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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 820 | 858 | 73 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.05 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 |
time (sec) |
N/A | 0.674 | 0.020 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 780 | 822 | 71 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.05 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.668 | 0.017 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 813 | 860 | 71 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.06 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.677 | 0.017 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.490 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 858 | 908 | 73 | 0 | 0 | 0 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.06 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.738 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.877 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 440 | 468 | 73 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.06 | 0.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.349 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.803 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 405 | 427 | 73 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.05 | 0.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.321 | 0.024 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.502 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 386 | 73 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.04 | 0.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.297 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 343 | 357 | 71 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.04 | 0.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.280 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 386 | 71 | 0 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.04 | 0.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.318 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.419 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 410 | 434 | 73 | 0 | 0 | 0 | 0 | 0 | 211 | 0 |
N.S. |
1 | 1.06 | 0.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.329 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.695 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 880 | 929 | 73 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.711 | 0.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 5.111 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 844 | 888 | 73 | 0 | 0 | 0 | 0 | 0 | 372 | 0 |
N.S. |
1 | 1.05 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.699 | 0.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.719 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 806 | 847 | 73 | 0 | 0 | 0 | 0 | 0 | 276 | 0 |
N.S. |
1 | 1.05 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.692 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 817 | 864 | 71 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.06 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.696 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 844 | 910 | 71 | 0 | 0 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.08 | 0.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.704 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.419 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 890 | 958 | 73 | 0 | 0 | 0 | 0 | 0 | 293 | 0 |
N.S. |
1 | 1.08 | 0.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.729 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.722 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 205 | 248 | 0 | 0 | 717 | 0 | 0 | 326 | 0 |
N.S. |
1 | 0.93 | 1.13 | 0.00 | 0.00 | 3.26 | 0.00 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.227 | 0.471 | 0.000 | 0.000 | 0.114 | 0.000 | 0.000 | 23.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 164 | 228 | 0 | 0 | 596 | 0 | 0 | 17 | 0 |
N.S. |
1 | 0.95 | 1.32 | 0.00 | 0.00 | 3.45 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.202 | 0.349 | 0.000 | 0.000 | 0.102 | 0.000 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 155 | 209 | 0 | 0 | 233 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.03 | 1.39 | 0.00 | 0.00 | 1.55 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.190 | 0.219 | 0.000 | 0.000 | 0.077 | 0.000 | 0.000 | 0.356 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 65 | 0 | 0 | 41 | 92 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 2.03 | 0.00 | 0.00 | 1.28 | 2.88 |
time (sec) |
N/A | 0.138 | 0.026 | 0.161 | 0.000 | 0.083 | 0.000 | 0.000 | 0.235 | 0.387 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 54 | 0 | 175 | 0 | 0 | 143 | 127 |
N.S. |
1 | 1.00 | 0.70 | 0.82 | 0.00 | 2.65 | 0.00 | 0.00 | 2.17 | 1.92 |
time (sec) |
N/A | 0.156 | 0.131 | 0.159 | 0.000 | 0.074 | 0.000 | 0.000 | 0.239 | 0.469 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 337 | 0 | 0 | 302 | 203 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 3.34 | 0.00 | 0.00 | 2.99 | 2.01 |
time (sec) |
N/A | 0.179 | 0.275 | 0.299 | 0.000 | 0.077 | 0.000 | 0.000 | 0.284 | 0.580 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 533 | 0 | 0 | 508 | 293 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 3.92 | 0.00 | 0.00 | 3.74 | 2.15 |
time (sec) |
N/A | 0.202 | 0.396 | 0.302 | 0.000 | 0.087 | 0.000 | 0.000 | 0.311 | 0.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 504 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.69 | 0.00 |
time (sec) |
N/A | 0.166 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 3.008 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 399 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 6.88 | 0.00 |
time (sec) |
N/A | 0.163 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.861 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 72 | 71 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.29 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.162 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 6.483 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.163 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 85.611 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.162 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 205 | 249 | 0 | 0 | 740 | 0 | 0 | 40 | 0 |
N.S. |
1 | 0.94 | 1.15 | 0.00 | 0.00 | 3.41 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.222 | 0.462 | 0.000 | 0.000 | 0.121 | 0.000 | 0.000 | 0.597 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 164 | 229 | 0 | 0 | 618 | 0 | 0 | 17 | 0 |
N.S. |
1 | 0.95 | 1.33 | 0.00 | 0.00 | 3.59 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.200 | 0.338 | 0.000 | 0.000 | 0.087 | 0.000 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 126 | 173 | 0 | 0 | 519 | 0 | 0 | 17 | 0 |
N.S. |
1 | 0.99 | 1.36 | 0.00 | 0.00 | 4.09 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.171 | 0.159 | 0.000 | 0.000 | 0.101 | 0.000 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 42 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 1.31 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.136 | 0.024 | 0.158 | 0.000 | 0.084 | 0.000 | 0.000 | 0.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 54 | 0 | 118 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.00 | 0.70 | 0.82 | 0.00 | 1.79 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.153 | 0.088 | 0.163 | 0.000 | 0.092 | 0.000 | 0.000 | 0.406 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 251 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 2.49 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.171 | 0.236 | 0.162 | 0.000 | 0.100 | 0.000 | 0.000 | 0.439 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 420 | 0 | 0 | 113 | 0 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 3.09 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.201 | 0.329 | 0.166 | 0.000 | 0.169 | 0.000 | 0.000 | 0.522 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.163 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.848 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.161 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.606 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.158 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.160 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 72 | 71 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.29 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.159 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.393 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 205 | 249 | 0 | 0 | 741 | 0 | 0 | 40 | 0 |
N.S. |
1 | 0.94 | 1.15 | 0.00 | 0.00 | 3.41 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.211 | 0.487 | 0.000 | 0.000 | 0.109 | 0.000 | 0.000 | 0.358 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 164 | 229 | 0 | 0 | 619 | 0 | 0 | 17 | 0 |
N.S. |
1 | 0.96 | 1.35 | 0.00 | 0.00 | 3.64 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.187 | 0.333 | 0.000 | 0.000 | 0.100 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 126 | 173 | 0 | 0 | 521 | 0 | 0 | 17 | 0 |
N.S. |
1 | 0.99 | 1.36 | 0.00 | 0.00 | 4.10 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.173 | 0.160 | 0.000 | 0.000 | 0.096 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 27 | 0 | 42 | 0 | 0 | 38 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.00 | 1.40 | 0.00 | 0.00 | 1.27 | 0.87 |
time (sec) |
N/A | 0.138 | 0.026 | 0.160 | 0.000 | 0.084 | 0.000 | 0.000 | 0.277 | 0.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 45 | 54 | 0 | 118 | 0 | 0 | 63 | 71 |
N.S. |
1 | 1.00 | 0.68 | 0.82 | 0.00 | 1.79 | 0.00 | 0.00 | 0.95 | 1.08 |
time (sec) |
N/A | 0.153 | 0.088 | 0.158 | 0.000 | 0.081 | 0.000 | 0.000 | 0.408 | 0.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 75 | 105 | 0 | 251 | 0 | 0 | 88 | 133 |
N.S. |
1 | 1.13 | 0.74 | 1.04 | 0.00 | 2.49 | 0.00 | 0.00 | 0.87 | 1.32 |
time (sec) |
N/A | 0.179 | 0.199 | 0.161 | 0.000 | 0.081 | 0.000 | 0.000 | 0.612 | 0.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 116 | 171 | 0 | 419 | 0 | 0 | 113 | 209 |
N.S. |
1 | 1.19 | 0.85 | 1.26 | 0.00 | 3.08 | 0.00 | 0.00 | 0.83 | 1.54 |
time (sec) |
N/A | 0.198 | 0.301 | 0.166 | 0.000 | 0.086 | 0.000 | 0.000 | 0.862 | 0.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.165 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 25.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.162 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 19.672 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.158 | 0.022 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 6.839 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 72 | 71 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.29 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.157 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.157 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 235 | 285 | 0 | 0 | 423 | 0 | 0 | 113 | 0 |
N.S. |
1 | 0.97 | 1.18 | 0.00 | 0.00 | 1.75 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.233 | 0.548 | 0.000 | 0.000 | 0.107 | 0.000 | 0.000 | 1.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 194 | 247 | 0 | 0 | 306 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.99 | 1.26 | 0.00 | 0.00 | 1.56 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.211 | 0.486 | 0.000 | 0.000 | 0.169 | 0.000 | 0.000 | 0.737 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 155 | 209 | 0 | 0 | 233 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.03 | 1.39 | 0.00 | 0.00 | 1.55 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.188 | 0.210 | 0.000 | 0.000 | 0.094 | 0.000 | 0.000 | 0.364 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 27 | 0 | 42 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.00 | 1.40 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.132 | 0.019 | 0.160 | 0.000 | 0.102 | 0.000 | 0.000 | 0.337 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 66 | 45 | 53 | 0 | 126 | 0 | 0 | 78 | 0 |
N.S. |
1 | 1.03 | 0.70 | 0.83 | 0.00 | 1.97 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.150 | 0.081 | 0.165 | 0.000 | 0.081 | 0.000 | 0.000 | 0.427 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 114 | 75 | 105 | 0 | 273 | 0 | 0 | 130 | 0 |
N.S. |
1 | 1.16 | 0.77 | 1.07 | 0.00 | 2.79 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.182 | 0.195 | 0.312 | 0.000 | 0.087 | 0.000 | 0.000 | 0.477 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 162 | 116 | 171 | 0 | 456 | 0 | 0 | 182 | 0 |
N.S. |
1 | 1.21 | 0.87 | 1.28 | 0.00 | 3.40 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.201 | 0.250 | 0.174 | 0.000 | 0.115 | 0.000 | 0.000 | 0.558 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 81 | 73 | 0 | 0 | 0 | 0 | 0 | 113 | 0 |
N.S. |
1 | 1.40 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.95 | 0.00 |
time (sec) |
N/A | 0.164 | 0.046 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 81 | 73 | 0 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.40 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.165 | 0.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.821 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 81 | 73 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.40 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.164 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.360 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 81 | 73 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.40 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.168 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.388 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 79 | 71 | 0 | 0 | 0 | 0 | 0 | 78 | 0 |
N.S. |
1 | 1.41 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 0.166 | 0.028 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.407 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 116 | 123 | 417 | 0 | 124 | 42 | 0 | 34 | 0 |
N.S. |
1 | 1.04 | 1.10 | 3.72 | 0.00 | 1.11 | 0.38 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.179 | 0.155 | 0.411 | 0.000 | 0.091 | 4.293 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 91 | 118 | 412 | 0 | 118 | 41 | 0 | 15 | 0 |
N.S. |
1 | 1.07 | 1.39 | 4.85 | 0.00 | 1.39 | 0.48 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.162 | 0.106 | 0.339 | 0.000 | 0.079 | 1.376 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 97 | 0 | 0 | 103 | 41 | 0 | 15 | 0 |
N.S. |
1 | 1.00 | 1.41 | 0.00 | 0.00 | 1.49 | 0.59 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.147 | 0.060 | 0.000 | 0.000 | 0.081 | 1.024 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 15 | 0 | 19 | 56 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.00 | 0.95 | 2.80 | 0.00 | 1.75 | 0.00 |
time (sec) |
N/A | 0.126 | 0.012 | 0.115 | 0.000 | 0.073 | 0.691 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 25 | 20 | 0 | 29 | 257 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 0.61 | 0.49 | 0.00 | 0.71 | 6.27 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.137 | 0.029 | 0.118 | 0.000 | 0.072 | 3.623 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 66 | 30 | 25 | 0 | 39 | 563 | 0 | 69 | 0 |
N.S. |
1 | 1.08 | 0.49 | 0.41 | 0.00 | 0.64 | 9.23 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.145 | 0.036 | 0.119 | 0.000 | 0.066 | 21.779 | 0.000 | 0.337 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 91 | 35 | 30 | 0 | 49 | 984 | 0 | 83 | 0 |
N.S. |
1 | 1.12 | 0.43 | 0.37 | 0.00 | 0.60 | 12.15 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.156 | 0.043 | 0.124 | 0.000 | 0.064 | 126.947 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 86 | 158 | 573 | 0 | 107 | 39 | 0 | 13 | 0 |
N.S. |
1 | 1.10 | 2.03 | 7.35 | 0.00 | 1.37 | 0.50 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.158 | 0.112 | 0.388 | 0.000 | 0.070 | 1.557 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | C | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 235 | 174 | 0 | 0 | 1786 | 0 | 0 | 521 | 0 |
N.S. |
1 | 1.15 | 0.85 | 0.00 | 0.00 | 8.71 | 0.00 | 0.00 | 2.54 | 0.00 |
time (sec) |
N/A | 0.291 | 0.396 | 0.000 | 0.000 | 0.125 | 0.000 | 0.000 | 1.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 193 | 143 | 0 | 0 | 1219 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.16 | 0.86 | 0.00 | 0.00 | 7.30 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.264 | 0.256 | 0.000 | 0.000 | 0.102 | 0.000 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 182 | 140 | 0 | 0 | 754 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.20 | 0.92 | 0.00 | 0.00 | 4.96 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.249 | 0.296 | 0.000 | 0.000 | 0.094 | 0.000 | 0.000 | 0.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 178 | 123 | 0 | 0 | 385 | 0 | 0 | 321 | 0 |
N.S. |
1 | 1.33 | 0.92 | 0.00 | 0.00 | 2.87 | 0.00 | 0.00 | 2.40 | 0.00 |
time (sec) |
N/A | 0.247 | 0.244 | 0.000 | 0.000 | 0.104 | 0.000 | 0.000 | 0.477 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 104 | 0 | 0 | 81 | 99 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 3.25 | 0.00 | 0.00 | 2.53 | 3.09 |
time (sec) |
N/A | 0.136 | 0.029 | 0.168 | 0.000 | 0.095 | 0.000 | 0.000 | 0.229 | 0.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 54 | 0 | 235 | 0 | 0 | 208 | 178 |
N.S. |
1 | 1.00 | 0.70 | 0.82 | 0.00 | 3.56 | 0.00 | 0.00 | 3.15 | 2.70 |
time (sec) |
N/A | 0.158 | 0.369 | 0.306 | 0.000 | 0.123 | 0.000 | 0.000 | 0.257 | 0.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 426 | 0 | 0 | 401 | 268 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 4.22 | 0.00 | 0.00 | 3.97 | 2.65 |
time (sec) |
N/A | 0.176 | 0.855 | 0.312 | 0.000 | 0.162 | 0.000 | 0.000 | 0.274 | 0.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 649 | 0 | 0 | 641 | 376 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 4.77 | 0.00 | 0.00 | 4.71 | 2.76 |
time (sec) |
N/A | 0.200 | 1.691 | 0.184 | 0.000 | 0.227 | 0.000 | 0.000 | 0.306 | 0.774 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 260 | 73 | 0 | 0 | 0 | 0 | 0 | 823 | 0 |
N.S. |
1 | 1.12 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.55 | 0.00 |
time (sec) |
N/A | 0.372 | 0.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.044 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 219 | 73 | 0 | 0 | 0 | 0 | 0 | 504 | 0 |
N.S. |
1 | 1.13 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.60 | 0.00 |
time (sec) |
N/A | 0.342 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 178 | 71 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.14 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.315 | 0.032 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 171 | 73 | 0 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.15 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.307 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.385 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 175 | 73 | 0 | 0 | 0 | 0 | 0 | 106 | 0 |
N.S. |
1 | 1.17 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.294 | 0.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.439 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 216 | 73 | 0 | 0 | 0 | 0 | 0 | 142 | 0 |
N.S. |
1 | 1.16 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.335 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.603 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 264 | 73 | 0 | 0 | 0 | 0 | 0 | 178 | 0 |
N.S. |
1 | 1.17 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.378 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.771 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 197 | 143 | 0 | 0 | 1219 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.18 | 0.86 | 0.00 | 0.00 | 7.30 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.258 | 0.327 | 0.000 | 0.000 | 0.111 | 0.000 | 0.000 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 156 | 123 | 0 | 0 | 686 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.23 | 0.97 | 0.00 | 0.00 | 5.40 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.217 | 0.217 | 0.000 | 0.000 | 0.094 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 122 | 75 | 0 | 0 | 222 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.44 | 0.88 | 0.00 | 0.00 | 2.61 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.195 | 0.089 | 0.000 | 0.000 | 0.081 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 42 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 1.31 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.136 | 0.024 | 0.161 | 0.000 | 0.068 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 54 | 0 | 118 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.00 | 0.70 | 0.82 | 0.00 | 1.79 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.155 | 0.122 | 0.165 | 0.000 | 0.166 | 0.000 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 252 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 2.50 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.180 | 0.354 | 0.167 | 0.000 | 0.408 | 0.000 | 0.000 | 0.365 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 419 | 0 | 0 | 113 | 0 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 3.08 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.195 | 0.862 | 0.169 | 0.000 | 1.032 | 0.000 | 0.000 | 0.504 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 242 | 73 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.51 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.361 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 201 | 73 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.61 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.332 | 0.022 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 164 | 73 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.71 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.307 | 0.019 | 0.000 | 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 | B | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 206 | 71 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 2.24 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.335 | 0.020 | 0.000 | 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 | F | F | F | F | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 254 | 73 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.98 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.381 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 302 | 73 | 0 | 0 | 0 | 0 | 0 | 159 | 0 |
N.S. |
1 | 1.85 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.414 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |