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 | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 42 | 0 | 24 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.75 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.218 | 0.174 | 0.046 | 0.337 | 0.345 | 0.000 | 2.230 | 1.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 40 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.82 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.211 | 0.202 | 0.044 | 0.377 | 0.326 | 0.000 | 2.273 | 1.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 20 | 38 | 0 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.90 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.200 | 0.036 | 0.043 | 0.343 | 0.323 | 0.000 | 1.784 | 1.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 42 | 0 | 24 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.75 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.217 | 0.149 | 0.046 | 0.329 | 0.377 | 0.000 | 2.329 | 1.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 42 | 0 | 24 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.75 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.218 | 0.137 | 0.049 | 0.352 | 0.321 | 0.000 | 2.297 | 1.455 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F(-2) | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 631 | 609 | 373 | 0 | 754 | 1196 | 0 | 556 | 0 |
N.S. |
1 | 0.97 | 0.59 | 0.00 | 1.19 | 1.90 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.869 | 0.241 | 0.000 | 0.287 | 0.344 | 0.000 | 0.389 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F(-2) | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 603 | 581 | 332 | 0 | 731 | 1162 | 0 | 448 | 0 |
N.S. |
1 | 0.96 | 0.55 | 0.00 | 1.21 | 1.93 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.845 | 0.319 | 0.000 | 0.292 | 0.368 | 0.000 | 0.385 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F(-2) | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 588 | 575 | 271 | 0 | 707 | 1236 | 0 | 471 | 0 |
N.S. |
1 | 0.98 | 0.46 | 0.00 | 1.20 | 2.10 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.784 | 0.290 | 0.000 | 0.289 | 0.399 | 0.000 | 0.384 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | A | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 620 | 608 | 235 | 0 | 723 | 1348 | 0 | 494 | 0 |
N.S. |
1 | 0.98 | 0.38 | 0.00 | 1.17 | 2.17 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.823 | 0.161 | 0.000 | 0.297 | 0.381 | 0.000 | 0.398 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | A | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 641 | 629 | 100 | 0 | 739 | 1369 | 0 | 511 | 0 |
N.S. |
1 | 0.98 | 0.16 | 0.00 | 1.15 | 2.14 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.861 | 0.052 | 0.000 | 0.327 | 0.412 | 0.000 | 0.418 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F(-2) | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1002 | 976 | 628 | 0 | 1165 | 2178 | 0 | 885 | 0 |
N.S. |
1 | 0.97 | 0.63 | 0.00 | 1.16 | 2.17 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 1.138 | 0.564 | 0.000 | 0.319 | 0.428 | 0.000 | 0.389 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F(-2) | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 949 | 922 | 478 | 0 | 1119 | 2118 | 0 | 577 | 0 |
N.S. |
1 | 0.97 | 0.50 | 0.00 | 1.18 | 2.23 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 1.175 | 0.622 | 0.000 | 0.315 | 0.460 | 0.000 | 0.431 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F(-2) | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 932 | 904 | 527 | 0 | 1102 | 2112 | 0 | 641 | 0 |
N.S. |
1 | 0.97 | 0.57 | 0.00 | 1.18 | 2.27 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 1.152 | 0.647 | 0.000 | 0.303 | 0.440 | 0.000 | 0.440 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | A | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 935 | 913 | 340 | 0 | 1088 | 2205 | 0 | 675 | 0 |
N.S. |
1 | 0.98 | 0.36 | 0.00 | 1.16 | 2.36 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 1.126 | 0.637 | 0.000 | 0.313 | 0.461 | 0.000 | 0.426 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | A | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 968 | 947 | 294 | 0 | 1110 | 2283 | 0 | 688 | 0 |
N.S. |
1 | 0.98 | 0.30 | 0.00 | 1.15 | 2.36 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 1.148 | 0.183 | 0.000 | 0.312 | 0.434 | 0.000 | 0.438 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1680 | 1677 | 1506 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.522 | 0.911 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1361 | 1261 | 1297 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.659 | 0.296 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1659 | 1658 | 1336 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.259 | 1.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 148 | 0 | 35 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.48 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.228 | 0.012 | 2.543 | 0.000 | 0.352 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 220 | 496 | 0 | 105 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.93 | 6.61 | 0.00 | 1.40 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.375 | 0.176 | 1.418 | 0.000 | 0.338 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 161 | 179 | 659 | 0 | 0 | 417 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 4.09 | 0.00 | 0.00 | 2.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.648 | 0.202 | 0.000 | 0.000 | 0.383 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 132 | 149 | 456 | 0 | 0 | 281 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 3.45 | 0.00 | 0.00 | 2.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.551 | 0.157 | 0.000 | 0.000 | 0.318 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 102 | 118 | 265 | 0 | 0 | 161 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 2.60 | 0.00 | 0.00 | 1.58 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.457 | 0.148 | 0.000 | 0.000 | 0.327 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 49 | 47 | 49 | 180 | 0 | 69 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.00 | 3.67 | 0.00 | 1.41 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.236 | 0.009 | 2.135 | 0.000 | 0.309 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 28 | 44 | 30 | 24 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.57 | 1.07 | 0.86 | 1.07 | 1.07 |
time (sec) |
N/A | 0.407 | 0.441 | 0.079 | 0.376 | 0.302 | 53.375 | 0.333 | 1.720 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 28 | 91 | 30 | 0 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 3.25 | 1.07 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.310 | 2.150 | 0.085 | 0.319 | 0.315 | 0.000 | 0.332 | 1.799 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 28 | 238 | 30 | 0 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 8.50 | 1.07 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.301 | 8.834 | 0.063 | 0.315 | 0.308 | 0.000 | 0.341 | 2.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 76 | 74 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.221 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 174 | 147 | 132 | 0 | 1134 | 0 | 261 | 192 |
N.S. |
1 | 1.03 | 0.87 | 0.78 | 0.00 | 6.71 | 0.00 | 1.54 | 1.14 |
time (sec) |
N/A | 0.354 | 0.079 | 1.463 | 0.000 | 1.067 | 0.000 | 0.445 | 1.619 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 70 | 63 | 105 | 0 | 206 | 235 | 92 | 82 |
N.S. |
1 | 1.11 | 1.00 | 1.67 | 0.00 | 3.27 | 3.73 | 1.46 | 1.30 |
time (sec) |
N/A | 0.205 | 0.027 | 0.762 | 0.000 | 0.323 | 95.181 | 0.338 | 0.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 44 | 47 | 47 | 54 | 46 | 80 | 64 | 46 |
N.S. |
1 | 1.26 | 1.34 | 1.34 | 1.54 | 1.31 | 2.29 | 1.83 | 1.31 |
time (sec) |
N/A | 0.189 | 0.030 | 0.518 | 0.230 | 0.332 | 0.287 | 0.353 | 1.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 43 | 56 | 65 | 65 | 65 | 102 | 171 | 67 |
N.S. |
1 | 0.96 | 1.24 | 1.44 | 1.44 | 1.44 | 2.27 | 3.80 | 1.49 |
time (sec) |
N/A | 0.195 | 0.040 | 0.306 | 0.226 | 0.350 | 0.775 | 0.346 | 1.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 57 | 79 | 111 | 0 | 287 | 0 | 139 | 163 |
N.S. |
1 | 0.97 | 1.34 | 1.88 | 0.00 | 4.86 | 0.00 | 2.36 | 2.76 |
time (sec) |
N/A | 0.200 | 0.096 | 0.927 | 0.000 | 0.338 | 0.000 | 0.533 | 1.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 158 | 66 | 138 | 0 | 1169 | 0 | 319 | 499 |
N.S. |
1 | 0.96 | 0.40 | 0.84 | 0.00 | 7.08 | 0.00 | 1.93 | 3.02 |
time (sec) |
N/A | 0.336 | 0.349 | 1.964 | 0.000 | 1.060 | 0.000 | 0.743 | 1.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 24 | 30 | 19 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.36 | 0.86 | 1.09 | 1.09 |
time (sec) |
N/A | 0.161 | 0.264 | 0.095 | 1.330 | 0.345 | 18.083 | 0.433 | 2.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 221 | 196 | 743 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 3.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.672 | 0.921 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 168 | 150 | 441 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 2.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.561 | 0.432 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 115 | 103 | 219 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.344 | 0.169 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 70 | 77 | 70 | 76 | 107 | 176 | 61 |
N.S. |
1 | 1.00 | 1.40 | 1.54 | 1.40 | 1.52 | 2.14 | 3.52 | 1.22 |
time (sec) |
N/A | 0.189 | 0.034 | 0.201 | 0.211 | 0.323 | 0.757 | 0.321 | 1.500 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 24 | 30 | 19 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.36 | 0.86 | 1.09 | 1.09 |
time (sec) |
N/A | 0.159 | 0.315 | 0.078 | 0.348 | 0.304 | 1.148 | 1.038 | 1.484 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 148 | 62 | 20 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 6.73 | 2.82 | 0.91 | 1.09 | 1.09 |
time (sec) |
N/A | 0.157 | 0.394 | 0.076 | 0.397 | 0.356 | 3.460 | 0.481 | 1.601 |