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 | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 365 | 365 | 437 | 360 | 0 | 58 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.20 | 0.99 | 0.00 | 0.16 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.140 | 32.422 | 0.722 | 0.000 | 0.084 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 326 | 326 | 423 | 345 | 0 | 46 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.30 | 1.06 | 0.00 | 0.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.106 | 32.135 | 0.487 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 275 | 275 | 389 | 313 | 0 | 18 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.41 | 1.14 | 0.00 | 0.07 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.083 | 31.825 | 0.639 | 0.000 | 0.083 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 304 | 304 | 417 | 341 | 0 | 62 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.37 | 1.12 | 0.00 | 0.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.116 | 31.700 | 1.014 | 0.000 | 0.105 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 351 | 351 | 435 | 360 | 0 | 95 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.24 | 1.03 | 0.00 | 0.27 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.133 | 32.179 | 1.289 | 0.000 | 0.108 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 133 | 251 | 271 | 244 | 244 | 332 | 324 | 270 |
N.S. |
1 | 0.99 | 1.87 | 2.02 | 1.82 | 1.82 | 2.48 | 2.42 | 2.01 |
time (sec) |
N/A | 0.174 | 0.090 | 0.283 | 0.193 | 0.273 | 0.041 | 0.269 | 0.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 133 | 192 | 207 | 188 | 188 | 252 | 247 | 206 |
N.S. |
1 | 0.99 | 1.43 | 1.54 | 1.40 | 1.40 | 1.88 | 1.84 | 1.54 |
time (sec) |
N/A | 0.131 | 0.059 | 0.278 | 0.196 | 0.380 | 0.034 | 0.293 | 11.026 |
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 | 134 | 133 | 137 | 144 | 132 | 132 | 172 | 171 | 143 |
N.S. |
1 | 0.99 | 1.02 | 1.07 | 0.99 | 0.99 | 1.28 | 1.28 | 1.07 |
time (sec) |
N/A | 0.089 | 0.040 | 0.273 | 0.185 | 0.440 | 0.028 | 0.275 | 10.950 |
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 | 80 | 80 | 80 | 76 | 76 | 76 | 94 | 94 | 79 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.95 | 0.95 | 1.18 | 1.18 | 0.99 |
time (sec) |
N/A | 0.056 | 0.018 | 0.045 | 0.187 | 0.457 | 0.022 | 0.267 | 0.035 |
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 | 42 | 42 | 42 | 37 | 36 | 36 | 39 | 40 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.86 | 0.86 | 0.93 | 0.95 | 0.90 |
time (sec) |
N/A | 0.023 | 0.008 | 0.023 | 0.187 | 0.423 | 0.019 | 0.264 | 0.046 |
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 | 111 | 109 | 100 | 124 | 122 | 123 | 107 | 140 | 130 |
N.S. |
1 | 0.98 | 0.90 | 1.12 | 1.10 | 1.11 | 0.96 | 1.26 | 1.17 |
time (sec) |
N/A | 0.085 | 0.035 | 0.277 | 0.189 | 0.670 | 0.230 | 0.275 | 11.031 |
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 | 116 | 114 | 106 | 129 | 126 | 192 | 143 | 203 | 137 |
N.S. |
1 | 0.98 | 0.91 | 1.11 | 1.09 | 1.66 | 1.23 | 1.75 | 1.18 |
time (sec) |
N/A | 0.084 | 0.049 | 0.299 | 0.186 | 0.280 | 0.492 | 0.265 | 0.096 |
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 | 119 | 119 | 135 | 131 | 136 | 203 | 162 | 132 | 142 |
N.S. |
1 | 1.00 | 1.13 | 1.10 | 1.14 | 1.71 | 1.36 | 1.11 | 1.19 |
time (sec) |
N/A | 0.076 | 0.046 | 0.274 | 0.191 | 0.306 | 1.690 | 0.273 | 0.129 |
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 | 127 | 126 | 130 | 133 | 154 | 185 | 184 | 141 | 154 |
N.S. |
1 | 0.99 | 1.02 | 1.05 | 1.21 | 1.46 | 1.45 | 1.11 | 1.21 |
time (sec) |
N/A | 0.071 | 0.043 | 0.276 | 0.185 | 0.305 | 5.252 | 0.272 | 11.048 |
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 | 132 | 131 | 118 | 126 | 157 | 157 | 194 | 207 | 158 |
N.S. |
1 | 0.99 | 0.89 | 0.95 | 1.19 | 1.19 | 1.47 | 1.57 | 1.20 |
time (sec) |
N/A | 0.066 | 0.040 | 0.276 | 0.204 | 0.309 | 15.254 | 0.274 | 0.080 |
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 | 134 | 133 | 122 | 136 | 173 | 173 | 212 | 143 | 180 |
N.S. |
1 | 0.99 | 0.91 | 1.01 | 1.29 | 1.29 | 1.58 | 1.07 | 1.34 |
time (sec) |
N/A | 0.066 | 0.041 | 0.290 | 0.202 | 0.328 | 80.686 | 0.276 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 133 | 119 | 127 | 178 | 178 | 0 | 140 | 182 |
N.S. |
1 | 0.99 | 0.89 | 0.95 | 1.33 | 1.33 | 0.00 | 1.04 | 1.36 |
time (sec) |
N/A | 0.069 | 0.043 | 0.279 | 0.187 | 0.300 | 0.000 | 0.272 | 11.034 |
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 | 304 | 302 | 665 | 671 | 648 | 648 | 957 | 919 | 739 |
N.S. |
1 | 0.99 | 2.19 | 2.21 | 2.13 | 2.13 | 3.15 | 3.02 | 2.43 |
time (sec) |
N/A | 0.526 | 0.243 | 0.368 | 0.191 | 0.300 | 0.065 | 0.280 | 11.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 304 | 302 | 550 | 545 | 532 | 532 | 765 | 743 | 594 |
N.S. |
1 | 0.99 | 1.81 | 1.79 | 1.75 | 1.75 | 2.52 | 2.44 | 1.95 |
time (sec) |
N/A | 0.394 | 0.175 | 0.364 | 0.188 | 0.319 | 0.063 | 0.281 | 11.280 |
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 | 304 | 302 | 421 | 419 | 416 | 416 | 583 | 568 | 450 |
N.S. |
1 | 0.99 | 1.38 | 1.38 | 1.37 | 1.37 | 1.92 | 1.87 | 1.48 |
time (sec) |
N/A | 0.330 | 0.133 | 0.337 | 0.185 | 0.330 | 0.051 | 0.286 | 0.145 |
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 | 304 | 302 | 301 | 293 | 300 | 300 | 405 | 396 | 310 |
N.S. |
1 | 0.99 | 0.99 | 0.96 | 0.99 | 0.99 | 1.33 | 1.30 | 1.02 |
time (sec) |
N/A | 0.268 | 0.096 | 0.367 | 0.187 | 0.315 | 0.050 | 0.272 | 11.037 |
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 | 180 | 180 | 180 | 167 | 184 | 184 | 231 | 225 | 184 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.02 | 1.02 | 1.28 | 1.25 | 1.02 |
time (sec) |
N/A | 0.181 | 0.054 | 0.359 | 0.196 | 0.289 | 0.035 | 0.271 | 11.026 |
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 | 96 | 96 | 96 | 90 | 90 | 90 | 100 | 99 | 89 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.94 | 0.94 | 1.04 | 1.03 | 0.93 |
time (sec) |
N/A | 0.065 | 0.017 | 0.343 | 0.177 | 0.299 | 0.029 | 0.274 | 10.955 |
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 | 257 | 257 | 298 | 424 | 378 | 379 | 372 | 494 | 423 |
N.S. |
1 | 1.00 | 1.16 | 1.65 | 1.47 | 1.47 | 1.45 | 1.92 | 1.65 |
time (sec) |
N/A | 0.311 | 0.123 | 0.385 | 0.192 | 0.423 | 0.594 | 0.268 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 267 | 264 | 250 | 445 | 387 | 567 | 442 | 575 | 499 |
N.S. |
1 | 0.99 | 0.94 | 1.67 | 1.45 | 2.12 | 1.66 | 2.15 | 1.87 |
time (sec) |
N/A | 0.280 | 0.074 | 0.365 | 0.200 | 0.433 | 1.670 | 0.267 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 281 | 280 | 262 | 438 | 397 | 620 | 534 | 461 | 468 |
N.S. |
1 | 1.00 | 0.93 | 1.56 | 1.41 | 2.21 | 1.90 | 1.64 | 1.67 |
time (sec) |
N/A | 0.285 | 0.085 | 0.373 | 0.202 | 0.375 | 9.344 | 0.261 | 11.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 286 | 284 | 263 | 438 | 409 | 618 | 547 | 455 | 465 |
N.S. |
1 | 0.99 | 0.92 | 1.53 | 1.43 | 2.16 | 1.91 | 1.59 | 1.63 |
time (sec) |
N/A | 0.257 | 0.079 | 0.365 | 0.198 | 0.382 | 167.869 | 0.293 | 11.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 289 | 287 | 391 | 434 | 417 | 572 | 0 | 719 | 475 |
N.S. |
1 | 0.99 | 1.35 | 1.50 | 1.44 | 1.98 | 0.00 | 2.49 | 1.64 |
time (sec) |
N/A | 0.229 | 0.182 | 0.370 | 0.198 | 0.363 | 0.000 | 0.284 | 11.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 297 | 295 | 386 | 440 | 438 | 505 | 0 | 456 | 483 |
N.S. |
1 | 0.99 | 1.30 | 1.48 | 1.47 | 1.70 | 0.00 | 1.54 | 1.63 |
time (sec) |
N/A | 0.219 | 0.149 | 0.362 | 0.203 | 0.635 | 0.000 | 0.272 | 11.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 302 | 300 | 372 | 431 | 438 | 438 | 0 | 495 | 485 |
N.S. |
1 | 0.99 | 1.23 | 1.43 | 1.45 | 1.45 | 0.00 | 1.64 | 1.61 |
time (sec) |
N/A | 0.195 | 0.130 | 0.363 | 0.210 | 0.318 | 0.000 | 0.270 | 0.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 304 | 302 | 377 | 439 | 457 | 457 | 0 | 497 | 505 |
N.S. |
1 | 0.99 | 1.24 | 1.44 | 1.50 | 1.50 | 0.00 | 1.63 | 1.66 |
time (sec) |
N/A | 0.195 | 0.148 | 0.391 | 0.208 | 0.325 | 0.000 | 0.271 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 304 | 302 | 375 | 439 | 468 | 468 | 0 | 497 | 516 |
N.S. |
1 | 0.99 | 1.23 | 1.44 | 1.54 | 1.54 | 0.00 | 1.63 | 1.70 |
time (sec) |
N/A | 0.192 | 0.142 | 0.369 | 0.210 | 0.309 | 0.000 | 0.285 | 11.230 |
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 | 555 | 553 | 1178 | 1263 | 1114 | 1114 | 1731 | 1663 | 1348 |
N.S. |
1 | 1.00 | 2.12 | 2.28 | 2.01 | 2.01 | 3.12 | 3.00 | 2.43 |
time (sec) |
N/A | 1.040 | 0.423 | 0.376 | 0.194 | 0.331 | 0.103 | 0.288 | 11.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 555 | 553 | 957 | 1041 | 919 | 919 | 1401 | 1353 | 1093 |
N.S. |
1 | 1.00 | 1.72 | 1.88 | 1.66 | 1.66 | 2.52 | 2.44 | 1.97 |
time (sec) |
N/A | 0.810 | 0.339 | 0.378 | 0.200 | 0.315 | 0.088 | 0.311 | 0.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 555 | 553 | 715 | 819 | 713 | 713 | 1080 | 1040 | 835 |
N.S. |
1 | 1.00 | 1.29 | 1.48 | 1.28 | 1.28 | 1.95 | 1.87 | 1.50 |
time (sec) |
N/A | 0.695 | 0.243 | 0.342 | 0.189 | 0.322 | 0.072 | 0.269 | 0.243 |
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 | 555 | 553 | 526 | 594 | 529 | 529 | 753 | 727 | 578 |
N.S. |
1 | 1.00 | 0.95 | 1.07 | 0.95 | 0.95 | 1.36 | 1.31 | 1.04 |
time (sec) |
N/A | 0.546 | 0.178 | 0.364 | 0.186 | 0.334 | 0.058 | 0.267 | 11.225 |
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 | 310 | 310 | 310 | 339 | 334 | 334 | 435 | 417 | 338 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.08 | 1.08 | 1.40 | 1.35 | 1.09 |
time (sec) |
N/A | 0.405 | 0.102 | 0.345 | 0.181 | 0.309 | 0.044 | 0.272 | 0.128 |
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 | 158 | 158 | 158 | 164 | 162 | 162 | 190 | 187 | 163 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.03 | 1.03 | 1.20 | 1.18 | 1.03 |
time (sec) |
N/A | 0.142 | 0.030 | 0.342 | 0.188 | 0.295 | 0.033 | 0.286 | 0.071 |
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 | 544 | 541 | 700 | 1030 | 842 | 843 | 979 | 1209 | 968 |
N.S. |
1 | 0.99 | 1.29 | 1.89 | 1.55 | 1.55 | 1.80 | 2.22 | 1.78 |
time (sec) |
N/A | 0.746 | 0.304 | 0.371 | 0.195 | 0.313 | 1.113 | 0.289 | 11.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 525 | 522 | 922 | 1054 | 853 | 1189 | 1056 | 1264 | 1483 |
N.S. |
1 | 0.99 | 1.76 | 2.01 | 1.62 | 2.26 | 2.01 | 2.41 | 2.82 |
time (sec) |
N/A | 0.675 | 0.336 | 0.367 | 0.192 | 0.316 | 3.903 | 0.282 | 11.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 531 | 530 | 503 | 1044 | 861 | 1311 | 1149 | 1127 | 1297 |
N.S. |
1 | 1.00 | 0.95 | 1.97 | 1.62 | 2.47 | 2.16 | 2.12 | 2.44 |
time (sec) |
N/A | 0.697 | 0.168 | 0.365 | 0.198 | 0.318 | 32.646 | 0.279 | 11.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 521 | 519 | 488 | 1045 | 875 | 1369 | 0 | 1100 | 1151 |
N.S. |
1 | 1.00 | 0.94 | 2.01 | 1.68 | 2.63 | 0.00 | 2.11 | 2.21 |
time (sec) |
N/A | 0.656 | 0.168 | 0.362 | 0.209 | 0.341 | 0.000 | 0.269 | 11.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 533 | 531 | 496 | 1042 | 884 | 1343 | 0 | 1581 | 1106 |
N.S. |
1 | 1.00 | 0.93 | 1.95 | 1.66 | 2.52 | 0.00 | 2.97 | 2.08 |
time (sec) |
N/A | 0.625 | 0.177 | 0.336 | 0.213 | 0.345 | 0.000 | 0.304 | 11.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 534 | 532 | 885 | 1042 | 898 | 1247 | 0 | 1077 | 1106 |
N.S. |
1 | 1.00 | 1.66 | 1.95 | 1.68 | 2.34 | 0.00 | 2.02 | 2.07 |
time (sec) |
N/A | 0.548 | 0.390 | 0.374 | 0.217 | 0.324 | 0.000 | 0.292 | 11.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 541 | 539 | 868 | 1047 | 905 | 1145 | 0 | 1067 | 1598 |
N.S. |
1 | 1.00 | 1.60 | 1.94 | 1.67 | 2.12 | 0.00 | 1.97 | 2.95 |
time (sec) |
N/A | 0.521 | 0.520 | 0.372 | 0.225 | 0.329 | 0.000 | 0.270 | 11.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 548 | 546 | 863 | 1047 | 926 | 1023 | 0 | 1079 | 1353 |
N.S. |
1 | 1.00 | 1.57 | 1.91 | 1.69 | 1.87 | 0.00 | 1.97 | 2.47 |
time (sec) |
N/A | 0.476 | 0.321 | 0.391 | 0.226 | 0.319 | 0.000 | 0.284 | 11.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 550 | 548 | 847 | 1034 | 922 | 922 | 0 | 1210 | 1115 |
N.S. |
1 | 1.00 | 1.54 | 1.88 | 1.68 | 1.68 | 0.00 | 2.20 | 2.03 |
time (sec) |
N/A | 0.462 | 0.341 | 0.367 | 0.224 | 0.277 | 0.000 | 0.280 | 0.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 555 | 553 | 852 | 1048 | 945 | 945 | 0 | 1212 | 1142 |
N.S. |
1 | 1.00 | 1.54 | 1.89 | 1.70 | 1.70 | 0.00 | 2.18 | 2.06 |
time (sec) |
N/A | 0.437 | 0.335 | 0.365 | 0.229 | 0.296 | 0.000 | 0.281 | 11.345 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 555 | 553 | 849 | 1048 | 956 | 956 | 0 | 1212 | 1153 |
N.S. |
1 | 1.00 | 1.53 | 1.89 | 1.72 | 1.72 | 0.00 | 2.18 | 2.08 |
time (sec) |
N/A | 0.429 | 0.341 | 0.362 | 0.248 | 0.314 | 0.000 | 0.276 | 11.429 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 142 | 281 | 215 | 342 | 3267 | 604 | 300 |
N.S. |
1 | 1.00 | 1.17 | 2.32 | 1.78 | 2.83 | 27.00 | 4.99 | 2.48 |
time (sec) |
N/A | 0.060 | 0.233 | 0.302 | 0.214 | 0.326 | 0.912 | 0.282 | 11.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 166 | 169 | 168 | 168 | 192 | 186 | 160 |
N.S. |
1 | 1.00 | 1.61 | 1.64 | 1.63 | 1.63 | 1.86 | 1.81 | 1.55 |
time (sec) |
N/A | 0.109 | 0.031 | 0.284 | 0.186 | 0.279 | 0.032 | 0.268 | 11.137 |
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 | 103 | 103 | 140 | 136 | 138 | 138 | 153 | 149 | 132 |
N.S. |
1 | 1.00 | 1.36 | 1.32 | 1.34 | 1.34 | 1.49 | 1.45 | 1.28 |
time (sec) |
N/A | 0.084 | 0.023 | 0.250 | 0.181 | 0.287 | 0.034 | 0.276 | 0.057 |
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 | 103 | 103 | 109 | 105 | 105 | 105 | 116 | 114 | 104 |
N.S. |
1 | 1.00 | 1.06 | 1.02 | 1.02 | 1.02 | 1.13 | 1.11 | 1.01 |
time (sec) |
N/A | 0.069 | 0.021 | 0.286 | 0.184 | 0.280 | 0.026 | 0.270 | 11.069 |
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 | 78 | 78 | 70 | 73 | 72 | 72 | 80 | 79 | 73 |
N.S. |
1 | 1.00 | 0.90 | 0.94 | 0.92 | 0.92 | 1.03 | 1.01 | 0.94 |
time (sec) |
N/A | 0.048 | 0.018 | 0.285 | 0.181 | 0.291 | 0.025 | 0.272 | 0.035 |
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 | 47 | 47 | 41 | 40 | 39 | 39 | 42 | 43 | 41 |
N.S. |
1 | 1.00 | 0.87 | 0.85 | 0.83 | 0.83 | 0.89 | 0.91 | 0.87 |
time (sec) |
N/A | 0.025 | 0.009 | 0.035 | 0.188 | 0.377 | 0.022 | 0.263 | 0.045 |
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 | 25 | 25 | 25 | 20 | 19 | 19 | 19 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.76 | 0.76 | 0.76 | 0.76 | 0.76 |
time (sec) |
N/A | 0.005 | 0.002 | 0.033 | 0.178 | 0.428 | 0.018 | 0.259 | 0.028 |
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 | 79 | 79 | 74 | 76 | 81 | 82 | 71 | 84 | 85 |
N.S. |
1 | 1.00 | 0.94 | 0.96 | 1.03 | 1.04 | 0.90 | 1.06 | 1.08 |
time (sec) |
N/A | 0.049 | 0.019 | 0.295 | 0.191 | 0.418 | 0.138 | 0.265 | 11.104 |
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 | 84 | 84 | 79 | 78 | 85 | 131 | 82 | 134 | 88 |
N.S. |
1 | 1.00 | 0.94 | 0.93 | 1.01 | 1.56 | 0.98 | 1.60 | 1.05 |
time (sec) |
N/A | 0.064 | 0.041 | 0.280 | 0.185 | 0.409 | 0.226 | 0.270 | 11.091 |
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 | 89 | 89 | 80 | 83 | 96 | 147 | 97 | 83 | 96 |
N.S. |
1 | 1.00 | 0.90 | 0.93 | 1.08 | 1.65 | 1.09 | 0.93 | 1.08 |
time (sec) |
N/A | 0.053 | 0.036 | 0.286 | 0.186 | 0.342 | 0.414 | 0.266 | 11.129 |
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 | 96 | 96 | 86 | 84 | 113 | 141 | 114 | 89 | 107 |
N.S. |
1 | 1.00 | 0.90 | 0.88 | 1.18 | 1.47 | 1.19 | 0.93 | 1.11 |
time (sec) |
N/A | 0.053 | 0.024 | 0.280 | 0.187 | 0.563 | 0.701 | 0.276 | 11.148 |
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 | 101 | 101 | 77 | 79 | 116 | 116 | 126 | 122 | 111 |
N.S. |
1 | 1.00 | 0.76 | 0.78 | 1.15 | 1.15 | 1.25 | 1.21 | 1.10 |
time (sec) |
N/A | 0.049 | 0.020 | 0.280 | 0.191 | 0.265 | 1.059 | 0.273 | 0.057 |
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 | 103 | 103 | 79 | 84 | 132 | 132 | 141 | 84 | 128 |
N.S. |
1 | 1.00 | 0.77 | 0.82 | 1.28 | 1.28 | 1.37 | 0.82 | 1.24 |
time (sec) |
N/A | 0.050 | 0.021 | 0.267 | 0.179 | 0.293 | 1.801 | 0.280 | 0.065 |
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 | 103 | 103 | 77 | 78 | 137 | 137 | 150 | 82 | 133 |
N.S. |
1 | 1.00 | 0.75 | 0.76 | 1.33 | 1.33 | 1.46 | 0.80 | 1.29 |
time (sec) |
N/A | 0.050 | 0.021 | 0.287 | 0.196 | 0.304 | 3.705 | 0.269 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 357 | 357 | 352 | 437 | 0 | 1139 | 2759 | 421 | 539 |
N.S. |
1 | 1.00 | 0.99 | 1.22 | 0.00 | 3.19 | 7.73 | 1.18 | 1.51 |
time (sec) |
N/A | 0.423 | 0.189 | 0.546 | 0.000 | 0.565 | 13.658 | 0.268 | 11.904 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 205 | 205 | 203 | 221 | 0 | 673 | 1532 | 223 | 316 |
N.S. |
1 | 1.00 | 0.99 | 1.08 | 0.00 | 3.28 | 7.47 | 1.09 | 1.54 |
time (sec) |
N/A | 0.249 | 0.104 | 0.497 | 0.000 | 0.324 | 5.606 | 0.273 | 11.772 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 108 | 108 | 0 | 369 | 677 | 106 | 163 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 3.42 | 6.27 | 0.98 | 1.51 |
time (sec) |
N/A | 0.075 | 0.052 | 0.468 | 0.000 | 0.323 | 1.864 | 0.273 | 0.409 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 66 | 62 | 0 | 207 | 280 | 63 | 162 |
N.S. |
1 | 1.00 | 1.03 | 0.97 | 0.00 | 3.23 | 4.38 | 0.98 | 2.53 |
time (sec) |
N/A | 0.029 | 0.036 | 0.413 | 0.000 | 0.290 | 0.391 | 0.267 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 146 | 125 | 145 | 0 | 409 | 0 | 152 | 1027 |
N.S. |
1 | 1.00 | 0.86 | 0.99 | 0.00 | 2.80 | 0.00 | 1.04 | 7.03 |
time (sec) |
N/A | 0.137 | 0.078 | 0.541 | 0.000 | 3.332 | 0.000 | 0.272 | 18.563 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 255 | 255 | 219 | 276 | 0 | 1594 | 0 | 392 | 2650 |
N.S. |
1 | 1.00 | 0.86 | 1.08 | 0.00 | 6.25 | 0.00 | 1.54 | 10.39 |
time (sec) |
N/A | 0.271 | 0.213 | 0.458 | 0.000 | 48.330 | 0.000 | 0.289 | 16.805 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 414 | 414 | 413 | 487 | 0 | 0 | 0 | 844 | 7042 |
N.S. |
1 | 1.00 | 1.00 | 1.18 | 0.00 | 0.00 | 0.00 | 2.04 | 17.01 |
time (sec) |
N/A | 0.496 | 0.294 | 0.447 | 0.000 | 0.000 | 0.000 | 0.290 | 43.997 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 543 | 543 | 897 | 1501 | 0 | 5676 | 0 | 1368 | 1763 |
N.S. |
1 | 1.00 | 1.65 | 2.76 | 0.00 | 10.45 | 0.00 | 2.52 | 3.25 |
time (sec) |
N/A | 0.838 | 1.158 | 0.559 | 0.000 | 1.724 | 0.000 | 0.293 | 14.897 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 195 | 550 | 982 | 0 | 3941 | 0 | 1002 | 1167 |
N.S. |
1 | 1.00 | 2.82 | 5.04 | 0.00 | 20.21 | 0.00 | 5.14 | 5.98 |
time (sec) |
N/A | 0.110 | 0.553 | 0.441 | 0.000 | 0.600 | 0.000 | 0.297 | 12.538 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 305 | 303 | 408 | 646 | 0 | 2906 | 2076 | 647 | 913 |
N.S. |
1 | 0.99 | 1.34 | 2.12 | 0.00 | 9.53 | 6.81 | 2.12 | 2.99 |
time (sec) |
N/A | 0.252 | 0.407 | 0.441 | 0.000 | 0.583 | 56.989 | 0.308 | 12.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 221 | 219 | 216 | 381 | 0 | 1879 | 1234 | 353 | 555 |
N.S. |
1 | 0.99 | 0.98 | 1.72 | 0.00 | 8.50 | 5.58 | 1.60 | 2.51 |
time (sec) |
N/A | 0.113 | 0.217 | 0.414 | 0.000 | 0.446 | 5.778 | 0.293 | 0.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 128 | 137 | 0 | 1116 | 651 | 199 | 353 |
N.S. |
1 | 1.00 | 0.98 | 1.05 | 0.00 | 8.52 | 4.97 | 1.52 | 2.69 |
time (sec) |
N/A | 0.038 | 0.084 | 0.447 | 0.000 | 0.361 | 1.020 | 0.272 | 11.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 666 | 664 | 668 | 2087 | 0 | 0 | 0 | 2398 | 25467 |
N.S. |
1 | 1.00 | 1.00 | 3.13 | 0.00 | 0.00 | 0.00 | 3.60 | 38.24 |
time (sec) |
N/A | 1.672 | 1.843 | 0.582 | 0.000 | 0.000 | 0.000 | 0.309 | 18.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1043 | 1043 | 1050 | 3177 | 0 | 0 | 0 | 3633 | 40079 |
N.S. |
1 | 1.00 | 1.01 | 3.05 | 0.00 | 0.00 | 0.00 | 3.48 | 38.43 |
time (sec) |
N/A | 4.250 | 5.113 | 1.512 | 0.000 | 0.000 | 0.000 | 0.765 | 22.095 |
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 | 43 | 43 | 43 | 32 | 33 | 33 | 41 | 35 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.77 | 0.77 | 0.95 | 0.81 | 0.72 |
time (sec) |
N/A | 0.016 | 0.018 | 0.308 | 0.180 | 0.279 | 0.059 | 0.269 | 0.054 |
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 | 36 | 36 | 35 | 27 | 28 | 28 | 34 | 30 | 26 |
N.S. |
1 | 1.00 | 0.97 | 0.75 | 0.78 | 0.78 | 0.94 | 0.83 | 0.72 |
time (sec) |
N/A | 0.016 | 0.012 | 0.306 | 0.187 | 0.291 | 0.056 | 0.262 | 11.756 |
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 | 29 | 29 | 34 | 22 | 23 | 23 | 27 | 25 | 21 |
N.S. |
1 | 1.00 | 1.17 | 0.76 | 0.79 | 0.79 | 0.93 | 0.86 | 0.72 |
time (sec) |
N/A | 0.014 | 0.012 | 0.280 | 0.183 | 0.278 | 0.056 | 0.277 | 0.035 |
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 | 22 | 22 | 22 | 17 | 18 | 18 | 20 | 20 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.82 | 0.82 | 0.91 | 0.91 | 0.73 |
time (sec) |
N/A | 0.009 | 0.005 | 0.301 | 0.178 | 0.274 | 0.052 | 0.279 | 0.039 |
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 | 17 | 17 | 17 | 14 | 15 | 15 | 15 | 17 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.88 | 0.88 | 0.88 | 1.00 | 0.76 |
time (sec) |
N/A | 0.004 | 0.003 | 0.290 | 0.180 | 0.278 | 0.048 | 0.271 | 11.747 |
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 | 27 | 27 | 27 | 20 | 23 | 23 | 26 | 26 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.85 | 0.85 | 0.96 | 0.96 | 0.70 |
time (sec) |
N/A | 0.015 | 0.006 | 0.309 | 0.175 | 0.288 | 0.077 | 0.268 | 0.056 |
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 | 38 | 38 | 38 | 31 | 32 | 48 | 32 | 40 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.84 | 1.26 | 0.84 | 1.05 | 0.74 |
time (sec) |
N/A | 0.020 | 0.017 | 0.315 | 0.177 | 0.305 | 0.081 | 0.269 | 0.039 |
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 | 49 | 49 | 47 | 37 | 42 | 71 | 41 | 40 | 36 |
N.S. |
1 | 1.00 | 0.96 | 0.76 | 0.86 | 1.45 | 0.84 | 0.82 | 0.73 |
time (sec) |
N/A | 0.022 | 0.018 | 0.324 | 0.176 | 0.294 | 0.092 | 0.262 | 0.043 |
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 | 60 | 60 | 62 | 42 | 52 | 96 | 51 | 45 | 46 |
N.S. |
1 | 1.00 | 1.03 | 0.70 | 0.87 | 1.60 | 0.85 | 0.75 | 0.77 |
time (sec) |
N/A | 0.025 | 0.028 | 0.309 | 0.178 | 0.276 | 0.097 | 0.259 | 11.648 |
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 | 50 | 50 | 56 | 40 | 42 | 68 | 42 | 44 | 38 |
N.S. |
1 | 1.00 | 1.12 | 0.80 | 0.84 | 1.36 | 0.84 | 0.88 | 0.76 |
time (sec) |
N/A | 0.035 | 0.022 | 0.321 | 0.176 | 0.276 | 0.085 | 0.271 | 0.041 |
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 | 43 | 43 | 47 | 35 | 37 | 63 | 36 | 39 | 33 |
N.S. |
1 | 1.00 | 1.09 | 0.81 | 0.86 | 1.47 | 0.84 | 0.91 | 0.77 |
time (sec) |
N/A | 0.033 | 0.026 | 0.323 | 0.178 | 0.270 | 0.080 | 0.273 | 11.476 |
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 | 38 | 38 | 38 | 32 | 34 | 53 | 31 | 36 | 30 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.89 | 1.39 | 0.82 | 0.95 | 0.79 |
time (sec) |
N/A | 0.024 | 0.020 | 0.306 | 0.181 | 0.255 | 0.076 | 0.262 | 0.053 |
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 | 36 | 36 | 34 | 32 | 34 | 53 | 29 | 36 | 26 |
N.S. |
1 | 1.00 | 0.94 | 0.89 | 0.94 | 1.47 | 0.81 | 1.00 | 0.72 |
time (sec) |
N/A | 0.010 | 0.011 | 0.287 | 0.174 | 0.265 | 0.063 | 0.269 | 0.041 |
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 | 34 | 34 | 33 | 32 | 34 | 53 | 29 | 36 | 26 |
N.S. |
1 | 1.00 | 0.97 | 0.94 | 1.00 | 1.56 | 0.85 | 1.06 | 0.76 |
time (sec) |
N/A | 0.007 | 0.009 | 0.319 | 0.183 | 0.287 | 0.063 | 0.274 | 11.399 |
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 | 48 | 48 | 48 | 40 | 42 | 71 | 41 | 45 | 36 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.88 | 1.48 | 0.85 | 0.94 | 0.75 |
time (sec) |
N/A | 0.026 | 0.023 | 0.330 | 0.174 | 0.282 | 0.096 | 0.272 | 0.042 |
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 | 66 | 66 | 57 | 49 | 52 | 96 | 51 | 77 | 46 |
N.S. |
1 | 1.00 | 0.86 | 0.74 | 0.79 | 1.45 | 0.77 | 1.17 | 0.70 |
time (sec) |
N/A | 0.029 | 0.020 | 0.310 | 0.187 | 0.268 | 0.094 | 0.271 | 0.042 |
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 | 77 | 77 | 66 | 58 | 62 | 121 | 60 | 62 | 56 |
N.S. |
1 | 1.00 | 0.86 | 0.75 | 0.81 | 1.57 | 0.78 | 0.81 | 0.73 |
time (sec) |
N/A | 0.030 | 0.022 | 0.316 | 0.179 | 0.280 | 0.101 | 0.263 | 11.335 |
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 | 88 | 88 | 75 | 64 | 72 | 146 | 71 | 67 | 66 |
N.S. |
1 | 1.00 | 0.85 | 0.73 | 0.82 | 1.66 | 0.81 | 0.76 | 0.75 |
time (sec) |
N/A | 0.035 | 0.031 | 0.319 | 0.185 | 0.287 | 0.109 | 0.273 | 11.748 |
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 | 64 | 64 | 81 | 48 | 57 | 103 | 58 | 49 | 52 |
N.S. |
1 | 1.00 | 1.27 | 0.75 | 0.89 | 1.61 | 0.91 | 0.77 | 0.81 |
time (sec) |
N/A | 0.054 | 0.023 | 0.317 | 0.185 | 0.287 | 0.093 | 0.268 | 11.721 |
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 | 59 | 59 | 62 | 44 | 54 | 93 | 53 | 46 | 49 |
N.S. |
1 | 1.00 | 1.05 | 0.75 | 0.92 | 1.58 | 0.90 | 0.78 | 0.83 |
time (sec) |
N/A | 0.036 | 0.024 | 0.312 | 0.175 | 0.265 | 0.099 | 0.262 | 0.056 |
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 | 69 | 69 | 59 | 44 | 54 | 93 | 51 | 46 | 45 |
N.S. |
1 | 1.00 | 0.86 | 0.64 | 0.78 | 1.35 | 0.74 | 0.67 | 0.65 |
time (sec) |
N/A | 0.020 | 0.020 | 0.309 | 0.177 | 0.288 | 0.076 | 0.266 | 11.750 |
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 | 57 | 57 | 56 | 44 | 54 | 93 | 51 | 46 | 45 |
N.S. |
1 | 1.00 | 0.98 | 0.77 | 0.95 | 1.63 | 0.89 | 0.81 | 0.79 |
time (sec) |
N/A | 0.029 | 0.021 | 0.328 | 0.186 | 0.292 | 0.074 | 0.280 | 11.525 |
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 | 57 | 57 | 57 | 44 | 54 | 93 | 51 | 46 | 45 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.95 | 1.63 | 0.89 | 0.81 | 0.79 |
time (sec) |
N/A | 0.013 | 0.013 | 0.299 | 0.180 | 0.274 | 0.071 | 0.271 | 0.044 |