Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 341 | 341 | 483 | 356 | 614 | 811 | 1013 | 1751 | 1029 | 364 |
N.S. |
1 | 1.00 | 1.42 | 1.04 | 1.80 | 2.38 | 2.97 | 5.13 | 3.02 | 1.07 |
time (sec) |
N/A | 0.575 | 0.422 | 0.990 | 0.039 | 0.085 | 1.774 | 0.139 | 0.170 | 1.879 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 247 | 304 | 255 | 376 | 519 | 620 | 1147 | 633 | 259 |
N.S. |
1 | 1.00 | 1.23 | 1.03 | 1.52 | 2.10 | 2.51 | 4.64 | 2.56 | 1.05 |
time (sec) |
N/A | 0.504 | 0.246 | 0.947 | 0.037 | 0.073 | 1.524 | 0.133 | 0.164 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 166 | 138 | 180 | 265 | 303 | 638 | 313 | 155 |
N.S. |
1 | 1.00 | 1.04 | 0.87 | 1.13 | 1.67 | 1.91 | 4.01 | 1.97 | 0.97 |
time (sec) |
N/A | 0.333 | 0.122 | 0.823 | 0.041 | 0.066 | 1.207 | 0.122 | 0.162 | 1.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 70 | 61 | 80 | 123 | 124 | 261 | 119 | 80 |
N.S. |
1 | 1.00 | 0.86 | 0.75 | 0.99 | 1.52 | 1.53 | 3.22 | 1.47 | 0.99 |
time (sec) |
N/A | 0.224 | 0.045 | 0.575 | 0.031 | 0.071 | 0.823 | 0.128 | 0.158 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 133 | 162 | 170 | 0 | 468 | 236 | 278 | 402 | 231 |
N.S. |
1 | 0.85 | 1.04 | 1.09 | 0.00 | 3.00 | 1.51 | 1.78 | 2.58 | 1.48 |
time (sec) |
N/A | 0.270 | 0.272 | 0.590 | 0.000 | 0.087 | 13.547 | 0.131 | 0.160 | 1.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 215 | 186 | 191 | 0 | 884 | 0 | 250 | 989 | 219 |
N.S. |
1 | 1.18 | 1.02 | 1.05 | 0.00 | 4.86 | 0.00 | 1.37 | 5.43 | 1.20 |
time (sec) |
N/A | 0.349 | 0.482 | 0.473 | 0.000 | 0.100 | 0.000 | 0.130 | 0.162 | 1.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 282 | 253 | 264 | 0 | 1420 | 0 | 497 | 1706 | 353 |
N.S. |
1 | 1.15 | 1.03 | 1.08 | 0.00 | 5.80 | 0.00 | 2.03 | 6.96 | 1.44 |
time (sec) |
N/A | 0.471 | 0.920 | 0.508 | 0.000 | 0.159 | 0.000 | 0.136 | 0.165 | 2.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 289 | 374 | 376 | 0 | 2256 | 0 | 852 | 2619 | 644 |
N.S. |
1 | 0.90 | 1.16 | 1.17 | 0.00 | 7.01 | 0.00 | 2.65 | 8.13 | 2.00 |
time (sec) |
N/A | 0.473 | 1.487 | 0.527 | 0.000 | 0.206 | 0.000 | 0.145 | 0.170 | 2.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 422 | 334 | 562 | 536 | 0 | 3384 | 0 | 1350 | 3715 | 862 |
N.S. |
1 | 0.79 | 1.33 | 1.27 | 0.00 | 8.02 | 0.00 | 3.20 | 8.80 | 2.04 |
time (sec) |
N/A | 0.519 | 3.364 | 0.583 | 0.000 | 0.338 | 0.000 | 0.166 | 0.185 | 2.290 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 579 | 579 | 843 | 569 | 1152 | 1467 | 1909 | 2999 | 1941 | 692 |
N.S. |
1 | 1.00 | 1.46 | 0.98 | 1.99 | 2.53 | 3.30 | 5.18 | 3.35 | 1.20 |
time (sec) |
N/A | 0.981 | 0.953 | 1.060 | 0.044 | 0.105 | 2.403 | 0.156 | 0.198 | 1.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 411 | 411 | 547 | 412 | 695 | 919 | 1204 | 2001 | 1225 | 470 |
N.S. |
1 | 1.00 | 1.33 | 1.00 | 1.69 | 2.24 | 2.93 | 4.87 | 2.98 | 1.14 |
time (sec) |
N/A | 0.698 | 0.467 | 1.006 | 0.044 | 0.082 | 2.025 | 0.140 | 0.168 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 248 | 308 | 255 | 376 | 519 | 620 | 1147 | 633 | 259 |
N.S. |
1 | 1.00 | 1.24 | 1.03 | 1.52 | 2.09 | 2.50 | 4.62 | 2.55 | 1.04 |
time (sec) |
N/A | 0.489 | 0.236 | 0.903 | 0.047 | 0.077 | 1.645 | 0.135 | 0.200 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 130 | 116 | 165 | 244 | 257 | 486 | 251 | 115 |
N.S. |
1 | 1.00 | 1.03 | 0.92 | 1.31 | 1.94 | 2.04 | 3.86 | 1.99 | 0.91 |
time (sec) |
N/A | 0.282 | 0.083 | 0.674 | 0.040 | 0.067 | 1.010 | 0.125 | 0.193 | 1.941 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 255 | 277 | 310 | 0 | 956 | 486 | 581 | 865 | 571 |
N.S. |
1 | 0.99 | 1.08 | 1.21 | 0.00 | 3.72 | 1.89 | 2.26 | 3.37 | 2.22 |
time (sec) |
N/A | 0.455 | 0.457 | 0.496 | 0.000 | 0.097 | 12.137 | 0.140 | 0.175 | 2.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 292 | 304 | 322 | 0 | 1738 | 0 | 482 | 1921 | 570 |
N.S. |
1 | 1.18 | 1.23 | 1.30 | 0.00 | 7.01 | 0.00 | 1.94 | 7.75 | 2.30 |
time (sec) |
N/A | 0.455 | 0.762 | 0.546 | 0.000 | 0.124 | 0.000 | 0.143 | 0.165 | 2.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 352 | 435 | 465 | 492 | 0 | 2678 | 0 | 903 | 3292 | 639 |
N.S. |
1 | 1.24 | 1.32 | 1.40 | 0.00 | 7.61 | 0.00 | 2.57 | 9.35 | 1.82 |
time (sec) |
N/A | 0.583 | 1.262 | 0.639 | 0.000 | 0.254 | 0.000 | 0.157 | 0.194 | 2.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 484 | 587 | 625 | 621 | 0 | 3796 | 0 | 1561 | 4809 | 931 |
N.S. |
1 | 1.21 | 1.29 | 1.28 | 0.00 | 7.84 | 0.00 | 3.23 | 9.94 | 1.92 |
time (sec) |
N/A | 0.795 | 1.984 | 0.704 | 0.000 | 0.380 | 0.000 | 0.162 | 0.204 | 2.326 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 640 | 588 | 904 | 872 | 0 | 5434 | 0 | 2457 | 6626 | 1670 |
N.S. |
1 | 0.92 | 1.41 | 1.36 | 0.00 | 8.49 | 0.00 | 3.84 | 10.35 | 2.61 |
time (sec) |
N/A | 0.815 | 4.377 | 0.794 | 0.000 | 0.595 | 0.000 | 0.187 | 0.244 | 2.838 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 242 | 197 | 214 | 239 | 646 | 355 | 330 | 481 | 413 |
N.S. |
1 | 1.08 | 0.88 | 0.95 | 1.06 | 2.87 | 1.58 | 1.47 | 2.14 | 1.84 |
time (sec) |
N/A | 0.457 | 0.277 | 0.333 | 0.126 | 0.084 | 12.525 | 0.134 | 0.168 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 151 | 131 | 144 | 152 | 402 | 223 | 196 | 295 | 263 |
N.S. |
1 | 1.03 | 0.89 | 0.98 | 1.03 | 2.73 | 1.52 | 1.33 | 2.01 | 1.79 |
time (sec) |
N/A | 0.290 | 0.172 | 0.316 | 0.138 | 0.085 | 9.051 | 0.120 | 0.171 | 1.910 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 77 | 81 | 83 | 91 | 216 | 122 | 102 | 153 | 136 |
N.S. |
1 | 0.89 | 0.93 | 0.95 | 1.05 | 2.48 | 1.40 | 1.17 | 1.76 | 1.56 |
time (sec) |
N/A | 0.203 | 0.096 | 0.275 | 0.122 | 0.082 | 9.834 | 0.127 | 0.162 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 55 | 53 | 46 | 60 | 108 | 70 | 55 | 71 | 45 |
N.S. |
1 | 1.02 | 0.98 | 0.85 | 1.11 | 2.00 | 1.30 | 1.02 | 1.31 | 0.83 |
time (sec) |
N/A | 0.188 | 0.046 | 0.267 | 0.107 | 0.098 | 1.671 | 0.123 | 0.163 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 107 | 101 | 103 | 0 | 443 | 196 | 109 | 134 | 2368 |
N.S. |
1 | 1.06 | 1.00 | 1.02 | 0.00 | 4.39 | 1.94 | 1.08 | 1.33 | 23.45 |
time (sec) |
N/A | 0.291 | 0.193 | 0.377 | 0.000 | 0.163 | 13.547 | 0.132 | 0.162 | 2.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 140 | 123 | 132 | 0 | 1012 | 0 | 140 | 516 | 1827 |
N.S. |
1 | 1.10 | 0.97 | 1.04 | 0.00 | 7.97 | 0.00 | 1.10 | 4.06 | 14.39 |
time (sec) |
N/A | 0.271 | 0.417 | 0.414 | 0.000 | 0.166 | 0.000 | 0.123 | 0.170 | 0.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 238 | 195 | 213 | 0 | 2210 | 0 | 292 | 1311 | 4852 |
N.S. |
1 | 1.14 | 0.94 | 1.02 | 0.00 | 10.62 | 0.00 | 1.40 | 6.30 | 23.33 |
time (sec) |
N/A | 0.404 | 0.757 | 0.442 | 0.000 | 0.537 | 0.000 | 0.136 | 0.175 | 3.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 241 | 236 | 217 | 238 | 638 | 355 | 330 | 481 | 413 |
N.S. |
1 | 1.08 | 1.06 | 0.97 | 1.07 | 2.86 | 1.59 | 1.48 | 2.16 | 1.85 |
time (sec) |
N/A | 0.417 | 0.272 | 0.336 | 0.113 | 0.108 | 11.208 | 0.131 | 0.166 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 150 | 157 | 145 | 152 | 400 | 223 | 196 | 295 | 263 |
N.S. |
1 | 1.03 | 1.08 | 0.99 | 1.04 | 2.74 | 1.53 | 1.34 | 2.02 | 1.80 |
time (sec) |
N/A | 0.277 | 0.175 | 0.304 | 0.113 | 0.083 | 8.870 | 0.131 | 0.162 | 1.940 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 77 | 91 | 86 | 90 | 214 | 122 | 102 | 153 | 136 |
N.S. |
1 | 0.89 | 1.05 | 0.99 | 1.03 | 2.46 | 1.40 | 1.17 | 1.76 | 1.56 |
time (sec) |
N/A | 0.199 | 0.115 | 0.269 | 0.117 | 0.091 | 10.106 | 0.123 | 0.165 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 55 | 53 | 46 | 60 | 108 | 70 | 55 | 71 | 45 |
N.S. |
1 | 1.02 | 0.98 | 0.85 | 1.11 | 2.00 | 1.30 | 1.02 | 1.31 | 0.83 |
time (sec) |
N/A | 0.182 | 0.045 | 0.323 | 0.115 | 0.119 | 1.618 | 0.128 | 0.164 | 1.939 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 107 | 101 | 103 | 0 | 444 | 199 | 109 | 134 | 2355 |
N.S. |
1 | 1.06 | 1.00 | 1.02 | 0.00 | 4.40 | 1.97 | 1.08 | 1.33 | 23.32 |
time (sec) |
N/A | 0.292 | 0.174 | 0.425 | 0.000 | 0.117 | 12.209 | 0.124 | 0.163 | 2.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 140 | 122 | 110 | 0 | 1002 | 0 | 137 | 520 | 1814 |
N.S. |
1 | 1.09 | 0.95 | 0.86 | 0.00 | 7.83 | 0.00 | 1.07 | 4.06 | 14.17 |
time (sec) |
N/A | 0.290 | 0.421 | 0.388 | 0.000 | 0.162 | 0.000 | 0.124 | 0.165 | 2.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 236 | 194 | 214 | 0 | 2205 | 0 | 291 | 1311 | 4839 |
N.S. |
1 | 1.15 | 0.95 | 1.04 | 0.00 | 10.76 | 0.00 | 1.42 | 6.40 | 23.60 |
time (sec) |
N/A | 0.431 | 0.842 | 0.408 | 0.000 | 0.520 | 0.000 | 0.136 | 0.169 | 3.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 427 | 0 | 456 | 513 | 0 | 1697 | 899 | 1050 | 1557 | 865 |
N.S. |
1 | 0.00 | 1.07 | 1.20 | 0.00 | 3.97 | 2.11 | 2.46 | 3.65 | 2.03 |
time (sec) |
N/A | 0.000 | 0.770 | 0.581 | 0.000 | 0.102 | 23.463 | 0.152 | 0.175 | 2.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 0 | 277 | 310 | 0 | 946 | 486 | 581 | 865 | 571 |
N.S. |
1 | 0.00 | 1.09 | 1.22 | 0.00 | 3.71 | 1.91 | 2.28 | 3.39 | 2.24 |
time (sec) |
N/A | 0.000 | 0.443 | 0.493 | 0.000 | 0.133 | 12.899 | 0.137 | 0.162 | 2.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 134 | 162 | 171 | 0 | 467 | 236 | 278 | 402 | 231 |
N.S. |
1 | 0.86 | 1.04 | 1.10 | 0.00 | 2.99 | 1.51 | 1.78 | 2.58 | 1.48 |
time (sec) |
N/A | 0.279 | 0.254 | 0.441 | 0.000 | 0.105 | 15.139 | 0.137 | 0.156 | 0.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 95 | 95 | 103 | 0 | 214 | 124 | 122 | 139 | 108 |
N.S. |
1 | 0.97 | 0.97 | 1.05 | 0.00 | 2.18 | 1.27 | 1.24 | 1.42 | 1.10 |
time (sec) |
N/A | 0.229 | 0.169 | 0.391 | 0.000 | 0.095 | 3.666 | 0.115 | 0.163 | 1.991 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 159 | 159 | 166 | 0 | 680 | 196 | 169 | 212 | 6793 |
N.S. |
1 | 1.07 | 1.07 | 1.11 | 0.00 | 4.56 | 1.32 | 1.13 | 1.42 | 45.59 |
time (sec) |
N/A | 0.399 | 0.441 | 0.682 | 0.000 | 0.543 | 34.982 | 0.124 | 0.155 | 3.380 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 222 | 188 | 223 | 0 | 2100 | 0 | 254 | 1168 | 11558 |
N.S. |
1 | 1.09 | 0.93 | 1.10 | 0.00 | 10.34 | 0.00 | 1.25 | 5.75 | 56.94 |
time (sec) |
N/A | 0.405 | 0.670 | 0.658 | 0.000 | 1.412 | 0.000 | 0.136 | 0.158 | 4.856 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 355 | 399 | 352 | 413 | 0 | 6490 | 0 | 743 | 3843 | 278260 |
N.S. |
1 | 1.12 | 0.99 | 1.16 | 0.00 | 18.28 | 0.00 | 2.09 | 10.83 | 783.83 |
time (sec) |
N/A | 0.708 | 2.138 | 0.825 | 0.000 | 26.663 | 0.000 | 0.159 | 0.188 | 15.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 588 | 656 | 710 | 766 | 0 | 0 | 0 | 1939 | 9171 | 533756 |
N.S. |
1 | 1.12 | 1.21 | 1.30 | 0.00 | 0.00 | 0.00 | 3.30 | 15.60 | 907.75 |
time (sec) |
N/A | 1.373 | 5.434 | 1.365 | 0.000 | 0.000 | 0.000 | 0.225 | 0.250 | 23.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 942 | 1032 | 5481 | 1522 | 0 | 0 | 0 | 4286 | 17810 | 875071 |
N.S. |
1 | 1.10 | 5.82 | 1.62 | 0.00 | 0.00 | 0.00 | 4.55 | 18.91 | 928.95 |
time (sec) |
N/A | 2.444 | 16.223 | 15.162 | 0.000 | 0.000 | 0.000 | 0.330 | 0.446 | 40.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 348 | 474 | 479 | 513 | 0 | 2878 | 0 | 830 | 3133 | 913 |
N.S. |
1 | 1.36 | 1.38 | 1.47 | 0.00 | 8.27 | 0.00 | 2.39 | 9.00 | 2.62 |
time (sec) |
N/A | 0.902 | 1.115 | 0.658 | 0.000 | 0.201 | 0.000 | 0.155 | 0.182 | 0.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 294 | 302 | 323 | 0 | 1741 | 0 | 484 | 1921 | 570 |
N.S. |
1 | 1.19 | 1.22 | 1.31 | 0.00 | 7.05 | 0.00 | 1.96 | 7.78 | 2.31 |
time (sec) |
N/A | 0.487 | 0.759 | 0.557 | 0.000 | 0.148 | 0.000 | 0.136 | 0.165 | 0.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 213 | 187 | 193 | 0 | 906 | 0 | 249 | 989 | 219 |
N.S. |
1 | 1.17 | 1.03 | 1.06 | 0.00 | 4.98 | 0.00 | 1.37 | 5.43 | 1.20 |
time (sec) |
N/A | 0.376 | 0.472 | 0.473 | 0.000 | 0.148 | 0.000 | 0.131 | 0.159 | 0.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 134 | 96 | 107 | 0 | 381 | 0 | 115 | 363 | 107 |
N.S. |
1 | 1.25 | 0.90 | 1.00 | 0.00 | 3.56 | 0.00 | 1.07 | 3.39 | 1.00 |
time (sec) |
N/A | 0.331 | 0.277 | 0.418 | 0.000 | 0.091 | 0.000 | 0.128 | 0.156 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 223 | 200 | 226 | 0 | 2088 | 0 | 253 | 1168 | 11557 |
N.S. |
1 | 1.09 | 0.98 | 1.11 | 0.00 | 10.24 | 0.00 | 1.24 | 5.73 | 56.65 |
time (sec) |
N/A | 0.431 | 0.599 | 0.596 | 0.000 | 1.566 | 0.000 | 0.137 | 0.165 | 5.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 334 | 276 | 306 | 0 | 8168 | 0 | 471 | 5334 | 26654 |
N.S. |
1 | 1.10 | 0.91 | 1.01 | 0.00 | 26.87 | 0.00 | 1.55 | 17.55 | 87.68 |
time (sec) |
N/A | 0.573 | 1.899 | 0.672 | 0.000 | 5.732 | 0.000 | 0.187 | 0.199 | 7.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 530 | 569 | 516 | 574 | 0 | 14998 | 0 | 983 | 13393 | 451052 |
N.S. |
1 | 1.07 | 0.97 | 1.08 | 0.00 | 28.30 | 0.00 | 1.85 | 25.27 | 851.04 |
time (sec) |
N/A | 1.215 | 6.984 | 1.155 | 0.000 | 89.796 | 0.000 | 0.179 | 0.267 | 21.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 872 | 938 | 6117 | 1143 | 0 | 0 | 0 | 2352 | 25836 | 783233 |
N.S. |
1 | 1.08 | 7.01 | 1.31 | 0.00 | 0.00 | 0.00 | 2.70 | 29.63 | 898.20 |
time (sec) |
N/A | 2.236 | 16.299 | 10.829 | 0.000 | 0.000 | 0.000 | 0.263 | 0.487 | 35.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1368 | 1456 | 12952 | 1940 | 0 | 0 | 0 | 4916 | 29 | 1195213 |
N.S. |
1 | 1.06 | 9.47 | 1.42 | 0.00 | 0.00 | 0.00 | 3.59 | 0.02 | 873.69 |
time (sec) |
N/A | 3.788 | 16.490 | 69.895 | 0.000 | 0.000 | 0.000 | 0.370 | 200.064 | 46.612 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 420 | 595 | 704 | 684 | 0 | 4303 | 0 | 1382 | 5248 | 1361 |
N.S. |
1 | 1.42 | 1.68 | 1.63 | 0.00 | 10.25 | 0.00 | 3.29 | 12.50 | 3.24 |
time (sec) |
N/A | 1.022 | 1.953 | 0.801 | 0.000 | 0.333 | 0.000 | 0.164 | 0.401 | 0.435 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 434 | 462 | 492 | 0 | 2688 | 0 | 904 | 3292 | 639 |
N.S. |
1 | 1.23 | 1.31 | 1.39 | 0.00 | 7.61 | 0.00 | 2.56 | 9.33 | 1.81 |
time (sec) |
N/A | 0.644 | 1.273 | 0.704 | 0.000 | 0.311 | 0.000 | 0.160 | 0.176 | 0.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 289 | 262 | 264 | 0 | 1444 | 0 | 497 | 1706 | 353 |
N.S. |
1 | 1.17 | 1.06 | 1.07 | 0.00 | 5.85 | 0.00 | 2.01 | 6.91 | 1.43 |
time (sec) |
N/A | 0.502 | 0.935 | 0.530 | 0.000 | 0.202 | 0.000 | 0.135 | 0.162 | 0.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 144 | 142 | 136 | 0 | 736 | 0 | 234 | 687 | 222 |
N.S. |
1 | 0.99 | 0.98 | 0.94 | 0.00 | 5.08 | 0.00 | 1.61 | 4.74 | 1.53 |
time (sec) |
N/A | 0.265 | 0.575 | 0.394 | 0.000 | 0.127 | 0.000 | 0.138 | 0.157 | 0.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 405 | 373 | 413 | 0 | 6495 | 0 | 743 | 3843 | 278260 |
N.S. |
1 | 1.12 | 1.04 | 1.15 | 0.00 | 18.04 | 0.00 | 2.06 | 10.68 | 772.94 |
time (sec) |
N/A | 0.720 | 1.540 | 0.803 | 0.000 | 27.202 | 0.000 | 0.167 | 0.196 | 17.268 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 473 | 531 | 520 | 568 | 0 | 15006 | 0 | 984 | 13393 | 451051 |
N.S. |
1 | 1.12 | 1.10 | 1.20 | 0.00 | 31.73 | 0.00 | 2.08 | 28.32 | 953.60 |
time (sec) |
N/A | 0.925 | 8.705 | 1.273 | 0.000 | 91.619 | 0.000 | 0.177 | 0.270 | 23.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 762 | 817 | 6193 | 1019 | 0 | 0 | 0 | 3442 | 26875 | 794225 |
N.S. |
1 | 1.07 | 8.13 | 1.34 | 0.00 | 0.00 | 0.00 | 4.52 | 35.27 | 1042.29 |
time (sec) |
N/A | 1.655 | 16.286 | 13.435 | 0.000 | 0.000 | 0.000 | 0.403 | 0.482 | 38.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1204 | 1285 | 13191 | 1745 | 0 | 0 | 0 | 3092 | 48332 | 1218467 |
N.S. |
1 | 1.07 | 10.96 | 1.45 | 0.00 | 0.00 | 0.00 | 2.57 | 40.14 | 1012.02 |
time (sec) |
N/A | 2.928 | 16.498 | 95.632 | 0.000 | 0.000 | 0.000 | 0.367 | 16.471 | 48.258 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1821 | 1924 | 24162 | 3167 | 0 | 0 | 0 | 5728 | 29 | 0 |
N.S. |
1 | 1.06 | 13.27 | 1.74 | 0.00 | 0.00 | 0.00 | 3.15 | 0.02 | 0.00 |
time (sec) |
N/A | 4.748 | 16.937 | 362.917 | 0.000 | 0.000 | 0.000 | 0.526 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 341 | 341 | 487 | 356 | 614 | 998 | 1013 | 2956 | 1293 | 364 |
N.S. |
1 | 1.00 | 1.43 | 1.04 | 1.80 | 2.93 | 2.97 | 8.67 | 3.79 | 1.07 |
time (sec) |
N/A | 0.621 | 0.470 | 0.942 | 0.038 | 0.124 | 2.078 | 0.160 | 0.163 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 247 | 311 | 255 | 376 | 658 | 620 | 1968 | 821 | 259 |
N.S. |
1 | 1.00 | 1.26 | 1.03 | 1.52 | 2.66 | 2.51 | 7.97 | 3.32 | 1.05 |
time (sec) |
N/A | 0.512 | 0.252 | 0.947 | 0.047 | 0.093 | 1.765 | 0.149 | 0.150 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 169 | 139 | 180 | 349 | 303 | 1124 | 425 | 155 |
N.S. |
1 | 1.00 | 1.06 | 0.87 | 1.13 | 2.19 | 1.91 | 7.07 | 2.67 | 0.97 |
time (sec) |
N/A | 0.346 | 0.136 | 0.844 | 0.039 | 0.078 | 1.384 | 0.136 | 0.161 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 70 | 61 | 80 | 172 | 124 | 473 | 171 | 80 |
N.S. |
1 | 1.00 | 0.86 | 0.75 | 0.99 | 2.12 | 1.53 | 5.84 | 2.11 | 0.99 |
time (sec) |
N/A | 0.228 | 0.050 | 0.645 | 0.029 | 0.073 | 0.913 | 0.123 | 0.158 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 162 | 246 | 266 | 0 | 854 | 345 | 497 | 835 | 497 |
N.S. |
1 | 0.83 | 1.26 | 1.36 | 0.00 | 4.36 | 1.76 | 2.54 | 4.26 | 2.54 |
time (sec) |
N/A | 0.279 | 0.344 | 0.444 | 0.000 | 0.105 | 14.749 | 0.137 | 0.166 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 245 | 287 | 292 | 0 | 928 | 0 | 518 | 1045 | 383 |
N.S. |
1 | 0.99 | 1.16 | 1.18 | 0.00 | 3.76 | 0.00 | 2.10 | 4.23 | 1.55 |
time (sec) |
N/A | 0.366 | 0.638 | 0.494 | 0.000 | 0.141 | 0.000 | 0.139 | 0.164 | 0.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 313 | 273 | 275 | 0 | 1500 | 0 | 541 | 1779 | 449 |
N.S. |
1 | 1.13 | 0.98 | 0.99 | 0.00 | 5.40 | 0.00 | 1.95 | 6.40 | 1.62 |
time (sec) |
N/A | 0.488 | 0.862 | 0.506 | 0.000 | 0.165 | 0.000 | 0.141 | 0.173 | 0.250 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 312 | 391 | 389 | 0 | 2236 | 0 | 881 | 2616 | 756 |
N.S. |
1 | 0.94 | 1.18 | 1.18 | 0.00 | 6.76 | 0.00 | 2.66 | 7.90 | 2.28 |
time (sec) |
N/A | 0.494 | 1.556 | 0.531 | 0.000 | 0.197 | 0.000 | 0.150 | 0.172 | 0.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 414 | 322 | 557 | 538 | 0 | 3224 | 0 | 1320 | 3637 | 863 |
N.S. |
1 | 0.78 | 1.35 | 1.30 | 0.00 | 7.79 | 0.00 | 3.19 | 8.79 | 2.08 |
time (sec) |
N/A | 0.489 | 3.269 | 0.543 | 0.000 | 0.318 | 0.000 | 0.173 | 0.186 | 0.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 579 | 579 | 850 | 569 | 1152 | 1773 | 1909 | 4992 | 2377 | 692 |
N.S. |
1 | 1.00 | 1.47 | 0.98 | 1.99 | 3.06 | 3.30 | 8.62 | 4.11 | 1.20 |
time (sec) |
N/A | 0.999 | 0.933 | 1.090 | 0.041 | 0.102 | 2.597 | 0.190 | 0.203 | 2.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 411 | 411 | 554 | 412 | 695 | 1128 | 1204 | 3372 | 1537 | 470 |
N.S. |
1 | 1.00 | 1.35 | 1.00 | 1.69 | 2.74 | 2.93 | 8.20 | 3.74 | 1.14 |
time (sec) |
N/A | 0.711 | 0.543 | 1.043 | 0.040 | 0.098 | 2.061 | 0.165 | 0.178 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 248 | 315 | 255 | 376 | 658 | 620 | 1968 | 821 | 259 |
N.S. |
1 | 1.00 | 1.27 | 1.03 | 1.52 | 2.65 | 2.50 | 7.94 | 3.31 | 1.04 |
time (sec) |
N/A | 0.470 | 0.273 | 0.882 | 0.046 | 0.079 | 1.699 | 0.140 | 0.168 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 133 | 118 | 165 | 323 | 257 | 854 | 339 | 115 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.31 | 2.56 | 2.04 | 6.78 | 2.69 | 0.91 |
time (sec) |
N/A | 0.271 | 0.101 | 0.645 | 0.035 | 0.073 | 1.083 | 0.134 | 0.157 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 284 | 408 | 480 | 0 | 1630 | 677 | 944 | 1635 | 855 |
N.S. |
1 | 0.95 | 1.36 | 1.61 | 0.00 | 5.45 | 2.26 | 3.16 | 5.47 | 2.86 |
time (sec) |
N/A | 0.486 | 0.568 | 0.553 | 0.000 | 0.156 | 12.333 | 0.144 | 0.161 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 321 | 322 | 470 | 495 | 0 | 1822 | 0 | 941 | 2025 | 715 |
N.S. |
1 | 1.00 | 1.46 | 1.54 | 0.00 | 5.68 | 0.00 | 2.93 | 6.31 | 2.23 |
time (sec) |
N/A | 0.503 | 0.986 | 0.602 | 0.000 | 0.152 | 0.000 | 0.151 | 0.173 | 2.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 422 | 468 | 505 | 510 | 0 | 2866 | 0 | 1040 | 3464 | 856 |
N.S. |
1 | 1.11 | 1.20 | 1.21 | 0.00 | 6.79 | 0.00 | 2.46 | 8.21 | 2.03 |
time (sec) |
N/A | 0.648 | 1.416 | 0.609 | 0.000 | 0.233 | 0.000 | 0.168 | 0.198 | 2.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 517 | 608 | 674 | 673 | 0 | 3942 | 0 | 1653 | 4947 | 1109 |
N.S. |
1 | 1.18 | 1.30 | 1.30 | 0.00 | 7.62 | 0.00 | 3.20 | 9.57 | 2.15 |
time (sec) |
N/A | 0.810 | 2.356 | 0.721 | 0.000 | 0.385 | 0.000 | 0.171 | 0.202 | 0.409 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 650 | 617 | 920 | 896 | 0 | 5410 | 0 | 2444 | 6644 | 1797 |
N.S. |
1 | 0.95 | 1.42 | 1.38 | 0.00 | 8.32 | 0.00 | 3.76 | 10.22 | 2.76 |
time (sec) |
N/A | 0.822 | 4.365 | 0.779 | 0.000 | 0.566 | 0.000 | 0.189 | 0.237 | 3.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 469 | 0 | 643 | 774 | 0 | 2737 | 1171 | 1557 | 2725 | 1247 |
N.S. |
1 | 0.00 | 1.37 | 1.65 | 0.00 | 5.84 | 2.50 | 3.32 | 5.81 | 2.66 |
time (sec) |
N/A | 0.000 | 0.927 | 0.660 | 0.000 | 0.130 | 15.733 | 0.168 | 0.225 | 0.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 0 | 412 | 480 | 0 | 1616 | 677 | 944 | 1635 | 855 |
N.S. |
1 | 0.00 | 1.39 | 1.62 | 0.00 | 5.44 | 2.28 | 3.18 | 5.51 | 2.88 |
time (sec) |
N/A | 0.000 | 0.590 | 0.533 | 0.000 | 0.113 | 11.674 | 0.150 | 0.166 | 2.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 163 | 250 | 266 | 0 | 853 | 345 | 497 | 835 | 497 |
N.S. |
1 | 0.83 | 1.28 | 1.36 | 0.00 | 4.35 | 1.76 | 2.54 | 4.26 | 2.54 |
time (sec) |
N/A | 0.293 | 0.334 | 0.457 | 0.000 | 0.101 | 14.010 | 0.130 | 0.169 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 124 | 138 | 137 | 0 | 390 | 175 | 226 | 323 | 236 |
N.S. |
1 | 0.95 | 1.06 | 1.05 | 0.00 | 3.00 | 1.35 | 1.74 | 2.48 | 1.82 |
time (sec) |
N/A | 0.238 | 0.191 | 0.389 | 0.000 | 0.089 | 3.539 | 0.126 | 0.157 | 2.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 213 | 179 | 217 | 0 | 1213 | 252 | 307 | 512 | 13380 |
N.S. |
1 | 1.12 | 0.94 | 1.14 | 0.00 | 6.35 | 1.32 | 1.61 | 2.68 | 70.05 |
time (sec) |
N/A | 0.568 | 0.362 | 0.625 | 0.000 | 20.546 | 25.803 | 0.138 | 0.162 | 3.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 268 | 232 | 281 | 0 | 2136 | 0 | 399 | 1199 | 18554 |
N.S. |
1 | 1.09 | 0.94 | 1.14 | 0.00 | 8.65 | 0.00 | 1.62 | 4.85 | 75.12 |
time (sec) |
N/A | 0.585 | 1.027 | 0.707 | 0.000 | 12.388 | 0.000 | 0.142 | 0.176 | 9.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 348 | 381 | 357 | 390 | 0 | 6207 | 0 | 687 | 4005 | 283348 |
N.S. |
1 | 1.09 | 1.03 | 1.12 | 0.00 | 17.84 | 0.00 | 1.97 | 11.51 | 814.22 |
time (sec) |
N/A | 0.749 | 2.064 | 0.802 | 0.000 | 31.949 | 0.000 | 0.167 | 0.201 | 16.542 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 579 | 642 | 719 | 771 | 0 | 0 | 0 | 1853 | 9592 | 544718 |
N.S. |
1 | 1.11 | 1.24 | 1.33 | 0.00 | 0.00 | 0.00 | 3.20 | 16.57 | 940.79 |
time (sec) |
N/A | 1.250 | 5.906 | 1.217 | 0.000 | 0.000 | 0.000 | 0.235 | 0.252 | 24.802 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 932 | 1020 | 5574 | 1526 | 0 | 0 | 0 | 4118 | 18831 | 894172 |
N.S. |
1 | 1.09 | 5.98 | 1.64 | 0.00 | 0.00 | 0.00 | 4.42 | 20.20 | 959.41 |
time (sec) |
N/A | 2.272 | 16.288 | 22.644 | 0.000 | 0.000 | 0.000 | 0.336 | 0.473 | 38.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 424 | 504 | 710 | 767 | 0 | 3008 | 0 | 1485 | 3285 | 1602 |
N.S. |
1 | 1.19 | 1.67 | 1.81 | 0.00 | 7.09 | 0.00 | 3.50 | 7.75 | 3.78 |
time (sec) |
N/A | 0.873 | 1.591 | 0.758 | 0.000 | 0.218 | 0.000 | 0.165 | 0.196 | 0.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 324 | 467 | 496 | 0 | 1833 | 0 | 942 | 2025 | 715 |
N.S. |
1 | 1.01 | 1.45 | 1.54 | 0.00 | 5.69 | 0.00 | 2.93 | 6.29 | 2.22 |
time (sec) |
N/A | 0.484 | 1.003 | 0.595 | 0.000 | 0.206 | 0.000 | 0.156 | 0.190 | 0.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 243 | 288 | 291 | 0 | 944 | 0 | 517 | 1045 | 383 |
N.S. |
1 | 0.98 | 1.16 | 1.17 | 0.00 | 3.81 | 0.00 | 2.08 | 4.21 | 1.54 |
time (sec) |
N/A | 0.363 | 0.654 | 0.484 | 0.000 | 0.138 | 0.000 | 0.137 | 0.171 | 0.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 164 | 138 | 138 | 0 | 384 | 0 | 225 | 379 | 175 |
N.S. |
1 | 1.12 | 0.95 | 0.95 | 0.00 | 2.63 | 0.00 | 1.54 | 2.60 | 1.20 |
time (sec) |
N/A | 0.286 | 0.335 | 0.413 | 0.000 | 0.100 | 0.000 | 0.131 | 0.165 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 267 | 230 | 281 | 0 | 2120 | 0 | 398 | 1199 | 18557 |
N.S. |
1 | 1.08 | 0.93 | 1.14 | 0.00 | 8.58 | 0.00 | 1.61 | 4.85 | 75.13 |
time (sec) |
N/A | 0.561 | 1.003 | 0.781 | 0.000 | 14.099 | 0.000 | 0.146 | 0.178 | 8.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 348 | 339 | 348 | 0 | 4238 | 0 | 804 | 2886 | 38955 |
N.S. |
1 | 1.10 | 1.08 | 1.10 | 0.00 | 13.45 | 0.00 | 2.55 | 9.16 | 123.67 |
time (sec) |
N/A | 0.682 | 2.708 | 0.854 | 0.000 | 13.129 | 0.000 | 0.211 | 0.193 | 8.693 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 520 | 562 | 510 | 570 | 0 | 12461 | 0 | 958 | 8595 | 97983 |
N.S. |
1 | 1.08 | 0.98 | 1.10 | 0.00 | 23.96 | 0.00 | 1.84 | 16.53 | 188.43 |
time (sec) |
N/A | 1.115 | 6.078 | 1.139 | 0.000 | 23.599 | 0.000 | 0.193 | 0.256 | 114.839 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 856 | 918 | 6288 | 1136 | 0 | 0 | 0 | 2299 | 18011 | 671141 |
N.S. |
1 | 1.07 | 7.35 | 1.33 | 0.00 | 0.00 | 0.00 | 2.69 | 21.04 | 784.04 |
time (sec) |
N/A | 2.005 | 16.363 | 14.802 | 0.000 | 0.000 | 0.000 | 0.279 | 0.551 | 31.474 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1359 | 1443 | 16895 | 1909 | 0 | 0 | 0 | 4781 | 29 | 1058660 |
N.S. |
1 | 1.06 | 12.43 | 1.40 | 0.00 | 0.00 | 0.00 | 3.52 | 0.02 | 779.00 |
time (sec) |
N/A | 3.448 | 16.654 | 103.167 | 0.000 | 0.000 | 0.000 | 0.388 | 200.023 | 42.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 494 | 625 | 743 | 758 | 0 | 4563 | 0 | 1617 | 5520 | 1753 |
N.S. |
1 | 1.27 | 1.50 | 1.53 | 0.00 | 9.24 | 0.00 | 3.27 | 11.17 | 3.55 |
time (sec) |
N/A | 0.971 | 2.001 | 0.792 | 0.000 | 0.302 | 0.000 | 0.193 | 1.089 | 0.500 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 423 | 469 | 501 | 510 | 0 | 2866 | 0 | 1040 | 3464 | 856 |
N.S. |
1 | 1.11 | 1.18 | 1.21 | 0.00 | 6.78 | 0.00 | 2.46 | 8.19 | 2.02 |
time (sec) |
N/A | 0.660 | 1.329 | 0.629 | 0.000 | 0.260 | 0.000 | 0.162 | 0.189 | 0.400 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 317 | 275 | 276 | 0 | 1522 | 0 | 541 | 1779 | 449 |
N.S. |
1 | 1.14 | 0.99 | 0.99 | 0.00 | 5.46 | 0.00 | 1.94 | 6.38 | 1.61 |
time (sec) |
N/A | 0.511 | 0.888 | 0.555 | 0.000 | 0.176 | 0.000 | 0.129 | 0.167 | 0.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 166 | 139 | 146 | 0 | 706 | 0 | 226 | 681 | 257 |
N.S. |
1 | 1.09 | 0.91 | 0.96 | 0.00 | 4.64 | 0.00 | 1.49 | 4.48 | 1.69 |
time (sec) |
N/A | 0.280 | 0.528 | 0.444 | 0.000 | 0.180 | 0.000 | 0.128 | 0.162 | 2.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 388 | 365 | 388 | 0 | 6213 | 0 | 687 | 4007 | 283348 |
N.S. |
1 | 1.10 | 1.03 | 1.10 | 0.00 | 17.60 | 0.00 | 1.95 | 11.35 | 802.69 |
time (sec) |
N/A | 0.725 | 1.594 | 0.810 | 0.000 | 35.302 | 0.000 | 0.162 | 0.201 | 16.480 |