Detailed conclusion table per each integral is given by the 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 as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 62 | 0 | 24 | 1778 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 2.38 | 0.00 | 0.92 | 68.38 | 0.92 |
time (sec) |
N/A | 0.288 | 1.603 | 0.476 | 0.000 | 0.113 | 0.000 | 0.191 | 0.671 | 0.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | F(-2) | F(-1) | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 275 | 255 | 0 | 0 | 0 | 0 | 0 | 77 | 0 |
N.S. |
1 | 1.45 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 1.535 | 0.726 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.367 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | F(-2) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 414 | 311 | 0 | 0 | 0 | 0 | 0 | 77 | 0 |
N.S. |
1 | 1.85 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 3.410 | 0.616 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.378 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | F(-2) | F(-1) | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 411 | 261 | 0 | 0 | 0 | 0 | 0 | 550 | 0 |
N.S. |
1 | 1.85 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.48 | 0.00 |
time (sec) |
N/A | 2.126 | 0.714 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.353 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | F(-2) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 268 | 300 | 0 | 0 | 0 | 0 | 0 | 572 | 0 |
N.S. |
1 | 1.46 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.13 | 0.00 |
time (sec) |
N/A | 1.856 | 0.400 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 0 | 76 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 2.92 | 0.92 |
time (sec) |
N/A | 2.356 | 8.745 | 0.334 | 0.000 | 0.000 | 0.000 | 0.000 | 0.255 | 0.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 24 | 78 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.92 | 3.00 | 0.92 |
time (sec) |
N/A | 3.069 | 8.676 | 0.387 | 0.000 | 0.000 | 0.000 | 0.177 | 0.240 | 0.635 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 0 | 78 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 3.00 | 0.92 |
time (sec) |
N/A | 1.197 | 14.131 | 0.392 | 0.000 | 0.000 | 0.000 | 0.000 | 0.261 | 0.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 24 | 78 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.92 | 3.00 | 0.92 |
time (sec) |
N/A | 1.197 | 36.706 | 0.402 | 0.000 | 0.000 | 0.000 | 0.182 | 0.253 | 0.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 0 | 22 | 19 | 22 | 25 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 0.00 | 1.10 | 0.95 | 1.10 | 1.25 | 1.10 |
time (sec) |
N/A | 0.287 | 0.758 | 0.112 | 0.000 | 0.120 | 0.561 | 0.133 | 0.198 | 0.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 21 | 0 | 21 | 0 | 20 | 22 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 0.00 | 1.05 | 0.00 | 1.00 | 1.10 | 1.00 |
time (sec) |
N/A | 0.202 | 0.005 | 0.313 | 0.000 | 0.107 | 0.000 | 0.114 | 0.201 | 0.669 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 28 | 30 | 30 | 0 | 30 | 32 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.07 | 0.00 | 1.07 | 1.14 | 1.07 |
time (sec) |
N/A | 0.264 | 0.579 | 1.407 | 0.517 | 0.101 | 0.000 | 0.349 | 0.225 | 0.952 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 87 | 127 | 108 | 108 | 110 | 138 | 138 | 117 | 105 |
N.S. |
1 | 0.81 | 1.19 | 1.01 | 1.01 | 1.03 | 1.29 | 1.29 | 1.09 | 0.98 |
time (sec) |
N/A | 0.326 | 0.009 | 0.355 | 0.133 | 0.092 | 0.383 | 0.156 | 0.210 | 0.954 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 93 | 119 | 104 | 105 | 107 | 128 | 115 | 115 | 101 |
N.S. |
1 | 0.99 | 1.27 | 1.11 | 1.12 | 1.14 | 1.36 | 1.22 | 1.22 | 1.07 |
time (sec) |
N/A | 0.330 | 0.018 | 0.299 | 0.039 | 0.093 | 0.339 | 0.126 | 0.199 | 0.910 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 83 | 103 | 87 | 88 | 89 | 114 | 97 | 97 | 85 |
N.S. |
1 | 1.01 | 1.26 | 1.06 | 1.07 | 1.09 | 1.39 | 1.18 | 1.18 | 1.04 |
time (sec) |
N/A | 0.282 | 0.006 | 0.416 | 0.119 | 0.089 | 0.287 | 0.223 | 0.185 | 0.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 67 | 85 | 76 | 80 | 82 | 94 | 90 | 90 | 75 |
N.S. |
1 | 0.99 | 1.25 | 1.12 | 1.18 | 1.21 | 1.38 | 1.32 | 1.32 | 1.10 |
time (sec) |
N/A | 0.270 | 0.007 | 0.155 | 0.052 | 0.088 | 0.255 | 0.128 | 0.201 | 0.839 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 83 | 120 | 104 | 0 | 0 | 0 | 67 | 88 |
N.S. |
1 | 1.00 | 1.08 | 1.56 | 1.35 | 0.00 | 0.00 | 0.00 | 0.87 | 1.14 |
time (sec) |
N/A | 0.293 | 0.001 | 0.230 | 0.320 | 0.000 | 0.000 | 0.000 | 0.207 | 1.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 61 | 73 | 74 | 73 | 74 | 80 | 86 | 86 | 69 |
N.S. |
1 | 1.07 | 1.28 | 1.30 | 1.28 | 1.30 | 1.40 | 1.51 | 1.51 | 1.21 |
time (sec) |
N/A | 0.292 | 0.005 | 0.160 | 0.041 | 0.106 | 0.300 | 0.127 | 0.209 | 0.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 86 | 129 | 0 | 0 | 0 | 0 | 64 | 91 |
N.S. |
1 | 1.00 | 1.12 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 1.18 |
time (sec) |
N/A | 0.305 | 0.006 | 0.263 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 1.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 79 | 98 | 97 | 93 | 85 | 116 | 101 | 101 | 92 |
N.S. |
1 | 0.95 | 1.18 | 1.17 | 1.12 | 1.02 | 1.40 | 1.22 | 1.22 | 1.11 |
time (sec) |
N/A | 0.314 | 0.024 | 0.165 | 0.035 | 0.134 | 0.345 | 0.118 | 0.195 | 0.904 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 72 | 97 | 96 | 80 | 75 | 99 | 128 | 88 | 162 |
N.S. |
1 | 0.91 | 1.23 | 1.22 | 1.01 | 0.95 | 1.25 | 1.62 | 1.11 | 2.05 |
time (sec) |
N/A | 0.277 | 0.007 | 0.202 | 0.128 | 0.082 | 0.265 | 0.182 | 0.190 | 0.931 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 105 | 131 | 119 | 116 | 111 | 153 | 124 | 124 | 111 |
N.S. |
1 | 0.95 | 1.19 | 1.08 | 1.05 | 1.01 | 1.39 | 1.13 | 1.13 | 1.01 |
time (sec) |
N/A | 0.340 | 0.031 | 0.173 | 0.041 | 0.109 | 0.476 | 0.118 | 0.192 | 0.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 86 | 97 | 109 | 103 | 98 | 122 | 148 | 108 | 130 |
N.S. |
1 | 0.82 | 0.92 | 1.04 | 0.98 | 0.93 | 1.16 | 1.41 | 1.03 | 1.24 |
time (sec) |
N/A | 0.286 | 0.007 | 0.213 | 0.144 | 0.091 | 0.342 | 0.308 | 0.199 | 0.921 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 182 | 173 | 197 | 184 | 201 | 260 | 220 | 220 | 374 |
N.S. |
1 | 0.98 | 0.94 | 1.06 | 0.99 | 1.09 | 1.41 | 1.19 | 1.19 | 2.02 |
time (sec) |
N/A | 0.490 | 0.065 | 0.381 | 0.115 | 0.096 | 0.511 | 0.221 | 0.190 | 0.867 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 157 | 162 | 181 | 181 | 186 | 245 | 211 | 211 | 191 |
N.S. |
1 | 0.98 | 1.01 | 1.12 | 1.12 | 1.16 | 1.52 | 1.31 | 1.31 | 1.19 |
time (sec) |
N/A | 0.492 | 0.077 | 0.348 | 0.036 | 0.116 | 0.452 | 0.126 | 0.186 | 1.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 140 | 186 | 156 | 166 | 219 | 223 | 185 | 167 |
N.S. |
1 | 1.00 | 1.22 | 1.62 | 1.36 | 1.44 | 1.90 | 1.94 | 1.61 | 1.45 |
time (sec) |
N/A | 0.329 | 0.054 | 0.453 | 0.123 | 0.102 | 0.400 | 0.238 | 0.191 | 0.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 122 | 130 | 137 | 147 | 150 | 194 | 172 | 172 | 150 |
N.S. |
1 | 0.98 | 1.05 | 1.10 | 1.19 | 1.21 | 1.56 | 1.39 | 1.39 | 1.21 |
time (sec) |
N/A | 0.418 | 0.047 | 0.190 | 0.036 | 0.105 | 0.355 | 0.233 | 0.219 | 1.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 123 | 175 | 172 | 0 | 0 | 0 | 141 | 157 |
N.S. |
1 | 1.00 | 0.90 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 1.03 | 1.15 |
time (sec) |
N/A | 0.415 | 0.068 | 0.308 | 0.330 | 0.000 | 0.000 | 0.000 | 0.206 | 1.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 111 | 114 | 134 | 130 | 140 | 165 | 164 | 164 | 135 |
N.S. |
1 | 1.02 | 1.05 | 1.23 | 1.19 | 1.28 | 1.51 | 1.50 | 1.50 | 1.24 |
time (sec) |
N/A | 0.441 | 0.065 | 0.223 | 0.050 | 0.107 | 0.429 | 0.123 | 0.198 | 1.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | F | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 118 | 178 | 153 | 0 | 0 | 0 | 139 | 157 |
N.S. |
1 | 1.00 | 0.92 | 1.39 | 1.20 | 0.00 | 0.00 | 0.00 | 1.09 | 1.23 |
time (sec) |
N/A | 0.398 | 0.077 | 0.379 | 0.294 | 0.000 | 0.000 | 0.000 | 0.197 | 1.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 112 | 119 | 139 | 135 | 139 | 180 | 171 | 171 | 142 |
N.S. |
1 | 0.97 | 1.03 | 1.21 | 1.17 | 1.21 | 1.57 | 1.49 | 1.49 | 1.23 |
time (sec) |
N/A | 0.426 | 0.074 | 0.238 | 0.046 | 0.103 | 0.415 | 0.128 | 0.222 | 0.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 130 | 194 | 0 | 0 | 0 | 0 | 132 | 177 |
N.S. |
1 | 1.00 | 0.94 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 1.27 |
time (sec) |
N/A | 0.384 | 0.071 | 0.388 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 1.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 143 | 149 | 167 | 166 | 160 | 235 | 195 | 195 | 179 |
N.S. |
1 | 0.95 | 0.99 | 1.11 | 1.11 | 1.07 | 1.57 | 1.30 | 1.30 | 1.19 |
time (sec) |
N/A | 0.458 | 0.087 | 0.215 | 0.045 | 0.103 | 0.522 | 0.123 | 0.198 | 0.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 113 | 112 | 167 | 145 | 145 | 192 | 238 | 173 | 256 |
N.S. |
1 | 1.02 | 1.01 | 1.50 | 1.31 | 1.31 | 1.73 | 2.14 | 1.56 | 2.31 |
time (sec) |
N/A | 0.364 | 0.065 | 0.266 | 0.123 | 0.104 | 0.389 | 0.866 | 0.194 | 1.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 178 | 177 | 202 | 197 | 194 | 289 | 232 | 232 | 232 |
N.S. |
1 | 0.96 | 0.95 | 1.09 | 1.06 | 1.04 | 1.55 | 1.25 | 1.25 | 1.25 |
time (sec) |
N/A | 0.488 | 0.136 | 0.223 | 0.035 | 0.113 | 0.667 | 0.124 | 0.190 | 0.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 303 | 244 | 301 | 268 | 304 | 411 | 393 | 338 | 599 |
N.S. |
1 | 1.26 | 1.02 | 1.25 | 1.12 | 1.27 | 1.71 | 1.64 | 1.41 | 2.50 |
time (sec) |
N/A | 0.661 | 0.133 | 0.399 | 0.135 | 0.120 | 0.723 | 0.455 | 0.192 | 0.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 236 | 252 | 272 | 265 | 277 | 389 | 322 | 322 | 296 |
N.S. |
1 | 0.99 | 1.05 | 1.14 | 1.11 | 1.16 | 1.63 | 1.35 | 1.35 | 1.24 |
time (sec) |
N/A | 0.682 | 0.138 | 0.347 | 0.040 | 0.156 | 0.631 | 0.124 | 0.206 | 1.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 157 | 217 | 264 | 232 | 258 | 350 | 288 | 288 | 442 |
N.S. |
1 | 0.99 | 1.37 | 1.67 | 1.47 | 1.63 | 2.22 | 1.82 | 1.82 | 2.80 |
time (sec) |
N/A | 0.382 | 0.076 | 0.566 | 0.134 | 0.146 | 0.529 | 0.370 | 0.198 | 0.921 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 185 | 192 | 210 | 222 | 229 | 306 | 268 | 268 | 238 |
N.S. |
1 | 0.98 | 1.02 | 1.12 | 1.18 | 1.22 | 1.63 | 1.43 | 1.43 | 1.27 |
time (sec) |
N/A | 0.575 | 0.065 | 0.216 | 0.043 | 0.117 | 0.477 | 0.207 | 0.201 | 0.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 190 | 257 | 251 | 0 | 0 | 0 | 229 | 232 |
N.S. |
1 | 1.00 | 0.83 | 1.13 | 1.10 | 0.00 | 0.00 | 0.00 | 1.00 | 1.02 |
time (sec) |
N/A | 0.469 | 0.100 | 0.338 | 0.365 | 0.000 | 0.000 | 0.000 | 0.199 | 1.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 161 | 169 | 193 | 197 | 206 | 258 | 247 | 247 | 236 |
N.S. |
1 | 1.01 | 1.06 | 1.21 | 1.23 | 1.29 | 1.61 | 1.54 | 1.54 | 1.48 |
time (sec) |
N/A | 0.592 | 0.087 | 0.243 | 0.046 | 0.134 | 0.577 | 0.133 | 0.189 | 1.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | F | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 170 | 240 | 223 | 0 | 0 | 0 | 218 | 224 |
N.S. |
1 | 1.00 | 0.85 | 1.20 | 1.12 | 0.00 | 0.00 | 0.00 | 1.09 | 1.12 |
time (sec) |
N/A | 0.465 | 0.108 | 0.525 | 0.300 | 0.000 | 0.000 | 0.000 | 0.201 | 1.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 152 | 166 | 195 | 193 | 205 | 272 | 255 | 255 | 203 |
N.S. |
1 | 0.96 | 1.05 | 1.23 | 1.22 | 1.30 | 1.72 | 1.61 | 1.61 | 1.28 |
time (sec) |
N/A | 0.599 | 0.104 | 0.254 | 0.045 | 0.140 | 0.592 | 0.124 | 0.209 | 0.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | F | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 169 | 241 | 218 | 0 | 0 | 0 | 218 | 234 |
N.S. |
1 | 1.00 | 0.84 | 1.20 | 1.09 | 0.00 | 0.00 | 0.00 | 1.09 | 1.17 |
time (sec) |
N/A | 0.461 | 0.150 | 0.537 | 0.324 | 0.000 | 0.000 | 0.000 | 0.215 | 1.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 171 | 184 | 208 | 208 | 214 | 289 | 268 | 269 | 194 |
N.S. |
1 | 0.97 | 1.04 | 1.18 | 1.18 | 1.21 | 1.63 | 1.51 | 1.52 | 1.10 |
time (sec) |
N/A | 0.664 | 0.107 | 0.257 | 0.049 | 0.124 | 0.585 | 0.131 | 0.213 | 0.964 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 175 | 258 | 0 | 0 | 0 | 0 | 217 | 261 |
N.S. |
1 | 1.00 | 0.77 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 1.14 |
time (sec) |
N/A | 0.515 | 0.097 | 0.523 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 1.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 216 | 230 | 247 | 247 | 243 | 362 | 303 | 303 | 236 |
N.S. |
1 | 0.96 | 1.03 | 1.10 | 1.10 | 1.08 | 1.62 | 1.35 | 1.35 | 1.05 |
time (sec) |
N/A | 0.690 | 0.109 | 0.243 | 0.057 | 0.127 | 0.694 | 0.127 | 0.202 | 1.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | B | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 150 | 154 | 249 | 218 | 228 | 309 | 363 | 273 | 301 |
N.S. |
1 | 0.99 | 1.01 | 1.64 | 1.43 | 1.50 | 2.03 | 2.39 | 1.80 | 1.98 |
time (sec) |
N/A | 0.441 | 0.116 | 0.357 | 0.165 | 0.113 | 0.518 | 5.627 | 0.187 | 0.959 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 244 | 212 | 245 | 226 | 237 | 314 | 233 | 296 | 233 |
N.S. |
1 | 1.00 | 0.87 | 1.00 | 0.93 | 0.97 | 1.29 | 0.95 | 1.21 | 0.95 |
time (sec) |
N/A | 0.674 | 0.068 | 0.326 | 0.043 | 0.095 | 0.581 | 0.124 | 0.207 | 0.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 361 | 359 | 475 | 503 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.99 | 1.32 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.836 | 0.246 | 0.556 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 311 | 441 | 394 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 1.42 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.551 | 0.082 | 0.420 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 353 | 484 | 435 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 1.37 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.668 | 0.131 | 0.474 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 409 | 399 | 514 | 571 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 0.98 | 1.26 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.937 | 0.232 | 0.593 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 555 | 550 | 766 | 526 | 0 | 0 | 0 | 0 | 151 | 0 |
N.S. |
1 | 0.99 | 1.38 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.076 | 2.340 | 1.189 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 517 | 510 | 461 | 400 | 0 | 0 | 0 | 0 | 116 | 0 |
N.S. |
1 | 0.99 | 0.89 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.778 | 0.163 | 0.821 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 561 | 558 | 467 | 537 | 0 | 0 | 0 | 0 | 157 | 0 |
N.S. |
1 | 0.99 | 0.83 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 1.090 | 0.502 | 1.253 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 403 | 403 | 522 | 716 | 0 | 0 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.00 | 1.30 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.786 | 6.752 | 0.588 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 88 | 98 | 99 | 0 | 234 | 0 | 192 | 126 | 696 |
N.S. |
1 | 0.97 | 1.08 | 1.09 | 0.00 | 2.57 | 0.00 | 2.11 | 1.38 | 7.65 |
time (sec) |
N/A | 0.300 | 0.124 | 0.564 | 0.000 | 0.126 | 0.000 | 0.213 | 0.197 | 1.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 443 | 443 | 590 | 808 | 0 | 0 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.00 | 1.33 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.864 | 4.656 | 0.598 | 0.000 | 0.000 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 489 | 489 | 643 | 851 | 0 | 0 | 0 | 0 | 168 | 0 |
N.S. |
1 | 1.00 | 1.31 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.871 | 9.019 | 0.804 | 0.000 | 0.000 | 0.000 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1335 | 1335 | 877 | 2305 | 0 | 0 | 0 | 0 | 1308 | 0 |
N.S. |
1 | 1.00 | 0.66 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 2.271 | 8.938 | 3.131 | 0.000 | 0.000 | 0.000 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 819 | 806 | 861 | 2173 | 0 | 0 | 0 | 0 | 1297 | 0 |
N.S. |
1 | 0.98 | 1.05 | 2.65 | 0.00 | 0.00 | 0.00 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 1.245 | 8.989 | 2.146 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1382 | 1382 | 992 | 2568 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.72 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.061 | 12.675 | 1.860 | 0.000 | 0.000 | 0.000 | 0.000 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 532 | 532 | 589 | 817 | 0 | 0 | 0 | 0 | 238 | 0 |
N.S. |
1 | 1.00 | 1.11 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 1.021 | 8.930 | 0.772 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 151 | 158 | 211 | 0 | 697 | 0 | 762 | 408 | 273 |
N.S. |
1 | 1.16 | 1.22 | 1.62 | 0.00 | 5.36 | 0.00 | 5.86 | 3.14 | 2.10 |
time (sec) |
N/A | 0.373 | 3.120 | 0.875 | 0.000 | 0.199 | 0.000 | 2.270 | 0.219 | 3.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 150 | 131 | 157 | 0 | 637 | 0 | 533 | 397 | 201 |
N.S. |
1 | 1.15 | 1.00 | 1.20 | 0.00 | 4.86 | 0.00 | 4.07 | 3.03 | 1.53 |
time (sec) |
N/A | 0.345 | 0.866 | 0.765 | 0.000 | 0.176 | 0.000 | 1.094 | 0.211 | 3.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 574 | 574 | 645 | 903 | 0 | 0 | 0 | 0 | 265 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.976 | 8.489 | 0.761 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 629 | 629 | 723 | 951 | 0 | 0 | 0 | 0 | 299 | 0 |
N.S. |
1 | 1.00 | 1.15 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 1.051 | 11.305 | 1.140 | 0.000 | 0.000 | 0.000 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 966 | 966 | 1744 | 3774 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.81 | 3.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.206 | 12.056 | 3.333 | 0.000 | 0.000 | 0.000 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 893 | 875 | 1745 | 4007 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.95 | 4.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.386 | 10.393 | 3.426 | 0.000 | 0.000 | 0.000 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1518 | 1518 | 2005 | 5730 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.32 | 3.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.844 | 12.886 | 3.141 | 0.000 | 0.000 | 0.000 | 0.000 | 0.322 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 233 | 391 | 0 | 0 | 1200 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.04 | 1.75 | 0.00 | 0.00 | 5.38 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.596 | 0.354 | 0.000 | 0.000 | 2.286 | 0.000 | 0.000 | 0.564 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 27 | 22 | 23 | 87 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.17 | 0.96 | 1.00 | 3.78 | 1.00 |
time (sec) |
N/A | 0.489 | 12.319 | 0.308 | 0.000 | 0.094 | 21.228 | 0.139 | 0.309 | 0.959 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 148 | 279 | 0 | 0 | 879 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.06 | 1.99 | 0.00 | 0.00 | 6.28 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.394 | 0.358 | 0.000 | 0.000 | 0.529 | 0.000 | 0.000 | 0.387 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 0 | 20 | 19 | 20 | 61 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.00 | 0.95 | 1.00 | 3.05 | 1.00 |
time (sec) |
N/A | 0.208 | 5.119 | 0.293 | 0.000 | 0.093 | 6.443 | 0.129 | 0.271 | 0.880 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 23 | 20 | 23 | 84 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.00 | 0.87 | 1.00 | 3.65 | 1.00 |
time (sec) |
N/A | 0.396 | 9.176 | 0.310 | 0.000 | 0.114 | 5.293 | 0.122 | 0.318 | 1.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 23 | 22 | 23 | 67 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.00 | 0.96 | 1.00 | 2.91 | 1.00 |
time (sec) |
N/A | 0.403 | 9.076 | 0.298 | 0.000 | 0.117 | 2.893 | 0.123 | 0.319 | 1.330 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 23 | 22 | 23 | 107 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.00 | 0.96 | 1.00 | 4.65 | 1.00 |
time (sec) |
N/A | 0.405 | 10.539 | 0.311 | 0.000 | 0.091 | 3.848 | 0.120 | 0.527 | 1.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 142 | 288 | 0 | 0 | 864 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.04 | 2.10 | 0.00 | 0.00 | 6.31 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.415 | 0.424 | 0.000 | 0.000 | 0.254 | 0.000 | 0.000 | 0.430 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 23 | 22 | 23 | 131 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.00 | 0.96 | 1.00 | 5.70 | 1.00 |
time (sec) |
N/A | 0.427 | 12.277 | 0.344 | 0.000 | 0.095 | 9.133 | 0.122 | 1.135 | 1.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 226 | 413 | 0 | 0 | 1162 | 0 | 0 | 94 | 0 |
N.S. |
1 | 1.01 | 1.84 | 0.00 | 0.00 | 5.19 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.535 | 0.384 | 0.000 | 0.000 | 0.470 | 0.000 | 0.000 | 0.828 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 294 | 418 | 0 | 0 | 1566 | 0 | 0 | 121 | 0 |
N.S. |
1 | 1.05 | 1.50 | 0.00 | 0.00 | 5.61 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.673 | 0.474 | 0.000 | 0.000 | 8.723 | 0.000 | 0.000 | 2.441 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 43 | 22 | 23 | 133 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.87 | 0.96 | 1.00 | 5.78 | 1.00 |
time (sec) |
N/A | 0.505 | 12.185 | 0.356 | 0.000 | 0.093 | 59.800 | 0.161 | 0.424 | 1.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 197 | 313 | 0 | 0 | 1192 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.09 | 1.73 | 0.00 | 0.00 | 6.59 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.451 | 0.301 | 0.000 | 0.000 | 2.082 | 0.000 | 0.000 | 0.656 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 0 | 37 | 19 | 20 | 108 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.85 | 0.95 | 1.00 | 5.40 | 1.00 |
time (sec) |
N/A | 0.203 | 5.491 | 0.370 | 0.000 | 0.093 | 27.816 | 0.152 | 0.365 | 0.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 40 | 20 | 23 | 123 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.74 | 0.87 | 1.00 | 5.35 | 1.00 |
time (sec) |
N/A | 0.446 | 9.449 | 0.397 | 0.000 | 0.112 | 21.172 | 0.156 | 0.382 | 1.218 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 40 | 22 | 23 | 109 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.74 | 0.96 | 1.00 | 4.74 | 1.00 |
time (sec) |
N/A | 0.456 | 10.203 | 0.369 | 0.000 | 0.097 | 14.817 | 0.138 | 0.386 | 1.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 40 | 22 | 23 | 145 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.74 | 0.96 | 1.00 | 6.30 | 1.00 |
time (sec) |
N/A | 0.470 | 10.932 | 0.394 | 0.000 | 0.109 | 11.363 | 0.164 | 0.643 | 1.435 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 40 | 22 | 23 | 111 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.74 | 0.96 | 1.00 | 4.83 | 1.00 |
time (sec) |
N/A | 0.461 | 32.685 | 0.414 | 0.000 | 0.105 | 11.434 | 0.135 | 0.536 | 1.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 40 | 22 | 23 | 158 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.74 | 0.96 | 1.00 | 6.87 | 1.00 |
time (sec) |
N/A | 0.466 | 11.876 | 0.403 | 0.000 | 0.093 | 19.943 | 0.139 | 1.399 | 1.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 186 | 334 | 0 | 0 | 1151 | 0 | 0 | 120 | 0 |
N.S. |
1 | 1.04 | 1.88 | 0.00 | 0.00 | 6.47 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.471 | 0.377 | 0.000 | 0.000 | 0.560 | 0.000 | 0.000 | 1.122 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 365 | 470 | 0 | 0 | 1978 | 0 | 0 | 168 | 0 |
N.S. |
1 | 1.06 | 1.36 | 0.00 | 0.00 | 5.73 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.785 | 0.589 | 0.000 | 0.000 | 29.102 | 0.000 | 0.000 | 112.040 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 67 | 0 | 23 | 180 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.91 | 0.00 | 1.00 | 7.83 | 1.00 |
time (sec) |
N/A | 0.520 | 12.666 | 0.720 | 0.000 | 0.128 | 0.000 | 0.163 | 1.175 | 1.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 257 | 353 | 0 | 0 | 1562 | 0 | 0 | 143 | 0 |
N.S. |
1 | 1.10 | 1.52 | 0.00 | 0.00 | 6.70 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.547 | 0.369 | 0.000 | 0.000 | 8.564 | 0.000 | 0.000 | 2.454 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 0 | 61 | 19 | 20 | 155 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 3.05 | 0.95 | 1.00 | 7.75 | 1.00 |
time (sec) |
N/A | 0.203 | 5.772 | 0.351 | 0.000 | 0.099 | 91.838 | 0.166 | 0.530 | 0.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 64 | 20 | 23 | 174 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.78 | 0.87 | 1.00 | 7.57 | 1.00 |
time (sec) |
N/A | 0.471 | 9.428 | 0.409 | 0.000 | 0.118 | 48.884 | 0.154 | 0.584 | 1.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 64 | 22 | 23 | 161 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.78 | 0.96 | 1.00 | 7.00 | 1.00 |
time (sec) |
N/A | 0.468 | 10.327 | 0.400 | 0.000 | 0.113 | 69.303 | 0.160 | 0.469 | 1.851 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 64 | 22 | 23 | 195 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.78 | 0.96 | 1.00 | 8.48 | 1.00 |
time (sec) |
N/A | 0.463 | 11.350 | 0.430 | 0.000 | 0.118 | 47.819 | 0.169 | 0.729 | 1.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 64 | 22 | 23 | 169 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.78 | 0.96 | 1.00 | 7.35 | 1.00 |
time (sec) |
N/A | 0.479 | 10.379 | 0.767 | 0.000 | 0.118 | 47.283 | 0.152 | 0.652 | 1.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 181 | 377 | 0 | 0 | 882 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.03 | 2.14 | 0.00 | 0.00 | 5.01 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.458 | 0.376 | 0.000 | 0.000 | 0.562 | 0.000 | 0.000 | 0.428 | 0.000 |