Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica was abbreviated to MMA
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 324 | 558 | 225 | 278 | 0 | 208 | 0 | 0 | 280 | 0 |
| N.S. |
1 | 1.72 | 0.69 | 0.86 | 0.00 | 0.64 | 0.00 | 0.00 | 0.86 | 0.00 |
| time (sec) |
N/A | 0.751 | 7.990 | 5.357 | 0.000 | 0.080 | 0.000 | 0.000 | 0.465 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 278 | 227 | 233 | 287 | 0 | 212 | 0 | 0 | 296 | 0 |
| N.S. |
1 | 0.82 | 0.84 | 1.03 | 0.00 | 0.76 | 0.00 | 0.00 | 1.06 | 0.00 |
| time (sec) |
N/A | 0.499 | 8.105 | 5.413 | 0.000 | 0.083 | 0.000 | 0.000 | 0.495 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 281 | 231 | 236 | 287 | 0 | 223 | 0 | 0 | 296 | 0 |
| N.S. |
1 | 0.82 | 0.84 | 1.02 | 0.00 | 0.79 | 0.00 | 0.00 | 1.05 | 0.00 |
| time (sec) |
N/A | 0.510 | 8.325 | 5.522 | 0.000 | 0.087 | 0.000 | 0.000 | 0.491 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | B | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 274 | 562 | 239 | 291 | 0 | 214 | 0 | 0 | 302 | 0 |
| N.S. |
1 | 2.05 | 0.87 | 1.06 | 0.00 | 0.78 | 0.00 | 0.00 | 1.10 | 0.00 |
| time (sec) |
N/A | 0.761 | 8.322 | 5.592 | 0.000 | 0.084 | 0.000 | 0.000 | 0.505 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 993 | 1247 | 701 | 1927 | 0 | 1009 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.26 | 0.71 | 1.94 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.730 | 12.358 | 10.881 | 0.000 | 0.097 | 0.000 | 0.000 | 1.775 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 563 | 801 | 388 | 594 | 0 | 517 | 0 | 0 | 903 | 0 |
| N.S. |
1 | 1.42 | 0.69 | 1.06 | 0.00 | 0.92 | 0.00 | 0.00 | 1.60 | 0.00 |
| time (sec) |
N/A | 1.053 | 4.986 | 9.639 | 0.000 | 0.085 | 0.000 | 0.000 | 0.797 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 324 | 558 | 225 | 278 | 0 | 208 | 0 | 0 | 280 | 0 |
| N.S. |
1 | 1.72 | 0.69 | 0.86 | 0.00 | 0.64 | 0.00 | 0.00 | 0.86 | 0.00 |
| time (sec) |
N/A | 0.663 | 0.407 | 5.346 | 0.000 | 0.082 | 0.000 | 0.000 | 0.454 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | B | C | A | F | B | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 325 | 674 | 307 | 572 | 0 | 807 | 0 | 0 | 1473 | 0 |
| N.S. |
1 | 2.07 | 0.94 | 1.76 | 0.00 | 2.48 | 0.00 | 0.00 | 4.53 | 0.00 |
| time (sec) |
N/A | 0.856 | 12.205 | 3.880 | 0.000 | 0.094 | 0.000 | 0.000 | 0.942 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 593 | 1094 | 517 | 1125 | 0 | 2688 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.84 | 0.87 | 1.90 | 0.00 | 4.53 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.497 | 13.298 | 3.674 | 0.000 | 0.301 | 0.000 | 0.000 | 3.534 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 821 | 793 | 707 | 1970 | 0 | 1012 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.86 | 2.40 | 0.00 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.415 | 12.616 | 12.099 | 0.000 | 0.101 | 0.000 | 0.000 | 1.872 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 463 | 423 | 393 | 624 | 0 | 518 | 0 | 0 | 948 | 0 |
| N.S. |
1 | 0.91 | 0.85 | 1.35 | 0.00 | 1.12 | 0.00 | 0.00 | 2.05 | 0.00 |
| time (sec) |
N/A | 0.808 | 4.859 | 11.377 | 0.000 | 0.102 | 0.000 | 0.000 | 0.849 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 278 | 227 | 233 | 287 | 0 | 212 | 0 | 0 | 296 | 0 |
| N.S. |
1 | 0.82 | 0.84 | 1.03 | 0.00 | 0.76 | 0.00 | 0.00 | 1.06 | 0.00 |
| time (sec) |
N/A | 0.456 | 0.451 | 5.558 | 0.000 | 0.078 | 0.000 | 0.000 | 0.473 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 378 | 330 | 312 | 584 | 0 | 811 | 0 | 0 | 1493 | 0 |
| N.S. |
1 | 0.87 | 0.83 | 1.54 | 0.00 | 2.15 | 0.00 | 0.00 | 3.95 | 0.00 |
| time (sec) |
N/A | 0.635 | 12.365 | 3.700 | 0.000 | 0.107 | 0.000 | 0.000 | 1.066 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 713 | 671 | 520 | 1147 | 0 | 2641 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.73 | 1.61 | 0.00 | 3.70 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.172 | 13.428 | 3.667 | 0.000 | 0.260 | 0.000 | 0.000 | 3.984 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | B | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 254 | 510 | 262 | 426 | 0 | 283 | 0 | 0 | 170 | 0 |
| N.S. |
1 | 2.01 | 1.03 | 1.68 | 0.00 | 1.11 | 0.00 | 0.00 | 0.67 | 0.00 |
| time (sec) |
N/A | 0.773 | 10.370 | 3.651 | 0.000 | 0.081 | 0.000 | 0.000 | 0.477 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 147 | 96 | 128 | 0 | 90 | 0 | 0 | 277 | 0 |
| N.S. |
1 | 1.27 | 0.83 | 1.10 | 0.00 | 0.78 | 0.00 | 0.00 | 2.39 | 0.00 |
| time (sec) |
N/A | 0.300 | 10.117 | 3.132 | 0.000 | 0.080 | 0.000 | 0.000 | 0.194 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | B | C | B | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 399 | 236 | 383 | 0 | 242 | 0 | 0 | 50 | 0 |
| N.S. |
1 | 3.22 | 1.90 | 3.09 | 0.00 | 1.95 | 0.00 | 0.00 | 0.40 | 0.00 |
| time (sec) |
N/A | 0.695 | 4.325 | 12.115 | 0.000 | 0.087 | 0.000 | 0.000 | 0.608 | 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 | 133 | 133 | 161 | 0 | 0 | 0 | 0 | 0 | 247 | 0 |
| N.S. |
1 | 1.00 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.86 | 0.00 |
| time (sec) |
N/A | 0.294 | 0.263 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 274 | 274 | 232 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.409 | 0.672 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.211 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 353 | 345 | 298 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.556 | 0.725 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.268 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 484 | 466 | 363 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.899 | 1.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 16.131 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | A | A | A | F | F | F | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 19 | 350 | 19 | 18 | 17 | 17 | 0 | 0 | 128 | 17 |
| N.S. |
1 | 18.42 | 1.00 | 0.95 | 0.89 | 0.89 | 0.00 | 0.00 | 6.74 | 0.89 |
| time (sec) |
N/A | 0.650 | 0.934 | 0.149 | 0.077 | 0.079 | 0.000 | 0.000 | 0.180 | 18.034 |
| 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 | 19 | 19 | 19 | 20 | 32 | 32 | 58 | 59 | 29 | 32 |
| N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.68 | 1.68 | 3.05 | 3.11 | 1.53 | 1.68 |
| time (sec) |
N/A | 0.181 | 0.508 | 0.164 | 0.071 | 0.076 | 76.888 | 0.150 | 0.154 | 18.102 |
| 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 | 40 | 40 | 42 | 45 | 86 | 90 | 235 | 223 | 98 | 88 |
| N.S. |
1 | 1.00 | 1.05 | 1.12 | 2.15 | 2.25 | 5.88 | 5.58 | 2.45 | 2.20 |
| time (sec) |
N/A | 0.299 | 1.047 | 0.340 | 0.072 | 0.085 | 169.223 | 0.212 | 0.179 | 18.401 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 55 | 58 | 62 | 51 | 51 | 2195 | 55 | 85 | 63 |
| N.S. |
1 | 1.08 | 1.14 | 1.22 | 1.00 | 1.00 | 43.04 | 1.08 | 1.67 | 1.24 |
| time (sec) |
N/A | 0.279 | 0.033 | 0.060 | 0.032 | 0.118 | 62.792 | 0.125 | 0.161 | 18.158 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 126 | 112 | 105 | 106 | 217 | 2689 | 109 | 369 | 107 |
| N.S. |
1 | 1.06 | 0.94 | 0.88 | 0.89 | 1.82 | 22.60 | 0.92 | 3.10 | 0.90 |
| time (sec) |
N/A | 0.385 | 0.094 | 0.071 | 0.032 | 0.128 | 67.778 | 0.132 | 0.159 | 17.986 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 193 | 161 | 139 | 155 | 389 | 2822 | 149 | 655 | 151 |
| N.S. |
1 | 1.05 | 0.88 | 0.76 | 0.85 | 2.13 | 15.42 | 0.81 | 3.58 | 0.83 |
| time (sec) |
N/A | 0.504 | 0.134 | 0.099 | 0.028 | 0.138 | 72.867 | 0.149 | 0.165 | 18.061 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | A | A | C | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 108 | 121 | 82 | 75 | 75 | 3589 | 75 | 141 | 159 |
| N.S. |
1 | 1.46 | 1.64 | 1.11 | 1.01 | 1.01 | 48.50 | 1.01 | 1.91 | 2.15 |
| time (sec) |
N/A | 0.352 | 0.172 | 0.169 | 0.110 | 0.097 | 56.500 | 0.125 | 0.166 | 18.272 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | A | A | C | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 178 | 186 | 154 | 120 | 212 | 4106 | 124 | 525 | 201 |
| N.S. |
1 | 1.20 | 1.26 | 1.04 | 0.81 | 1.43 | 27.74 | 0.84 | 3.55 | 1.36 |
| time (sec) |
N/A | 0.464 | 0.516 | 0.176 | 0.115 | 0.105 | 62.681 | 0.112 | 0.169 | 0.341 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | A | B | C | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 206 | 240 | 235 | 202 | 173 | 384 | 4496 | 165 | 905 | 249 |
| N.S. |
1 | 1.17 | 1.14 | 0.98 | 0.84 | 1.86 | 21.83 | 0.80 | 4.39 | 1.21 |
| time (sec) |
N/A | 0.573 | 0.692 | 0.237 | 0.109 | 0.128 | 64.838 | 0.144 | 0.155 | 18.388 |
| 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 | 154 | 154 | 154 | 139 | 138 | 138 | 165 | 151 | 152 | 138 |
| N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.90 | 0.90 | 1.07 | 0.98 | 0.99 | 0.90 |
| time (sec) |
N/A | 0.377 | 0.058 | 0.146 | 0.032 | 0.063 | 0.026 | 0.130 | 0.157 | 0.112 |
| 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 | 69 | 69 | 69 | 58 | 57 | 57 | 65 | 61 | 62 | 59 |
| N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.83 | 0.83 | 0.94 | 0.88 | 0.90 | 0.86 |
| time (sec) |
N/A | 0.242 | 0.011 | 0.071 | 0.041 | 0.060 | 0.018 | 0.135 | 0.169 | 17.963 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 211 | 234 | 48 | 0 | 723401 | 0 | 1712 | 829 | 3942 |
| N.S. |
1 | 1.00 | 1.11 | 0.23 | 0.00 | 3428.44 | 0.00 | 8.11 | 3.93 | 18.68 |
| time (sec) |
N/A | 0.453 | 0.243 | 0.103 | 0.000 | 17.186 | 0.000 | 0.884 | 0.173 | 19.298 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 368 | 356 | 398 | 232 | 0 | 0 | 0 | 5159 | 4754 | 4707 |
| N.S. |
1 | 0.97 | 1.08 | 0.63 | 0.00 | 0.00 | 0.00 | 14.02 | 12.92 | 12.79 |
| time (sec) |
N/A | 0.675 | 1.245 | 0.226 | 0.000 | 0.000 | 0.000 | 1.237 | 0.566 | 18.851 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 621 | 605 | 625 | 607 | 0 | 0 | 0 | 5375 | 13638 | 8689 |
| N.S. |
1 | 0.97 | 1.01 | 0.98 | 0.00 | 0.00 | 0.00 | 8.66 | 21.96 | 13.99 |
| time (sec) |
N/A | 1.105 | 3.431 | 0.455 | 0.000 | 0.000 | 0.000 | 1.778 | 9.249 | 20.571 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 209 | 234 | 48 | 0 | 578003 | 0 | 1712 | 829 | 3942 |
| N.S. |
1 | 1.00 | 1.12 | 0.23 | 0.00 | 2765.56 | 0.00 | 8.19 | 3.97 | 18.86 |
| time (sec) |
N/A | 0.496 | 0.252 | 0.122 | 0.000 | 26.824 | 0.000 | 0.880 | 0.173 | 19.010 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 224 | 224 | 245 | 54 | 0 | 540080 | 0 | 1723 | 863 | 3046 |
| N.S. |
1 | 1.00 | 1.09 | 0.24 | 0.00 | 2411.07 | 0.00 | 7.69 | 3.85 | 13.60 |
| time (sec) |
N/A | 0.448 | 0.239 | 0.135 | 0.000 | 76.278 | 0.000 | 0.789 | 0.178 | 1.135 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 23 | 23 | 12 | 8 | 0 | 7 | 7 | 30 | 17 | 7 |
| N.S. |
1 | 1.00 | 0.52 | 0.35 | 0.00 | 0.30 | 0.30 | 1.30 | 0.74 | 0.30 |
| time (sec) |
N/A | 0.184 | 0.011 | 0.063 | 0.000 | 0.064 | 0.045 | 0.138 | 0.166 | 17.844 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 47 | 46 | 60 | 38 | 0 | 35 | 46 | 37 | 41 | 151 |
| N.S. |
1 | 0.98 | 1.28 | 0.81 | 0.00 | 0.74 | 0.98 | 0.79 | 0.87 | 3.21 |
| time (sec) |
N/A | 0.265 | 0.336 | 0.069 | 0.000 | 0.079 | 0.091 | 0.116 | 0.160 | 0.109 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 111 | 114 | 45 | 0 | 68 | 1185 | 70 | 70 | 88 |
| N.S. |
1 | 1.56 | 1.61 | 0.63 | 0.00 | 0.96 | 16.69 | 0.99 | 0.99 | 1.24 |
| time (sec) |
N/A | 0.358 | 0.278 | 0.062 | 0.000 | 0.081 | 0.502 | 0.134 | 0.171 | 0.215 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 78 | 98 | 107 | 88 | 88 | 0 | 92 | 178 | 108 |
| N.S. |
1 | 1.03 | 1.29 | 1.41 | 1.16 | 1.16 | 0.00 | 1.21 | 2.34 | 1.42 |
| time (sec) |
N/A | 0.515 | 0.077 | 0.087 | 0.033 | 4.594 | 0.000 | 0.142 | 0.162 | 18.419 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 167 | 185 | 161 | 163 | 346 | 0 | 173 | 721 | 164 |
| N.S. |
1 | 1.03 | 1.14 | 0.99 | 1.01 | 2.14 | 0.00 | 1.07 | 4.45 | 1.01 |
| time (sec) |
N/A | 0.575 | 0.092 | 0.099 | 0.029 | 5.903 | 0.000 | 0.132 | 0.162 | 18.414 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 252 | 242 | 261 | 217 | 238 | 616 | 0 | 249 | 1283 | 233 |
| N.S. |
1 | 0.96 | 1.04 | 0.86 | 0.94 | 2.44 | 0.00 | 0.99 | 5.09 | 0.92 |
| time (sec) |
N/A | 0.700 | 0.129 | 0.108 | 0.035 | 6.459 | 0.000 | 0.141 | 0.174 | 18.529 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 150 | 187 | 117 | 106 | 106 | 0 | 106 | 290 | 1509 |
| N.S. |
1 | 1.10 | 1.38 | 0.86 | 0.78 | 0.78 | 0.00 | 0.78 | 2.13 | 11.10 |
| time (sec) |
N/A | 0.526 | 0.802 | 0.370 | 0.109 | 4.203 | 0.000 | 0.121 | 0.155 | 26.952 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 208 | 243 | 214 | 155 | 279 | 0 | 165 | 955 | 1894 |
| N.S. |
1 | 1.18 | 1.38 | 1.22 | 0.88 | 1.59 | 0.00 | 0.94 | 5.43 | 10.76 |
| time (sec) |
N/A | 0.604 | 0.812 | 0.332 | 0.109 | 4.269 | 0.000 | 0.118 | 0.163 | 28.058 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 249 | 285 | 325 | 292 | 229 | 521 | 0 | 249 | 1637 | 1963 |
| N.S. |
1 | 1.14 | 1.31 | 1.17 | 0.92 | 2.09 | 0.00 | 1.00 | 6.57 | 7.88 |
| time (sec) |
N/A | 0.744 | 1.130 | 0.359 | 0.129 | 4.780 | 0.000 | 0.159 | 0.171 | 27.390 |
| 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 | 272 | 272 | 272 | 255 | 254 | 254 | 303 | 304 | 305 | 258 |
| N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.93 | 0.93 | 1.11 | 1.12 | 1.12 | 0.95 |
| time (sec) |
N/A | 0.626 | 0.121 | 1.289 | 0.027 | 0.066 | 0.037 | 0.128 | 0.157 | 0.188 |
| 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 | 122 | 122 | 122 | 105 | 104 | 104 | 121 | 124 | 125 | 112 |
| N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.85 | 0.85 | 0.99 | 1.02 | 1.02 | 0.92 |
| time (sec) |
N/A | 0.332 | 0.039 | 1.263 | 0.035 | 0.069 | 0.020 | 0.125 | 0.168 | 0.088 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 321 | 321 | 441 | 99 | 0 | 0 | 0 | 5944 | 2036 | 11383 |
| N.S. |
1 | 1.00 | 1.37 | 0.31 | 0.00 | 0.00 | 0.00 | 18.52 | 6.34 | 35.46 |
| time (sec) |
N/A | 1.050 | 0.717 | 0.123 | 0.000 | 0.000 | 0.000 | 0.940 | 0.183 | 19.786 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 468 | 460 | 524 | 304 | 0 | 0 | 0 | 7965 | 7607 | 18449 |
| N.S. |
1 | 0.98 | 1.12 | 0.65 | 0.00 | 0.00 | 0.00 | 17.02 | 16.25 | 39.42 |
| time (sec) |
N/A | 0.983 | 2.146 | 0.170 | 0.000 | 0.000 | 0.000 | 1.336 | 0.802 | 20.884 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 732 | 732 | 980 | 795 | 0 | 0 | 0 | 7058 | 20724 | 36653 |
| N.S. |
1 | 1.00 | 1.34 | 1.09 | 0.00 | 0.00 | 0.00 | 9.64 | 28.31 | 50.07 |
| time (sec) |
N/A | 1.555 | 6.660 | 0.271 | 0.000 | 0.000 | 0.000 | 2.622 | 14.410 | 25.900 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 545 | 545 | 816 | 246 | 0 | 0 | 0 | 11830 | 4445 | 49150 |
| N.S. |
1 | 1.00 | 1.50 | 0.45 | 0.00 | 0.00 | 0.00 | 21.71 | 8.16 | 90.18 |
| time (sec) |
N/A | 3.074 | 1.268 | 0.597 | 0.000 | 0.000 | 0.000 | 1.354 | 0.209 | 23.346 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 770 | 788 | 935 | 506 | 0 | 0 | 0 | 20158 | 15020 | 82785 |
| N.S. |
1 | 1.02 | 1.21 | 0.66 | 0.00 | 0.00 | 0.00 | 26.18 | 19.51 | 107.51 |
| time (sec) |
N/A | 4.427 | 5.618 | 0.799 | 0.000 | 0.000 | 0.000 | 2.570 | 2.175 | 49.924 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1150 | 1172 | 1590 | 1167 | 0 | 0 | 0 | 22427 | 32760 | 114377 |
| N.S. |
1 | 1.02 | 1.38 | 1.01 | 0.00 | 0.00 | 0.00 | 19.50 | 28.49 | 99.46 |
| time (sec) |
N/A | 2.916 | 7.411 | 1.020 | 0.000 | 0.000 | 0.000 | 3.046 | 19.812 | 66.817 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 641 | 653 | 775 | 422 | 0 | 0 | 0 | 16214 | 11710 | 53538 |
| N.S. |
1 | 1.02 | 1.21 | 0.66 | 0.00 | 0.00 | 0.00 | 25.29 | 18.27 | 83.52 |
| time (sec) |
N/A | 1.540 | 4.089 | 0.447 | 0.000 | 0.000 | 0.000 | 2.265 | 1.071 | 28.534 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1177 | 1236 | 1649 | 1182 | 0 | 0 | 0 | 29140 | 30922 | 97905 |
| N.S. |
1 | 1.05 | 1.40 | 1.00 | 0.00 | 0.00 | 0.00 | 24.76 | 26.27 | 83.18 |
| time (sec) |
N/A | 3.045 | 7.329 | 0.815 | 0.000 | 0.000 | 0.000 | 3.921 | 20.046 | 55.461 |
| 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 | 416 | 416 | 416 | 412 | 418 | 418 | 503 | 463 | 467 | 398 |
| N.S. |
1 | 1.00 | 1.00 | 0.99 | 1.00 | 1.00 | 1.21 | 1.11 | 1.12 | 0.96 |
| time (sec) |
N/A | 0.919 | 0.124 | 24.537 | 0.041 | 0.106 | 0.048 | 0.132 | 0.181 | 0.524 |
| 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 | 259 | 259 | 259 | 259 | 251 | 251 | 309 | 285 | 287 | 246 |
| N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.97 | 0.97 | 1.19 | 1.10 | 1.11 | 0.95 |
| time (sec) |
N/A | 0.609 | 0.055 | 24.451 | 0.035 | 0.087 | 0.034 | 0.118 | 0.165 | 0.205 |
| 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 | 154 | 154 | 154 | 141 | 138 | 138 | 165 | 151 | 152 | 138 |
| N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.90 | 0.90 | 1.07 | 0.98 | 0.99 | 0.90 |
| time (sec) |
N/A | 0.376 | 0.043 | 0.134 | 0.036 | 0.093 | 0.025 | 0.145 | 0.166 | 17.983 |
| 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 | 20 | 20 | 20 | 17 | 16 | 16 | 15 | 16 | 17 | 16 |
| N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.80 | 0.80 | 0.75 | 0.80 | 0.85 | 0.80 |
| time (sec) |
N/A | 0.201 | 0.003 | 0.028 | 0.037 | 0.202 | 0.026 | 0.370 | 0.178 | 0.029 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | C | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 211 | 234 | 48 | 0 | 723401 | 0 | 1618 | 829 | 3942 |
| N.S. |
1 | 1.00 | 1.11 | 0.23 | 0.00 | 3428.44 | 0.00 | 7.67 | 3.93 | 18.68 |
| time (sec) |
N/A | 0.482 | 0.226 | 0.079 | 0.000 | 17.128 | 0.000 | 0.748 | 0.184 | 1.242 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 368 | 356 | 398 | 232 | 0 | 0 | 0 | 5158 | 4754 | 4707 |
| N.S. |
1 | 0.97 | 1.08 | 0.63 | 0.00 | 0.00 | 0.00 | 14.02 | 12.92 | 12.79 |
| time (sec) |
N/A | 0.709 | 1.206 | 0.204 | 0.000 | 0.000 | 0.000 | 2.014 | 0.593 | 19.048 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 621 | 605 | 625 | 607 | 0 | 0 | 0 | 5280 | 13638 | 8689 |
| N.S. |
1 | 0.97 | 1.01 | 0.98 | 0.00 | 0.00 | 0.00 | 8.50 | 21.96 | 13.99 |
| time (sec) |
N/A | 1.135 | 3.473 | 0.412 | 0.000 | 0.000 | 0.000 | 1.045 | 9.534 | 20.453 |
| 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 | 4 | 4 | 4 | 5 | 4 | 4 | 3 | 5 | 4 | 4 |
| N.S. |
1 | 1.00 | 1.00 | 1.25 | 1.00 | 1.00 | 0.75 | 1.25 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.154 | 0.001 | 0.021 | 0.037 | 0.063 | 0.023 | 0.120 | 0.169 | 0.019 |
| 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 | 14 | 14 | 16 | 15 | 14 | 14 | 12 | 15 | 17 | 14 |
| N.S. |
1 | 1.00 | 1.14 | 1.07 | 1.00 | 1.00 | 0.86 | 1.07 | 1.21 | 1.00 |
| time (sec) |
N/A | 0.186 | 0.006 | 0.031 | 0.031 | 0.065 | 0.057 | 0.134 | 0.164 | 0.030 |
| 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 | 31 | 31 | 30 | 28 | 27 | 27 | 26 | 28 | 34 | 27 |
| N.S. |
1 | 1.00 | 0.97 | 0.90 | 0.87 | 0.87 | 0.84 | 0.90 | 1.10 | 0.87 |
| time (sec) |
N/A | 0.226 | 0.014 | 0.036 | 0.031 | 0.086 | 0.069 | 0.131 | 0.184 | 17.981 |
| 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 | 47 | 51 | 45 | 45 | 43 | 43 | 41 | 47 | 57 | 44 |
| N.S. |
1 | 1.09 | 0.96 | 0.96 | 0.91 | 0.91 | 0.87 | 1.00 | 1.21 | 0.94 |
| time (sec) |
N/A | 0.280 | 0.028 | 0.039 | 0.026 | 0.086 | 0.086 | 0.131 | 0.166 | 0.040 |
| 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 | 68 | 68 | 68 | 65 | 62 | 62 | 63 | 72 | 86 | 64 |
| N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.91 | 0.91 | 0.93 | 1.06 | 1.26 | 0.94 |
| time (sec) |
N/A | 0.317 | 0.028 | 0.042 | 0.031 | 0.093 | 0.097 | 0.136 | 0.170 | 17.986 |
| 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 | 92 | 92 | 92 | 88 | 84 | 84 | 88 | 103 | 121 | 87 |
| N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.91 | 0.91 | 0.96 | 1.12 | 1.32 | 0.95 |
| time (sec) |
N/A | 0.368 | 0.040 | 0.044 | 0.037 | 0.085 | 0.114 | 0.138 | 0.175 | 0.040 |
| 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 | 11 | 11 | 11 | 12 | 11 | 11 | 8 | 13 | 11 | 8 |
| N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 0.73 | 1.18 | 1.00 | 0.73 |
| time (sec) |
N/A | 0.177 | 0.005 | 0.029 | 0.026 | 0.086 | 0.045 | 0.107 | 0.166 | 0.082 |
| 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 | 22 | 22 | 23 | 24 | 22 | 22 | 29 | 24 | 28 | 22 |
| N.S. |
1 | 1.00 | 1.05 | 1.09 | 1.00 | 1.00 | 1.32 | 1.09 | 1.27 | 1.00 |
| time (sec) |
N/A | 0.201 | 0.013 | 0.038 | 0.031 | 0.085 | 0.151 | 0.131 | 0.185 | 0.067 |
| 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 | 29 | 29 | 30 | 31 | 29 | 29 | 44 | 31 | 44 | 29 |
| N.S. |
1 | 1.00 | 1.03 | 1.07 | 1.00 | 1.00 | 1.52 | 1.07 | 1.52 | 1.00 |
| time (sec) |
N/A | 0.253 | 0.018 | 0.045 | 0.033 | 0.086 | 0.281 | 0.134 | 0.171 | 18.003 |
| 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 | 47 | 47 | 44 | 47 | 45 | 45 | 66 | 47 | 68 | 45 |
| N.S. |
1 | 1.00 | 0.94 | 1.00 | 0.96 | 0.96 | 1.40 | 1.00 | 1.45 | 0.96 |
| time (sec) |
N/A | 0.279 | 0.026 | 0.049 | 0.038 | 0.167 | 0.473 | 0.138 | 0.162 | 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 | 66 | 66 | 67 | 65 | 62 | 62 | 94 | 67 | 97 | 63 |
| N.S. |
1 | 1.00 | 1.02 | 0.98 | 0.94 | 0.94 | 1.42 | 1.02 | 1.47 | 0.95 |
| time (sec) |
N/A | 0.307 | 0.032 | 0.053 | 0.027 | 0.078 | 0.820 | 0.134 | 0.179 | 17.967 |
| 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 | 90 | 90 | 91 | 88 | 84 | 84 | 122 | 95 | 133 | 86 |
| N.S. |
1 | 1.00 | 1.01 | 0.98 | 0.93 | 0.93 | 1.36 | 1.06 | 1.48 | 0.96 |
| time (sec) |
N/A | 0.342 | 0.041 | 0.066 | 0.033 | 0.068 | 1.350 | 0.112 | 0.170 | 17.920 |
| 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 | 29 | 29 | 29 | 20 | 19 | 19 | 19 | 22 | 19 | 19 |
| N.S. |
1 | 1.00 | 1.00 | 0.69 | 0.66 | 0.66 | 0.66 | 0.76 | 0.66 | 0.66 |
| time (sec) |
N/A | 0.203 | 0.007 | 0.032 | 0.033 | 0.066 | 0.063 | 0.126 | 0.170 | 0.063 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 42 | 39 | 38 | 32 | 32 | 304 | 35 | 43 | 38 |
| N.S. |
1 | 1.00 | 0.93 | 0.90 | 0.76 | 0.76 | 7.24 | 0.83 | 1.02 | 0.90 |
| time (sec) |
N/A | 0.250 | 0.020 | 0.044 | 0.028 | 0.071 | 1.027 | 0.119 | 0.179 | 0.088 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 47 | 47 | 44 | 47 | 37 | 37 | 716 | 40 | 64 | 47 |
| N.S. |
1 | 1.00 | 0.94 | 1.00 | 0.79 | 0.79 | 15.23 | 0.85 | 1.36 | 1.00 |
| time (sec) |
N/A | 0.273 | 0.023 | 0.047 | 0.025 | 0.073 | 7.126 | 0.131 | 0.162 | 0.110 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 55 | 59 | 47 | 47 | 1389 | 50 | 88 | 59 |
| N.S. |
1 | 1.00 | 0.96 | 1.04 | 0.82 | 0.82 | 24.37 | 0.88 | 1.54 | 1.04 |
| time (sec) |
N/A | 0.276 | 0.029 | 0.059 | 0.038 | 0.082 | 49.289 | 0.123 | 0.178 | 0.101 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 71 | 78 | 62 | 62 | 0 | 65 | 119 | 78 |
| N.S. |
1 | 1.00 | 0.96 | 1.05 | 0.84 | 0.84 | 0.00 | 0.88 | 1.61 | 1.05 |
| time (sec) |
N/A | 0.312 | 0.038 | 0.064 | 0.031 | 0.103 | 0.000 | 0.143 | 0.167 | 17.844 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 96 | 91 | 99 | 82 | 82 | 0 | 87 | 155 | 99 |
| N.S. |
1 | 1.00 | 0.95 | 1.03 | 0.85 | 0.85 | 0.00 | 0.91 | 1.61 | 1.03 |
| time (sec) |
N/A | 0.355 | 0.051 | 0.074 | 0.029 | 0.135 | 0.000 | 0.128 | 0.164 | 17.971 |
| 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 | 46 | 46 | 42 | 33 | 32 | 45 | 34 | 36 | 64 | 32 |
| N.S. |
1 | 1.00 | 0.91 | 0.72 | 0.70 | 0.98 | 0.74 | 0.78 | 1.39 | 0.70 |
| time (sec) |
N/A | 0.236 | 0.025 | 0.047 | 0.031 | 0.065 | 0.115 | 0.111 | 0.187 | 0.051 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 66 | 64 | 57 | 93 | 1188 | 61 | 137 | 64 |
| N.S. |
1 | 1.00 | 0.93 | 0.90 | 0.80 | 1.31 | 16.73 | 0.86 | 1.93 | 0.90 |
| time (sec) |
N/A | 0.312 | 0.048 | 0.062 | 0.042 | 0.082 | 5.785 | 0.123 | 0.172 | 17.847 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 82 | 77 | 79 | 68 | 116 | 0 | 72 | 201 | 79 |
| N.S. |
1 | 1.00 | 0.94 | 0.96 | 0.83 | 1.41 | 0.00 | 0.88 | 2.45 | 0.96 |
| time (sec) |
N/A | 0.350 | 0.060 | 0.063 | 0.027 | 0.146 | 0.000 | 0.133 | 0.172 | 17.846 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 90 | 94 | 81 | 141 | 0 | 85 | 265 | 94 |
| N.S. |
1 | 1.00 | 0.95 | 0.99 | 0.85 | 1.48 | 0.00 | 0.89 | 2.79 | 0.99 |
| time (sec) |
N/A | 0.381 | 0.061 | 0.073 | 0.033 | 0.555 | 0.000 | 0.138 | 0.174 | 17.950 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 106 | 102 | 109 | 92 | 164 | 0 | 96 | 329 | 108 |
| N.S. |
1 | 1.00 | 0.96 | 1.03 | 0.87 | 1.55 | 0.00 | 0.91 | 3.10 | 1.02 |
| time (sec) |
N/A | 0.400 | 0.066 | 0.084 | 0.033 | 3.188 | 0.000 | 0.141 | 0.166 | 18.437 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 122 | 118 | 127 | 108 | 200 | 0 | 112 | 399 | 127 |
| N.S. |
1 | 1.00 | 0.97 | 1.04 | 0.89 | 1.64 | 0.00 | 0.92 | 3.27 | 1.04 |
| time (sec) |
N/A | 0.451 | 0.073 | 0.108 | 0.033 | 21.721 | 0.000 | 0.131 | 0.179 | 18.939 |
| 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 | 55 | 55 | 48 | 40 | 42 | 72 | 46 | 46 | 107 | 42 |
| N.S. |
1 | 1.00 | 0.87 | 0.73 | 0.76 | 1.31 | 0.84 | 0.84 | 1.95 | 0.76 |
| time (sec) |
N/A | 0.225 | 0.027 | 0.048 | 0.029 | 0.098 | 0.123 | 0.117 | 0.177 | 0.048 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 94 | 80 | 78 | 75 | 153 | 1255 | 79 | 231 | 79 |
| N.S. |
1 | 1.06 | 0.90 | 0.88 | 0.84 | 1.72 | 14.10 | 0.89 | 2.60 | 0.89 |
| time (sec) |
N/A | 0.439 | 0.057 | 0.063 | 0.036 | 0.199 | 5.837 | 0.116 | 0.170 | 0.100 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 110 | 97 | 96 | 91 | 191 | 0 | 95 | 340 | 97 |
| N.S. |
1 | 1.05 | 0.92 | 0.91 | 0.87 | 1.82 | 0.00 | 0.90 | 3.24 | 0.92 |
| time (sec) |
N/A | 0.533 | 0.083 | 0.068 | 0.040 | 0.288 | 0.000 | 0.130 | 0.168 | 18.013 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 117 | 114 | 114 | 107 | 229 | 0 | 111 | 449 | 115 |
| N.S. |
1 | 0.97 | 0.94 | 0.94 | 0.88 | 1.89 | 0.00 | 0.92 | 3.71 | 0.95 |
| time (sec) |
N/A | 0.495 | 0.064 | 0.094 | 0.048 | 0.548 | 0.000 | 0.117 | 0.167 | 18.069 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 131 | 136 | 132 | 123 | 267 | 0 | 127 | 558 | 133 |
| N.S. |
1 | 0.96 | 0.99 | 0.96 | 0.90 | 1.95 | 0.00 | 0.93 | 4.07 | 0.97 |
| time (sec) |
N/A | 0.535 | 0.073 | 0.088 | 0.033 | 3.090 | 0.000 | 0.125 | 0.174 | 18.916 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 147 | 153 | 150 | 139 | 305 | 0 | 143 | 667 | 151 |
| N.S. |
1 | 0.96 | 1.00 | 0.98 | 0.91 | 1.99 | 0.00 | 0.93 | 4.36 | 0.99 |
| time (sec) |
N/A | 0.569 | 0.094 | 0.103 | 0.037 | 21.778 | 0.000 | 0.120 | 0.164 | 19.371 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 68 | 60 | 47 | 52 | 103 | 53 | 56 | 151 | 52 |
| N.S. |
1 | 1.00 | 0.88 | 0.69 | 0.76 | 1.51 | 0.78 | 0.82 | 2.22 | 0.76 |
| time (sec) |
N/A | 0.250 | 0.032 | 0.054 | 0.029 | 0.067 | 0.141 | 0.123 | 0.173 | 0.047 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 105 | 97 | 92 | 88 | 211 | 1034 | 92 | 322 | 90 |
| N.S. |
1 | 1.00 | 0.92 | 0.88 | 0.84 | 2.01 | 9.85 | 0.88 | 3.07 | 0.86 |
| time (sec) |
N/A | 0.346 | 0.099 | 0.070 | 0.032 | 0.086 | 5.036 | 0.166 | 0.180 | 0.099 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 122 | 121 | 113 | 108 | 267 | 0 | 112 | 472 | 113 |
| N.S. |
1 | 1.00 | 0.99 | 0.93 | 0.89 | 2.19 | 0.00 | 0.92 | 3.87 | 0.93 |
| time (sec) |
N/A | 0.375 | 0.060 | 0.073 | 0.034 | 0.144 | 0.000 | 0.114 | 0.163 | 18.094 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 141 | 144 | 134 | 126 | 321 | 0 | 130 | 625 | 131 |
| N.S. |
1 | 1.00 | 1.02 | 0.95 | 0.89 | 2.28 | 0.00 | 0.92 | 4.43 | 0.93 |
| time (sec) |
N/A | 0.409 | 0.079 | 0.081 | 0.037 | 0.544 | 0.000 | 0.140 | 0.171 | 18.207 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 158 | 158 | 169 | 155 | 145 | 376 | 0 | 149 | 775 | 152 |
| N.S. |
1 | 1.00 | 1.07 | 0.98 | 0.92 | 2.38 | 0.00 | 0.94 | 4.91 | 0.96 |
| time (sec) |
N/A | 0.453 | 0.098 | 0.090 | 0.029 | 3.088 | 0.000 | 0.137 | 0.165 | 18.783 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 177 | 195 | 176 | 163 | 430 | 0 | 167 | 928 | 170 |
| N.S. |
1 | 1.00 | 1.10 | 0.99 | 0.92 | 2.43 | 0.00 | 0.94 | 5.24 | 0.96 |
| time (sec) |
N/A | 0.507 | 0.113 | 0.106 | 0.029 | 21.598 | 0.000 | 0.144 | 0.164 | 19.120 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 724 | 693 | 2588 | 1205 | 0 | 911 | 0 | 0 | 32 | 0 |
| N.S. |
1 | 0.96 | 3.57 | 1.66 | 0.00 | 1.26 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 1.252 | 12.950 | 4.411 | 0.000 | 0.260 | 0.000 | 0.000 | 200.030 | 0.000 |