Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 118 | 121 | 128 | 187 | 139 | 120 | 135 |
N.S. |
1 | 1.00 | 1.06 | 1.09 | 1.15 | 1.68 | 1.25 | 1.08 | 1.22 |
time (sec) |
N/A | 0.065 | 0.046 | 0.292 | 0.202 | 0.289 | 0.728 | 0.280 | 10.725 |
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 | 111 | 122 | 146 | 179 | 158 | 127 | 144 |
N.S. |
1 | 1.00 | 0.93 | 1.03 | 1.23 | 1.50 | 1.33 | 1.07 | 1.21 |
time (sec) |
N/A | 0.062 | 0.046 | 0.542 | 0.196 | 0.355 | 1.452 | 0.269 | 10.753 |
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 | 122 | 122 | 100 | 118 | 150 | 150 | 170 | 176 | 151 |
N.S. |
1 | 1.00 | 0.82 | 0.97 | 1.23 | 1.23 | 1.39 | 1.44 | 1.24 |
time (sec) |
N/A | 0.060 | 0.048 | 0.541 | 0.186 | 0.341 | 2.844 | 0.260 | 10.782 |
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 | 240 | 240 | 433 | 473 | 430 | 430 | 552 | 561 | 454 |
N.S. |
1 | 1.00 | 1.80 | 1.97 | 1.79 | 1.79 | 2.30 | 2.34 | 1.89 |
time (sec) |
N/A | 0.273 | 0.192 | 0.596 | 0.193 | 0.361 | 0.050 | 0.275 | 0.171 |
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 | 240 | 240 | 351 | 363 | 343 | 343 | 430 | 429 | 349 |
N.S. |
1 | 1.00 | 1.46 | 1.51 | 1.43 | 1.43 | 1.79 | 1.79 | 1.45 |
time (sec) |
N/A | 0.197 | 0.106 | 0.392 | 0.184 | 0.382 | 0.043 | 0.263 | 0.114 |
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 | 240 | 240 | 244 | 254 | 241 | 241 | 294 | 298 | 242 |
N.S. |
1 | 1.00 | 1.02 | 1.06 | 1.00 | 1.00 | 1.22 | 1.24 | 1.01 |
time (sec) |
N/A | 0.164 | 0.098 | 0.382 | 0.191 | 0.410 | 0.036 | 0.265 | 10.760 |
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 | 153 | 153 | 153 | 145 | 151 | 151 | 168 | 167 | 144 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.99 | 0.99 | 1.10 | 1.09 | 0.94 |
time (sec) |
N/A | 0.096 | 0.036 | 0.385 | 0.196 | 0.339 | 0.027 | 0.263 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 36 | 15 | 14 | 67 | 65 | 40 | 62 |
N.S. |
1 | 1.00 | 2.25 | 0.94 | 0.88 | 4.19 | 4.06 | 2.50 | 3.88 |
time (sec) |
N/A | 0.005 | 0.020 | 0.575 | 0.199 | 0.348 | 0.029 | 0.285 | 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 | 229 | 229 | 228 | 320 | 307 | 308 | 280 | 360 | 326 |
N.S. |
1 | 1.00 | 1.00 | 1.40 | 1.34 | 1.34 | 1.22 | 1.57 | 1.42 |
time (sec) |
N/A | 0.188 | 0.128 | 0.599 | 0.193 | 0.596 | 0.364 | 0.264 | 10.725 |
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 | 223 | 223 | 241 | 331 | 310 | 444 | 325 | 437 | 387 |
N.S. |
1 | 1.00 | 1.08 | 1.48 | 1.39 | 1.99 | 1.46 | 1.96 | 1.74 |
time (sec) |
N/A | 0.185 | 0.185 | 0.397 | 0.191 | 0.403 | 0.788 | 0.269 | 10.719 |
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 | 219 | 219 | 233 | 326 | 317 | 487 | 360 | 340 | 358 |
N.S. |
1 | 1.00 | 1.06 | 1.49 | 1.45 | 2.22 | 1.64 | 1.55 | 1.63 |
time (sec) |
N/A | 0.164 | 0.094 | 0.371 | 0.195 | 0.299 | 2.595 | 0.272 | 0.122 |
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 | 217 | 217 | 300 | 319 | 327 | 487 | 379 | 337 | 349 |
N.S. |
1 | 1.00 | 1.38 | 1.47 | 1.51 | 2.24 | 1.75 | 1.55 | 1.61 |
time (sec) |
N/A | 0.152 | 0.139 | 0.418 | 0.204 | 0.331 | 21.561 | 0.262 | 10.682 |
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 | 227 | 227 | 292 | 329 | 338 | 458 | 0 | 526 | 369 |
N.S. |
1 | 1.00 | 1.29 | 1.45 | 1.49 | 2.02 | 0.00 | 2.32 | 1.63 |
time (sec) |
N/A | 0.144 | 0.168 | 0.388 | 0.196 | 0.315 | 0.000 | 0.266 | 10.760 |
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 | 411 | 411 | 735 | 783 | 729 | 729 | 935 | 936 | 768 |
N.S. |
1 | 1.00 | 1.79 | 1.91 | 1.77 | 1.77 | 2.27 | 2.28 | 1.87 |
time (sec) |
N/A | 0.471 | 0.247 | 0.382 | 0.190 | 0.292 | 0.068 | 0.275 | 0.256 |
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 | 411 | 411 | 562 | 603 | 565 | 565 | 726 | 719 | 589 |
N.S. |
1 | 1.00 | 1.37 | 1.47 | 1.37 | 1.37 | 1.77 | 1.75 | 1.43 |
time (sec) |
N/A | 0.370 | 0.192 | 0.380 | 0.198 | 0.292 | 0.058 | 0.268 | 0.205 |
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 | 411 | 411 | 413 | 423 | 417 | 417 | 503 | 502 | 414 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.01 | 1.01 | 1.22 | 1.22 | 1.01 |
time (sec) |
N/A | 0.297 | 0.136 | 0.382 | 0.207 | 0.337 | 0.048 | 0.265 | 10.748 |
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 | 251 | 251 | 251 | 244 | 261 | 261 | 291 | 286 | 243 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 1.04 | 1.04 | 1.16 | 1.14 | 0.97 |
time (sec) |
N/A | 0.154 | 0.059 | 0.378 | 0.189 | 0.280 | 0.035 | 0.258 | 10.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 51 | 15 | 14 | 121 | 121 | 56 | 112 |
N.S. |
1 | 1.00 | 3.19 | 0.94 | 0.88 | 7.56 | 7.56 | 3.50 | 7.00 |
time (sec) |
N/A | 0.009 | 0.028 | 0.382 | 0.204 | 0.254 | 0.035 | 0.271 | 10.608 |
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 | 399 | 399 | 483 | 695 | 644 | 645 | 641 | 795 | 697 |
N.S. |
1 | 1.00 | 1.21 | 1.74 | 1.61 | 1.62 | 1.61 | 1.99 | 1.75 |
time (sec) |
N/A | 0.377 | 0.224 | 0.591 | 0.196 | 0.322 | 0.666 | 0.261 | 0.101 |
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 | 396 | 396 | 637 | 709 | 649 | 903 | 688 | 870 | 1090 |
N.S. |
1 | 1.00 | 1.61 | 1.79 | 1.64 | 2.28 | 1.74 | 2.20 | 2.75 |
time (sec) |
N/A | 0.353 | 0.194 | 0.408 | 0.200 | 0.318 | 1.638 | 0.285 | 0.138 |
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 | 390 | 390 | 403 | 702 | 656 | 990 | 733 | 747 | 936 |
N.S. |
1 | 1.00 | 1.03 | 1.80 | 1.68 | 2.54 | 1.88 | 1.92 | 2.40 |
time (sec) |
N/A | 0.338 | 0.152 | 0.412 | 0.226 | 0.343 | 7.082 | 0.270 | 10.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 396 | 396 | 404 | 703 | 670 | 1031 | 0 | 731 | 807 |
N.S. |
1 | 1.00 | 1.02 | 1.78 | 1.69 | 2.60 | 0.00 | 1.85 | 2.04 |
time (sec) |
N/A | 0.343 | 0.140 | 0.420 | 0.226 | 0.264 | 0.000 | 0.282 | 10.770 |
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 | 389 | 389 | 614 | 701 | 679 | 1017 | 0 | 1066 | 763 |
N.S. |
1 | 1.00 | 1.58 | 1.80 | 1.75 | 2.61 | 0.00 | 2.74 | 1.96 |
time (sec) |
N/A | 0.328 | 0.244 | 0.407 | 0.221 | 0.276 | 0.000 | 0.271 | 10.774 |
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 | 299 | 299 | 297 | 474 | 0 | 709 | 0 | 424 | 726 |
N.S. |
1 | 1.00 | 0.99 | 1.59 | 0.00 | 2.37 | 0.00 | 1.42 | 2.43 |
time (sec) |
N/A | 0.260 | 0.208 | 0.533 | 0.000 | 0.312 | 0.000 | 0.261 | 0.402 |
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 | 188 | 188 | 177 | 290 | 0 | 458 | 561 | 262 | 433 |
N.S. |
1 | 1.00 | 0.94 | 1.54 | 0.00 | 2.44 | 2.98 | 1.39 | 2.30 |
time (sec) |
N/A | 0.159 | 0.165 | 0.506 | 0.000 | 0.297 | 13.637 | 0.271 | 10.872 |
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 | 114 | 114 | 111 | 163 | 0 | 282 | 335 | 146 | 230 |
N.S. |
1 | 1.00 | 0.97 | 1.43 | 0.00 | 2.47 | 2.94 | 1.28 | 2.02 |
time (sec) |
N/A | 0.092 | 0.085 | 0.476 | 0.000 | 0.295 | 0.905 | 0.261 | 10.833 |
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 | 70 | 70 | 72 | 88 | 0 | 176 | 134 | 77 | 129 |
N.S. |
1 | 1.00 | 1.03 | 1.26 | 0.00 | 2.51 | 1.91 | 1.10 | 1.84 |
time (sec) |
N/A | 0.058 | 0.065 | 0.431 | 0.000 | 0.281 | 0.373 | 0.266 | 0.326 |
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 | 11 | 11 | 10 | 12 | 11 | 11 | 10 | 12 | 11 |
N.S. |
1 | 1.00 | 0.91 | 1.09 | 1.00 | 1.00 | 0.91 | 1.09 | 1.00 |
time (sec) |
N/A | 0.003 | 0.007 | 0.843 | 0.187 | 0.256 | 0.072 | 0.257 | 0.039 |
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 | 130 | 130 | 116 | 151 | 0 | 229 | 0 | 146 | 515 |
N.S. |
1 | 1.00 | 0.89 | 1.16 | 0.00 | 1.76 | 0.00 | 1.12 | 3.96 |
time (sec) |
N/A | 0.118 | 0.119 | 0.661 | 0.000 | 0.336 | 0.000 | 0.347 | 13.281 |
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 | 210 | 210 | 177 | 276 | 0 | 745 | 0 | 368 | 1637 |
N.S. |
1 | 1.00 | 0.84 | 1.31 | 0.00 | 3.55 | 0.00 | 1.75 | 7.80 |
time (sec) |
N/A | 0.190 | 0.252 | 0.540 | 0.000 | 1.327 | 0.000 | 0.274 | 13.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 303 | 303 | 268 | 452 | 0 | 1961 | 0 | 750 | 2608 |
N.S. |
1 | 1.00 | 0.88 | 1.49 | 0.00 | 6.47 | 0.00 | 2.48 | 8.61 |
time (sec) |
N/A | 0.310 | 0.264 | 0.488 | 0.000 | 8.863 | 0.000 | 0.268 | 21.721 |
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 | 172 | 172 | 241 | 306 | 0 | 1701 | 1071 | 304 | 358 |
N.S. |
1 | 1.00 | 1.40 | 1.78 | 0.00 | 9.89 | 6.23 | 1.77 | 2.08 |
time (sec) |
N/A | 0.150 | 0.220 | 0.915 | 0.000 | 0.311 | 18.026 | 0.266 | 0.335 |
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 | 126 | 126 | 161 | 187 | 0 | 1050 | 733 | 182 | 226 |
N.S. |
1 | 1.00 | 1.28 | 1.48 | 0.00 | 8.33 | 5.82 | 1.44 | 1.79 |
time (sec) |
N/A | 0.098 | 0.149 | 0.465 | 0.000 | 0.302 | 4.587 | 0.268 | 10.895 |
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 | 87 | 87 | 98 | 110 | 0 | 573 | 340 | 116 | 248 |
N.S. |
1 | 1.00 | 1.13 | 1.26 | 0.00 | 6.59 | 3.91 | 1.33 | 2.85 |
time (sec) |
N/A | 0.040 | 0.132 | 0.650 | 0.000 | 0.304 | 1.697 | 0.271 | 0.186 |
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 | 55 | 55 | 58 | 58 | 0 | 269 | 158 | 55 | 73 |
N.S. |
1 | 1.00 | 1.05 | 1.05 | 0.00 | 4.89 | 2.87 | 1.00 | 1.33 |
time (sec) |
N/A | 0.021 | 0.028 | 0.465 | 0.000 | 0.281 | 0.553 | 0.256 | 0.063 |
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 | 14 | 14 | 13 | 15 | 14 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 0.93 | 1.07 | 1.00 | 1.00 | 0.86 | 1.00 | 1.00 |
time (sec) |
N/A | 0.003 | 0.014 | 0.614 | 0.192 | 0.264 | 0.200 | 0.280 | 10.633 |
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 | 236 | 236 | 173 | 249 | 0 | 1834 | 0 | 375 | 1833 |
N.S. |
1 | 1.00 | 0.73 | 1.06 | 0.00 | 7.77 | 0.00 | 1.59 | 7.77 |
time (sec) |
N/A | 0.239 | 0.198 | 0.923 | 0.000 | 1.954 | 0.000 | 0.285 | 17.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 327 | 327 | 275 | 429 | 0 | 4494 | 0 | 767 | 3631 |
N.S. |
1 | 1.00 | 0.84 | 1.31 | 0.00 | 13.74 | 0.00 | 2.35 | 11.10 |
time (sec) |
N/A | 0.356 | 0.449 | 0.512 | 0.000 | 31.603 | 0.000 | 0.300 | 18.001 |
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 | 293 | 293 | 480 | 753 | 0 | 3618 | 0 | 672 | 1148 |
N.S. |
1 | 1.00 | 1.64 | 2.57 | 0.00 | 12.35 | 0.00 | 2.29 | 3.92 |
time (sec) |
N/A | 0.480 | 0.546 | 0.572 | 0.000 | 0.404 | 0.000 | 0.282 | 11.903 |
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 | 197 | 197 | 334 | 518 | 0 | 2400 | 0 | 459 | 753 |
N.S. |
1 | 1.00 | 1.70 | 2.63 | 0.00 | 12.18 | 0.00 | 2.33 | 3.82 |
time (sec) |
N/A | 0.227 | 0.362 | 0.513 | 0.000 | 0.345 | 0.000 | 0.265 | 11.789 |
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 | 126 | 126 | 216 | 300 | 0 | 1455 | 762 | 300 | 412 |
N.S. |
1 | 1.00 | 1.71 | 2.38 | 0.00 | 11.55 | 6.05 | 2.38 | 3.27 |
time (sec) |
N/A | 0.064 | 0.202 | 0.484 | 0.000 | 0.313 | 108.034 | 0.262 | 10.967 |
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 | 112 | 112 | 143 | 197 | 0 | 1004 | 530 | 183 | 284 |
N.S. |
1 | 1.00 | 1.28 | 1.76 | 0.00 | 8.96 | 4.73 | 1.63 | 2.54 |
time (sec) |
N/A | 0.043 | 0.143 | 0.665 | 0.000 | 0.310 | 4.982 | 0.279 | 10.844 |
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 | 94 | 91 | 93 | 146 | 0 | 681 | 377 | 116 | 213 |
N.S. |
1 | 0.97 | 0.99 | 1.55 | 0.00 | 7.24 | 4.01 | 1.23 | 2.27 |
time (sec) |
N/A | 0.030 | 0.117 | 0.473 | 0.000 | 0.324 | 1.389 | 0.270 | 10.816 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 15 | 15 | 14 | 39 | 44 | 14 | 43 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.88 | 2.44 | 2.75 | 0.88 | 2.69 |
time (sec) |
N/A | 0.003 | 0.013 | 0.644 | 0.187 | 0.282 | 0.455 | 0.272 | 0.059 |
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 | 397 | 397 | 356 | 875 | 0 | 6667 | 0 | 1183 | 2461 |
N.S. |
1 | 1.00 | 0.90 | 2.20 | 0.00 | 16.79 | 0.00 | 2.98 | 6.20 |
time (sec) |
N/A | 0.574 | 0.699 | 0.744 | 0.000 | 56.928 | 0.000 | 0.282 | 14.756 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 431 | 431 | 552 | 809 | 0 | 1445 | 3818 | 796 | 2712 |
N.S. |
1 | 1.00 | 1.28 | 1.88 | 0.00 | 3.35 | 8.86 | 1.85 | 6.29 |
time (sec) |
N/A | 0.505 | 5.577 | 0.842 | 0.000 | 0.537 | 1.292 | 0.292 | 21.831 |
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 | 312 | 312 | 375 | 515 | 0 | 985 | 2142 | 523 | 1679 |
N.S. |
1 | 1.00 | 1.20 | 1.65 | 0.00 | 3.16 | 6.87 | 1.68 | 5.38 |
time (sec) |
N/A | 0.280 | 3.212 | 0.691 | 0.000 | 0.453 | 1.135 | 0.294 | 14.143 |
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 | 195 | 195 | 236 | 288 | 0 | 617 | 1136 | 309 | 876 |
N.S. |
1 | 1.00 | 1.21 | 1.48 | 0.00 | 3.16 | 5.83 | 1.58 | 4.49 |
time (sec) |
N/A | 0.213 | 1.805 | 0.813 | 0.000 | 0.426 | 1.029 | 0.300 | 12.590 |
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 | 122 | 122 | 174 | 141 | 0 | 343 | 508 | 159 | 395 |
N.S. |
1 | 1.00 | 1.43 | 1.16 | 0.00 | 2.81 | 4.16 | 1.30 | 3.24 |
time (sec) |
N/A | 0.061 | 1.151 | 0.698 | 0.000 | 0.442 | 1.113 | 0.300 | 11.706 |
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 | 18 | 18 | 17 | 15 | 14 | 14 | 60 | 14 | 14 |
N.S. |
1 | 1.00 | 0.94 | 0.83 | 0.78 | 0.78 | 3.33 | 0.78 | 0.78 |
time (sec) |
N/A | 0.004 | 0.008 | 0.425 | 0.199 | 0.374 | 0.071 | 0.291 | 10.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 199 | 199 | 227 | 297 | 0 | 1196 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.49 | 0.00 | 6.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.166 | 1.413 | 0.727 | 0.000 | 10.742 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 203 | 203 | 210 | 561 | 0 | 1964 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 2.76 | 0.00 | 9.67 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.140 | 1.623 | 0.560 | 0.000 | 13.538 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 280 | 280 | 389 | 1823 | 0 | 3684 | 0 | 1148 | 0 |
N.S. |
1 | 1.00 | 1.39 | 6.51 | 0.00 | 13.16 | 0.00 | 4.10 | 0.00 |
time (sec) |
N/A | 0.205 | 10.862 | 0.695 | 0.000 | 181.625 | 0.000 | 0.610 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 217 | 217 | 214 | 2401 | 0 | 2040 | 0 | 2677 | 0 |
N.S. |
1 | 1.00 | 0.99 | 11.06 | 0.00 | 9.40 | 0.00 | 12.34 | 0.00 |
time (sec) |
N/A | 0.150 | 10.287 | 0.914 | 0.000 | 2.333 | 0.000 | 0.683 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 307 | 307 | 290 | 3788 | 0 | 3996 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 12.34 | 0.00 | 13.02 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.303 | 10.513 | 1.154 | 0.000 | 12.179 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 430 | 430 | 401 | 6447 | 0 | 6858 | 0 | 10398 | 0 |
N.S. |
1 | 1.00 | 0.93 | 14.99 | 0.00 | 15.95 | 0.00 | 24.18 | 0.00 |
time (sec) |
N/A | 0.440 | 11.760 | 1.139 | 0.000 | 65.717 | 0.000 | 7.874 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 379 | 379 | 616 | 907 | 0 | 1587 | 6965 | 883 | 0 |
N.S. |
1 | 1.00 | 1.63 | 2.39 | 0.00 | 4.19 | 18.38 | 2.33 | 0.00 |
time (sec) |
N/A | 0.324 | 6.848 | 0.650 | 0.000 | 0.529 | 1.203 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 242 | 242 | 391 | 529 | 0 | 1015 | 3582 | 536 | 0 |
N.S. |
1 | 1.00 | 1.62 | 2.19 | 0.00 | 4.19 | 14.80 | 2.21 | 0.00 |
time (sec) |
N/A | 0.262 | 3.319 | 0.619 | 0.000 | 0.493 | 1.123 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 224 | 259 | 0 | 559 | 1564 | 276 | 0 |
N.S. |
1 | 1.00 | 1.40 | 1.62 | 0.00 | 3.49 | 9.78 | 1.72 | 0.00 |
time (sec) |
N/A | 0.084 | 2.090 | 0.499 | 0.000 | 0.426 | 1.162 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 17 | 15 | 14 | 49 | 136 | 14 | 14 |
N.S. |
1 | 1.00 | 0.94 | 0.83 | 0.78 | 2.72 | 7.56 | 0.78 | 0.78 |
time (sec) |
N/A | 0.004 | 0.015 | 0.439 | 0.197 | 0.313 | 0.118 | 0.259 | 11.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 360 | 360 | 353 | 538 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.391 | 2.860 | 0.731 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 303 | 303 | 395 | 767 | 0 | 2231 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.30 | 2.53 | 0.00 | 7.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.327 | 10.658 | 0.600 | 0.000 | 91.163 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 309 | 309 | 544 | 1317 | 0 | 3955 | 0 | 1210 | 0 |
N.S. |
1 | 1.00 | 1.76 | 4.26 | 0.00 | 12.80 | 0.00 | 3.92 | 0.00 |
time (sec) |
N/A | 0.239 | 11.473 | 0.874 | 0.000 | 128.199 | 0.000 | 0.560 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 462 | 462 | 485 | 2273 | 0 | 0 | 0 | 2889 | 0 |
N.S. |
1 | 1.00 | 1.05 | 4.92 | 0.00 | 0.00 | 0.00 | 6.25 | 0.00 |
time (sec) |
N/A | 0.413 | 11.840 | 0.858 | 0.000 | 0.000 | 0.000 | 4.450 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 446 | 446 | 345 | 1422 | 0 | 2343 | 21208 | 1341 | 0 |
N.S. |
1 | 1.00 | 0.77 | 3.19 | 0.00 | 5.25 | 47.55 | 3.01 | 0.00 |
time (sec) |
N/A | 0.408 | 10.709 | 0.953 | 0.000 | 0.938 | 1.389 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 289 | 289 | 596 | 851 | 0 | 1523 | 10924 | 827 | 0 |
N.S. |
1 | 1.00 | 2.06 | 2.94 | 0.00 | 5.27 | 37.80 | 2.86 | 0.00 |
time (sec) |
N/A | 0.352 | 6.730 | 0.614 | 0.000 | 0.757 | 1.201 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 198 | 342 | 418 | 0 | 841 | 4765 | 425 | 0 |
N.S. |
1 | 1.00 | 1.73 | 2.11 | 0.00 | 4.25 | 24.07 | 2.15 | 0.00 |
time (sec) |
N/A | 0.107 | 3.805 | 0.698 | 0.000 | 0.534 | 1.262 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 17 | 15 | 14 | 86 | 243 | 14 | 14 |
N.S. |
1 | 1.00 | 0.94 | 0.83 | 0.78 | 4.78 | 13.50 | 0.78 | 0.78 |
time (sec) |
N/A | 0.004 | 0.023 | 0.421 | 0.190 | 0.454 | 0.214 | 0.293 | 10.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 627 | 627 | 622 | 998 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.727 | 9.053 | 0.954 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 508 | 508 | 659 | 1192 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.30 | 2.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.504 | 11.556 | 0.598 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 464 | 464 | 535 | 1703 | 0 | 0 | 0 | 2125 | 0 |
N.S. |
1 | 1.00 | 1.15 | 3.67 | 0.00 | 0.00 | 0.00 | 4.58 | 0.00 |
time (sec) |
N/A | 0.529 | 11.406 | 0.924 | 0.000 | 0.000 | 0.000 | 0.585 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 473 | 473 | 535 | 2650 | 0 | 0 | 0 | 3027 | 0 |
N.S. |
1 | 1.00 | 1.13 | 5.60 | 0.00 | 0.00 | 0.00 | 6.40 | 0.00 |
time (sec) |
N/A | 0.509 | 11.855 | 0.912 | 0.000 | 0.000 | 0.000 | 4.987 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 245 | 245 | 202 | 248 | 0 | 545 | 806 | 261 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.01 | 0.00 | 2.22 | 3.29 | 1.07 | 0.00 |
time (sec) |
N/A | 0.196 | 1.245 | 0.681 | 0.000 | 0.403 | 1.128 | 0.345 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 128 | 134 | 0 | 335 | 468 | 146 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.91 | 0.00 | 2.26 | 3.16 | 0.99 | 0.00 |
time (sec) |
N/A | 0.117 | 0.727 | 0.611 | 0.000 | 0.353 | 0.958 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 84 | 73 | 0 | 197 | 236 | 78 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.00 | 2.35 | 2.81 | 0.93 | 0.00 |
time (sec) |
N/A | 0.037 | 0.584 | 0.506 | 0.000 | 0.345 | 1.117 | 0.335 | 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 | 16 | 16 | 15 | 15 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.004 | 0.006 | 0.438 | 0.186 | 0.308 | 0.070 | 0.289 | 10.757 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 198 | 199 | 0 | 1048 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.49 | 1.50 | 0.00 | 7.88 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.064 | 0.845 | 0.710 | 0.000 | 1.281 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 150 | 437 | 0 | 686 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.06 | 3.10 | 0.00 | 4.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.067 | 0.628 | 0.545 | 0.000 | 0.438 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 225 | 225 | 220 | 842 | 0 | 1500 | 0 | 1068 | 0 |
N.S. |
1 | 1.00 | 0.98 | 3.74 | 0.00 | 6.67 | 0.00 | 4.75 | 0.00 |
time (sec) |
N/A | 0.176 | 10.221 | 0.575 | 0.000 | 0.830 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 328 | 328 | 323 | 1537 | 0 | 2998 | 0 | 2742 | 0 |
N.S. |
1 | 1.00 | 0.98 | 4.69 | 0.00 | 9.14 | 0.00 | 8.36 | 0.00 |
time (sec) |
N/A | 0.290 | 10.356 | 0.724 | 0.000 | 3.724 | 0.000 | 0.358 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 247 | 640 | 0 | 965 | 0 | 573 | 0 |
N.S. |
1 | 1.00 | 1.22 | 3.17 | 0.00 | 4.78 | 0.00 | 2.84 | 0.00 |
time (sec) |
N/A | 0.130 | 2.918 | 0.928 | 0.000 | 0.582 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 166 | 447 | 0 | 615 | 0 | 360 | 0 |
N.S. |
1 | 1.00 | 1.08 | 2.92 | 0.00 | 4.02 | 0.00 | 2.35 | 0.00 |
time (sec) |
N/A | 0.103 | 1.203 | 0.723 | 0.000 | 0.509 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 97 | 165 | 0 | 363 | 0 | 199 | 0 |
N.S. |
1 | 1.00 | 1.04 | 1.77 | 0.00 | 3.90 | 0.00 | 2.14 | 0.00 |
time (sec) |
N/A | 0.036 | 0.688 | 0.599 | 0.000 | 0.426 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 60 | 211 | 0 | 211 | 0 | 96 | 161 |
N.S. |
1 | 1.00 | 1.00 | 3.52 | 0.00 | 3.52 | 0.00 | 1.60 | 2.68 |
time (sec) |
N/A | 0.019 | 0.475 | 0.726 | 0.000 | 0.548 | 0.000 | 0.288 | 11.632 |
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 | 16 | 16 | 15 | 15 | 14 | 14 | 15 | 14 | 14 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.88 | 0.88 | 0.94 | 0.88 | 0.88 |
time (sec) |
N/A | 0.004 | 0.005 | 0.434 | 0.196 | 0.415 | 0.112 | 0.279 | 10.901 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 133 | 445 | 0 | 918 | 0 | 515 | 0 |
N.S. |
1 | 1.00 | 0.80 | 2.68 | 0.00 | 5.53 | 0.00 | 3.10 | 0.00 |
time (sec) |
N/A | 0.087 | 1.135 | 0.714 | 0.000 | 0.841 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 248 | 248 | 215 | 1065 | 0 | 2102 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 4.29 | 0.00 | 8.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.195 | 10.364 | 0.533 | 0.000 | 2.360 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 208 | 346 | 1971 | 0 | 1493 | 0 | 781 | 0 |
N.S. |
1 | 1.00 | 1.66 | 9.48 | 0.00 | 7.18 | 0.00 | 3.75 | 0.00 |
time (sec) |
N/A | 0.146 | 2.643 | 0.973 | 0.000 | 1.557 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 231 | 1160 | 0 | 958 | 0 | 502 | 0 |
N.S. |
1 | 1.00 | 1.46 | 7.34 | 0.00 | 6.06 | 0.00 | 3.18 | 0.00 |
time (sec) |
N/A | 0.081 | 1.987 | 0.697 | 0.000 | 1.347 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 110 | 123 | 0 | 194 | 0 | 289 | 122 |
N.S. |
1 | 1.00 | 1.49 | 1.66 | 0.00 | 2.62 | 0.00 | 3.91 | 1.65 |
time (sec) |
N/A | 0.023 | 1.383 | 0.888 | 0.000 | 1.035 | 0.000 | 0.305 | 11.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 64 | 67 | 0 | 145 | 0 | 197 | 66 |
N.S. |
1 | 1.00 | 1.08 | 1.14 | 0.00 | 2.46 | 0.00 | 3.34 | 1.12 |
time (sec) |
N/A | 0.015 | 1.038 | 0.757 | 0.000 | 0.897 | 0.000 | 0.309 | 11.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 17 | 15 | 14 | 51 | 76 | 14 | 14 |
N.S. |
1 | 1.00 | 0.94 | 0.83 | 0.78 | 2.83 | 4.22 | 0.78 | 0.78 |
time (sec) |
N/A | 0.004 | 0.013 | 0.465 | 0.189 | 0.421 | 0.446 | 0.287 | 10.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 291 | 291 | 249 | 847 | 0 | 3858 | 0 | 8951 | 0 |
N.S. |
1 | 1.00 | 0.86 | 2.91 | 0.00 | 13.26 | 0.00 | 30.76 | 0.00 |
time (sec) |
N/A | 0.210 | 10.287 | 0.730 | 0.000 | 1.936 | 0.000 | 0.482 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 423 | 423 | 384 | 1919 | 0 | 7442 | 0 | 6874 | 0 |
N.S. |
1 | 1.00 | 0.91 | 4.54 | 0.00 | 17.59 | 0.00 | 16.25 | 0.00 |
time (sec) |
N/A | 0.371 | 11.012 | 0.527 | 0.000 | 6.214 | 0.000 | 0.908 | 0.000 |
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 | 132 | 132 | 111 | 94 | 121 | 272 | 643 | 1026 | 118 |
N.S. |
1 | 1.00 | 0.84 | 0.71 | 0.92 | 2.06 | 4.87 | 7.77 | 0.89 |
time (sec) |
N/A | 0.068 | 0.167 | 0.435 | 0.204 | 0.277 | 0.420 | 0.275 | 0.099 |
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 | 132 | 132 | 109 | 94 | 121 | 220 | 173 | 673 | 118 |
N.S. |
1 | 1.00 | 0.83 | 0.71 | 0.92 | 1.67 | 1.31 | 5.10 | 0.89 |
time (sec) |
N/A | 0.049 | 0.087 | 0.659 | 0.188 | 0.284 | 1.084 | 0.268 | 10.816 |
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 | 132 | 132 | 110 | 97 | 121 | 167 | 173 | 380 | 118 |
N.S. |
1 | 1.00 | 0.83 | 0.73 | 0.92 | 1.27 | 1.31 | 2.88 | 0.89 |
time (sec) |
N/A | 0.045 | 0.077 | 0.580 | 0.195 | 0.272 | 0.981 | 0.255 | 0.069 |
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 | 130 | 130 | 109 | 97 | 121 | 116 | 172 | 159 | 118 |
N.S. |
1 | 1.00 | 0.84 | 0.75 | 0.93 | 0.89 | 1.32 | 1.22 | 0.91 |
time (sec) |
N/A | 0.042 | 0.077 | 0.592 | 0.189 | 0.261 | 0.929 | 0.268 | 0.069 |
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 | 126 | 126 | 106 | 97 | 129 | 126 | 150 | 166 | 133 |
N.S. |
1 | 1.00 | 0.84 | 0.77 | 1.02 | 1.00 | 1.19 | 1.32 | 1.06 |
time (sec) |
N/A | 0.044 | 0.078 | 0.585 | 0.212 | 0.285 | 2.754 | 0.270 | 0.076 |
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 | 128 | 128 | 108 | 99 | 126 | 137 | 536 | 153 | 139 |
N.S. |
1 | 1.00 | 0.84 | 0.77 | 0.98 | 1.07 | 4.19 | 1.20 | 1.09 |
time (sec) |
N/A | 0.043 | 0.088 | 0.596 | 0.199 | 0.272 | 0.347 | 0.278 | 10.936 |