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 | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 70 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.283 | 11.079 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 70 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.269 | 11.065 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 68 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.240 | 11.047 | 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 | 69 | 69 | 143 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.276 | 11.148 | 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 | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 91 | 91 | 0 | 289 | 0 | 106 | 102 |
N.S. |
1 | 1.00 | 0.88 | 0.88 | 0.00 | 2.78 | 0.00 | 1.02 | 0.98 |
time (sec) |
N/A | 0.275 | 0.293 | 5.060 | 0.000 | 0.312 | 0.000 | 0.277 | 9.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 73 | 72 | 0 | 205 | 0 | 64 | 58 |
N.S. |
1 | 1.00 | 0.99 | 0.97 | 0.00 | 2.77 | 0.00 | 0.86 | 0.78 |
time (sec) |
N/A | 0.207 | 0.167 | 4.917 | 0.000 | 0.307 | 0.000 | 0.268 | 9.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 39 | 0 | 130 | 87 | 40 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.00 | 2.55 | 1.71 | 0.78 | 0.78 |
time (sec) |
N/A | 0.190 | 0.070 | 4.959 | 0.000 | 0.325 | 5.884 | 0.284 | 9.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 80 | 78 | 0 | 431 | 114 | 71 | 652 |
N.S. |
1 | 1.00 | 0.94 | 0.92 | 0.00 | 5.07 | 1.34 | 0.84 | 7.67 |
time (sec) |
N/A | 0.223 | 0.191 | 4.896 | 0.000 | 0.329 | 5.308 | 0.282 | 9.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 127 | 109 | 92 | 0 | 565 | 0 | 104 | 396 |
N.S. |
1 | 1.09 | 0.93 | 0.79 | 0.00 | 4.83 | 0.00 | 0.89 | 3.38 |
time (sec) |
N/A | 0.269 | 0.439 | 4.979 | 0.000 | 0.363 | 0.000 | 0.266 | 9.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 134 | 136 | 152 | 0 | 739 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.11 | 1.24 | 0.00 | 6.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.291 | 0.946 | 5.620 | 0.000 | 0.338 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 90 | 108 | 85 | 0 | 632 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.19 | 0.93 | 0.00 | 6.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.239 | 0.530 | 5.210 | 0.000 | 0.312 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 74 | 42 | 0 | 245 | 0 | 72 | 0 |
N.S. |
1 | 1.00 | 1.37 | 0.78 | 0.00 | 4.54 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.183 | 0.789 | 5.126 | 0.000 | 0.300 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 100 | 80 | 0 | 332 | 0 | 116 | 0 |
N.S. |
1 | 1.00 | 1.25 | 1.00 | 0.00 | 4.15 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.226 | 0.571 | 5.349 | 0.000 | 0.300 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 127 | 121 | 103 | 0 | 418 | 0 | 205 | 0 |
N.S. |
1 | 1.10 | 1.05 | 0.90 | 0.00 | 3.63 | 0.00 | 1.78 | 0.00 |
time (sec) |
N/A | 0.294 | 1.084 | 6.302 | 0.000 | 0.309 | 0.000 | 1.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 872 | 1002 | 249 | 298 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 0.29 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.444 | 10.346 | 6.114 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 638 | 958 | 65 | 265 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.50 | 0.10 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.355 | 10.056 | 4.722 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 638 | 860 | 161 | 191 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.35 | 0.25 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.234 | 10.076 | 4.687 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 677 | 988 | 337 | 288 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.46 | 0.50 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.387 | 10.288 | 6.319 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 804 | 1089 | 65 | 292 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.35 | 0.08 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.545 | 10.055 | 4.760 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 656 | 865 | 65 | 191 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.32 | 0.10 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.193 | 10.055 | 4.798 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 833 | 999 | 141 | 310 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.20 | 0.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.518 | 10.121 | 6.489 | 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 | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 182 | 175 | 171 | 0 | 622 | 0 | 180 | 186 |
N.S. |
1 | 1.04 | 1.00 | 0.98 | 0.00 | 3.55 | 0.00 | 1.03 | 1.06 |
time (sec) |
N/A | 0.299 | 0.679 | 5.152 | 0.000 | 0.623 | 0.000 | 0.295 | 9.455 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 144 | 130 | 133 | 0 | 475 | 0 | 134 | 144 |
N.S. |
1 | 1.17 | 1.06 | 1.08 | 0.00 | 3.86 | 0.00 | 1.09 | 1.17 |
time (sec) |
N/A | 0.282 | 0.492 | 5.176 | 0.000 | 0.642 | 0.000 | 0.297 | 9.834 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 98 | 100 | 83 | 0 | 348 | 0 | 116 | 95 |
N.S. |
1 | 0.99 | 1.01 | 0.84 | 0.00 | 3.52 | 0.00 | 1.17 | 0.96 |
time (sec) |
N/A | 0.237 | 0.283 | 5.224 | 0.000 | 0.911 | 0.000 | 0.277 | 9.690 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 86 | 86 | 90 | 0 | 302 | 0 | 93 | 84 |
N.S. |
1 | 0.99 | 0.99 | 1.03 | 0.00 | 3.47 | 0.00 | 1.07 | 0.97 |
time (sec) |
N/A | 0.218 | 0.281 | 4.886 | 0.000 | 0.353 | 0.000 | 0.278 | 9.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 155 | 124 | 146 | 0 | 862 | 0 | 139 | 3017 |
N.S. |
1 | 1.17 | 0.94 | 1.11 | 0.00 | 6.53 | 0.00 | 1.05 | 22.86 |
time (sec) |
N/A | 0.286 | 0.529 | 5.007 | 0.000 | 0.538 | 0.000 | 0.281 | 10.723 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 213 | 163 | 191 | 0 | 1236 | 0 | 257 | 3822 |
N.S. |
1 | 1.15 | 0.88 | 1.03 | 0.00 | 6.68 | 0.00 | 1.39 | 20.66 |
time (sec) |
N/A | 0.366 | 0.975 | 5.134 | 0.000 | 0.543 | 0.000 | 0.308 | 11.896 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 191 | 213 | 189 | 164 | 0 | 1386 | 0 | 333 | 0 |
N.S. |
1 | 1.12 | 0.99 | 0.86 | 0.00 | 7.26 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 0.456 | 2.768 | 6.404 | 0.000 | 1.448 | 0.000 | 0.388 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 166 | 153 | 117 | 0 | 1077 | 0 | 298 | 0 |
N.S. |
1 | 1.18 | 1.09 | 0.83 | 0.00 | 7.64 | 0.00 | 2.11 | 0.00 |
time (sec) |
N/A | 0.319 | 1.957 | 5.705 | 0.000 | 0.522 | 0.000 | 0.373 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 97 | 112 | 81 | 0 | 426 | 0 | 244 | 0 |
N.S. |
1 | 1.04 | 1.20 | 0.87 | 0.00 | 4.58 | 0.00 | 2.62 | 0.00 |
time (sec) |
N/A | 0.239 | 1.161 | 5.564 | 0.000 | 0.448 | 0.000 | 0.858 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 108 | 124 | 90 | 0 | 467 | 0 | 237 | 0 |
N.S. |
1 | 1.04 | 1.19 | 0.87 | 0.00 | 4.49 | 0.00 | 2.28 | 0.00 |
time (sec) |
N/A | 0.244 | 1.454 | 5.847 | 0.000 | 0.661 | 0.000 | 0.318 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 157 | 157 | 112 | 0 | 612 | 0 | 418 | 0 |
N.S. |
1 | 1.05 | 1.05 | 0.75 | 0.00 | 4.11 | 0.00 | 2.81 | 0.00 |
time (sec) |
N/A | 0.325 | 1.500 | 6.038 | 0.000 | 0.720 | 0.000 | 0.891 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 212 | 201 | 134 | 0 | 760 | 0 | 395 | 0 |
N.S. |
1 | 1.02 | 0.97 | 0.64 | 0.00 | 3.65 | 0.00 | 1.90 | 0.00 |
time (sec) |
N/A | 0.415 | 2.497 | 6.751 | 0.000 | 0.737 | 0.000 | 0.942 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 996 | 1032 | 253 | 337 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.25 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.510 | 10.297 | 5.311 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 908 | 1013 | 238 | 324 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 0.26 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.503 | 10.229 | 5.204 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 983 | 1016 | 392 | 333 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.40 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.439 | 10.276 | 4.959 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1046 | 1074 | 408 | 364 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.39 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.587 | 10.549 | 8.392 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1146 | 1085 | 162 | 353 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.14 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.553 | 10.391 | 5.024 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1144 | 1071 | 172 | 359 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.15 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.426 | 10.175 | 4.980 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1225 | 1148 | 226 | 392 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.18 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.539 | 10.283 | 8.135 | 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 | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 200 | 195 | 164 | 0 | 0 | 0 | 182 | 0 | 0 |
N.S. |
1 | 0.98 | 0.82 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 | 0.00 |
time (sec) |
N/A | 0.368 | 11.133 | 0.000 | 0.000 | 0.000 | 6.383 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 123 | 117 | 110 | 0 | 0 | 0 | 117 | 0 | 0 |
N.S. |
1 | 0.95 | 0.89 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 | 0.00 |
time (sec) |
N/A | 0.252 | 2.272 | 0.000 | 0.000 | 0.000 | 2.194 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 66 | 0 | 0 | 0 | 56 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 | 0.00 |
time (sec) |
N/A | 0.188 | 0.785 | 0.000 | 0.000 | 0.000 | 0.601 | 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 | 81 | 81 | 125 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.222 | 5.606 | 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 | 81 | 81 | 179 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.223 | 11.181 | 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 | 81 | 81 | 77 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.219 | 11.109 | 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 | 198 | 200 | 167 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.373 | 11.186 | 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 | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 113 | 0 | 0 | 0 | 117 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 | 0.00 |
time (sec) |
N/A | 0.253 | 5.577 | 0.000 | 0.000 | 0.000 | 17.871 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 69 | 0 | 0 | 0 | 56 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 |
time (sec) |
N/A | 0.190 | 1.934 | 0.000 | 0.000 | 0.000 | 0.734 | 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 | 84 | 84 | 169 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.227 | 11.188 | 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 | 84 | 84 | 77 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.223 | 11.112 | 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 | 84 | 84 | 77 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.230 | 11.113 | 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 | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 91 | 91 | 0 | 288 | 0 | 106 | 103 |
N.S. |
1 | 1.00 | 0.88 | 0.88 | 0.00 | 2.77 | 0.00 | 1.02 | 0.99 |
time (sec) |
N/A | 0.267 | 0.292 | 7.314 | 0.000 | 0.527 | 0.000 | 0.292 | 9.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 73 | 72 | 0 | 205 | 0 | 64 | 58 |
N.S. |
1 | 1.00 | 0.99 | 0.97 | 0.00 | 2.77 | 0.00 | 0.86 | 0.78 |
time (sec) |
N/A | 0.205 | 0.155 | 5.396 | 0.000 | 0.434 | 0.000 | 0.286 | 9.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 39 | 0 | 130 | 87 | 40 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.00 | 2.55 | 1.71 | 0.78 | 0.78 |
time (sec) |
N/A | 0.189 | 0.073 | 5.112 | 0.000 | 0.320 | 8.628 | 0.298 | 9.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 80 | 78 | 0 | 431 | 114 | 71 | 652 |
N.S. |
1 | 1.00 | 0.94 | 0.92 | 0.00 | 5.07 | 1.34 | 0.84 | 7.67 |
time (sec) |
N/A | 0.220 | 0.193 | 5.272 | 0.000 | 0.305 | 6.994 | 0.299 | 9.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 127 | 109 | 92 | 0 | 565 | 0 | 104 | 396 |
N.S. |
1 | 1.09 | 0.93 | 0.79 | 0.00 | 4.83 | 0.00 | 0.89 | 3.38 |
time (sec) |
N/A | 0.265 | 0.432 | 5.389 | 0.000 | 0.330 | 0.000 | 0.288 | 9.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 134 | 136 | 152 | 0 | 739 | 0 | 237 | 0 |
N.S. |
1 | 1.09 | 1.11 | 1.24 | 0.00 | 6.01 | 0.00 | 1.93 | 0.00 |
time (sec) |
N/A | 0.291 | 1.410 | 9.611 | 0.000 | 0.825 | 0.000 | 0.434 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 90 | 108 | 85 | 0 | 632 | 0 | 156 | 0 |
N.S. |
1 | 0.99 | 1.19 | 0.93 | 0.00 | 6.95 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.231 | 0.697 | 7.217 | 0.000 | 0.608 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 74 | 42 | 0 | 245 | 0 | 72 | 0 |
N.S. |
1 | 1.00 | 1.37 | 0.78 | 0.00 | 4.54 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.186 | 0.859 | 6.881 | 0.000 | 0.733 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 100 | 80 | 0 | 332 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.25 | 1.00 | 0.00 | 4.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.224 | 0.720 | 8.124 | 0.000 | 0.372 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 127 | 121 | 103 | 0 | 416 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 1.05 | 0.90 | 0.00 | 3.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.297 | 1.490 | 10.953 | 0.000 | 0.389 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.210 | 10.049 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.222 | 10.044 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.210 | 10.049 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 161 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.184 | 10.189 | 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 | 62 | 62 | 141 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.205 | 10.122 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 141 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.233 | 10.122 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 141 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.228 | 10.134 | 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 | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 144 | 130 | 133 | 0 | 475 | 0 | 134 | 144 |
N.S. |
1 | 1.17 | 1.06 | 1.08 | 0.00 | 3.86 | 0.00 | 1.09 | 1.17 |
time (sec) |
N/A | 0.273 | 0.535 | 5.356 | 0.000 | 0.641 | 0.000 | 0.276 | 9.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 98 | 100 | 83 | 0 | 348 | 0 | 116 | 95 |
N.S. |
1 | 0.99 | 1.01 | 0.84 | 0.00 | 3.52 | 0.00 | 1.17 | 0.96 |
time (sec) |
N/A | 0.225 | 0.276 | 5.325 | 0.000 | 0.378 | 0.000 | 0.279 | 9.795 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 86 | 86 | 90 | 0 | 302 | 0 | 93 | 84 |
N.S. |
1 | 0.99 | 0.99 | 1.03 | 0.00 | 3.47 | 0.00 | 1.07 | 0.97 |
time (sec) |
N/A | 0.210 | 0.251 | 5.159 | 0.000 | 0.411 | 0.000 | 0.273 | 9.241 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 155 | 124 | 146 | 0 | 862 | 0 | 139 | 3025 |
N.S. |
1 | 1.17 | 0.94 | 1.11 | 0.00 | 6.53 | 0.00 | 1.05 | 22.92 |
time (sec) |
N/A | 0.281 | 0.521 | 5.352 | 0.000 | 0.480 | 0.000 | 0.281 | 10.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 213 | 163 | 189 | 0 | 1236 | 0 | 257 | 3860 |
N.S. |
1 | 1.15 | 0.88 | 1.02 | 0.00 | 6.68 | 0.00 | 1.39 | 20.86 |
time (sec) |
N/A | 0.352 | 1.007 | 5.446 | 0.000 | 0.478 | 0.000 | 0.284 | 11.632 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 166 | 153 | 117 | 0 | 1077 | 0 | 343 | 0 |
N.S. |
1 | 1.18 | 1.09 | 0.83 | 0.00 | 7.64 | 0.00 | 2.43 | 0.00 |
time (sec) |
N/A | 0.312 | 2.987 | 10.579 | 0.000 | 0.848 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 97 | 112 | 81 | 0 | 426 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.20 | 0.87 | 0.00 | 4.58 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.230 | 1.433 | 9.337 | 0.000 | 0.361 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 108 | 124 | 90 | 0 | 467 | 0 | 237 | 0 |
N.S. |
1 | 1.04 | 1.19 | 0.87 | 0.00 | 4.49 | 0.00 | 2.28 | 0.00 |
time (sec) |
N/A | 0.241 | 1.599 | 9.441 | 0.000 | 0.506 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 157 | 157 | 112 | 0 | 612 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.05 | 0.75 | 0.00 | 4.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.321 | 1.789 | 12.056 | 0.000 | 0.515 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 212 | 201 | 134 | 0 | 760 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.97 | 0.64 | 0.00 | 3.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.406 | 3.176 | 18.346 | 0.000 | 0.686 | 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 | 64 | 64 | 169 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.206 | 10.201 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 168 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.222 | 10.193 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 172 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.205 | 10.175 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 329 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 5.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.183 | 10.297 | 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 | 62 | 62 | 226 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.206 | 10.297 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 226 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.235 | 10.281 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 225 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.232 | 10.288 | 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 | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 91 | 91 | 0 | 288 | 0 | 106 | 103 |
N.S. |
1 | 1.00 | 0.88 | 0.88 | 0.00 | 2.77 | 0.00 | 1.02 | 0.99 |
time (sec) |
N/A | 0.261 | 0.287 | 8.891 | 0.000 | 0.402 | 0.000 | 0.274 | 9.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 73 | 72 | 0 | 205 | 0 | 64 | 58 |
N.S. |
1 | 1.00 | 0.99 | 0.97 | 0.00 | 2.77 | 0.00 | 0.86 | 0.78 |
time (sec) |
N/A | 0.204 | 0.153 | 5.986 | 0.000 | 0.422 | 0.000 | 0.280 | 9.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 39 | 0 | 130 | 87 | 40 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.00 | 2.55 | 1.71 | 0.78 | 0.78 |
time (sec) |
N/A | 0.187 | 0.072 | 5.898 | 0.000 | 0.452 | 10.988 | 0.274 | 9.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 80 | 78 | 0 | 431 | 114 | 71 | 652 |
N.S. |
1 | 1.00 | 0.94 | 0.92 | 0.00 | 5.07 | 1.34 | 0.84 | 7.67 |
time (sec) |
N/A | 0.216 | 0.190 | 6.177 | 0.000 | 0.492 | 9.149 | 0.269 | 9.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 127 | 109 | 92 | 0 | 565 | 0 | 104 | 396 |
N.S. |
1 | 1.09 | 0.93 | 0.79 | 0.00 | 4.83 | 0.00 | 0.89 | 3.38 |
time (sec) |
N/A | 0.261 | 0.429 | 6.098 | 0.000 | 0.877 | 0.000 | 0.314 | 10.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 134 | 136 | 152 | 0 | 739 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.11 | 1.24 | 0.00 | 6.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.287 | 2.361 | 22.368 | 0.000 | 0.381 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 90 | 108 | 85 | 0 | 632 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.19 | 0.93 | 0.00 | 6.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.235 | 1.093 | 12.914 | 0.000 | 0.395 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 74 | 42 | 0 | 245 | 0 | 72 | 0 |
N.S. |
1 | 1.00 | 1.37 | 0.78 | 0.00 | 4.54 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.191 | 0.959 | 10.886 | 0.000 | 0.445 | 0.000 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 100 | 80 | 0 | 332 | 0 | 116 | 0 |
N.S. |
1 | 1.00 | 1.25 | 1.00 | 0.00 | 4.15 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.226 | 0.878 | 14.678 | 0.000 | 0.505 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 127 | 121 | 103 | 0 | 416 | 0 | 205 | 0 |
N.S. |
1 | 1.10 | 1.05 | 0.90 | 0.00 | 3.62 | 0.00 | 1.78 | 0.00 |
time (sec) |
N/A | 0.297 | 2.498 | 25.258 | 0.000 | 0.521 | 0.000 | 1.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 851 | 976 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 0.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.387 | 10.063 | 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 | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 754 | 876 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.224 | 10.058 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 878 | 1006 | 141 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 0.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.417 | 10.157 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1005 | 1111 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.570 | 10.069 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |