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, 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 }
B grade: { 35, 36, 37 }
C grade: { }
F grade: { }
2.1.2 Mathematica
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, 37, 38, 39, 40, 43, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60
}
B grade: { 35, 36, 41, 42, 44, 45, 46, 47, 54 }
C grade: { 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78 }
F grade: { }
2.1.3 Maple
A grade: { 23, 28, 29, 30 }
B grade: { 20, 21, 22, 24, 25, 26, 27, 31, 32, 33, 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
}
C grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 34, 35, 36, 37, 38, 39
}
F grade: { }
2.1.4 Maxima
A grade: { 1, 2, 3, 4, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 27, 28, 29, 30, 34, 36, 37, 38, 39
}
B grade: { 35 }
C grade: { }
F grade: { 5, 6, 7, 12, 13, 14, 24, 25, 26, 31, 32, 33, 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
}
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 27, 28, 29, 30, 34, 35, 36, 37, 38, 39,
41, 42, 43, 47, 48, 49, 54, 55, 56 }
B grade: { 5, 6, 7, 12, 13, 14, 40 }
C grade: { }
F grade: { 24, 25, 31, 32, 33, 44, 45, 46, 50, 51, 52, 53, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
71, 72, 73, 74, 75, 76, 77, 78 }
2.1.6 Sympy
A grade: { }
B grade: { }
C grade: { 10, 11, 15, 16, 17, 18, 19, 30, 34, 35, 36, 37, 38, 39 }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 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 }
2.1.7 Giac
A grade: { 8, 9, 10, 11, 15, 16, 34, 35, 36, 37, 47, 48, 49, 54, 55, 56 }
B grade: { 1, 2, 3, 4, 26, 33, 38, 39, 40, 41, 42, 43, 45, 46, 51, 52, 58 }
C grade: { }
F grade: { 5, 6, 7, 12, 13, 14, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 44, 50, 53, 57, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78 }
2.1.8 Mupad
A grade: { }
B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32,
33, 34, 35, 36, 37, 38, 39, 40, 49, 55, 56 }
C grade: { }
F grade: { 20, 21, 25, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66,
67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78 }
2.2 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2)
if the failure was due to an exception being raised, which could indicate a bug in the system. If
the failure was due to integral not being evaluated within the time limit, then it is given just an
F.
In this table,the column normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
A |
A |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 415 | 415 | 355 | 959 | 444 | 406 | 0 | 1948 | 3993 |
normalized size | 1 | 1.00 | 0.86 | 2.31 | 1.07 | 0.98 | 0.00 | 4.69 | 9.62 |
time (sec) |
N/A |
0.673 |
0.544 |
0.035 |
1.002 |
1.193 |
0.000 |
3.113 |
47.789 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
A |
A |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 286 | 286 | 244 | 652 | 307 | 279 | 0 | 1327 | 2920 |
normalized size | 1 | 1.00 | 0.85 | 2.28 | 1.07 | 0.98 | 0.00 | 4.64 | 10.21 |
time (sec) |
N/A |
0.563 |
0.349 |
0.018 |
1.006 |
0.995 |
0.000 |
2.581 |
36.028 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
A |
A |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 168 | 170 | 141 | 377 | 174 | 170 | 0 | 782 | 736 |
normalized size | 1 | 1.01 | 0.84 | 2.24 | 1.04 | 1.01 | 0.00 | 4.65 | 4.38 |
time (sec) |
N/A |
0.250 |
0.212 |
0.013 |
1.070 |
0.905 |
0.000 |
1.996 |
12.065 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
A |
A |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 71 | 185 | 93 | 95 | 0 | 336 | 361 |
normalized size | 1 | 1.00 | 0.75 | 1.95 | 0.98 | 1.00 | 0.00 | 3.54 | 3.80 |
time (sec) |
N/A |
0.073 |
0.064 |
0.012 |
0.981 |
0.954 |
0.000 |
1.536 |
7.209 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F(-2) |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 117 | 373 | 0 | 493 | 0 | 0 | 5803 |
normalized size | 1 | 1.00 | 0.96 | 3.06 | 0.00 | 4.04 | 0.00 | 0.00 | 47.57 |
time (sec) |
N/A |
0.311 |
0.150 |
0.049 |
0.000 |
15.087 |
0.000 |
0.000 |
25.801 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F(-2) |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 163 | 163 | 211 | 899 | 0 | 1025 | 0 | 0 | 10198 |
normalized size | 1 | 1.00 | 1.29 | 5.52 | 0.00 | 6.29 | 0.00 | 0.00 | 62.56 |
time (sec) |
N/A |
0.331 |
0.473 |
0.039 |
0.000 |
58.600 |
0.000 |
0.000 |
52.173 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F(-2) |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 248 | 248 | 273 | 1449 | 0 | 1580 | 0 | 0 | 9097 |
normalized size | 1 | 1.00 | 1.10 | 5.84 | 0.00 | 6.37 | 0.00 | 0.00 | 36.68 |
time (sec) |
N/A |
0.355 |
0.416 |
0.050 |
0.000 |
1.073 |
0.000 |
0.000 |
59.182 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
A |
A |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 340 | 340 | 241 | 643 | 355 | 286 | 0 | 427 | 2606 |
normalized size | 1 | 1.00 | 0.71 | 1.89 | 1.04 | 0.84 | 0.00 | 1.26 | 7.66 |
time (sec) |
N/A |
0.633 |
0.392 |
0.029 |
1.045 |
1.120 |
0.000 |
1.819 |
35.295 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
A |
A |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 228 | 228 | 160 | 423 | 231 | 192 | 0 | 277 | 1732 |
normalized size | 1 | 1.00 | 0.70 | 1.86 | 1.01 | 0.84 | 0.00 | 1.21 | 7.60 |
time (sec) |
N/A |
0.493 |
0.221 |
0.028 |
1.273 |
0.777 |
0.000 |
1.643 |
33.636 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
A |
A |
C |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 133 | 88 | 235 | 131 | 114 | 617 | 146 | 492 |
normalized size | 1 | 1.02 | 0.68 | 1.81 | 1.01 | 0.88 | 4.75 | 1.12 | 3.78 |
time (sec) |
N/A |
0.230 |
0.104 |
0.023 |
1.315 |
0.635 |
158.075 |
1.310 |
12.857 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
A |
A |
C |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 45 | 117 | 57 | 67 | 282 | 76 | 232 |
normalized size | 1 | 1.00 | 0.71 | 1.86 | 0.90 | 1.06 | 4.48 | 1.21 | 3.68 |
time (sec) |
N/A |
0.061 |
0.036 |
0.017 |
1.416 |
0.946 |
49.744 |
1.286 |
7.525 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F(-2) |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 117 | 373 | 0 | 493 | 0 | 0 | 5803 |
normalized size | 1 | 1.00 | 0.96 | 3.06 | 0.00 | 4.04 | 0.00 | 0.00 | 47.57 |
time (sec) |
N/A |
0.283 |
0.131 |
0.000 |
0.000 |
15.017 |
0.000 |
0.000 |
0.005 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F(-2) |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 163 | 163 | 211 | 899 | 0 | 1025 | 0 | 0 | 10198 |
normalized size | 1 | 1.00 | 1.29 | 5.52 | 0.00 | 6.29 | 0.00 | 0.00 | 62.56 |
time (sec) |
N/A |
0.295 |
0.431 |
0.000 |
0.000 |
59.963 |
0.000 |
0.000 |
0.008 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F(-2) |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 248 | 248 | 273 | 1449 | 0 | 1580 | 0 | 0 | 9097 |
normalized size | 1 | 1.00 | 1.10 | 5.84 | 0.00 | 6.37 | 0.00 | 0.00 | 36.68 |
time (sec) |
N/A |
0.329 |
0.384 |
0.000 |
0.000 |
0.866 |
0.000 |
0.000 |
0.007 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
A |
A |
C |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 57 | 139 | 87 | 78 | 313 | 101 | 244 |
normalized size | 1 | 1.00 | 0.72 | 1.76 | 1.10 | 0.99 | 3.96 | 1.28 | 3.09 |
time (sec) |
N/A |
0.139 |
0.068 |
0.000 |
1.270 |
0.805 |
82.521 |
1.305 |
7.606 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
A |
A |
C |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 45 | 117 | 57 | 67 | 282 | 76 | 232 |
normalized size | 1 | 1.00 | 0.71 | 1.86 | 0.90 | 1.06 | 4.48 | 1.21 | 3.68 |
time (sec) |
N/A |
0.061 |
0.034 |
0.000 |
1.281 |
0.917 |
49.685 |
1.324 |
7.411 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
A |
A |
C |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 48 | 96 | 57 | 81 | 245 | 0 | 122 |
normalized size | 1 | 1.00 | 1.00 | 2.00 | 1.19 | 1.69 | 5.10 | 0.00 | 2.54 |
time (sec) |
N/A |
0.183 |
0.055 |
0.001 |
1.275 |
0.847 |
55.715 |
0.000 |
4.331 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
A |
A |
C |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 48 | 97 | 57 | 84 | 221 | 0 | 114 |
normalized size | 1 | 1.00 | 1.00 | 2.02 | 1.19 | 1.75 | 4.60 | 0.00 | 2.38 |
time (sec) |
N/A |
0.176 |
0.061 |
0.000 |
1.325 |
0.952 |
50.054 |
0.000 |
4.266 |
|
|
|
|
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 56 | 108 | 98 | 65 | 218 | 0 | 312 |
normalized size | 1 | 1.00 | 0.79 | 1.52 | 1.38 | 0.92 | 3.07 | 0.00 | 4.39 |
time (sec) |
N/A |
0.184 |
0.049 |
0.000 |
1.285 |
0.975 |
80.629 |
0.000 |
6.304 |
|
|
|
|
|
|
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|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 591 | 584 | 427 | 1446 | 584 | 1001 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 0.72 | 2.45 | 0.99 | 1.69 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.517 |
1.463 |
0.043 |
1.461 |
1.043 |
0.000 |
0.000 |
0.000 |
|
|
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|
|
|
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|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 451 | 450 | 311 | 987 | 417 | 703 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.69 | 2.19 | 0.92 | 1.56 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.010 |
1.016 |
0.018 |
2.067 |
1.015 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 300 | 297 | 200 | 588 | 248 | 441 | 0 | 0 | 1765 |
normalized size | 1 | 0.99 | 0.67 | 1.96 | 0.83 | 1.47 | 0.00 | 0.00 | 5.88 |
time (sec) |
N/A |
0.446 |
0.682 |
0.014 |
2.255 |
0.973 |
0.000 |
0.000 |
30.577 |
|
|
|
|
|
|
|
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|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 221 | 142 | 287 | 140 | 265 | 0 | 0 | 876 |
normalized size | 1 | 1.00 | 0.64 | 1.30 | 0.63 | 1.20 | 0.00 | 0.00 | 3.96 |
time (sec) |
N/A |
0.147 |
0.408 |
0.013 |
2.028 |
0.895 |
0.000 |
0.000 |
16.517 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 278 | 278 | 225 | 503 | 0 | 0 | 0 | 0 | 9298 |
normalized size | 1 | 1.00 | 0.81 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 33.45 |
time (sec) |
N/A |
0.490 |
0.768 |
0.069 |
0.000 |
0.000 |
0.000 |
0.000 |
44.562 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 322 | 322 | 309 | 1200 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 3.73 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.579 |
0.852 |
0.044 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
|
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|
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|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 363 | 361 | 492 | 1848 | 0 | 1355 | 0 | 1658 | 9344 |
normalized size | 1 | 0.99 | 1.36 | 5.09 | 0.00 | 3.73 | 0.00 | 4.57 | 25.74 |
time (sec) |
N/A |
0.677 |
1.795 |
0.057 |
0.000 |
147.153 |
0.000 |
7.021 |
86.666 |
|
|
|
|
|
|
|
|
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|
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|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 501 | 496 | 727 | 965 | 471 | 700 | 0 | 0 | 4167 |
normalized size | 1 | 0.99 | 1.45 | 1.93 | 0.94 | 1.40 | 0.00 | 0.00 | 8.32 |
time (sec) |
N/A |
1.281 |
4.902 |
0.031 |
1.972 |
0.780 |
0.000 |
0.000 |
161.428 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 368 | 369 | 555 | 635 | 317 | 482 | 0 | 0 | 2799 |
normalized size | 1 | 1.00 | 1.51 | 1.73 | 0.86 | 1.31 | 0.00 | 0.00 | 7.61 |
time (sec) |
N/A |
0.875 |
2.684 |
0.029 |
2.021 |
1.040 |
0.000 |
0.000 |
81.648 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 246 | 249 | 390 | 365 | 189 | 302 | 0 | 0 | 1011 |
normalized size | 1 | 1.01 | 1.59 | 1.48 | 0.77 | 1.23 | 0.00 | 0.00 | 4.11 |
time (sec) |
N/A |
0.400 |
1.429 |
0.026 |
2.055 |
0.750 |
0.000 |
0.000 |
30.743 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
C |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 177 | 169 | 180 | 88 | 196 | 338 | 0 | 489 |
normalized size | 1 | 1.00 | 0.95 | 1.02 | 0.50 | 1.11 | 1.91 | 0.00 | 2.76 |
time (sec) |
N/A |
0.124 |
0.437 |
0.020 |
2.501 |
0.898 |
56.834 |
0.000 |
14.952 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 278 | 278 | 225 | 503 | 0 | 0 | 0 | 0 | 9298 |
normalized size | 1 | 1.00 | 0.81 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 33.45 |
time (sec) |
N/A |
0.464 |
0.711 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.008 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 322 | 322 | 309 | 1200 | 0 | 0 | 0 | 0 | 106511 |
normalized size | 1 | 1.00 | 0.96 | 3.73 | 0.00 | 0.00 | 0.00 | 0.00 | 330.78 |
time (sec) |
N/A |
0.530 |
0.794 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
19.397 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 363 | 361 | 492 | 1848 | 0 | 0 | 0 | 1658 | 9344 |
normalized size | 1 | 0.99 | 1.36 | 5.09 | 0.00 | 0.00 | 0.00 | 4.57 | 25.74 |
time (sec) |
N/A |
0.588 |
1.310 |
0.000 |
0.000 |
0.000 |
0.000 |
9.490 |
0.008 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
A |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 151 | 149 | 137 | 100 | 73 | 308 | 105 | 318 |
normalized size | 1 | 1.74 | 1.71 | 1.57 | 1.15 | 0.84 | 3.54 | 1.21 | 3.66 |
time (sec) |
N/A |
0.146 |
0.358 |
0.000 |
1.020 |
1.445 |
80.462 |
1.457 |
14.762 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
B |
C |
B |
A |
C |
A |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 52 | 135 | 126 | 120 | 90 | 61 | 277 | 80 | 312 |
normalized size | 1 | 2.60 | 2.42 | 2.31 | 1.73 | 1.17 | 5.33 | 1.54 | 6.00 |
time (sec) |
N/A |
0.071 |
0.222 |
0.000 |
1.107 |
1.277 |
48.757 |
1.386 |
14.587 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
B |
C |
A |
A |
C |
A |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 135 | 128 | 95 | 56 | 73 | 240 | 71 | 118 |
normalized size | 1 | 2.45 | 2.33 | 1.73 | 1.02 | 1.33 | 4.36 | 1.29 | 2.15 |
time (sec) |
N/A |
0.185 |
0.421 |
0.000 |
2.343 |
1.666 |
47.371 |
1.366 |
5.391 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
C |
A |
A |
C |
A |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 135 | 89 | 96 | 56 | 82 | 216 | 83 | 118 |
normalized size | 1 | 2.45 | 1.62 | 1.75 | 1.02 | 1.49 | 3.93 | 1.51 | 2.15 |
time (sec) |
N/A |
0.180 |
0.182 |
0.001 |
2.348 |
1.117 |
45.808 |
1.517 |
5.151 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 129 | 82 | 103 | 61 | 69 | 212 | 145 | 316 |
normalized size | 1 | 1.55 | 0.99 | 1.24 | 0.73 | 0.83 | 2.55 | 1.75 | 3.81 |
time (sec) |
N/A |
0.191 |
0.125 |
0.000 |
2.468 |
1.122 |
75.514 |
1.442 |
12.773 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
C |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 171 | 94 | 123 | 86 | 90 | 219 | 197 | 304 |
normalized size | 1 | 1.47 | 0.81 | 1.06 | 0.74 | 0.78 | 1.89 | 1.70 | 2.62 |
time (sec) |
N/A |
0.217 |
0.124 |
0.000 |
3.046 |
0.640 |
128.739 |
1.403 |
11.819 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 199 | 242 | 343 | 1095 | 0 | 1186 | 0 | 605 | 7235 |
normalized size | 1 | 1.22 | 1.72 | 5.50 | 0.00 | 5.96 | 0.00 | 3.04 | 36.36 |
time (sec) |
N/A |
0.328 |
0.761 |
0.053 |
0.000 |
1.062 |
0.000 |
3.245 |
66.847 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
A |
F(-1) |
B |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1348 | 1345 | 3599 | 6728 | 0 | 3096 | 0 | 4708 | -1 |
normalized size | 1 | 1.00 | 2.67 | 4.99 | 0.00 | 2.30 | 0.00 | 3.49 | -0.00 |
time (sec) |
N/A |
2.366 |
7.131 |
0.053 |
0.000 |
6.800 |
0.000 |
6.328 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
A |
F |
B |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 721 | 719 | 2722 | 3571 | 0 | 1620 | 0 | 2643 | -1 |
normalized size | 1 | 1.00 | 3.78 | 4.95 | 0.00 | 2.25 | 0.00 | 3.67 | -0.00 |
time (sec) |
N/A |
0.963 |
6.606 |
0.024 |
0.000 |
2.724 |
0.000 |
3.389 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
B |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 330 | 330 | 306 | 1431 | 0 | 840 | 0 | 1103 | -1 |
normalized size | 1 | 1.00 | 0.93 | 4.34 | 0.00 | 2.55 | 0.00 | 3.34 | -0.00 |
time (sec) |
N/A |
0.298 |
1.716 |
0.020 |
0.000 |
1.411 |
0.000 |
2.334 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 450 | 453 | 1936 | 4227 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.01 | 4.30 | 9.39 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.369 |
6.215 |
0.051 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
F(-1) |
F(-1) |
B |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 521 | 521 | 2532 | 5051 | 0 | 0 | 0 | 1585 | -1 |
normalized size | 1 | 1.00 | 4.86 | 9.69 | 0.00 | 0.00 | 0.00 | 3.04 | -0.00 |
time (sec) |
N/A |
1.696 |
6.375 |
0.048 |
0.000 |
0.000 |
0.000 |
13.122 |
0.000 |
|
|
|
|
|
|
|
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|
|
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|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
F(-1) |
F(-1) |
B |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 658 | 657 | 2150 | 12065 | 0 | 0 | 0 | 8347 | -1 |
normalized size | 1 | 1.00 | 3.27 | 18.34 | 0.00 | 0.00 | 0.00 | 12.69 | -0.00 |
time (sec) |
N/A |
2.680 |
6.443 |
0.072 |
0.000 |
0.000 |
0.000 |
39.569 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
A |
F(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1032 | 1032 | 3220 | 3958 | 0 | 2176 | 0 | 1505 | -1 |
normalized size | 1 | 1.00 | 3.12 | 3.84 | 0.00 | 2.11 | 0.00 | 1.46 | -0.00 |
time (sec) |
N/A |
1.788 |
6.702 |
0.046 |
0.000 |
15.238 |
0.000 |
2.759 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 540 | 540 | 478 | 2002 | 0 | 1114 | 0 | 736 | -1 |
normalized size | 1 | 1.00 | 0.89 | 3.71 | 0.00 | 2.06 | 0.00 | 1.36 | -0.00 |
time (sec) |
N/A |
0.713 |
3.539 |
0.030 |
0.000 |
3.381 |
0.000 |
1.819 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 246 | 246 | 225 | 763 | 0 | 576 | 0 | 315 | 1832 |
normalized size | 1 | 1.00 | 0.91 | 3.10 | 0.00 | 2.34 | 0.00 | 1.28 | 7.45 |
time (sec) |
N/A |
0.230 |
1.070 |
0.024 |
0.000 |
1.472 |
0.000 |
1.348 |
90.550 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 290 | 290 | 465 | 1822 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.60 | 6.28 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.672 |
3.449 |
0.039 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
B |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 364 | 364 | 417 | 3670 | 0 | 0 | 0 | 1388 | -1 |
normalized size | 1 | 1.00 | 1.15 | 10.08 | 0.00 | 0.00 | 0.00 | 3.81 | -0.00 |
time (sec) |
N/A |
1.097 |
2.396 |
0.049 |
0.000 |
0.000 |
0.000 |
10.820 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
B |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 484 | 484 | 523 | 9100 | 0 | 0 | 0 | 8004 | -1 |
normalized size | 1 | 1.00 | 1.08 | 18.80 | 0.00 | 0.00 | 0.00 | 16.54 | -0.00 |
time (sec) |
N/A |
1.563 |
5.675 |
0.095 |
0.000 |
0.000 |
0.000 |
134.872 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 685 | 685 | 729 | 15990 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.06 | 23.34 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.778 |
6.336 |
0.159 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
A |
F(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 718 | 715 | 2195 | 2528 | 0 | 1436 | 0 | 951 | -1 |
normalized size | 1 | 1.00 | 3.06 | 3.52 | 0.00 | 2.00 | 0.00 | 1.32 | -0.00 |
time (sec) |
N/A |
1.336 |
6.487 |
0.046 |
0.000 |
6.271 |
0.000 |
2.512 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 371 | 369 | 379 | 1199 | 0 | 720 | 0 | 447 | 2621 |
normalized size | 1 | 0.99 | 1.02 | 3.23 | 0.00 | 1.94 | 0.00 | 1.20 | 7.06 |
time (sec) |
N/A |
0.509 |
1.963 |
0.033 |
0.000 |
1.594 |
0.000 |
1.968 |
105.189 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 164 | 164 | 173 | 425 | 0 | 380 | 0 | 194 | 833 |
normalized size | 1 | 1.00 | 1.05 | 2.59 | 0.00 | 2.32 | 0.00 | 1.18 | 5.08 |
time (sec) |
N/A |
0.149 |
0.792 |
0.023 |
0.000 |
0.807 |
0.000 |
1.216 |
25.888 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 188 | 304 | 746 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.62 | 3.97 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.341 |
0.938 |
0.034 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
B |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 254 | 254 | 325 | 2973 | 0 | 0 | 0 | 1356 | -1 |
normalized size | 1 | 1.00 | 1.28 | 11.70 | 0.00 | 0.00 | 0.00 | 5.34 | -0.00 |
time (sec) |
N/A |
0.638 |
1.863 |
0.059 |
0.000 |
0.000 |
0.000 |
9.374 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 424 | 424 | 512 | 7119 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.21 | 16.79 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.967 |
2.090 |
0.130 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 826 | 826 | 794 | 18802 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 22.76 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.433 |
6.107 |
0.312 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1182 | 1154 | 11933 | 14778 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.98 | 10.10 | 12.50 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
4.166 |
17.301 |
0.094 |
0.000 |
0.952 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 774 | 769 | 917 | 10268 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 1.18 | 13.27 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.230 |
13.389 |
0.050 |
0.000 |
0.818 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 706 | 706 | 633 | 6265 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 8.87 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.845 |
8.125 |
0.060 |
0.000 |
0.872 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 687 | 687 | 938 | 16172 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.37 | 23.54 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.903 |
13.300 |
0.111 |
0.000 |
0.913 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 964 | 964 | 9529 | 34389 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 9.88 | 35.67 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.116 |
16.421 |
0.235 |
0.000 |
1.044 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1716 | 1716 | 15719 | 68345 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 9.16 | 39.83 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
7.045 |
18.556 |
0.398 |
0.000 |
0.944 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1235 | 1235 | 12483 | 15855 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 10.11 | 12.84 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
4.395 |
17.635 |
0.069 |
0.000 |
1.069 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 766 | 766 | 922 | 9543 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.20 | 12.46 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.061 |
12.907 |
0.045 |
0.000 |
0.846 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 527 | 527 | 562 | 6049 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.07 | 11.48 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.980 |
9.627 |
0.038 |
0.000 |
0.943 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 540 | 540 | 551 | 4732 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.02 | 8.76 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.111 |
6.735 |
0.049 |
0.000 |
0.666 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 597 | 596 | 724 | 13614 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.21 | 22.80 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.359 |
11.757 |
0.108 |
0.000 |
0.605 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1034 | 1034 | 9186 | 33007 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 8.88 | 31.92 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.160 |
16.094 |
0.315 |
0.000 |
0.611 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 838 | 831 | 1000 | 10546 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 1.19 | 12.58 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.167 |
13.872 |
0.068 |
0.000 |
0.579 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 528 | 524 | 615 | 6174 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 1.16 | 11.69 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.028 |
8.033 |
0.039 |
0.000 |
0.556 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 387 | 384 | 418 | 2497 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 1.08 | 6.45 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.505 |
6.072 |
0.035 |
0.000 |
0.534 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 422 | 422 | 477 | 3984 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.13 | 9.44 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.691 |
5.442 |
0.052 |
0.000 |
0.552 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 642 | 642 | 699 | 12988 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.09 | 20.23 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.517 |
10.908 |
0.140 |
0.000 |
0.585 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1116 | 1116 | 8844 | 34102 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 7.92 | 30.56 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.342 |
16.224 |
0.354 |
0.000 |
0.601 |
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 [36] had the largest ratio of
[.2500]
|
|
|
|
|
|
|
| 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 |
7 |
6 |
1.00 |
37 |
0.162 |
|
|
|
|
|
|
|
2 |
A |
6 |
6 |
1.00 |
37 |
0.162 |
|
|
|
|
|
|
|
3 |
A |
5 |
5 |
1.01 |
35 |
0.143 |
|
|
|
|
|
|
|
4 |
A |
5 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
5 |
A |
6 |
6 |
1.00 |
37 |
0.162 |
|
|
|
|
|
|
|
6 |
A |
6 |
6 |
1.00 |
37 |
0.162 |
|
|
|
|
|
|
|
7 |
A |
5 |
5 |
1.00 |
37 |
0.135 |
|
|
|
|
|
|
|
8 |
A |
6 |
5 |
1.00 |
37 |
0.135 |
|
|
|
|
|
|
|
9 |
A |
5 |
5 |
1.00 |
37 |
0.135 |
|
|
|
|
|
|
|
10 |
A |
4 |
4 |
1.02 |
35 |
0.114 |
|
|
|
|
|
|
|
11 |
A |
4 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
12 |
A |
6 |
6 |
1.00 |
37 |
0.162 |
|
|
|
|
|
|
|
13 |
A |
6 |
6 |
1.00 |
37 |
0.162 |
|
|
|
|
|
|
|
14 |
A |
5 |
5 |
1.00 |
37 |
0.135 |
|
|
|
|
|
|
|
15 |
A |
4 |
4 |
1.00 |
31 |
0.129 |
|
|
|
|
|
|
|
16 |
A |
4 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
17 |
A |
7 |
7 |
1.00 |
33 |
0.212 |
|
|
|
|
|
|
|
18 |
A |
7 |
7 |
1.00 |
33 |
0.212 |
|
|
|
|
|
|
|
19 |
A |
6 |
6 |
1.00 |
33 |
0.182 |
|
|
|
|
|
|
|
20 |
A |
8 |
7 |
0.99 |
40 |
0.175 |
|
|
|
|
|
|
|
21 |
A |
7 |
7 |
1.00 |
40 |
0.175 |
|
|
|
|
|
|
|
22 |
A |
6 |
6 |
0.99 |
38 |
0.158 |
|
|
|
|
|
|
|
23 |
A |
6 |
6 |
1.00 |
33 |
0.182 |
|
|
|
|
|
|
|
24 |
A |
7 |
7 |
1.00 |
40 |
0.175 |
|
|
|
|
|
|
|
25 |
A |
7 |
7 |
1.00 |
40 |
0.175 |
|
|
|
|
|
|
|
26 |
A |
5 |
5 |
0.99 |
40 |
0.125 |
|
|
|
|
|
|
|
27 |
A |
7 |
6 |
0.99 |
40 |
0.150 |
|
|
|
|
|
|
|
28 |
A |
6 |
6 |
1.00 |
40 |
0.150 |
|
|
|
|
|
|
|
29 |
A |
5 |
5 |
1.01 |
38 |
0.132 |
|
|
|
|
|
|
|
30 |
A |
5 |
5 |
1.00 |
33 |
0.152 |
|
|
|
|
|
|
|
31 |
A |
7 |
7 |
1.00 |
40 |
0.175 |
|
|
|
|
|
|
|
32 |
A |
7 |
7 |
1.00 |
40 |
0.175 |
|
|
|
|
|
|
|
33 |
A |
5 |
5 |
0.99 |
40 |
0.125 |
|
|
|
|
|
|
|
34 |
A |
5 |
5 |
1.74 |
30 |
0.167 |
|
|
|
|
|
|
|
35 |
B |
5 |
5 |
2.60 |
29 |
0.172 |
|
|
|
|
|
|
|
36 |
B |
8 |
8 |
2.45 |
32 |
0.250 |
|
|
|
|
|
|
|
37 |
B |
8 |
8 |
2.45 |
32 |
0.250 |
|
|
|
|
|
|
|
38 |
A |
6 |
6 |
1.55 |
32 |
0.188 |
|
|
|
|
|
|
|
39 |
A |
7 |
7 |
1.47 |
32 |
0.219 |
|
|
|
|
|
|
|
40 |
A |
5 |
5 |
1.22 |
32 |
0.156 |
|
|
|
|
|
|
|
41 |
A |
8 |
7 |
1.00 |
36 |
0.194 |
|
|
|
|
|
|
|
42 |
A |
7 |
6 |
1.00 |
34 |
0.176 |
|
|
|
|
|
|
|
43 |
A |
7 |
6 |
1.00 |
29 |
0.207 |
|
|
|
|
|
|
|
44 |
A |
9 |
8 |
1.01 |
36 |
0.222 |
|
|
|
|
|
|
|
45 |
A |
9 |
8 |
1.00 |
36 |
0.222 |
|
|
|
|
|
|
|
46 |
A |
9 |
9 |
1.00 |
36 |
0.250 |
|
|
|
|
|
|
|
47 |
A |
7 |
7 |
1.00 |
36 |
0.194 |
|
|
|
|
|
|
|
48 |
A |
6 |
6 |
1.00 |
34 |
0.176 |
|
|
|
|
|
|
|
49 |
A |
6 |
6 |
1.00 |
29 |
0.207 |
|
|
|
|
|
|
|
50 |
A |
8 |
8 |
1.00 |
36 |
0.222 |
|
|
|
|
|
|
|
51 |
A |
8 |
8 |
1.00 |
36 |
0.222 |
|
|
|
|
|
|
|
52 |
A |
8 |
8 |
1.00 |
36 |
0.222 |
|
|
|
|
|
|
|
53 |
A |
6 |
6 |
1.00 |
36 |
0.167 |
|
|
|
|
|
|
|
54 |
A |
6 |
6 |
1.00 |
36 |
0.167 |
|
|
|
|
|
|
|
55 |
A |
5 |
5 |
0.99 |
34 |
0.147 |
|
|
|
|
|
|
|
56 |
A |
5 |
5 |
1.00 |
29 |
0.172 |
|
|
|
|
|
|
|
57 |
A |
7 |
7 |
1.00 |
36 |
0.194 |
|
|
|
|
|
|
|
58 |
A |
7 |
7 |
1.00 |
36 |
0.194 |
|
|
|
|
|
|
|
59 |
A |
5 |
5 |
1.00 |
36 |
0.139 |
|
|
|
|
|
|
|
60 |
A |
6 |
5 |
1.00 |
36 |
0.139 |
|
|
|
|
|
|
|
61 |
A |
10 |
7 |
0.98 |
38 |
0.184 |
|
|
|
|
|
|
|
62 |
A |
9 |
7 |
0.99 |
38 |
0.184 |
|
|
|
|
|
|
|
63 |
A |
9 |
7 |
1.00 |
38 |
0.184 |
|
|
|
|
|
|
|
64 |
A |
9 |
8 |
1.00 |
38 |
0.210 |
|
|
|
|
|
|
|
65 |
A |
9 |
7 |
1.00 |
38 |
0.184 |
|
|
|
|
|
|
|
66 |
A |
10 |
8 |
1.00 |
38 |
0.210 |
|
|
|
|
|
|
|
67 |
A |
10 |
7 |
1.00 |
38 |
0.184 |
|
|
|
|
|
|
|
68 |
A |
9 |
7 |
1.00 |
38 |
0.184 |
|
|
|
|
|
|
|
69 |
A |
8 |
7 |
1.00 |
38 |
0.184 |
|
|
|
|
|
|
|
70 |
A |
8 |
7 |
1.00 |
38 |
0.184 |
|
|
|
|
|
|
|
71 |
A |
8 |
7 |
1.00 |
38 |
0.184 |
|
|
|
|
|
|
|
72 |
A |
9 |
8 |
1.00 |
38 |
0.210 |
|
|
|
|
|
|
|
73 |
A |
9 |
7 |
0.99 |
38 |
0.184 |
|
|
|
|
|
|
|
74 |
A |
8 |
7 |
0.99 |
38 |
0.184 |
|
|
|
|
|
|
|
75 |
A |
7 |
6 |
0.99 |
38 |
0.158 |
|
|
|
|
|
|
|
76 |
A |
7 |
6 |
1.00 |
38 |
0.158 |
|
|
|
|
|
|
|
77 |
A |
8 |
7 |
1.00 |
38 |
0.184 |
|
|
|
|
|
|
|
78 |
A |
9 |
7 |
1.00 |
38 |
0.184 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|