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 | C | A | F(-2) | B | F(-1) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 649 | 686 | 658 | 767 | 0 | 3385 | 0 | 1436 | 5074 | 21924 |
N.S. |
1 | 1.06 | 1.01 | 1.18 | 0.00 | 5.22 | 0.00 | 2.21 | 7.82 | 33.78 |
time (sec) |
N/A | 3.877 | 11.695 | 4.315 | 0.000 | 0.500 | 0.000 | 0.244 | 0.199 | 12.706 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 461 | 518 | 532 | 640 | 0 | 2777 | 0 | 1225 | 4628 | 9423 |
N.S. |
1 | 1.12 | 1.15 | 1.39 | 0.00 | 6.02 | 0.00 | 2.66 | 10.04 | 20.44 |
time (sec) |
N/A | 2.657 | 10.204 | 2.725 | 0.000 | 0.338 | 0.000 | 0.211 | 0.200 | 5.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F(-1) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 349 | 405 | 863 | 561 | 0 | 2045 | 0 | 1104 | 3079 | 11947 |
N.S. |
1 | 1.16 | 2.47 | 1.61 | 0.00 | 5.86 | 0.00 | 3.16 | 8.82 | 34.23 |
time (sec) |
N/A | 1.817 | 6.981 | 1.354 | 0.000 | 0.271 | 0.000 | 0.197 | 0.172 | 8.556 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 359 | 307 | 449 | 0 | 1410 | 0 | 966 | 1883 | 516 |
N.S. |
1 | 1.14 | 0.98 | 1.43 | 0.00 | 4.49 | 0.00 | 3.08 | 6.00 | 1.64 |
time (sec) |
N/A | 1.259 | 3.282 | 1.148 | 0.000 | 0.180 | 0.000 | 0.191 | 0.183 | 2.615 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 338 | 301 | 448 | 0 | 1404 | 0 | 966 | 2136 | 516 |
N.S. |
1 | 1.13 | 1.01 | 1.50 | 0.00 | 4.70 | 0.00 | 3.23 | 7.14 | 1.73 |
time (sec) |
N/A | 1.078 | 2.024 | 1.085 | 0.000 | 0.225 | 0.000 | 0.179 | 0.194 | 2.546 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | B | B |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 410 | 587 | 580 | 0 | 2458 | 0 | 1127 | 3572 | 11939 |
N.S. |
1 | 1.19 | 1.70 | 1.68 | 0.00 | 7.12 | 0.00 | 3.27 | 10.35 | 34.61 |
time (sec) |
N/A | 2.126 | 8.717 | 2.347 | 0.000 | 70.099 | 0.000 | 0.247 | 0.224 | 8.677 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 480 | 536 | 709 | 675 | 0 | 3598 | 0 | 1255 | 4678 | 15980 |
N.S. |
1 | 1.12 | 1.48 | 1.41 | 0.00 | 7.50 | 0.00 | 2.61 | 9.75 | 33.29 |
time (sec) |
N/A | 3.601 | 7.473 | 3.567 | 0.000 | 162.444 | 0.000 | 0.223 | 0.214 | 9.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 657 | 692 | 686 | 834 | 0 | 0 | 0 | 1482 | 9075 | 21844 |
N.S. |
1 | 1.05 | 1.04 | 1.27 | 0.00 | 0.00 | 0.00 | 2.26 | 13.81 | 33.25 |
time (sec) |
N/A | 5.005 | 9.104 | 6.388 | 0.000 | 0.000 | 0.000 | 0.245 | 0.242 | 12.767 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 32 | 34 | 23 | 0 | 27 | 58 | 48 | 26 | 25 |
N.S. |
1 | 1.39 | 1.48 | 1.00 | 0.00 | 1.17 | 2.52 | 2.09 | 1.13 | 1.09 |
time (sec) |
N/A | 0.192 | 0.009 | 0.352 | 0.000 | 0.076 | 0.321 | 0.129 | 0.178 | 0.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 71 | 68 | 67 | 0 | 240 | 0 | 318 | 136 | 248 |
N.S. |
1 | 1.16 | 1.11 | 1.10 | 0.00 | 3.93 | 0.00 | 5.21 | 2.23 | 4.07 |
time (sec) |
N/A | 0.372 | 0.287 | 0.393 | 0.000 | 0.110 | 0.000 | 0.149 | 0.183 | 1.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 130 | 107 | 138 | 0 | 421 | 0 | 170 | 455 | 124 |
N.S. |
1 | 1.18 | 0.97 | 1.25 | 0.00 | 3.83 | 0.00 | 1.55 | 4.14 | 1.13 |
time (sec) |
N/A | 0.433 | 0.664 | 0.528 | 0.000 | 0.106 | 0.000 | 0.166 | 0.162 | 0.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 212 | 171 | 244 | 0 | 803 | 0 | 381 | 1140 | 268 |
N.S. |
1 | 1.21 | 0.98 | 1.39 | 0.00 | 4.59 | 0.00 | 2.18 | 6.51 | 1.53 |
time (sec) |
N/A | 0.699 | 1.049 | 0.792 | 0.000 | 0.163 | 0.000 | 0.177 | 0.177 | 2.684 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 304 | 246 | 384 | 0 | 1305 | 0 | 711 | 2116 | 462 |
N.S. |
1 | 1.22 | 0.99 | 1.54 | 0.00 | 5.24 | 0.00 | 2.86 | 8.50 | 1.86 |
time (sec) |
N/A | 1.048 | 1.306 | 1.200 | 0.000 | 0.168 | 0.000 | 0.239 | 0.176 | 2.932 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 416 | 438 | 321 | 2143 | 0 | 698 | 0 | 0 | 73 | 0 |
N.S. |
1 | 1.05 | 0.77 | 5.15 | 0.00 | 1.68 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 2.351 | 2.658 | 37.075 | 0.000 | 0.135 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 321 | 335 | 249 | 1635 | 0 | 603 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.04 | 0.78 | 5.09 | 0.00 | 1.88 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.679 | 1.782 | 13.338 | 0.000 | 0.124 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 243 | 189 | 1187 | 0 | 512 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.03 | 0.80 | 5.01 | 0.00 | 2.16 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.217 | 1.954 | 23.722 | 0.000 | 0.109 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 244 | 393 | 740 | 0 | 0 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.02 | 1.64 | 3.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 1.934 | 4.557 | 18.439 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 231 | 385 | 988 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.06 | 1.77 | 4.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 1.881 | 3.292 | 18.300 | 0.000 | 0.000 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 305 | 428 | 1395 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.02 | 1.43 | 4.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 2.607 | 6.186 | 23.369 | 0.000 | 0.000 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 399 | 410 | 661 | 2319 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.03 | 1.66 | 5.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 3.577 | 7.178 | 29.691 | 0.000 | 0.000 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 518 | 542 | 407 | 2603 | 0 | 811 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.05 | 0.79 | 5.03 | 0.00 | 1.57 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 3.020 | 4.270 | 62.243 | 0.000 | 0.154 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 408 | 424 | 321 | 2143 | 0 | 699 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.04 | 0.79 | 5.25 | 0.00 | 1.71 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 2.185 | 3.018 | 52.291 | 0.000 | 0.135 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 323 | 257 | 1635 | 0 | 604 | 0 | 0 | 118 | 0 |
N.S. |
1 | 1.03 | 0.82 | 5.19 | 0.00 | 1.92 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 1.615 | 3.069 | 39.306 | 0.000 | 0.116 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 315 | 455 | 1330 | 0 | 0 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.03 | 1.49 | 4.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 2.596 | 10.124 | 29.750 | 0.000 | 0.000 | 0.000 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 300 | 434 | 1441 | 0 | 0 | 0 | 0 | 159 | 0 |
N.S. |
1 | 1.05 | 1.52 | 5.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 2.630 | 12.138 | 26.192 | 0.000 | 0.000 | 0.000 | 0.000 | 0.492 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 315 | 579 | 1743 | 0 | 0 | 0 | 0 | 159 | 0 |
N.S. |
1 | 1.03 | 1.89 | 5.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 2.700 | 7.358 | 26.787 | 0.000 | 0.000 | 0.000 | 0.000 | 0.441 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 399 | 410 | 667 | 2441 | 0 | 0 | 0 | 0 | 159 | 0 |
N.S. |
1 | 1.03 | 1.67 | 6.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 3.565 | 7.726 | 34.887 | 0.000 | 0.000 | 0.000 | 0.000 | 0.317 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 503 | 519 | 783 | 3551 | 0 | 0 | 0 | 0 | 159 | 0 |
N.S. |
1 | 1.03 | 1.56 | 7.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 4.592 | 7.547 | 41.058 | 0.000 | 0.000 | 0.000 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 629 | 655 | 501 | 3165 | 0 | 929 | 0 | 0 | 190 | 0 |
N.S. |
1 | 1.04 | 0.80 | 5.03 | 0.00 | 1.48 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 3.732 | 5.634 | 148.691 | 0.000 | 0.185 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 510 | 528 | 405 | 2603 | 0 | 810 | 0 | 0 | 188 | 0 |
N.S. |
1 | 1.04 | 0.79 | 5.10 | 0.00 | 1.59 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 2.825 | 4.165 | 85.996 | 0.000 | 0.156 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 412 | 327 | 2143 | 0 | 698 | 0 | 0 | 179 | 0 |
N.S. |
1 | 1.02 | 0.81 | 5.33 | 0.00 | 1.74 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 2.120 | 3.775 | 59.497 | 0.000 | 0.137 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 383 | 397 | 526 | 1713 | 0 | 0 | 0 | 0 | 222 | 0 |
N.S. |
1 | 1.04 | 1.37 | 4.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 3.295 | 12.856 | 56.590 | 0.000 | 0.000 | 0.000 | 0.000 | 0.358 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 357 | 376 | 502 | 2152 | 0 | 0 | 0 | 0 | 236 | 0 |
N.S. |
1 | 1.05 | 1.41 | 6.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 3.306 | 13.326 | 61.953 | 0.000 | 0.000 | 0.000 | 0.000 | 0.400 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 385 | 492 | 2365 | 0 | 0 | 0 | 0 | 236 | 0 |
N.S. |
1 | 1.03 | 1.32 | 6.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 3.426 | 6.181 | 157.845 | 0.000 | 0.000 | 0.000 | 0.000 | 0.408 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 407 | 420 | 519 | 2791 | 0 | 0 | 0 | 0 | 236 | 0 |
N.S. |
1 | 1.03 | 1.28 | 6.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 3.756 | 7.372 | 437.792 | 0.000 | 0.000 | 0.000 | 0.000 | 0.411 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 502 | 518 | 792 | 3673 | 0 | 0 | 0 | 0 | 236 | 0 |
N.S. |
1 | 1.03 | 1.58 | 7.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 4.688 | 7.814 | 1137.179 | 0.000 | 0.000 | 0.000 | 0.000 | 0.403 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 624 | 645 | 930 | 5171 | 0 | 0 | 0 | 0 | 236 | 0 |
N.S. |
1 | 1.03 | 1.49 | 8.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 5.647 | 8.047 | 1958.421 | 0.000 | 0.000 | 0.000 | 0.000 | 0.410 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 312 | 259 | 1302 | 0 | 562 | 0 | 0 | 174 | 0 |
N.S. |
1 | 1.09 | 0.91 | 4.57 | 0.00 | 1.97 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 1.757 | 2.638 | 28.601 | 0.000 | 0.115 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 241 | 178 | 990 | 0 | 492 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.09 | 0.81 | 4.48 | 0.00 | 2.23 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 1.359 | 2.353 | 20.372 | 0.000 | 0.109 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 344 | 364 | 252 | 1635 | 0 | 604 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.06 | 0.73 | 4.75 | 0.00 | 1.76 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 1.884 | 2.636 | 28.504 | 0.000 | 0.119 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 270 | 186 | 1258 | 0 | 517 | 0 | 0 | 107 | 0 |
N.S. |
1 | 1.05 | 0.72 | 4.88 | 0.00 | 2.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 1.280 | 2.033 | 17.765 | 0.000 | 0.109 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 192 | 160 | 732 | 0 | 445 | 0 | 0 | 99 | 252 |
N.S. |
1 | 1.02 | 0.85 | 3.89 | 0.00 | 2.37 | 0.00 | 0.00 | 0.53 | 1.34 |
time (sec) |
N/A | 0.878 | 1.914 | 9.385 | 0.000 | 0.099 | 0.000 | 0.000 | 0.181 | 0.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | F | F | F | F | F | F(-1) |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 192 | 0 | 275 | 0 | 0 | 0 | 0 | 117 | 0 |
N.S. |
1 | 1.02 | 0.00 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 1.439 | 0.000 | 6.913 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 231 | 600 | 738 | 0 | 0 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.05 | 2.73 | 3.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 1.891 | 21.086 | 7.341 | 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 | C | B | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 309 | 562 | 1282 | 0 | 0 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.02 | 1.85 | 4.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 2.622 | 7.334 | 11.200 | 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 | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 405 | 419 | 665 | 2205 | 0 | 0 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.03 | 1.64 | 5.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 3.510 | 7.378 | 14.561 | 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 | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 426 | 431 | 328 | 1335 | 0 | 992 | 0 | 0 | 157 | 0 |
N.S. |
1 | 1.01 | 0.77 | 3.13 | 0.00 | 2.33 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 2.389 | 3.734 | 11.613 | 0.000 | 0.168 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 299 | 236 | 1058 | 0 | 836 | 0 | 0 | 155 | 0 |
N.S. |
1 | 1.07 | 0.84 | 3.78 | 0.00 | 2.99 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 1.574 | 2.671 | 5.245 | 0.000 | 0.137 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 234 | 182 | 526 | 0 | 700 | 0 | 0 | 147 | 0 |
N.S. |
1 | 1.07 | 0.83 | 2.40 | 0.00 | 3.20 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 1.062 | 1.305 | 3.850 | 0.000 | 0.113 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 292 | 0 | 546 | 0 | 0 | 0 | 0 | 165 | 0 |
N.S. |
1 | 1.08 | 0.00 | 2.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 2.223 | 0.000 | 3.830 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 345 | 751 | 919 | 0 | 0 | 0 | 0 | 171 | 0 |
N.S. |
1 | 1.10 | 2.40 | 2.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 2.875 | 9.262 | 5.531 | 0.000 | 0.000 | 0.000 | 0.000 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 416 | 442 | 723 | 1581 | 0 | 0 | 0 | 0 | 171 | 0 |
N.S. |
1 | 1.06 | 1.74 | 3.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 3.833 | 7.573 | 7.589 | 0.000 | 0.000 | 0.000 | 0.000 | 0.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 622 | 628 | 422 | 1784 | 0 | 1742 | 0 | 0 | 205 | 0 |
N.S. |
1 | 1.01 | 0.68 | 2.87 | 0.00 | 2.80 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 3.731 | 7.043 | 11.510 | 0.000 | 0.298 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 453 | 462 | 377 | 1502 | 0 | 1480 | 0 | 0 | 205 | 0 |
N.S. |
1 | 1.02 | 0.83 | 3.32 | 0.00 | 3.27 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 2.606 | 5.326 | 5.853 | 0.000 | 0.241 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 367 | 323 | 967 | 0 | 1276 | 0 | 0 | 203 | 0 |
N.S. |
1 | 1.02 | 0.90 | 2.69 | 0.00 | 3.55 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 1.767 | 4.300 | 4.300 | 0.000 | 0.180 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 333 | 343 | 278 | 871 | 0 | 1141 | 0 | 0 | 195 | 0 |
N.S. |
1 | 1.03 | 0.83 | 2.62 | 0.00 | 3.43 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 1.542 | 2.946 | 2.559 | 0.000 | 0.142 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 401 | 422 | 0 | 882 | 0 | 0 | 0 | 0 | 213 | 0 |
N.S. |
1 | 1.05 | 0.00 | 2.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 3.239 | 0.000 | 5.856 | 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 | C | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 461 | 495 | 915 | 1353 | 0 | 0 | 0 | 0 | 219 | 0 |
N.S. |
1 | 1.07 | 1.98 | 2.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 4.066 | 9.661 | 5.932 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 572 | 610 | 922 | 2024 | 0 | 0 | 0 | 0 | 219 | 0 |
N.S. |
1 | 1.07 | 1.61 | 3.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 5.176 | 8.135 | 8.120 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 449 | 472 | 433 | 1320 | 0 | 1767 | 0 | 0 | 243 | 0 |
N.S. |
1 | 1.05 | 0.96 | 2.94 | 0.00 | 3.94 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 2.267 | 4.549 | 10.950 | 0.000 | 0.214 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 180 | 144 | 598 | 0 | 437 | 0 | 0 | 58 | 303 |
N.S. |
1 | 1.08 | 0.86 | 3.58 | 0.00 | 2.62 | 0.00 | 0.00 | 0.35 | 1.81 |
time (sec) |
N/A | 1.010 | 1.587 | 4.336 | 0.000 | 0.111 | 0.000 | 0.000 | 0.189 | 1.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 134 | 90 | 246 | 0 | 371 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.08 | 0.73 | 1.98 | 0.00 | 2.99 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.659 | 0.395 | 1.161 | 0.000 | 0.103 | 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 | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 203 | 150 | 426 | 0 | 587 | 0 | 0 | 144 | 0 |
N.S. |
1 | 1.13 | 0.83 | 2.37 | 0.00 | 3.26 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.991 | 0.835 | 0.868 | 0.000 | 0.111 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 295 | 193 | 748 | 0 | 922 | 0 | 0 | 192 | 0 |
N.S. |
1 | 1.09 | 0.71 | 2.76 | 0.00 | 3.40 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 1.428 | 1.833 | 1.815 | 0.000 | 0.137 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 180 | 143 | 565 | 0 | 246 | 0 | 0 | 107 | 254 |
N.S. |
1 | 0.95 | 0.75 | 2.97 | 0.00 | 1.29 | 0.00 | 0.00 | 0.56 | 1.34 |
time (sec) |
N/A | 0.826 | 2.279 | 20.575 | 0.000 | 0.113 | 0.000 | 0.000 | 0.190 | 1.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 152 | 117 | 515 | 0 | 222 | 0 | 0 | 98 | 216 |
N.S. |
1 | 0.99 | 0.76 | 3.34 | 0.00 | 1.44 | 0.00 | 0.00 | 0.64 | 1.40 |
time (sec) |
N/A | 0.796 | 2.086 | 6.318 | 0.000 | 0.107 | 0.000 | 0.000 | 0.200 | 1.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 122 | 94 | 465 | 0 | 195 | 0 | 0 | 96 | 162 |
N.S. |
1 | 1.05 | 0.81 | 4.01 | 0.00 | 1.68 | 0.00 | 0.00 | 0.83 | 1.40 |
time (sec) |
N/A | 0.696 | 1.788 | 4.166 | 0.000 | 0.097 | 0.000 | 0.000 | 0.204 | 1.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 110 | 90 | 389 | 0 | 216 | 0 | 0 | 89 | 146 |
N.S. |
1 | 1.03 | 0.84 | 3.64 | 0.00 | 2.02 | 0.00 | 0.00 | 0.83 | 1.36 |
time (sec) |
N/A | 0.673 | 1.424 | 3.814 | 0.000 | 0.110 | 0.000 | 0.000 | 0.187 | 1.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 114 | 115 | 562 | 0 | 229 | 0 | 0 | 100 | 184 |
N.S. |
1 | 1.03 | 1.04 | 5.06 | 0.00 | 2.06 | 0.00 | 0.00 | 0.90 | 1.66 |
time (sec) |
N/A | 0.693 | 1.732 | 4.183 | 0.000 | 0.114 | 0.000 | 0.000 | 0.171 | 1.833 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 146 | 136 | 715 | 0 | 260 | 0 | 0 | 109 | 217 |
N.S. |
1 | 0.96 | 0.89 | 4.70 | 0.00 | 1.71 | 0.00 | 0.00 | 0.72 | 1.43 |
time (sec) |
N/A | 0.799 | 2.473 | 5.805 | 0.000 | 0.109 | 0.000 | 0.000 | 0.176 | 2.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 176 | 173 | 824 | 0 | 288 | 0 | 0 | 109 | 223 |
N.S. |
1 | 0.93 | 0.91 | 4.34 | 0.00 | 1.52 | 0.00 | 0.00 | 0.57 | 1.17 |
time (sec) |
N/A | 0.854 | 5.672 | 6.943 | 0.000 | 0.106 | 0.000 | 0.000 | 0.201 | 2.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 273 | 239 | 863 | 0 | 358 | 0 | 0 | 160 | 401 |
N.S. |
1 | 0.90 | 0.78 | 2.83 | 0.00 | 1.17 | 0.00 | 0.00 | 0.52 | 1.31 |
time (sec) |
N/A | 1.404 | 3.128 | 15.759 | 0.000 | 0.159 | 0.000 | 0.000 | 0.202 | 1.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 244 | 195 | 784 | 0 | 318 | 0 | 0 | 151 | 366 |
N.S. |
1 | 0.97 | 0.78 | 3.12 | 0.00 | 1.27 | 0.00 | 0.00 | 0.60 | 1.46 |
time (sec) |
N/A | 1.382 | 2.716 | 7.627 | 0.000 | 0.111 | 0.000 | 0.000 | 0.201 | 1.556 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 214 | 160 | 706 | 0 | 281 | 0 | 0 | 149 | 303 |
N.S. |
1 | 1.05 | 0.79 | 3.48 | 0.00 | 1.38 | 0.00 | 0.00 | 0.73 | 1.49 |
time (sec) |
N/A | 1.216 | 3.470 | 5.237 | 0.000 | 0.108 | 0.000 | 0.000 | 0.205 | 1.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 195 | 144 | 679 | 0 | 292 | 0 | 0 | 140 | 260 |
N.S. |
1 | 1.03 | 0.76 | 3.59 | 0.00 | 1.54 | 0.00 | 0.00 | 0.74 | 1.38 |
time (sec) |
N/A | 1.179 | 3.397 | 4.298 | 0.000 | 0.114 | 0.000 | 0.000 | 0.214 | 1.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 179 | 157 | 768 | 0 | 292 | 0 | 0 | 142 | 268 |
N.S. |
1 | 0.99 | 0.87 | 4.27 | 0.00 | 1.62 | 0.00 | 0.00 | 0.79 | 1.49 |
time (sec) |
N/A | 1.146 | 3.245 | 4.224 | 0.000 | 0.110 | 0.000 | 0.000 | 0.197 | 1.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 204 | 202 | 947 | 0 | 319 | 0 | 0 | 153 | 310 |
N.S. |
1 | 1.02 | 1.01 | 4.74 | 0.00 | 1.60 | 0.00 | 0.00 | 0.76 | 1.55 |
time (sec) |
N/A | 1.223 | 3.916 | 5.017 | 0.000 | 0.127 | 0.000 | 0.000 | 0.194 | 2.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 237 | 217 | 920 | 0 | 357 | 0 | 0 | 162 | 343 |
N.S. |
1 | 0.96 | 0.88 | 3.71 | 0.00 | 1.44 | 0.00 | 0.00 | 0.65 | 1.38 |
time (sec) |
N/A | 1.363 | 7.505 | 5.872 | 0.000 | 0.121 | 0.000 | 0.000 | 0.218 | 2.815 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 267 | 266 | 1169 | 0 | 400 | 0 | 0 | 162 | 851 |
N.S. |
1 | 0.88 | 0.88 | 3.87 | 0.00 | 1.32 | 0.00 | 0.00 | 0.54 | 2.82 |
time (sec) |
N/A | 1.385 | 8.783 | 8.108 | 0.000 | 0.130 | 0.000 | 0.000 | 0.191 | 3.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 361 | 343 | 285 | 1082 | 0 | 429 | 0 | 0 | 204 | 514 |
N.S. |
1 | 0.95 | 0.79 | 3.00 | 0.00 | 1.19 | 0.00 | 0.00 | 0.57 | 1.42 |
time (sec) |
N/A | 1.989 | 3.646 | 9.366 | 0.000 | 0.132 | 0.000 | 0.000 | 0.231 | 1.828 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 308 | 230 | 975 | 0 | 376 | 0 | 0 | 202 | 452 |
N.S. |
1 | 1.04 | 0.78 | 3.29 | 0.00 | 1.27 | 0.00 | 0.00 | 0.68 | 1.53 |
time (sec) |
N/A | 1.815 | 4.608 | 9.000 | 0.000 | 0.136 | 0.000 | 0.000 | 0.241 | 1.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 290 | 212 | 983 | 0 | 378 | 0 | 0 | 193 | 398 |
N.S. |
1 | 1.04 | 0.76 | 3.52 | 0.00 | 1.35 | 0.00 | 0.00 | 0.69 | 1.43 |
time (sec) |
N/A | 1.804 | 4.137 | 6.257 | 0.000 | 0.136 | 0.000 | 0.000 | 0.212 | 1.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 275 | 186 | 997 | 0 | 369 | 0 | 0 | 193 | 379 |
N.S. |
1 | 1.01 | 0.69 | 3.68 | 0.00 | 1.36 | 0.00 | 0.00 | 0.71 | 1.40 |
time (sec) |
N/A | 1.781 | 4.979 | 5.693 | 0.000 | 0.126 | 0.000 | 0.000 | 0.263 | 2.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 275 | 248 | 1153 | 0 | 382 | 0 | 0 | 195 | 414 |
N.S. |
1 | 1.01 | 0.91 | 4.22 | 0.00 | 1.40 | 0.00 | 0.00 | 0.71 | 1.52 |
time (sec) |
N/A | 1.801 | 5.049 | 6.170 | 0.000 | 0.139 | 0.000 | 0.000 | 0.307 | 2.788 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 294 | 303 | 251 | 1178 | 0 | 415 | 0 | 0 | 206 | 442 |
N.S. |
1 | 1.03 | 0.85 | 4.01 | 0.00 | 1.41 | 0.00 | 0.00 | 0.70 | 1.50 |
time (sec) |
N/A | 1.831 | 9.522 | 6.961 | 0.000 | 0.151 | 0.000 | 0.000 | 0.308 | 3.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 357 | 332 | 414 | 1265 | 0 | 467 | 0 | 0 | 215 | 463 |
N.S. |
1 | 0.93 | 1.16 | 3.54 | 0.00 | 1.31 | 0.00 | 0.00 | 0.60 | 1.30 |
time (sec) |
N/A | 2.012 | 11.013 | 7.833 | 0.000 | 0.135 | 0.000 | 0.000 | 0.196 | 3.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 477 | 455 | 381 | 1407 | 0 | 549 | 0 | 0 | 257 | 903 |
N.S. |
1 | 0.95 | 0.80 | 2.95 | 0.00 | 1.15 | 0.00 | 0.00 | 0.54 | 1.89 |
time (sec) |
N/A | 2.769 | 5.570 | 18.705 | 0.000 | 0.160 | 0.000 | 0.000 | 0.243 | 2.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 404 | 421 | 319 | 1265 | 0 | 487 | 0 | 0 | 255 | 600 |
N.S. |
1 | 1.04 | 0.79 | 3.13 | 0.00 | 1.21 | 0.00 | 0.00 | 0.63 | 1.49 |
time (sec) |
N/A | 2.531 | 6.122 | 26.592 | 0.000 | 0.145 | 0.000 | 0.000 | 0.229 | 1.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 379 | 391 | 275 | 1222 | 0 | 474 | 0 | 0 | 246 | 547 |
N.S. |
1 | 1.03 | 0.73 | 3.22 | 0.00 | 1.25 | 0.00 | 0.00 | 0.65 | 1.44 |
time (sec) |
N/A | 2.520 | 8.343 | 14.702 | 0.000 | 0.164 | 0.000 | 0.000 | 0.229 | 1.981 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 373 | 380 | 257 | 1223 | 0 | 455 | 0 | 0 | 246 | 516 |
N.S. |
1 | 1.02 | 0.69 | 3.28 | 0.00 | 1.22 | 0.00 | 0.00 | 0.66 | 1.38 |
time (sec) |
N/A | 2.528 | 7.394 | 14.853 | 0.000 | 0.158 | 0.000 | 0.000 | 0.217 | 2.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 386 | 386 | 316 | 1382 | 0 | 455 | 0 | 0 | 246 | 524 |
N.S. |
1 | 1.00 | 0.82 | 3.58 | 0.00 | 1.18 | 0.00 | 0.00 | 0.64 | 1.36 |
time (sec) |
N/A | 2.598 | 6.613 | 14.490 | 0.000 | 0.143 | 0.000 | 0.000 | 0.256 | 3.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 383 | 390 | 271 | 1423 | 0 | 478 | 0 | 0 | 248 | 559 |
N.S. |
1 | 1.02 | 0.71 | 3.72 | 0.00 | 1.25 | 0.00 | 0.00 | 0.65 | 1.46 |
time (sec) |
N/A | 2.650 | 10.367 | 14.625 | 0.000 | 0.171 | 0.000 | 0.000 | 0.205 | 4.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 401 | 411 | 463 | 1523 | 0 | 525 | 0 | 0 | 259 | 866 |
N.S. |
1 | 1.02 | 1.15 | 3.80 | 0.00 | 1.31 | 0.00 | 0.00 | 0.65 | 2.16 |
time (sec) |
N/A | 2.639 | 13.351 | 16.408 | 0.000 | 0.164 | 0.000 | 0.000 | 0.222 | 5.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 475 | 445 | 381 | 1523 | 0 | 588 | 0 | 0 | 268 | 1161 |
N.S. |
1 | 0.94 | 0.80 | 3.21 | 0.00 | 1.24 | 0.00 | 0.00 | 0.56 | 2.44 |
time (sec) |
N/A | 2.869 | 13.501 | 17.951 | 0.000 | 0.165 | 0.000 | 0.000 | 0.223 | 5.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 311 | 335 | 1097 | 0 | 0 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.09 | 1.18 | 3.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 2.346 | 4.858 | 17.559 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 228 | 272 | 803 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.09 | 1.30 | 3.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 1.675 | 3.951 | 6.087 | 0.000 | 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 | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 158 | 214 | 981 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.07 | 1.46 | 6.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 1.189 | 2.450 | 5.731 | 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 | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 102 | 173 | 323 | 0 | 0 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.05 | 1.78 | 3.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.759 | 2.076 | 4.753 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 212 | 383 | 0 | 0 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.00 | 1.80 | 3.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 1.073 | 1.683 | 3.805 | 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(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 169 | 264 | 447 | 0 | 0 | 0 | 0 | 104 | 0 |
N.S. |
1 | 1.07 | 1.67 | 2.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 1.586 | 2.984 | 4.723 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |