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, 84, 85
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 9, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 61, 63, 75, 76, 77, 78, 79, 80, 82,
83, 84, 85 }
B grade: { }
C grade: { 6, 7, 8, 10, 11, 12, 56, 57, 58, 59, 60, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 81
}
F grade: { 35 }
2.1.3 Maple
A grade: { 2, 9, 10, 11, 19, 43, 44, 45, 47, 48, 49, 50, 51, 54, 55, 76, 77, 78, 79, 80, 82, 83, 84, 85
}
B grade: { 1, 4, 5, 6, 7, 8, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
35, 36, 37, 38, 39, 40, 41, 42, 46, 52, 53, 58, 59, 63, 74 }
C grade: { 3, 56, 57, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 81 }
F grade: { }
2.1.4 Maxima
A grade: { 1, 3, 37, 44, 49, 54, 76 }
B grade: { 2, 4, 5, 13, 14, 15, 16, 17, 18, 21, 23, 25, 27, 29, 31, 33, 34, 35, 36, 38, 39, 40, 63
}
C grade: { 43, 48, 53, 80 }
F grade: { 6, 7, 8, 9, 10, 11, 12, 19, 20, 22, 24, 26, 28, 30, 32, 41, 42, 45, 46, 47, 50, 51, 52, 55, 56,
57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 81, 82, 83, 84, 85
}
2.1.5 FriCAS
A grade: { 1, 2, 3, 15, 25, 43, 44, 48, 49, 53, 54, 80, 84, 85 }
B grade: { 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31,
32, 33, 34, 35, 36, 37, 38, 39, 40, 58, 59, 60, 61, 62, 63, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 83
}
C grade: { 81 }
F grade: { 41, 42, 45, 46, 47, 50, 51, 52, 55, 56, 57, 64, 65, 66, 67, 68, 69, 82 }
2.1.6 Sympy
A grade: { 2, 3, 9, 16, 19, 27 }
B grade: { 1, 35, 36, 37, 38, 39, 40, 58, 59, 63, 74 }
C grade: { }
F grade: { 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 41,
42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73,
75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85 }
2.1.7 Giac
A grade: { 1, 2, 3, 4, 5, 15, 16, 19, 25, 27, 29, 31, 33, 37, 39, 40, 65, 66, 68, 69, 72, 74, 76, 81
}
B grade: { 13, 14, 17, 18, 21, 23, 34, 35, 36, 38, 44, 49, 54, 58, 59, 63, 71 }
C grade: { 43, 48, 53, 62, 80 }
F grade: { 6, 7, 8, 9, 10, 11, 12, 20, 22, 24, 26, 28, 30, 32, 41, 42, 45, 46, 47, 50, 51, 52, 55, 56, 57, 60, 61,
64, 67, 70, 73, 75, 77, 78, 79, 82, 83, 84, 85 }
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, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 35, 36, 37, 38, 39, 40, 43, 44, 56, 57, 58, 59, 60, 61, 62, 63, 65, 68, 71, 74, 75, 76, 81
}
C grade: { }
F grade: { 33, 34, 41, 42, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 64, 66, 67, 69, 70, 72, 73, 77, 78, 79, 80,
82, 83, 84, 85 }
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 |
B |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 19 | 78 | 25 | 14 | 153 | 26 | 25 |
normalized size | 1 | 1.00 | 0.95 | 3.90 | 1.25 | 0.70 | 7.65 | 1.30 | 1.25 |
time (sec) |
N/A |
0.046 |
0.004 |
0.086 |
0.313 |
0.506 |
2.263 |
0.133 |
0.944 |
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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 |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 7 | 7 | 7 | 8 | 17 | 7 | 10 | 12 | 7 |
normalized size | 1 | 1.00 | 1.00 | 1.14 | 2.43 | 1.00 | 1.43 | 1.71 | 1.00 |
time (sec) |
N/A |
0.044 |
0.003 |
0.061 |
0.312 |
0.497 |
1.301 |
0.114 |
0.905 |
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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 |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 6 | 6 | 6 | 11 | 6 | 6 | 3 | 6 | 6 |
normalized size | 1 | 1.00 | 1.00 | 1.83 | 1.00 | 1.00 | 0.50 | 1.00 | 1.00 |
time (sec) |
N/A |
0.039 |
0.000 |
0.077 |
0.322 |
0.450 |
0.760 |
0.135 |
0.027 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 22 | 37 | 61 | 100 | 0 | 21 | 21 |
normalized size | 1 | 1.00 | 1.16 | 1.95 | 3.21 | 5.26 | 0.00 | 1.11 | 1.11 |
time (sec) |
N/A |
0.048 |
0.004 |
0.107 |
0.311 |
0.428 |
0.000 |
0.132 |
0.908 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 32 | 53 | 135 | 216 | 0 | 27 | 27 |
normalized size | 1 | 1.00 | 1.10 | 1.83 | 4.66 | 7.45 | 0.00 | 0.93 | 0.93 |
time (sec) |
N/A |
0.051 |
0.004 |
0.107 |
0.318 |
0.389 |
0.000 |
0.135 |
0.919 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 148 | 395 | 0 | 2346 | 0 | 0 | 805 |
normalized size | 1 | 1.00 | 1.90 | 5.06 | 0.00 | 30.08 | 0.00 | 0.00 | 10.32 |
time (sec) |
N/A |
0.105 |
0.246 |
0.089 |
0.000 |
0.453 |
0.000 |
0.000 |
1.546 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 120 | 214 | 0 | 1064 | 0 | 0 | 548 |
normalized size | 1 | 1.00 | 2.22 | 3.96 | 0.00 | 19.70 | 0.00 | 0.00 | 10.15 |
time (sec) |
N/A |
0.087 |
0.187 |
0.085 |
0.000 |
0.544 |
0.000 |
0.000 |
1.304 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 83 | 97 | 0 | 416 | 0 | 0 | 257 |
normalized size | 1 | 1.00 | 2.31 | 2.69 | 0.00 | 11.56 | 0.00 | 0.00 | 7.14 |
time (sec) |
N/A |
0.065 |
0.188 |
0.085 |
0.000 |
0.488 |
0.000 |
0.000 |
1.366 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
F |
B |
A |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 17 | 0 | 300 | 87 | 0 | 16 |
normalized size | 1 | 1.00 | 1.00 | 0.68 | 0.00 | 12.00 | 3.48 | 0.00 | 0.64 |
time (sec) |
N/A |
0.036 |
0.022 |
0.053 |
0.000 |
0.516 |
1.062 |
0.000 |
0.971 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
A |
F |
B |
F |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 99 | 52 | 0 | 349 | 0 | 0 | 462 |
normalized size | 1 | 1.00 | 2.36 | 1.24 | 0.00 | 8.31 | 0.00 | 0.00 | 11.00 |
time (sec) |
N/A |
0.062 |
0.144 |
0.096 |
0.000 |
0.637 |
0.000 |
0.000 |
1.389 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
A |
F |
B |
F |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 61 | 61 | 154 | 94 | 0 | 1332 | 0 | 0 | 2225 |
normalized size | 1 | 1.00 | 2.52 | 1.54 | 0.00 | 21.84 | 0.00 | 0.00 | 36.48 |
time (sec) |
N/A |
0.104 |
0.291 |
0.110 |
0.000 |
0.489 |
0.000 |
0.000 |
6.894 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 219 | 184 | 0 | 5326 | 0 | 0 | 5056 |
normalized size | 1 | 1.00 | 2.33 | 1.96 | 0.00 | 56.66 | 0.00 | 0.00 | 53.79 |
time (sec) |
N/A |
0.172 |
0.607 |
0.118 |
0.000 |
0.599 |
0.000 |
0.000 |
14.741 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 76 | 575 | 651 | 1308 | 0 | 166 | 248 |
normalized size | 1 | 1.00 | 0.86 | 6.53 | 7.40 | 14.86 | 0.00 | 1.89 | 2.82 |
time (sec) |
N/A |
0.168 |
0.173 |
0.132 |
0.455 |
0.514 |
0.000 |
0.128 |
1.720 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 52 | 351 | 348 | 568 | 0 | 103 | 146 |
normalized size | 1 | 1.00 | 0.88 | 5.95 | 5.90 | 9.63 | 0.00 | 1.75 | 2.47 |
time (sec) |
N/A |
0.116 |
0.099 |
0.114 |
0.427 |
0.484 |
0.000 |
0.141 |
1.266 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
A |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 36 | 183 | 120 | 300 | 0 | 52 | 79 |
normalized size | 1 | 1.00 | 0.92 | 4.69 | 3.08 | 7.69 | 0.00 | 1.33 | 2.03 |
time (sec) |
N/A |
0.067 |
0.060 |
0.104 |
0.423 |
0.551 |
0.000 |
0.131 |
0.219 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 78 | 53 | 293 | 12026 | 39 | 267 |
normalized size | 1 | 1.00 | 1.00 | 2.69 | 1.83 | 10.10 | 414.69 | 1.34 | 9.21 |
time (sec) |
N/A |
0.022 |
0.067 |
0.093 |
0.422 |
0.459 |
46.720 |
0.133 |
0.346 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 59 | 177 | 161 | 1875 | 0 | 107 | 245 |
normalized size | 1 | 1.00 | 1.00 | 3.00 | 2.73 | 31.78 | 0.00 | 1.81 | 4.15 |
time (sec) |
N/A |
0.086 |
0.219 |
0.143 |
0.427 |
0.544 |
0.000 |
0.394 |
1.448 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 92 | 307 | 307 | 4977 | 0 | 189 | 333 |
normalized size | 1 | 1.00 | 1.03 | 3.45 | 3.45 | 55.92 | 0.00 | 2.12 | 3.74 |
time (sec) |
N/A |
0.108 |
0.374 |
0.148 |
0.479 |
0.529 |
0.000 |
0.589 |
1.546 |
|
|
|
|
|
|
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|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 77 | 80 | 0 | 305 | 85 | 80 | 205 |
normalized size | 1 | 1.00 | 0.79 | 0.82 | 0.00 | 3.11 | 0.87 | 0.82 | 2.09 |
time (sec) |
N/A |
0.117 |
0.092 |
0.051 |
0.000 |
0.520 |
1.541 |
0.147 |
3.512 |
|
|
|
|
|
|
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|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 86 | 317 | 0 | 2508 | 0 | 0 | 293 |
normalized size | 1 | 1.00 | 1.10 | 4.06 | 0.00 | 32.15 | 0.00 | 0.00 | 3.76 |
time (sec) |
N/A |
0.090 |
0.290 |
0.124 |
0.000 |
0.519 |
0.000 |
0.000 |
1.394 |
|
|
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Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 76 | 326 | 651 | 1245 | 0 | 150 | 178 |
normalized size | 1 | 1.00 | 0.86 | 3.70 | 7.40 | 14.15 | 0.00 | 1.70 | 2.02 |
time (sec) |
N/A |
0.210 |
0.224 |
0.109 |
0.501 |
0.482 |
0.000 |
0.135 |
1.330 |
|
|
|
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Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 61 | 176 | 0 | 1184 | 0 | 0 | 243 |
normalized size | 1 | 1.00 | 1.09 | 3.14 | 0.00 | 21.14 | 0.00 | 0.00 | 4.34 |
time (sec) |
N/A |
0.073 |
0.171 |
0.101 |
0.000 |
0.526 |
0.000 |
0.000 |
1.255 |
|
|
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Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 52 | 188 | 347 | 573 | 0 | 95 | 142 |
normalized size | 1 | 1.00 | 0.88 | 3.19 | 5.88 | 9.71 | 0.00 | 1.61 | 2.41 |
time (sec) |
N/A |
0.106 |
0.133 |
0.098 |
0.561 |
0.584 |
0.000 |
0.126 |
1.168 |
|
|
|
|
|
|
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|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 38 | 38 | 96 | 0 | 498 | 0 | 0 | 204 |
normalized size | 1 | 1.00 | 1.00 | 2.53 | 0.00 | 13.11 | 0.00 | 0.00 | 5.37 |
time (sec) |
N/A |
0.059 |
0.031 |
0.091 |
0.000 |
0.453 |
0.000 |
0.000 |
1.162 |
|
|
|
|
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|
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|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 36 | 110 | 120 | 317 | 0 | 50 | 376 |
normalized size | 1 | 1.00 | 0.92 | 2.82 | 3.08 | 8.13 | 0.00 | 1.28 | 9.64 |
time (sec) |
N/A |
0.070 |
0.084 |
0.096 |
0.514 |
0.491 |
0.000 |
0.126 |
1.383 |
|
|
|
|
|
|
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|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 66 | 0 | 337 | 0 | 0 | 87 |
normalized size | 1 | 1.00 | 1.00 | 2.28 | 0.00 | 11.62 | 0.00 | 0.00 | 3.00 |
time (sec) |
N/A |
0.032 |
0.012 |
0.073 |
0.000 |
0.457 |
0.000 |
0.000 |
1.189 |
|
|
|
|
|
|
|
|
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|
|
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|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 78 | 53 | 293 | 12026 | 39 | 267 |
normalized size | 1 | 1.00 | 1.00 | 2.69 | 1.83 | 10.10 | 414.69 | 1.34 | 9.21 |
time (sec) |
N/A |
0.022 |
0.050 |
0.082 |
0.414 |
0.560 |
44.772 |
0.132 |
0.002 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 45 | 84 | 0 | 360 | 0 | 0 | 208 |
normalized size | 1 | 1.00 | 1.10 | 2.05 | 0.00 | 8.78 | 0.00 | 0.00 | 5.07 |
time (sec) |
N/A |
0.054 |
0.100 |
0.127 |
0.000 |
0.471 |
0.000 |
0.000 |
1.303 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 38 | 38 | 102 | 70 | 457 | 0 | 58 | 108 |
normalized size | 1 | 1.00 | 1.00 | 2.68 | 1.84 | 12.03 | 0.00 | 1.53 | 2.84 |
time (sec) |
N/A |
0.079 |
0.087 |
0.142 |
0.557 |
0.452 |
0.000 |
0.121 |
0.279 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 58 | 131 | 0 | 963 | 0 | 0 | 447 |
normalized size | 1 | 1.00 | 0.98 | 2.22 | 0.00 | 16.32 | 0.00 | 0.00 | 7.58 |
time (sec) |
N/A |
0.091 |
0.175 |
0.144 |
0.000 |
0.528 |
0.000 |
0.000 |
1.555 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 55 | 139 | 119 | 1377 | 0 | 87 | 239 |
normalized size | 1 | 1.00 | 1.00 | 2.53 | 2.16 | 25.04 | 0.00 | 1.58 | 4.35 |
time (sec) |
N/A |
0.099 |
0.154 |
0.165 |
0.420 |
0.445 |
0.000 |
0.419 |
1.317 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 86 | 274 | 0 | 3239 | 0 | 0 | 1305 |
normalized size | 1 | 1.00 | 0.96 | 3.04 | 0.00 | 35.99 | 0.00 | 0.00 | 14.50 |
time (sec) |
N/A |
0.138 |
0.309 |
0.148 |
0.000 |
0.583 |
0.000 |
0.000 |
36.098 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-1) |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 68 | 236 | 134 | 1239 | 0 | 104 | -1 |
normalized size | 1 | 1.00 | 1.05 | 3.63 | 2.06 | 19.06 | 0.00 | 1.60 | -0.02 |
time (sec) |
N/A |
0.057 |
0.232 |
0.111 |
0.525 |
0.466 |
0.000 |
0.144 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-1) |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 106 | 477 | 344 | 5117 | 0 | 228 | -1 |
normalized size | 1 | 1.00 | 0.99 | 4.46 | 3.21 | 47.82 | 0.00 | 2.13 | -0.01 |
time (sec) |
N/A |
0.123 |
0.628 |
0.125 |
0.592 |
0.601 |
0.000 |
0.682 |
0.000 |
|
|
|
|
|
|
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|
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|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
B |
B |
B |
B |
B |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 0 | 86 | 34 | 66 | 60 | 34 | 50 |
normalized size | 1 | 1.00 | 0.00 | 5.73 | 2.27 | 4.40 | 4.00 | 2.27 | 3.33 |
time (sec) |
N/A |
0.012 |
0.023 |
0.054 |
0.591 |
0.400 |
0.678 |
0.143 |
0.136 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
B |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 35 | 113 | 59 | 214 | 211 | 59 | 76 |
normalized size | 1 | 1.00 | 1.00 | 3.23 | 1.69 | 6.11 | 6.03 | 1.69 | 2.17 |
time (sec) |
N/A |
0.025 |
0.131 |
0.058 |
0.417 |
0.534 |
3.467 |
0.133 |
1.049 |
|
|
|
|
|
|
|
|
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|
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|
|
|
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|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 51 | 129 | 83 | 575 | 428 | 71 | 112 |
normalized size | 1 | 1.00 | 1.00 | 2.53 | 1.63 | 11.27 | 8.39 | 1.39 | 2.20 |
time (sec) |
N/A |
0.051 |
0.179 |
0.059 |
0.424 |
0.556 |
13.574 |
0.119 |
0.995 |
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
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|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
B |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2 | 2 | 2 | 16 | 10 | 20 | 14 | 10 | 10 |
normalized size | 1 | 1.00 | 1.00 | 8.00 | 5.00 | 10.00 | 7.00 | 5.00 | 5.00 |
time (sec) |
N/A |
0.016 |
0.003 |
0.068 |
0.310 |
0.503 |
0.413 |
0.109 |
0.063 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 17 | 32 | 49 | 84 | 34 | 18 | 18 |
normalized size | 1 | 1.00 | 1.55 | 2.91 | 4.45 | 7.64 | 3.09 | 1.64 | 1.64 |
time (sec) |
N/A |
0.018 |
0.003 |
0.066 |
0.346 |
0.425 |
1.093 |
0.137 |
0.980 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 27 | 48 | 111 | 185 | 54 | 24 | 24 |
normalized size | 1 | 1.00 | 1.42 | 2.53 | 5.84 | 9.74 | 2.84 | 1.26 | 1.26 |
time (sec) |
N/A |
0.020 |
0.004 |
0.071 |
0.353 |
0.482 |
2.785 |
0.113 |
0.064 |
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 53 | 114 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.08 | 2.33 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.031 |
0.080 |
0.282 |
0.000 |
0.419 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 18 | 58 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.06 | 3.41 | 0.00 | 0.00 | 0.00 | 0.00 | -0.06 |
time (sec) |
N/A |
0.009 |
0.023 |
0.354 |
0.000 |
0.461 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 15 | 11 | 1 | 0 | 31 | 13 |
normalized size | 1 | 1.00 | 1.00 | 1.15 | 0.85 | 0.08 | 0.00 | 2.38 | 1.00 |
time (sec) |
N/A |
0.022 |
0.005 |
0.144 |
0.588 |
0.573 |
0.000 |
0.128 |
1.016 |
|
|
|
|
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|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 11 | 14 | 11 | 2 | 0 | 31 | 11 |
normalized size | 1 | 1.00 | 1.00 | 1.27 | 1.00 | 0.18 | 0.00 | 2.82 | 1.00 |
time (sec) |
N/A |
0.018 |
0.007 |
0.160 |
1.416 |
0.392 |
0.000 |
0.131 |
0.953 |
|
|
|
|
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|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 40 | 62 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.021 |
0.042 |
0.328 |
0.000 |
0.684 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 135 | 321 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.02 | 2.41 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.154 |
0.475 |
0.324 |
0.000 |
0.581 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 51 | 99 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.93 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.061 |
0.052 |
0.377 |
0.000 |
0.475 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 25 | 21 | 23 | 1 | 0 | 66 | -1 |
normalized size | 1 | 1.00 | 0.76 | 0.64 | 0.70 | 0.03 | 0.00 | 2.00 | -0.03 |
time (sec) |
N/A |
0.028 |
0.031 |
0.201 |
0.879 |
0.571 |
0.000 |
0.148 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
Problem 49 |
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 | 29 | 29 | 23 | 21 | 23 | 19 | 0 | 66 | -1 |
normalized size | 1 | 1.00 | 0.79 | 0.72 | 0.79 | 0.66 | 0.00 | 2.28 | -0.03 |
time (sec) |
N/A |
0.026 |
0.023 |
0.239 |
0.431 |
0.483 |
0.000 |
0.136 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 78 | 96 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.77 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.092 |
0.074 |
0.423 |
0.000 |
0.806 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 53 | 66 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.08 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.030 |
0.077 |
0.192 |
0.000 |
0.504 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 18 | 45 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.06 | 2.65 | 0.00 | 0.00 | 0.00 | 0.00 | -0.06 |
time (sec) |
N/A |
0.009 |
0.039 |
0.291 |
0.000 |
0.475 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 20 | 34 | 19 | 1 | 0 | 40 | -1 |
normalized size | 1 | 1.00 | 1.18 | 2.00 | 1.12 | 0.06 | 0.00 | 2.35 | -0.06 |
time (sec) |
N/A |
0.022 |
0.009 |
0.145 |
0.824 |
0.486 |
0.000 |
0.154 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
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 | 15 | 15 | 18 | 16 | 17 | 17 | 0 | 39 | -1 |
normalized size | 1 | 1.00 | 1.20 | 1.07 | 1.13 | 1.13 | 0.00 | 2.60 | -0.07 |
time (sec) |
N/A |
0.019 |
0.009 |
0.173 |
1.342 |
0.778 |
0.000 |
0.116 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 40 | 61 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.020 |
0.049 |
0.341 |
0.000 |
0.654 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 288 | 288 | 105 | 100 | 0 | 0 | 0 | 0 | 633 |
normalized size | 1 | 1.00 | 0.36 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 2.20 |
time (sec) |
N/A |
0.478 |
0.129 |
0.786 |
0.000 |
0.000 |
0.000 |
0.000 |
5.157 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 288 | 288 | 105 | 94 | 0 | 0 | 0 | 0 | 633 |
normalized size | 1 | 1.00 | 0.36 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 2.20 |
time (sec) |
N/A |
0.233 |
0.093 |
0.702 |
0.000 |
0.000 |
0.000 |
0.000 |
5.894 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
B |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 133 | 216 | 0 | 602 | 330 | 275 | 291 |
normalized size | 1 | 1.00 | 1.46 | 2.37 | 0.00 | 6.62 | 3.63 | 3.02 | 3.20 |
time (sec) |
N/A |
0.130 |
0.995 |
0.054 |
0.000 |
0.538 |
3.261 |
0.140 |
3.431 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
B |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 147 | 212 | 0 | 602 | 405 | 275 | 295 |
normalized size | 1 | 1.00 | 1.55 | 2.23 | 0.00 | 6.34 | 4.26 | 2.89 | 3.11 |
time (sec) |
N/A |
0.121 |
0.614 |
0.066 |
0.000 |
0.569 |
3.719 |
0.165 |
3.416 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 361 | 485 | 121 | 121 | 0 | 771 | 0 | 0 | 1563 |
normalized size | 1 | 1.34 | 0.34 | 0.34 | 0.00 | 2.14 | 0.00 | 0.00 | 4.33 |
time (sec) |
N/A |
1.037 |
0.240 |
0.090 |
0.000 |
0.913 |
0.000 |
0.000 |
7.553 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F(-1) |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 109 | 127 | 0 | 779 | 0 | 0 | 1487 |
normalized size | 1 | 1.00 | 1.08 | 1.26 | 0.00 | 7.71 | 0.00 | 0.00 | 14.72 |
time (sec) |
N/A |
0.125 |
0.199 |
0.088 |
0.000 |
0.506 |
0.000 |
0.000 |
8.901 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 176 | 176 | 45 | 37 | 0 | 590 | 0 | 281 | 205 |
normalized size | 1 | 1.00 | 0.26 | 0.21 | 0.00 | 3.35 | 0.00 | 1.60 | 1.16 |
time (sec) |
N/A |
0.155 |
0.076 |
0.073 |
0.000 |
0.477 |
0.000 |
0.215 |
1.010 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
B |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 24 | 100 | 45 | 115 | 75 | 43 | 61 |
normalized size | 1 | 1.00 | 0.96 | 4.00 | 1.80 | 4.60 | 3.00 | 1.72 | 2.44 |
time (sec) |
N/A |
0.017 |
0.107 |
0.077 |
0.444 |
0.629 |
1.874 |
0.119 |
0.118 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-2) |
F |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 494 | 494 | 139 | 156 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.28 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.904 |
0.287 |
0.111 |
0.000 |
0.000 |
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 |
C |
F |
F(-1) |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 132 | 177 | 0 | 0 | 0 | 1 | 844 |
normalized size | 1 | 1.00 | 0.77 | 1.04 | 0.00 | 0.00 | 0.00 | 0.01 | 4.94 |
time (sec) |
N/A |
0.226 |
0.218 |
0.095 |
0.000 |
0.000 |
0.000 |
0.320 |
58.392 |
|
|
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Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 245 | 245 | 158 | 233 | 0 | 0 | 0 | 1 | -1 |
normalized size | 1 | 1.00 | 0.64 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.487 |
0.282 |
0.102 |
0.000 |
0.000 |
0.000 |
0.839 |
0.000 |
|
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Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-2) |
F |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 494 | 494 | 139 | 150 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.28 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.625 |
0.269 |
0.090 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
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Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 132 | 183 | 0 | 0 | 0 | 1 | 855 |
normalized size | 1 | 1.00 | 0.75 | 1.05 | 0.00 | 0.00 | 0.00 | 0.01 | 4.89 |
time (sec) |
N/A |
0.231 |
0.174 |
0.097 |
0.000 |
0.000 |
0.000 |
0.354 |
57.402 |
|
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Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 213 | 213 | 158 | 239 | 0 | 0 | 0 | 1 | -1 |
normalized size | 1 | 1.00 | 0.74 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.235 |
0.218 |
0.095 |
0.000 |
0.000 |
0.000 |
0.833 |
0.000 |
|
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Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 223 | 223 | 445 | 62 | 0 | 3228 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.00 | 0.28 | 0.00 | 14.48 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.562 |
0.104 |
0.074 |
0.000 |
1.045 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 68 | 208 | 0 | 158 | 0 | 140 | 337 |
normalized size | 1 | 1.00 | 0.82 | 2.51 | 0.00 | 1.90 | 0.00 | 1.69 | 4.06 |
time (sec) |
N/A |
0.105 |
0.464 |
0.087 |
0.000 |
1.593 |
0.000 |
0.140 |
2.555 |
|
|
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Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 127 | 47 | 0 | 3773 | 0 | 1 | -1 |
normalized size | 1 | 1.00 | 0.98 | 0.36 | 0.00 | 29.25 | 0.00 | 0.01 | -0.01 |
time (sec) |
N/A |
0.185 |
0.138 |
0.090 |
0.000 |
1.281 |
0.000 |
0.139 |
0.000 |
|
|
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Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 445 | 64 | 0 | 3260 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.17 | 0.31 | 0.00 | 15.90 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.463 |
0.096 |
0.073 |
0.000 |
2.123 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 111 | 426 | 0 | 694 | 632 | 10 | 329 |
normalized size | 1 | 1.00 | 1.56 | 6.00 | 0.00 | 9.77 | 8.90 | 0.14 | 4.63 |
time (sec) |
N/A |
0.122 |
0.234 |
0.089 |
0.000 |
1.666 |
22.047 |
0.141 |
4.524 |
|
|
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Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F(-1) |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 64 | 136 | 0 | 713 | 0 | 0 | 271 |
normalized size | 1 | 1.00 | 0.93 | 1.97 | 0.00 | 10.33 | 0.00 | 0.00 | 3.93 |
time (sec) |
N/A |
0.077 |
0.455 |
0.125 |
0.000 |
1.874 |
0.000 |
0.000 |
2.628 |
|
|
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|
Problem 76 |
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 | 15 | 15 | 15 | 14 | 23 | 47 | 0 | 23 | 27 |
normalized size | 1 | 1.00 | 1.00 | 0.93 | 1.53 | 3.13 | 0.00 | 1.53 | 1.80 |
time (sec) |
N/A |
0.033 |
0.009 |
0.093 |
0.300 |
1.143 |
0.000 |
1.001 |
1.112 |
|
|
|
|
|
|
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|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 39 | 42 | 0 | 357 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.08 | 0.00 | 9.15 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.069 |
0.026 |
0.082 |
0.000 |
1.205 |
0.000 |
0.000 |
0.000 |
|
|
|
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|
|
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|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 26 | 31 | 0 | 248 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.19 | 0.00 | 9.54 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.064 |
0.017 |
0.100 |
0.000 |
3.996 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 12 | 0 | 63 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.92 | 0.00 | 4.85 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A |
0.041 |
0.011 |
0.094 |
0.000 |
0.486 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 21 | 12 | 7 | 1 | 0 | 38 | -1 |
normalized size | 1 | 1.00 | 1.62 | 0.92 | 0.54 | 0.08 | 0.00 | 2.92 | -0.08 |
time (sec) |
N/A |
0.061 |
0.012 |
0.174 |
0.428 |
0.457 |
0.000 |
0.722 |
0.000 |
|
|
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|
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|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 153 | 153 | 145 | 150 | 0 | 1138 | 0 | 191 | 1173 |
normalized size | 1 | 1.00 | 0.95 | 0.98 | 0.00 | 7.44 | 0.00 | 1.25 | 7.67 |
time (sec) |
N/A |
0.235 |
1.419 |
0.140 |
0.000 |
1.445 |
0.000 |
8.022 |
0.915 |
|
|
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|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 28 | 21 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.075 |
0.021 |
0.111 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
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|
|
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|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 45 | 34 | 0 | 1648 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.76 | 0.00 | 36.62 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.082 |
0.022 |
0.087 |
0.000 |
1.428 |
0.000 |
0.000 |
0.000 |
|
|
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|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 24 | 0 | 113 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.83 | 0.00 | 3.90 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.087 |
0.023 |
0.072 |
0.000 |
0.480 |
0.000 |
0.000 |
0.000 |
|
|
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|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 45 | 38 | 0 | 156 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 0.81 | 0.00 | 3.32 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.089 |
0.022 |
0.046 |
0.000 |
0.474 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
|
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 [62] had the largest ratio of
[.7500]
|
|
|
|
|
|
|
| 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 |
3 |
3 |
1.00 |
16 |
0.188 |
|
|
|
|
|
|
|
2 |
A |
2 |
2 |
1.00 |
16 |
0.125 |
|
|
|
|
|
|
|
3 |
A |
2 |
2 |
1.00 |
16 |
0.125 |
|
|
|
|
|
|
|
4 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
|
|
|
|
|
|
|
5 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
|
|
|
|
|
|
|
6 |
A |
4 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
7 |
A |
4 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
8 |
A |
3 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
9 |
A |
2 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
10 |
A |
4 |
4 |
1.00 |
13 |
0.308 |
|
|
|
|
|
|
|
11 |
A |
5 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
12 |
A |
6 |
6 |
1.00 |
15 |
0.400 |
|
|
|
|
|
|
|
13 |
A |
6 |
6 |
1.00 |
15 |
0.400 |
|
|
|
|
|
|
|
14 |
A |
5 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
15 |
A |
4 |
4 |
1.00 |
15 |
0.267 |
|
|
|
|
|
|
|
16 |
A |
2 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
17 |
A |
4 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
18 |
A |
4 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
19 |
A |
7 |
7 |
1.00 |
13 |
0.538 |
|
|
|
|
|
|
|
20 |
A |
4 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
21 |
A |
6 |
6 |
1.00 |
15 |
0.400 |
|
|
|
|
|
|
|
22 |
A |
4 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
23 |
A |
5 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
24 |
A |
3 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
25 |
A |
3 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
26 |
A |
2 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
27 |
A |
2 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
28 |
A |
4 |
4 |
1.00 |
13 |
0.308 |
|
|
|
|
|
|
|
29 |
A |
3 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
30 |
A |
5 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
31 |
A |
4 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
32 |
A |
6 |
6 |
1.00 |
15 |
0.400 |
|
|
|
|
|
|
|
33 |
A |
4 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
34 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
35 |
A |
2 |
2 |
1.00 |
8 |
0.250 |
|
|
|
|
|
|
|
36 |
A |
4 |
4 |
1.00 |
8 |
0.500 |
|
|
|
|
|
|
|
37 |
A |
5 |
5 |
1.00 |
8 |
0.625 |
|
|
|
|
|
|
|
38 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
39 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
40 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
41 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
42 |
A |
1 |
1 |
1.00 |
10 |
0.100 |
|
|
|
|
|
|
|
43 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
44 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
45 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
46 |
A |
6 |
6 |
1.00 |
12 |
0.500 |
|
|
|
|
|
|
|
47 |
A |
4 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
48 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
49 |
A |
4 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
50 |
A |
6 |
6 |
1.00 |
12 |
0.500 |
|
|
|
|
|
|
|
51 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
52 |
A |
1 |
1 |
1.00 |
10 |
0.100 |
|
|
|
|
|
|
|
53 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
54 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
55 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
56 |
A |
8 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
57 |
A |
8 |
3 |
1.00 |
11 |
0.273 |
|
|
|
|
|
|
|
58 |
A |
7 |
5 |
1.00 |
8 |
0.625 |
|
|
|
|
|
|
|
59 |
A |
7 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
60 |
A |
10 |
6 |
1.34 |
10 |
0.600 |
|
|
|
|
|
|
|
61 |
A |
4 |
3 |
1.00 |
11 |
0.273 |
|
|
|
|
|
|
|
62 |
A |
10 |
6 |
1.00 |
8 |
0.750 |
|
|
|
|
|
|
|
63 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
64 |
A |
12 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
65 |
A |
7 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
66 |
A |
9 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
67 |
A |
12 |
3 |
1.00 |
11 |
0.273 |
|
|
|
|
|
|
|
68 |
A |
7 |
3 |
1.00 |
11 |
0.273 |
|
|
|
|
|
|
|
69 |
A |
9 |
3 |
1.00 |
11 |
0.273 |
|
|
|
|
|
|
|
70 |
A |
11 |
5 |
1.00 |
8 |
0.625 |
|
|
|
|
|
|
|
71 |
A |
7 |
3 |
1.00 |
8 |
0.375 |
|
|
|
|
|
|
|
72 |
A |
9 |
3 |
1.00 |
8 |
0.375 |
|
|
|
|
|
|
|
73 |
A |
11 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
74 |
A |
8 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
75 |
A |
10 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
76 |
A |
4 |
4 |
1.00 |
11 |
0.364 |
|
|
|
|
|
|
|
77 |
A |
4 |
4 |
1.00 |
15 |
0.267 |
|
|
|
|
|
|
|
78 |
A |
3 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
79 |
A |
3 |
3 |
1.00 |
13 |
0.231 |
|
|
|
|
|
|
|
80 |
A |
4 |
4 |
1.00 |
15 |
0.267 |
|
|
|
|
|
|
|
81 |
A |
11 |
10 |
1.00 |
15 |
0.667 |
|
|
|
|
|
|
|
82 |
A |
4 |
4 |
1.00 |
15 |
0.267 |
|
|
|
|
|
|
|
83 |
A |
5 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
84 |
A |
4 |
4 |
1.00 |
15 |
0.267 |
|
|
|
|
|
|
|
85 |
A |
5 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|