | 0. |
time (sec) |
N/A |
0.077 |
0.104 |
0.184 |
0. |
2.194 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 146 | 146 | 76 | 71 | 81 | 151 | 0 | 0 |
normalized size | 1 | 1. | 0.52 | 0.49 | 0.55 | 1.03 | 0. | 0. |
time (sec) |
N/A |
0.071 |
0.085 |
0.191 |
1.037 |
2.129 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 145 | 152 | 0 | 348 | 0 | 0 |
normalized size | 1 | 1. | 0.75 | 0.78 | 0. | 1.79 | 0. | 0. |
time (sec) |
N/A |
0.098 |
0.133 |
0.203 |
0. |
2.133 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F(-1) |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 111 | 137 | 0 | 251 | 0 | 360 |
normalized size |
1 |
1. |
1. |
1.23 |
0. |
2.26 |
0. |
3.24 |
time (sec) |
N/A |
0.062 |
0.181 |
0.322 |
0. |
2.125 |
0. |
1.195 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 139 | 114 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.21 |
0.99 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.051 |
0.332 |
0.19 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 71 | 56 | 60 | 57 | 126 | 0 | 240 |
normalized size |
1 |
1.22 |
0.97 |
1.03 |
0.98 |
2.17 |
0. |
4.14 |
time (sec) |
N/A |
0.041 |
0.094 |
0.178 |
1.068 |
2.061 |
0. |
1.182 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 112 | 112 | 140 | 136 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.25 | 1.21 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.067 |
0.435 |
0.181 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 92 | 112 | 0 | 225 | 0 | 107 |
normalized size | 1 | 1. | 1.46 | 1.78 | 0. | 3.57 | 0. | 1.7 |
time (sec) |
N/A |
0.037 |
0.104 |
0.33 |
0. |
2.053 |
0. |
1.163 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 116 | 102 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.73 | 1.52 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.028 |
0.189 |
0.204 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 100 | 127 | 0 | 298 | 0 | 0 |
normalized size |
1 |
1. |
1.47 |
1.87 |
0. |
4.38 |
0. |
0. |
time (sec) |
N/A |
0.043 |
0.063 |
0.312 |
0. |
2.099 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 135 | 132 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.92 | 0.9 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.068 |
0.282 |
0.187 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F(-2) |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 93 | 113 | 103 | 0 | 230 | 0 | 0 |
normalized size |
1 |
1.16 |
1.41 |
1.29 |
0. |
2.88 |
0. |
0. |
time (sec) |
N/A |
0.053 |
0.144 |
0.284 |
0. |
2.013 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 123 | 104 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.07 | 0.9 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.051 |
0.192 |
0.208 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F(-2) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 118 | 118 | 105 | 129 | 0 | 319 | 0 | 0 |
normalized size |
1 |
1. |
0.89 |
1.09 |
0. |
2.7 |
0. |
0. |
time (sec) |
N/A |
0.061 |
0.256 |
0.299 |
0. |
2.034 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 159 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.46 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.068 |
2.495 |
0.23 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 159 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.49 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.056 |
2.303 |
0.194 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 145 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.59 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.04 |
0.302 |
0.174 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
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 | 109 | 109 | 139 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.28 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.075 |
0.825 |
0.643 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 186 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.4 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.083 |
4.953 |
1.224 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 159 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.34 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.053 |
0.297 |
1.102 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 139 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.32 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.047 |
0.386 |
1.154 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
A |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 106 | 96 | 145 | 0 | 197 | 0 | 0 |
normalized size |
1 |
1.22 |
1.1 |
1.67 |
0. |
2.26 |
0. |
0. |
time (sec) |
N/A |
0.069 |
0.137 |
0.326 |
0. |
2.454 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 156 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.46 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.06 |
0.259 |
1.182 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 203 | 203 | 105 | 123 | 0 | 225 | 0 | 0 |
normalized size |
1 |
1. |
0.52 |
0.61 |
0. |
1.11 |
0. |
0. |
time (sec) |
N/A |
0.7 |
0.141 |
0.206 |
0. |
2.091 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 52 | 72 | 57 | 131 | 0 | 0 |
normalized size | 1 | 1. | 0.44 | 0.62 | 0.49 | 1.12 | 0. | 0. |
time (sec) |
N/A |
0.546 |
0.068 |
0.181 |
1.045 |
1.946 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 169 | 169 | 86 | 97 | 0 | 192 | 0 | 0 |
normalized size |
1 |
1. |
0.51 |
0.57 |
0. |
1.14 |
0. |
0. |
time (sec) |
N/A |
0.465 |
0.07 |
0.182 |
0. |
2.116 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 89 | 89 | 0 | 281 | 0 | 0 |
normalized size |
1 |
1. |
1.05 |
1.05 |
0. |
3.31 |
0. |
0. |
time (sec) |
N/A |
0.434 |
0.06 |
0.208 |
0. |
2.106 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 75 | 98 | 0 | 186 | 0 | 0 |
normalized size | 1 | 1. | 1.32 | 1.72 | 0. | 3.26 | 0. | 0. |
time (sec) |
N/A |
0.174 |
0.095 |
0.209 |
0. |
2.301 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 86 | 97 | 0 | 306 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.13 | 0. | 3.56 | 0. | 0. |
time (sec) |
N/A |
0.446 |
0.066 |
0.187 |
0. |
2.149 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
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 | 57 | 57 | 52 | 73 | 62 | 130 | 0 | 126 |
normalized size | 1 | 1. | 0.91 | 1.28 | 1.09 | 2.28 | 0. | 2.21 |
time (sec) |
N/A |
0.39 |
0.066 |
0.194 |
1.043 |
2.055 |
0. |
1.152 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 121 | 131 | 0 | 316 | 0 | 0 |
normalized size | 1 | 1. | 0.82 | 0.89 | 0. | 2.15 | 0. | 0. |
time (sec) |
N/A |
0.453 |
0.123 |
0.192 |
0. |
2.123 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 183 | 183 | 69 | 84 | 76 | 150 | 0 | 0 |
normalized size | 1 | 1. | 0.38 | 0.46 | 0.42 | 0.82 | 0. | 0. |
time (sec) |
N/A |
0.505 |
0.079 |
0.196 |
1.046 |
2.166 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 267 | 267 | 137 | 153 | 0 | 344 | 0 | 0 |
normalized size | 1 | 1. | 0.51 | 0.57 | 0. | 1.29 | 0. | 0. |
time (sec) |
N/A |
0.543 |
0.143 |
0.227 |
0. |
2.116 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 301 | 301 | 85 | 92 | 88 | 174 | 0 | 0 |
normalized size | 1 | 1. | 0.28 | 0.31 | 0.29 | 0.58 | 0. | 0. |
time (sec) |
N/A |
0.576 |
0.099 |
0.24 |
1.078 |
2.082 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 65 | 531 | 0 | 135 | 0 | 0 |
normalized size | 1 | 1. | 0.44 | 3.61 | 0. | 0.92 | 0. | 0. |
time (sec) |
N/A |
0.619 |
0.09 |
0.54 |
0. |
2.037 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 163 | 163 | 97 | 0 | 0 | 203 | 0 | 0 |
normalized size | 1 | 1. | 0.6 | 0. | 0. | 1.25 | 0. | 0. |
time (sec) |
N/A |
0.569 |
0.113 |
180. |
0. |
2.07 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 48 | 269 | 0 | 111 | 0 | 0 |
normalized size | 1 | 1. | 0.64 | 3.59 | 0. | 1.48 | 0. | 0. |
time (sec) |
N/A |
0.513 |
0.055 |
0.496 |
0. |
1.91 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 75 | 0 | 0 | 173 | 0 | 0 |
normalized size | 1 | 1. | 0.8 | 0. | 0. | 1.84 | 0. | 0. |
time (sec) |
N/A |
0.309 |
0.068 |
180. |
0. |
2.024 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 72 | 2632 | 0 | 259 | 0 | 0 |
normalized size | 1 | 1. | 1.11 | 40.49 | 0. | 3.98 | 0. | 0. |
time (sec) |
N/A |
0.166 |
0.031 |
0.475 |
0. |
2.081 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 74 | 0 | 0 | 163 | 0 | 0 |
normalized size | 1 | 1. | 1.61 | 0. | 0. | 3.54 | 0. | 0. |
time (sec) |
N/A |
0.401 |
0.036 |
180. |
0. |
2.303 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 92 | 0 | 0 | 279 | 0 | 0 |
normalized size | 1 | 1. | 1.28 | 0. | 0. | 3.88 | 0. | 0. |
time (sec) |
N/A |
0.383 |
0.057 |
180. |
0. |
2.028 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 43 | 0 | 0 | 109 | 0 | 0 |
normalized size | 1 | 1. | 0.37 | 0. | 0. | 0.94 | 0. | 0. |
time (sec) |
N/A |
0.424 |
0.052 |
180. |
0. |
2.066 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 200 | 200 | 110 | 0 | 0 | 300 | 0 | 0 |
normalized size | 1 | 1. | 0.55 | 0. | 0. | 1.5 | 0. | 0. |
time (sec) |
N/A |
0.5 |
0.1 |
180. |
0. |
2.077 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 233 | 233 | 60 | 0 | 0 | 130 | 0 | 0 |
normalized size | 1 | 1. | 0.26 | 0. | 0. | 0.56 | 0. | 0. |
time (sec) |
N/A |
0.5 |
0.069 |
180. |
0. |
2.032 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 320 | 320 | 129 | 0 | 0 | 325 | 0 | 0 |
normalized size | 1 | 1. | 0.4 | 0. | 0. | 1.02 | 0. | 0. |
time (sec) |
N/A |
0.567 |
0.141 |
180. |
0. |
2.096 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 353 | 353 | 76 | 0 | 0 | 153 | 0 | 0 |
normalized size | 1 | 1. | 0.22 | 0. | 0. | 0.43 | 0. | 0. |
time (sec) |
N/A |
0.605 |
0.097 |
180. |
0. |
2.094 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.272 |
0.635 |
0.434 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 69 | 69 | 0 | 149 | 0 | 0 |
normalized size |
1 |
1. |
0.78 |
0.78 |
0. |
1.69 |
0. |
0. |
time (sec) |
N/A |
0.181 |
0.189 |
0.211 |
0. |
2.067 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 110 | 117 | 0 | 213 | 0 | 0 |
normalized size |
1 |
1. |
1.47 |
1.56 |
0. |
2.84 |
0. |
0. |
time (sec) |
N/A |
0.165 |
0.154 |
0.213 |
0. |
2.093 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 44 | 52 | 0 | 111 | 0 | 0 |
normalized size | 1 | 1. | 0.98 | 1.16 | 0. | 2.47 | 0. | 0. |
time (sec) |
N/A |
0.125 |
0.09 |
0.2 |
0. |
2.117 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 68 | 92 | 0 | 131 | 0 | 0 |
normalized size | 1 | 1. | 1.84 | 2.49 | 0. | 3.54 | 0. | 0. |
time (sec) |
N/A |
0.114 |
0.044 |
0.227 |
0. |
2.102 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
A |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 73 | 87 | 0 | 213 | 48 | 0 |
normalized size | 1 | 1. | 1.03 | 1.23 | 0. | 3. | 0.68 | 0. |
time (sec) |
N/A |
0.119 |
0.04 |
0.204 |
0. |
2.076 |
15.488 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 59 | 61 | 0 | 144 | 0 | 0 |
normalized size | 1 | 1. | 1.4 | 1.45 | 0. | 3.43 | 0. | 0. |
time (sec) |
N/A |
0.143 |
0.164 |
0.21 |
0. |
2.162 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 108 | 111 | 0 | 344 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.03 | 0. | 3.19 | 0. | 0. |
time (sec) |
N/A |
0.176 |
0.151 |
0.227 |
0. |
2.12 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 90 | 86 | 0 | 197 | 0 | 0 |
normalized size | 1 | 1. | 1.06 | 1.01 | 0. | 2.32 | 0. | 0. |
time (sec) |
N/A |
0.165 |
0.242 |
0.22 |
0. |
2.206 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
B |
B |
A |
F |
A |
F |
F |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 26 | 28 | 36 | 0 | 69 | 0 | 0 |
normalized size | 1 | 2.17 | 2.33 | 3. | 0. | 5.75 | 0. | 0. |
time (sec) |
N/A |
1.052 |
0.244 |
0.15 |
0. |
2.042 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
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 | 61 | 61 | 52 | 104 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.85 | 1.7 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.098 |
0.055 |
0.283 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 84 | 62 | 51 | 613 | 0 | 0 |
normalized size |
1 |
1. |
1.47 |
1.09 |
0.89 |
10.75 |
0. |
0. |
time (sec) |
N/A |
0.115 |
0.202 |
0.289 |
0.994 |
2.473 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 84 | 0 | 54 | 1138 | 0 | 0 |
normalized size |
1 |
1. |
1.45 |
0. |
0.93 |
19.62 |
0. |
0. |
time (sec) |
N/A |
0.113 |
0.248 |
0.401 |
0.999 |
2.608 |
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 [15] had the largest ratio of [ 1.2
]
|
|
|
|
|
|
|
| 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 |
8 |
7 |
1. |
10 |
0.7 |
|
|
|
|
|
|
|
2 |
A |
7 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
3 |
A |
6 |
6 |
1. |
8 |
0.75 |
|
|
|
|
|
|
|
4 |
A |
4 |
4 |
1. |
6 |
0.667 |
|
|
|
|
|
|
|
5 |
A |
14 |
8 |
1. |
10 |
0.8 |
|
|
|
|
|
|
|
6 |
A |
5 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
7 |
A |
7 |
7 |
1. |
10 |
0.7 |
|
|
|
|
|
|
|
8 |
A |
8 |
8 |
1. |
10 |
0.8 |
|
|
|
|
|
|
|
9 |
A |
17 |
9 |
1. |
12 |
0.75 |
|
|
|
|
|
|
|
10 |
A |
11 |
8 |
1. |
10 |
0.8 |
|
|
|
|
|
|
|
11 |
A |
8 |
6 |
1. |
8 |
0.75 |
|
|
|
|
|
|
|
12 |
A |
17 |
9 |
1. |
12 |
0.75 |
|
|
|
|
|
|
|
13 |
A |
12 |
8 |
1. |
12 |
0.667 |
|
|
|
|
|
|
|
14 |
A |
23 |
11 |
1. |
12 |
0.917 |
|
|
|
|
|
|
|
15 |
A |
16 |
12 |
1. |
10 |
1.2 |
|
|
|
|
|
|
|
16 |
A |
10 |
7 |
1. |
8 |
0.875 |
|
|
|
|
|
|
|
17 |
A |
20 |
10 |
1. |
12 |
0.833 |
|
|
|
|
|
|
|
18 |
A |
14 |
9 |
1. |
12 |
0.75 |
|
|
|
|
|
|
|
19 |
A |
32 |
13 |
1. |
12 |
1.083 |
|
|
|
|
|
|
|
20 |
A |
4 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
|
21 |
A |
4 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
22 |
A |
4 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
23 |
A |
3 |
3 |
1. |
6 |
0.5 |
|
|
|
|
|
|
|
24 |
A |
7 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
25 |
A |
5 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
26 |
A |
6 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
27 |
A |
7 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
28 |
A |
3 |
3 |
1. |
4 |
0.75 |
|
|
|
|
|
|
|
29 |
A |
7 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
30 |
A |
7 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
31 |
A |
7 |
7 |
1. |
10 |
0.7 |
|
|
|
|
|
|
|
32 |
A |
5 |
5 |
1.3 |
10 |
0.5 |
|
|
|
|
|
|
|
33 |
A |
5 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
34 |
A |
3 |
3 |
1.37 |
10 |
0.3 |
|
|
|
|
|
|
|
35 |
A |
4 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
36 |
A |
3 |
3 |
1.62 |
6 |
0.5 |
|
|
|
|
|
|
|
37 |
A |
5 |
5 |
1.33 |
10 |
0.5 |
|
|
|
|
|
|
|
38 |
B |
6 |
6 |
2.83 |
10 |
0.6 |
|
|
|
|
|
|
|
39 |
C |
5 |
5 |
1.53 |
10 |
0.5 |
|
|
|
|
|
|
|
40 |
A |
8 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
|
41 |
A |
7 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
42 |
A |
10 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
43 |
A |
9 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
44 |
A |
12 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
45 |
A |
6 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
46 |
A |
5 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
47 |
A |
4 |
4 |
1.22 |
12 |
0.333 |
|
|
|
|
|
|
|
48 |
A |
7 |
7 |
1. |
12 |
0.583 |
|
|
|
|
|
|
|
49 |
A |
5 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
50 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
51 |
A |
6 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
52 |
A |
8 |
8 |
1. |
8 |
1. |
|
|
|
|
|
|
|
53 |
A |
5 |
5 |
1.16 |
12 |
0.417 |
|
|
|
|
|
|
|
54 |
A |
5 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
55 |
A |
7 |
7 |
1. |
12 |
0.583 |
|
|
|
|
|
|
|
56 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
57 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
58 |
A |
4 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
59 |
A |
5 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
60 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
|
61 |
A |
4 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
62 |
A |
4 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
63 |
A |
6 |
6 |
1.22 |
12 |
0.5 |
|
|
|
|
|
|
|
64 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
65 |
A |
9 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
66 |
A |
8 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
67 |
A |
7 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
68 |
A |
8 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
69 |
A |
7 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
70 |
A |
5 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
71 |
A |
4 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
72 |
A |
5 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
73 |
A |
4 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
74 |
A |
5 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
75 |
A |
4 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
76 |
A |
8 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
77 |
A |
7 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
78 |
A |
6 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
79 |
A |
5 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
80 |
A |
6 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
|
81 |
A |
5 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
82 |
A |
5 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
83 |
A |
4 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
84 |
A |
5 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
85 |
A |
4 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
86 |
A |
5 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
87 |
A |
4 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
88 |
A |
5 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
89 |
A |
8 |
7 |
1. |
22 |
0.318 |
|
|
|
|
|
|
|
90 |
A |
7 |
7 |
1. |
22 |
0.318 |
|
|
|
|
|
|
|
91 |
A |
4 |
4 |
1. |
22 |
0.182 |
|
|
|
|
|
|
|
92 |
A |
5 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
93 |
A |
8 |
8 |
1. |
19 |
0.421 |
|
|
|
|
|
|
|
94 |
A |
5 |
5 |
1. |
22 |
0.227 |
|
|
|
|
|
|
|
95 |
A |
9 |
8 |
1. |
22 |
0.364 |
|
|
|
|
|
|
|
96 |
A |
8 |
7 |
1. |
22 |
0.318 |
|
|
|
|
|
|
|
97 |
B |
7 |
5 |
2.17 |
25 |
0.2 |
|
|
|
|
|
|
|
98 |
A |
8 |
8 |
1. |
19 |
0.421 |
|
|
|
|
|
|
|
99 |
A |
5 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
100 |
A |
5 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|