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, 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 }
B grade: { }
C grade: { }
F grade: { 17 }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31,
32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63
}
B grade: { 7, 13, 36, 44, 45, 49, 50, 61 }
C grade: { }
F grade: { }
2.1.3 Maple
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 21, 22, 23, 27, 28, 32, 33, 34, 35, 41, 42, 43, 46, 47,
48, 51, 52, 53, 57, 58, 62, 63 }
B grade: { 18, 19, 20, 24, 25, 26, 29, 30, 31, 39, 40, 44, 45, 49, 50, 54, 55, 56, 59, 60, 61 }
C grade: { }
F grade: { 16, 17, 36, 37, 38 }
2.1.4 Maxima
A grade: { 4, 5, 9, 10, 14, 15, 21, 22, 23, 27, 28, 32, 33, 34, 35, 41, 42, 43, 47, 48, 52, 53 }
B grade: { 1, 2, 3, 6, 7, 8, 11, 12, 13, 39, 40, 44, 45, 46, 49, 50, 51, 54, 55, 56, 59, 60, 61 }
C grade: { }
F grade: { 16, 17, 18, 19, 20, 24, 25, 26, 29, 30, 31, 36, 37, 38, 57, 58, 62, 63 }
2.1.5 FriCAS
A grade: { 4, 5, 8, 9, 10, 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, 42, 43, 46, 47, 48, 51, 52, 53, 57, 58, 62, 63 }
B grade: { 3, 7, 13, 41, 56, 61 }
C grade: { 1, 2, 6, 11, 12, 39, 40, 44, 45, 49, 50, 54, 55, 59, 60 }
F grade: { }
2.1.6 Sympy
A grade: { 4, 5, 8, 9, 10, 14, 15, 18, 19, 20, 24, 25, 26, 29, 30, 31, 34, 35, 42, 43, 47, 48, 52, 53, 57, 58, 62,
63 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 6, 7, 11, 12, 13, 16, 17, 21, 22, 23, 27, 28, 32, 33, 36, 37, 38, 39, 40, 41, 44, 45, 46, 49, 50,
51, 54, 55, 56, 59, 60, 61 }
2.1.7 Giac
A grade: { 4, 5, 9, 10, 14, 15, 18, 19, 20, 21, 24, 25, 26, 27, 29, 30, 31, 34, 35, 42, 43, 47, 48, 52, 53, 57, 62
}
B grade: { 8, 22, 23, 32 }
C grade: { }
F grade: { 1, 2, 3, 6, 7, 11, 12, 13, 16, 17, 28, 33, 36, 37, 38, 39, 40, 41, 44, 45, 46, 49, 50, 51, 54, 55, 56, 58,
59, 60, 61, 63 }
2.1.8 Mupad
A grade: { 4, 5, 9, 10, 14, 15, 34, 35, 42, 43, 47, 48, 52, 53, 57, 58, 62, 63 }
B grade: { 3, 8, 16, 17, 18, 19, 20, 24, 25, 26, 29, 30, 31, 41 }
C grade: { }
F grade: { 1, 2, 6, 7, 11, 12, 13, 21, 22, 23, 27, 28, 32, 33, 36, 37, 38, 39, 40, 44, 45, 46, 49, 50, 51, 54, 55,
56, 59, 60, 61 }
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 |
A |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 106 | 106 | 106 | 125 | 241 | 286 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.18 | 2.27 | 2.70 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.155 |
0.043 |
0.259 |
1.046 |
0.551 |
0.000 |
0.000 |
0.000 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 77 | 103 | 162 | 200 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.34 | 2.10 | 2.60 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.134 |
0.010 |
0.250 |
1.189 |
0.568 |
0.000 |
0.000 |
0.000 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 54 | 78 | 92 | 122 | 0 | 0 | 129 |
normalized size | 1 | 1.00 | 1.00 | 1.44 | 1.70 | 2.26 | 0.00 | 0.00 | 2.39 |
time (sec) |
N/A |
0.081 |
0.006 |
0.243 |
1.145 |
0.553 |
0.000 |
0.000 |
2.464 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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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 | 13 | 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 | -0.08 |
time (sec) |
N/A |
0.015 |
2.127 |
0.300 |
0.000 |
0.575 |
0.000 |
0.000 |
0.000 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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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 | 13 | 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 | -0.08 |
time (sec) |
N/A |
0.016 |
3.013 |
0.296 |
0.000 |
0.468 |
0.000 |
0.000 |
0.000 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 115 | 133 | 640 | 225 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.17 | 1.36 | 6.53 | 2.30 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.167 |
0.789 |
0.361 |
2.988 |
0.641 |
0.000 |
0.000 |
0.000 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
A |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 189 | 108 | 256 | 144 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.59 | 1.48 | 3.51 | 1.97 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.112 |
6.185 |
0.348 |
1.347 |
0.534 |
0.000 |
0.000 |
0.000 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 43 | 29 | 214 | 38 | 41 | 182 | 35 |
normalized size | 1 | 1.00 | 1.43 | 0.97 | 7.13 | 1.27 | 1.37 | 6.07 | 1.17 |
time (sec) |
N/A |
0.023 |
0.182 |
0.258 |
0.931 |
0.572 |
0.179 |
1.263 |
0.113 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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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 | 15 | 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 | -0.07 |
time (sec) |
N/A |
0.028 |
2.762 |
0.365 |
0.000 |
0.454 |
0.000 |
0.000 |
0.000 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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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 | 15 | 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 | -0.07 |
time (sec) |
N/A |
0.030 |
2.978 |
0.363 |
0.000 |
0.581 |
0.000 |
0.000 |
0.000 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 359 | 251 | 1203 | 342 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.75 | 1.22 | 5.87 | 1.67 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.292 |
6.672 |
0.319 |
2.581 |
0.570 |
0.000 |
0.000 |
0.000 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 172 | 180 | 740 | 240 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.34 | 1.41 | 5.78 | 1.88 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.180 |
3.143 |
0.289 |
1.180 |
0.536 |
0.000 |
0.000 |
0.000 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
A |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 210 | 122 | 388 | 146 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.33 | 1.36 | 4.31 | 1.62 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.103 |
6.149 |
0.217 |
3.041 |
0.495 |
0.000 |
0.000 |
0.000 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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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 | 15 | 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 | -0.07 |
time (sec) |
N/A |
0.027 |
5.121 |
1.208 |
0.000 |
0.464 |
0.000 |
0.000 |
0.000 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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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 | 15 | 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 | -0.07 |
time (sec) |
N/A |
0.028 |
3.422 |
1.361 |
0.000 |
0.573 |
0.000 |
0.000 |
0.000 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 18 | 18 | 0 | 0 | 16 | 0 | 0 | 50 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.89 | 0.00 | 0.00 | 2.78 |
time (sec) |
N/A |
0.123 |
0.965 |
0.873 |
0.000 |
0.610 |
0.000 |
0.000 |
3.123 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
F |
A |
F |
F |
A |
F |
F |
B |
verified |
N/A |
N/A |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 0 | 17 | 0 | 0 | 15 | 0 | 0 | 45 |
normalized size | 1 | 0.00 | 1.00 | 0.00 | 0.00 | 0.88 | 0.00 | 0.00 | 2.65 |
time (sec) |
N/A |
0.035 |
0.603 |
1.057 |
0.000 |
0.861 |
0.000 |
0.000 |
4.173 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 278 | 1061 | 0 | 162 | 262 | 193 | 423 |
normalized size | 1 | 1.00 | 1.47 | 5.61 | 0.00 | 0.86 | 1.39 | 1.02 | 2.24 |
time (sec) |
N/A |
0.199 |
0.705 |
0.646 |
0.000 |
0.506 |
0.384 |
0.671 |
3.559 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 178 | 509 | 0 | 104 | 168 | 123 | 241 |
normalized size | 1 | 1.00 | 1.30 | 3.72 | 0.00 | 0.76 | 1.23 | 0.90 | 1.76 |
time (sec) |
N/A |
0.123 |
0.403 |
0.618 |
0.000 |
0.563 |
0.308 |
0.793 |
3.078 |
|
|
|
|
|
|
|
|
|
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|
|
|
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|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 96 | 187 | 0 | 55 | 97 | 65 | 105 |
normalized size | 1 | 1.00 | 1.14 | 2.23 | 0.00 | 0.65 | 1.15 | 0.77 | 1.25 |
time (sec) |
N/A |
0.054 |
0.437 |
0.555 |
0.000 |
0.521 |
0.240 |
0.703 |
2.815 |
|
|
|
|
|
|
|
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|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 166 | 204 | 110 | 49 | 0 | 142 | -1 |
normalized size | 1 | 1.00 | 1.03 | 1.27 | 0.68 | 0.30 | 0.00 | 0.88 | -0.01 |
time (sec) |
N/A |
0.277 |
0.355 |
0.513 |
0.795 |
0.575 |
0.000 |
0.776 |
0.000 |
|
|
|
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|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 168 | 168 | 224 | 285 | 117 | 84 | 0 | 1099 | -1 |
normalized size | 1 | 1.00 | 1.33 | 1.70 | 0.70 | 0.50 | 0.00 | 6.54 | -0.01 |
time (sec) |
N/A |
0.240 |
0.853 |
0.474 |
0.858 |
0.581 |
0.000 |
74.992 |
0.000 |
|
|
|
|
|
|
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|
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|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 227 | 227 | 285 | 358 | 156 | 128 | 0 | 542 | -1 |
normalized size | 1 | 1.00 | 1.26 | 1.58 | 0.69 | 0.56 | 0.00 | 2.39 | -0.00 |
time (sec) |
N/A |
0.322 |
1.201 |
0.491 |
1.051 |
0.745 |
0.000 |
0.876 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 270 | 270 | 473 | 2070 | 0 | 262 | 666 | 383 | 289 |
normalized size | 1 | 1.00 | 1.75 | 7.67 | 0.00 | 0.97 | 2.47 | 1.42 | 1.07 |
time (sec) |
N/A |
0.293 |
1.380 |
0.869 |
0.000 |
0.536 |
0.577 |
0.948 |
3.231 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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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) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 202 | 202 | 282 | 968 | 0 | 160 | 420 | 227 | 183 |
normalized size | 1 | 1.00 | 1.40 | 4.79 | 0.00 | 0.79 | 2.08 | 1.12 | 0.91 |
time (sec) |
N/A |
0.208 |
0.888 |
0.751 |
0.000 |
0.638 |
0.447 |
1.054 |
2.987 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 130 | 350 | 0 | 78 | 228 | 107 | 103 |
normalized size | 1 | 1.00 | 0.86 | 2.32 | 0.00 | 0.52 | 1.51 | 0.71 | 0.68 |
time (sec) |
N/A |
0.142 |
0.594 |
0.679 |
0.000 |
0.610 |
0.341 |
2.032 |
2.768 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 305 | 305 | 211 | 382 | 190 | 80 | 0 | 420 | -1 |
normalized size | 1 | 1.00 | 0.69 | 1.25 | 0.62 | 0.26 | 0.00 | 1.38 | -0.00 |
time (sec) |
N/A |
0.772 |
0.523 |
0.572 |
0.839 |
0.557 |
0.000 |
1.136 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 436 | 436 | 467 | 536 | 210 | 140 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.07 | 1.23 | 0.48 | 0.32 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.739 |
1.610 |
0.568 |
1.077 |
0.438 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 396 | 396 | 667 | 3404 | 0 | 362 | 949 | 573 | 411 |
normalized size | 1 | 1.00 | 1.68 | 8.60 | 0.00 | 0.91 | 2.40 | 1.45 | 1.04 |
time (sec) |
N/A |
0.404 |
2.739 |
0.930 |
0.000 |
0.611 |
0.916 |
2.326 |
3.851 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 294 | 294 | 405 | 1525 | 0 | 216 | 592 | 331 | 263 |
normalized size | 1 | 1.00 | 1.38 | 5.19 | 0.00 | 0.73 | 2.01 | 1.13 | 0.89 |
time (sec) |
N/A |
0.265 |
1.805 |
0.892 |
0.000 |
0.524 |
0.702 |
2.564 |
3.375 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 209 | 209 | 205 | 527 | 0 | 103 | 320 | 151 | 146 |
normalized size | 1 | 1.00 | 0.98 | 2.52 | 0.00 | 0.49 | 1.53 | 0.72 | 0.70 |
time (sec) |
N/A |
0.264 |
0.912 |
0.849 |
0.000 |
0.704 |
0.516 |
2.129 |
3.030 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 449 | 449 | 336 | 560 | 270 | 111 | 0 | 846 | -1 |
normalized size | 1 | 1.00 | 0.75 | 1.25 | 0.60 | 0.25 | 0.00 | 1.88 | -0.00 |
time (sec) |
N/A |
1.783 |
0.802 |
0.615 |
3.022 |
0.439 |
0.000 |
1.464 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 712 | 712 | 833 | 787 | 294 | 192 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.17 | 1.11 | 0.41 | 0.27 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.732 |
3.157 |
0.630 |
4.084 |
0.447 |
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 | 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 |
0.050 |
39.441 |
0.404 |
0.000 |
0.523 |
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 | 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 |
0.028 |
15.611 |
0.560 |
0.000 |
0.574 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 205 | 0 | 0 | 84 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.09 | 0.00 | 0.00 | 0.86 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.123 |
1.367 |
0.831 |
0.000 |
0.458 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 192 | 0 | 0 | 140 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.12 | 0.00 | 0.00 | 0.82 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.184 |
48.069 |
0.914 |
0.000 |
0.603 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 251 | 251 | 269 | 0 | 0 | 192 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.07 | 0.00 | 0.00 | 0.76 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.242 |
68.698 |
1.030 |
0.000 |
0.619 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 152 | 152 | 255 | 481 | 665 | 498 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.68 | 3.16 | 4.38 | 3.28 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.251 |
0.358 |
0.519 |
3.412 |
0.699 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 191 | 295 | 369 | 315 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.66 | 2.57 | 3.21 | 2.74 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.208 |
0.132 |
0.434 |
1.233 |
0.559 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 87 | 143 | 130 | 160 | 0 | 0 | 161 |
normalized size | 1 | 1.00 | 1.04 | 1.70 | 1.55 | 1.90 | 0.00 | 0.00 | 1.92 |
time (sec) |
N/A |
0.119 |
0.015 |
0.393 |
0.748 |
0.551 |
0.000 |
0.000 |
3.220 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
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 |
2.134 |
0.757 |
0.000 |
0.464 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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|
|
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|
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|
|
Problem 43 |
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 |
0.027 |
6.138 |
0.779 |
0.000 |
0.527 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 300 | 300 | 1326 | 919 | 2521 | 757 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 4.42 | 3.06 | 8.40 | 2.52 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.522 |
8.039 |
0.818 |
2.787 |
0.655 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
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|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 229 | 229 | 649 | 542 | 1269 | 448 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.83 | 2.37 | 5.54 | 1.96 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.412 |
7.185 |
0.678 |
1.287 |
0.505 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
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Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 200 | 238 | 529 | 219 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.47 | 1.75 | 3.89 | 1.61 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.190 |
2.321 |
0.638 |
0.817 |
0.535 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
Problem 47 |
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 |
0.053 |
20.272 |
2.697 |
0.000 |
0.624 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
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|
Problem 48 |
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 |
0.051 |
15.691 |
3.307 |
0.000 |
0.479 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 612 | 612 | 2572 | 1882 | 6819 | 1175 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 4.20 | 3.08 | 11.14 | 1.92 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.982 |
8.476 |
1.007 |
23.828 |
0.541 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 436 | 436 | 1846 | 1090 | 3396 | 686 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 4.23 | 2.50 | 7.79 | 1.57 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.720 |
7.848 |
0.842 |
3.978 |
0.535 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 277 | 277 | 277 | 493 | 1327 | 327 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.78 | 4.79 | 1.18 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.338 |
3.686 |
0.769 |
1.677 |
0.631 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
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|
|
|
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|
Problem 52 |
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 |
0.053 |
14.572 |
4.502 |
0.000 |
0.948 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
Problem 53 |
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 |
0.050 |
20.110 |
6.923 |
0.000 |
0.516 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
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|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 243 | 243 | 297 | 1450 | 977 | 1183 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.22 | 5.97 | 4.02 | 4.87 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.334 |
2.315 |
1.184 |
1.607 |
0.540 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 181 | 181 | 236 | 922 | 712 | 836 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.30 | 5.09 | 3.93 | 4.62 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.272 |
1.861 |
1.099 |
1.218 |
1.222 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 177 | 462 | 399 | 533 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.42 | 3.70 | 3.19 | 4.26 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.159 |
1.917 |
0.964 |
1.761 |
0.463 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
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 | 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 |
0.062 |
1.971 |
1.720 |
0.000 |
0.643 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
F(-1) |
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 |
0.058 |
4.976 |
3.202 |
0.000 |
0.491 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 848 | 848 | 1673 | 3488 | 4668 | 2535 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.97 | 4.11 | 5.50 | 2.99 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.004 |
10.850 |
1.346 |
8.203 |
0.688 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 654 | 654 | 714 | 2160 | 2558 | 1578 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.09 | 3.30 | 3.91 | 2.41 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.537 |
9.597 |
1.228 |
4.428 |
0.599 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 214 | 745 | 999 | 1164 | 849 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.48 | 4.67 | 5.44 | 3.97 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.275 |
7.075 |
1.146 |
1.494 |
0.588 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
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 | 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 |
0.061 |
19.524 |
10.733 |
0.000 |
0.447 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
F(-1) |
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 |
0.059 |
19.415 |
18.371 |
0.000 |
0.457 |
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 [11] had the largest ratio of
[.8333]
|
|
|
|
|
|
|
| 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 |
6 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
2 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
3 |
A |
4 |
4 |
1.00 |
8 |
0.500 |
|
|
|
|
|
|
|
4 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
5 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
6 |
A |
7 |
7 |
1.00 |
12 |
0.583 |
|
|
|
|
|
|
|
7 |
A |
6 |
6 |
1.00 |
12 |
0.500 |
|
|
|
|
|
|
|
8 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
9 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
10 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
11 |
A |
13 |
10 |
1.00 |
12 |
0.833 |
|
|
|
|
|
|
|
12 |
A |
9 |
8 |
1.00 |
12 |
0.667 |
|
|
|
|
|
|
|
13 |
A |
7 |
7 |
1.00 |
10 |
0.700 |
|
|
|
|
|
|
|
14 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
15 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
16 |
A |
2 |
1 |
1.00 |
45 |
0.022 |
|
|
|
|
|
|
|
17 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
18 |
A |
5 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
19 |
A |
4 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
20 |
A |
3 |
3 |
1.00 |
21 |
0.143 |
|
|
|
|
|
|
|
21 |
A |
7 |
4 |
1.00 |
23 |
0.174 |
|
|
|
|
|
|
|
22 |
A |
7 |
4 |
1.00 |
23 |
0.174 |
|
|
|
|
|
|
|
23 |
A |
8 |
5 |
1.00 |
23 |
0.217 |
|
|
|
|
|
|
|
24 |
A |
10 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
25 |
A |
8 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
26 |
A |
7 |
3 |
1.00 |
21 |
0.143 |
|
|
|
|
|
|
|
27 |
A |
21 |
5 |
1.00 |
23 |
0.217 |
|
|
|
|
|
|
|
28 |
A |
24 |
7 |
1.00 |
23 |
0.304 |
|
|
|
|
|
|
|
29 |
A |
14 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
30 |
A |
11 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
31 |
A |
11 |
3 |
1.00 |
21 |
0.143 |
|
|
|
|
|
|
|
32 |
A |
53 |
7 |
1.00 |
23 |
0.304 |
|
|
|
|
|
|
|
33 |
A |
60 |
9 |
1.00 |
23 |
0.391 |
|
|
|
|
|
|
|
34 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
35 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
36 |
A |
2 |
2 |
1.00 |
23 |
0.087 |
|
|
|
|
|
|
|
37 |
A |
4 |
2 |
1.00 |
23 |
0.087 |
|
|
|
|
|
|
|
38 |
A |
5 |
2 |
1.00 |
23 |
0.087 |
|
|
|
|
|
|
|
39 |
A |
8 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
40 |
A |
7 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
41 |
A |
6 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
42 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
43 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
44 |
A |
15 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
45 |
A |
13 |
10 |
1.00 |
20 |
0.500 |
|
|
|
|
|
|
|
46 |
A |
9 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
47 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
48 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
49 |
A |
28 |
11 |
1.00 |
20 |
0.550 |
|
|
|
|
|
|
|
50 |
A |
22 |
11 |
1.00 |
20 |
0.550 |
|
|
|
|
|
|
|
51 |
A |
16 |
9 |
1.00 |
18 |
0.500 |
|
|
|
|
|
|
|
52 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
53 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
54 |
A |
6 |
6 |
1.00 |
20 |
0.300 |
|
|
|
|
|
|
|
55 |
A |
5 |
5 |
1.00 |
20 |
0.250 |
|
|
|
|
|
|
|
56 |
A |
4 |
4 |
1.00 |
18 |
0.222 |
|
|
|
|
|
|
|
57 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
58 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
59 |
A |
21 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
60 |
A |
18 |
10 |
1.00 |
20 |
0.500 |
|
|
|
|
|
|
|
61 |
A |
5 |
5 |
1.00 |
18 |
0.278 |
|
|
|
|
|
|
|
62 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
63 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|