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 | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 491 | 529 | 527 | 560 | 0 | 12465 | 0 | 959 | 8595 | 97984 |
N.S. |
1 | 1.08 | 1.07 | 1.14 | 0.00 | 25.39 | 0.00 | 1.95 | 17.51 | 199.56 |
time (sec) |
N/A | 0.984 | 3.826 | 1.172 | 0.000 | 23.305 | 0.000 | 0.189 | 0.248 | 116.802 |
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 | 686 | 732 | 6339 | 775 | 0 | 27720 | 0 | 2182 | 19308 | 133067 |
N.S. |
1 | 1.07 | 9.24 | 1.13 | 0.00 | 40.41 | 0.00 | 3.18 | 28.15 | 193.98 |
time (sec) |
N/A | 1.412 | 16.364 | 2.944 | 0.000 | 54.029 | 0.000 | 0.414 | 0.363 | 153.829 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1108 | 1165 | 17142 | 1520 | 0 | 0 | 0 | 2698 | 36506 | 0 |
N.S. |
1 | 1.05 | 15.47 | 1.37 | 0.00 | 0.00 | 0.00 | 2.44 | 32.95 | 0.00 |
time (sec) |
N/A | 2.774 | 16.653 | 52.517 | 0.000 | 0.000 | 0.000 | 0.356 | 98.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1700 | 1781 | 29680 | 2761 | 0 | 0 | 0 | 5220 | 29 | 1321612 |
N.S. |
1 | 1.05 | 17.46 | 1.62 | 0.00 | 0.00 | 0.00 | 3.07 | 0.02 | 777.42 |
time (sec) |
N/A | 4.749 | 17.181 | 252.766 | 0.000 | 0.000 | 0.000 | 0.481 | 200.059 | 51.163 |
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 | 339 | 339 | 486 | 355 | 614 | 628 | 1012 | 772 | 769 | 364 |
N.S. |
1 | 1.00 | 1.43 | 1.05 | 1.81 | 1.85 | 2.99 | 2.28 | 2.27 | 1.07 |
time (sec) |
N/A | 0.616 | 0.393 | 0.977 | 0.038 | 0.095 | 1.632 | 0.131 | 0.179 | 0.124 |
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 | 245 | 245 | 307 | 254 | 376 | 386 | 619 | 495 | 449 | 259 |
N.S. |
1 | 1.00 | 1.25 | 1.04 | 1.53 | 1.58 | 2.53 | 2.02 | 1.83 | 1.06 |
time (sec) |
N/A | 0.523 | 0.232 | 0.925 | 0.041 | 0.090 | 1.495 | 0.125 | 0.165 | 0.072 |
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 | 157 | 157 | 166 | 139 | 180 | 186 | 301 | 268 | 205 | 155 |
N.S. |
1 | 1.00 | 1.06 | 0.89 | 1.15 | 1.18 | 1.92 | 1.71 | 1.31 | 0.99 |
time (sec) |
N/A | 0.331 | 0.113 | 0.832 | 0.036 | 0.082 | 1.120 | 0.121 | 0.166 | 2.455 |
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 | 79 | 79 | 68 | 61 | 80 | 78 | 122 | 105 | 71 | 80 |
N.S. |
1 | 1.00 | 0.86 | 0.77 | 1.01 | 0.99 | 1.54 | 1.33 | 0.90 | 1.01 |
time (sec) |
N/A | 0.221 | 0.042 | 0.585 | 0.033 | 0.100 | 0.727 | 0.116 | 0.165 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 114 | 112 | 113 | 0 | 424 | 180 | 160 | 342 | 169 |
N.S. |
1 | 0.92 | 0.90 | 0.91 | 0.00 | 3.42 | 1.45 | 1.29 | 2.76 | 1.36 |
time (sec) |
N/A | 0.241 | 0.167 | 0.407 | 0.000 | 0.097 | 4.374 | 0.115 | 0.187 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 177 | 175 | 185 | 0 | 793 | 0 | 215 | 900 | 176 |
N.S. |
1 | 1.15 | 1.14 | 1.20 | 0.00 | 5.15 | 0.00 | 1.40 | 5.84 | 1.14 |
time (sec) |
N/A | 0.314 | 0.461 | 0.437 | 0.000 | 0.120 | 0.000 | 0.130 | 0.177 | 0.209 |
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 | 237 | 249 | 240 | 248 | 0 | 1432 | 0 | 509 | 1691 | 337 |
N.S. |
1 | 1.05 | 1.01 | 1.05 | 0.00 | 6.04 | 0.00 | 2.15 | 7.14 | 1.42 |
time (sec) |
N/A | 0.488 | 0.782 | 0.473 | 0.000 | 0.185 | 0.000 | 0.130 | 0.170 | 2.741 |
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 | 329 | 295 | 380 | 379 | 0 | 2380 | 0 | 922 | 2680 | 662 |
N.S. |
1 | 0.90 | 1.16 | 1.15 | 0.00 | 7.23 | 0.00 | 2.80 | 8.15 | 2.01 |
time (sec) |
N/A | 0.508 | 1.691 | 0.498 | 0.000 | 0.284 | 0.000 | 0.138 | 0.182 | 0.434 |
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 | 435 | 344 | 563 | 531 | 0 | 3548 | 0 | 1376 | 3797 | 869 |
N.S. |
1 | 0.79 | 1.29 | 1.22 | 0.00 | 8.16 | 0.00 | 3.16 | 8.73 | 2.00 |
time (sec) |
N/A | 0.512 | 2.573 | 0.593 | 0.000 | 0.385 | 0.000 | 0.154 | 0.197 | 3.018 |
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 | 577 | 577 | 853 | 568 | 1152 | 1174 | 1907 | 1344 | 1509 | 692 |
N.S. |
1 | 1.00 | 1.48 | 0.98 | 2.00 | 2.03 | 3.31 | 2.33 | 2.62 | 1.20 |
time (sec) |
N/A | 1.012 | 0.791 | 1.089 | 0.040 | 0.095 | 2.106 | 0.135 | 0.215 | 0.173 |
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 | 409 | 409 | 553 | 411 | 695 | 712 | 1202 | 884 | 917 | 470 |
N.S. |
1 | 1.00 | 1.35 | 1.00 | 1.70 | 1.74 | 2.94 | 2.16 | 2.24 | 1.15 |
time (sec) |
N/A | 0.702 | 0.489 | 1.024 | 0.038 | 0.091 | 1.759 | 0.137 | 0.172 | 0.112 |
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 | 246 | 246 | 311 | 254 | 376 | 386 | 619 | 495 | 449 | 259 |
N.S. |
1 | 1.00 | 1.26 | 1.03 | 1.53 | 1.57 | 2.52 | 2.01 | 1.83 | 1.05 |
time (sec) |
N/A | 0.480 | 0.222 | 0.912 | 0.049 | 0.079 | 1.464 | 0.127 | 0.178 | 0.079 |
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 | 124 | 131 | 117 | 165 | 171 | 255 | 206 | 167 | 115 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.33 | 1.38 | 2.06 | 1.66 | 1.35 | 0.93 |
time (sec) |
N/A | 0.280 | 0.083 | 0.674 | 0.030 | 0.072 | 0.903 | 0.127 | 0.186 | 2.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 235 | 193 | 192 | 0 | 872 | 393 | 382 | 757 | 328 |
N.S. |
1 | 1.05 | 0.87 | 0.86 | 0.00 | 3.91 | 1.76 | 1.71 | 3.39 | 1.47 |
time (sec) |
N/A | 0.453 | 0.291 | 0.442 | 0.000 | 0.119 | 7.805 | 0.124 | 0.171 | 2.504 |
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 | 219 | 271 | 291 | 226 | 0 | 1546 | 0 | 408 | 1740 | 450 |
N.S. |
1 | 1.24 | 1.33 | 1.03 | 0.00 | 7.06 | 0.00 | 1.86 | 7.95 | 2.05 |
time (sec) |
N/A | 0.454 | 0.699 | 0.530 | 0.000 | 0.129 | 0.000 | 0.133 | 0.172 | 0.221 |
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 | 329 | 400 | 425 | 448 | 0 | 2500 | 0 | 864 | 3133 | 591 |
N.S. |
1 | 1.22 | 1.29 | 1.36 | 0.00 | 7.60 | 0.00 | 2.63 | 9.52 | 1.80 |
time (sec) |
N/A | 0.595 | 1.198 | 0.641 | 0.000 | 0.261 | 0.000 | 0.155 | 0.218 | 2.754 |
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 | 475 | 556 | 616 | 601 | 0 | 3808 | 0 | 1618 | 4777 | 908 |
N.S. |
1 | 1.17 | 1.30 | 1.27 | 0.00 | 8.02 | 0.00 | 3.41 | 10.06 | 1.91 |
time (sec) |
N/A | 0.763 | 1.869 | 0.626 | 0.000 | 0.445 | 0.000 | 0.158 | 0.215 | 2.934 |
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 | 653 | 607 | 908 | 860 | 0 | 5612 | 0 | 2483 | 6708 | 1676 |
N.S. |
1 | 0.93 | 1.39 | 1.32 | 0.00 | 8.59 | 0.00 | 3.80 | 10.27 | 2.57 |
time (sec) |
N/A | 0.822 | 5.531 | 0.763 | 0.000 | 0.723 | 0.000 | 0.180 | 0.247 | 3.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 393 | 0 | 334 | 319 | 0 | 1561 | 768 | 767 | 1402 | 533 |
N.S. |
1 | 0.00 | 0.85 | 0.81 | 0.00 | 3.97 | 1.95 | 1.95 | 3.57 | 1.36 |
time (sec) |
N/A | 0.000 | 0.566 | 0.535 | 0.000 | 0.111 | 14.122 | 0.131 | 0.194 | 0.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 0 | 193 | 192 | 0 | 858 | 393 | 382 | 757 | 328 |
N.S. |
1 | 0.00 | 0.87 | 0.87 | 0.00 | 3.88 | 1.78 | 1.73 | 3.43 | 1.48 |
time (sec) |
N/A | 0.000 | 0.312 | 0.444 | 0.000 | 0.098 | 7.695 | 0.128 | 0.175 | 2.469 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 114 | 112 | 112 | 0 | 421 | 180 | 160 | 342 | 169 |
N.S. |
1 | 0.92 | 0.90 | 0.90 | 0.00 | 3.40 | 1.45 | 1.29 | 2.76 | 1.36 |
time (sec) |
N/A | 0.255 | 0.160 | 0.389 | 0.000 | 0.088 | 4.239 | 0.125 | 0.169 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 74 | 64 | 0 | 208 | 92 | 66 | 122 | 62 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.00 | 2.81 | 1.24 | 0.89 | 1.65 | 0.84 |
time (sec) |
N/A | 0.197 | 0.112 | 0.369 | 0.000 | 0.075 | 1.514 | 0.124 | 0.185 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 131 | 101 | 0 | 971 | 162 | 113 | 405 | 3821 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.00 | 7.41 | 1.24 | 0.86 | 3.09 | 29.17 |
time (sec) |
N/A | 0.246 | 0.318 | 0.543 | 0.000 | 0.344 | 20.737 | 0.128 | 0.206 | 4.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 243 | 195 | 230 | 0 | 2580 | 0 | 282 | 2158 | 24052 |
N.S. |
1 | 1.16 | 0.93 | 1.10 | 0.00 | 12.34 | 0.00 | 1.35 | 10.33 | 115.08 |
time (sec) |
N/A | 0.452 | 0.779 | 0.578 | 0.000 | 9.624 | 0.000 | 0.131 | 0.204 | 6.550 |
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 | 363 | 418 | 363 | 400 | 0 | 7674 | 0 | 835 | 6282 | 351830 |
N.S. |
1 | 1.15 | 1.00 | 1.10 | 0.00 | 21.14 | 0.00 | 2.30 | 17.31 | 969.23 |
time (sec) |
N/A | 0.707 | 2.347 | 0.822 | 0.000 | 177.670 | 0.000 | 0.157 | 0.237 | 19.376 |
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 | 599 | 678 | 724 | 758 | 0 | 0 | 0 | 2114 | 13481 | 634320 |
N.S. |
1 | 1.13 | 1.21 | 1.27 | 0.00 | 0.00 | 0.00 | 3.53 | 22.51 | 1058.96 |
time (sec) |
N/A | 1.298 | 6.688 | 1.218 | 0.000 | 0.000 | 0.000 | 0.228 | 0.300 | 29.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 946 | 1051 | 4159 | 1405 | 0 | 0 | 0 | 4455 | 24455 | 998307 |
N.S. |
1 | 1.11 | 4.40 | 1.49 | 0.00 | 0.00 | 0.00 | 4.71 | 25.85 | 1055.29 |
time (sec) |
N/A | 2.327 | 16.163 | 15.543 | 0.000 | 0.000 | 0.000 | 0.331 | 0.475 | 43.569 |
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 | 316 | 454 | 453 | 370 | 0 | 2564 | 0 | 707 | 2831 | 680 |
N.S. |
1 | 1.44 | 1.43 | 1.17 | 0.00 | 8.11 | 0.00 | 2.24 | 8.96 | 2.15 |
time (sec) |
N/A | 0.819 | 1.279 | 0.582 | 0.000 | 0.204 | 0.000 | 0.145 | 0.233 | 0.272 |
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 | 218 | 271 | 286 | 223 | 0 | 1547 | 0 | 407 | 1740 | 450 |
N.S. |
1 | 1.24 | 1.31 | 1.02 | 0.00 | 7.10 | 0.00 | 1.87 | 7.98 | 2.06 |
time (sec) |
N/A | 0.455 | 0.709 | 0.533 | 0.000 | 0.129 | 0.000 | 0.134 | 0.182 | 0.214 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 176 | 176 | 182 | 0 | 807 | 0 | 214 | 900 | 176 |
N.S. |
1 | 1.14 | 1.14 | 1.18 | 0.00 | 5.24 | 0.00 | 1.39 | 5.84 | 1.14 |
time (sec) |
N/A | 0.338 | 0.437 | 0.466 | 0.000 | 0.108 | 0.000 | 0.130 | 0.178 | 0.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 99 | 89 | 0 | 402 | 0 | 122 | 358 | 100 |
N.S. |
1 | 1.00 | 0.99 | 0.89 | 0.00 | 4.02 | 0.00 | 1.22 | 3.58 | 1.00 |
time (sec) |
N/A | 0.245 | 0.289 | 0.362 | 0.000 | 0.089 | 0.000 | 0.123 | 0.183 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 241 | 196 | 231 | 0 | 2596 | 0 | 281 | 2158 | 24052 |
N.S. |
1 | 1.16 | 0.95 | 1.12 | 0.00 | 12.54 | 0.00 | 1.36 | 10.43 | 116.19 |
time (sec) |
N/A | 0.422 | 0.788 | 0.622 | 0.000 | 9.441 | 0.000 | 0.133 | 0.208 | 6.905 |
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 | 347 | 402 | 351 | 361 | 0 | 7176 | 0 | 840 | 8083 | 384543 |
N.S. |
1 | 1.16 | 1.01 | 1.04 | 0.00 | 20.68 | 0.00 | 2.42 | 23.29 | 1108.19 |
time (sec) |
N/A | 0.675 | 3.032 | 0.871 | 0.000 | 172.737 | 0.000 | 0.174 | 0.245 | 19.301 |
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 | 595 | 670 | 721 | 709 | 0 | 0 | 0 | 1273 | 18732 | 691756 |
N.S. |
1 | 1.13 | 1.21 | 1.19 | 0.00 | 0.00 | 0.00 | 2.14 | 31.48 | 1162.62 |
time (sec) |
N/A | 1.234 | 13.014 | 3.350 | 0.000 | 0.000 | 0.000 | 0.189 | 0.321 | 33.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 964 | 1063 | 5396 | 1477 | 0 | 0 | 0 | 2757 | 34058 | 1088917 |
N.S. |
1 | 1.10 | 5.60 | 1.53 | 0.00 | 0.00 | 0.00 | 2.86 | 35.33 | 1129.58 |
time (sec) |
N/A | 2.455 | 16.206 | 50.119 | 0.000 | 0.000 | 0.000 | 0.278 | 0.503 | 44.957 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1482 | 1606 | 9480 | 2496 | 0 | 0 | 0 | 5347 | 55226 | 1563828 |
N.S. |
1 | 1.08 | 6.40 | 1.68 | 0.00 | 0.00 | 0.00 | 3.61 | 37.26 | 1055.21 |
time (sec) |
N/A | 3.820 | 16.339 | 213.833 | 0.000 | 0.000 | 0.000 | 0.397 | 1.232 | 58.380 |
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 | 390 | 573 | 643 | 589 | 0 | 3979 | 0 | 1306 | 4932 | 1242 |
N.S. |
1 | 1.47 | 1.65 | 1.51 | 0.00 | 10.20 | 0.00 | 3.35 | 12.65 | 3.18 |
time (sec) |
N/A | 0.959 | 1.625 | 0.786 | 0.000 | 0.340 | 0.000 | 0.151 | 0.225 | 0.476 |
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 | 324 | 395 | 422 | 451 | 0 | 2518 | 0 | 864 | 3133 | 591 |
N.S. |
1 | 1.22 | 1.30 | 1.39 | 0.00 | 7.77 | 0.00 | 2.67 | 9.67 | 1.82 |
time (sec) |
N/A | 0.573 | 1.151 | 0.619 | 0.000 | 0.251 | 0.000 | 0.144 | 0.206 | 0.400 |
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 | 239 | 253 | 245 | 249 | 0 | 1442 | 0 | 509 | 1691 | 337 |
N.S. |
1 | 1.06 | 1.03 | 1.04 | 0.00 | 6.03 | 0.00 | 2.13 | 7.08 | 1.41 |
time (sec) |
N/A | 0.464 | 0.736 | 0.474 | 0.000 | 0.145 | 0.000 | 0.126 | 0.169 | 0.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 150 | 142 | 149 | 0 | 839 | 0 | 257 | 735 | 228 |
N.S. |
1 | 0.97 | 0.92 | 0.96 | 0.00 | 5.41 | 0.00 | 1.66 | 4.74 | 1.47 |
time (sec) |
N/A | 0.268 | 0.593 | 0.410 | 0.000 | 0.106 | 0.000 | 0.131 | 0.168 | 2.625 |
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 | 363 | 418 | 370 | 384 | 0 | 7703 | 0 | 835 | 6278 | 351830 |
N.S. |
1 | 1.15 | 1.02 | 1.06 | 0.00 | 21.22 | 0.00 | 2.30 | 17.29 | 969.23 |
time (sec) |
N/A | 0.702 | 2.220 | 0.875 | 0.000 | 172.558 | 0.000 | 0.155 | 0.221 | 18.452 |
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 | 582 | 649 | 727 | 706 | 0 | 0 | 0 | 1274 | 18732 | 691757 |
N.S. |
1 | 1.12 | 1.25 | 1.21 | 0.00 | 0.00 | 0.00 | 2.19 | 32.19 | 1188.59 |
time (sec) |
N/A | 1.242 | 12.230 | 3.364 | 0.000 | 0.000 | 0.000 | 0.189 | 0.326 | 33.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 922 | 1006 | 5488 | 1094 | 0 | 0 | 0 | 5069 | 29 | 1098262 |
N.S. |
1 | 1.09 | 5.95 | 1.19 | 0.00 | 0.00 | 0.00 | 5.50 | 0.03 | 1191.17 |
time (sec) |
N/A | 2.075 | 16.204 | 59.856 | 0.000 | 0.000 | 0.000 | 0.468 | 200.025 | 44.433 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1417 | 1526 | 9721 | 1854 | 0 | 0 | 0 | 3617 | 60838 | 1590452 |
N.S. |
1 | 1.08 | 6.86 | 1.31 | 0.00 | 0.00 | 0.00 | 2.55 | 42.93 | 1122.41 |
time (sec) |
N/A | 3.652 | 16.341 | 293.424 | 0.000 | 0.000 | 0.000 | 0.399 | 1.744 | 56.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2077 | 2212 | 14739 | 3250 | 0 | 0 | 0 | 6287 | 92781 | 0 |
N.S. |
1 | 1.06 | 7.10 | 1.56 | 0.00 | 0.00 | 0.00 | 3.03 | 44.67 | 0.00 |
time (sec) |
N/A | 5.536 | 16.583 | 0.089 | 0.000 | 0.000 | 0.000 | 0.526 | 9.734 | 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 | 337 | 337 | 480 | 428 | 622 | 637 | 804 | 965 | 771 | 537 |
N.S. |
1 | 1.00 | 1.42 | 1.27 | 1.85 | 1.89 | 2.39 | 2.86 | 2.29 | 1.59 |
time (sec) |
N/A | 0.599 | 0.415 | 0.391 | 0.039 | 0.125 | 62.598 | 0.148 | 0.274 | 0.152 |
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 | 243 | 243 | 302 | 276 | 384 | 396 | 486 | 573 | 451 | 368 |
N.S. |
1 | 1.00 | 1.24 | 1.14 | 1.58 | 1.63 | 2.00 | 2.36 | 1.86 | 1.51 |
time (sec) |
N/A | 0.505 | 0.264 | 0.349 | 0.041 | 0.091 | 23.217 | 0.137 | 0.297 | 2.471 |
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 | 155 | 155 | 161 | 150 | 188 | 195 | 241 | 273 | 207 | 201 |
N.S. |
1 | 1.00 | 1.04 | 0.97 | 1.21 | 1.26 | 1.55 | 1.76 | 1.34 | 1.30 |
time (sec) |
N/A | 0.337 | 0.120 | 0.303 | 0.035 | 0.110 | 6.319 | 0.133 | 0.265 | 0.065 |
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 | 77 | 77 | 67 | 64 | 87 | 87 | 107 | 100 | 72 | 79 |
N.S. |
1 | 1.00 | 0.87 | 0.83 | 1.13 | 1.13 | 1.39 | 1.30 | 0.94 | 1.03 |
time (sec) |
N/A | 0.231 | 0.054 | 0.276 | 0.029 | 0.072 | 1.575 | 0.122 | 0.261 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 137 | 131 | 141 | 0 | 656 | 175 | 143 | 373 | 182 |
N.S. |
1 | 1.11 | 1.07 | 1.15 | 0.00 | 5.33 | 1.42 | 1.16 | 3.03 | 1.48 |
time (sec) |
N/A | 0.279 | 0.224 | 0.405 | 0.000 | 0.097 | 8.188 | 0.127 | 0.274 | 0.143 |
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 | 180 | 229 | 215 | 209 | 0 | 1437 | 0 | 360 | 1089 | 269 |
N.S. |
1 | 1.27 | 1.19 | 1.16 | 0.00 | 7.98 | 0.00 | 2.00 | 6.05 | 1.49 |
time (sec) |
N/A | 0.415 | 0.657 | 0.447 | 0.000 | 0.135 | 0.000 | 0.138 | 0.305 | 0.284 |
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 | 278 | 299 | 347 | 357 | 0 | 2506 | 0 | 607 | 2007 | 442 |
N.S. |
1 | 1.08 | 1.25 | 1.28 | 0.00 | 9.01 | 0.00 | 2.18 | 7.22 | 1.59 |
time (sec) |
N/A | 0.460 | 1.526 | 0.512 | 0.000 | 0.248 | 0.000 | 0.146 | 0.308 | 2.803 |
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 | 374 | 345 | 527 | 519 | 0 | 3796 | 0 | 1033 | 3040 | 785 |
N.S. |
1 | 0.92 | 1.41 | 1.39 | 0.00 | 10.15 | 0.00 | 2.76 | 8.13 | 2.10 |
time (sec) |
N/A | 0.483 | 2.353 | 0.573 | 0.000 | 0.494 | 0.000 | 0.152 | 0.284 | 0.724 |
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 | 477 | 391 | 747 | 709 | 0 | 5254 | 0 | 1508 | 4152 | 991 |
N.S. |
1 | 0.82 | 1.57 | 1.49 | 0.00 | 11.01 | 0.00 | 3.16 | 8.70 | 2.08 |
time (sec) |
N/A | 0.524 | 4.749 | 0.674 | 0.000 | 1.100 | 0.000 | 0.176 | 0.308 | 3.365 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 575 | 575 | 845 | 736 | 1160 | 1183 | 0 | 1849 | 1511 | 1011 |
N.S. |
1 | 1.00 | 1.47 | 1.28 | 2.02 | 2.06 | 0.00 | 3.22 | 2.63 | 1.76 |
time (sec) |
N/A | 0.971 | 0.811 | 0.480 | 0.044 | 0.098 | 0.000 | 0.167 | 0.374 | 0.177 |
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 | 407 | 407 | 546 | 479 | 703 | 721 | 949 | 1137 | 919 | 683 |
N.S. |
1 | 1.00 | 1.34 | 1.18 | 1.73 | 1.77 | 2.33 | 2.79 | 2.26 | 1.68 |
time (sec) |
N/A | 0.726 | 0.470 | 0.443 | 0.061 | 0.088 | 88.517 | 0.153 | 0.197 | 0.122 |
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 | 244 | 244 | 306 | 276 | 384 | 396 | 486 | 573 | 451 | 368 |
N.S. |
1 | 1.00 | 1.25 | 1.13 | 1.57 | 1.62 | 1.99 | 2.35 | 1.85 | 1.51 |
time (sec) |
N/A | 0.462 | 0.245 | 0.356 | 0.045 | 0.087 | 23.098 | 0.139 | 0.168 | 0.082 |
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 | 122 | 122 | 129 | 125 | 173 | 180 | 207 | 221 | 169 | 154 |
N.S. |
1 | 1.00 | 1.06 | 1.02 | 1.42 | 1.48 | 1.70 | 1.81 | 1.39 | 1.26 |
time (sec) |
N/A | 0.292 | 0.094 | 0.313 | 0.040 | 0.083 | 3.636 | 0.125 | 0.246 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 224 | 221 | 231 | 0 | 1266 | 304 | 290 | 790 | 326 |
N.S. |
1 | 1.29 | 1.28 | 1.34 | 0.00 | 7.32 | 1.76 | 1.68 | 4.57 | 1.88 |
time (sec) |
N/A | 0.441 | 0.455 | 0.471 | 0.000 | 0.131 | 14.705 | 0.131 | 0.254 | 0.135 |
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 | 216 | 326 | 331 | 352 | 0 | 2405 | 0 | 620 | 1935 | 601 |
N.S. |
1 | 1.51 | 1.53 | 1.63 | 0.00 | 11.13 | 0.00 | 2.87 | 8.96 | 2.78 |
time (sec) |
N/A | 0.515 | 0.985 | 0.587 | 0.000 | 0.183 | 0.000 | 0.143 | 0.309 | 2.847 |
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 | 354 | 539 | 559 | 580 | 0 | 3998 | 0 | 981 | 3593 | 781 |
N.S. |
1 | 1.52 | 1.58 | 1.64 | 0.00 | 11.29 | 0.00 | 2.77 | 10.15 | 2.21 |
time (sec) |
N/A | 0.770 | 1.945 | 0.681 | 0.000 | 0.390 | 0.000 | 0.151 | 0.287 | 2.934 |
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 | 517 | 604 | 831 | 862 | 0 | 5894 | 0 | 1761 | 5440 | 1085 |
N.S. |
1 | 1.17 | 1.61 | 1.67 | 0.00 | 11.40 | 0.00 | 3.41 | 10.52 | 2.10 |
time (sec) |
N/A | 0.843 | 3.826 | 0.769 | 0.000 | 0.722 | 0.000 | 0.169 | 0.329 | 3.160 |
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 | 695 | 654 | 1191 | 1179 | 0 | 8170 | 0 | 2648 | 7371 | 1824 |
N.S. |
1 | 0.94 | 1.71 | 1.70 | 0.00 | 11.76 | 0.00 | 3.81 | 10.61 | 2.62 |
time (sec) |
N/A | 0.892 | 9.845 | 1.005 | 0.000 | 1.236 | 0.000 | 0.203 | 0.378 | 4.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 403 | 381 | 419 | 0 | 2179 | 547 | 542 | 1423 | 512 |
N.S. |
1 | 1.49 | 1.41 | 1.55 | 0.00 | 8.07 | 2.03 | 2.01 | 5.27 | 1.90 |
time (sec) |
N/A | 0.835 | 0.785 | 0.553 | 0.000 | 0.160 | 25.131 | 0.147 | 0.275 | 0.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 223 | 224 | 230 | 0 | 1262 | 304 | 290 | 790 | 326 |
N.S. |
1 | 1.29 | 1.29 | 1.33 | 0.00 | 7.29 | 1.76 | 1.68 | 4.57 | 1.88 |
time (sec) |
N/A | 0.452 | 0.432 | 0.475 | 0.000 | 0.110 | 14.628 | 0.125 | 0.260 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 137 | 131 | 140 | 0 | 657 | 175 | 143 | 373 | 182 |
N.S. |
1 | 1.11 | 1.07 | 1.14 | 0.00 | 5.34 | 1.42 | 1.16 | 3.03 | 1.48 |
time (sec) |
N/A | 0.287 | 0.211 | 0.395 | 0.000 | 0.094 | 8.195 | 0.127 | 0.281 | 0.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 88 | 77 | 0 | 377 | 109 | 87 | 161 | 96 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 4.28 | 1.24 | 0.99 | 1.83 | 1.09 |
time (sec) |
N/A | 0.226 | 0.199 | 0.353 | 0.000 | 0.100 | 3.283 | 0.122 | 0.240 | 2.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 208 | 169 | 169 | 0 | 1604 | 204 | 197 | 909 | 30821 |
N.S. |
1 | 1.22 | 0.99 | 0.99 | 0.00 | 9.44 | 1.20 | 1.16 | 5.35 | 181.30 |
time (sec) |
N/A | 0.404 | 0.669 | 0.572 | 0.000 | 20.211 | 18.177 | 0.139 | 0.289 | 6.502 |
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 | 287 | 344 | 290 | 277 | 0 | 0 | 0 | 623 | 4163 | 404752 |
N.S. |
1 | 1.20 | 1.01 | 0.97 | 0.00 | 0.00 | 0.00 | 2.17 | 14.51 | 1410.29 |
time (sec) |
N/A | 0.685 | 1.750 | 0.720 | 0.000 | 0.000 | 0.000 | 0.158 | 0.303 | 27.358 |
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 | 506 | 580 | 657 | 680 | 0 | 0 | 0 | 1130 | 10467 | 802142 |
N.S. |
1 | 1.15 | 1.30 | 1.34 | 0.00 | 0.00 | 0.00 | 2.23 | 20.69 | 1585.26 |
time (sec) |
N/A | 1.186 | 6.497 | 1.197 | 0.000 | 0.000 | 0.000 | 0.233 | 0.395 | 79.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 831 | 929 | 565 | 1318 | 0 | 0 | 0 | 2492 | 20501 | 0 |
N.S. |
1 | 1.12 | 0.68 | 1.59 | 0.00 | 0.00 | 0.00 | 3.00 | 24.67 | 0.00 |
time (sec) |
N/A | 2.133 | 10.662 | 30.698 | 0.000 | 0.000 | 0.000 | 0.436 | 0.485 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1290 | 1414 | 918 | 2320 | 0 | 0 | 0 | 4921 | 34973 | 0 |
N.S. |
1 | 1.10 | 0.71 | 1.80 | 0.00 | 0.00 | 0.00 | 3.81 | 27.11 | 0.00 |
time (sec) |
N/A | 3.527 | 11.755 | 207.014 | 0.000 | 0.000 | 0.000 | 0.999 | 0.717 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 471 | 526 | 514 | 0 | 3748 | 0 | 936 | 3035 | 837 |
N.S. |
1 | 1.78 | 1.98 | 1.94 | 0.00 | 14.14 | 0.00 | 3.53 | 11.45 | 3.16 |
time (sec) |
N/A | 0.804 | 1.415 | 0.733 | 0.000 | 0.276 | 0.000 | 0.149 | 0.180 | 0.364 |
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 | 218 | 317 | 333 | 349 | 0 | 2423 | 0 | 623 | 1935 | 601 |
N.S. |
1 | 1.45 | 1.53 | 1.60 | 0.00 | 11.11 | 0.00 | 2.86 | 8.88 | 2.76 |
time (sec) |
N/A | 0.491 | 0.851 | 0.608 | 0.000 | 0.178 | 0.000 | 0.137 | 0.162 | 0.387 |
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 | 181 | 227 | 216 | 209 | 0 | 1445 | 0 | 360 | 1089 | 269 |
N.S. |
1 | 1.25 | 1.19 | 1.15 | 0.00 | 7.98 | 0.00 | 1.99 | 6.02 | 1.49 |
time (sec) |
N/A | 0.397 | 0.654 | 0.513 | 0.000 | 0.141 | 0.000 | 0.133 | 0.160 | 2.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 142 | 122 | 129 | 0 | 796 | 0 | 193 | 476 | 154 |
N.S. |
1 | 1.11 | 0.95 | 1.01 | 0.00 | 6.22 | 0.00 | 1.51 | 3.72 | 1.20 |
time (sec) |
N/A | 0.274 | 0.401 | 0.431 | 0.000 | 0.101 | 0.000 | 0.126 | 0.162 | 0.118 |
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 | 288 | 345 | 289 | 275 | 0 | 0 | 0 | 618 | 4163 | 404752 |
N.S. |
1 | 1.20 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 2.15 | 14.45 | 1405.39 |
time (sec) |
N/A | 0.661 | 2.350 | 0.791 | 0.000 | 0.000 | 0.000 | 0.157 | 0.202 | 27.665 |
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 | 494 | 565 | 608 | 391 | 0 | 0 | 0 | 1867 | 12668 | 853229 |
N.S. |
1 | 1.14 | 1.23 | 0.79 | 0.00 | 0.00 | 0.00 | 3.78 | 25.64 | 1727.18 |
time (sec) |
N/A | 1.171 | 10.945 | 1.618 | 0.000 | 0.000 | 0.000 | 0.251 | 0.274 | 99.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 848 | 936 | 561 | 815 | 0 | 0 | 0 | 2417 | 26977 | 0 |
N.S. |
1 | 1.10 | 0.66 | 0.96 | 0.00 | 0.00 | 0.00 | 2.85 | 31.81 | 0.00 |
time (sec) |
N/A | 2.209 | 10.886 | 99.398 | 0.000 | 0.000 | 0.000 | 0.321 | 0.445 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1340 | 1452 | 902 | 1943 | 0 | 0 | 0 | 4339 | 46641 | 0 |
N.S. |
1 | 1.08 | 0.67 | 1.45 | 0.00 | 0.00 | 0.00 | 3.24 | 34.81 | 0.00 |
time (sec) |
N/A | 3.775 | 11.646 | 398.569 | 0.000 | 0.000 | 0.000 | 0.493 | 1.005 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | F(-1) | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1991 | 2129 | 1410 | 3944 | 0 | 0 | 0 | 7412 | 72551 | 0 |
N.S. |
1 | 1.07 | 0.71 | 1.98 | 0.00 | 0.00 | 0.00 | 3.72 | 36.44 | 0.00 |
time (sec) |
N/A | 6.048 | 13.789 | 0.085 | 0.000 | 0.000 | 0.000 | 0.847 | 5.785 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 385 | 638 | 786 | 782 | 0 | 5799 | 0 | 1383 | 5447 | 1540 |
N.S. |
1 | 1.66 | 2.04 | 2.03 | 0.00 | 15.06 | 0.00 | 3.59 | 14.15 | 4.00 |
time (sec) |
N/A | 1.019 | 2.237 | 1.109 | 0.000 | 0.506 | 0.000 | 0.170 | 0.260 | 0.980 |
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 | 355 | 513 | 562 | 582 | 0 | 3988 | 0 | 980 | 3593 | 781 |
N.S. |
1 | 1.45 | 1.58 | 1.64 | 0.00 | 11.23 | 0.00 | 2.76 | 10.12 | 2.20 |
time (sec) |
N/A | 0.731 | 1.976 | 0.750 | 0.000 | 0.398 | 0.000 | 0.155 | 0.208 | 3.535 |
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 | 280 | 293 | 351 | 358 | 0 | 2496 | 0 | 607 | 2007 | 442 |
N.S. |
1 | 1.05 | 1.25 | 1.28 | 0.00 | 8.91 | 0.00 | 2.17 | 7.17 | 1.58 |
time (sec) |
N/A | 0.442 | 1.445 | 0.584 | 0.000 | 0.238 | 0.000 | 0.147 | 0.185 | 0.387 |
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 | 181 | 188 | 186 | 193 | 0 | 1468 | 0 | 340 | 892 | 296 |
N.S. |
1 | 1.04 | 1.03 | 1.07 | 0.00 | 8.11 | 0.00 | 1.88 | 4.93 | 1.64 |
time (sec) |
N/A | 0.292 | 0.869 | 0.474 | 0.000 | 0.144 | 0.000 | 0.135 | 0.182 | 0.214 |
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 | 516 | 589 | 649 | 680 | 0 | 0 | 0 | 1130 | 10467 | 802140 |
N.S. |
1 | 1.14 | 1.26 | 1.32 | 0.00 | 0.00 | 0.00 | 2.19 | 20.28 | 1554.53 |
time (sec) |
N/A | 1.171 | 5.695 | 1.418 | 0.000 | 0.000 | 0.000 | 0.232 | 0.255 | 84.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 838 | 915 | 544 | 817 | 0 | 0 | 0 | 2420 | 26977 | 0 |
N.S. |
1 | 1.09 | 0.65 | 0.97 | 0.00 | 0.00 | 0.00 | 2.89 | 32.19 | 0.00 |
time (sec) |
N/A | 2.196 | 11.122 | 126.088 | 0.000 | 0.000 | 0.000 | 0.367 | 0.450 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1292 | 1388 | 871 | 1287 | 0 | 0 | 0 | 7132 | 29 | 0 |
N.S. |
1 | 1.07 | 0.67 | 1.00 | 0.00 | 0.00 | 0.00 | 5.52 | 0.02 | 0.00 |
time (sec) |
N/A | 3.617 | 11.722 | 539.704 | 0.000 | 0.000 | 0.000 | 6.871 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1935 | 2056 | 1338 | 2348 | 0 | 0 | 0 | 4418 | 29 | 0 |
N.S. |
1 | 1.06 | 0.69 | 1.21 | 0.00 | 0.00 | 0.00 | 2.28 | 0.01 | 0.00 |
time (sec) |
N/A | 5.798 | 12.760 | 0.118 | 0.000 | 0.000 | 0.000 | 0.995 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2754 | 2899 | 14143 | 4394 | 0 | 0 | 0 | 7241 | 29 | 0 |
N.S. |
1 | 1.05 | 5.14 | 1.60 | 0.00 | 0.00 | 0.00 | 2.63 | 0.01 | 0.00 |
time (sec) |
N/A | 8.832 | 16.568 | 0.124 | 0.000 | 0.000 | 0.000 | 1.545 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 395 | 461 | 337 | 4511 | 0 | 0 | 0 | 1652 | 29 | 0 |
N.S. |
1 | 1.17 | 0.85 | 11.42 | 0.00 | 0.00 | 0.00 | 4.18 | 0.07 | 0.00 |
time (sec) |
N/A | 0.932 | 1.739 | 0.445 | 0.000 | 0.000 | 0.000 | 1.299 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 396 | 425 | 339 | 4511 | 0 | 0 | 0 | 1657 | 29 | 0 |
N.S. |
1 | 1.07 | 0.86 | 11.39 | 0.00 | 0.00 | 0.00 | 4.18 | 0.07 | 0.00 |
time (sec) |
N/A | 0.795 | 1.757 | 0.419 | 0.000 | 0.000 | 0.000 | 1.342 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 479 | 285 | 461 | 2383 | 0 | 1746 | 0 | 2485 | 27 | 0 |
N.S. |
1 | 0.59 | 0.96 | 4.97 | 0.00 | 3.65 | 0.00 | 5.19 | 0.06 | 0.00 |
time (sec) |
N/A | 0.366 | 1.476 | 0.323 | 0.000 | 2.094 | 0.000 | 0.462 | 200.071 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 382 | 246 | 332 | 1627 | 0 | 1190 | 0 | 1366 | 1398 | 0 |
N.S. |
1 | 0.64 | 0.87 | 4.26 | 0.00 | 3.12 | 0.00 | 3.58 | 3.66 | 0.00 |
time (sec) |
N/A | 0.326 | 1.100 | 0.329 | 0.000 | 0.781 | 0.000 | 0.320 | 3.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 202 | 254 | 1019 | 0 | 774 | 0 | 559 | 878 | 2493 |
N.S. |
1 | 0.73 | 0.91 | 3.67 | 0.00 | 2.78 | 0.00 | 2.01 | 3.16 | 8.97 |
time (sec) |
N/A | 0.302 | 10.665 | 0.332 | 0.000 | 0.381 | 0.000 | 0.211 | 0.281 | 60.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 242 | 201 | 1118 | 0 | 802 | 0 | 404 | 729 | 0 |
N.S. |
1 | 1.09 | 0.90 | 5.01 | 0.00 | 3.60 | 0.00 | 1.81 | 3.27 | 0.00 |
time (sec) |
N/A | 0.338 | 0.483 | 0.332 | 0.000 | 3.844 | 0.000 | 0.294 | 0.249 | 0.000 |