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 | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 615 | 677 | 12289 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 19.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 5.186 | 7.243 | 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 | 161 | 161 | 545 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.355 | 2.564 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 388 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.335 | 0.708 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 183 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.335 | 0.367 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 163 | 163 | 428 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.340 | 1.452 | 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 | 158 | 158 | 181 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.315 | 0.477 | 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 | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 41 | 150 | 162 | 142 | 142 | 178 | 160 | 141 |
N.S. |
1 | 0.89 | 3.26 | 3.52 | 3.09 | 3.09 | 3.87 | 3.48 | 3.07 |
time (sec) |
N/A | 0.194 | 0.047 | 0.601 | 0.202 | 0.268 | 0.035 | 0.275 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 81 | 401 | 494 | 403 | 403 | 559 | 475 | 383 |
N.S. |
1 | 0.91 | 4.51 | 5.55 | 4.53 | 4.53 | 6.28 | 5.34 | 4.30 |
time (sec) |
N/A | 0.266 | 0.082 | 0.627 | 0.206 | 0.254 | 0.072 | 0.296 | 8.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 121 | 797 | 1130 | 872 | 872 | 1314 | 1079 | 777 |
N.S. |
1 | 0.88 | 5.78 | 8.19 | 6.32 | 6.32 | 9.52 | 7.82 | 5.63 |
time (sec) |
N/A | 0.307 | 0.203 | 0.641 | 0.217 | 0.260 | 0.130 | 0.307 | 9.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 44 | 154 | 179 | 166 | 166 | 240 | 204 | 164 |
N.S. |
1 | 0.80 | 2.80 | 3.25 | 3.02 | 3.02 | 4.36 | 3.71 | 2.98 |
time (sec) |
N/A | 0.198 | 0.019 | 0.629 | 0.207 | 0.265 | 0.046 | 0.301 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 84 | 405 | 566 | 439 | 439 | 722 | 597 | 419 |
N.S. |
1 | 0.81 | 3.89 | 5.44 | 4.22 | 4.22 | 6.94 | 5.74 | 4.03 |
time (sec) |
N/A | 0.250 | 0.059 | 0.597 | 0.217 | 0.256 | 0.071 | 0.299 | 0.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 124 | 801 | 1318 | 920 | 920 | 1654 | 1330 | 825 |
N.S. |
1 | 0.78 | 5.04 | 8.29 | 5.79 | 5.79 | 10.40 | 8.36 | 5.19 |
time (sec) |
N/A | 0.282 | 0.025 | 0.638 | 0.220 | 0.261 | 0.148 | 0.306 | 8.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 193 | 199 | 219 | 158 | 0 | 1231 | 178 | 1315 | 3988 |
N.S. |
1 | 1.03 | 1.13 | 0.82 | 0.00 | 6.38 | 0.92 | 6.81 | 20.66 |
time (sec) |
N/A | 0.365 | 0.106 | 0.595 | 0.000 | 0.285 | 1.735 | 0.299 | 9.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 79 | 77 | 151 | 0 | 434 | 280 | 126 | 278 |
N.S. |
1 | 0.98 | 0.95 | 1.86 | 0.00 | 5.36 | 3.46 | 1.56 | 3.43 |
time (sec) |
N/A | 0.256 | 0.037 | 0.635 | 0.000 | 0.293 | 0.921 | 0.299 | 8.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 164 | 170 | 175 | 140 | 0 | 703 | 104 | 1403 | 590 |
N.S. |
1 | 1.04 | 1.07 | 0.85 | 0.00 | 4.29 | 0.63 | 8.55 | 3.60 |
time (sec) |
N/A | 0.288 | 0.063 | 0.592 | 0.000 | 0.255 | 0.726 | 0.294 | 0.213 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 46 | 129 | 0 | 272 | 168 | 52 | 61 |
N.S. |
1 | 1.00 | 1.07 | 3.00 | 0.00 | 6.33 | 3.91 | 1.21 | 1.42 |
time (sec) |
N/A | 0.200 | 0.013 | 0.083 | 0.000 | 0.284 | 0.566 | 0.290 | 8.683 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 92 | 128 | 155 | 0 | 468 | 320 | 280 | 2173 |
N.S. |
1 | 0.98 | 1.36 | 1.65 | 0.00 | 4.98 | 3.40 | 2.98 | 23.12 |
time (sec) |
N/A | 0.278 | 0.062 | 0.633 | 0.000 | 0.277 | 13.829 | 0.357 | 9.564 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 188 | 206 | 168 | 0 | 1339 | 211 | 932 | 3844 |
N.S. |
1 | 0.96 | 1.06 | 0.86 | 0.00 | 6.87 | 1.08 | 4.78 | 19.71 |
time (sec) |
N/A | 0.331 | 0.232 | 0.635 | 0.000 | 0.279 | 2.956 | 0.307 | 9.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 118 | 154 | 213 | 0 | 810 | 0 | 101 | 4950 |
N.S. |
1 | 0.98 | 1.27 | 1.76 | 0.00 | 6.69 | 0.00 | 0.83 | 40.91 |
time (sec) |
N/A | 0.329 | 0.096 | 0.664 | 0.000 | 0.295 | 0.000 | 0.300 | 12.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 224 | 223 | 235 | 188 | 0 | 2044 | 347 | 1347 | 5214 |
N.S. |
1 | 1.00 | 1.05 | 0.84 | 0.00 | 9.12 | 1.55 | 6.01 | 23.28 |
time (sec) |
N/A | 0.429 | 0.133 | 0.702 | 0.000 | 0.331 | 104.662 | 0.304 | 9.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 270 | 255 | 263 | 323 | 0 | 2454 | 573 | 1408 | 7327 |
N.S. |
1 | 0.94 | 0.97 | 1.20 | 0.00 | 9.09 | 2.12 | 5.21 | 27.14 |
time (sec) |
N/A | 0.397 | 0.304 | 0.630 | 0.000 | 0.321 | 11.780 | 0.366 | 10.483 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 95 | 100 | 276 | 0 | 1021 | 495 | 162 | 427 |
N.S. |
1 | 0.98 | 1.03 | 2.85 | 0.00 | 10.53 | 5.10 | 1.67 | 4.40 |
time (sec) |
N/A | 0.252 | 0.084 | 0.655 | 0.000 | 0.310 | 2.651 | 0.304 | 8.604 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 254 | 241 | 247 | 319 | 0 | 2474 | 0 | 1416 | 7200 |
N.S. |
1 | 0.95 | 0.97 | 1.26 | 0.00 | 9.74 | 0.00 | 5.57 | 28.35 |
time (sec) |
N/A | 0.363 | 0.615 | 0.615 | 0.000 | 0.345 | 0.000 | 0.322 | 9.932 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 95 | 98 | 270 | 0 | 1042 | 495 | 163 | 417 |
N.S. |
1 | 0.97 | 1.00 | 2.76 | 0.00 | 10.63 | 5.05 | 1.66 | 4.26 |
time (sec) |
N/A | 0.245 | 0.089 | 0.169 | 0.000 | 0.300 | 2.521 | 0.295 | 8.619 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 299 | 264 | 271 | 364 | 0 | 3228 | 0 | 1460 | 9056 |
N.S. |
1 | 0.88 | 0.91 | 1.22 | 0.00 | 10.80 | 0.00 | 4.88 | 30.29 |
time (sec) |
N/A | 0.432 | 0.546 | 0.134 | 0.000 | 0.350 | 0.000 | 0.297 | 10.568 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 162 | 184 | 235 | 399 | 0 | 2476 | 0 | 467 | 11072 |
N.S. |
1 | 1.14 | 1.45 | 2.46 | 0.00 | 15.28 | 0.00 | 2.88 | 68.35 |
time (sec) |
N/A | 0.397 | 0.261 | 0.737 | 0.000 | 0.445 | 0.000 | 0.401 | 14.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 348 | 339 | 339 | 441 | 0 | 4330 | 0 | 879 | 10556 |
N.S. |
1 | 0.97 | 0.97 | 1.27 | 0.00 | 12.44 | 0.00 | 2.53 | 30.33 |
time (sec) |
N/A | 0.630 | 0.961 | 0.727 | 0.000 | 0.447 | 0.000 | 0.353 | 11.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 213 | 226 | 284 | 462 | 0 | 4562 | 0 | 219 | 12436 |
N.S. |
1 | 1.06 | 1.33 | 2.17 | 0.00 | 21.42 | 0.00 | 1.03 | 58.38 |
time (sec) |
N/A | 0.452 | 0.328 | 0.750 | 0.000 | 0.607 | 0.000 | 0.292 | 15.322 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 408 | 394 | 384 | 489 | 0 | 5734 | 0 | 2122 | 12239 |
N.S. |
1 | 0.97 | 0.94 | 1.20 | 0.00 | 14.05 | 0.00 | 5.20 | 30.00 |
time (sec) |
N/A | 1.137 | 1.781 | 0.781 | 0.000 | 0.639 | 0.000 | 0.359 | 13.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 341 | 340 | 328 | 704 | 0 | 6633 | 0 | 1802 | 12677 |
N.S. |
1 | 1.00 | 0.96 | 2.06 | 0.00 | 19.45 | 0.00 | 5.28 | 37.18 |
time (sec) |
N/A | 0.490 | 2.600 | 0.693 | 0.000 | 0.452 | 0.000 | 0.367 | 12.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 150 | 160 | 146 | 544 | 0 | 3739 | 1671 | 349 | 1182 |
N.S. |
1 | 1.07 | 0.97 | 3.63 | 0.00 | 24.93 | 11.14 | 2.33 | 7.88 |
time (sec) |
N/A | 0.295 | 0.127 | 0.727 | 0.000 | 0.460 | 7.147 | 0.345 | 10.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 363 | 378 | 382 | 885 | 0 | 7701 | 0 | 2447 | 14584 |
N.S. |
1 | 1.04 | 1.05 | 2.44 | 0.00 | 21.21 | 0.00 | 6.74 | 40.18 |
time (sec) |
N/A | 0.537 | 2.857 | 0.689 | 0.000 | 0.624 | 0.000 | 0.336 | 12.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 157 | 147 | 541 | 0 | 3708 | 1646 | 349 | 1157 |
N.S. |
1 | 1.03 | 0.97 | 3.56 | 0.00 | 24.39 | 10.83 | 2.30 | 7.61 |
time (sec) |
N/A | 0.292 | 0.119 | 0.352 | 0.000 | 0.426 | 6.932 | 0.312 | 9.812 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 437 | 405 | 424 | 1010 | 0 | 8554 | 0 | 2641 | 16086 |
N.S. |
1 | 0.93 | 0.97 | 2.31 | 0.00 | 19.57 | 0.00 | 6.04 | 36.81 |
time (sec) |
N/A | 0.600 | 4.490 | 0.328 | 0.000 | 0.768 | 0.000 | 0.307 | 12.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 255 | 297 | 391 | 966 | 0 | 9908 | 0 | 1045 | 19440 |
N.S. |
1 | 1.16 | 1.53 | 3.79 | 0.00 | 38.85 | 0.00 | 4.10 | 76.24 |
time (sec) |
N/A | 0.547 | 2.658 | 1.426 | 0.000 | 0.951 | 0.000 | 0.451 | 18.815 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 484 | 471 | 560 | 1197 | 0 | 10260 | 0 | 1458 | 18112 |
N.S. |
1 | 0.97 | 1.16 | 2.47 | 0.00 | 21.20 | 0.00 | 3.01 | 37.42 |
time (sec) |
N/A | 0.746 | 6.181 | 0.902 | 0.000 | 1.107 | 0.000 | 0.398 | 16.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 325 | 353 | 491 | 1141 | 0 | 15165 | 0 | 379 | 21465 |
N.S. |
1 | 1.09 | 1.51 | 3.51 | 0.00 | 46.66 | 0.00 | 1.17 | 66.05 |
time (sec) |
N/A | 0.601 | 6.158 | 0.943 | 0.000 | 1.608 | 0.000 | 0.318 | 22.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 222 | 162 | 0 | 1346 | 219 | 1366 | 4605 |
N.S. |
1 | 1.00 | 1.10 | 0.80 | 0.00 | 6.66 | 1.08 | 6.76 | 22.80 |
time (sec) |
N/A | 0.361 | 0.097 | 0.593 | 0.000 | 0.290 | 1.930 | 0.303 | 0.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 82 | 80 | 154 | 0 | 446 | 332 | 158 | 287 |
N.S. |
1 | 0.94 | 0.92 | 1.77 | 0.00 | 5.13 | 3.82 | 1.82 | 3.30 |
time (sec) |
N/A | 0.263 | 0.028 | 0.616 | 0.000 | 0.273 | 1.010 | 0.292 | 0.258 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 173 | 178 | 143 | 0 | 799 | 124 | 1443 | 683 |
N.S. |
1 | 1.02 | 1.05 | 0.84 | 0.00 | 4.70 | 0.73 | 8.49 | 4.02 |
time (sec) |
N/A | 0.292 | 0.073 | 0.593 | 0.000 | 0.285 | 0.778 | 0.328 | 8.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 47 | 130 | 0 | 274 | 189 | 61 | 477 |
N.S. |
1 | 1.00 | 1.07 | 2.95 | 0.00 | 6.23 | 4.30 | 1.39 | 10.84 |
time (sec) |
N/A | 0.202 | 0.011 | 0.076 | 0.000 | 0.262 | 0.594 | 0.386 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 95 | 131 | 173 | 0 | 474 | 348 | 291 | 2520 |
N.S. |
1 | 0.92 | 1.27 | 1.68 | 0.00 | 4.60 | 3.38 | 2.83 | 24.47 |
time (sec) |
N/A | 0.282 | 0.055 | 0.662 | 0.000 | 0.312 | 17.677 | 0.400 | 9.526 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | A | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 204 | 191 | 209 | 172 | 0 | 1477 | 258 | 0 | 4339 |
N.S. |
1 | 0.94 | 1.02 | 0.84 | 0.00 | 7.24 | 1.26 | 0.00 | 21.27 |
time (sec) |
N/A | 0.331 | 0.236 | 0.665 | 0.000 | 0.306 | 3.196 | 0.000 | 9.834 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 121 | 157 | 217 | 0 | 828 | 0 | 356 | 5947 |
N.S. |
1 | 0.91 | 1.18 | 1.63 | 0.00 | 6.23 | 0.00 | 2.68 | 44.71 |
time (sec) |
N/A | 0.327 | 0.091 | 0.668 | 0.000 | 0.378 | 0.000 | 0.406 | 12.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 236 | 226 | 238 | 192 | 0 | 2212 | 411 | 1353 | 5771 |
N.S. |
1 | 0.96 | 1.01 | 0.81 | 0.00 | 9.37 | 1.74 | 5.73 | 24.45 |
time (sec) |
N/A | 0.421 | 0.133 | 0.696 | 0.000 | 0.302 | 105.919 | 0.294 | 9.417 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 279 | 258 | 266 | 327 | 0 | 2578 | 641 | 1474 | 8025 |
N.S. |
1 | 0.92 | 0.95 | 1.17 | 0.00 | 9.24 | 2.30 | 5.28 | 28.76 |
time (sec) |
N/A | 0.396 | 0.283 | 0.625 | 0.000 | 0.319 | 11.975 | 0.302 | 10.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 98 | 103 | 280 | 0 | 1077 | 556 | 202 | 460 |
N.S. |
1 | 0.95 | 1.00 | 2.72 | 0.00 | 10.46 | 5.40 | 1.96 | 4.47 |
time (sec) |
N/A | 0.260 | 0.083 | 0.685 | 0.000 | 0.322 | 2.768 | 0.294 | 8.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 263 | 244 | 250 | 323 | 0 | 2600 | 0 | 1482 | 7835 |
N.S. |
1 | 0.93 | 0.95 | 1.23 | 0.00 | 9.89 | 0.00 | 5.63 | 29.79 |
time (sec) |
N/A | 0.357 | 0.599 | 0.630 | 0.000 | 0.304 | 0.000 | 0.299 | 9.982 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 96 | 99 | 272 | 0 | 1066 | 525 | 202 | 442 |
N.S. |
1 | 0.98 | 1.01 | 2.78 | 0.00 | 10.88 | 5.36 | 2.06 | 4.51 |
time (sec) |
N/A | 0.246 | 0.079 | 0.181 | 0.000 | 0.298 | 2.607 | 0.299 | 8.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 174 | 187 | 238 | 403 | 0 | 2486 | 0 | 489 | 13434 |
N.S. |
1 | 1.07 | 1.37 | 2.32 | 0.00 | 14.29 | 0.00 | 2.81 | 77.21 |
time (sec) |
N/A | 0.396 | 0.277 | 0.740 | 0.000 | 0.543 | 0.000 | 0.398 | 14.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 360 | 342 | 342 | 445 | 0 | 4520 | 0 | 1031 | 12008 |
N.S. |
1 | 0.95 | 0.95 | 1.24 | 0.00 | 12.56 | 0.00 | 2.86 | 33.36 |
time (sec) |
N/A | 0.617 | 0.973 | 0.753 | 0.000 | 0.389 | 0.000 | 0.342 | 11.869 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 229 | 287 | 466 | 0 | 4604 | 0 | 705 | 14830 |
N.S. |
1 | 1.00 | 1.26 | 2.04 | 0.00 | 20.19 | 0.00 | 3.09 | 65.04 |
time (sec) |
N/A | 0.442 | 0.306 | 0.810 | 0.000 | 1.194 | 0.000 | 0.414 | 15.937 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 423 | 397 | 387 | 493 | 0 | 5954 | 0 | 2137 | 13781 |
N.S. |
1 | 0.94 | 0.91 | 1.17 | 0.00 | 14.08 | 0.00 | 5.05 | 32.58 |
time (sec) |
N/A | 1.031 | 1.727 | 0.801 | 0.000 | 0.488 | 0.000 | 0.323 | 13.999 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 353 | 343 | 331 | 708 | 0 | 6770 | 0 | 1958 | 13840 |
N.S. |
1 | 0.97 | 0.94 | 2.01 | 0.00 | 19.18 | 0.00 | 5.55 | 39.21 |
time (sec) |
N/A | 0.495 | 2.605 | 0.691 | 0.000 | 0.464 | 0.000 | 0.330 | 12.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 163 | 149 | 548 | 0 | 3843 | 1794 | 431 | 1267 |
N.S. |
1 | 1.03 | 0.94 | 3.45 | 0.00 | 24.17 | 11.28 | 2.71 | 7.97 |
time (sec) |
N/A | 0.310 | 0.147 | 0.737 | 0.000 | 0.388 | 7.323 | 0.330 | 9.802 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 375 | 381 | 385 | 889 | 0 | 7838 | 0 | 2679 | 16025 |
N.S. |
1 | 1.02 | 1.03 | 2.37 | 0.00 | 20.90 | 0.00 | 7.14 | 42.73 |
time (sec) |
N/A | 0.537 | 2.782 | 0.698 | 0.000 | 0.534 | 0.000 | 0.334 | 12.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 158 | 148 | 543 | 0 | 3748 | 1707 | 429 | 1199 |
N.S. |
1 | 1.03 | 0.97 | 3.55 | 0.00 | 24.50 | 11.16 | 2.80 | 7.84 |
time (sec) |
N/A | 0.292 | 0.115 | 0.379 | 0.000 | 0.556 | 7.207 | 0.327 | 9.757 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 270 | 300 | 394 | 970 | 0 | 9926 | 0 | 1077 | 22621 |
N.S. |
1 | 1.11 | 1.46 | 3.59 | 0.00 | 36.76 | 0.00 | 3.99 | 83.78 |
time (sec) |
N/A | 0.545 | 2.373 | 0.904 | 0.000 | 1.582 | 0.000 | 0.432 | 19.421 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 499 | 474 | 575 | 1201 | 0 | 10518 | 0 | 1704 | 20580 |
N.S. |
1 | 0.95 | 1.15 | 2.41 | 0.00 | 21.08 | 0.00 | 3.41 | 41.24 |
time (sec) |
N/A | 0.698 | 6.144 | 0.925 | 0.000 | 1.136 | 0.000 | 0.396 | 17.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 343 | 356 | 461 | 1145 | 0 | 15231 | 0 | 1791 | 25334 |
N.S. |
1 | 1.04 | 1.34 | 3.34 | 0.00 | 44.41 | 0.00 | 5.22 | 73.86 |
time (sec) |
N/A | 0.590 | 6.058 | 0.999 | 0.000 | 4.422 | 0.000 | 0.432 | 24.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 340 | 338 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.502 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 398 | 393 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.544 | 0.000 | 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 | B | B | B | B | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 104 | 104 | 104 | 107 | 28 | 29 |
N.S. |
1 | 1.00 | 1.00 | 3.06 | 3.06 | 3.06 | 3.15 | 0.82 | 0.85 |
time (sec) |
N/A | 0.187 | 0.016 | 0.561 | 0.210 | 0.267 | 0.042 | 0.353 | 8.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 48 | 188 | 174 | 174 | 174 | 187 | 46 | 46 |
N.S. |
1 | 0.86 | 3.36 | 3.11 | 3.11 | 3.11 | 3.34 | 0.82 | 0.82 |
time (sec) |
N/A | 0.224 | 0.011 | 0.587 | 0.232 | 0.236 | 0.068 | 0.325 | 0.084 |