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, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112,
113, 114, 115 }
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, 57, 58, 59, 60, 61, 62, 96,
97, 98, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115 }
B grade: { }
C grade: { 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, 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, 99, 100, 101, 102 }
F grade: { 108 }
2.1.3 Maple
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 25, 26, 31, 37, 38, 39, 43, 44, 45, 46, 48, 49,
50, 51, 52, 53, 66, 67, 68, 73, 77, 78, 79, 80, 81, 83, 85, 86, 87, 91, 92, 94, 95, 96, 97, 100, 103, 107, 110,
112, 115 }
B grade: { 13, 14, 20, 21, 22, 23, 24, 27, 28, 29, 30, 32, 33, 34, 35, 36, 40, 41, 42, 47, 54, 57, 58, 59, 60, 61,
62, 63, 64, 65, 69, 70, 71, 72, 74, 75, 76, 82, 84, 88, 93, 98, 99, 101, 102 }
C grade: { 89, 90 }
F grade: { 55, 56, 104, 105, 106, 108, 109, 111, 113, 114 }
2.1.4 Maxima
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 103, 107, 110, 112, 115
}
B grade: { }
C grade: { }
F grade: { 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, 99, 100, 101, 102, 104, 105,
106, 108, 109, 111, 113, 114 }
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 57, 58, 59, 110, 115
}
B grade: { 8, 15, 22, 60, 61, 98 }
C grade: { }
F grade: { 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, 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, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109,
111, 112, 113, 114 }
2.1.6 Sympy
A grade: { 1, 2, 3, 4, 6, 8, 9, 10, 11, 16, 17, 18, 97, 103, 107, 110, 112, 115 }
B grade: { 5, 7, 12, 13, 14, 15, 19, 20, 21 }
C grade: { }
F grade: { 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, 98, 99, 100, 101, 102, 104, 105,
106, 108, 109, 111, 113, 114 }
2.1.7 Giac
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 61, 62, 103, 107, 110,
112, 115 }
B grade: { 63, 98 }
C grade: { }
F grade: { 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, 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, 99, 100, 101, 102, 104, 105, 106, 108, 109,
111, 113, 114 }
2.1.8 Mupad
A grade: { 103, 107, 110, 112, 115 }
B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 }
C grade: { }
F grade: { 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, 99, 100, 101, 102, 104, 105,
106, 108, 109, 111, 113, 114 }
2.2 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2)
if the failure was due to an exception being raised, which could indicate a bug in the system. If
the failure was due to integral not being evaluated within the time limit, then it is given just an
F.
In this table,the column normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 172 | 172 | 172 | 176 | 175 | 218 | 236 | 210 | 182 |
normalized size | 1 | 1.00 | 1.00 | 1.02 | 1.02 | 1.27 | 1.37 | 1.22 | 1.06 |
time (sec) |
N/A |
0.192 |
0.087 |
0.000 |
0.668 |
0.653 |
0.101 |
0.308 |
0.102 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 130 | 130 | 135 | 134 | 165 | 173 | 161 | 143 |
normalized size | 1 | 1.00 | 1.00 | 1.04 | 1.03 | 1.27 | 1.33 | 1.24 | 1.10 |
time (sec) |
N/A |
0.135 |
0.070 |
0.001 |
0.754 |
0.814 |
0.092 |
0.294 |
0.838 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 96 | 94 | 93 | 114 | 121 | 114 | 99 |
normalized size | 1 | 1.00 | 1.02 | 1.00 | 0.99 | 1.21 | 1.29 | 1.21 | 1.05 |
time (sec) |
N/A |
0.083 |
0.037 |
0.001 |
0.566 |
0.721 |
0.082 |
0.281 |
0.047 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 56 | 53 | 52 | 62 | 63 | 66 | 54 |
normalized size | 1 | 1.00 | 1.00 | 0.95 | 0.93 | 1.11 | 1.12 | 1.18 | 0.96 |
time (sec) |
N/A |
0.037 |
0.013 |
0.002 |
0.554 |
0.633 |
0.070 |
0.335 |
0.048 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 72 | 119 | 74 | 191 | 206 | 80 | 108 |
normalized size | 1 | 1.00 | 0.89 | 1.47 | 0.91 | 2.36 | 2.54 | 0.99 | 1.33 |
time (sec) |
N/A |
0.080 |
0.054 |
0.006 |
1.237 |
0.566 |
0.618 |
0.310 |
0.115 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 95 | 163 | 101 | 318 | 190 | 95 | 95 |
normalized size | 1 | 1.00 | 0.88 | 1.51 | 0.94 | 2.94 | 1.76 | 0.88 | 0.88 |
time (sec) |
N/A |
0.085 |
0.065 |
0.012 |
1.205 |
0.977 |
1.366 |
0.363 |
0.167 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 130 | 130 | 175 | 145 | 471 | 246 | 135 | 136 |
normalized size | 1 | 1.00 | 1.00 | 1.35 | 1.12 | 3.62 | 1.89 | 1.04 | 1.05 |
time (sec) |
N/A |
0.108 |
0.083 |
0.010 |
1.431 |
0.813 |
3.133 |
0.458 |
0.968 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 171 | 210 | 194 | 642 | 313 | 184 | 176 |
normalized size | 1 | 1.00 | 1.00 | 1.23 | 1.13 | 3.75 | 1.83 | 1.08 | 1.03 |
time (sec) |
N/A |
0.163 |
0.104 |
0.010 |
1.570 |
0.871 |
6.658 |
0.343 |
0.177 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 226 | 226 | 226 | 237 | 236 | 289 | 304 | 283 | 233 |
normalized size | 1 | 1.00 | 1.00 | 1.05 | 1.04 | 1.28 | 1.35 | 1.25 | 1.03 |
time (sec) |
N/A |
0.214 |
0.085 |
0.001 |
0.634 |
0.785 |
0.112 |
0.241 |
0.857 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 158 | 158 | 158 | 169 | 168 | 202 | 216 | 202 | 158 |
normalized size | 1 | 1.00 | 1.00 | 1.07 | 1.06 | 1.28 | 1.37 | 1.28 | 1.00 |
time (sec) |
N/A |
0.167 |
0.064 |
0.001 |
0.614 |
0.786 |
0.099 |
0.357 |
0.069 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 96 | 101 | 100 | 114 | 121 | 120 | 99 |
normalized size | 1 | 1.00 | 1.02 | 1.07 | 1.06 | 1.21 | 1.29 | 1.28 | 1.05 |
time (sec) |
N/A |
0.081 |
0.031 |
0.000 |
0.765 |
0.668 |
0.082 |
0.288 |
0.047 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 142 | 142 | 115 | 243 | 160 | 366 | 347 | 178 | 203 |
normalized size | 1 | 1.00 | 0.81 | 1.71 | 1.13 | 2.58 | 2.44 | 1.25 | 1.43 |
time (sec) |
N/A |
0.208 |
0.071 |
0.006 |
1.351 |
0.910 |
1.038 |
0.294 |
0.857 |
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Problem 13 |
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 | 164 | 164 | 134 | 299 | 186 | 552 | 483 | 195 | 257 |
normalized size | 1 | 1.00 | 0.82 | 1.82 | 1.13 | 3.37 | 2.95 | 1.19 | 1.57 |
time (sec) |
N/A |
0.232 |
0.099 |
0.013 |
1.939 |
0.840 |
2.827 |
0.327 |
0.167 |
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Problem 14 |
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 | 207 | 207 | 183 | 397 | 236 | 777 | 400 | 238 | 243 |
normalized size | 1 | 1.00 | 0.88 | 1.92 | 1.14 | 3.75 | 1.93 | 1.15 | 1.17 |
time (sec) |
N/A |
0.239 |
0.130 |
0.013 |
2.012 |
0.831 |
11.984 |
0.449 |
0.976 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
B |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 240 | 240 | 242 | 360 | 304 | 1024 | 486 | 311 | 303 |
normalized size | 1 | 1.00 | 1.01 | 1.50 | 1.27 | 4.27 | 2.02 | 1.30 | 1.26 |
time (sec) |
N/A |
0.280 |
0.177 |
0.013 |
2.007 |
0.934 |
42.072 |
0.304 |
0.976 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 310 | 310 | 310 | 339 | 326 | 409 | 423 | 401 | 335 |
normalized size | 1 | 1.00 | 1.00 | 1.09 | 1.05 | 1.32 | 1.36 | 1.29 | 1.08 |
time (sec) |
N/A |
0.387 |
0.130 |
0.003 |
0.859 |
0.810 |
0.126 |
0.376 |
0.116 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 226 | 226 | 226 | 244 | 239 | 289 | 304 | 289 | 233 |
normalized size | 1 | 1.00 | 1.00 | 1.08 | 1.06 | 1.28 | 1.35 | 1.28 | 1.03 |
time (sec) |
N/A |
0.216 |
0.088 |
0.001 |
0.836 |
0.731 |
0.111 |
0.347 |
0.846 |
|
|
|
|
|
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|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 130 | 130 | 149 | 146 | 165 | 173 | 173 | 143 |
normalized size | 1 | 1.00 | 1.00 | 1.15 | 1.12 | 1.27 | 1.33 | 1.33 | 1.10 |
time (sec) |
N/A |
0.135 |
0.055 |
0.001 |
0.841 |
0.695 |
0.093 |
0.353 |
0.815 |
|
|
|
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|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 227 | 227 | 179 | 401 | 266 | 586 | 508 | 307 | 312 |
normalized size | 1 | 1.00 | 0.79 | 1.77 | 1.17 | 2.58 | 2.24 | 1.35 | 1.37 |
time (sec) |
N/A |
0.371 |
0.108 |
0.007 |
2.029 |
0.942 |
1.492 |
0.494 |
0.849 |
|
|
|
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|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 242 | 242 | 176 | 475 | 296 | 834 | 661 | 321 | 389 |
normalized size | 1 | 1.00 | 0.73 | 1.96 | 1.22 | 3.45 | 2.73 | 1.33 | 1.61 |
time (sec) |
N/A |
0.399 |
0.128 |
0.015 |
1.978 |
0.888 |
4.749 |
0.370 |
0.977 |
|
|
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Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 291 | 291 | 219 | 589 | 343 | 1102 | 865 | 371 | 495 |
normalized size | 1 | 1.00 | 0.75 | 2.02 | 1.18 | 3.79 | 2.97 | 1.27 | 1.70 |
time (sec) |
N/A |
0.416 |
0.168 |
0.015 |
1.944 |
0.841 |
26.162 |
0.387 |
0.223 |
|
|
|
|
|
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|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 348 | 348 | 295 | 735 | 416 | 1422 | 0 | 447 | 444 |
normalized size | 1 | 1.00 | 0.85 | 2.11 | 1.20 | 4.09 | 0.00 | 1.28 | 1.28 |
time (sec) |
N/A |
0.450 |
0.219 |
0.014 |
2.389 |
0.970 |
0.000 |
0.368 |
1.187 |
|
|
|
|
|
|
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|
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|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 544 | 544 | 373 | 1332 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.69 | 2.45 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.681 |
1.335 |
0.049 |
0.000 |
0.908 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 381 | 381 | 267 | 865 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.70 | 2.27 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.378 |
0.799 |
0.017 |
0.000 |
0.923 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 283 | 283 | 212 | 394 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.75 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.181 |
0.426 |
0.023 |
0.000 |
0.744 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 271 | 271 | 192 | 328 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.71 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.171 |
0.369 |
0.043 |
0.000 |
0.890 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 274 | 274 | 297 | 1236 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.08 | 4.51 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.205 |
1.267 |
0.059 |
0.000 |
0.954 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 385 | 385 | 379 | 2856 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 7.42 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.380 |
1.843 |
0.067 |
0.000 |
0.728 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 543 | 543 | 372 | 1331 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.69 | 2.45 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.645 |
1.709 |
0.025 |
0.000 |
0.891 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 400 | 400 | 275 | 870 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.69 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.439 |
1.177 |
0.024 |
0.000 |
0.957 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 369 | 369 | 248 | 671 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.67 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.400 |
0.986 |
0.031 |
0.000 |
0.887 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 373 | 373 | 296 | 1231 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.79 | 3.30 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.394 |
1.226 |
0.034 |
0.000 |
0.614 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 376 | 376 | 382 | 2860 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.02 | 7.61 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.423 |
1.666 |
0.042 |
0.000 |
0.868 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 531 | 531 | 545 | 5113 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 9.63 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.615 |
2.593 |
0.078 |
0.000 |
0.786 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 551 | 551 | 386 | 1386 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.70 | 2.52 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.628 |
1.306 |
0.028 |
0.000 |
0.852 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 396 | 396 | 279 | 924 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.70 | 2.33 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.448 |
0.984 |
0.023 |
0.000 |
0.929 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 282 | 282 | 215 | 501 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.76 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.184 |
0.512 |
0.017 |
0.000 |
0.847 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 206 | 206 | 131 | 158 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.64 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.102 |
0.222 |
0.020 |
0.000 |
0.958 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 209 | 209 | 206 | 334 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.085 |
0.759 |
0.035 |
0.000 |
0.913 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 284 | 284 | 302 | 1352 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.06 | 4.76 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.211 |
1.233 |
0.039 |
0.000 |
0.902 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 401 | 401 | 393 | 3039 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 7.58 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.413 |
1.403 |
0.052 |
0.000 |
0.910 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 501 | 501 | 369 | 1169 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.74 | 2.33 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.599 |
1.231 |
0.055 |
0.000 |
0.874 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 358 | 358 | 260 | 750 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.73 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.363 |
0.827 |
0.030 |
0.000 |
0.883 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 258 | 258 | 208 | 393 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.81 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.162 |
0.406 |
0.029 |
0.000 |
0.872 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 209 | 209 | 212 | 349 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.085 |
0.384 |
0.031 |
0.000 |
0.691 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 272 | 272 | 262 | 581 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 2.14 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.221 |
0.788 |
0.036 |
0.000 |
0.798 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 375 | 375 | 428 | 1742 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.14 | 4.65 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.392 |
2.219 |
0.042 |
0.000 |
0.718 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 209 | 209 | 212 | 349 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.086 |
0.437 |
0.059 |
0.000 |
0.808 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 247 | 247 | 220 | 359 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.89 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.240 |
0.771 |
0.062 |
0.000 |
0.840 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 237 | 237 | 213 | 345 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.218 |
0.487 |
0.056 |
0.000 |
0.676 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 242 | 242 | 221 | 354 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.91 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.237 |
0.551 |
0.060 |
0.000 |
1.013 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 191 | 191 | 81 | 105 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.42 | 0.55 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.096 |
0.158 |
0.042 |
0.000 |
0.722 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 262 | 262 | 142 | 367 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.54 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.168 |
0.223 |
0.025 |
0.000 |
0.609 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 356 | 356 | 186 | 775 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.52 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.322 |
0.355 |
0.026 |
0.000 |
0.569 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 104 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.204 |
0.438 |
0.273 |
0.000 |
0.998 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 526 | 526 | 203 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.630 |
0.450 |
0.217 |
0.000 |
0.956 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 124 | 1942 | 0 | 777 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 15.17 | 0.00 | 6.07 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.142 |
0.265 |
0.033 |
0.000 |
3.312 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 304 | 304 | 265 | 1541 | 0 | 1718 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.87 | 5.07 | 0.00 | 5.65 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.299 |
0.366 |
0.038 |
0.000 |
16.432 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 150 | 1052 | 0 | 1111 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 6.34 | 0.00 | 6.69 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.105 |
0.339 |
0.016 |
0.000 |
4.900 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 88 | 646 | 0 | 737 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 7.10 | 0.00 | 8.10 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.048 |
0.116 |
0.011 |
0.000 |
3.427 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 49 | 306 | 0 | 241 | 0 | 74 | -1 |
normalized size | 1 | 1.00 | 1.00 | 6.24 | 0.00 | 4.92 | 0.00 | 1.51 | -0.02 |
time (sec) |
N/A |
0.020 |
0.011 |
0.011 |
0.000 |
0.859 |
0.000 |
0.363 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 113 | 782 | 0 | 0 | 0 | 173 | -1 |
normalized size | 1 | 1.00 | 0.93 | 6.41 | 0.00 | 0.00 | 0.00 | 1.42 | -0.01 |
time (sec) |
N/A |
0.111 |
0.210 |
0.031 |
0.000 |
0.000 |
0.000 |
0.524 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
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Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
B |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 203 | 203 | 531 | 1865 | 0 | 0 | 0 | 479 | -1 |
normalized size | 1 | 1.00 | 2.62 | 9.19 | 0.00 | 0.00 | 0.00 | 2.36 | -0.00 |
time (sec) |
N/A |
0.265 |
2.639 |
0.036 |
0.000 |
0.000 |
0.000 |
26.049 |
0.000 |
|
|
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Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 608 | 776 | 456 | 1891 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.28 | 0.75 | 3.11 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.763 |
2.802 |
0.062 |
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 |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 400 | 400 | 346 | 1059 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.86 | 2.65 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.289 |
1.584 |
0.020 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 321 | 321 | 184 | 340 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.57 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.191 |
0.387 |
0.016 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 143 | 191 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.40 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.034 |
0.244 |
0.023 |
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 |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 209 | 209 | 347 | 390 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.66 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.105 |
0.804 |
0.029 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 401 | 401 | 427 | 2068 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.06 | 5.16 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.367 |
3.627 |
0.043 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
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|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 630 | 630 | 584 | 6245 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.93 | 9.91 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.719 |
3.083 |
0.068 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 659 | 784 | 445 | 1939 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.19 | 0.68 | 2.94 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.753 |
2.659 |
0.026 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 403 | 403 | 739 | 1028 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.83 | 2.55 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.304 |
1.148 |
0.022 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 328 | 328 | 184 | 300 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.56 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.191 |
0.359 |
0.023 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 224 | 224 | 492 | 630 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.20 | 2.81 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.112 |
1.518 |
0.031 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 391 | 391 | 999 | 1879 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.55 | 4.81 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.404 |
1.864 |
0.043 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 639 | 639 | 570 | 6215 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.89 | 9.73 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.779 |
3.239 |
0.068 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 621 | 621 | 350 | 992 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.56 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.463 |
1.619 |
0.028 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 319 | 319 | 197 | 341 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.62 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.176 |
0.459 |
0.025 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 143 | 191 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.40 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.033 |
0.245 |
0.023 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 100 | 101 | 118 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.121 |
0.226 |
0.023 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 344 | 344 | 365 | 413 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.06 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.220 |
0.954 |
0.033 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 435 | 435 | 433 | 2062 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 4.74 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.554 |
4.125 |
0.051 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 980 | 980 | 352 | 1063 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.36 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.113 |
1.675 |
0.033 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 223 | 223 | 304 | 594 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.36 | 2.66 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.120 |
1.110 |
0.031 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 209 | 209 | 207 | 285 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.105 |
0.665 |
0.032 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 344 | 344 | 221 | 303 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.64 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.222 |
0.643 |
0.031 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 539 | 539 | 418 | 956 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.78 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.479 |
4.399 |
0.040 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 814 | 814 | 1645 | 4115 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.02 | 5.06 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.958 |
7.273 |
0.066 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 242 | 239 | 204 | 370 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 0.84 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.147 |
0.508 |
0.066 |
0.000 |
22.279 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 192 | 192 | 71 | 120 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.37 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.092 |
0.250 |
0.012 |
0.000 |
1.761 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 50 | 64 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.86 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.022 |
0.176 |
0.021 |
0.000 |
17.872 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 121 | 122 | 147 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.060 |
0.468 |
0.038 |
0.000 |
16.687 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 215 | 215 | 357 | 477 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.66 | 2.22 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.145 |
0.497 |
0.040 |
0.000 |
18.465 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 298 | 298 | 134 | 293 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.45 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.179 |
0.398 |
0.045 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 93 | 93 | 94 | 133 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.036 |
0.270 |
0.024 |
0.000 |
155.242 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 49 | 53 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.042 |
0.018 |
0.025 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 37 | 35 | 0 | 0 | 19 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 0.97 | 0.00 | 0.00 | 0.53 | 0.00 | -0.03 |
time (sec) |
N/A |
0.025 |
0.058 |
0.033 |
0.000 |
1.181 |
7.560 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 191 | 1622 | 0 | 513 | 0 | 336 | -1 |
normalized size | 1 | 1.00 | 1.69 | 14.35 | 0.00 | 4.54 | 0.00 | 2.97 | -0.01 |
time (sec) |
N/A |
0.119 |
0.808 |
0.029 |
0.000 |
4.357 |
0.000 |
3.395 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 359 | 359 | 422 | 793 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.18 | 2.21 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.324 |
2.819 |
0.066 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 381 | 381 | 401 | 765 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.05 | 2.01 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.291 |
2.164 |
0.054 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 426 | 426 | 617 | 1105 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.45 | 2.59 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.373 |
6.066 |
0.056 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 485 | 485 | 587 | 1078 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.21 | 2.22 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.347 |
2.885 |
0.032 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.057 |
0.748 |
0.132 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 545 | 545 | 503 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.487 |
1.469 |
0.083 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 163 | 163 | 162 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.134 |
0.103 |
0.073 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 148 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.085 |
0.117 |
0.073 |
0.000 |
0.860 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.061 |
0.911 |
0.077 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 484 | 484 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.753 |
0.885 |
0.076 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 319 | 319 | 148 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.467 |
0.118 |
0.082 |
0.000 |
1.412 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.060 |
1.113 |
0.079 |
0.000 |
1.068 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 541 | 541 | 512 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.436 |
2.173 |
0.074 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.056 |
0.176 |
0.073 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 159 | 159 | 159 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.135 |
0.100 |
0.075 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 148 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.080 |
0.121 |
0.077 |
0.000 |
1.800 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.055 |
0.998 |
0.072 |
0.000 |
1.291 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
2.3 Detailed conclusion table specific for Rubi results
The following table is specific to Rubi. It gives additional statistics for each integral. the column
steps is the number of steps used by Rubi to obtain the antiderivative. The rules
column is the number of unique rules used. The integrand size column is the leaf
size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder
the integral was to solve. In this test, problem number [64] had the largest ratio of
[.2812]
|
|
|
|
|
|
|
| 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 |
2 |
1 |
1.00 |
24 |
0.042 |
|
|
|
|
|
|
|
2 |
A |
2 |
1 |
1.00 |
24 |
0.042 |
|
|
|
|
|
|
|
3 |
A |
2 |
1 |
1.00 |
24 |
0.042 |
|
|
|
|
|
|
|
4 |
A |
2 |
1 |
1.00 |
22 |
0.045 |
|
|
|
|
|
|
|
5 |
A |
3 |
3 |
1.00 |
24 |
0.125 |
|
|
|
|
|
|
|
6 |
A |
3 |
3 |
1.00 |
24 |
0.125 |
|
|
|
|
|
|
|
7 |
A |
3 |
3 |
1.00 |
24 |
0.125 |
|
|
|
|
|
|
|
8 |
A |
4 |
4 |
1.00 |
24 |
0.167 |
|
|
|
|
|
|
|
9 |
A |
2 |
1 |
1.00 |
26 |
0.038 |
|
|
|
|
|
|
|
10 |
A |
2 |
1 |
1.00 |
26 |
0.038 |
|
|
|
|
|
|
|
11 |
A |
2 |
1 |
1.00 |
24 |
0.042 |
|
|
|
|
|
|
|
12 |
A |
4 |
3 |
1.00 |
26 |
0.115 |
|
|
|
|
|
|
|
13 |
A |
4 |
4 |
1.00 |
26 |
0.154 |
|
|
|
|
|
|
|
14 |
A |
4 |
3 |
1.00 |
26 |
0.115 |
|
|
|
|
|
|
|
15 |
A |
4 |
3 |
1.00 |
26 |
0.115 |
|
|
|
|
|
|
|
16 |
A |
2 |
1 |
1.00 |
26 |
0.038 |
|
|
|
|
|
|
|
17 |
A |
2 |
1 |
1.00 |
26 |
0.038 |
|
|
|
|
|
|
|
18 |
A |
2 |
1 |
1.00 |
24 |
0.042 |
|
|
|
|
|
|
|
19 |
A |
5 |
3 |
1.00 |
26 |
0.115 |
|
|
|
|
|
|
|
20 |
A |
5 |
4 |
1.00 |
26 |
0.154 |
|
|
|
|
|
|
|
21 |
A |
5 |
4 |
1.00 |
26 |
0.154 |
|
|
|
|
|
|
|
22 |
A |
5 |
3 |
1.00 |
26 |
0.115 |
|
|
|
|
|
|
|
23 |
A |
7 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
24 |
A |
6 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
25 |
A |
5 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
26 |
A |
5 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
27 |
A |
4 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
28 |
A |
5 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
29 |
A |
7 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
30 |
A |
6 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
31 |
A |
6 |
6 |
1.00 |
30 |
0.200 |
|
|
|
|
|
|
|
32 |
A |
6 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
33 |
A |
5 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
34 |
A |
6 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
35 |
A |
7 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
36 |
A |
6 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
37 |
A |
5 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
38 |
A |
4 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
39 |
A |
3 |
3 |
1.00 |
30 |
0.100 |
|
|
|
|
|
|
|
40 |
A |
4 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
41 |
A |
5 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
42 |
A |
7 |
6 |
1.00 |
30 |
0.200 |
|
|
|
|
|
|
|
43 |
A |
6 |
6 |
1.00 |
30 |
0.200 |
|
|
|
|
|
|
|
44 |
A |
5 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
45 |
A |
3 |
3 |
1.00 |
30 |
0.100 |
|
|
|
|
|
|
|
46 |
A |
4 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
47 |
A |
5 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
48 |
A |
3 |
3 |
1.00 |
30 |
0.100 |
|
|
|
|
|
|
|
49 |
A |
8 |
7 |
1.00 |
31 |
0.226 |
|
|
|
|
|
|
|
50 |
A |
8 |
7 |
1.00 |
31 |
0.226 |
|
|
|
|
|
|
|
51 |
A |
8 |
7 |
1.00 |
32 |
0.219 |
|
|
|
|
|
|
|
52 |
A |
4 |
4 |
1.00 |
30 |
0.133 |
|
|
|
|
|
|
|
53 |
A |
5 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
54 |
A |
6 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
55 |
A |
2 |
2 |
1.00 |
87 |
0.023 |
|
|
|
|
|
|
|
56 |
A |
5 |
5 |
1.00 |
81 |
0.062 |
|
|
|
|
|
|
|
57 |
A |
6 |
6 |
1.00 |
28 |
0.214 |
|
|
|
|
|
|
|
58 |
A |
14 |
8 |
1.00 |
30 |
0.267 |
|
|
|
|
|
|
|
59 |
A |
9 |
7 |
1.00 |
30 |
0.233 |
|
|
|
|
|
|
|
60 |
A |
5 |
5 |
1.00 |
28 |
0.179 |
|
|
|
|
|
|
|
61 |
A |
2 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
62 |
A |
5 |
3 |
1.00 |
30 |
0.100 |
|
|
|
|
|
|
|
63 |
A |
7 |
5 |
1.00 |
30 |
0.167 |
|
|
|
|
|
|
|
64 |
A |
14 |
9 |
1.28 |
32 |
0.281 |
|
|
|
|
|
|
|
65 |
A |
7 |
7 |
1.00 |
32 |
0.219 |
|
|
|
|
|
|
|
66 |
A |
6 |
6 |
1.00 |
32 |
0.188 |
|
|
|
|
|
|
|
67 |
A |
1 |
1 |
1.00 |
32 |
0.031 |
|
|
|
|
|
|
|
68 |
A |
3 |
3 |
1.00 |
32 |
0.094 |
|
|
|
|
|
|
|
69 |
A |
6 |
6 |
1.00 |
32 |
0.188 |
|
|
|
|
|
|
|
70 |
A |
9 |
8 |
1.00 |
32 |
0.250 |
|
|
|
|
|
|
|
71 |
A |
14 |
9 |
1.19 |
32 |
0.281 |
|
|
|
|
|
|
|
72 |
A |
7 |
7 |
1.00 |
32 |
0.219 |
|
|
|
|
|
|
|
73 |
A |
6 |
6 |
1.00 |
32 |
0.188 |
|
|
|
|
|
|
|
74 |
A |
3 |
3 |
1.00 |
32 |
0.094 |
|
|
|
|
|
|
|
75 |
A |
6 |
6 |
1.00 |
32 |
0.188 |
|
|
|
|
|
|
|
76 |
A |
9 |
8 |
1.00 |
32 |
0.250 |
|
|
|
|
|
|
|
77 |
A |
12 |
8 |
1.00 |
32 |
0.250 |
|
|
|
|
|
|
|
78 |
A |
6 |
6 |
1.00 |
32 |
0.188 |
|
|
|
|
|
|
|
79 |
A |
1 |
1 |
1.00 |
32 |
0.031 |
|
|
|
|
|
|
|
80 |
A |
3 |
2 |
1.00 |
32 |
0.062 |
|
|
|
|
|
|
|
81 |
A |
5 |
5 |
1.00 |
32 |
0.156 |
|
|
|
|
|
|
|
82 |
A |
8 |
7 |
1.00 |
32 |
0.219 |
|
|
|
|
|
|
|
83 |
A |
14 |
9 |
1.00 |
32 |
0.281 |
|
|
|
|
|
|
|
84 |
A |
3 |
3 |
1.00 |
32 |
0.094 |
|
|
|
|
|
|
|
85 |
A |
3 |
3 |
1.00 |
32 |
0.094 |
|
|
|
|
|
|
|
86 |
A |
5 |
5 |
1.00 |
32 |
0.156 |
|
|
|
|
|
|
|
87 |
A |
8 |
7 |
1.00 |
32 |
0.219 |
|
|
|
|
|
|
|
88 |
A |
11 |
6 |
1.00 |
32 |
0.188 |
|
|
|
|
|
|
|
89 |
A |
7 |
7 |
0.99 |
28 |
0.250 |
|
|
|
|
|
|
|
90 |
A |
6 |
6 |
1.00 |
28 |
0.214 |
|
|
|
|
|
|
|
91 |
A |
1 |
1 |
1.00 |
28 |
0.036 |
|
|
|
|
|
|
|
92 |
A |
3 |
3 |
1.00 |
28 |
0.107 |
|
|
|
|
|
|
|
93 |
A |
6 |
6 |
1.00 |
28 |
0.214 |
|
|
|
|
|
|
|
94 |
A |
6 |
6 |
1.00 |
32 |
0.188 |
|
|
|
|
|
|
|
95 |
A |
1 |
1 |
1.00 |
32 |
0.031 |
|
|
|
|
|
|
|
96 |
A |
1 |
1 |
1.00 |
32 |
0.031 |
|
|
|
|
|
|
|
97 |
A |
3 |
3 |
1.00 |
30 |
0.100 |
|
|
|
|
|
|
|
98 |
A |
4 |
4 |
1.00 |
28 |
0.143 |
|
|
|
|
|
|
|
99 |
A |
11 |
9 |
1.00 |
33 |
0.273 |
|
|
|
|
|
|
|
100 |
A |
8 |
7 |
1.00 |
32 |
0.219 |
|
|
|
|
|
|
|
101 |
A |
11 |
9 |
1.00 |
33 |
0.273 |
|
|
|
|
|
|
|
102 |
A |
8 |
7 |
1.00 |
32 |
0.219 |
|
|
|
|
|
|
|
103 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
104 |
A |
7 |
7 |
1.00 |
34 |
0.206 |
|
|
|
|
|
|
|
105 |
A |
2 |
2 |
1.00 |
34 |
0.059 |
|
|
|
|
|
|
|
106 |
A |
2 |
2 |
1.00 |
34 |
0.059 |
|
|
|
|
|
|
|
107 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
108 |
A |
8 |
8 |
1.00 |
34 |
0.235 |
|
|
|
|
|
|
|
109 |
A |
5 |
5 |
1.00 |
34 |
0.147 |
|
|
|
|
|
|
|
110 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
111 |
A |
7 |
7 |
1.00 |
34 |
0.206 |
|
|
|
|
|
|
|
112 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
113 |
A |
2 |
2 |
1.00 |
34 |
0.059 |
|
|
|
|
|
|
|
114 |
A |
2 |
2 |
1.00 |
34 |
0.059 |
|
|
|
|
|
|
|
115 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|