Chapter 2
detailed summary tables of results
2.1 List of integrals sorted by grade for each CAS
2.1.1 Rubi
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57,
58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 6, 7, 9, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 27, 31, 32, 33, 34, 35, 36, 37,
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, 75, 76, 78, 81 }
B grade: { 5, 8, 10, 38 }
C grade: { 18, 79, 82 }
F grade: { 24, 26, 28, 29, 30, 74, 77, 80, 83 }
2.1.3 Maple
A grade: { 2, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 24, 26, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49,
50, 53, 54, 55, 58, 59, 60, 63, 64, 65, 69, 70, 71 }
B grade: { 27, 68 }
C grade: { 72, 73, 75, 78, 79, 81 }
F grade: { 1, 3, 8, 10, 16, 18, 23, 25, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 61, 62, 66,
67, 74, 76, 77, 80, 82, 83 }
2.1.4 Maxima
A grade: { 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 17, 19, 20, 21, 22, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36,
37, 38, 39, 40, 44, 45, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 63, 64, 65, 68, 69, 70, 71, 72, 75
}
B grade: { 15 }
C grade: { }
F grade: { 1, 3, 10, 16, 18, 23, 25, 41, 42, 43, 46, 47, 48, 60, 61, 62, 66, 67, 73, 74, 76, 77, 78, 79, 80, 81, 82,
83 }
2.1.5 FriCAS
A grade: { 2, 4, 6, 7, 9, 11, 13, 14, 17, 19, 21, 22, 24, 26, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50, 54, 55,
59, 60, 64, 65, 69, 70, 71 }
B grade: { 3, 5, 10, 12, 15, 18, 20, 25, 27, 53, 58, 63, 68, 72, 73, 75, 76, 78, 79, 81, 82 }
C grade: { 1, 8, 16, 23, 74, 77, 80 }
F grade: { 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 61, 62, 66, 67, 83 }
2.1.6 Sympy
A grade: { 2, 4, 6, 7, 9, 11, 13, 14, 17, 19, 21, 22, 24, 26, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50, 54, 55,
59, 60, 64, 65, 69, 70, 71 }
B grade: { }
C grade: { }
F grade: { 1, 3, 5, 8, 10, 12, 15, 16, 18, 20, 23, 25, 27, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46,
47, 48, 51, 52, 53, 56, 57, 58, 61, 62, 63, 66, 67, 68, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83
}
2.1.7 Giac
A grade: { 2, 4, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 24, 26, 27, 28, 29, 30, 34, 35, 39, 40, 44, 45,
49, 50, 54, 55, 58, 59, 60, 63, 64, 65, 68, 69, 70, 71 }
B grade: { 5, 53 }
C grade: { }
F grade: { 1, 3, 8, 10, 16, 18, 23, 25, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 61, 62, 66,
67, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83 }
2.1.8 Mupad
A grade: { 2, 4, 6, 7, 9, 11, 13, 14, 17, 19, 21, 22, 24, 26, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50, 54, 55,
59, 60, 64, 65, 69, 70, 71 }
B grade: { 5, 12, 15, 20, 27, 53, 58, 63, 68, 72, 75, 78, 81 }
C grade: { }
F grade: { 1, 3, 8, 10, 16, 18, 23, 25, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 61, 62, 66,
67, 73, 74, 76, 77, 79, 80, 82, 83 }
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 |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 138 | 0 | 0 | 209 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.33 | 0.00 | 0.00 | 2.01 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.137 |
0.099 |
0.332 |
0.000 |
0.407 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.018 |
12.880 |
0.331 |
0.000 |
0.413 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 108 | 0 | 0 | 144 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.59 | 0.00 | 0.00 | 2.12 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.078 |
0.143 |
0.327 |
0.000 |
0.441 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.018 |
10.542 |
0.372 |
0.000 |
0.436 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 57 | 33 | 25 | 55 | 0 | 49 | 47 |
normalized size | 1 | 1.00 | 2.19 | 1.27 | 0.96 | 2.12 | 0.00 | 1.88 | 1.81 |
time (sec) |
N/A |
0.027 |
0.034 |
0.061 |
0.356 |
0.446 |
0.000 |
0.136 |
0.116 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.018 |
9.653 |
0.337 |
0.000 |
0.432 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.019 |
11.216 |
0.340 |
0.000 |
0.427 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
A |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 196 | 196 | 595 | 0 | 271 | 1031 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.04 | 0.00 | 1.38 | 5.26 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.375 |
6.266 |
0.434 |
0.795 |
0.501 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.025 |
34.713 |
0.427 |
0.000 |
0.447 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 260 | 0 | 0 | 683 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.41 | 0.00 | 0.00 | 6.32 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.165 |
4.496 |
0.461 |
0.000 |
0.431 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.026 |
31.397 |
0.402 |
0.000 |
0.398 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 69 | 44 | 49 | 271 | 0 | 75 | 81 |
normalized size | 1 | 1.00 | 1.53 | 0.98 | 1.09 | 6.02 | 0.00 | 1.67 | 1.80 |
time (sec) |
N/A |
0.061 |
0.277 |
0.309 |
0.381 |
0.496 |
0.000 |
0.141 |
1.624 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.025 |
66.898 |
0.442 |
0.000 |
0.416 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.026 |
43.913 |
0.461 |
0.000 |
0.414 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 147 | 62 | 205 | 2590 | 0 | 158 | 399 |
normalized size | 1 | 1.00 | 1.63 | 0.69 | 2.28 | 28.78 | 0.00 | 1.76 | 4.43 |
time (sec) |
N/A |
0.110 |
0.092 |
0.327 |
0.406 |
0.584 |
0.000 |
0.132 |
0.129 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 325 | 325 | 256 | 0 | 0 | 686 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.79 | 0.00 | 0.00 | 2.11 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.820 |
0.205 |
0.360 |
0.000 |
0.433 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.029 |
9.817 |
0.375 |
0.000 |
0.394 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 225 | 225 | 1166 | 0 | 0 | 505 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 5.18 | 0.00 | 0.00 | 2.24 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.506 |
3.214 |
0.329 |
0.000 |
0.534 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.029 |
8.607 |
0.315 |
0.000 |
0.386 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 71 | 94 | 92 | 213 | 0 | 92 | 175 |
normalized size | 1 | 1.00 | 1.18 | 1.57 | 1.53 | 3.55 | 0.00 | 1.53 | 2.92 |
time (sec) |
N/A |
0.098 |
0.133 |
0.247 |
0.906 |
0.440 |
0.000 |
0.147 |
2.040 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.028 |
5.358 |
0.316 |
0.000 |
0.592 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.016 |
0.222 |
0.018 |
0.000 |
0.470 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 922 | 922 | 1502 | 0 | 0 | 3756 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.63 | 0.00 | 0.00 | 4.07 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.033 |
14.097 |
0.595 |
0.000 |
0.547 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
F(-1) |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.028 |
180.001 |
0.560 |
0.000 |
0.464 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 519 | 519 | 747 | 0 | 0 | 2383 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.44 | 0.00 | 0.00 | 4.59 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.083 |
6.438 |
0.576 |
0.000 |
0.481 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
F(-1) |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.028 |
180.001 |
0.526 |
0.000 |
0.416 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 161 | 255 | 200 | 711 | 0 | 177 | 290 |
normalized size | 1 | 1.00 | 1.42 | 2.26 | 1.77 | 6.29 | 0.00 | 1.57 | 2.57 |
time (sec) |
N/A |
0.231 |
0.480 |
0.344 |
0.867 |
0.451 |
0.000 |
0.167 |
1.972 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
F(-1) |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.027 |
180.003 |
0.560 |
0.000 |
0.408 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
F(-1) |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.027 |
180.002 |
0.569 |
0.000 |
0.408 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
F(-1) |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.026 |
180.005 |
0.613 |
0.000 |
0.390 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 356 | 356 | 365 | 0 | 349 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 0.00 | 0.98 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.401 |
2.901 |
0.637 |
0.895 |
0.439 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 260 | 260 | 273 | 0 | 261 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.05 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.274 |
2.836 |
0.636 |
0.646 |
0.426 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 164 | 164 | 181 | 0 | 173 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 0.00 | 1.05 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.173 |
2.769 |
0.633 |
0.580 |
0.425 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.018 |
18.269 |
0.727 |
0.000 |
0.429 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.020 |
20.992 |
0.737 |
0.000 |
0.428 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 597 | 597 | 1077 | 0 | 648 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.80 | 0.00 | 1.09 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.817 |
12.629 |
0.744 |
0.559 |
0.440 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 441 | 441 | 833 | 0 | 496 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.89 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.631 |
12.070 |
0.743 |
0.784 |
0.427 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 287 | 287 | 616 | 0 | 343 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.15 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.449 |
11.513 |
0.743 |
0.796 |
0.417 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.025 |
130.848 |
0.706 |
0.000 |
0.409 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.026 |
62.455 |
0.702 |
0.000 |
0.409 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 897 | 897 | 905 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.343 |
2.621 |
0.778 |
0.000 |
0.421 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 673 | 673 | 716 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.167 |
2.025 |
0.737 |
0.000 |
0.423 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 449 | 449 | 488 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.901 |
2.042 |
0.790 |
0.000 |
0.408 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.027 |
5.322 |
0.714 |
0.000 |
0.424 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.018 |
1.589 |
0.013 |
0.000 |
0.430 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2663 | 2663 | 2923 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.748 |
21.076 |
1.220 |
0.000 |
0.437 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1983 | 1983 | 2153 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.925 |
19.793 |
1.207 |
0.000 |
0.432 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1303 | 1303 | 1333 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.295 |
16.238 |
1.073 |
0.000 |
0.449 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.026 |
141.856 |
1.040 |
0.000 |
0.448 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.026 |
73.592 |
1.040 |
0.000 |
0.433 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 214 | 238 | 0 | 217 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.11 | 0.00 | 1.01 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.219 |
3.284 |
0.630 |
1.559 |
0.421 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 120 | 120 | 142 | 0 | 129 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.18 | 0.00 | 1.08 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.118 |
9.693 |
0.582 |
1.636 |
0.474 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 34 | 26 | 25 | 55 | 0 | 49 | 47 |
normalized size | 1 | 1.00 | 1.31 | 1.00 | 0.96 | 2.12 | 0.00 | 1.88 | 1.81 |
time (sec) |
N/A |
0.025 |
0.043 |
0.166 |
0.415 |
0.461 |
0.000 |
0.122 |
1.437 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.016 |
24.234 |
0.737 |
0.000 |
0.398 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.016 |
25.759 |
0.736 |
0.000 |
0.429 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 363 | 363 | 718 | 0 | 422 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.98 | 0.00 | 1.16 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.530 |
10.992 |
0.817 |
2.481 |
0.407 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 209 | 209 | 316 | 0 | 264 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.51 | 0.00 | 1.26 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.329 |
9.277 |
0.735 |
1.147 |
0.428 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 75 | 44 | 51 | 271 | 0 | 76 | 81 |
normalized size | 1 | 1.00 | 1.60 | 0.94 | 1.09 | 5.77 | 0.00 | 1.62 | 1.72 |
time (sec) |
N/A |
0.060 |
0.276 |
0.414 |
0.458 |
0.445 |
0.000 |
0.191 |
1.434 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.025 |
59.535 |
0.743 |
0.000 |
0.437 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.024 |
60.095 |
0.730 |
0.000 |
0.453 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 561 | 561 | 602 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.969 |
2.230 |
0.739 |
0.000 |
0.422 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 337 | 337 | 374 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.764 |
8.056 |
0.735 |
0.000 |
0.408 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 73 | 94 | 92 | 123 | 0 | 92 | 145 |
normalized size | 1 | 1.00 | 1.16 | 1.49 | 1.46 | 1.95 | 0.00 | 1.46 | 2.30 |
time (sec) |
N/A |
0.095 |
0.149 |
0.447 |
0.533 |
0.445 |
0.000 |
0.207 |
1.742 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.028 |
7.698 |
0.720 |
0.000 |
0.431 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.028 |
7.605 |
0.727 |
0.000 |
0.433 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1639 | 1639 | 1761 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.587 |
18.413 |
1.211 |
0.000 |
0.422 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 959 | 959 | 934 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.896 |
15.271 |
1.080 |
0.000 |
0.432 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 118 | 118 | 175 | 257 | 200 | 670 | 0 | 178 | 319 |
normalized size | 1 | 1.00 | 1.48 | 2.18 | 1.69 | 5.68 | 0.00 | 1.51 | 2.70 |
time (sec) |
N/A |
0.213 |
0.442 |
0.574 |
0.566 |
0.483 |
0.000 |
0.232 |
1.971 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.027 |
67.506 |
1.130 |
0.000 |
0.450 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.027 |
68.548 |
1.047 |
0.000 |
0.446 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.055 |
17.449 |
0.781 |
0.000 |
0.430 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 45 | 155 | 75 | 180 | 0 | 0 | 112 |
normalized size | 1 | 1.00 | 1.00 | 3.44 | 1.67 | 4.00 | 0.00 | 0.00 | 2.49 |
time (sec) |
N/A |
0.054 |
0.062 |
0.781 |
0.491 |
0.420 |
0.000 |
0.000 |
4.370 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 175 | 326 | 0 | 555 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.41 | 2.63 | 0.00 | 4.48 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.110 |
0.150 |
0.919 |
0.000 |
0.435 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 197 | 197 | 0 | 0 | 0 | 951 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 4.83 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.175 |
28.258 |
1.335 |
0.000 |
0.469 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 87 | 271 | 109 | 854 | 0 | 0 | 160 |
normalized size | 1 | 1.00 | 1.09 | 3.39 | 1.36 | 10.68 | 0.00 | 0.00 | 2.00 |
time (sec) |
N/A |
0.102 |
0.370 |
0.770 |
0.371 |
0.440 |
0.000 |
0.000 |
1.608 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 198 | 198 | 278 | 0 | 0 | 2678 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.40 | 0.00 | 0.00 | 13.53 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.211 |
5.489 |
0.655 |
0.000 |
0.504 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 344 | 344 | 0 | 0 | 0 | 4967 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 14.44 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.408 |
101.561 |
0.634 |
0.000 |
0.523 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 84 | 319 | 0 | 248 | 0 | 0 | 410 |
normalized size | 1 | 1.00 | 1.02 | 3.89 | 0.00 | 3.02 | 0.00 | 0.00 | 5.00 |
time (sec) |
N/A |
0.144 |
0.173 |
0.757 |
0.000 |
0.426 |
0.000 |
0.000 |
8.664 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 291 | 291 | 1181 | 577 | 0 | 1183 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 4.06 | 1.98 | 0.00 | 4.07 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.545 |
4.520 |
0.788 |
0.000 |
0.491 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 428 | 428 | 0 | 0 | 0 | 1850 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 4.32 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.844 |
6.993 |
1.207 |
0.000 |
0.488 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 167 | 490 | 0 | 1729 | 0 | 0 | 1449 |
normalized size | 1 | 1.00 | 1.12 | 3.29 | 0.00 | 11.60 | 0.00 | 0.00 | 9.72 |
time (sec) |
N/A |
0.290 |
0.590 |
0.878 |
0.000 |
0.465 |
0.000 |
0.000 |
19.088 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 681 | 681 | 3259 | 0 | 0 | 8453 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 4.79 | 0.00 | 0.00 | 12.41 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.147 |
33.990 |
1.228 |
0.000 |
0.616 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1218 | 1218 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.121 |
118.961 |
1.573 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
2.3 Detailed conclusion table specific for Rubi results
The following table is specific to Rubi. It gives additional statistics for each integral. the column
steps is the number of steps used by Rubi to obtain the antiderivative. The rules
column is the number of unique rules used. The integrand size column is the leaf
size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder
the integral was to solve. In this test, problem number [23] had the largest ratio of
[.6667]
|
|
|
|
|
|
|
| Table 2.1:Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
10 |
6 |
1.00 |
16 |
0.375 |
|
|
|
|
|
|
|
2 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
3 |
A |
8 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
4 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
5 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
6 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
7 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
8 |
A |
15 |
11 |
1.00 |
18 |
0.611 |
|
|
|
|
|
|
|
9 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
10 |
A |
10 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
11 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
12 |
A |
5 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
13 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
14 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
15 |
A |
5 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
16 |
A |
13 |
8 |
1.00 |
18 |
0.444 |
|
|
|
|
|
|
|
17 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
18 |
A |
11 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
19 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
20 |
A |
5 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
21 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
22 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
23 |
A |
31 |
12 |
1.00 |
18 |
0.667 |
|
|
|
|
|
|
|
24 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
25 |
A |
22 |
10 |
1.00 |
18 |
0.556 |
|
|
|
|
|
|
|
26 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
27 |
A |
7 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
28 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
29 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
30 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
31 |
A |
20 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
32 |
A |
16 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
33 |
A |
12 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
34 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
35 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
36 |
A |
30 |
10 |
1.00 |
20 |
0.500 |
|
|
|
|
|
|
|
37 |
A |
24 |
10 |
1.00 |
20 |
0.500 |
|
|
|
|
|
|
|
38 |
A |
18 |
10 |
1.00 |
18 |
0.556 |
|
|
|
|
|
|
|
39 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
40 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
41 |
A |
23 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
42 |
A |
19 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
43 |
A |
15 |
9 |
1.00 |
18 |
0.500 |
|
|
|
|
|
|
|
44 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
45 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
46 |
A |
61 |
11 |
1.00 |
20 |
0.550 |
|
|
|
|
|
|
|
47 |
A |
49 |
11 |
1.00 |
20 |
0.550 |
|
|
|
|
|
|
|
48 |
A |
37 |
11 |
1.00 |
18 |
0.611 |
|
|
|
|
|
|
|
49 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
50 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
51 |
A |
14 |
7 |
1.00 |
20 |
0.350 |
|
|
|
|
|
|
|
52 |
A |
10 |
6 |
1.00 |
20 |
0.300 |
|
|
|
|
|
|
|
53 |
A |
4 |
3 |
1.00 |
20 |
0.150 |
|
|
|
|
|
|
|
54 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
55 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
56 |
A |
21 |
10 |
1.00 |
22 |
0.454 |
|
|
|
|
|
|
|
57 |
A |
15 |
11 |
1.00 |
22 |
0.500 |
|
|
|
|
|
|
|
58 |
A |
5 |
5 |
1.00 |
22 |
0.227 |
|
|
|
|
|
|
|
59 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
60 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
61 |
A |
17 |
9 |
1.00 |
22 |
0.409 |
|
|
|
|
|
|
|
62 |
A |
13 |
8 |
1.00 |
22 |
0.364 |
|
|
|
|
|
|
|
63 |
A |
5 |
5 |
1.00 |
22 |
0.227 |
|
|
|
|
|
|
|
64 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
65 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
66 |
A |
43 |
11 |
1.00 |
22 |
0.500 |
|
|
|
|
|
|
|
67 |
A |
31 |
12 |
1.00 |
22 |
0.546 |
|
|
|
|
|
|
|
68 |
A |
7 |
7 |
1.00 |
22 |
0.318 |
|
|
|
|
|
|
|
69 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
70 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
71 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
72 |
A |
5 |
4 |
1.00 |
20 |
0.200 |
|
|
|
|
|
|
|
73 |
A |
9 |
6 |
1.00 |
22 |
0.273 |
|
|
|
|
|
|
|
74 |
A |
11 |
7 |
1.00 |
22 |
0.318 |
|
|
|
|
|
|
|
75 |
A |
6 |
6 |
1.00 |
22 |
0.273 |
|
|
|
|
|
|
|
76 |
A |
11 |
8 |
1.00 |
24 |
0.333 |
|
|
|
|
|
|
|
77 |
A |
16 |
12 |
1.00 |
24 |
0.500 |
|
|
|
|
|
|
|
78 |
A |
6 |
6 |
1.00 |
22 |
0.273 |
|
|
|
|
|
|
|
79 |
A |
12 |
8 |
1.00 |
24 |
0.333 |
|
|
|
|
|
|
|
80 |
A |
14 |
9 |
1.00 |
24 |
0.375 |
|
|
|
|
|
|
|
81 |
A |
8 |
8 |
1.00 |
22 |
0.364 |
|
|
|
|
|
|
|
82 |
A |
23 |
11 |
1.00 |
24 |
0.458 |
|
|
|
|
|
|
|
83 |
A |
32 |
13 |
1.00 |
24 |
0.542 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|