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 | 370 | 614 | 246 | 343 | 0 | 237 | 0 | 0 | 334 | 0 |
N.S. |
1 | 1.66 | 0.66 | 0.93 | 0.00 | 0.64 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 1.378 | 3.098 | 5.260 | 0.000 | 0.086 | 0.000 | 0.000 | 0.390 | 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 | 296 | 531 | 198 | 265 | 0 | 161 | 0 | 0 | 174 | 0 |
N.S. |
1 | 1.79 | 0.67 | 0.90 | 0.00 | 0.54 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 1.029 | 2.537 | 3.927 | 0.000 | 0.075 | 0.000 | 0.000 | 0.308 | 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 | 137 | 447 | 119 | 124 | 0 | 117 | 0 | 0 | 46 | 0 |
N.S. |
1 | 3.26 | 0.87 | 0.91 | 0.00 | 0.85 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.877 | 1.705 | 1.312 | 0.000 | 0.077 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 190 | 83 | 87 | 0 | 42 | 0 | 0 | 43 | 0 |
N.S. |
1 | 2.02 | 0.88 | 0.93 | 0.00 | 0.45 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.407 | 0.029 | 0.751 | 0.000 | 0.081 | 0.000 | 0.000 | 0.170 | 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 | 138 | 493 | 143 | 160 | 0 | 112 | 0 | 0 | 46 | 0 |
N.S. |
1 | 3.57 | 1.04 | 1.16 | 0.00 | 0.81 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.989 | 2.141 | 1.822 | 0.000 | 0.072 | 0.000 | 0.000 | 0.203 | 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 | 301 | 586 | 226 | 293 | 0 | 162 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.95 | 0.75 | 0.97 | 0.00 | 0.54 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 1.213 | 2.720 | 3.987 | 0.000 | 0.078 | 0.000 | 0.000 | 0.230 | 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 | 375 | 681 | 293 | 388 | 0 | 239 | 0 | 0 | 224 | 0 |
N.S. |
1 | 1.82 | 0.78 | 1.03 | 0.00 | 0.64 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 1.502 | 3.311 | 5.287 | 0.000 | 0.081 | 0.000 | 0.000 | 0.737 | 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 | 428 | 525 | 311 | 442 | 0 | 269 | 0 | 0 | 407 | 0 |
N.S. |
1 | 1.23 | 0.73 | 1.03 | 0.00 | 0.63 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 1.299 | 3.839 | 6.204 | 0.000 | 0.085 | 0.000 | 0.000 | 0.404 | 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 | 331 | 437 | 246 | 353 | 0 | 184 | 0 | 0 | 216 | 0 |
N.S. |
1 | 1.32 | 0.74 | 1.07 | 0.00 | 0.56 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.930 | 2.794 | 4.519 | 0.000 | 0.090 | 0.000 | 0.000 | 0.327 | 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 | 157 | 354 | 148 | 188 | 0 | 130 | 0 | 0 | 60 | 0 |
N.S. |
1 | 2.25 | 0.94 | 1.20 | 0.00 | 0.83 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.728 | 1.899 | 1.539 | 0.000 | 0.074 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 154 | 104 | 109 | 0 | 51 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.47 | 0.99 | 1.04 | 0.00 | 0.49 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.374 | 1.726 | 0.884 | 0.000 | 0.080 | 0.000 | 0.000 | 0.175 | 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 | 153 | 396 | 180 | 224 | 0 | 144 | 0 | 0 | 60 | 0 |
N.S. |
1 | 2.59 | 1.18 | 1.46 | 0.00 | 0.94 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.849 | 2.378 | 2.460 | 0.000 | 0.075 | 0.000 | 0.000 | 0.204 | 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 | 334 | 494 | 295 | 409 | 0 | 214 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.48 | 0.88 | 1.22 | 0.00 | 0.64 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 1.112 | 3.333 | 4.546 | 0.000 | 0.076 | 0.000 | 0.000 | 0.221 | 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 | 426 | 592 | 379 | 510 | 0 | 300 | 0 | 0 | 262 | 0 |
N.S. |
1 | 1.39 | 0.89 | 1.20 | 0.00 | 0.70 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 1.437 | 4.155 | 6.066 | 0.000 | 0.076 | 0.000 | 0.000 | 0.655 | 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 | 447 | 727 | 343 | 505 | 0 | 451 | 0 | 0 | 1411 | 0 |
N.S. |
1 | 1.63 | 0.77 | 1.13 | 0.00 | 1.01 | 0.00 | 0.00 | 3.16 | 0.00 |
time (sec) |
N/A | 1.707 | 4.505 | 5.355 | 0.000 | 0.104 | 0.000 | 0.000 | 0.538 | 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 | 351 | 607 | 256 | 424 | 0 | 312 | 0 | 0 | 491 | 0 |
N.S. |
1 | 1.73 | 0.73 | 1.21 | 0.00 | 0.89 | 0.00 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 1.142 | 3.514 | 4.147 | 0.000 | 0.078 | 0.000 | 0.000 | 0.349 | 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 | 172 | 510 | 153 | 202 | 0 | 227 | 0 | 0 | 66 | 0 |
N.S. |
1 | 2.97 | 0.89 | 1.17 | 0.00 | 1.32 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.952 | 2.267 | 1.271 | 0.000 | 0.088 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 214 | 105 | 132 | 0 | 72 | 0 | 0 | 63 | 0 |
N.S. |
1 | 2.06 | 1.01 | 1.27 | 0.00 | 0.69 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.455 | 2.087 | 0.781 | 0.000 | 0.086 | 0.000 | 0.000 | 0.185 | 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 | 151 | 562 | 233 | 252 | 0 | 193 | 0 | 0 | 66 | 0 |
N.S. |
1 | 3.72 | 1.54 | 1.67 | 0.00 | 1.28 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 1.104 | 2.789 | 2.090 | 0.000 | 0.087 | 0.000 | 0.000 | 0.209 | 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 | 315 | 639 | 256 | 442 | 0 | 226 | 0 | 0 | 66 | 0 |
N.S. |
1 | 2.03 | 0.81 | 1.40 | 0.00 | 0.72 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 1.358 | 3.375 | 4.494 | 0.000 | 0.089 | 0.000 | 0.000 | 0.264 | 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 | 396 | 756 | 364 | 535 | 0 | 316 | 0 | 0 | 415 | 0 |
N.S. |
1 | 1.91 | 0.92 | 1.35 | 0.00 | 0.80 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 1.826 | 4.535 | 5.390 | 0.000 | 0.093 | 0.000 | 0.000 | 0.940 | 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 | 384 | 333 | 321 | 411 | 0 | 258 | 0 | 0 | 385 | 0 |
N.S. |
1 | 0.87 | 0.84 | 1.07 | 0.00 | 0.67 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 1.099 | 3.825 | 20.372 | 0.000 | 0.095 | 0.000 | 0.000 | 0.569 | 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 | 306 | 246 | 270 | 346 | 0 | 172 | 0 | 0 | 218 | 0 |
N.S. |
1 | 0.80 | 0.88 | 1.13 | 0.00 | 0.56 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.745 | 3.257 | 16.484 | 0.000 | 0.090 | 0.000 | 0.000 | 0.396 | 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 | 256 | 191 | 155 | 178 | 0 | 147 | 0 | 0 | 60 | 0 |
N.S. |
1 | 0.75 | 0.61 | 0.70 | 0.00 | 0.57 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.604 | 2.050 | 3.455 | 0.000 | 0.086 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 110 | 110 | 0 | 71 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.87 | 0.00 | 0.56 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.406 | 1.928 | 1.859 | 0.000 | 0.082 | 0.000 | 0.000 | 0.190 | 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 | 178 | 259 | 262 | 245 | 0 | 217 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.46 | 1.47 | 1.38 | 0.00 | 1.22 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.782 | 3.443 | 4.619 | 0.000 | 0.085 | 0.000 | 0.000 | 0.204 | 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 | 378 | 338 | 330 | 423 | 0 | 305 | 0 | 0 | 63 | 0 |
N.S. |
1 | 0.89 | 0.87 | 1.12 | 0.00 | 0.81 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 1.003 | 4.019 | 16.559 | 0.000 | 0.095 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 31 | 67 | 51 | 0 | 43 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.62 | 1.34 | 1.02 | 0.00 | 0.86 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.332 | 10.031 | 1.043 | 0.000 | 0.078 | 0.000 | 0.000 | 0.167 | 0.000 |
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 | 25 | 25 | 25 | 20 | 19 | 19 | 19 | 19 | 21 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.76 | 0.76 | 0.76 | 0.76 | 0.84 | 0.76 |
time (sec) |
N/A | 0.277 | 0.002 | 0.042 | 0.031 | 0.072 | 0.016 | 0.106 | 0.165 | 0.032 |
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 | 25 | 26 | 25 | 20 | 19 | 19 | 19 | 19 | 21 | 19 |
N.S. |
1 | 1.04 | 1.00 | 0.80 | 0.76 | 0.76 | 0.76 | 0.76 | 0.84 | 0.76 |
time (sec) |
N/A | 0.282 | 0.002 | 0.040 | 0.028 | 0.061 | 0.017 | 0.124 | 0.166 | 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 | 20 | 20 | 20 | 17 | 16 | 16 | 15 | 16 | 19 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.80 | 0.80 | 0.75 | 0.80 | 0.95 | 0.80 |
time (sec) |
N/A | 0.258 | 0.000 | 0.033 | 0.035 | 0.065 | 0.016 | 0.117 | 0.161 | 0.027 |
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 | 21 | 21 | 21 | 18 | 20 | 17 | 17 | 20 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.95 | 0.81 | 0.81 | 0.95 | 0.81 | 0.81 |
time (sec) |
N/A | 0.274 | 0.001 | 0.063 | 0.030 | 0.071 | 0.031 | 0.126 | 0.164 | 0.027 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 17 | 16 | 20 | 12 | 16 | 20 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.89 | 1.11 | 0.67 | 0.89 | 1.11 | 0.89 |
time (sec) |
N/A | 0.273 | 0.002 | 0.043 | 0.029 | 0.064 | 0.031 | 0.124 | 0.164 | 0.032 |
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 | 21 | 21 | 21 | 18 | 20 | 22 | 17 | 26 | 22 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.95 | 1.05 | 0.81 | 1.24 | 1.05 | 0.81 |
time (sec) |
N/A | 0.273 | 0.002 | 0.046 | 0.031 | 0.073 | 0.045 | 0.137 | 0.159 | 17.914 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 17 | 17 | 21 | 17 | 17 | 21 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.94 | 1.17 | 0.94 | 0.94 | 1.17 | 1.00 |
time (sec) |
N/A | 0.273 | 0.004 | 0.045 | 0.031 | 0.074 | 0.050 | 0.106 | 0.199 | 0.028 |
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 | 21 | 21 | 21 | 18 | 21 | 23 | 19 | 27 | 23 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 1.00 | 1.10 | 0.90 | 1.29 | 1.10 | 0.95 |
time (sec) |
N/A | 0.272 | 0.003 | 0.045 | 0.037 | 0.056 | 0.101 | 0.113 | 0.227 | 0.047 |
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 | 23 | 23 | 23 | 20 | 21 | 21 | 22 | 21 | 21 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.91 | 0.91 | 0.96 | 0.91 | 0.91 | 0.87 |
time (sec) |
N/A | 0.277 | 0.002 | 0.043 | 0.029 | 0.059 | 0.116 | 0.110 | 0.230 | 0.034 |
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 | 25 | 25 | 25 | 20 | 21 | 21 | 22 | 21 | 21 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.84 | 0.84 | 0.88 | 0.84 | 0.84 | 0.84 |
time (sec) |
N/A | 0.277 | 0.002 | 0.045 | 0.027 | 0.055 | 0.156 | 0.132 | 0.224 | 0.034 |
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 | 25 | 25 | 25 | 20 | 21 | 21 | 22 | 21 | 21 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.84 | 0.84 | 0.88 | 0.84 | 0.84 | 0.84 |
time (sec) |
N/A | 0.275 | 0.003 | 0.046 | 0.033 | 0.056 | 0.148 | 0.109 | 0.231 | 0.034 |
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 | 54 | 54 | 54 | 45 | 44 | 44 | 51 | 46 | 48 | 45 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.81 | 0.81 | 0.94 | 0.85 | 0.89 | 0.83 |
time (sec) |
N/A | 0.334 | 0.006 | 0.105 | 0.027 | 0.059 | 0.018 | 0.106 | 0.224 | 0.029 |
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 | 54 | 52 | 48 | 45 | 44 | 44 | 46 | 46 | 48 | 45 |
N.S. |
1 | 0.96 | 0.89 | 0.83 | 0.81 | 0.81 | 0.85 | 0.85 | 0.89 | 0.83 |
time (sec) |
N/A | 0.359 | 0.006 | 0.095 | 0.033 | 0.056 | 0.018 | 0.108 | 0.224 | 0.022 |
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 | 49 | 49 | 49 | 42 | 45 | 41 | 48 | 43 | 46 | 42 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.92 | 0.84 | 0.98 | 0.88 | 0.94 | 0.86 |
time (sec) |
N/A | 0.321 | 0.004 | 0.042 | 0.033 | 0.057 | 0.019 | 0.126 | 0.228 | 0.021 |
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 | 54 | 47 | 43 | 44 | 41 | 42 | 46 | 43 | 42 |
N.S. |
1 | 1.15 | 1.00 | 0.91 | 0.94 | 0.87 | 0.89 | 0.98 | 0.91 | 0.89 |
time (sec) |
N/A | 0.358 | 0.010 | 0.108 | 0.033 | 0.063 | 0.047 | 0.135 | 0.233 | 0.026 |
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 | 48 | 48 | 48 | 45 | 42 | 46 | 44 | 44 | 48 | 43 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.96 | 0.92 | 0.92 | 1.00 | 0.90 |
time (sec) |
N/A | 0.337 | 0.013 | 0.087 | 0.032 | 0.063 | 0.046 | 0.107 | 0.226 | 0.025 |
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 | 51 | 49 | 46 | 45 | 44 | 47 | 44 | 53 | 49 | 43 |
N.S. |
1 | 0.96 | 0.90 | 0.88 | 0.86 | 0.92 | 0.86 | 1.04 | 0.96 | 0.84 |
time (sec) |
N/A | 0.380 | 0.012 | 0.058 | 0.025 | 0.061 | 0.062 | 0.133 | 0.173 | 0.028 |
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 | 47 | 42 | 42 | 46 | 46 | 42 | 48 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.89 | 0.98 | 0.98 | 0.89 | 1.02 | 0.94 |
time (sec) |
N/A | 0.322 | 0.017 | 0.056 | 0.027 | 0.061 | 0.069 | 0.107 | 0.163 | 0.043 |
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 | 45 | 52 | 41 | 42 | 45 | 47 | 44 | 60 | 51 | 43 |
N.S. |
1 | 1.16 | 0.91 | 0.93 | 1.00 | 1.04 | 0.98 | 1.33 | 1.13 | 0.96 |
time (sec) |
N/A | 0.348 | 0.014 | 0.079 | 0.027 | 0.058 | 0.175 | 0.119 | 0.165 | 0.038 |
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 | 48 | 48 | 49 | 43 | 45 | 46 | 48 | 47 | 48 | 44 |
N.S. |
1 | 1.00 | 1.02 | 0.90 | 0.94 | 0.96 | 1.00 | 0.98 | 1.00 | 0.92 |
time (sec) |
N/A | 0.319 | 0.016 | 0.057 | 0.026 | 0.056 | 0.197 | 0.105 | 0.168 | 0.043 |
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 | 51 | 50 | 50 | 44 | 45 | 48 | 48 | 54 | 50 | 46 |
N.S. |
1 | 0.98 | 0.98 | 0.86 | 0.88 | 0.94 | 0.94 | 1.06 | 0.98 | 0.90 |
time (sec) |
N/A | 0.343 | 0.014 | 0.057 | 0.030 | 0.062 | 0.354 | 0.128 | 0.161 | 18.141 |
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 | 49 | 42 | 44 | 46 | 46 | 46 | 48 | 45 |
N.S. |
1 | 1.00 | 1.04 | 0.89 | 0.94 | 0.98 | 0.98 | 0.98 | 1.02 | 0.96 |
time (sec) |
N/A | 0.314 | 0.018 | 0.056 | 0.026 | 0.058 | 0.342 | 0.112 | 0.169 | 0.037 |
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 | 48 | 54 | 50 | 43 | 48 | 48 | 48 | 58 | 50 | 45 |
N.S. |
1 | 1.12 | 1.04 | 0.90 | 1.00 | 1.00 | 1.00 | 1.21 | 1.04 | 0.94 |
time (sec) |
N/A | 0.348 | 0.019 | 0.056 | 0.029 | 0.065 | 0.621 | 0.124 | 0.170 | 0.056 |
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 | 52 | 52 | 50 | 45 | 46 | 46 | 49 | 48 | 48 | 46 |
N.S. |
1 | 1.00 | 0.96 | 0.87 | 0.88 | 0.88 | 0.94 | 0.92 | 0.92 | 0.88 |
time (sec) |
N/A | 0.312 | 0.016 | 0.057 | 0.031 | 0.059 | 0.667 | 0.104 | 0.166 | 17.918 |
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 | 54 | 54 | 53 | 45 | 46 | 46 | 49 | 48 | 48 | 47 |
N.S. |
1 | 1.00 | 0.98 | 0.83 | 0.85 | 0.85 | 0.91 | 0.89 | 0.89 | 0.87 |
time (sec) |
N/A | 0.356 | 0.012 | 0.059 | 0.031 | 0.056 | 0.911 | 0.102 | 0.172 | 18.498 |
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 | 54 | 54 | 56 | 45 | 46 | 46 | 49 | 48 | 48 | 47 |
N.S. |
1 | 1.00 | 1.04 | 0.83 | 0.85 | 0.85 | 0.91 | 0.89 | 0.89 | 0.87 |
time (sec) |
N/A | 0.324 | 0.020 | 0.059 | 0.034 | 0.056 | 0.929 | 0.113 | 0.165 | 0.036 |
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 | 54 | 58 | 50 | 45 | 46 | 46 | 49 | 48 | 48 | 47 |
N.S. |
1 | 1.07 | 0.93 | 0.83 | 0.85 | 0.85 | 0.91 | 0.89 | 0.89 | 0.87 |
time (sec) |
N/A | 0.342 | 0.012 | 0.062 | 0.029 | 0.060 | 1.199 | 0.145 | 0.179 | 0.036 |
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 | 89 | 89 | 89 | 85 | 81 | 81 | 97 | 87 | 89 | 76 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.91 | 0.91 | 1.09 | 0.98 | 1.00 | 0.85 |
time (sec) |
N/A | 0.382 | 0.011 | 0.114 | 0.034 | 0.056 | 0.024 | 0.104 | 0.168 | 0.037 |
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 | 89 | 87 | 79 | 85 | 81 | 81 | 92 | 87 | 89 | 76 |
N.S. |
1 | 0.98 | 0.89 | 0.96 | 0.91 | 0.91 | 1.03 | 0.98 | 1.00 | 0.85 |
time (sec) |
N/A | 0.419 | 0.012 | 0.102 | 0.034 | 0.060 | 0.023 | 0.103 | 0.163 | 0.032 |
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 | 81 | 81 | 81 | 81 | 85 | 77 | 87 | 83 | 87 | 72 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.05 | 0.95 | 1.07 | 1.02 | 1.07 | 0.89 |
time (sec) |
N/A | 0.389 | 0.007 | 0.048 | 0.031 | 0.078 | 0.023 | 0.102 | 0.169 | 0.033 |
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 | 85 | 89 | 85 | 82 | 82 | 79 | 92 | 87 | 84 | 73 |
N.S. |
1 | 1.05 | 1.00 | 0.96 | 0.96 | 0.93 | 1.08 | 1.02 | 0.99 | 0.86 |
time (sec) |
N/A | 0.413 | 0.015 | 0.093 | 0.039 | 0.057 | 0.072 | 0.148 | 0.167 | 0.036 |
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 | 80 | 80 | 80 | 84 | 78 | 83 | 82 | 83 | 89 | 73 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 0.98 | 1.04 | 1.02 | 1.04 | 1.11 | 0.91 |
time (sec) |
N/A | 0.376 | 0.017 | 0.099 | 0.029 | 0.061 | 0.072 | 0.138 | 0.166 | 0.034 |
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 | 86 | 85 | 78 | 86 | 82 | 85 | 92 | 98 | 91 | 75 |
N.S. |
1 | 0.99 | 0.91 | 1.00 | 0.95 | 0.99 | 1.07 | 1.14 | 1.06 | 0.87 |
time (sec) |
N/A | 0.420 | 0.024 | 0.065 | 0.027 | 0.066 | 0.090 | 0.106 | 0.176 | 0.038 |
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 | 83 | 83 | 83 | 84 | 80 | 83 | 90 | 84 | 89 | 77 |
N.S. |
1 | 1.00 | 1.00 | 1.01 | 0.96 | 1.00 | 1.08 | 1.01 | 1.07 | 0.93 |
time (sec) |
N/A | 0.381 | 0.019 | 0.068 | 0.032 | 0.057 | 0.094 | 0.108 | 0.166 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 99 | 93 | 105 | 0 | 313 | 391 | 92 | 458 | 842 |
N.S. |
1 | 0.99 | 0.93 | 1.05 | 0.00 | 3.13 | 3.91 | 0.92 | 4.58 | 8.42 |
time (sec) |
N/A | 0.506 | 0.060 | 0.168 | 0.000 | 0.072 | 1.398 | 0.390 | 0.170 | 0.268 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 80 | 78 | 83 | 0 | 254 | 316 | 75 | 366 | 655 |
N.S. |
1 | 0.99 | 0.96 | 1.02 | 0.00 | 3.14 | 3.90 | 0.93 | 4.52 | 8.09 |
time (sec) |
N/A | 0.435 | 0.031 | 0.125 | 0.000 | 0.075 | 1.026 | 0.377 | 0.168 | 19.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 64 | 62 | 60 | 0 | 197 | 223 | 59 | 236 | 118 |
N.S. |
1 | 1.02 | 0.98 | 0.95 | 0.00 | 3.13 | 3.54 | 0.94 | 3.75 | 1.87 |
time (sec) |
N/A | 0.400 | 0.018 | 0.095 | 0.000 | 0.078 | 0.465 | 0.356 | 0.168 | 18.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 39 | 36 | 0 | 129 | 131 | 35 | 95 | 41 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 0.00 | 3.58 | 3.64 | 0.97 | 2.64 | 1.14 |
time (sec) |
N/A | 0.296 | 0.008 | 0.061 | 0.000 | 0.068 | 0.234 | 0.353 | 0.177 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 73 | 113 | 65 | 0 | 223 | 253 | 68 | 247 | 1014 |
N.S. |
1 | 1.06 | 1.64 | 0.94 | 0.00 | 3.23 | 3.67 | 0.99 | 3.58 | 14.70 |
time (sec) |
N/A | 0.415 | 0.052 | 0.082 | 0.000 | 0.081 | 2.293 | 0.402 | 0.169 | 18.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 95 | 135 | 85 | 0 | 293 | 345 | 94 | 409 | 2033 |
N.S. |
1 | 1.07 | 1.52 | 0.96 | 0.00 | 3.29 | 3.88 | 1.06 | 4.60 | 22.84 |
time (sec) |
N/A | 0.510 | 0.086 | 0.098 | 0.000 | 0.084 | 80.874 | 0.340 | 0.168 | 19.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 123 | 188 | 134 | 0 | 374 | 423 | 126 | 517 | 2451 |
N.S. |
1 | 1.08 | 1.65 | 1.18 | 0.00 | 3.28 | 3.71 | 1.11 | 4.54 | 21.50 |
time (sec) |
N/A | 0.574 | 0.153 | 0.117 | 0.000 | 0.099 | 175.638 | 0.394 | 0.175 | 19.410 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 214 | 250 | 73 | 0 | 1564 | 194 | 2457 | 761 | 4127 |
N.S. |
1 | 1.05 | 1.23 | 0.36 | 0.00 | 7.70 | 0.96 | 12.10 | 3.75 | 20.33 |
time (sec) |
N/A | 0.827 | 0.108 | 0.126 | 0.000 | 0.131 | 2.220 | 0.666 | 0.262 | 19.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 183 | 202 | 57 | 0 | 1059 | 129 | 2109 | 547 | 3026 |
N.S. |
1 | 1.02 | 1.13 | 0.32 | 0.00 | 5.92 | 0.72 | 11.78 | 3.06 | 16.91 |
time (sec) |
N/A | 0.560 | 0.076 | 0.095 | 0.000 | 0.083 | 1.084 | 0.624 | 0.249 | 0.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 158 | 165 | 41 | 0 | 559 | 75 | 503 | 351 | 416 |
N.S. |
1 | 1.05 | 1.10 | 0.27 | 0.00 | 3.73 | 0.50 | 3.35 | 2.34 | 2.77 |
time (sec) |
N/A | 0.444 | 0.061 | 0.093 | 0.000 | 0.092 | 0.377 | 0.687 | 0.238 | 0.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 129 | 38 | 0 | 613 | 87 | 1026 | 351 | 763 |
N.S. |
1 | 1.00 | 0.86 | 0.25 | 0.00 | 4.09 | 0.58 | 6.84 | 2.34 | 5.09 |
time (sec) |
N/A | 0.403 | 0.053 | 0.066 | 0.000 | 0.090 | 0.565 | 0.319 | 0.236 | 0.490 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 172 | 191 | 159 | 0 | 1116 | 148 | 1839 | 560 | 2997 |
N.S. |
1 | 0.99 | 1.10 | 0.91 | 0.00 | 6.41 | 0.85 | 10.57 | 3.22 | 17.22 |
time (sec) |
N/A | 0.508 | 0.277 | 0.118 | 0.000 | 0.102 | 1.260 | 0.558 | 0.260 | 18.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 203 | 216 | 179 | 0 | 1622 | 211 | 1640 | 810 | 4160 |
N.S. |
1 | 1.04 | 1.10 | 0.91 | 0.00 | 8.28 | 1.08 | 8.37 | 4.13 | 21.22 |
time (sec) |
N/A | 0.679 | 0.097 | 0.128 | 0.000 | 0.119 | 4.707 | 0.744 | 0.298 | 0.815 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 106 | 93 | 106 | 0 | 313 | 391 | 95 | 458 | 842 |
N.S. |
1 | 0.99 | 0.87 | 0.99 | 0.00 | 2.93 | 3.65 | 0.89 | 4.28 | 7.87 |
time (sec) |
N/A | 0.539 | 0.062 | 0.174 | 0.000 | 0.085 | 1.420 | 0.361 | 0.234 | 17.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 86 | 78 | 83 | 0 | 256 | 316 | 77 | 366 | 655 |
N.S. |
1 | 0.99 | 0.90 | 0.95 | 0.00 | 2.94 | 3.63 | 0.89 | 4.21 | 7.53 |
time (sec) |
N/A | 0.420 | 0.032 | 0.124 | 0.000 | 0.079 | 1.037 | 0.391 | 0.267 | 0.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 69 | 62 | 60 | 0 | 194 | 223 | 59 | 236 | 118 |
N.S. |
1 | 1.03 | 0.93 | 0.90 | 0.00 | 2.90 | 3.33 | 0.88 | 3.52 | 1.76 |
time (sec) |
N/A | 0.375 | 0.017 | 0.095 | 0.000 | 0.086 | 0.468 | 0.383 | 0.187 | 17.626 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 36 | 0 | 121 | 131 | 35 | 95 | 41 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.00 | 3.10 | 3.36 | 0.90 | 2.44 | 1.05 |
time (sec) |
N/A | 0.299 | 0.007 | 0.062 | 0.000 | 0.079 | 0.244 | 0.393 | 0.172 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 76 | 113 | 65 | 0 | 222 | 253 | 68 | 247 | 1012 |
N.S. |
1 | 1.04 | 1.55 | 0.89 | 0.00 | 3.04 | 3.47 | 0.93 | 3.38 | 13.86 |
time (sec) |
N/A | 0.416 | 0.053 | 0.085 | 0.000 | 0.089 | 2.775 | 0.349 | 0.176 | 17.995 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 101 | 133 | 85 | 0 | 296 | 0 | 96 | 409 | 2033 |
N.S. |
1 | 1.06 | 1.40 | 0.89 | 0.00 | 3.12 | 0.00 | 1.01 | 4.31 | 21.40 |
time (sec) |
N/A | 0.519 | 0.108 | 0.100 | 0.000 | 0.098 | 0.000 | 0.383 | 0.168 | 19.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 130 | 184 | 134 | 0 | 371 | 0 | 132 | 517 | 2451 |
N.S. |
1 | 1.06 | 1.50 | 1.09 | 0.00 | 3.02 | 0.00 | 1.07 | 4.20 | 19.93 |
time (sec) |
N/A | 0.606 | 0.202 | 0.115 | 0.000 | 0.112 | 0.000 | 0.332 | 0.169 | 19.910 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 355 | 532 | 282 | 101 | 0 | 2133 | 262 | 3064 | 992 | 5317 |
N.S. |
1 | 1.50 | 0.79 | 0.28 | 0.00 | 6.01 | 0.74 | 8.63 | 2.79 | 14.98 |
time (sec) |
N/A | 1.665 | 0.172 | 0.165 | 0.000 | 0.159 | 9.743 | 0.646 | 0.179 | 0.813 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 451 | 250 | 73 | 0 | 1604 | 194 | 2479 | 761 | 4127 |
N.S. |
1 | 1.48 | 0.82 | 0.24 | 0.00 | 5.28 | 0.64 | 8.15 | 2.50 | 13.58 |
time (sec) |
N/A | 1.318 | 0.157 | 0.106 | 0.000 | 0.120 | 1.901 | 0.606 | 0.192 | 0.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 402 | 202 | 57 | 0 | 1119 | 129 | 2133 | 547 | 3026 |
N.S. |
1 | 1.50 | 0.75 | 0.21 | 0.00 | 4.18 | 0.48 | 7.96 | 2.04 | 11.29 |
time (sec) |
N/A | 1.070 | 0.119 | 0.097 | 0.000 | 0.111 | 1.081 | 0.587 | 0.200 | 18.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 336 | 165 | 41 | 0 | 639 | 75 | 503 | 351 | 416 |
N.S. |
1 | 1.51 | 0.74 | 0.18 | 0.00 | 2.88 | 0.34 | 2.27 | 1.58 | 1.87 |
time (sec) |
N/A | 0.830 | 0.057 | 0.089 | 0.000 | 0.085 | 0.373 | 0.678 | 0.175 | 0.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 365 | 129 | 38 | 0 | 701 | 87 | 1038 | 351 | 763 |
N.S. |
1 | 1.64 | 0.58 | 0.17 | 0.00 | 3.16 | 0.39 | 4.68 | 1.58 | 3.44 |
time (sec) |
N/A | 0.855 | 0.052 | 0.082 | 0.000 | 0.094 | 0.567 | 0.354 | 0.174 | 18.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 435 | 191 | 159 | 0 | 1172 | 148 | 1857 | 560 | 2997 |
N.S. |
1 | 1.65 | 0.72 | 0.60 | 0.00 | 4.44 | 0.56 | 7.03 | 2.12 | 11.35 |
time (sec) |
N/A | 1.007 | 0.269 | 0.115 | 0.000 | 0.109 | 1.251 | 0.665 | 0.198 | 18.795 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 481 | 214 | 179 | 0 | 1654 | 211 | 1664 | 810 | 4162 |
N.S. |
1 | 1.58 | 0.70 | 0.59 | 0.00 | 5.42 | 0.69 | 5.46 | 2.66 | 13.65 |
time (sec) |
N/A | 1.223 | 0.143 | 0.131 | 0.000 | 0.110 | 3.516 | 0.819 | 0.222 | 18.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 139 | 121 | 179 | 0 | 663 | 745 | 152 | 1427 | 1336 |
N.S. |
1 | 1.05 | 0.92 | 1.36 | 0.00 | 5.02 | 5.64 | 1.15 | 10.81 | 10.12 |
time (sec) |
N/A | 0.558 | 0.119 | 0.195 | 0.000 | 0.094 | 11.603 | 0.321 | 0.180 | 18.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 79 | 93 | 104 | 0 | 407 | 282 | 96 | 479 | 187 |
N.S. |
1 | 1.01 | 1.19 | 1.33 | 0.00 | 5.22 | 3.62 | 1.23 | 6.14 | 2.40 |
time (sec) |
N/A | 0.387 | 0.061 | 0.122 | 0.000 | 0.090 | 0.741 | 0.388 | 0.172 | 17.856 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 76 | 79 | 77 | 0 | 360 | 269 | 82 | 457 | 178 |
N.S. |
1 | 1.01 | 1.05 | 1.03 | 0.00 | 4.80 | 3.59 | 1.09 | 6.09 | 2.37 |
time (sec) |
N/A | 0.373 | 0.047 | 0.111 | 0.000 | 0.083 | 0.642 | 0.342 | 0.175 | 17.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 76 | 79 | 75 | 0 | 361 | 267 | 82 | 477 | 172 |
N.S. |
1 | 1.03 | 1.07 | 1.01 | 0.00 | 4.88 | 3.61 | 1.11 | 6.45 | 2.32 |
time (sec) |
N/A | 0.358 | 0.051 | 0.115 | 0.000 | 0.082 | 0.624 | 0.351 | 0.173 | 0.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 153 | 207 | 185 | 0 | 813 | 0 | 166 | 1533 | 5048 |
N.S. |
1 | 1.25 | 1.70 | 1.52 | 0.00 | 6.66 | 0.00 | 1.36 | 12.57 | 41.38 |
time (sec) |
N/A | 0.624 | 0.220 | 0.147 | 0.000 | 0.136 | 0.000 | 0.374 | 0.178 | 22.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 187 | 248 | 213 | 0 | 1007 | 0 | 182 | 2043 | 5491 |
N.S. |
1 | 1.15 | 1.53 | 1.31 | 0.00 | 6.22 | 0.00 | 1.12 | 12.61 | 33.90 |
time (sec) |
N/A | 0.727 | 0.178 | 0.154 | 0.000 | 0.192 | 0.000 | 0.348 | 0.251 | 22.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 306 | 327 | 174 | 0 | 2856 | 0 | 3335 | 3084 | 7599 |
N.S. |
1 | 1.01 | 1.08 | 0.57 | 0.00 | 9.43 | 0.00 | 11.01 | 10.18 | 25.08 |
time (sec) |
N/A | 0.980 | 0.426 | 0.154 | 0.000 | 0.296 | 0.000 | 0.656 | 2.289 | 19.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 253 | 282 | 151 | 0 | 2257 | 379 | 2736 | 2411 | 6293 |
N.S. |
1 | 0.92 | 1.03 | 0.55 | 0.00 | 8.24 | 1.38 | 9.99 | 8.80 | 22.97 |
time (sec) |
N/A | 0.777 | 0.326 | 0.138 | 0.000 | 0.150 | 20.547 | 0.673 | 0.335 | 19.417 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 227 | 235 | 123 | 0 | 1668 | 296 | 2132 | 1795 | 4973 |
N.S. |
1 | 0.96 | 0.99 | 0.52 | 0.00 | 7.04 | 1.25 | 9.00 | 7.57 | 20.98 |
time (sec) |
N/A | 0.621 | 0.286 | 0.129 | 0.000 | 0.112 | 2.226 | 0.534 | 0.327 | 19.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 213 | 222 | 122 | 0 | 1680 | 298 | 1970 | 1795 | 4854 |
N.S. |
1 | 0.96 | 1.00 | 0.55 | 0.00 | 7.60 | 1.35 | 8.91 | 8.12 | 21.96 |
time (sec) |
N/A | 0.566 | 0.314 | 0.184 | 0.000 | 0.107 | 7.522 | 0.522 | 0.325 | 19.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 236 | 243 | 151 | 0 | 2309 | 394 | 2682 | 2409 | 6404 |
N.S. |
1 | 0.94 | 0.96 | 0.60 | 0.00 | 9.16 | 1.56 | 10.64 | 9.56 | 25.41 |
time (sec) |
N/A | 0.705 | 0.294 | 0.143 | 0.000 | 0.162 | 103.353 | 0.365 | 0.347 | 19.640 |