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 | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 267 | 266 | 97 | 0 | 0 | 243 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.36 | 0.00 | 0.00 | 0.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.416 | 0.019 | 0.000 | 0.000 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 92 | 96 | 69 | 0 | 0 | 152 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.75 | 0.00 | 0.00 | 1.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.218 | 0.012 | 0.000 | 0.000 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 132 | 135 | 81 | 0 | 0 | 176 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.61 | 0.00 | 0.00 | 1.33 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.240 | 0.016 | 0.000 | 0.000 | 0.264 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 170 | 172 | 93 | 0 | 0 | 184 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.55 | 0.00 | 0.00 | 1.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.275 | 0.019 | 0.000 | 0.000 | 0.275 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 202 | 207 | 99 | 0 | 0 | 192 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.49 | 0.00 | 0.00 | 0.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.303 | 0.027 | 0.000 | 0.000 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 373 | 372 | 100 | 0 | 0 | 304 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.27 | 0.00 | 0.00 | 0.82 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.503 | 0.034 | 0.000 | 0.000 | 0.285 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 371 | 354 | 91 | 0 | 0 | 296 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.25 | 0.00 | 0.00 | 0.80 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.465 | 0.027 | 0.000 | 0.000 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 324 | 314 | 63 | 0 | 0 | 289 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.19 | 0.00 | 0.00 | 0.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.428 | 0.022 | 0.000 | 0.000 | 0.271 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 299 | 273 | 39 | 0 | 0 | 261 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 0.13 | 0.00 | 0.00 | 0.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.384 | 0.039 | 0.000 | 0.000 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 293 | 292 | 106 | 0 | 0 | 329 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.36 | 0.00 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.458 | 0.041 | 0.000 | 0.000 | 0.281 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 121 | 127 | 69 | 0 | 0 | 212 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.57 | 0.00 | 0.00 | 1.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.239 | 0.013 | 0.000 | 0.000 | 0.282 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 163 | 166 | 81 | 0 | 0 | 238 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.50 | 0.00 | 0.00 | 1.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.261 | 0.018 | 0.000 | 0.000 | 0.270 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 203 | 205 | 93 | 0 | 0 | 246 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.46 | 0.00 | 0.00 | 1.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.313 | 0.022 | 0.000 | 0.000 | 0.280 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 233 | 240 | 99 | 0 | 0 | 254 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.42 | 0.00 | 0.00 | 1.09 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.343 | 0.027 | 0.000 | 0.000 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 319 | 302 | 73 | 0 | 0 | 208 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.23 | 0.00 | 0.00 | 0.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.409 | 0.030 | 0.000 | 0.000 | 0.262 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 278 | 270 | 57 | 0 | 0 | 195 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.21 | 0.00 | 0.00 | 0.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.378 | 0.016 | 0.000 | 0.000 | 0.293 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 262 | 237 | 34 | 0 | 0 | 195 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.13 | 0.00 | 0.00 | 0.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.345 | 0.016 | 0.000 | 0.000 | 0.252 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 430 | 437 | 90 | 0 | 0 | 339 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.21 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.469 | 0.024 | 0.000 | 0.000 | 0.253 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 253 | 258 | 64 | 0 | 0 | 211 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.25 | 0.00 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.312 | 0.010 | 0.000 | 0.000 | 0.275 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 280 | 294 | 72 | 0 | 0 | 234 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.26 | 0.00 | 0.00 | 0.84 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.337 | 0.013 | 0.000 | 0.000 | 0.272 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 319 | 328 | 81 | 0 | 0 | 243 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.25 | 0.00 | 0.00 | 0.76 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.356 | 0.015 | 0.000 | 0.000 | 0.268 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 177 | 186 | 73 | 0 | 0 | 117 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.41 | 0.00 | 0.00 | 0.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.258 | 0.026 | 0.000 | 0.000 | 0.286 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 140 | 156 | 54 | 0 | 0 | 116 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.39 | 0.00 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.220 | 0.018 | 0.000 | 0.000 | 0.260 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 116 | 123 | 34 | 0 | 0 | 104 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.29 | 0.00 | 0.00 | 0.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.196 | 0.017 | 0.000 | 0.000 | 0.261 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 163 | 175 | 90 | 0 | 0 | 145 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.55 | 0.00 | 0.00 | 0.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.235 | 0.019 | 0.000 | 0.000 | 0.260 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 111 | 113 | 59 | 0 | 0 | 120 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.53 | 0.00 | 0.00 | 1.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.213 | 0.010 | 0.000 | 0.000 | 0.260 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 142 | 149 | 69 | 0 | 0 | 138 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.49 | 0.00 | 0.00 | 0.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.225 | 0.012 | 0.000 | 0.000 | 0.290 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 741 | 734 | 83 | 0 | 0 | 435 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.11 | 0.00 | 0.00 | 0.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.807 | 0.030 | 0.000 | 0.000 | 0.280 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 689 | 697 | 63 | 0 | 0 | 428 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.09 | 0.00 | 0.00 | 0.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.742 | 0.017 | 0.000 | 0.000 | 0.284 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 674 | 656 | 41 | 0 | 0 | 383 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.06 | 0.00 | 0.00 | 0.57 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.699 | 0.022 | 0.000 | 0.000 | 0.288 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 859 | 918 | 97 | 0 | 0 | 509 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.11 | 0.00 | 0.00 | 0.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.057 | 0.026 | 0.000 | 0.000 | 0.279 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 328 | 331 | 71 | 0 | 0 | 345 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.22 | 0.00 | 0.00 | 1.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.403 | 0.015 | 0.000 | 0.000 | 0.282 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 364 | 370 | 84 | 0 | 0 | 381 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.23 | 0.00 | 0.00 | 1.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.426 | 0.017 | 0.000 | 0.000 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 94 | 748 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 6.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.270 | 0.034 | 0.757 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 58 | 417 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.16 | 8.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.211 | 0.018 | 0.452 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 29 | 175 | 0 | 0 | 126 | 0 | 0 |
N.S. |
1 | 1.00 | 0.74 | 4.49 | 0.00 | 0.00 | 3.23 | 0.00 | 0.00 |
time (sec) |
N/A | 0.186 | 0.006 | 0.296 | 0.000 | 0.000 | 1.629 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 29 | 158 | 0 | 0 | 133 | 0 | 0 |
N.S. |
1 | 1.00 | 0.74 | 4.05 | 0.00 | 0.00 | 3.41 | 0.00 | 0.00 |
time (sec) |
N/A | 0.186 | 0.010 | 0.296 | 0.000 | 0.000 | 2.403 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 58 | 428 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.16 | 8.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.215 | 0.018 | 0.569 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 94 | 1196 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 10.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.271 | 0.032 | 1.280 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 161 | 113 | 146 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.71 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.520 | 0.059 | 0.234 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | A | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 85 | 71 | 0 | 0 | 94 | 0 | 0 |
N.S. |
1 | 1.00 | 1.08 | 0.90 | 0.00 | 0.00 | 1.19 | 0.00 | 0.00 |
time (sec) |
N/A | 0.219 | 0.038 | 0.205 | 0.000 | 0.000 | 1.419 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 85 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.219 | 0.032 | 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(-2) | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 159 | 161 | 113 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.497 | 0.059 | 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(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.183 | 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(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.182 | 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(-2) | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.179 | 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(-2) | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.180 | 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(-2) | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.185 | 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(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.186 | 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 | 38 | 38 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.178 | 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 | 38 | 38 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.179 | 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(-2) | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.182 | 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 | 40 | 40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.186 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 171 | 177 | 210 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.299 | 0.154 | 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 | 159 | 165 | 116 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.263 | 0.043 | 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 | 107 | 107 | 105 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.219 | 0.023 | 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 | 71 | 71 | 53 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.184 | 0.027 | 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 | 125 | 125 | 106 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.234 | 0.019 | 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 | 79 | 79 | 82 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.204 | 0.013 | 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 | 120 | 120 | 114 | 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 | 0.229 | 0.026 | 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 | 171 | 174 | 119 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.264 | 0.058 | 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 | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 276 | 284 | 217 | 197 | 749 | 177 | 1222 | 205 | 0 |
N.S. |
1 | 1.03 | 0.79 | 0.71 | 2.71 | 0.64 | 4.43 | 0.74 | 0.00 |
time (sec) |
N/A | 0.446 | 0.452 | 0.806 | 0.209 | 0.291 | 1.857 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 208 | 176 | 150 | 529 | 139 | 857 | 155 | 0 |
N.S. |
1 | 1.03 | 0.88 | 0.75 | 2.63 | 0.69 | 4.26 | 0.77 | 0.00 |
time (sec) |
N/A | 0.346 | 0.247 | 0.591 | 0.206 | 0.278 | 1.596 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 180 | 135 | 113 | 351 | 106 | 585 | 113 | 0 |
N.S. |
1 | 1.05 | 0.79 | 0.66 | 2.05 | 0.62 | 3.42 | 0.66 | 0.00 |
time (sec) |
N/A | 0.314 | 0.113 | 0.545 | 0.174 | 0.259 | 1.330 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 121 | 108 | 87 | 209 | 79 | 362 | 75 | 0 |
N.S. |
1 | 1.10 | 0.98 | 0.79 | 1.90 | 0.72 | 3.29 | 0.68 | 0.00 |
time (sec) |
N/A | 0.257 | 0.089 | 0.414 | 0.183 | 0.274 | 0.916 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 65 | 28 | 69 | 62 | 60 | 36 | 51 | 97 |
N.S. |
1 | 1.25 | 0.54 | 1.33 | 1.19 | 1.15 | 0.69 | 0.98 | 1.87 |
time (sec) |
N/A | 0.211 | 0.013 | 0.375 | 0.176 | 0.268 | 0.773 | 0.303 | 1.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 111 | 142 | 107 | 233 | 144 | 0 | 112 | 118 |
N.S. |
1 | 1.25 | 1.60 | 1.20 | 2.62 | 1.62 | 0.00 | 1.26 | 1.33 |
time (sec) |
N/A | 0.274 | 0.055 | 0.304 | 0.177 | 0.287 | 0.000 | 0.345 | 1.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 120 | 93 | 239 | 224 | 0 | 145 | 218 |
N.S. |
1 | 1.00 | 0.92 | 0.72 | 1.84 | 1.72 | 0.00 | 1.12 | 1.68 |
time (sec) |
N/A | 0.245 | 0.061 | 0.681 | 0.178 | 0.271 | 0.000 | 0.350 | 1.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 198 | 154 | 187 | 424 | 452 | 0 | 471 | 0 |
N.S. |
1 | 0.99 | 0.77 | 0.93 | 2.11 | 2.25 | 0.00 | 2.34 | 0.00 |
time (sec) |
N/A | 0.296 | 0.095 | 0.435 | 0.217 | 0.274 | 0.000 | 0.362 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 283 | 294 | 234 | 281 | 644 | 690 | 0 | 884 | 0 |
N.S. |
1 | 1.04 | 0.83 | 0.99 | 2.28 | 2.44 | 0.00 | 3.12 | 0.00 |
time (sec) |
N/A | 0.364 | 0.248 | 0.796 | 0.208 | 0.289 | 0.000 | 0.343 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 92 | 160 | 149 | 105 | 110 | 123 | 201 |
N.S. |
1 | 1.00 | 1.00 | 1.74 | 1.62 | 1.14 | 1.20 | 1.34 | 2.18 |
time (sec) |
N/A | 0.272 | 0.053 | 0.319 | 0.259 | 0.267 | 0.252 | 0.287 | 0.682 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 72 | 109 | 116 | 77 | 75 | 83 | 153 |
N.S. |
1 | 1.00 | 1.00 | 1.51 | 1.61 | 1.07 | 1.04 | 1.15 | 2.12 |
time (sec) |
N/A | 0.246 | 0.048 | 0.298 | 0.256 | 0.264 | 0.177 | 0.279 | 0.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 70 | 87 | 53 | 46 | 53 | 107 |
N.S. |
1 | 1.00 | 1.00 | 1.30 | 1.61 | 0.98 | 0.85 | 0.98 | 1.98 |
time (sec) |
N/A | 0.224 | 0.026 | 0.285 | 0.258 | 0.253 | 0.148 | 0.288 | 0.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 41 | 64 | 35 | 29 | 35 | 60 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.73 | 0.95 | 0.78 | 0.95 | 1.62 |
time (sec) |
N/A | 0.198 | 0.017 | 0.280 | 0.256 | 0.275 | 0.116 | 0.274 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 32 | 21 | 46 | 22 | 14 | 16 | 21 |
N.S. |
1 | 1.00 | 1.60 | 1.05 | 2.30 | 1.10 | 0.70 | 0.80 | 1.05 |
time (sec) |
N/A | 0.175 | 0.009 | 0.269 | 0.258 | 0.263 | 0.074 | 0.282 | 0.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 31 | 47 | 78 | 27 | 100 | 33 | 32 |
N.S. |
1 | 1.00 | 0.82 | 1.24 | 2.05 | 0.71 | 2.63 | 0.87 | 0.84 |
time (sec) |
N/A | 0.205 | 0.016 | 0.285 | 0.287 | 0.262 | 0.398 | 0.282 | 0.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 39 | 96 | 126 | 40 | 156 | 61 | 98 |
N.S. |
1 | 1.00 | 0.71 | 1.75 | 2.29 | 0.73 | 2.84 | 1.11 | 1.78 |
time (sec) |
N/A | 0.219 | 0.022 | 0.319 | 0.285 | 0.273 | 0.310 | 0.289 | 0.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 63 | 201 | 188 | 69 | 228 | 89 | 154 |
N.S. |
1 | 1.00 | 0.83 | 2.64 | 2.47 | 0.91 | 3.00 | 1.17 | 2.03 |
time (sec) |
N/A | 0.240 | 0.026 | 0.336 | 0.268 | 0.266 | 0.442 | 0.290 | 0.787 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 88 | 267 | 263 | 94 | 286 | 126 | 199 |
N.S. |
1 | 1.00 | 0.95 | 2.87 | 2.83 | 1.01 | 3.08 | 1.35 | 2.14 |
time (sec) |
N/A | 0.255 | 0.040 | 0.352 | 0.264 | 0.251 | 0.558 | 0.290 | 0.829 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 324 | 342 | 249 | 436 | 3081 | 264 | 0 | 334 | 0 |
N.S. |
1 | 1.06 | 0.77 | 1.35 | 9.51 | 0.81 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.490 | 0.419 | 2.174 | 0.222 | 0.281 | 0.000 | 0.323 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 249 | 264 | 201 | 342 | 2295 | 216 | 0 | 285 | 0 |
N.S. |
1 | 1.06 | 0.81 | 1.37 | 9.22 | 0.87 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.412 | 0.227 | 1.382 | 0.206 | 0.285 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 227 | 229 | 160 | 259 | 1608 | 174 | 0 | 243 | 0 |
N.S. |
1 | 1.01 | 0.70 | 1.14 | 7.08 | 0.77 | 0.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.369 | 0.190 | 1.214 | 0.196 | 0.275 | 0.000 | 0.315 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 171 | 132 | 186 | 1108 | 136 | 0 | 209 | 0 |
N.S. |
1 | 1.05 | 0.81 | 1.14 | 6.80 | 0.83 | 0.00 | 1.28 | 0.00 |
time (sec) |
N/A | 0.290 | 0.135 | 0.822 | 0.218 | 0.280 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 109 | 45 | 120 | 736 | 99 | 0 | 180 | 0 |
N.S. |
1 | 1.16 | 0.48 | 1.28 | 7.83 | 1.05 | 0.00 | 1.91 | 0.00 |
time (sec) |
N/A | 0.235 | 0.033 | 0.811 | 0.213 | 0.282 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 162 | 196 | 485 | 733 | 356 | 0 | 252 | 0 |
N.S. |
1 | 1.21 | 1.46 | 3.62 | 5.47 | 2.66 | 0.00 | 1.88 | 0.00 |
time (sec) |
N/A | 0.321 | 0.556 | 0.503 | 0.186 | 0.278 | 0.000 | 0.398 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 176 | 185 | 145 | 181 | 992 | 389 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.82 | 1.03 | 5.64 | 2.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.273 | 0.114 | 1.577 | 0.207 | 0.298 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 264 | 253 | 194 | 269 | 1536 | 574 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.73 | 1.02 | 5.82 | 2.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.325 | 0.161 | 1.182 | 0.212 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 338 | 356 | 282 | 379 | 2313 | 839 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.83 | 1.12 | 6.84 | 2.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.449 | 0.306 | 1.343 | 0.209 | 0.314 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 276 | 284 | 248 | 197 | 456 | 177 | 0 | 205 | 0 |
N.S. |
1 | 1.03 | 0.90 | 0.71 | 1.65 | 0.64 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.439 | 0.619 | 0.840 | 0.285 | 0.268 | 0.000 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 208 | 202 | 150 | 308 | 139 | 0 | 155 | 0 |
N.S. |
1 | 1.03 | 1.00 | 0.75 | 1.53 | 0.69 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.359 | 0.417 | 0.675 | 0.297 | 0.282 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 180 | 162 | 113 | 161 | 106 | 0 | 113 | 0 |
N.S. |
1 | 1.05 | 0.95 | 0.66 | 0.94 | 0.62 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.331 | 0.236 | 0.597 | 0.261 | 0.277 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 121 | 131 | 87 | 97 | 79 | 0 | 75 | 0 |
N.S. |
1 | 1.10 | 1.19 | 0.79 | 0.88 | 0.72 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.259 | 0.107 | 0.518 | 0.261 | 0.279 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 65 | 28 | 69 | 35 | 60 | 0 | 51 | 0 |
N.S. |
1 | 1.25 | 0.54 | 1.33 | 0.67 | 1.15 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.209 | 0.014 | 0.466 | 0.265 | 0.275 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 111 | 142 | 260 | 0 | 144 | 0 | 112 | 0 |
N.S. |
1 | 1.25 | 1.60 | 2.92 | 0.00 | 1.62 | 0.00 | 1.26 | 0.00 |
time (sec) |
N/A | 0.261 | 0.061 | 0.456 | 0.000 | 0.274 | 0.000 | 0.339 | 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 | 130 | 130 | 119 | 93 | 0 | 224 | 0 | 145 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.72 | 0.00 | 1.72 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.251 | 0.056 | 0.612 | 0.000 | 0.273 | 0.000 | 0.334 | 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 | 201 | 198 | 154 | 187 | 0 | 452 | 0 | 471 | 0 |
N.S. |
1 | 0.99 | 0.77 | 0.93 | 0.00 | 2.25 | 0.00 | 2.34 | 0.00 |
time (sec) |
N/A | 0.301 | 0.097 | 0.602 | 0.000 | 0.288 | 0.000 | 0.338 | 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 | 283 | 294 | 233 | 281 | 0 | 690 | 0 | 884 | 0 |
N.S. |
1 | 1.04 | 0.82 | 0.99 | 0.00 | 2.44 | 0.00 | 3.12 | 0.00 |
time (sec) |
N/A | 0.377 | 0.269 | 0.978 | 0.000 | 0.292 | 0.000 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 95 | 125 | 105 | 105 | 114 | 215 | 165 |
N.S. |
1 | 1.00 | 0.96 | 1.26 | 1.06 | 1.06 | 1.15 | 2.17 | 1.67 |
time (sec) |
N/A | 0.281 | 0.058 | 0.260 | 0.175 | 0.259 | 0.232 | 0.288 | 0.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 77 | 85 | 73 | 77 | 76 | 158 | 129 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 0.95 | 1.00 | 0.99 | 2.05 | 1.68 |
time (sec) |
N/A | 0.247 | 0.046 | 0.238 | 0.178 | 0.256 | 0.187 | 0.285 | 0.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 55 | 59 | 53 | 53 | 49 | 109 | 90 |
N.S. |
1 | 1.00 | 0.93 | 1.00 | 0.90 | 0.90 | 0.83 | 1.85 | 1.53 |
time (sec) |
N/A | 0.230 | 0.026 | 0.222 | 0.176 | 0.268 | 0.151 | 0.271 | 0.610 |