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, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130,
131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149,
150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168,
169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187,
188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 208
}
B grade: { }
C grade: { }
F grade: { 206, 207}
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 19, 20, 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, 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, 94, 96, 97, 98, 99, 100, 101, 102, 120,
130, 131, 132, 133, 134, 137, 140, 141, 142, 143, 144, 145, 146, 150, 151, 152, 153, 154, 155, 156, 157, 159,
160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182,
183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 207, 208
}
B grade: { 21, 55, 56, 57, 58, 59, 60, 88, 89, 90, 93, 105, 106, 110, 126, 127, 128, 129, 158, 179, 206
}
C grade: { 11, 12, 13, 91, 92, 95, 103, 104, 107, 108, 109, 111, 112, 113, 114, 115, 116, 117, 118, 119, 123,
124, 136, 138, 147, 148, 149, 203, 204, 205 }
F grade: { 121, 122, 125, 135, 139}
2.1.3 Maple
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 19, 20, 21, 22, 23, 27, 28, 31, 32, 33, 36, 37, 40, 41, 42,
43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 56, 57, 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, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150,
151, 152, 153, 154, 155, 156, 157, 158, 159, 161, 162, 163, 165, 166, 167, 168, 169, 170, 171, 172, 173,
174, 175, 176, 177, 181, 182, 183, 184, 185, 186, 187, 188, 192, 193, 194, 195, 196, 197, 208
}
B grade: { 14, 15, 17, 18, 24, 25, 26, 29, 30, 34, 35, 38, 39, 53, 54, 58, 59, 60, 160, 164, 178, 179, 180, 189,
190, 191, 198, 199, 200, 201, 202 }
C grade: { }
F grade: { 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133,
134, 135, 136, 137, 138, 139, 203, 204, 205, 206, 207 }
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, 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, 55, 56, 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, 96, 100, 140, 141, 142,
143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164,
165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 182, 183, 184, 185, 186, 193, 194, 195, 196, 197,
208
B grade: { 53, 54, 57, 58, 59, 60, 87, 88, 89, 90, 99, 181, 192 }
C grade: { }
F grade: { 91, 92, 93, 94, 95, 97, 98, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114,
115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136,
137, 138, 139, 176, 177, 178, 179, 180, 187, 188, 189, 190, 191, 198, 199, 200, 201, 202, 203, 204, 205, 206,
207 }
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 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, 61, 62, 63, 64, 65, 66, 67, 68, 69,
70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 91, 92, 95, 96, 99, 100, 103, 107, 111, 112, 140,
141, 142, 143, 144, 145, 146, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165,
166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 183, 184, 187, 188, 198, 199, 208
}
B grade: { 10, 11, 12, 13, 17, 24, 30, 57, 58, 59, 60, 74, 84, 88, 89, 90, 93, 94, 97, 98, 101, 102, 104, 105,
106, 108, 109, 110, 113, 114, 147, 148, 149, 181, 182, 185, 186, 189, 190, 191, 192, 193, 194, 195, 196, 197,
200, 201, 202 }
C grade: { }
F grade: { 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133,
134, 135, 136, 137, 138, 139, 203, 204, 205, 206, 207 }
2.1.6 Sympy
A grade: { 22, 32, 40, 56 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30,
31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 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, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132,
133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151,
152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170,
171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189,
190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208
}
2.1.7 Giac
A grade: { 4, 5, 6, 7, 12, 13, 17, 18, 22, 28, 32, 33, 37, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55,
56, 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, 142, 143, 144, 148, 149, 152, 153, 154, 157, 158, 159, 162, 163, 164, 169, 170, 171, 172, 173, 174,
175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 196, 197, 198,
199, 200, 201, 202, 208 }
B grade: { 3, 10, 11, 16, 21, 23, 24, 42, 53, 57, 58, 59, 60, 93, 94, 97, 98, 101, 102, 103, 104, 105, 106, 109,
110, 114, 141, 146, 147, 151, 156, 167, 168, 181, 193 }
C grade: { }
F grade: { 1, 2, 8, 9, 14, 15, 19, 20, 25, 26, 27, 29, 30, 31, 34, 35, 36, 38, 39, 91, 92, 95, 96, 99, 100, 107,
108, 111, 112, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132,
133, 134, 135, 136, 137, 138, 139, 140, 145, 150, 155, 160, 161, 165, 166, 203, 204, 205, 206, 207
}
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 |
A |
A |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 123 | 147 | 128 | 410 | 0 | 0 |
normalized size |
1 |
1. |
1.07 |
1.28 |
1.11 |
3.57 |
0. |
0. |
time (sec) |
N/A |
0.072 |
0.446 |
0.064 |
1.049 |
1.552 |
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 |
A |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 77 | 96 | 69 | 224 | 0 | 0 |
normalized size |
1 |
1. |
1.08 |
1.35 |
0.97 |
3.15 |
0. |
0. |
time (sec) |
N/A |
0.048 |
0.108 |
0.056 |
0.992 |
1.532 |
0. |
0. |
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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 |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 38 | 29 | 34 | 65 | 0 | 1966 |
normalized size | 1 | 1. | 1.27 | 0.97 | 1.13 | 2.17 | 0. | 65.53 |
time (sec) |
N/A |
0.021 |
0.021 |
0.031 |
1.076 |
1.371 |
0. |
1.611 |
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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 |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 26 | 25 | 30 | 62 | 0 | 31 |
normalized size | 1 | 1. | 1.08 | 1.04 | 1.25 | 2.58 | 0. | 1.29 |
time (sec) |
N/A |
0.02 |
0.033 |
0.016 |
1.092 |
1.573 |
0. |
1.268 |
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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 |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 60 | 83 | 61 | 167 | 0 | 81 |
normalized size | 1 | 1. | 1.11 | 1.54 | 1.13 | 3.09 | 0. | 1.5 |
time (sec) |
N/A |
0.037 |
0.118 |
0.037 |
1.09 |
1.496 |
0. |
1.325 |
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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 |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 87 | 136 | 93 | 292 | 0 | 111 |
normalized size | 1 | 1. | 1.07 | 1.68 | 1.15 | 3.6 | 0. | 1.37 |
time (sec) |
N/A |
0.048 |
0.198 |
0.036 |
1.081 |
1.573 |
0. |
1.389 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 111 | 195 | 123 | 412 | 0 | 140 |
normalized size |
1 |
1. |
0.97 |
1.7 |
1.07 |
3.58 |
0. |
1.22 |
time (sec) |
N/A |
0.059 |
0.399 |
0.039 |
1.153 |
1.599 |
0. |
1.387 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 110 | 135 | 117 | 300 | 0 | 0 |
normalized size |
1 |
1. |
1.09 |
1.34 |
1.16 |
2.97 |
0. |
0. |
time (sec) |
N/A |
0.092 |
0.065 |
0.071 |
1.659 |
1.467 |
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 |
A |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 81 | 98 | 88 | 224 | 0 | 0 |
normalized size |
1 |
1. |
1.12 |
1.36 |
1.22 |
3.11 |
0. |
0. |
time (sec) |
N/A |
0.074 |
0.048 |
0.057 |
1.825 |
1.476 |
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 |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 47 | 59 | 53 | 194 | 0 | 1361 |
normalized size | 1 | 1. | 1.21 | 1.51 | 1.36 | 4.97 | 0. | 34.9 |
time (sec) |
N/A |
0.104 |
0.045 |
0.039 |
1.688 |
1.421 |
0. |
3.472 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 75 | 57 | 73 | 236 | 0 | 146 |
normalized size | 1 | 1. | 1.83 | 1.39 | 1.78 | 5.76 | 0. | 3.56 |
time (sec) |
N/A |
0.052 |
0.048 |
0.029 |
2.303 |
1.438 |
0. |
1.25 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 125 | 106 | 124 | 425 | 0 | 190 |
normalized size | 1 | 1. | 1.52 | 1.29 | 1.51 | 5.18 | 0. | 2.32 |
time (sec) |
N/A |
0.08 |
0.053 |
0.034 |
1.691 |
1.504 |
0. |
1.278 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 164 | 159 | 169 | 620 | 0 | 269 |
normalized size |
1 |
1. |
1.34 |
1.3 |
1.39 |
5.08 |
0. |
2.2 |
time (sec) |
N/A |
0.096 |
0.071 |
0.038 |
1.63 |
1.538 |
0. |
1.293 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 75 | 261 | 130 | 412 | 0 | 0 |
normalized size |
1 |
1. |
0.63 |
2.19 |
1.09 |
3.46 |
0. |
0. |
time (sec) |
N/A |
0.082 |
0.245 |
0.085 |
1.129 |
1.557 |
0. |
0. |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 54 | 162 | 78 | 212 | 0 | 0 |
normalized size |
1 |
1. |
0.75 |
2.25 |
1.08 |
2.94 |
0. |
0. |
time (sec) |
N/A |
0.062 |
0.103 |
0.071 |
1.112 |
1.482 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 52 | 52 | 40 | 69 | 58 | 108 | 0 | 9038 |
normalized size | 1 | 1. | 0.77 | 1.33 | 1.12 | 2.08 | 0. | 173.81 |
time (sec) |
N/A |
0.038 |
0.038 |
0.042 |
1.125 |
1.418 |
0. |
4.572 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 28 | 94 | 72 | 173 | 0 | 63 |
normalized size | 1 | 1. | 0.93 | 3.13 | 2.4 | 5.77 | 0. | 2.1 |
time (sec) |
N/A |
0.039 |
0.041 |
0.049 |
1.113 |
1.44 |
0. |
1.371 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 86 | 313 | 144 | 508 | 0 | 163 |
normalized size |
1 |
1. |
0.65 |
2.37 |
1.09 |
3.85 |
0. |
1.23 |
time (sec) |
N/A |
0.075 |
0.216 |
0.049 |
1.086 |
1.768 |
0. |
1.496 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 174 | 251 | 205 | 382 | 0 | 0 |
normalized size |
1 |
1. |
1.17 |
1.68 |
1.38 |
2.56 |
0. |
0. |
time (sec) |
N/A |
0.165 |
0.838 |
0.078 |
1.602 |
1.701 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 120 | 120 | 159 | 186 | 162 | 468 | 0 | 0 |
normalized size |
1 |
1. |
1.32 |
1.55 |
1.35 |
3.9 |
0. |
0. |
time (sec) |
N/A |
0.203 |
1.306 |
0.071 |
1.625 |
1.471 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 145 | 117 | 113 | 296 | 0 | 7250 |
normalized size | 1 | 1. | 2.04 | 1.65 | 1.59 | 4.17 | 0. | 102.11 |
time (sec) |
N/A |
0.089 |
0.438 |
0.049 |
1.615 |
1.537 |
0. |
64.982 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
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 | 45 | 45 | 34 | 52 | 63 | 97 | 78 | 51 |
normalized size | 1 | 1. | 0.76 | 1.16 | 1.4 | 2.16 | 1.73 | 1.13 |
time (sec) |
N/A |
0.014 |
0.193 |
0.023 |
1.085 |
1.558 |
0.697 |
1.853 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 94 | 89 | 107 | 281 | 0 | 193 |
normalized size | 1 | 1. | 1.27 | 1.2 | 1.45 | 3.8 | 0. | 2.61 |
time (sec) |
N/A |
0.102 |
0.58 |
0.036 |
1.64 |
1.524 |
0. |
1.732 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 191 | 190 | 188 | 474 | 0 | 282 |
normalized size | 1 | 1. | 1.95 | 1.94 | 1.92 | 4.84 | 0. | 2.88 |
time (sec) |
N/A |
0.161 |
5.581 |
0.044 |
1.647 |
1.703 |
0. |
1.762 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 99 | 445 | 180 | 594 | 0 | 0 |
normalized size |
1 |
1. |
0.62 |
2.78 |
1.12 |
3.71 |
0. |
0. |
time (sec) |
N/A |
0.109 |
0.564 |
0.105 |
1.077 |
1.575 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 66 | 205 | 97 | 248 | 0 | 0 |
normalized size |
1 |
1. |
0.73 |
2.25 |
1.07 |
2.73 |
0. |
0. |
time (sec) |
N/A |
0.071 |
0.157 |
0.078 |
1.071 |
1.599 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 52 | 85 | 77 | 147 | 0 | 0 |
normalized size |
1 |
1. |
0.74 |
1.21 |
1.1 |
2.1 |
0. |
0. |
time (sec) |
N/A |
0.045 |
0.045 |
0.051 |
1.071 |
1.516 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
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 | 98 | 98 | 67 | 109 | 108 | 284 | 0 | 127 |
normalized size | 1 | 1. | 0.68 | 1.11 | 1.1 | 2.9 | 0. | 1.3 |
time (sec) |
N/A |
0.065 |
0.202 |
0.053 |
1.06 |
1.483 |
0. |
1.372 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 180 | 180 | 243 | 359 | 282 | 734 | 0 | 0 |
normalized size |
1 |
1. |
1.35 |
1.99 |
1.57 |
4.08 |
0. |
0. |
time (sec) |
N/A |
0.357 |
5.614 |
0.131 |
1.648 |
1.598 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 177 | 266 | 223 | 539 | 0 | 0 |
normalized size |
1 |
1. |
1.49 |
2.24 |
1.87 |
4.53 |
0. |
0. |
time (sec) |
N/A |
0.194 |
2.25 |
0.085 |
1.612 |
1.583 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 115 | 167 | 158 | 378 | 0 | 0 |
normalized size |
1 |
1. |
1.29 |
1.88 |
1.78 |
4.25 |
0. |
0. |
time (sec) |
N/A |
0.125 |
0.49 |
0.053 |
1.57 |
1.42 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
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 | 63 | 63 | 44 | 74 | 97 | 134 | 121 | 74 |
normalized size | 1 | 1. | 0.7 | 1.17 | 1.54 | 2.13 | 1.92 | 1.17 |
time (sec) |
N/A |
0.054 |
0.326 |
0.027 |
1.074 |
1.458 |
0.655 |
1.64 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 92 | 92 | 106 | 105 | 126 | 321 | 0 | 219 |
normalized size | 1 | 1. | 1.15 | 1.14 | 1.37 | 3.49 | 0. | 2.38 |
time (sec) |
N/A |
0.137 |
1.065 |
0.043 |
1.637 |
1.566 |
0. |
2.059 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 83 | 387 | 147 | 394 | 0 | 0 |
normalized size |
1 |
1. |
0.64 |
3. |
1.14 |
3.05 |
0. |
0. |
time (sec) |
N/A |
0.095 |
0.469 |
0.1 |
1.107 |
1.672 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 76 | 245 | 115 | 293 | 0 | 0 |
normalized size |
1 |
1. |
0.71 |
2.29 |
1.07 |
2.74 |
0. |
0. |
time (sec) |
N/A |
0.079 |
0.155 |
0.084 |
1.065 |
1.532 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 62 | 101 | 95 | 182 | 0 | 0 |
normalized size |
1 |
1. |
0.7 |
1.15 |
1.08 |
2.07 |
0. |
0. |
time (sec) |
N/A |
0.053 |
0.07 |
0.052 |
1.076 |
1.538 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
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 | 102 | 102 | 78 | 125 | 111 | 324 | 0 | 130 |
normalized size |
1 |
1. |
0.76 |
1.23 |
1.09 |
3.18 |
0. |
1.27 |
time (sec) |
N/A |
0.067 |
0.137 |
0.054 |
1.118 |
1.734 |
0. |
1.393 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 252 | 360 | 321 | 620 | 0 | 0 |
normalized size |
1 |
1. |
1.76 |
2.52 |
2.24 |
4.34 |
0. |
0. |
time (sec) |
N/A |
0.199 |
1.651 |
0.092 |
1.673 |
1.563 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 125 | 231 | 244 | 456 | 0 | 0 |
normalized size |
1 |
1. |
1.11 |
2.04 |
2.16 |
4.04 |
0. |
0. |
time (sec) |
N/A |
0.161 |
1.126 |
0.06 |
1.589 |
1.589 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
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 | 87 | 87 | 57 | 111 | 146 | 177 | 224 | 97 |
normalized size | 1 | 1. | 0.66 | 1.28 | 1.68 | 2.03 | 2.57 | 1.11 |
time (sec) |
N/A |
0.082 |
0.425 |
0.029 |
1.114 |
1.479 |
2.074 |
1.381 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
Problem 41 |
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 | 116 | 116 | 136 | 127 | 158 | 360 | 0 | 262 |
normalized size | 1 | 1. | 1.17 | 1.09 | 1.36 | 3.1 | 0. | 2.26 |
time (sec) |
N/A |
0.159 |
1.574 |
0.045 |
1.573 |
1.693 |
0. |
1.396 |
|
|
|
|
|
|
|
|
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|
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|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 209 | 190 | 294 | 560 | 0 | 370 |
normalized size |
1 |
1. |
1.49 |
1.36 |
2.1 |
4. |
0. |
2.64 |
time (sec) |
N/A |
0.225 |
5.36 |
0.05 |
1.527 |
1.977 |
0. |
1.482 |
|
|
|
|
|
|
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|
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|
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|
Problem 43 |
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 | 198 | 198 | 283 | 293 | 423 | 770 | 0 | 458 |
normalized size |
1 |
1. |
1.43 |
1.48 |
2.14 |
3.89 |
0. |
2.31 |
time (sec) |
N/A |
0.428 |
1.52 |
0.054 |
1.692 |
2.085 |
0. |
1.703 |
|
|
|
|
|
|
|
|
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|
|
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|
Problem 44 |
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 | 130 | 130 | 101 | 162 | 236 | 464 | 0 | 184 |
normalized size |
1 |
1. |
0.78 |
1.25 |
1.82 |
3.57 |
0. |
1.42 |
time (sec) |
N/A |
0.161 |
1.009 |
0.059 |
1.028 |
2.054 |
0. |
8.07 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
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 | 106 | 106 | 84 | 126 | 176 | 398 | 0 | 157 |
normalized size | 1 | 1. | 0.79 | 1.19 | 1.66 | 3.75 | 0. | 1.48 |
time (sec) |
N/A |
0.136 |
0.308 |
0.056 |
1. |
1.836 |
0. |
3.934 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
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 | 82 | 82 | 54 | 90 | 120 | 338 | 0 | 130 |
normalized size | 1 | 1. | 0.66 | 1.1 | 1.46 | 4.12 | 0. | 1.59 |
time (sec) |
N/A |
0.116 |
0.165 |
0.053 |
1. |
1.343 |
0. |
2.115 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
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 | 37 | 58 | 28 | 54 | 63 | 163 | 0 | 78 |
normalized size | 1 | 1.57 | 0.76 | 1.46 | 1.7 | 4.41 | 0. | 2.11 |
time (sec) |
N/A |
0.067 |
0.039 |
0.058 |
1.088 |
1.636 |
0. |
1.341 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
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 | 32 | 32 | 32 | 33 | 42 | 74 | 0 | 45 |
normalized size | 1 | 1. | 1. | 1.03 | 1.31 | 2.31 | 0. | 1.41 |
time (sec) |
N/A |
0.039 |
0.019 |
0.023 |
1.047 |
1.407 |
0. |
1.283 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
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 | 32 | 32 | 24 | 30 | 35 | 73 | 0 | 35 |
normalized size | 1 | 1. | 0.75 | 0.94 | 1.09 | 2.28 | 0. | 1.09 |
time (sec) |
N/A |
0.068 |
0.033 |
0.032 |
1.118 |
1.37 |
0. |
1.323 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
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 | 51 | 51 | 30 | 49 | 62 | 162 | 0 | 62 |
normalized size | 1 | 1. | 0.59 | 0.96 | 1.22 | 3.18 | 0. | 1.22 |
time (sec) |
N/A |
0.089 |
0.049 |
0.085 |
1.106 |
1.4 |
0. |
1.321 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
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 | 68 | 68 | 61 | 67 | 89 | 248 | 0 | 89 |
normalized size |
1 |
1. |
0.9 |
0.99 |
1.31 |
3.65 |
0. |
1.31 |
time (sec) |
N/A |
0.093 |
0.149 |
0.095 |
1.128 |
1.413 |
0. |
1.462 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
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 | 84 | 84 | 77 | 87 | 116 | 343 | 0 | 116 |
normalized size |
1 |
1. |
0.92 |
1.04 |
1.38 |
4.08 |
0. |
1.38 |
time (sec) |
N/A |
0.1 |
0.209 |
0.115 |
1.108 |
1.517 |
0. |
1.438 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 146 | 175 | 456 | 248 | 0 | 232 |
normalized size | 1 | 1. | 1.74 | 2.08 | 5.43 | 2.95 | 0. | 2.76 |
time (sec) |
N/A |
0.097 |
0.319 |
0.057 |
1.095 |
1.673 |
0. |
5.32 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 106 | 130 | 289 | 194 | 0 | 162 |
normalized size | 1 | 1. | 1.54 | 1.88 | 4.19 | 2.81 | 0. | 2.35 |
time (sec) |
N/A |
0.092 |
0.32 |
0.055 |
1.081 |
1.511 |
0. |
2.567 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 50 | 50 | 106 | 70 | 122 | 127 | 0 | 92 |
normalized size | 1 | 1. | 2.12 | 1.4 | 2.44 | 2.54 | 0. | 1.84 |
time (sec) |
N/A |
0.088 |
0.164 |
0.047 |
1.095 |
1.371 |
0. |
1.659 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 48 | 22 | 36 | 108 | 27 | 28 |
normalized size | 1 | 1. | 2.09 | 0.96 | 1.57 | 4.7 | 1.17 | 1.22 |
time (sec) |
N/A |
0.012 |
0.041 |
0.022 |
1.078 |
1.46 |
1.726 |
1.27 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
B |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 69 | 56 | 95 | 173 | 0 | 88 |
normalized size | 1 | 1. | 2.38 | 1.93 | 3.28 | 5.97 | 0. | 3.03 |
time (sec) |
N/A |
0.051 |
0.218 |
0.068 |
1.087 |
1.539 |
0. |
1.286 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 124 | 132 | 209 | 311 | 0 | 171 |
normalized size | 1 | 1. | 2.14 | 2.28 | 3.6 | 5.36 | 0. | 2.95 |
time (sec) |
N/A |
0.088 |
0.491 |
0.075 |
1.027 |
1.416 |
0. |
1.416 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 189 | 208 | 316 | 431 | 0 | 252 |
normalized size | 1 | 1. | 2.3 | 2.54 | 3.85 | 5.26 | 0. | 3.07 |
time (sec) |
N/A |
0.106 |
0.743 |
0.088 |
1.02 |
1.396 |
0. |
1.578 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 106 | 106 | 284 | 284 | 425 | 545 | 0 | 329 |
normalized size |
1 |
1. |
2.68 |
2.68 |
4.01 |
5.14 |
0. |
3.1 |
time (sec) |
N/A |
0.127 |
0.914 |
0.102 |
1.125 |
1.579 |
0. |
1.979 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
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 | 189 | 189 | 112 | 180 | 273 | 599 | 0 | 197 |
normalized size |
1 |
1. |
0.59 |
0.95 |
1.44 |
3.17 |
0. |
1.04 |
time (sec) |
N/A |
0.149 |
1.693 |
0.096 |
1.106 |
1.728 |
0. |
9.844 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
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 | 146 | 146 | 91 | 144 | 225 | 532 | 0 | 170 |
normalized size | 1 | 1. | 0.62 | 0.99 | 1.54 | 3.64 | 0. | 1.16 |
time (sec) |
N/A |
0.108 |
0.45 |
0.084 |
1.054 |
1.528 |
0. |
5.289 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
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 | 104 | 104 | 70 | 108 | 149 | 467 | 0 | 138 |
normalized size | 1 | 1. | 0.67 | 1.04 | 1.43 | 4.49 | 0. | 1.33 |
time (sec) |
N/A |
0.086 |
0.311 |
0.083 |
1.055 |
1.531 |
0. |
2.998 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
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 | 60 | 60 | 36 | 72 | 95 | 274 | 0 | 122 |
normalized size | 1 | 1. | 0.6 | 1.2 | 1.58 | 4.57 | 0. | 2.03 |
time (sec) |
N/A |
0.048 |
0.081 |
0.082 |
1.025 |
1.456 |
0. |
1.848 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
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 | 52 | 52 | 36 | 50 | 62 | 162 | 0 | 61 |
normalized size | 1 | 1. | 0.69 | 0.96 | 1.19 | 3.12 | 0. | 1.17 |
time (sec) |
N/A |
0.05 |
0.055 |
0.034 |
1.119 |
1.509 |
0. |
1.795 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
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 | 65 | 65 | 49 | 66 | 74 | 204 | 0 | 155 |
normalized size | 1 | 1. | 0.75 | 1.02 | 1.14 | 3.14 | 0. | 2.38 |
time (sec) |
N/A |
0.059 |
0.07 |
0.106 |
1.384 |
1.548 |
0. |
2.102 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 67 |
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 | 55 | 55 | 38 | 39 | 49 | 138 | 0 | 49 |
normalized size | 1 | 1. | 0.69 | 0.71 | 0.89 | 2.51 | 0. | 0.89 |
time (sec) |
N/A |
0.051 |
0.074 |
0.092 |
0.956 |
1.466 |
0. |
1.962 |
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 68 |
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 | 73 | 73 | 73 | 49 | 62 | 234 | 0 | 62 |
normalized size |
1 |
1. |
1. |
0.67 |
0.85 |
3.21 |
0. |
0.85 |
time (sec) |
N/A |
0.057 |
0.073 |
0.108 |
1.072 |
1.401 |
0. |
2.364 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 69 |
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 | 127 | 127 | 78 | 79 | 103 | 331 | 0 | 103 |
normalized size |
1 |
1. |
0.61 |
0.62 |
0.81 |
2.61 |
0. |
0.81 |
time (sec) |
N/A |
0.074 |
0.143 |
0.125 |
1.762 |
1.446 |
0. |
2.225 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
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 | 145 | 145 | 88 | 89 | 116 | 431 | 0 | 116 |
normalized size |
1 |
1. |
0.61 |
0.61 |
0.8 |
2.97 |
0. |
0.8 |
time (sec) |
N/A |
0.081 |
0.205 |
0.139 |
1.837 |
1.676 |
0. |
1.931 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
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 | 199 | 199 | 118 | 119 | 157 | 541 | 0 | 157 |
normalized size |
1 |
1. |
0.59 |
0.6 |
0.79 |
2.72 |
0. |
0.79 |
time (sec) |
N/A |
0.102 |
0.329 |
0.165 |
1.835 |
1.654 |
0. |
2.161 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
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 | 171 | 171 | 102 | 162 | 254 | 657 | 0 | 184 |
normalized size |
1 |
1. |
0.6 |
0.95 |
1.49 |
3.84 |
0. |
1.08 |
time (sec) |
N/A |
0.123 |
0.926 |
0.106 |
1.961 |
1.671 |
0. |
4.824 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
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 | 126 | 126 | 82 | 126 | 197 | 586 | 0 | 154 |
normalized size | 1 | 1. | 0.65 | 1. | 1.56 | 4.65 | 0. | 1.22 |
time (sec) |
N/A |
0.091 |
0.363 |
0.092 |
1.938 |
1.581 |
0. |
2.552 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 52 | 90 | 132 | 409 | 0 | 109 |
normalized size | 1 | 1. | 0.63 | 1.1 | 1.61 | 4.99 | 0. | 1.33 |
time (sec) |
N/A |
0.057 |
0.145 |
0.095 |
2.143 |
1.553 |
0. |
2.19 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
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 | 74 | 74 | 52 | 68 | 97 | 284 | 0 | 80 |
normalized size | 1 | 1. | 0.7 | 0.92 | 1.31 | 3.84 | 0. | 1.08 |
time (sec) |
N/A |
0.058 |
0.175 |
0.037 |
1.769 |
1.607 |
0. |
1.98 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
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 | 86 | 86 | 61 | 84 | 108 | 393 | 0 | 208 |
normalized size | 1 | 1. | 0.71 | 0.98 | 1.26 | 4.57 | 0. | 2.42 |
time (sec) |
N/A |
0.07 |
0.191 |
0.129 |
1.951 |
1.547 |
0. |
1.734 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
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 | 96 | 96 | 69 | 97 | 101 | 348 | 0 | 235 |
normalized size | 1 | 1. | 0.72 | 1.01 | 1.05 | 3.62 | 0. | 2.45 |
time (sec) |
N/A |
0.071 |
0.328 |
0.126 |
2.056 |
1.652 |
0. |
2.575 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
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 | 73 | 73 | 48 | 49 | 62 | 208 | 0 | 62 |
normalized size |
1 |
1. |
0.66 |
0.67 |
0.85 |
2.85 |
0. |
0.85 |
time (sec) |
N/A |
0.057 |
0.099 |
0.119 |
1.539 |
1.461 |
0. |
1.64 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
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 | 109 | 109 | 68 | 69 | 89 | 302 | 0 | 89 |
normalized size |
1 |
1. |
0.62 |
0.63 |
0.82 |
2.77 |
0. |
0.82 |
time (sec) |
N/A |
0.069 |
0.072 |
0.136 |
1.212 |
1.476 |
0. |
1.619 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
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 | 145 | 145 | 88 | 89 | 116 | 398 | 0 | 116 |
normalized size |
1 |
1. |
0.61 |
0.61 |
0.8 |
2.74 |
0. |
0.8 |
time (sec) |
N/A |
0.081 |
0.113 |
0.153 |
1.965 |
1.591 |
0. |
2.013 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
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 | 145 | 145 | 88 | 89 | 116 | 498 | 0 | 116 |
normalized size |
1 |
1. |
0.61 |
0.61 |
0.8 |
3.43 |
0. |
0.8 |
time (sec) |
N/A |
0.078 |
0.118 |
0.174 |
2.733 |
1.669 |
0. |
1.993 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
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 | 195 | 195 | 112 | 180 | 288 | 775 | 0 | 197 |
normalized size |
1 |
1. |
0.57 |
0.92 |
1.48 |
3.97 |
0. |
1.01 |
time (sec) |
N/A |
0.135 |
1.489 |
0.088 |
3.476 |
1.734 |
0. |
5.53 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
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 | 132 | 132 | 50 | 81 | 128 | 250 | 0 | 103 |
normalized size | 1 | 1. | 0.38 | 0.61 | 0.97 | 1.89 | 0. | 0.78 |
time (sec) |
N/A |
0.089 |
0.115 |
0.088 |
2.939 |
1.354 |
0. |
2.775 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 62 | 108 | 163 | 525 | 0 | 123 |
normalized size | 1 | 1. | 0.59 | 1.03 | 1.55 | 5. | 0. | 1.17 |
time (sec) |
N/A |
0.065 |
0.254 |
0.092 |
3.157 |
1.591 |
0. |
2.141 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
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 | 106 | 106 | 73 | 101 | 139 | 522 | 0 | 250 |
normalized size | 1 | 1. | 0.69 | 0.95 | 1.31 | 4.92 | 0. | 2.36 |
time (sec) |
N/A |
0.083 |
0.839 |
0.139 |
2.616 |
1.583 |
0. |
1.819 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
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 | 135 | 135 | 89 | 130 | 128 | 502 | 0 | 313 |
normalized size |
1 |
1. |
0.66 |
0.96 |
0.95 |
3.72 |
0. |
2.32 |
time (sec) |
N/A |
0.086 |
0.171 |
0.148 |
2.681 |
1.598 |
0. |
1.93 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 124 | 158 | 481 | 338 | 0 | 197 |
normalized size | 1 | 1. | 0.98 | 1.24 | 3.79 | 2.66 | 0. | 1.55 |
time (sec) |
N/A |
0.31 |
0.416 |
0.076 |
3.082 |
1.496 |
0. |
2.539 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
B |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 315 | 161 | 389 | 992 | 0 | 182 |
normalized size | 1 | 1. | 2.92 | 1.49 | 3.6 | 9.19 | 0. | 1.69 |
time (sec) |
N/A |
0.318 |
0.42 |
0.125 |
3.729 |
1.597 |
0. |
1.945 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
B |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 120 | 120 | 589 | 195 | 385 | 1187 | 0 | 242 |
normalized size | 1 | 1. | 4.91 | 1.62 | 3.21 | 9.89 | 0. | 2.02 |
time (sec) |
N/A |
0.249 |
6.089 |
0.138 |
3.069 |
1.581 |
0. |
2.401 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
B |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 733 | 229 | 377 | 1191 | 0 | 275 |
normalized size |
1 |
1. |
5.51 |
1.72 |
2.83 |
8.95 |
0. |
2.07 |
time (sec) |
N/A |
0.249 |
6.145 |
0.149 |
3.619 |
1.787 |
0. |
1.735 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 162 | 195 | 394 | 172 | 0 | 548 | 0 | 0 |
normalized size |
1 |
1.2 |
2.43 |
1.06 |
0. |
3.38 |
0. |
0. |
time (sec) |
N/A |
0.923 |
5.54 |
0.464 |
0. |
2.006 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 114 | 89 | 0 | 459 | 0 | 0 |
normalized size | 1 | 1. | 1.13 | 0.88 | 0. | 4.54 | 0. | 0. |
time (sec) |
N/A |
0.185 |
0.328 |
0.502 |
0. |
1.822 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 206 | 125 | 0 | 749 | 0 | 570 |
normalized size | 1 | 1. | 2.31 | 1.4 | 0. | 8.42 | 0. | 6.4 |
time (sec) |
N/A |
0.192 |
0.955 |
0.55 |
0. |
1.936 |
0. |
2.091 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
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 | 163 | 163 | 309 | 170 | 0 | 1025 | 0 | 950 |
normalized size |
1 |
1. |
1.9 |
1.04 |
0. |
6.29 |
0. |
5.83 |
time (sec) |
N/A |
0.377 |
1.568 |
0.701 |
0. |
1.816 |
0. |
2.115 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-1) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 195 | 141 | 139 | 0 | 648 | 0 | 0 |
normalized size |
1 |
1.17 |
0.84 |
0.83 |
0. |
3.88 |
0. |
0. |
time (sec) |
N/A |
0.975 |
5.562 |
0.574 |
0. |
1.902 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
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 | 88 | 88 | 46 | 55 | 196 | 123 | 0 | 0 |
normalized size |
1 |
1. |
0.52 |
0.62 |
2.23 |
1.4 |
0. |
0. |
time (sec) |
N/A |
0.196 |
3.992 |
0.402 |
1.547 |
1.754 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
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 | 121 | 121 | 233 | 144 | 0 | 833 | 0 | 671 |
normalized size |
1 |
1. |
1.93 |
1.19 |
0. |
6.88 |
0. |
5.55 |
time (sec) |
N/A |
0.321 |
0.76 |
0.642 |
0. |
1.846 |
0. |
2.634 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
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 | 197 | 197 | 334 | 196 | 0 | 1123 | 0 | 1058 |
normalized size |
1 |
1. |
1.7 |
0.99 |
0. |
5.7 |
0. |
5.37 |
time (sec) |
N/A |
0.496 |
1.356 |
0.651 |
0. |
1.723 |
0. |
3.102 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 208 | 112 | 87 | 374 | 246 | 0 | 0 |
normalized size |
1 |
1.38 |
0.74 |
0.58 |
2.48 |
1.63 |
0. |
0. |
time (sec) |
N/A |
0.979 |
5.459 |
0.404 |
1.764 |
1.432 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
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 | 118 | 118 | 60 | 67 | 258 | 173 | 0 | 0 |
normalized size |
1 |
1. |
0.51 |
0.57 |
2.19 |
1.47 |
0. |
0. |
time (sec) |
N/A |
0.214 |
5.463 |
0.412 |
1.663 |
1.423 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
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 | 151 | 151 | 261 | 162 | 0 | 934 | 0 | 714 |
normalized size |
1 |
1. |
1.73 |
1.07 |
0. |
6.19 |
0. |
4.73 |
time (sec) |
N/A |
0.429 |
1.193 |
0.733 |
0. |
1.571 |
0. |
2.906 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-1) |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 227 | 227 | 360 | 222 | 0 | 1249 | 0 | 1135 |
normalized size |
1 |
1. |
1.59 |
0.98 |
0. |
5.5 |
0. |
5. |
time (sec) |
N/A |
0.627 |
1.899 |
0.694 |
0. |
1.732 |
0. |
3.194 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-1) |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 241 | 118 | 231 | 0 | 624 | 0 | 1056 |
normalized size |
1 |
1.61 |
0.79 |
1.54 |
0. |
4.16 |
0. |
7.04 |
time (sec) |
N/A |
0.933 |
0.673 |
0.766 |
0. |
1.639 |
0. |
5.889 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 118 | 130 | 0 | 549 | 0 | 594 |
normalized size | 1 | 1. | 1.1 | 1.21 | 0. | 5.13 | 0. | 5.55 |
time (sec) |
N/A |
0.195 |
0.269 |
0.462 |
0. |
1.543 |
0. |
2.823 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 138 | 103 | 0 | 706 | 0 | 502 |
normalized size | 1 | 1. | 2.23 | 1.66 | 0. | 11.39 | 0. | 8.1 |
time (sec) |
N/A |
0.11 |
0.308 |
0.59 |
0. |
1.609 |
0. |
2.219 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F(-1) |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 292 | 144 | 0 | 987 | 0 | 819 |
normalized size |
1 |
1. |
2.16 |
1.07 |
0. |
7.31 |
0. |
6.07 |
time (sec) |
N/A |
0.622 |
0.58 |
0.638 |
0. |
1.463 |
0. |
2.373 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-1) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 195 | 334 | 289 | 0 | 726 | 0 | 0 |
normalized size |
1 |
1.1 |
1.89 |
1.63 |
0. |
4.1 |
0. |
0. |
time (sec) |
N/A |
1.199 |
0.356 |
0.619 |
0. |
1.62 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-1) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 134 | 134 | 128 | 202 | 0 | 644 | 0 | 0 |
normalized size |
1 |
1. |
0.96 |
1.51 |
0. |
4.81 |
0. |
0. |
time (sec) |
N/A |
0.223 |
0.444 |
0.607 |
0. |
1.635 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-1) |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 206 | 134 | 0 | 1133 | 0 | 656 |
normalized size |
1 |
1. |
1.82 |
1.19 |
0. |
10.03 |
0. |
5.81 |
time (sec) |
N/A |
0.229 |
2.198 |
0.591 |
0. |
1.764 |
0. |
2.485 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F(-1) |
B |
F |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 144 | 144 | 294 | 144 | 0 | 1003 | 0 | 828 |
normalized size |
1 |
1. |
2.04 |
1. |
0. |
6.97 |
0. |
5.75 |
time (sec) |
N/A |
0.553 |
0.761 |
0.621 |
0. |
1.572 |
0. |
3.131 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-1) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 207 | 260 | 394 | 353 | 0 | 830 | 0 | 0 |
normalized size |
1 |
1.26 |
1.9 |
1.71 |
0. |
4.01 |
0. |
0. |
time (sec) |
N/A |
1.434 |
0.546 |
0.843 |
0. |
1.901 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-1) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 284 | 266 | 0 | 751 | 0 | 0 |
normalized size |
1 |
1. |
1.7 |
1.59 |
0. |
4.5 |
0. |
0. |
time (sec) |
N/A |
0.303 |
0.408 |
0.648 |
0. |
1.697 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-1) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 451 | 219 | 0 | 1436 | 0 | 0 |
normalized size |
1 |
1. |
3.2 |
1.55 |
0. |
10.18 |
0. |
0. |
time (sec) |
N/A |
0.346 |
0.718 |
0.57 |
0. |
1.859 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-1) |
B |
F(-1) |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 191 | 191 | 332 | 182 | 0 | 1504 | 0 | 975 |
normalized size |
1 |
1. |
1.74 |
0.95 |
0. |
7.87 |
0. |
5.1 |
time (sec) |
N/A |
0.959 |
2.389 |
0.722 |
0. |
1.745 |
0. |
3.16 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 982 | 982 | 318 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.32 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.271 |
3.273 |
0.128 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 290 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.36 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.193 |
2.746 |
0.104 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 2692 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
33.65 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.101 |
23.898 |
0.095 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 2796 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
34.95 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.094 |
22.599 |
0.102 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 119 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 551 | 551 | 128 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.23 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.494 |
0.796 |
0.119 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 126 | 100 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.79 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.216 |
0.513 |
0.105 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.095 |
12.766 |
0.093 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.094 |
9.129 |
0.105 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 269 | 269 | 5199 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
19.33 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.345 |
58.895 |
1.709 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 187 | 187 | 2054 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 10.98 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.227 |
18.053 |
1.421 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.139 |
2.025 |
0.907 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 232 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.15 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.126 |
4.033 |
0.178 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 667 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 4.83 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.275 |
14.178 |
0.41 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 128 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 248 | 248 | 1276 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
5.15 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.422 |
31.232 |
0.451 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 129 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 367 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
3.31 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.124 |
2.198 |
0.847 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 130 |
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 | 163 | 163 | 105 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.64 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.149 |
0.267 |
0.144 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 131 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 63 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.88 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.05 |
0.071 |
0.76 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 43 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.044 |
0.059 |
0.821 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 133 |
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 | 83 | 83 | 68 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.82 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.069 |
0.188 |
0.268 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 134 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-1) |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 83 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.67 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.098 |
0.275 |
0.352 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 135 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 311 | 311 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.355 |
1.064 |
0.152 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 11184 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
71.24 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.248 |
34.458 |
0.12 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 137 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 90 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.22 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.035 |
0.181 |
0.286 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 138 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 47487 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 533.56 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.102 |
99.938 |
0.231 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 139 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.099 |
0.741 |
0.294 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 77 | 96 | 99 | 236 | 0 | 0 |
normalized size |
1 |
1. |
0.88 |
1.09 |
1.12 |
2.68 |
0. |
0. |
time (sec) |
N/A |
0.077 |
0.119 |
0.032 |
1.901 |
1.68 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 141 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 38 | 46 | 58 | 124 | 0 | 1966 |
normalized size | 1 | 1. | 0.69 | 0.84 | 1.05 | 2.25 | 0. | 35.75 |
time (sec) |
N/A |
0.038 |
0.016 |
0.025 |
1.943 |
1.61 |
0. |
2.827 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
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|
|
Problem 142 |
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 | 24 | 24 | 43 | 25 | 30 | 62 | 0 | 31 |
normalized size | 1 | 1. | 1.79 | 1.04 | 1.25 | 2.58 | 0. | 1.29 |
time (sec) |
N/A |
0.021 |
0.033 |
0.019 |
1.698 |
1.505 |
0. |
2.282 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 143 |
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 | 54 | 54 | 60 | 83 | 61 | 167 | 0 | 81 |
normalized size | 1 | 1. | 1.11 | 1.54 | 1.13 | 3.09 | 0. | 1.5 |
time (sec) |
N/A |
0.041 |
0.21 |
0.039 |
1.44 |
1.601 |
0. |
2.007 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 144 |
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 | 81 | 81 | 87 | 136 | 93 | 292 | 0 | 111 |
normalized size | 1 | 1. | 1.07 | 1.68 | 1.15 | 3.6 | 0. | 1.37 |
time (sec) |
N/A |
0.052 |
0.239 |
0.04 |
1.281 |
1.536 |
0. |
2.1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 145 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 81 | 98 | 88 | 182 | 0 | 0 |
normalized size |
1 |
1. |
1.12 |
1.36 |
1.22 |
2.53 |
0. |
0. |
time (sec) |
N/A |
0.078 |
0.038 |
0.032 |
2.133 |
1.815 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 146 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 38 | 47 | 59 | 53 | 108 | 0 | 1361 |
normalized size | 1 | 1. | 1.24 | 1.55 | 1.39 | 2.84 | 0. | 35.82 |
time (sec) |
N/A |
0.059 |
0.033 |
0.026 |
2.723 |
1.705 |
0. |
8.562 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 147 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 75 | 57 | 73 | 236 | 0 | 146 |
normalized size | 1 | 1. | 1.83 | 1.39 | 1.78 | 5.76 | 0. | 3.56 |
time (sec) |
N/A |
0.053 |
0.031 |
0.029 |
2.207 |
1.836 |
0. |
2.308 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 148 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 125 | 106 | 124 | 425 | 0 | 190 |
normalized size | 1 | 1. | 1.52 | 1.29 | 1.51 | 5.18 | 0. | 2.32 |
time (sec) |
N/A |
0.08 |
0.042 |
0.036 |
1.873 |
1.864 |
0. |
2.177 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 149 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 164 | 159 | 169 | 620 | 0 | 269 |
normalized size |
1 |
1. |
1.34 |
1.3 |
1.39 |
5.08 |
0. |
2.2 |
time (sec) |
N/A |
0.097 |
0.06 |
0.039 |
2.7 |
1.706 |
0. |
2.224 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 150 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 108 | 172 | 142 | 348 | 0 | 0 |
normalized size |
1 |
1. |
0.97 |
1.55 |
1.28 |
3.14 |
0. |
0. |
time (sec) |
N/A |
0.173 |
0.432 |
0.049 |
1.676 |
1.548 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 151 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 64 | 82 | 95 | 186 | 0 | 10604 |
normalized size | 1 | 1. | 0.82 | 1.05 | 1.22 | 2.38 | 0. | 135.95 |
time (sec) |
N/A |
0.071 |
0.136 |
0.039 |
1.631 |
1.609 |
0. |
5.72 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 152 |
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 | 46 | 46 | 46 | 45 | 54 | 108 | 0 | 55 |
normalized size | 1 | 1. | 1. | 0.98 | 1.17 | 2.35 | 0. | 1.2 |
time (sec) |
N/A |
0.039 |
0.023 |
0.023 |
1.893 |
1.58 |
0. |
2.322 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 153 |
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 | 84 | 84 | 70 | 120 | 93 | 271 | 0 | 134 |
normalized size | 1 | 1. | 0.83 | 1.43 | 1.11 | 3.23 | 0. | 1.6 |
time (sec) |
N/A |
0.073 |
0.236 |
0.053 |
1.568 |
1.521 |
0. |
2.313 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 154 |
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 | 126 | 126 | 107 | 220 | 142 | 437 | 0 | 186 |
normalized size |
1 |
1. |
0.85 |
1.75 |
1.13 |
3.47 |
0. |
1.48 |
time (sec) |
N/A |
0.104 |
0.757 |
0.047 |
1.403 |
1.629 |
0. |
2.223 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 155 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 176 | 185 | 161 | 281 | 0 | 0 |
normalized size |
1 |
1. |
1.18 |
1.24 |
1.08 |
1.89 |
0. |
0. |
time (sec) |
N/A |
0.162 |
0.687 |
0.044 |
2.5 |
1.464 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 156 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 77 | 116 | 112 | 190 | 0 | 10355 |
normalized size | 1 | 1. | 0.82 | 1.23 | 1.19 | 2.02 | 0. | 110.16 |
time (sec) |
N/A |
0.122 |
0.457 |
0.039 |
2.52 |
1.37 |
0. |
30.612 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 157 |
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 | 78 | 78 | 116 | 102 | 107 | 308 | 0 | 200 |
normalized size | 1 | 1. | 1.49 | 1.31 | 1.37 | 3.95 | 0. | 2.56 |
time (sec) |
N/A |
0.086 |
0.416 |
0.039 |
2.595 |
1.65 |
0. |
2.237 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 158 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 293 | 199 | 186 | 539 | 0 | 325 |
normalized size | 1 | 1. | 2.2 | 1.5 | 1.4 | 4.05 | 0. | 2.44 |
time (sec) |
N/A |
0.149 |
6.233 |
0.049 |
2.453 |
1.827 |
0. |
2.059 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 159 |
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 | 202 | 202 | 351 | 302 | 247 | 786 | 0 | 455 |
normalized size |
1 |
1. |
1.74 |
1.5 |
1.22 |
3.89 |
0. |
2.25 |
time (sec) |
N/A |
0.169 |
1.093 |
0.052 |
1.676 |
1.639 |
0. |
2.779 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 160 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 141 | 279 | 219 | 470 | 0 | 0 |
normalized size |
1 |
1. |
0.94 |
1.86 |
1.46 |
3.13 |
0. |
0. |
time (sec) |
N/A |
0.242 |
0.263 |
0.056 |
1.546 |
1.721 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 161 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 90 | 139 | 153 | 277 | 0 | 0 |
normalized size |
1 |
1. |
0.86 |
1.32 |
1.46 |
2.64 |
0. |
0. |
time (sec) |
N/A |
0.114 |
0.19 |
0.046 |
1.707 |
1.606 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 162 |
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 | 67 | 67 | 67 | 64 | 77 | 158 | 0 | 78 |
normalized size | 1 | 1. | 1. | 0.96 | 1.15 | 2.36 | 0. | 1.16 |
time (sec) |
N/A |
0.045 |
0.025 |
0.027 |
1.567 |
1.492 |
0. |
2. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 163 |
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 | 116 | 116 | 97 | 165 | 132 | 358 | 0 | 177 |
normalized size | 1 | 1. | 0.84 | 1.42 | 1.14 | 3.09 | 0. | 1.53 |
time (sec) |
N/A |
0.094 |
0.321 |
0.065 |
1.9 |
1.563 |
0. |
2.022 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 164 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 144 | 316 | 192 | 536 | 0 | 250 |
normalized size |
1 |
1. |
0.87 |
1.92 |
1.16 |
3.25 |
0. |
1.52 |
time (sec) |
N/A |
0.141 |
1.164 |
0.062 |
1.354 |
1.6 |
0. |
2.141 |
|
|
|
|
|
|
|
|
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|
|
|
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|
Problem 165 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 220 | 226 | 268 | 225 | 369 | 0 | 0 |
normalized size |
1 |
1. |
1.03 |
1.22 |
1.02 |
1.68 |
0. |
0. |
time (sec) |
N/A |
0.224 |
0.678 |
0.058 |
1.824 |
1.593 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 166 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 146 | 146 | 113 | 169 | 161 | 271 | 0 | 0 |
normalized size |
1 |
1. |
0.77 |
1.16 |
1.1 |
1.86 |
0. |
0. |
time (sec) |
N/A |
0.169 |
0.729 |
0.047 |
3.013 |
1.485 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 167 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 143 | 125 | 128 | 370 | 0 | 269 |
normalized size | 1 | 1. | 1.4 | 1.23 | 1.25 | 3.63 | 0. | 2.64 |
time (sec) |
N/A |
0.112 |
1.295 |
0.052 |
1.515 |
1.605 |
0. |
2.628 |
|
|
|
|
|
|
|
|
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|
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|
Problem 168 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 355 | 264 | 252 | 699 | 0 | 568 |
normalized size |
1 |
1. |
1.83 |
1.36 |
1.3 |
3.6 |
0. |
2.93 |
time (sec) |
N/A |
0.184 |
6.236 |
0.062 |
2.21 |
1.652 |
0. |
2.652 |
|
|
|
|
|
|
|
|
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|
|
|
|
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|
Problem 169 |
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 | 291 | 291 | 346 | 415 | 340 | 1014 | 0 | 636 |
normalized size |
1 |
1. |
1.19 |
1.43 |
1.17 |
3.48 |
0. |
2.19 |
time (sec) |
N/A |
0.231 |
2.578 |
0.063 |
2.641 |
1.832 |
0. |
2.013 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 170 |
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 | 204 | 204 | 184 | 304 | 389 | 594 | 0 | 463 |
normalized size | 1 | 1. | 0.9 | 1.49 | 1.91 | 2.91 | 0. | 2.27 |
time (sec) |
N/A |
0.363 |
1.462 |
0.066 |
1.826 |
2.474 |
0. |
5.118 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 171 |
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 | 126 | 126 | 117 | 164 | 192 | 367 | 0 | 239 |
normalized size | 1 | 1. | 0.93 | 1.3 | 1.52 | 2.91 | 0. | 1.9 |
time (sec) |
N/A |
0.191 |
0.484 |
0.059 |
1.536 |
1.961 |
0. |
1.98 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 172 |
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 | 74 | 74 | 87 | 76 | 88 | 157 | 0 | 96 |
normalized size | 1 | 1. | 1.18 | 1.03 | 1.19 | 2.12 | 0. | 1.3 |
time (sec) |
N/A |
0.066 |
0.086 |
0.049 |
1.551 |
1.611 |
0. |
1.3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 173 |
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 | 34 | 34 | 34 | 35 | 45 | 80 | 0 | 47 |
normalized size | 1 | 1. | 1. | 1.03 | 1.32 | 2.35 | 0. | 1.38 |
time (sec) |
N/A |
0.04 |
0.02 |
0.026 |
1.465 |
1.57 |
0. |
1.695 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 174 |
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 | 84 | 84 | 65 | 106 | 104 | 271 | 0 | 154 |
normalized size | 1 | 1. | 0.77 | 1.26 | 1.24 | 3.23 | 0. | 1.83 |
time (sec) |
N/A |
0.089 |
0.161 |
0.063 |
1.616 |
1.596 |
0. |
2.011 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 175 |
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 | 148 | 148 | 115 | 216 | 188 | 629 | 0 | 271 |
normalized size | 1 | 1. | 0.78 | 1.46 | 1.27 | 4.25 | 0. | 1.83 |
time (sec) |
N/A |
0.138 |
3.847 |
0.063 |
1.463 |
1.663 |
0. |
1.538 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 176 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 177 | 195 | 269 | 0 | 1054 | 0 | 325 |
normalized size |
1 |
1. |
1.1 |
1.52 |
0. |
5.95 |
0. |
1.84 |
time (sec) |
N/A |
0.239 |
1.419 |
0.067 |
0. |
1.639 |
0. |
3.306 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 177 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 152 | 117 | 0 | 684 | 0 | 144 |
normalized size |
1 |
1. |
1.58 |
1.22 |
0. |
7.12 |
0. |
1.5 |
time (sec) |
N/A |
0.099 |
0.203 |
0.053 |
0. |
1.67 |
0. |
2.053 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 178 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 108 | 155 | 0 | 801 | 0 | 174 |
normalized size |
1 |
1. |
1.35 |
1.94 |
0. |
10.01 |
0. |
2.17 |
time (sec) |
N/A |
0.243 |
0.236 |
0.06 |
0. |
1.742 |
0. |
1.87 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 179 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 154 | 350 | 348 | 0 | 1507 | 0 | 369 |
normalized size |
1 |
1. |
2.27 |
2.26 |
0. |
9.79 |
0. |
2.4 |
time (sec) |
N/A |
0.426 |
6.119 |
0.069 |
0. |
2.929 |
0. |
1.911 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 180 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 307 | 307 | 504 | 629 | 0 | 2566 | 0 | 662 |
normalized size |
1 |
1. |
1.64 |
2.05 |
0. |
8.36 |
0. |
2.16 |
time (sec) |
N/A |
1.106 |
1.386 |
0.073 |
0. |
4.834 |
0. |
2.212 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 181 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 242 | 242 | 240 | 318 | 682 | 1231 | 0 | 667 |
normalized size | 1 | 1. | 0.99 | 1.31 | 2.82 | 5.09 | 0. | 2.76 |
time (sec) |
N/A |
0.633 |
6.252 |
0.093 |
1.828 |
3.386 |
0. |
4.672 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 182 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 145 | 182 | 370 | 869 | 0 | 335 |
normalized size | 1 | 1. | 0.9 | 1.13 | 2.3 | 5.4 | 0. | 2.08 |
time (sec) |
N/A |
0.312 |
0.719 |
0.087 |
1.753 |
2.394 |
0. |
1.843 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 183 |
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 | 109 | 109 | 162 | 132 | 167 | 463 | 0 | 211 |
normalized size | 1 | 1. | 1.49 | 1.21 | 1.53 | 4.25 | 0. | 1.94 |
time (sec) |
N/A |
0.096 |
0.287 |
0.078 |
1.764 |
1.695 |
0. |
1.284 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 184 |
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 | 53 | 53 | 42 | 54 | 63 | 176 | 0 | 69 |
normalized size | 1 | 1. | 0.79 | 1.02 | 1.19 | 3.32 | 0. | 1.3 |
time (sec) |
N/A |
0.053 |
0.076 |
0.038 |
1.47 |
1.637 |
0. |
1.499 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 185 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 114 | 96 | 150 | 157 | 599 | 0 | 223 |
normalized size | 1 | 1. | 0.84 | 1.32 | 1.38 | 5.25 | 0. | 1.96 |
time (sec) |
N/A |
0.115 |
0.608 |
0.089 |
1.364 |
1.619 |
0. |
1.976 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 186 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 188 | 187 | 282 | 255 | 1241 | 0 | 375 |
normalized size | 1 | 1. | 0.99 | 1.5 | 1.36 | 6.6 | 0. | 1.99 |
time (sec) |
N/A |
0.181 |
6.144 |
0.098 |
1.734 |
2.294 |
0. |
1.811 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 187 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 333 | 333 | 341 | 382 | 0 | 1790 | 0 | 548 |
normalized size |
1 |
1. |
1.02 |
1.15 |
0. |
5.38 |
0. |
1.65 |
time (sec) |
N/A |
0.627 |
1.967 |
0.098 |
0. |
2.504 |
0. |
2.784 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 188 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 200 | 200 | 169 | 282 | 0 | 1261 | 0 | 339 |
normalized size |
1 |
1. |
0.84 |
1.41 |
0. |
6.3 |
0. |
1.7 |
time (sec) |
N/A |
0.301 |
1.012 |
0.088 |
0. |
1.958 |
0. |
2.152 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 189 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 139 | 245 | 0 | 1681 | 0 | 294 |
normalized size |
1 |
1. |
1.21 |
2.13 |
0. |
14.62 |
0. |
2.56 |
time (sec) |
N/A |
0.453 |
0.746 |
0.086 |
0. |
2.816 |
0. |
1.715 |
|
|
|
|
|
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|
|
Problem 190 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 238 | 238 | 403 | 527 | 0 | 2639 | 0 | 481 |
normalized size |
1 |
1. |
1.69 |
2.21 |
0. |
11.09 |
0. |
2.02 |
time (sec) |
N/A |
0.695 |
6.295 |
0.096 |
0. |
3.101 |
0. |
1.859 |
|
|
|
|
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|
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|
Problem 191 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 424 | 424 | 361 | 897 | 0 | 4674 | 0 | 805 |
normalized size |
1 |
1. |
0.85 |
2.12 |
0. |
11.02 |
0. |
1.9 |
time (sec) |
N/A |
1.493 |
1.592 |
0.108 |
0. |
5.532 |
0. |
1.37 |
|
|
|
|
|
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|
Problem 192 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 321 | 321 | 304 | 465 | 986 | 2206 | 0 | 790 |
normalized size |
1 |
1. |
0.95 |
1.45 |
3.07 |
6.87 |
0. |
2.46 |
time (sec) |
N/A |
0.877 |
6.341 |
0.116 |
1.303 |
6.427 |
0. |
3.708 |
|
|
|
|
|
|
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|
Problem 193 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 232 | 232 | 196 | 323 | 595 | 1727 | 0 | 626 |
normalized size | 1 | 1. | 0.84 | 1.39 | 2.56 | 7.44 | 0. | 2.7 |
time (sec) |
N/A |
0.482 |
2.189 |
0.109 |
1.876 |
3.964 |
0. |
2.1 |
|
|
|
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|
Problem 194 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 213 | 198 | 308 | 995 | 0 | 347 |
normalized size | 1 | 1. | 1.43 | 1.33 | 2.07 | 6.68 | 0. | 2.33 |
time (sec) |
N/A |
0.132 |
2.02 |
0.1 |
1.915 |
2.649 |
0. |
1.582 |
|
|
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|
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|
Problem 195 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 60 | 74 | 109 | 365 | 0 | 93 |
normalized size | 1 | 1. | 0.8 | 0.99 | 1.45 | 4.87 | 0. | 1.24 |
time (sec) |
N/A |
0.06 |
0.262 |
0.046 |
1.547 |
2.004 |
0. |
1.746 |
|
|
|
|
|
|
|
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|
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|
Problem 196 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 121 | 194 | 211 | 911 | 0 | 208 |
normalized size | 1 | 1. | 0.83 | 1.34 | 1.46 | 6.28 | 0. | 1.43 |
time (sec) |
N/A |
0.133 |
0.931 |
0.111 |
1.921 |
2.342 |
0. |
1.8 |
|
|
|
|
|
|
|
|
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|
|
|
|
|
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|
Problem 197 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 221 | 195 | 348 | 319 | 1708 | 0 | 441 |
normalized size | 1 | 1. | 0.88 | 1.57 | 1.44 | 7.73 | 0. | 2. |
time (sec) |
N/A |
0.211 |
5.327 |
0.114 |
1.612 |
2.424 |
0. |
2.104 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 198 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 474 | 474 | 351 | 922 | 0 | 2765 | 0 | 853 |
normalized size |
1 |
1. |
0.74 |
1.95 |
0. |
5.83 |
0. |
1.8 |
time (sec) |
N/A |
0.872 |
1.043 |
0.131 |
0. |
2.853 |
0. |
3.399 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 199 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 350 | 350 | 212 | 766 | 0 | 2067 | 0 | 518 |
normalized size |
1 |
1. |
0.61 |
2.19 |
0. |
5.91 |
0. |
1.48 |
time (sec) |
N/A |
0.539 |
3.291 |
0.115 |
0. |
2.322 |
0. |
1.956 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 200 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 202 | 202 | 195 | 729 | 0 | 3044 | 0 | 458 |
normalized size |
1 |
1. |
0.97 |
3.61 |
0. |
15.07 |
0. |
2.27 |
time (sec) |
N/A |
0.788 |
5.784 |
0.116 |
0. |
5.548 |
0. |
1.552 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 201 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 289 | 289 | 459 | 780 | 0 | 4578 | 0 | 609 |
normalized size |
1 |
1. |
1.59 |
2.7 |
0. |
15.84 |
0. |
2.11 |
time (sec) |
N/A |
1.072 |
6.211 |
0.134 |
0. |
5.542 |
0. |
2.051 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 202 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 492 | 492 | 448 | 1252 | 0 | 6091 | 0 | 987 |
normalized size |
1 |
1. |
0.91 |
2.54 |
0. |
12.38 |
0. |
2.01 |
time (sec) |
N/A |
2.127 |
1.705 |
0.138 |
0. |
6.517 |
0. |
1.85 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 203 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 271 | 271 | 4791 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
17.68 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.38 |
18.403 |
1.514 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 204 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 186 | 186 | 2464 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 13.25 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.242 |
14.208 |
1.446 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 205 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 849 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 6.58 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.148 |
8.262 |
0.904 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 206 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
B |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 284 | 0 | 864 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 3.04 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.048 |
13.498 |
0.362 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 207 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
F |
F |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 737 | 0 | 908 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 1.23 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.045 |
14.227 |
0.677 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 208 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.04 |
2.695 |
0.862 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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 [159] had the largest ratio of [ 0.4762
]
|
|
|
|
|
|
|
| Table 2.1Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
2 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
3 |
A |
3 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
4 |
A |
3 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
5 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
6 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
7 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
8 |
A |
9 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
9 |
A |
8 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
10 |
A |
5 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
11 |
A |
7 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
12 |
A |
9 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
13 |
A |
11 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
14 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
15 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
16 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
17 |
A |
2 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
18 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
19 |
A |
14 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
20 |
A |
4 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
|
21 |
A |
6 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
22 |
A |
1 |
1 |
1. |
12 |
0.083 |
|
|
|
|
|
|
|
23 |
A |
8 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
24 |
A |
12 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
25 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
26 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
27 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
28 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
29 |
A |
9 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
30 |
A |
10 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
31 |
A |
8 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
32 |
A |
7 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
33 |
A |
10 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
34 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
35 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
36 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
37 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
38 |
A |
13 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
39 |
A |
11 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
40 |
A |
10 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
|
41 |
A |
12 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
42 |
A |
17 |
8 |
1. |
21 |
0.381 |
|
|
|
|
|
|
|
43 |
A |
21 |
8 |
1. |
21 |
0.381 |
|
|
|
|
|
|
|
44 |
A |
8 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
45 |
A |
7 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
46 |
A |
6 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
47 |
A |
5 |
5 |
1.57 |
19 |
0.263 |
|
|
|
|
|
|
|
48 |
A |
4 |
4 |
1. |
19 |
0.21 |
|
|
|
|
|
|
|
49 |
A |
5 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
50 |
A |
5 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
51 |
A |
6 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
52 |
A |
6 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
53 |
A |
6 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
54 |
A |
6 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
55 |
A |
5 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
56 |
A |
1 |
1 |
1. |
12 |
0.083 |
|
|
|
|
|
|
|
57 |
A |
4 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
58 |
A |
5 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
59 |
A |
6 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
60 |
A |
7 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
|
61 |
A |
4 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
62 |
A |
4 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
63 |
A |
4 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
64 |
A |
4 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
65 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
66 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
67 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
68 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
69 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
70 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
71 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
72 |
A |
4 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
73 |
A |
4 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
74 |
A |
4 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
75 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
76 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
77 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
78 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
79 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
80 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
|
81 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
82 |
A |
4 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
83 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
84 |
A |
4 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
85 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
86 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
87 |
A |
17 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
88 |
A |
14 |
8 |
1. |
21 |
0.381 |
|
|
|
|
|
|
|
89 |
A |
14 |
8 |
1. |
21 |
0.381 |
|
|
|
|
|
|
|
90 |
A |
16 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
91 |
A |
15 |
10 |
1.2 |
23 |
0.435 |
|
|
|
|
|
|
|
92 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
93 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
94 |
A |
7 |
7 |
1. |
23 |
0.304 |
|
|
|
|
|
|
|
95 |
A |
14 |
9 |
1.17 |
23 |
0.391 |
|
|
|
|
|
|
|
96 |
A |
3 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
97 |
A |
5 |
5 |
1. |
23 |
0.217 |
|
|
|
|
|
|
|
98 |
A |
8 |
8 |
1. |
23 |
0.348 |
|
|
|
|
|
|
|
99 |
A |
10 |
7 |
1.38 |
23 |
0.304 |
|
|
|
|
|
|
|
100 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
|
101 |
A |
6 |
5 |
1. |
23 |
0.217 |
|
|
|
|
|
|
|
102 |
A |
10 |
8 |
1. |
23 |
0.348 |
|
|
|
|
|
|
|
103 |
A |
17 |
9 |
1.61 |
23 |
0.391 |
|
|
|
|
|
|
|
104 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
105 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
106 |
A |
11 |
7 |
1. |
23 |
0.304 |
|
|
|
|
|
|
|
107 |
A |
20 |
9 |
1.1 |
23 |
0.391 |
|
|
|
|
|
|
|
108 |
A |
5 |
5 |
1. |
23 |
0.217 |
|
|
|
|
|
|
|
109 |
A |
6 |
5 |
1. |
23 |
0.217 |
|
|
|
|
|
|
|
110 |
A |
10 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
111 |
A |
23 |
9 |
1.26 |
23 |
0.391 |
|
|
|
|
|
|
|
112 |
A |
6 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
113 |
A |
7 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
114 |
A |
16 |
8 |
1. |
23 |
0.348 |
|
|
|
|
|
|
|
115 |
A |
10 |
9 |
1. |
23 |
0.391 |
|
|
|
|
|
|
|
116 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
117 |
A |
3 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
118 |
A |
3 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
119 |
A |
8 |
7 |
1. |
23 |
0.304 |
|
|
|
|
|
|
|
120 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
|
121 |
A |
3 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
122 |
A |
3 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
123 |
A |
10 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
124 |
A |
8 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
125 |
A |
6 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
126 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
127 |
A |
10 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
128 |
A |
13 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
129 |
A |
4 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
130 |
A |
4 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
131 |
A |
3 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
132 |
A |
2 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
133 |
A |
3 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
134 |
A |
4 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
135 |
A |
6 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
136 |
A |
5 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
137 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
138 |
A |
3 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
139 |
A |
3 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
140 |
A |
6 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
|
141 |
A |
5 |
4 |
1. |
17 |
0.235 |
|
|
|
|
|
|
|
142 |
A |
3 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
143 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
144 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
145 |
A |
8 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
146 |
A |
7 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
147 |
A |
7 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
148 |
A |
9 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
149 |
A |
11 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
150 |
A |
7 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
151 |
A |
6 |
4 |
1. |
19 |
0.21 |
|
|
|
|
|
|
|
152 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
153 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
154 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
155 |
A |
13 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
156 |
A |
11 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
157 |
A |
9 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
158 |
A |
13 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
159 |
A |
16 |
10 |
1. |
21 |
0.476 |
|
|
|
|
|
|
|
160 |
A |
7 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
|
161 |
A |
6 |
4 |
1. |
19 |
0.21 |
|
|
|
|
|
|
|
162 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
163 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
164 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
165 |
A |
16 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
166 |
A |
14 |
10 |
1. |
21 |
0.476 |
|
|
|
|
|
|
|
167 |
A |
11 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
168 |
A |
17 |
10 |
1. |
21 |
0.476 |
|
|
|
|
|
|
|
169 |
A |
21 |
10 |
1. |
21 |
0.476 |
|
|
|
|
|
|
|
170 |
A |
5 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
171 |
A |
4 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
172 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
173 |
A |
4 |
4 |
1. |
19 |
0.21 |
|
|
|
|
|
|
|
174 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
175 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
176 |
A |
13 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
177 |
A |
8 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
178 |
A |
7 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
179 |
A |
7 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
180 |
A |
9 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
|
181 |
A |
5 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
182 |
A |
4 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
183 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
184 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
185 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
186 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
187 |
A |
16 |
8 |
1. |
21 |
0.381 |
|
|
|
|
|
|
|
188 |
A |
12 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
189 |
A |
8 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
190 |
A |
8 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
191 |
A |
10 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
192 |
A |
5 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
193 |
A |
4 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
194 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
195 |
A |
3 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
196 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
197 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
198 |
A |
22 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
199 |
A |
18 |
8 |
1. |
21 |
0.381 |
|
|
|
|
|
|
|
200 |
A |
9 |
8 |
1. |
21 |
0.381 |
|
|
|
|
|
|
|
|
201 |
A |
9 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
202 |
A |
11 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
203 |
A |
10 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
204 |
A |
8 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
205 |
A |
6 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
206 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
207 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
208 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|