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 | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 89 | 125 | 509 | 0 | 497 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.47 | 5.99 | 0.00 | 5.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.266 | 0.139 | 4.486 | 0.000 | 0.408 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 87 | 138 | 992 | 408 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.23 | 3.54 | 25.44 | 10.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.188 | 0.060 | 2.726 | 0.431 | 0.387 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 55 | 48 | 33 | 47 | 0 | 0 | 74 |
N.S. |
1 | 1.00 | 1.67 | 1.45 | 1.00 | 1.42 | 0.00 | 0.00 | 2.24 |
time (sec) |
N/A | 0.235 | 0.095 | 2.250 | 0.206 | 0.259 | 0.000 | 0.000 | 18.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 76 | 74 | 77 | 96 | 96 | 0 | 0 | 123 |
N.S. |
1 | 0.97 | 0.95 | 0.99 | 1.23 | 1.23 | 0.00 | 0.00 | 1.58 |
time (sec) |
N/A | 0.261 | 0.156 | 3.635 | 0.210 | 0.303 | 0.000 | 0.000 | 22.952 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 137 | 100 | 120 | 191 | 171 | 0 | 0 | 723 |
N.S. |
1 | 1.04 | 0.76 | 0.91 | 1.45 | 1.30 | 0.00 | 0.00 | 5.48 |
time (sec) |
N/A | 0.314 | 0.271 | 5.022 | 0.211 | 0.588 | 0.000 | 0.000 | 30.640 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 160 | 130 | 169 | 250 | 136 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.76 | 0.99 | 1.46 | 0.80 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.338 | 6.908 | 5.043 | 0.217 | 0.326 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 106 | 93 | 115 | 141 | 98 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.82 | 1.01 | 1.24 | 0.86 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.288 | 2.612 | 1.459 | 0.209 | 0.306 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 60 | 64 | 59 | 57 | 67 | 0 | 48 | 155 |
N.S. |
1 | 0.97 | 1.03 | 0.95 | 0.92 | 1.08 | 0.00 | 0.77 | 2.50 |
time (sec) |
N/A | 0.234 | 0.941 | 0.101 | 0.211 | 0.277 | 0.000 | 0.369 | 24.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 78 | 113 | 1061 | 0 | 344 | 0 | 503 | 0 |
N.S. |
1 | 0.98 | 1.41 | 13.26 | 0.00 | 4.30 | 0.00 | 6.29 | 0.00 |
time (sec) |
N/A | 0.268 | 0.565 | 1.177 | 0.000 | 0.330 | 0.000 | 0.864 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 134 | 97 | 1714 | 0 | 547 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.77 | 13.60 | 0.00 | 4.34 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.332 | 0.263 | 1.086 | 0.000 | 0.376 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 177 | 200 | 100 | 3612 | 0 | 873 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 0.56 | 20.41 | 0.00 | 4.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.384 | 0.383 | 1.234 | 0.000 | 0.419 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 242 | 268 | 256 | 1162 | 0 | 813 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.06 | 4.80 | 0.00 | 3.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.486 | 6.295 | 9.328 | 0.000 | 5.907 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 194 | 229 | 833 | 0 | 703 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.31 | 4.76 | 0.00 | 4.02 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.376 | 3.333 | 7.286 | 0.000 | 1.825 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 125 | 190 | 532 | 0 | 607 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.57 | 4.40 | 0.00 | 5.02 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.312 | 1.102 | 5.306 | 0.000 | 0.674 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 75 | 168 | 515 | 2055 | 601 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 2.18 | 6.69 | 26.69 | 7.81 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.213 | 1.052 | 3.687 | 0.545 | 0.430 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 66 | 76 | 84 | 64 | 102 | 0 | 0 | 2151 |
N.S. |
1 | 0.97 | 1.12 | 1.24 | 0.94 | 1.50 | 0.00 | 0.00 | 31.63 |
time (sec) |
N/A | 0.251 | 1.274 | 3.986 | 0.210 | 0.343 | 0.000 | 0.000 | 26.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 117 | 102 | 142 | 156 | 189 | 0 | 0 | 124682 |
N.S. |
1 | 0.95 | 0.83 | 1.15 | 1.27 | 1.54 | 0.00 | 0.00 | 1013.67 |
time (sec) |
N/A | 0.292 | 0.534 | 4.528 | 0.208 | 0.667 | 0.000 | 0.000 | 40.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 183 | 176 | 126 | 217 | 282 | 314 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.69 | 1.19 | 1.54 | 1.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.346 | 0.739 | 7.085 | 0.199 | 2.338 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 219 | 195 | 182 | 217 | 334 | 189 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 0.83 | 0.99 | 1.53 | 0.86 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.343 | 3.114 | 5.671 | 0.218 | 0.464 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 138 | 129 | 147 | 195 | 138 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.88 | 1.01 | 1.34 | 0.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.299 | 2.189 | 1.531 | 0.209 | 0.385 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 88 | 90 | 86 | 101 | 0 | 70 | 26927 |
N.S. |
1 | 1.00 | 0.91 | 0.93 | 0.89 | 1.04 | 0.00 | 0.72 | 277.60 |
time (sec) |
N/A | 0.242 | 0.859 | 0.108 | 0.193 | 0.314 | 0.000 | 0.471 | 30.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 134 | 108 | 3290 | 0 | 592 | 0 | 1097 | 0 |
N.S. |
1 | 1.06 | 0.85 | 25.91 | 0.00 | 4.66 | 0.00 | 8.64 | 0.00 |
time (sec) |
N/A | 0.317 | 3.856 | 5.233 | 0.000 | 0.364 | 0.000 | 1.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 171 | 186 | 151 | 8689 | 0 | 941 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.88 | 50.81 | 0.00 | 5.50 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.371 | 1.032 | 5.541 | 0.000 | 0.435 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 234 | 263 | 129 | 8115 | 0 | 1307 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 0.55 | 34.68 | 0.00 | 5.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.468 | 1.311 | 6.063 | 0.000 | 0.557 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 288 | 315 | 1705 | 2211 | 0 | 1003 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 5.92 | 7.68 | 0.00 | 3.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.560 | 16.243 | 10.455 | 0.000 | 24.107 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 227 | 246 | 1315 | 1611 | 0 | 873 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 5.79 | 7.10 | 0.00 | 3.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.445 | 12.113 | 8.520 | 0.000 | 7.530 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 167 | 177 | 983 | 1592 | 0 | 879 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 5.89 | 9.53 | 0.00 | 5.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.365 | 8.398 | 7.014 | 0.000 | 2.094 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 135 | 1927 | 1263 | 0 | 881 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 15.42 | 10.10 | 0.00 | 7.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.278 | 15.750 | 5.537 | 0.000 | 0.711 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 108 | 108 | 136 | 94 | 192 | 0 | 0 | 336 |
N.S. |
1 | 1.02 | 1.02 | 1.28 | 0.89 | 1.81 | 0.00 | 0.00 | 3.17 |
time (sec) |
N/A | 0.272 | 1.561 | 5.666 | 0.197 | 0.714 | 0.000 | 0.000 | 29.970 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 154 | 138 | 225 | 216 | 320 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.87 | 1.42 | 1.37 | 2.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.315 | 4.513 | 7.221 | 0.203 | 2.353 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 226 | 211 | 173 | 332 | 373 | 460 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.77 | 1.47 | 1.65 | 2.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.362 | 4.934 | 6.231 | 0.198 | 9.338 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 123 | 0 | 286 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 2.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 4.196 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 182 | 180 | 253 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.345 | 3.665 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 117 | 115 | 178 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.274 | 2.397 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 68 | 0 | 0 | 0 | 0 | 0 | 79 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.16 |
time (sec) |
N/A | 0.225 | 0.790 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 19.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 1532 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 19.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.254 | 16.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 266 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.261 | 3.224 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 5878 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 66.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.278 | 25.843 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 3781 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 42.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.264 | 20.190 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 2137 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 25.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.224 | 14.980 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.252 | 0.998 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 128 | 126 | 132 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.285 | 1.583 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 192 | 197 | 149 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.345 | 1.443 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 62 | 72 | 97 | 129 | 82 | 0 | 66 | 61 |
N.S. |
1 | 0.84 | 0.97 | 1.31 | 1.74 | 1.11 | 0.00 | 0.89 | 0.82 |
time (sec) |
N/A | 0.418 | 0.036 | 0.862 | 0.187 | 0.262 | 0.000 | 0.303 | 19.402 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 49 | 58 | 75 | 81 | 69 | 0 | 53 | 49 |
N.S. |
1 | 0.88 | 1.04 | 1.34 | 1.45 | 1.23 | 0.00 | 0.95 | 0.88 |
time (sec) |
N/A | 0.342 | 0.027 | 0.550 | 0.197 | 0.240 | 0.000 | 0.286 | 19.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 32 | 42 | 47 | 45 | 56 | 0 | 39 | 33 |
N.S. |
1 | 0.84 | 1.11 | 1.24 | 1.18 | 1.47 | 0.00 | 1.03 | 0.87 |
time (sec) |
N/A | 0.278 | 0.018 | 0.378 | 0.182 | 0.249 | 0.000 | 0.276 | 18.012 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 26 | 17 | 16 | 32 | 0 | 16 | 16 |
N.S. |
1 | 1.00 | 1.62 | 1.06 | 1.00 | 2.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.144 | 0.002 | 0.171 | 0.197 | 0.246 | 0.000 | 0.261 | 18.292 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 20 | 31 | 24 | 26 | 31 | 0 | 45 | 19 |
N.S. |
1 | 1.05 | 1.63 | 1.26 | 1.37 | 1.63 | 0.00 | 2.37 | 1.00 |
time (sec) |
N/A | 0.221 | 0.016 | 0.152 | 0.277 | 0.239 | 0.000 | 0.266 | 18.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 31 | 36 | 34 | 40 | 75 | 0 | 80 | 31 |
N.S. |
1 | 0.84 | 0.97 | 0.92 | 1.08 | 2.03 | 0.00 | 2.16 | 0.84 |
time (sec) |
N/A | 0.280 | 0.020 | 0.190 | 0.273 | 0.243 | 0.000 | 0.274 | 18.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 50 | 36 | 44 | 50 | 109 | 0 | 111 | 41 |
N.S. |
1 | 0.91 | 0.65 | 0.80 | 0.91 | 1.98 | 0.00 | 2.02 | 0.75 |
time (sec) |
N/A | 0.348 | 0.044 | 0.254 | 0.280 | 0.245 | 0.000 | 0.291 | 18.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 61 | 36 | 54 | 60 | 147 | 0 | 139 | 51 |
N.S. |
1 | 0.84 | 0.49 | 0.74 | 0.82 | 2.01 | 0.00 | 1.90 | 0.70 |
time (sec) |
N/A | 0.417 | 0.016 | 0.324 | 0.281 | 0.240 | 0.000 | 0.314 | 19.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 94 | 137 | 108 | 126 | 114 | 0 | 121 | 102 |
N.S. |
1 | 0.96 | 1.40 | 1.10 | 1.29 | 1.16 | 0.00 | 1.23 | 1.04 |
time (sec) |
N/A | 0.439 | 0.037 | 0.898 | 0.206 | 0.247 | 0.000 | 0.289 | 18.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 68 | 93 | 85 | 97 | 95 | 0 | 98 | 78 |
N.S. |
1 | 0.97 | 1.33 | 1.21 | 1.39 | 1.36 | 0.00 | 1.40 | 1.11 |
time (sec) |
N/A | 0.345 | 0.023 | 0.585 | 0.192 | 0.250 | 0.000 | 0.285 | 0.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 48 | 55 | 58 | 72 | 0 | 60 | 41 |
N.S. |
1 | 1.00 | 1.20 | 1.38 | 1.45 | 1.80 | 0.00 | 1.50 | 1.02 |
time (sec) |
N/A | 0.248 | 0.014 | 0.342 | 0.191 | 0.246 | 0.000 | 0.280 | 18.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 35 | 30 | 38 | 40 | 0 | 40 | 22 |
N.S. |
1 | 1.00 | 1.46 | 1.25 | 1.58 | 1.67 | 0.00 | 1.67 | 0.92 |
time (sec) |
N/A | 0.237 | 0.041 | 0.199 | 0.198 | 0.248 | 0.000 | 0.266 | 18.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 50 | 31 | 27 | 28 | 0 | 34 | 28 |
N.S. |
1 | 1.00 | 1.67 | 1.03 | 0.90 | 0.93 | 0.00 | 1.13 | 0.93 |
time (sec) |
N/A | 0.268 | 0.034 | 0.283 | 0.204 | 0.232 | 0.000 | 0.275 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 47 | 71 | 49 | 43 | 45 | 0 | 57 | 43 |
N.S. |
1 | 0.94 | 1.42 | 0.98 | 0.86 | 0.90 | 0.00 | 1.14 | 0.86 |
time (sec) |
N/A | 0.299 | 0.021 | 0.431 | 0.198 | 0.257 | 0.000 | 0.280 | 18.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 70 | 81 | 78 | 60 | 74 | 0 | 79 | 56 |
N.S. |
1 | 0.80 | 0.93 | 0.90 | 0.69 | 0.85 | 0.00 | 0.91 | 0.64 |
time (sec) |
N/A | 0.302 | 0.237 | 0.685 | 0.183 | 0.253 | 0.000 | 0.282 | 18.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 58 | 61 | 58 | 43 | 56 | 0 | 57 | 42 |
N.S. |
1 | 0.89 | 0.94 | 0.89 | 0.66 | 0.86 | 0.00 | 0.88 | 0.65 |
time (sec) |
N/A | 0.293 | 0.151 | 0.475 | 0.191 | 0.236 | 0.000 | 0.274 | 18.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 36 | 35 | 34 | 37 | 0 | 34 | 28 |
N.S. |
1 | 1.00 | 0.84 | 0.81 | 0.79 | 0.86 | 0.00 | 0.79 | 0.65 |
time (sec) |
N/A | 0.269 | 0.069 | 0.366 | 0.186 | 0.234 | 0.000 | 0.278 | 17.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 15 | 31 | 0 | 15 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 2.07 | 0.00 | 1.00 | 1.13 |
time (sec) |
N/A | 0.143 | 0.001 | 0.161 | 0.183 | 0.246 | 0.000 | 0.267 | 18.417 |
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 | 31 | 31 | 33 | 24 | 37 | 28 | 51 | 37 | 25 |
N.S. |
1 | 1.00 | 1.06 | 0.77 | 1.19 | 0.90 | 1.65 | 1.19 | 0.81 |
time (sec) |
N/A | 0.199 | 0.026 | 0.188 | 0.271 | 0.249 | 2.475 | 0.281 | 19.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 59 | 45 | 44 | 73 | 49 | 0 | 73 | 67 |
N.S. |
1 | 0.97 | 0.74 | 0.72 | 1.20 | 0.80 | 0.00 | 1.20 | 1.10 |
time (sec) |
N/A | 0.268 | 0.104 | 0.333 | 0.274 | 0.257 | 0.000 | 0.274 | 18.806 |
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 | 89 | 85 | 68 | 61 | 103 | 68 | 0 | 96 | 91 |
N.S. |
1 | 0.96 | 0.76 | 0.69 | 1.16 | 0.76 | 0.00 | 1.08 | 1.02 |
time (sec) |
N/A | 0.339 | 0.108 | 0.498 | 0.268 | 0.265 | 0.000 | 0.281 | 19.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 165 | 258 | 180 | 200 | 168 | 0 | 221 | 170 |
N.S. |
1 | 1.00 | 1.56 | 1.09 | 1.21 | 1.02 | 0.00 | 1.34 | 1.03 |
time (sec) |
N/A | 0.303 | 0.048 | 1.380 | 0.194 | 0.261 | 0.000 | 0.302 | 18.832 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 136 | 187 | 147 | 166 | 143 | 0 | 183 | 134 |
N.S. |
1 | 1.05 | 1.45 | 1.14 | 1.29 | 1.11 | 0.00 | 1.42 | 1.04 |
time (sec) |
N/A | 0.302 | 0.031 | 1.027 | 0.194 | 0.255 | 0.000 | 0.307 | 18.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 105 | 109 | 107 | 119 | 116 | 0 | 120 | 86 |
N.S. |
1 | 1.15 | 1.20 | 1.18 | 1.31 | 1.27 | 0.00 | 1.32 | 0.95 |
time (sec) |
N/A | 0.261 | 0.026 | 0.645 | 0.203 | 0.258 | 0.000 | 0.290 | 18.690 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 59 | 80 | 69 | 87 | 94 | 0 | 79 | 55 |
N.S. |
1 | 1.05 | 1.43 | 1.23 | 1.55 | 1.68 | 0.00 | 1.41 | 0.98 |
time (sec) |
N/A | 0.257 | 0.051 | 0.517 | 0.184 | 0.248 | 0.000 | 0.294 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 44 | 72 | 55 | 63 | 66 | 0 | 70 | 48 |
N.S. |
1 | 0.90 | 1.47 | 1.12 | 1.29 | 1.35 | 0.00 | 1.43 | 0.98 |
time (sec) |
N/A | 0.245 | 0.052 | 0.418 | 0.198 | 0.251 | 0.000 | 0.287 | 17.975 |
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 | 53 | 48 | 106 | 67 | 55 | 59 | 0 | 76 | 44 |
N.S. |
1 | 0.91 | 2.00 | 1.26 | 1.04 | 1.11 | 0.00 | 1.43 | 0.83 |
time (sec) |
N/A | 0.254 | 0.040 | 0.474 | 0.182 | 0.265 | 0.000 | 0.287 | 18.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 95 | 96 | 134 | 103 | 120 | 0 | 152 | 94 |
N.S. |
1 | 0.90 | 0.91 | 1.26 | 0.97 | 1.13 | 0.00 | 1.43 | 0.89 |
time (sec) |
N/A | 0.293 | 0.350 | 1.094 | 0.200 | 0.250 | 0.000 | 0.328 | 18.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 72 | 75 | 104 | 81 | 94 | 0 | 114 | 70 |
N.S. |
1 | 0.90 | 0.94 | 1.30 | 1.01 | 1.18 | 0.00 | 1.42 | 0.88 |
time (sec) |
N/A | 0.267 | 0.306 | 0.839 | 0.189 | 0.243 | 0.000 | 0.305 | 18.593 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 48 | 48 | 71 | 71 | 69 | 0 | 76 | 44 |
N.S. |
1 | 0.91 | 0.91 | 1.34 | 1.34 | 1.30 | 0.00 | 1.43 | 0.83 |
time (sec) |
N/A | 0.250 | 0.208 | 0.619 | 0.190 | 0.246 | 0.000 | 0.302 | 18.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 44 | 41 | 46 | 44 | 58 | 0 | 49 | 42 |
N.S. |
1 | 1.10 | 1.02 | 1.15 | 1.10 | 1.45 | 0.00 | 1.22 | 1.05 |
time (sec) |
N/A | 0.213 | 0.084 | 0.369 | 0.188 | 0.251 | 0.000 | 0.268 | 18.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 57 | 52 | 51 | 53 | 56 | 0 | 53 | 66 |
N.S. |
1 | 1.21 | 1.11 | 1.09 | 1.13 | 1.19 | 0.00 | 1.13 | 1.40 |
time (sec) |
N/A | 0.252 | 0.163 | 0.421 | 0.278 | 0.271 | 0.000 | 0.289 | 18.780 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 100 | 58 | 54 | 87 | 62 | 0 | 87 | 76 |
N.S. |
1 | 1.23 | 0.72 | 0.67 | 1.07 | 0.77 | 0.00 | 1.07 | 0.94 |
time (sec) |
N/A | 0.270 | 0.301 | 0.371 | 0.273 | 0.263 | 0.000 | 0.287 | 18.618 |
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 | 119 | 129 | 99 | 82 | 135 | 89 | 0 | 150 | 123 |
N.S. |
1 | 1.08 | 0.83 | 0.69 | 1.13 | 0.75 | 0.00 | 1.26 | 1.03 |
time (sec) |
N/A | 0.298 | 0.269 | 0.493 | 0.273 | 0.253 | 0.000 | 0.296 | 19.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 74 | 70 | 84 | 83 | 90 | 0 | 91 | 73 |
N.S. |
1 | 1.01 | 0.96 | 1.15 | 1.14 | 1.23 | 0.00 | 1.25 | 1.00 |
time (sec) |
N/A | 0.240 | 1.031 | 0.704 | 0.186 | 0.256 | 0.000 | 0.287 | 18.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 109 | 106 | 130 | 134 | 130 | 0 | 148 | 119 |
N.S. |
1 | 0.98 | 0.95 | 1.17 | 1.21 | 1.17 | 0.00 | 1.33 | 1.07 |
time (sec) |
N/A | 0.269 | 3.596 | 1.082 | 0.187 | 0.246 | 0.000 | 0.307 | 18.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 95 | 1195 | 106 | 124 | 272 | 0 | 113 | 591 |
N.S. |
1 | 1.10 | 13.90 | 1.23 | 1.44 | 3.16 | 0.00 | 1.31 | 6.87 |
time (sec) |
N/A | 0.290 | 4.768 | 0.788 | 0.270 | 0.289 | 0.000 | 0.287 | 0.552 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 53 | 49 | 63 | 83 | 157 | 0 | 74 | 456 |
N.S. |
1 | 0.96 | 0.89 | 1.15 | 1.51 | 2.85 | 0.00 | 1.35 | 8.29 |
time (sec) |
N/A | 0.242 | 0.092 | 0.364 | 0.271 | 0.271 | 0.000 | 0.293 | 18.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 28 | 50 | 117 | 0 | 38 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 1.39 | 3.25 | 0.00 | 1.06 | 0.78 |
time (sec) |
N/A | 0.211 | 0.053 | 0.215 | 0.267 | 0.266 | 0.000 | 0.274 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 50 | 52 | 45 | 67 | 164 | 0 | 53 | 44 |
N.S. |
1 | 0.96 | 1.00 | 0.87 | 1.29 | 3.15 | 0.00 | 1.02 | 0.85 |
time (sec) |
N/A | 0.231 | 0.079 | 0.508 | 0.269 | 0.274 | 0.000 | 0.281 | 18.389 |
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 | 76 | 71 | 105 | 70 | 88 | 230 | 0 | 85 | 72 |
N.S. |
1 | 0.93 | 1.38 | 0.92 | 1.16 | 3.03 | 0.00 | 1.12 | 0.95 |
time (sec) |
N/A | 0.272 | 0.226 | 0.987 | 0.269 | 0.272 | 0.000 | 0.294 | 18.602 |
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 | 108 | 100 | 136 | 110 | 117 | 305 | 0 | 129 | 111 |
N.S. |
1 | 0.93 | 1.26 | 1.02 | 1.08 | 2.82 | 0.00 | 1.19 | 1.03 |
time (sec) |
N/A | 0.291 | 0.583 | 1.939 | 0.274 | 0.291 | 0.000 | 0.295 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 72 | 224 | 70 | 65 | 354 | 0 | 96 | 72 |
N.S. |
1 | 0.94 | 2.91 | 0.91 | 0.84 | 4.60 | 0.00 | 1.25 | 0.94 |
time (sec) |
N/A | 0.272 | 2.791 | 0.971 | 0.273 | 0.279 | 0.000 | 0.293 | 18.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 50 | 192 | 45 | 45 | 286 | 0 | 66 | 44 |
N.S. |
1 | 0.96 | 3.69 | 0.87 | 0.87 | 5.50 | 0.00 | 1.27 | 0.85 |
time (sec) |
N/A | 0.233 | 1.650 | 0.532 | 0.268 | 0.284 | 0.000 | 0.294 | 18.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 28 | 27 | 209 | 0 | 48 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.75 | 5.81 | 0.00 | 1.33 | 0.86 |
time (sec) |
N/A | 0.223 | 0.033 | 0.218 | 0.270 | 0.261 | 0.000 | 0.290 | 18.856 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 182 | 46 | 44 | 231 | 0 | 65 | 460 |
N.S. |
1 | 1.00 | 4.04 | 1.02 | 0.98 | 5.13 | 0.00 | 1.44 | 10.22 |
time (sec) |
N/A | 0.253 | 0.196 | 0.169 | 0.271 | 0.283 | 0.000 | 0.268 | 20.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 91 | 67 | 76 | 72 | 272 | 0 | 94 | 373 |
N.S. |
1 | 1.21 | 0.89 | 1.01 | 0.96 | 3.63 | 0.00 | 1.25 | 4.97 |
time (sec) |
N/A | 0.274 | 0.537 | 0.683 | 0.271 | 0.302 | 0.000 | 0.295 | 20.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 141 | 95 | 116 | 126 | 343 | 0 | 141 | 1114 |
N.S. |
1 | 1.21 | 0.81 | 0.99 | 1.08 | 2.93 | 0.00 | 1.21 | 9.52 |
time (sec) |
N/A | 0.334 | 3.202 | 1.371 | 0.269 | 0.289 | 0.000 | 0.289 | 20.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 197 | 133 | 165 | 189 | 424 | 0 | 216 | 1979 |
N.S. |
1 | 1.21 | 0.82 | 1.01 | 1.16 | 2.60 | 0.00 | 1.33 | 12.14 |
time (sec) |
N/A | 0.398 | 1.855 | 2.619 | 0.269 | 0.301 | 0.000 | 0.290 | 21.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 112 | 980 | 110 | 146 | 392 | 0 | 126 | 2039 |
N.S. |
1 | 1.10 | 9.61 | 1.08 | 1.43 | 3.84 | 0.00 | 1.24 | 19.99 |
time (sec) |
N/A | 0.291 | 4.729 | 1.060 | 0.276 | 0.312 | 0.000 | 0.305 | 21.326 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 72 | 71 | 68 | 98 | 262 | 0 | 76 | 62 |
N.S. |
1 | 0.97 | 0.96 | 0.92 | 1.32 | 3.54 | 0.00 | 1.03 | 0.84 |
time (sec) |
N/A | 0.247 | 0.363 | 0.522 | 0.265 | 0.280 | 0.000 | 0.307 | 0.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 81 | 82 | 80 | 111 | 301 | 0 | 91 | 71 |
N.S. |
1 | 0.98 | 0.99 | 0.96 | 1.34 | 3.63 | 0.00 | 1.10 | 0.86 |
time (sec) |
N/A | 0.237 | 0.300 | 0.549 | 0.271 | 0.268 | 0.000 | 0.306 | 19.736 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 96 | 89 | 92 | 133 | 391 | 0 | 113 | 94 |
N.S. |
1 | 0.95 | 0.88 | 0.91 | 1.32 | 3.87 | 0.00 | 1.12 | 0.93 |
time (sec) |
N/A | 0.303 | 0.451 | 1.275 | 0.268 | 0.285 | 0.000 | 0.295 | 0.247 |
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 | 126 | 118 | 139 | 120 | 154 | 490 | 0 | 146 | 124 |
N.S. |
1 | 0.94 | 1.10 | 0.95 | 1.22 | 3.89 | 0.00 | 1.16 | 0.98 |
time (sec) |
N/A | 0.328 | 0.834 | 3.095 | 0.277 | 0.308 | 0.000 | 0.300 | 19.791 |
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 | 157 | 146 | 171 | 158 | 183 | 583 | 0 | 188 | 173 |
N.S. |
1 | 0.93 | 1.09 | 1.01 | 1.17 | 3.71 | 0.00 | 1.20 | 1.10 |
time (sec) |
N/A | 0.349 | 1.654 | 4.722 | 0.270 | 0.310 | 0.000 | 0.310 | 0.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 95 | 248 | 89 | 110 | 516 | 0 | 120 | 113 |
N.S. |
1 | 0.95 | 2.48 | 0.89 | 1.10 | 5.16 | 0.00 | 1.20 | 1.13 |
time (sec) |
N/A | 0.304 | 3.164 | 1.211 | 0.268 | 0.305 | 0.000 | 0.305 | 19.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 80 | 84 | 76 | 88 | 406 | 0 | 89 | 70 |
N.S. |
1 | 0.98 | 1.02 | 0.93 | 1.07 | 4.95 | 0.00 | 1.09 | 0.85 |
time (sec) |
N/A | 0.249 | 0.288 | 0.619 | 0.277 | 0.283 | 0.000 | 0.301 | 19.611 |