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 | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 244 | 187 | 449 | 320 | 0 | 0 | 0 | 257 | 0 |
N.S. |
1 | 0.93 | 0.71 | 1.71 | 1.22 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.538 | 0.971 | 1.289 | 0.035 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 193 | 463 | 350 | 259 | 0 | 0 | 0 | 231 | 0 |
N.S. |
1 | 0.95 | 2.27 | 1.72 | 1.27 | 0.00 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.499 | 1.464 | 0.256 | 0.034 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 127 | 98 | 244 | 202 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 0.93 | 0.72 | 1.79 | 1.49 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.436 | 0.248 | 0.210 | 0.035 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 76 | 55 | 91 | 139 | 0 | 0 | 0 | 116 | 0 |
N.S. |
1 | 0.94 | 0.68 | 1.12 | 1.72 | 0.00 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.470 | 0.061 | 0.549 | 0.034 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 753 | 901 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 5.09 | 6.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.341 | 2.260 | 32.319 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 257 | 208 | 301 | 244 | 0 | 0 | 0 | 252 | 0 |
N.S. |
1 | 1.02 | 0.83 | 1.20 | 0.97 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 1.047 | 0.934 | 1.596 | 0.039 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 370 | 347 | 271 | 385 | 360 | 0 | 0 | 0 | 605 | 0 |
N.S. |
1 | 0.94 | 0.73 | 1.04 | 0.97 | 0.00 | 0.00 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 1.107 | 1.591 | 0.273 | 0.047 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 75 | 158 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.09 | 1.34 | 2.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.521 | 0.111 | 9.164 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 59 | 78 | 74 | 357 | 159 | 231 | 363 | 163 | 414 |
N.S. |
1 | 0.82 | 1.08 | 1.03 | 4.96 | 2.21 | 3.21 | 5.04 | 2.26 | 5.75 |
time (sec) |
N/A | 0.302 | 0.080 | 0.826 | 0.035 | 0.083 | 1.473 | 0.144 | 0.159 | 4.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 54 | 59 | 67 | 225 | 144 | 180 | 322 | 126 | 237 |
N.S. |
1 | 0.78 | 0.86 | 0.97 | 3.26 | 2.09 | 2.61 | 4.67 | 1.83 | 3.43 |
time (sec) |
N/A | 0.305 | 0.067 | 0.368 | 0.033 | 0.095 | 1.216 | 0.136 | 0.154 | 0.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 46 | 77 | 61 | 113 | 73 | 95 | 180 | 71 | 73 |
N.S. |
1 | 0.96 | 1.60 | 1.27 | 2.35 | 1.52 | 1.98 | 3.75 | 1.48 | 1.52 |
time (sec) |
N/A | 0.261 | 0.029 | 0.191 | 0.026 | 0.069 | 0.649 | 0.133 | 0.153 | 5.202 |
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 | 54 | 43 | 54 | 54 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.80 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.287 | 0.021 | 0.460 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 53 | 69 | 64 | 95 | 85 | 219 | 152 | 155 | 122 |
N.S. |
1 | 0.84 | 1.10 | 1.02 | 1.51 | 1.35 | 3.48 | 2.41 | 2.46 | 1.94 |
time (sec) |
N/A | 0.292 | 0.071 | 0.529 | 0.030 | 0.094 | 1.100 | 0.122 | 0.179 | 4.679 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 50 | 100 | 67 | 131 | 88 | 313 | 194 | 252 | 67 |
N.S. |
1 | 0.79 | 1.59 | 1.06 | 2.08 | 1.40 | 4.97 | 3.08 | 4.00 | 1.06 |
time (sec) |
N/A | 0.290 | 0.061 | 0.759 | 0.031 | 0.089 | 1.451 | 0.125 | 0.168 | 5.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 141 | 148 | 261 | 827 | 383 | 581 | 733 | 421 | 1730 |
N.S. |
1 | 0.89 | 0.93 | 1.64 | 5.20 | 2.41 | 3.65 | 4.61 | 2.65 | 10.88 |
time (sec) |
N/A | 0.917 | 0.121 | 1.451 | 0.256 | 0.109 | 2.406 | 0.169 | 0.168 | 5.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 143 | 150 | 251 | 619 | 0 | 0 | 0 | 321 | 0 |
N.S. |
1 | 0.80 | 0.84 | 1.40 | 3.46 | 0.00 | 0.00 | 0.00 | 1.79 | 0.00 |
time (sec) |
N/A | 0.871 | 0.316 | 1.989 | 0.236 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 91 | 134 | 221 | 316 | 191 | 238 | 351 | 193 | 432 |
N.S. |
1 | 0.96 | 1.41 | 2.33 | 3.33 | 2.01 | 2.51 | 3.69 | 2.03 | 4.55 |
time (sec) |
N/A | 0.521 | 0.089 | 0.314 | 0.230 | 0.095 | 1.100 | 0.145 | 0.162 | 0.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 158 | 424 | 705 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.94 | 2.52 | 4.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.839 | 0.230 | 12.455 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 95 | 126 | 252 | 0 | 0 | 0 | 0 | 554 | 0 |
N.S. |
1 | 0.91 | 1.21 | 2.42 | 0.00 | 0.00 | 0.00 | 0.00 | 5.33 | 0.00 |
time (sec) |
N/A | 0.574 | 0.237 | 1.154 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 98 | 136 | 238 | 329 | 270 | 1102 | 375 | 503 | 776 |
N.S. |
1 | 0.82 | 1.14 | 2.00 | 2.76 | 2.27 | 9.26 | 3.15 | 4.23 | 6.52 |
time (sec) |
N/A | 0.628 | 0.179 | 0.902 | 0.045 | 0.118 | 1.536 | 0.140 | 0.174 | 5.740 |
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 | 180 | 141 | 218 | 307 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.78 | 1.21 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.917 | 0.408 | 2.253 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 157 | 218 | 273 | 613 | 547 | 3516 | 730 | 989 | 2746 |
N.S. |
1 | 0.91 | 1.27 | 1.59 | 3.56 | 3.18 | 20.44 | 4.24 | 5.75 | 15.97 |
time (sec) |
N/A | 1.023 | 0.232 | 2.063 | 0.070 | 0.112 | 3.458 | 0.145 | 0.171 | 7.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 222 | 336 | 1099 | 0 | 0 | 0 | 0 | 593 | 0 |
N.S. |
1 | 0.84 | 1.28 | 4.18 | 0.00 | 0.00 | 0.00 | 0.00 | 2.25 | 0.00 |
time (sec) |
N/A | 1.632 | 0.474 | 11.551 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 143 | 220 | 931 | 629 | 0 | 0 | 0 | 327 | 0 |
N.S. |
1 | 0.89 | 1.38 | 5.82 | 3.93 | 0.00 | 0.00 | 0.00 | 2.04 | 0.00 |
time (sec) |
N/A | 1.007 | 0.168 | 3.312 | 0.245 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 231 | 581 | 1442 | 0 | 0 | 0 | 0 | 89 | 0 |
N.S. |
1 | 0.90 | 2.26 | 5.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 1.187 | 0.435 | 2.527 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 129 | 232 | 1466 | 0 | 0 | 0 | 0 | 1156 | 0 |
N.S. |
1 | 0.90 | 1.62 | 10.25 | 0.00 | 0.00 | 0.00 | 0.00 | 8.08 | 0.00 |
time (sec) |
N/A | 0.860 | 0.451 | 2.493 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 143 | 335 | 4949 | 0 | 0 | 0 | 0 | 1236 | 0 |
N.S. |
1 | 0.86 | 2.02 | 29.81 | 0.00 | 0.00 | 0.00 | 0.00 | 7.45 | 0.00 |
time (sec) |
N/A | 1.030 | 0.933 | 3.484 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 220 | 393 | 1768 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.82 | 1.46 | 6.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.894 | 0.952 | 7.735 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 25 | 31 | 14 | 58 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.19 | 1.48 | 0.67 | 2.76 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.237 | 0.004 | 0.934 | 0.025 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 30 | 52 | 29 | 132 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.94 | 1.62 | 0.91 | 4.12 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.258 | 0.007 | 0.632 | 0.032 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 167 | 270 | 599 | 333 | 386 | 644 | 2336 | 518 | 737 |
N.S. |
1 | 0.99 | 1.61 | 3.57 | 1.98 | 2.30 | 3.83 | 13.90 | 3.08 | 4.39 |
time (sec) |
N/A | 0.492 | 0.136 | 0.760 | 0.032 | 0.101 | 2.022 | 0.195 | 0.154 | 4.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 128 | 174 | 351 | 207 | 242 | 369 | 976 | 304 | 381 |
N.S. |
1 | 1.07 | 1.45 | 2.92 | 1.72 | 2.02 | 3.08 | 8.13 | 2.53 | 3.18 |
time (sec) |
N/A | 0.415 | 0.084 | 0.530 | 0.033 | 0.104 | 1.843 | 0.152 | 0.163 | 4.207 |
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 | 97 | 106 | 138 | 122 | 109 | 134 | 173 | 341 | 138 | 136 |
N.S. |
1 | 1.09 | 1.42 | 1.26 | 1.12 | 1.38 | 1.78 | 3.52 | 1.42 | 1.40 |
time (sec) |
N/A | 0.365 | 0.039 | 0.263 | 0.025 | 0.104 | 0.887 | 0.133 | 0.165 | 4.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 48 | 37 | 36 | 61 | 46 | 200 | 45 | 48 |
N.S. |
1 | 1.00 | 1.20 | 0.92 | 0.90 | 1.52 | 1.15 | 5.00 | 1.12 | 1.20 |
time (sec) |
N/A | 0.187 | 0.010 | 0.287 | 0.026 | 0.086 | 0.253 | 0.118 | 0.157 | 4.281 |
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 | 130 | 148 | 148 | 192 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.14 | 1.14 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.565 | 0.038 | 6.214 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 121 | 125 | 137 | 121 | 263 | 1605 | 474 | 412 | 170 |
N.S. |
1 | 1.06 | 1.10 | 1.20 | 1.06 | 2.31 | 14.08 | 4.16 | 3.61 | 1.49 |
time (sec) |
N/A | 0.419 | 0.115 | 0.757 | 0.039 | 0.204 | 4.566 | 0.131 | 0.157 | 4.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 170 | 174 | 197 | 291 | 834 | 19859 | 2567 | 2159 | 417 |
N.S. |
1 | 1.02 | 1.04 | 1.18 | 1.74 | 4.99 | 118.92 | 15.37 | 12.93 | 2.50 |
time (sec) |
N/A | 0.498 | 0.201 | 1.286 | 0.042 | 0.692 | 11.076 | 0.192 | 0.166 | 5.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 562 | 547 | 1082 | 2318 | 1363 | 0 | 0 | 0 | 1429 | 0 |
N.S. |
1 | 0.97 | 1.93 | 4.12 | 2.43 | 0.00 | 0.00 | 0.00 | 2.54 | 0.00 |
time (sec) |
N/A | 1.138 | 4.812 | 1.188 | 0.252 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 374 | 374 | 795 | 1411 | 806 | 0 | 0 | 0 | 792 | 0 |
N.S. |
1 | 1.00 | 2.13 | 3.77 | 2.16 | 0.00 | 0.00 | 0.00 | 2.12 | 0.00 |
time (sec) |
N/A | 0.808 | 2.255 | 0.608 | 0.250 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 231 | 271 | 453 | 415 | 0 | 0 | 0 | 350 | 0 |
N.S. |
1 | 1.05 | 1.23 | 2.05 | 1.88 | 0.00 | 0.00 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 0.663 | 0.837 | 0.426 | 0.233 | 0.000 | 0.000 | 0.000 | 0.176 | 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 | 97 | 93 | 103 | 134 | 0 | 0 | 0 | 0 | 106 | 0 |
N.S. |
1 | 0.96 | 1.06 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.552 | 0.133 | 0.715 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 241 | 3808 | 1700 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.13 | 17.79 | 7.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.436 | 90.239 | 39.939 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 401 | 491 | 419 | 592 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.22 | 1.04 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.906 | 5.058 | 3.580 | 0.000 | 0.000 | 0.000 | 0.000 | 0.223 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 621 | 739 | 1318 | 870 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.19 | 2.12 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.192 | 11.299 | 2.013 | 0.000 | 0.000 | 0.000 | 0.000 | 0.417 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 546 | 533 | 1646 | 10013 | 0 | 0 | 0 | 0 | 1397 | 0 |
N.S. |
1 | 0.98 | 3.01 | 18.34 | 0.00 | 0.00 | 0.00 | 0.00 | 2.56 | 0.00 |
time (sec) |
N/A | 1.221 | 6.606 | 42.682 | 0.000 | 0.000 | 0.000 | 0.000 | 0.376 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 326 | 324 | 566 | 10425 | 0 | 0 | 0 | 0 | 584 | 0 |
N.S. |
1 | 0.99 | 1.74 | 31.98 | 0.00 | 0.00 | 0.00 | 0.00 | 1.79 | 0.00 |
time (sec) |
N/A | 0.947 | 3.188 | 5.994 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 130 | 194 | 265 | 0 | 0 | 0 | 0 | 170 | 0 |
N.S. |
1 | 0.98 | 1.47 | 2.01 | 0.00 | 0.00 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.742 | 0.198 | 1.374 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 344 | 0 | 3441 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.12 | 0.00 | 11.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.479 | 0.000 | 5.136 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 634 | 1085 | 3878 | 5109 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.71 | 6.12 | 8.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.796 | 90.093 | 3.066 | 0.000 | 0.000 | 0.000 | 0.000 | 0.678 | 0.000 |
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 | 20 | 20 | 22 | 20 | 432 | 52 | 0 | 22 | 55220 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 21.60 | 2.60 | 0.00 | 1.10 | 2761.00 | 1.10 |
time (sec) |
N/A | 0.314 | 3.405 | 0.247 | 3.614 | 0.098 | 0.000 | 0.232 | 0.438 | 3.688 |
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 | 20 | 20 | 22 | 20 | 262 | 36 | 0 | 22 | 22801 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 13.10 | 1.80 | 0.00 | 1.10 | 1140.05 | 1.10 |
time (sec) |
N/A | 0.318 | 0.275 | 0.232 | 2.183 | 0.087 | 0.000 | 0.169 | 0.276 | 3.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 222 | 0 | 0 | 0 | 0 | 0 | 0 | 1358 | 0 |
N.S. |
1 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.38 | 0.00 |
time (sec) |
N/A | 0.494 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 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 | 649 | 800 | 623 | 259 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.23 | 0.96 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.556 | 0.484 | 0.536 | 0.000 | 0.000 | 0.000 | 0.000 | 41.956 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 491 | 365 | 444 | 591 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.71 | 1.27 | 1.55 | 2.06 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.915 | 0.196 | 0.471 | 0.238 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 138 | 138 | 181 | 192 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.15 | 1.15 | 1.51 | 1.60 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.536 | 0.016 | 0.449 | 0.033 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 191 | 394 | 259 | 192 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.03 | 2.12 | 1.39 | 1.03 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.517 | 8.765 | 0.483 | 0.035 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 545 | 560 | 555 | 581 | 651 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.03 | 1.02 | 1.07 | 1.19 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.158 | 0.374 | 1.063 | 0.215 | 0.000 | 0.000 | 0.000 | 0.186 | 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 | 832 | 847 | 791 | 366 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.02 | 0.95 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.573 | 0.668 | 0.561 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 213 | 203 | 184 | 198 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.58 | 1.50 | 1.36 | 1.47 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.538 | 0.030 | 0.480 | 0.035 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 618 | 0 | 576 | 675 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 0.00 | 0.93 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.000 | 12.028 | 0.175 | 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 | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 585 | 585 | 549 | 648 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.187 | 0.343 | 0.092 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 661 | 661 | 668 | 751 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.385 | 0.306 | 0.096 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 381 | 398 | 694 | 615 | 0 | 0 | 0 | 0 | 725 | 0 |
N.S. |
1 | 1.04 | 1.82 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 1.90 | 0.00 |
time (sec) |
N/A | 1.263 | 25.802 | 0.438 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 323 | 524 | 1198 | 639 | 0 | 0 | 0 | 0 | 75 | 0 |
N.S. |
1 | 1.62 | 3.71 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.164 | 11.079 | 1.987 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 300 | 410 | 474 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.03 | 1.40 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.874 | 0.145 | 0.275 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 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 | 273 | 474 | 365 | 467 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.74 | 1.34 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.831 | 0.162 | 0.615 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 325 | 594 | 567 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.05 | 1.92 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 1.175 | 6.534 | 0.355 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 355 | 562 | 1221 | 678 | 0 | 0 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.58 | 3.44 | 1.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.214 | 7.804 | 2.176 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 428 | 453 | 608 | 730 | 0 | 0 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.06 | 1.42 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 1.413 | 33.031 | 0.468 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 727 | 956 | 0 | 505 | 0 | 0 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.31 | 0.00 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 2.170 | 0.000 | 0.987 | 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 | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 463 | 467 | 679 | 327 | 0 | 0 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.01 | 1.47 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.248 | 0.380 | 0.329 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 679 | 778 | 652 | 338 | 0 | 0 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.15 | 0.96 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.508 | 0.736 | 0.721 | 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 | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 679 | 919 | 714 | 366 | 0 | 0 | 0 | 0 | 104 | 0 |
N.S. |
1 | 1.35 | 1.05 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 1.553 | 0.541 | 0.315 | 0.000 | 0.000 | 0.000 | 0.000 | 82.602 | 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 | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 480 | 491 | 915 | 420 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.02 | 1.91 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 1.527 | 16.802 | 0.310 | 0.000 | 0.000 | 0.000 | 0.000 | 54.092 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 761 | 865 | 2550 | 513 | 0 | 0 | 0 | 0 | 120 | 0 |
N.S. |
1 | 1.14 | 3.35 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.920 | 8.740 | 0.463 | 0.000 | 0.000 | 0.000 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 791 | 1028 | 1564 | 662 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.30 | 1.98 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.168 | 7.370 | 0.533 | 0.000 | 0.000 | 0.000 | 0.000 | 83.256 | 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 | 366 | 395 | 437 | 842 | 0 | 0 | 0 | 0 | 1076 | 0 |
N.S. |
1 | 1.08 | 1.19 | 2.30 | 0.00 | 0.00 | 0.00 | 0.00 | 2.94 | 0.00 |
time (sec) |
N/A | 1.116 | 0.422 | 1.046 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 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 | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1135 | 2120 | 2111 | 718 | 0 | 0 | 0 | 0 | 419 | 0 |
N.S. |
1 | 1.87 | 1.86 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 4.667 | 3.211 | 1.545 | 0.000 | 0.000 | 0.000 | 0.000 | 0.280 | 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 | 83 | 72 | 150 | 149 | 0 | 0 | 0 | 0 | 73 | 0 |
N.S. |
1 | 0.87 | 1.81 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.600 | 0.065 | 0.314 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |