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, 86, 87,
88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98 }
B grade: { }
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, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87,
88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98 }
B grade: { }
C grade: { }
F grade: { }
2.1.3 Maple
A grade: { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,
48, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 90, 91, 92, 93, 94 }
B grade: { 64, 95, 96, 97, 98 }
C grade: { 55, 83, 84, 85, 86, 87, 88, 89 }
F grade: { 1, 19, 20, 21, 22, 23, 24, 25, 26, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50 }
2.1.4 Maxima
A grade: { 3, 4, 5, 6, 13, 14, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 48, 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, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92,
93, 94, 95, 96, 97, 98
B grade: { 2, 12 }
C grade: { }
F grade: { 1, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 39, 40, 41, 42, 43, 44, 45, 46, 47,
49, 50, 78, 79, 80, 81, 82 }
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 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, 83, 90, 91, 92, 93, 94, 95, 96, 97, 98
}
B grade: { 81, 82 }
C grade: { }
F grade: { 20, 21, 22, 25, 26, 84, 85, 86, 87, 88, 89 }
2.1.6 Sympy
A grade: { 2, 3, 4, 5, 6, 12, 13, 14, 27, 28, 29, 35, 36, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66,
67, 68, 74, 75, 76, 77, 90, 91, 92, 93, 94 }
B grade: { }
C grade: { }
F grade: { 1, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 31, 32, 33, 34, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 55, 64, 69, 70, 71, 72, 73, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,
95, 96, 97, 98 }
2.1.7 Giac
A grade: { 6, 27, 28, 29, 30, 31, 32, 33, 34, 42, 43, 48, 56, 57, 58, 59, 60, 61, 62, 63, 74, 75, 76, 77, 78, 90,
91, 92, 93, 94, 95, 96, 97, 98 }
B grade: { 39, 40, 41, 79, 80, 81, 82 }
C grade: { 2, 3, 4, 5, 12, 13, 14, 51, 52, 53, 54, 65, 66, 67, 68 }
F grade: { 1, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 35, 36, 37, 38, 44, 45, 46, 47, 49,
50, 55, 64, 69, 70, 71, 72, 73, 83, 84, 85, 86, 87, 88, 89 }
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 |
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grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 67 | 0 | 0 | 153 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0. |
0. |
2.28 |
0. |
0. |
time (sec) |
N/A |
0.04 |
0.038 |
0.047 |
0. |
1.525 |
0. |
0. |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 100 | 260 | 417 | 474 | 350 | 10620 |
normalized size | 1 | 1. | 0.71 | 1.84 | 2.96 | 3.36 | 2.48 | 75.32 |
time (sec) |
N/A |
0.108 |
0.12 |
0.009 |
1.588 |
1.522 |
0.537 |
2.585 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 78 | 165 | 278 | 312 | 231 | 6336 |
normalized size | 1 | 1. | 0.71 | 1.5 | 2.53 | 2.84 | 2.1 | 57.6 |
time (sec) |
N/A |
0.073 |
0.083 |
0.007 |
1.02 |
1.525 |
0.299 |
6.128 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 56 | 91 | 166 | 186 | 133 | 3367 |
normalized size | 1 | 1. | 0.71 | 1.15 | 2.1 | 2.35 | 1.68 | 42.62 |
time (sec) |
N/A |
0.043 |
0.066 |
0.007 |
1.008 |
1.546 |
0.236 |
1.83 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 34 | 38 | 81 | 90 | 60 | 1462 |
normalized size | 1 | 1. | 0.71 | 0.79 | 1.69 | 1.88 | 1.25 | 30.46 |
time (sec) |
N/A |
0.017 |
0.037 |
0.003 |
0.976 |
1.5 |
0.234 |
7.068 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 21 | 21 | 27 | 41 | 20 | 27 |
normalized size | 1 | 1. | 1.05 | 1.05 | 1.35 | 2.05 | 1. | 1.35 |
time (sec) |
N/A |
0.004 |
0.005 |
0.001 |
0.945 |
1.511 |
0.108 |
3.585 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 31 | 56 | 0 | 78 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.81 | 0. | 2.52 | 0. | 0. |
time (sec) |
N/A |
0.024 |
0.041 |
0.033 |
0. |
1.546 |
0. |
0. |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 55 | 99 | 0 | 159 | 0 | 0 |
normalized size | 1 | 1. | 0.96 | 1.74 | 0. | 2.79 | 0. | 0. |
time (sec) |
N/A |
0.043 |
0.119 |
0.038 |
0. |
1.539 |
0. |
0. |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 88 | 155 | 0 | 278 | 0 | 0 |
normalized size | 1 | 1. | 0.93 | 1.63 | 0. | 2.93 | 0. | 0. |
time (sec) |
N/A |
0.071 |
0.157 |
0.04 |
0. |
1.503 |
0. |
0. |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 99 | 199 | 0 | 425 | 0 | 0 |
normalized size | 1 | 1. | 0.77 | 1.55 | 0. | 3.32 | 0. | 0. |
time (sec) |
N/A |
0.1 |
0.201 |
0.049 |
0. |
1.521 |
0. |
0. |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 121 | 243 | 0 | 606 | 0 | 0 |
normalized size |
1 |
1. |
0.75 |
1.51 |
0. |
3.76 |
0. |
0. |
time (sec) |
N/A |
0.134 |
0.172 |
0.056 |
0. |
1.567 |
0. |
0. |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 100 | 260 | 417 | 474 | 350 | 10620 |
normalized size | 1 | 1. | 0.71 | 1.84 | 2.96 | 3.36 | 2.48 | 75.32 |
time (sec) |
N/A |
0.122 |
0.065 |
0.007 |
1.058 |
1.51 |
0.235 |
1.493 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 78 | 165 | 278 | 312 | 231 | 6336 |
normalized size | 1 | 1. | 0.71 | 1.5 | 2.53 | 2.84 | 2.1 | 57.6 |
time (sec) |
N/A |
0.086 |
0.075 |
0.006 |
1.127 |
1.533 |
0.319 |
1.407 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 56 | 91 | 166 | 186 | 133 | 3367 |
normalized size | 1 | 1. | 0.71 | 1.15 | 2.1 | 2.35 | 1.68 | 42.62 |
time (sec) |
N/A |
0.045 |
0.039 |
0.004 |
1.15 |
1.529 |
0.274 |
1.284 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 55 | 99 | 0 | 159 | 0 | 0 |
normalized size | 1 | 1. | 0.96 | 1.74 | 0. | 2.79 | 0. | 0. |
time (sec) |
N/A |
0.043 |
0.06 |
0.043 |
0. |
1.536 |
0. |
0. |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 88 | 155 | 0 | 278 | 0 | 0 |
normalized size | 1 | 1. | 0.93 | 1.63 | 0. | 2.93 | 0. | 0. |
time (sec) |
N/A |
0.098 |
0.051 |
0.059 |
0. |
1.499 |
0. |
0. |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 99 | 199 | 0 | 425 | 0 | 0 |
normalized size |
1 |
1. |
0.77 |
1.55 |
0. |
3.32 |
0. |
0. |
time (sec) |
N/A |
0.134 |
0.08 |
0.076 |
0. |
1.575 |
0. |
0. |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 121 | 243 | 0 | 606 | 0 | 0 |
normalized size |
1 |
1. |
0.75 |
1.51 |
0. |
3.76 |
0. |
0. |
time (sec) |
N/A |
0.18 |
0.034 |
0.096 |
0. |
1.594 |
0. |
0. |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 72 | 0 | 0 | 158 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0. |
0. |
2.19 |
0. |
0. |
time (sec) |
N/A |
0.054 |
0.013 |
0.043 |
0. |
1.777 |
0. |
0. |
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 71 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.07 |
0.015 |
0.158 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 71 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.06 |
0.014 |
0.077 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 71 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.057 |
0.014 |
0.103 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 67 | 0 | 0 | 153 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0. |
0. |
2.28 |
0. |
0. |
time (sec) |
N/A |
0.022 |
0.012 |
0. |
0. |
1.54 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 69 | 0 | 0 | 153 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0. |
0. |
2.22 |
0. |
0. |
time (sec) |
N/A |
0.024 |
0.015 |
0.045 |
0. |
1.566 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 73 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.057 |
0.011 |
0.099 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 73 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.06 |
0.011 |
0.075 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 14 | 18 | 32 | 15 | 18 |
normalized size | 1 | 1. | 1. | 0.93 | 1.2 | 2.13 | 1. | 1.2 |
time (sec) |
N/A |
0.003 |
0.004 |
0.004 |
1.122 |
1.5 |
0.095 |
1.211 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 16 | 20 | 32 | 15 | 20 |
normalized size | 1 | 1. | 1. | 1.07 | 1.33 | 2.13 | 1. | 1.33 |
time (sec) |
N/A |
0.003 |
0.004 |
0.006 |
1.051 |
1.51 |
0.093 |
1.191 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 14 | 18 | 35 | 10 | 18 |
normalized size | 1 | 1. | 1. | 0.74 | 0.95 | 1.84 | 0.53 | 0.95 |
time (sec) |
N/A |
0.005 |
0.005 |
0.013 |
1.139 |
1.492 |
0.09 |
1.239 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 36 | 99 | 32 | 254 | 0 | 127 |
normalized size |
1 |
1. |
0.27 |
0.76 |
0.24 |
1.94 |
0. |
0.97 |
time (sec) |
N/A |
0.147 |
0.006 |
0.022 |
1.229 |
1.533 |
0. |
1.22 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 36 | 87 | 32 | 219 | 0 | 111 |
normalized size |
1 |
1. |
0.33 |
0.81 |
0.3 |
2.03 |
0. |
1.03 |
time (sec) |
N/A |
0.094 |
0.006 |
0.01 |
1.224 |
1.518 |
0. |
1.257 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 36 | 75 | 32 | 188 | 0 | 95 |
normalized size |
1 |
1. |
0.42 |
0.88 |
0.38 |
2.21 |
0. |
1.12 |
time (sec) |
N/A |
0.066 |
0.006 |
0.012 |
1.217 |
1.499 |
0. |
1.242 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 30 | 66 | 32 | 153 | 0 | 78 |
normalized size | 1 | 1. | 0.48 | 1.06 | 0.52 | 2.47 | 0. | 1.26 |
time (sec) |
N/A |
0.044 |
0.008 |
0.008 |
1.25 |
1.519 |
0. |
1.226 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 38 | 30 | 27 | 39 | 96 | 0 | 38 |
normalized size | 1 | 1. | 0.79 | 0.71 | 1.03 | 2.53 | 0. | 1. |
time (sec) |
N/A |
0.025 |
0.006 |
0.008 |
1.153 |
1.529 |
0. |
1.346 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 38 | 64 | 32 | 122 | 34 | 0 |
normalized size | 1 | 1. | 0.7 | 1.19 | 0.59 | 2.26 | 0.63 | 0. |
time (sec) |
N/A |
0.045 |
0.015 |
0.01 |
1.214 |
1.549 |
6.776 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 49 | 72 | 32 | 170 | 39 | 0 |
normalized size | 1 | 1. | 0.64 | 0.94 | 0.42 | 2.21 | 0.51 | 0. |
time (sec) |
N/A |
0.065 |
0.037 |
0.011 |
1.252 |
1.54 |
175.103 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 100 | 61 | 84 | 32 | 205 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
0.84 |
0.32 |
2.05 |
0. |
0. |
time (sec) |
N/A |
0.089 |
0.05 |
0.012 |
1.255 |
1.524 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 73 | 96 | 32 | 236 | 0 | 0 |
normalized size |
1 |
1. |
0.59 |
0.78 |
0.26 |
1.92 |
0. |
0. |
time (sec) |
N/A |
0.108 |
0.062 |
0.013 |
1.297 |
1.48 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 208 | 208 | 72 | 0 | 0 | 516 | 0 | 1301 |
normalized size |
1 |
1. |
0.35 |
0. |
0. |
2.48 |
0. |
6.25 |
time (sec) |
N/A |
0.266 |
0.03 |
0.02 |
0. |
1.556 |
0. |
1.378 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 173 | 173 | 72 | 0 | 0 | 383 | 0 | 779 |
normalized size |
1 |
1. |
0.42 |
0. |
0. |
2.21 |
0. |
4.5 |
time (sec) |
N/A |
0.166 |
0.027 |
0.019 |
0. |
1.542 |
0. |
1.334 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 63 | 0 | 0 | 288 | 0 | 408 |
normalized size |
1 |
1. |
0.46 |
0. |
0. |
2.09 |
0. |
2.96 |
time (sec) |
N/A |
0.119 |
0.07 |
0.02 |
0. |
1.916 |
0. |
1.191 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 63 | 0 | 0 | 220 | 0 | 170 |
normalized size | 1 | 1. | 0.6 | 0. | 0. | 2.1 | 0. | 1.62 |
time (sec) |
N/A |
0.077 |
0.038 |
0.019 |
0. |
2.089 |
0. |
1.302 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 63 | 0 | 0 | 142 | 0 | 78 |
normalized size | 1 | 1. | 0.88 | 0. | 0. | 1.97 | 0. | 1.08 |
time (sec) |
N/A |
0.045 |
0.028 |
0.022 |
0. |
2.046 |
0. |
1.254 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 75 | 0 | 0 | 205 | 0 | 0 |
normalized size | 1 | 1. | 0.77 | 0. | 0. | 2.11 | 0. | 0. |
time (sec) |
N/A |
0.085 |
0.074 |
0.02 |
0. |
1.836 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 130 | 92 | 0 | 0 | 327 | 0 | 0 |
normalized size |
1 |
1. |
0.71 |
0. |
0. |
2.52 |
0. |
0. |
time (sec) |
N/A |
0.119 |
0.234 |
0.018 |
0. |
1.573 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 118 | 0 | 0 | 497 | 0 | 0 |
normalized size |
1 |
1. |
0.72 |
0. |
0. |
3.01 |
0. |
0. |
time (sec) |
N/A |
0.165 |
0.138 |
0.019 |
0. |
1.569 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 200 | 200 | 144 | 0 | 0 | 679 | 0 | 0 |
normalized size |
1 |
1. |
0.72 |
0. |
0. |
3.4 |
0. |
0. |
time (sec) |
N/A |
0.203 |
0.165 |
0.019 |
0. |
1.59 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 24 | 145 | 107 | 242 | 0 | 108 |
normalized size |
1 |
1. |
0.16 |
0.96 |
0.71 |
1.6 |
0. |
0.72 |
time (sec) |
N/A |
0.155 |
0.004 |
0.135 |
1.073 |
1.519 |
0. |
1.161 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 63 | 0 | 0 | 281 | 0 | 0 |
normalized size |
1 |
1. |
0.89 |
0. |
0. |
3.96 |
0. |
0. |
time (sec) |
N/A |
0.031 |
0.08 |
0.018 |
0. |
1.571 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 78 | 0 | 0 | 316 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
0. |
0. |
3.22 |
0. |
0. |
time (sec) |
N/A |
0.104 |
0.134 |
0.044 |
0. |
1.559 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 34 | 38 | 81 | 90 | 60 | 1462 |
normalized size | 1 | 1. | 0.71 | 0.79 | 1.69 | 1.88 | 1.25 | 30.46 |
time (sec) |
N/A |
0.017 |
0.023 |
0. |
1.041 |
1.549 |
0.129 |
1.296 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 56 | 80 | 158 | 167 | 116 | 3362 |
normalized size | 1 | 1. | 0.41 | 0.59 | 1.17 | 1.24 | 0.86 | 24.9 |
time (sec) |
N/A |
0.103 |
0.075 |
0.003 |
1.188 |
1.513 |
0.156 |
1.384 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 229 | 229 | 84 | 138 | 262 | 269 | 190 | 5787 |
normalized size | 1 | 1. | 0.37 | 0.6 | 1.14 | 1.17 | 0.83 | 25.27 |
time (sec) |
N/A |
0.191 |
0.111 |
0.004 |
1.132 |
1.512 |
0.184 |
1.416 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 348 | 348 | 117 | 212 | 393 | 396 | 284 | 10024 |
normalized size | 1 | 1. | 0.34 | 0.61 | 1.13 | 1.14 | 0.82 | 28.8 |
time (sec) |
N/A |
0.312 |
0.162 |
0.005 |
1.065 |
1.565 |
0.217 |
1.512 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 61 | 334 | 166 | 297 | 0 | 0 |
normalized size |
1 |
1. |
0.53 |
2.88 |
1.43 |
2.56 |
0. |
0. |
time (sec) |
N/A |
0.175 |
0.057 |
0.08 |
1.236 |
1.562 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 397 | 397 | 121 | 182 | 265 | 301 | 236 | 273 |
normalized size | 1 | 1. | 0.3 | 0.46 | 0.67 | 0.76 | 0.59 | 0.69 |
time (sec) |
N/A |
0.516 |
0.323 |
0.004 |
1.063 |
1.472 |
0.192 |
1.251 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 318 | 318 | 130 | 143 | 221 | 242 | 196 | 220 |
normalized size | 1 | 1. | 0.41 | 0.45 | 0.69 | 0.76 | 0.62 | 0.69 |
time (sec) |
N/A |
0.412 |
0.198 |
0.005 |
1.056 |
1.521 |
0.176 |
1.361 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 96 | 102 | 178 | 182 | 148 | 166 |
normalized size | 1 | 1. | 0.52 | 0.55 | 0.97 | 0.99 | 0.8 | 0.9 |
time (sec) |
N/A |
0.242 |
0.122 |
0.004 |
1.092 |
1.502 |
0.163 |
1.353 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 41 | 68 | 139 | 128 | 104 | 117 |
normalized size | 1 | 1. | 0.51 | 0.85 | 1.74 | 1.6 | 1.3 | 1.46 |
time (sec) |
N/A |
0.068 |
0.047 |
0.003 |
1.062 |
1.472 |
0.146 |
1.315 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 52 | 113 | 93 | 108 | 70 | 128 |
normalized size | 1 | 1. | 0.51 | 1.11 | 0.91 | 1.06 | 0.69 | 1.25 |
time (sec) |
N/A |
0.156 |
0.05 |
0.008 |
1.152 |
1.465 |
15.072 |
1.32 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 54 | 92 | 82 | 117 | 99 | 124 |
normalized size | 1 | 1. | 0.57 | 0.98 | 0.87 | 1.24 | 1.05 | 1.32 |
time (sec) |
N/A |
0.161 |
0.065 |
0.008 |
1.162 |
1.468 |
6.476 |
1.383 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 130 | 68 | 112 | 86 | 146 | 56 | 169 |
normalized size | 1 | 1. | 0.52 | 0.86 | 0.66 | 1.12 | 0.43 | 1.3 |
time (sec) |
N/A |
0.213 |
0.072 |
0.009 |
1.272 |
1.48 |
6.583 |
1.334 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 198 | 198 | 81 | 167 | 85 | 182 | 53 | 247 |
normalized size | 1 | 1. | 0.41 | 0.84 | 0.43 | 0.92 | 0.27 | 1.25 |
time (sec) |
N/A |
0.29 |
0.106 |
0.008 |
1.233 |
1.441 |
6.899 |
1.367 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 139 | 86 | 433 | 166 | 386 | 0 | 0 |
normalized size | 1 | 1. | 0.62 | 3.12 | 1.19 | 2.78 | 0. | 0. |
time (sec) |
N/A |
0.309 |
0.124 |
0.097 |
1.274 |
1.609 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 414 | 414 | 159 | 250 | 443 | 493 | 323 | 13437 |
normalized size | 1 | 1. | 0.38 | 0.6 | 1.07 | 1.19 | 0.78 | 32.46 |
time (sec) |
N/A |
0.672 |
0.12 |
0.009 |
1.061 |
1.553 |
0.21 |
1.86 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 328 | 328 | 121 | 197 | 354 | 386 | 260 | 9532 |
normalized size | 1 | 1. | 0.37 | 0.6 | 1.08 | 1.18 | 0.79 | 29.06 |
time (sec) |
N/A |
0.532 |
0.238 |
0.007 |
1.044 |
1.482 |
0.194 |
2.007 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 242 | 242 | 91 | 144 | 265 | 288 | 199 | 6340 |
normalized size | 1 | 1. | 0.38 | 0.6 | 1.1 | 1.19 | 0.82 | 26.2 |
time (sec) |
N/A |
0.356 |
0.15 |
0.007 |
1.049 |
1.573 |
0.176 |
1.486 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 58 | 93 | 181 | 192 | 134 | 3708 |
normalized size | 1 | 1. | 0.68 | 1.09 | 2.13 | 2.26 | 1.58 | 43.62 |
time (sec) |
N/A |
0.12 |
0.069 |
0.007 |
1.022 |
1.487 |
0.155 |
1.38 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 54 | 126 | 117 | 180 | 0 | 0 |
normalized size | 1 | 1. | 0.56 | 1.31 | 1.22 | 1.88 | 0. | 0. |
time (sec) |
N/A |
0.258 |
0.126 |
0.045 |
1.157 |
1.528 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 58 | 135 | 92 | 189 | 0 | 0 |
normalized size | 1 | 1. | 0.68 | 1.59 | 1.08 | 2.22 | 0. | 0. |
time (sec) |
N/A |
0.277 |
0.149 |
0.053 |
1.193 |
1.492 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 76 | 204 | 100 | 215 | 0 | 0 |
normalized size | 1 | 1. | 0.56 | 1.5 | 0.74 | 1.58 | 0. | 0. |
time (sec) |
N/A |
0.363 |
0.148 |
0.059 |
1.324 |
1.505 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 217 | 217 | 116 | 290 | 115 | 317 | 0 | 0 |
normalized size | 1 | 1. | 0.53 | 1.34 | 0.53 | 1.46 | 0. | 0. |
time (sec) |
N/A |
0.459 |
0.224 |
0.065 |
1.21 |
1.53 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 321 | 321 | 156 | 382 | 126 | 421 | 0 | 0 |
normalized size | 1 | 1. | 0.49 | 1.19 | 0.39 | 1.31 | 0. | 0. |
time (sec) |
N/A |
0.578 |
0.297 |
0.066 |
1.243 |
1.501 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 754 | 754 | 458 | 1062 | 1207 | 1310 | 1445 | 1480 |
normalized size | 1 | 1. | 0.61 | 1.41 | 1.6 | 1.74 | 1.92 | 1.96 |
time (sec) |
N/A |
0.916 |
0.696 |
0.005 |
1.176 |
1.506 |
0.492 |
1.292 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 495 | 495 | 320 | 640 | 809 | 844 | 899 | 910 |
normalized size | 1 | 1. | 0.65 | 1.29 | 1.63 | 1.71 | 1.82 | 1.84 |
time (sec) |
N/A |
0.636 |
0.445 |
0.005 |
1.181 |
1.435 |
0.356 |
1.259 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 271 | 271 | 191 | 297 | 464 | 468 | 447 | 447 |
normalized size | 1 | 1. | 0.7 | 1.1 | 1.71 | 1.73 | 1.65 | 1.65 |
time (sec) |
N/A |
0.339 |
0.253 |
0.005 |
1.086 |
1.503 |
0.245 |
1.241 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 50 | 108 | 201 | 192 | 158 | 178 |
normalized size | 1 | 1. | 0.49 | 1.06 | 1.97 | 1.88 | 1.55 | 1.75 |
time (sec) |
N/A |
0.096 |
0.061 |
0.004 |
1.123 |
1.429 |
0.164 |
1.207 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 277 | 277 | 175 | 489 | 0 | 479 | 0 | 240 |
normalized size | 1 | 1. | 0.63 | 1.77 | 0. | 1.73 | 0. | 0.87 |
time (sec) |
N/A |
0.338 |
0.298 |
0.012 |
0. |
1.521 |
0. |
1.189 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 258 | 258 | 163 | 406 | 0 | 729 | 0 | 1037 |
normalized size |
1 |
1. |
0.63 |
1.57 |
0. |
2.83 |
0. |
4.02 |
time (sec) |
N/A |
0.379 |
0.437 |
0.015 |
0. |
1.534 |
0. |
1.742 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 294 | 294 | 267 | 418 | 0 | 1158 | 0 | 2419 |
normalized size |
1 |
1. |
0.91 |
1.42 |
0. |
3.94 |
0. |
8.23 |
time (sec) |
N/A |
0.408 |
0.652 |
0.015 |
0. |
1.569 |
0. |
1.312 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 396 | 396 | 389 | 511 | 0 | 1733 | 0 | 4180 |
normalized size |
1 |
1. |
0.98 |
1.29 |
0. |
4.38 |
0. |
10.56 |
time (sec) |
N/A |
0.521 |
0.807 |
0.013 |
0. |
1.595 |
0. |
1.294 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 557 | 557 | 669 | 596 | 0 | 2442 | 0 | 6118 |
normalized size |
1 |
1. |
1.2 |
1.07 |
0. |
4.38 |
0. |
10.98 |
time (sec) |
N/A |
0.684 |
0.726 |
0.013 |
0. |
1.643 |
0. |
1.516 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 24 | 192 | 57 | 90 | 0 | 0 |
normalized size |
1 |
1. |
1. |
8. |
2.38 |
3.75 |
0. |
0. |
time (sec) |
N/A |
0.146 |
0.366 |
0.2 |
1.443 |
1.558 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 23 | 198 | 57 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.05 |
9. |
2.59 |
0. |
0. |
0. |
time (sec) |
N/A |
0.131 |
0.299 |
0.098 |
1.374 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 23 | 198 | 57 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.05 |
9. |
2.59 |
0. |
0. |
0. |
time (sec) |
N/A |
0.09 |
0.269 |
0.097 |
1.404 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 21 | 186 | 51 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.05 |
9.3 |
2.55 |
0. |
0. |
0. |
time (sec) |
N/A |
0.046 |
0.171 |
0.108 |
1.358 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 180 | 49 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1. |
9.47 |
2.58 |
0. |
0. |
0. |
time (sec) |
N/A |
0.129 |
0.032 |
0.088 |
1.386 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 23 | 136 | 53 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.05 |
6.18 |
2.41 |
0. |
0. |
0. |
time (sec) |
N/A |
0.131 |
0.328 |
0.105 |
1.428 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 23 | 136 | 53 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.05 |
6.18 |
2.41 |
0. |
0. |
0. |
time (sec) |
N/A |
0.131 |
0.323 |
0.102 |
1.381 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 45 | 43 | 81 | 105 | 51 | 58 |
normalized size | 1 | 1. | 0.49 | 0.47 | 0.89 | 1.15 | 0.56 | 0.64 |
time (sec) |
N/A |
0.143 |
0.021 |
0.003 |
1.027 |
1.442 |
0.114 |
1.315 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 37 | 35 | 65 | 85 | 42 | 47 |
normalized size | 1 | 1. | 0.51 | 0.49 | 0.9 | 1.18 | 0.58 | 0.65 |
time (sec) |
N/A |
0.101 |
0.013 |
0.003 |
1.093 |
1.459 |
0.108 |
1.254 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 29 | 27 | 49 | 66 | 34 | 36 |
normalized size | 1 | 1. | 0.55 | 0.51 | 0.92 | 1.25 | 0.64 | 0.68 |
time (sec) |
N/A |
0.064 |
0.013 |
0.001 |
1.023 |
1.476 |
0.104 |
1.226 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 21 | 19 | 32 | 50 | 26 | 26 |
normalized size | 1 | 1. | 0.62 | 0.56 | 0.94 | 1.47 | 0.76 | 0.76 |
time (sec) |
N/A |
0.029 |
0.01 |
0.001 |
1.045 |
1.501 |
0.094 |
1.243 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 16 | 14 | 19 | 34 | 14 | 19 |
normalized size | 1 | 1. | 1. | 0.88 | 1.19 | 2.12 | 0.88 | 1.19 |
time (sec) |
N/A |
0.007 |
0.005 |
0.001 |
1.043 |
1.467 |
0.083 |
1.245 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 27 | 57 | 14 | 31 | 0 | 14 |
normalized size | 1 | 1. | 1. | 2.11 | 0.52 | 1.15 | 0. | 0.52 |
time (sec) |
N/A |
0.058 |
0.016 |
0.039 |
1.173 |
1.493 |
0. |
1.365 |
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Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
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|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 47 | 116 | 18 | 80 | 0 | 39 |
normalized size | 1 | 1. | 0.98 | 2.42 | 0.38 | 1.67 | 0. | 0.81 |
time (sec) |
N/A |
0.086 |
0.027 |
0.021 |
1.172 |
1.431 |
0. |
1.256 |
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Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 56 | 155 | 20 | 101 | 0 | 62 |
normalized size | 1 | 1. | 0.79 | 2.18 | 0.28 | 1.42 | 0. | 0.87 |
time (sec) |
N/A |
0.119 |
0.042 |
0.028 |
1.146 |
1.508 |
0. |
1.286 |
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Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 92 | 92 | 64 | 189 | 20 | 119 | 0 | 85 |
normalized size | 1 | 1. | 0.7 | 2.05 | 0.22 | 1.29 | 0. | 0.92 |
time (sec) |
N/A |
0.155 |
0.053 |
0.03 |
1.139 |
1.467 |
0. |
1.309 |
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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 [48] had the largest ratio of [ 0.25
]
|
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| Table 2.1Rubi specific breakdown of results for each
integral
|
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|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
|
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|
|
1 |
A |
1 |
1 |
1. |
17 |
0.059 |
|
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|
|
|
|
|
2 |
A |
5 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
3 |
A |
4 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
4 |
A |
3 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
5 |
A |
2 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
6 |
A |
1 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
7 |
A |
1 |
1 |
1. |
17 |
0.059 |
|
|
|
|
|
|
|
8 |
A |
2 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
9 |
A |
3 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
10 |
A |
4 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
11 |
A |
5 |
2 |
1. |
17 |
0.118 |
|
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|
|
|
|
|
12 |
A |
6 |
3 |
1. |
48 |
0.062 |
|
|
|
|
|
|
|
13 |
A |
5 |
3 |
1. |
37 |
0.081 |
|
|
|
|
|
|
|
14 |
A |
4 |
3 |
1. |
26 |
0.115 |
|
|
|
|
|
|
|
15 |
A |
3 |
3 |
1. |
28 |
0.107 |
|
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16 |
A |
4 |
3 |
1. |
39 |
0.077 |
|
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|
17 |
A |
5 |
3 |
1. |
50 |
0.06 |
|
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|
|
|
|
|
18 |
A |
6 |
3 |
1. |
61 |
0.049 |
|
|
|
|
|
|
|
19 |
A |
2 |
2 |
1. |
19 |
0.105 |
|
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|
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|
|
20 |
A |
2 |
2 |
1. |
50 |
0.04 |
|
|
|
|
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|
|
|
21 |
A |
2 |
2 |
1. |
39 |
0.051 |
|
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22 |
A |
2 |
2 |
1. |
28 |
0.071 |
|
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23 |
A |
1 |
1 |
1. |
17 |
0.059 |
|
|
|
|
|
|
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24 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
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|
25 |
A |
2 |
2 |
1. |
30 |
0.067 |
|
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26 |
A |
2 |
2 |
1. |
41 |
0.049 |
|
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27 |
A |
1 |
1 |
1. |
7 |
0.143 |
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|
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28 |
A |
1 |
1 |
1. |
7 |
0.143 |
|
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29 |
A |
1 |
1 |
1. |
7 |
0.143 |
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30 |
A |
6 |
3 |
1. |
13 |
0.231 |
|
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31 |
A |
5 |
3 |
1. |
13 |
0.231 |
|
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32 |
A |
4 |
3 |
1. |
13 |
0.231 |
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33 |
A |
3 |
3 |
1. |
13 |
0.231 |
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|
34 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
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|
35 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
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|
36 |
A |
4 |
3 |
1. |
13 |
0.231 |
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|
37 |
A |
5 |
3 |
1. |
13 |
0.231 |
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|
38 |
A |
6 |
3 |
1. |
13 |
0.231 |
|
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|
39 |
A |
6 |
3 |
1. |
19 |
0.158 |
|
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|
40 |
A |
5 |
3 |
1. |
19 |
0.158 |
|
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|
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|
41 |
A |
4 |
3 |
1. |
19 |
0.158 |
|
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|
42 |
A |
3 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
43 |
A |
2 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
44 |
A |
3 |
3 |
1. |
19 |
0.158 |
|
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|
45 |
A |
4 |
3 |
1. |
19 |
0.158 |
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|
46 |
A |
5 |
3 |
1. |
19 |
0.158 |
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|
47 |
A |
6 |
3 |
1. |
19 |
0.158 |
|
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|
48 |
A |
9 |
3 |
1. |
12 |
0.25 |
|
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|
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|
49 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
50 |
A |
2 |
2 |
1. |
21 |
0.095 |
|
|
|
|
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|
|
51 |
A |
2 |
2 |
1. |
15 |
0.133 |
|
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|
52 |
A |
8 |
3 |
1. |
20 |
0.15 |
|
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|
53 |
A |
12 |
3 |
1. |
25 |
0.12 |
|
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|
54 |
A |
17 |
3 |
1. |
30 |
0.1 |
|
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|
55 |
A |
6 |
2 |
1. |
21 |
0.095 |
|
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|
|
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|
56 |
A |
24 |
3 |
1. |
21 |
0.143 |
|
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|
|
|
|
|
57 |
A |
20 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
58 |
A |
11 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
59 |
A |
4 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
60 |
A |
9 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
|
61 |
A |
8 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
62 |
A |
9 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
63 |
A |
12 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
64 |
A |
5 |
2 |
1. |
22 |
0.091 |
|
|
|
|
|
|
|
65 |
A |
17 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
66 |
A |
14 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
67 |
A |
11 |
3 |
1. |
20 |
0.15 |
|
|
|
|
|
|
|
68 |
A |
4 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
69 |
A |
6 |
4 |
1. |
22 |
0.182 |
|
|
|
|
|
|
|
70 |
A |
6 |
4 |
1. |
22 |
0.182 |
|
|
|
|
|
|
|
71 |
A |
8 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
72 |
A |
11 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
73 |
A |
14 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
74 |
A |
28 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
75 |
A |
20 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
76 |
A |
13 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
77 |
A |
5 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
78 |
A |
13 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
79 |
A |
11 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
80 |
A |
11 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
|
81 |
A |
13 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
82 |
A |
17 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
83 |
A |
1 |
1 |
1. |
39 |
0.026 |
|
|
|
|
|
|
|
84 |
A |
1 |
1 |
1. |
38 |
0.026 |
|
|
|
|
|
|
|
85 |
A |
1 |
1 |
1. |
36 |
0.028 |
|
|
|
|
|
|
|
86 |
A |
1 |
1 |
1. |
35 |
0.029 |
|
|
|
|
|
|
|
87 |
A |
1 |
1 |
1. |
35 |
0.029 |
|
|
|
|
|
|
|
88 |
A |
1 |
1 |
1. |
38 |
0.026 |
|
|
|
|
|
|
|
89 |
A |
1 |
1 |
1. |
38 |
0.026 |
|
|
|
|
|
|
|
90 |
A |
5 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
91 |
A |
4 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
92 |
A |
3 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
93 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
94 |
A |
1 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
95 |
A |
2 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
96 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
97 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
98 |
A |
5 |
3 |
1. |
15 |
0.2 |
|
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|
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