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 | C | B | B | B | F | B | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 165 | 1341 | 240 | 362 | 3465 | 0 | 310 | 971 | 535 |
N.S. |
1 | 1.32 | 10.73 | 1.92 | 2.90 | 27.72 | 0.00 | 2.48 | 7.77 | 4.28 |
time (sec) |
N/A | 0.376 | 10.164 | 13.826 | 0.125 | 0.108 | 0.000 | 0.212 | 0.233 | 2.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 59 | 67 | 227 | 71 | 786 | 0 | 347 | 435 | 1050 |
N.S. |
1 | 0.88 | 1.00 | 3.39 | 1.06 | 11.73 | 0.00 | 5.18 | 6.49 | 15.67 |
time (sec) |
N/A | 0.275 | 0.156 | 42.457 | 0.038 | 0.084 | 0.000 | 0.225 | 0.243 | 2.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 197 | 158 | 291 | 553 | 6114 | 0 | 485 | 1394 | 951 |
N.S. |
1 | 1.15 | 0.92 | 1.69 | 3.22 | 35.55 | 0.00 | 2.82 | 8.10 | 5.53 |
time (sec) |
N/A | 0.438 | 12.142 | 80.239 | 0.137 | 0.124 | 0.000 | 0.219 | 0.245 | 0.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 91 | 218 | 269 | 1847 | 1185 | 0 | 447 | 572 | 1424 |
N.S. |
1 | 0.89 | 2.14 | 2.64 | 18.11 | 11.62 | 0.00 | 4.38 | 5.61 | 13.96 |
time (sec) |
N/A | 0.321 | 2.057 | 152.406 | 0.067 | 0.092 | 0.000 | 0.229 | 0.269 | 2.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 153 | 115 | 273 | 514 | 2180 | 0 | 301 | 333 | 967 |
N.S. |
1 | 1.28 | 0.96 | 2.28 | 4.28 | 18.17 | 0.00 | 2.51 | 2.78 | 8.06 |
time (sec) |
N/A | 0.472 | 0.584 | 21.668 | 0.182 | 0.133 | 0.000 | 0.948 | 0.271 | 3.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 75 | 79 | 230 | 0 | 1857 | 0 | 0 | 284 | 2194 |
N.S. |
1 | 0.94 | 0.99 | 2.88 | 0.00 | 23.21 | 0.00 | 0.00 | 3.55 | 27.42 |
time (sec) |
N/A | 0.565 | 0.322 | 7.809 | 0.000 | 0.115 | 0.000 | 0.000 | 0.264 | 3.954 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 97 | 77 | 159 | 316 | 948 | 0 | 155 | 181 | 880 |
N.S. |
1 | 1.26 | 1.00 | 2.06 | 4.10 | 12.31 | 0.00 | 2.01 | 2.35 | 11.43 |
time (sec) |
N/A | 0.519 | 0.435 | 2.750 | 0.166 | 0.156 | 0.000 | 0.600 | 0.279 | 3.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 51 | 53 | 149 | 0 | 773 | 0 | 0 | 195 | 154 |
N.S. |
1 | 0.96 | 1.00 | 2.81 | 0.00 | 14.58 | 0.00 | 0.00 | 3.68 | 2.91 |
time (sec) |
N/A | 0.438 | 0.081 | 1.366 | 0.000 | 0.119 | 0.000 | 0.000 | 0.251 | 2.768 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 102 | 0 | 519 | 0 | 0 | 63 | 147 |
N.S. |
1 | 1.00 | 1.00 | 2.83 | 0.00 | 14.42 | 0.00 | 0.00 | 1.75 | 4.08 |
time (sec) |
N/A | 0.398 | 0.026 | 1.915 | 0.000 | 0.122 | 0.000 | 0.000 | 0.248 | 0.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 114 | 36 | 455 | 0 | 44 | 61 | 81 |
N.S. |
1 | 1.00 | 1.00 | 3.56 | 1.12 | 14.22 | 0.00 | 1.38 | 1.91 | 2.53 |
time (sec) |
N/A | 0.412 | 0.305 | 6.200 | 0.124 | 0.108 | 0.000 | 0.274 | 0.282 | 2.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 53 | 55 | 144 | 0 | 540 | 0 | 0 | 80 | 449 |
N.S. |
1 | 0.96 | 1.00 | 2.62 | 0.00 | 9.82 | 0.00 | 0.00 | 1.45 | 8.16 |
time (sec) |
N/A | 0.311 | 0.183 | 16.032 | 0.000 | 0.138 | 0.000 | 0.000 | 0.274 | 3.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 48 | 50 | 197 | 63 | 649 | 0 | 70 | 307 | 176 |
N.S. |
1 | 0.96 | 1.00 | 3.94 | 1.26 | 12.98 | 0.00 | 1.40 | 6.14 | 3.52 |
time (sec) |
N/A | 0.283 | 0.326 | 38.356 | 0.153 | 0.115 | 0.000 | 0.282 | 0.292 | 3.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 94 | 79 | 236 | 0 | 1584 | 0 | 0 | 620 | 1012 |
N.S. |
1 | 1.09 | 0.92 | 2.74 | 0.00 | 18.42 | 0.00 | 0.00 | 7.21 | 11.77 |
time (sec) |
N/A | 0.317 | 0.433 | 86.950 | 0.000 | 0.150 | 0.000 | 0.000 | 0.280 | 3.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 70 | 71 | 252 | 140 | 2032 | 0 | 135 | 1042 | 252 |
N.S. |
1 | 0.93 | 0.95 | 3.36 | 1.87 | 27.09 | 0.00 | 1.80 | 13.89 | 3.36 |
time (sec) |
N/A | 0.299 | 0.474 | 174.331 | 0.164 | 0.123 | 0.000 | 0.307 | 0.281 | 2.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 120 | 111 | 378 | 0 | 6941 | 0 | 0 | 1442 | 0 |
N.S. |
1 | 0.94 | 0.87 | 2.95 | 0.00 | 54.23 | 0.00 | 0.00 | 11.27 | 0.00 |
time (sec) |
N/A | 0.384 | 0.751 | 27.800 | 0.000 | 0.192 | 0.000 | 0.000 | 0.343 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 162 | 110 | 386 | 840 | 4324 | 0 | 416 | 1269 | 0 |
N.S. |
1 | 1.16 | 0.79 | 2.76 | 6.00 | 30.89 | 0.00 | 2.97 | 9.06 | 0.00 |
time (sec) |
N/A | 0.380 | 0.899 | 9.181 | 0.281 | 0.183 | 0.000 | 0.735 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 96 | 84 | 286 | 0 | 3510 | 0 | 0 | 1145 | 0 |
N.S. |
1 | 0.95 | 0.83 | 2.83 | 0.00 | 34.75 | 0.00 | 0.00 | 11.34 | 0.00 |
time (sec) |
N/A | 0.345 | 0.488 | 3.810 | 0.000 | 0.153 | 0.000 | 0.000 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 81 | 78 | 252 | 0 | 2049 | 0 | 0 | 914 | 0 |
N.S. |
1 | 0.98 | 0.94 | 3.04 | 0.00 | 24.69 | 0.00 | 0.00 | 11.01 | 0.00 |
time (sec) |
N/A | 0.274 | 0.207 | 8.314 | 0.000 | 0.125 | 0.000 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 64 | 63 | 210 | 125 | 1515 | 0 | 138 | 508 | 0 |
N.S. |
1 | 0.97 | 0.95 | 3.18 | 1.89 | 22.95 | 0.00 | 2.09 | 7.70 | 0.00 |
time (sec) |
N/A | 0.263 | 0.586 | 26.228 | 0.201 | 0.123 | 0.000 | 0.331 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 70 | 69 | 183 | 0 | 1563 | 0 | 0 | 590 | 0 |
N.S. |
1 | 0.97 | 0.96 | 2.54 | 0.00 | 21.71 | 0.00 | 0.00 | 8.19 | 0.00 |
time (sec) |
N/A | 0.363 | 0.117 | 60.371 | 0.000 | 0.117 | 0.000 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 75 | 83 | 259 | 127 | 1443 | 0 | 143 | 637 | 0 |
N.S. |
1 | 0.97 | 1.08 | 3.36 | 1.65 | 18.74 | 0.00 | 1.86 | 8.27 | 0.00 |
time (sec) |
N/A | 0.461 | 0.543 | 127.205 | 0.189 | 0.129 | 0.000 | 0.346 | 0.323 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 107 | 203 | 273 | 0 | 2140 | 0 | 0 | 950 | 0 |
N.S. |
1 | 1.05 | 1.99 | 2.68 | 0.00 | 20.98 | 0.00 | 0.00 | 9.31 | 0.00 |
time (sec) |
N/A | 0.539 | 0.369 | 244.370 | 0.000 | 0.136 | 0.000 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 92 | 102 | 306 | 209 | 2869 | 0 | 232 | 1449 | 0 |
N.S. |
1 | 0.95 | 1.05 | 3.15 | 2.15 | 29.58 | 0.00 | 2.39 | 14.94 | 0.00 |
time (sec) |
N/A | 0.544 | 0.774 | 0.711 | 0.238 | 0.135 | 0.000 | 0.350 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 163 | 265 | 351 | 0 | 6396 | 0 | 0 | 2051 | 0 |
N.S. |
1 | 1.05 | 1.71 | 2.26 | 0.00 | 41.26 | 0.00 | 0.00 | 13.23 | 0.00 |
time (sec) |
N/A | 0.705 | 0.935 | 0.615 | 0.000 | 0.178 | 0.000 | 0.000 | 0.363 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 238 | 164 | 501 | 1806 | 13887 | 0 | 546 | 4226 | 0 |
N.S. |
1 | 1.20 | 0.83 | 2.53 | 9.12 | 70.14 | 0.00 | 2.76 | 21.34 | 0.00 |
time (sec) |
N/A | 0.510 | 1.341 | 28.587 | 0.409 | 0.373 | 0.000 | 1.101 | 0.398 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 146 | 136 | 375 | 0 | 11399 | 0 | 0 | 3187 | 0 |
N.S. |
1 | 0.95 | 0.88 | 2.44 | 0.00 | 74.02 | 0.00 | 0.00 | 20.69 | 0.00 |
time (sec) |
N/A | 0.414 | 1.296 | 11.767 | 0.000 | 0.327 | 0.000 | 0.000 | 0.415 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 154 | 134 | 394 | 0 | 7917 | 0 | 0 | 14353 | 0 |
N.S. |
1 | 1.10 | 0.96 | 2.81 | 0.00 | 56.55 | 0.00 | 0.00 | 102.52 | 0.00 |
time (sec) |
N/A | 0.350 | 0.686 | 29.847 | 0.000 | 0.184 | 0.000 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 99 | 77 | 284 | 366 | 5840 | 0 | 320 | 1906 | 0 |
N.S. |
1 | 1.03 | 0.80 | 2.96 | 3.81 | 60.83 | 0.00 | 3.33 | 19.85 | 0.00 |
time (sec) |
N/A | 0.286 | 1.450 | 83.826 | 0.269 | 0.167 | 0.000 | 0.607 | 0.335 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 121 | 123 | 342 | 0 | 6622 | 0 | 0 | 2228 | 0 |
N.S. |
1 | 0.94 | 0.95 | 2.65 | 0.00 | 51.33 | 0.00 | 0.00 | 17.27 | 0.00 |
time (sec) |
N/A | 0.318 | 0.507 | 173.548 | 0.000 | 0.188 | 0.000 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 113 | 115 | 334 | 360 | 5659 | 0 | 319 | 2949 | 0 |
N.S. |
1 | 0.98 | 1.00 | 2.90 | 3.13 | 49.21 | 0.00 | 2.77 | 25.64 | 0.00 |
time (sec) |
N/A | 0.289 | 1.168 | 0.690 | 0.305 | 0.167 | 0.000 | 0.611 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 107 | 87 | 276 | 0 | 5084 | 0 | 0 | 1507 | 0 |
N.S. |
1 | 1.03 | 0.84 | 2.65 | 0.00 | 48.88 | 0.00 | 0.00 | 14.49 | 0.00 |
time (sec) |
N/A | 0.293 | 0.269 | 0.648 | 0.000 | 0.159 | 0.000 | 0.000 | 0.334 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 143 | 128 | 376 | 332 | 5233 | 0 | 322 | 2976 | 0 |
N.S. |
1 | 1.08 | 0.97 | 2.85 | 2.52 | 39.64 | 0.00 | 2.44 | 22.55 | 0.00 |
time (sec) |
N/A | 0.471 | 1.161 | 0.636 | 0.334 | 0.197 | 0.000 | 0.579 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 170 | 317 | 389 | 0 | 8070 | 0 | 0 | 2818 | 0 |
N.S. |
1 | 1.09 | 2.03 | 2.49 | 0.00 | 51.73 | 0.00 | 0.00 | 18.06 | 0.00 |
time (sec) |
N/A | 0.712 | 2.113 | 0.630 | 0.000 | 0.263 | 0.000 | 0.000 | 0.334 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 49 | 97 | 68 | 199 | 339 | 82 | 134 | 67 | 50 |
N.S. |
1 | 0.91 | 1.80 | 1.26 | 3.69 | 6.28 | 1.52 | 2.48 | 1.24 | 0.93 |
time (sec) |
N/A | 0.623 | 0.036 | 0.298 | 0.045 | 0.088 | 0.142 | 0.156 | 0.308 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 59 | 46 | 71 | 168 | 1205 | 88 | 92 | 484 | 53 |
N.S. |
1 | 1.20 | 0.94 | 1.45 | 3.43 | 24.59 | 1.80 | 1.88 | 9.88 | 1.08 |
time (sec) |
N/A | 0.649 | 0.164 | 0.265 | 0.121 | 0.104 | 0.137 | 0.151 | 0.243 | 2.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 65 | 45 | 105 | 160 | 54 | 86 | 45 | 34 |
N.S. |
1 | 1.00 | 1.81 | 1.25 | 2.92 | 4.44 | 1.50 | 2.39 | 1.25 | 0.94 |
time (sec) |
N/A | 0.402 | 0.024 | 0.263 | 0.046 | 0.081 | 0.114 | 0.135 | 0.226 | 2.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 40 | 39 | 49 | 76 | 399 | 60 | 57 | 249 | 37 |
N.S. |
1 | 1.29 | 1.26 | 1.58 | 2.45 | 12.87 | 1.94 | 1.84 | 8.03 | 1.19 |
time (sec) |
N/A | 0.277 | 0.047 | 0.361 | 0.120 | 0.100 | 0.109 | 0.126 | 0.295 | 2.373 |
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 | 19 | 19 | 28 | 22 | 31 | 37 | 20 | 29 | 22 | 18 |
N.S. |
1 | 1.00 | 1.47 | 1.16 | 1.63 | 1.95 | 1.05 | 1.53 | 1.16 | 0.95 |
time (sec) |
N/A | 0.174 | 0.001 | 0.214 | 0.043 | 0.084 | 0.089 | 0.115 | 0.240 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 39 | 25 | 24 | 35 | 70 | 0 | 46 | 54 | 228 |
N.S. |
1 | 1.56 | 1.00 | 0.96 | 1.40 | 2.80 | 0.00 | 1.84 | 2.16 | 9.12 |
time (sec) |
N/A | 0.293 | 0.029 | 0.781 | 0.037 | 0.098 | 0.000 | 0.125 | 0.229 | 0.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 32 | 21 | 31 | 38 | 78 | 30 | 70 | 25 |
N.S. |
1 | 1.00 | 1.78 | 1.17 | 1.72 | 2.11 | 4.33 | 1.67 | 3.89 | 1.39 |
time (sec) |
N/A | 0.224 | 0.023 | 0.471 | 0.041 | 0.092 | 4.545 | 0.135 | 0.260 | 2.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 44 | 39 | 35 | 106 | 407 | 0 | 58 | 345 | 76 |
N.S. |
1 | 1.42 | 1.26 | 1.13 | 3.42 | 13.13 | 0.00 | 1.87 | 11.13 | 2.45 |
time (sec) |
N/A | 0.295 | 0.051 | 0.672 | 0.040 | 0.086 | 0.000 | 0.147 | 0.213 | 2.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 61 | 39 | 105 | 156 | 0 | 86 | 189 | 162 |
N.S. |
1 | 1.00 | 1.69 | 1.08 | 2.92 | 4.33 | 0.00 | 2.39 | 5.25 | 4.50 |
time (sec) |
N/A | 0.291 | 0.042 | 0.149 | 0.042 | 0.088 | 0.000 | 0.152 | 0.235 | 2.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 63 | 45 | 56 | 206 | 1216 | 0 | 93 | 664 | 177 |
N.S. |
1 | 1.29 | 0.92 | 1.14 | 4.20 | 24.82 | 0.00 | 1.90 | 13.55 | 3.61 |
time (sec) |
N/A | 0.371 | 0.192 | 0.184 | 0.041 | 0.125 | 0.000 | 0.171 | 0.256 | 2.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 81 | 190 | 135 | 369 | 796 | 165 | 300 | 134 | 91 |
N.S. |
1 | 0.98 | 2.29 | 1.63 | 4.45 | 9.59 | 1.99 | 3.61 | 1.61 | 1.10 |
time (sec) |
N/A | 0.305 | 0.063 | 0.093 | 0.050 | 0.090 | 0.255 | 0.209 | 0.266 | 0.174 |
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 | 76 | 76 | 76 | 130 | 333 | 3441 | 170 | 191 | 1141 | 100 |
N.S. |
1 | 1.00 | 1.00 | 1.71 | 4.38 | 45.28 | 2.24 | 2.51 | 15.01 | 1.32 |
time (sec) |
N/A | 0.329 | 0.125 | 0.074 | 0.123 | 0.126 | 0.227 | 0.195 | 0.238 | 2.516 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 65 | 137 | 97 | 231 | 483 | 117 | 218 | 96 | 67 |
N.S. |
1 | 1.03 | 2.17 | 1.54 | 3.67 | 7.67 | 1.86 | 3.46 | 1.52 | 1.06 |
time (sec) |
N/A | 0.329 | 0.051 | 0.070 | 0.047 | 0.093 | 0.238 | 0.177 | 0.249 | 2.517 |
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 | 57 | 60 | 49 | 92 | 186 | 1638 | 122 | 116 | 723 | 76 |
N.S. |
1 | 1.05 | 0.86 | 1.61 | 3.26 | 28.74 | 2.14 | 2.04 | 12.68 | 1.33 |
time (sec) |
N/A | 0.478 | 0.215 | 0.056 | 0.119 | 0.101 | 0.214 | 0.163 | 0.248 | 2.568 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 47 | 65 | 60 | 114 | 201 | 68 | 103 | 60 | 47 |
N.S. |
1 | 1.09 | 1.51 | 1.40 | 2.65 | 4.67 | 1.58 | 2.40 | 1.40 | 1.09 |
time (sec) |
N/A | 0.408 | 0.515 | 0.057 | 0.037 | 0.110 | 0.140 | 0.124 | 0.260 | 2.435 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 54 | 57 | 59 | 104 | 668 | 0 | 141 | 440 | 210 |
N.S. |
1 | 1.10 | 1.16 | 1.20 | 2.12 | 13.63 | 0.00 | 2.88 | 8.98 | 4.29 |
time (sec) |
N/A | 0.484 | 0.073 | 0.154 | 0.114 | 0.098 | 0.000 | 0.159 | 0.236 | 2.572 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 40 | 64 | 36 | 64 | 97 | 0 | 71 | 147 | 59 |
N.S. |
1 | 1.11 | 1.78 | 1.00 | 1.78 | 2.69 | 0.00 | 1.97 | 4.08 | 1.64 |
time (sec) |
N/A | 0.484 | 0.075 | 0.164 | 0.043 | 0.083 | 0.000 | 0.178 | 0.228 | 2.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 55 | 57 | 62 | 134 | 677 | 0 | 141 | 493 | 211 |
N.S. |
1 | 1.06 | 1.10 | 1.19 | 2.58 | 13.02 | 0.00 | 2.71 | 9.48 | 4.06 |
time (sec) |
N/A | 0.510 | 0.083 | 0.154 | 0.051 | 0.105 | 0.000 | 0.198 | 0.261 | 0.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 47 | 65 | 43 | 114 | 197 | 0 | 103 | 266 | 175 |
N.S. |
1 | 1.09 | 1.51 | 1.00 | 2.65 | 4.58 | 0.00 | 2.40 | 6.19 | 4.07 |
time (sec) |
N/A | 0.285 | 0.415 | 0.131 | 0.043 | 0.088 | 0.000 | 0.195 | 0.303 | 0.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 48 | 77 | 236 | 1649 | 0 | 118 | 1014 | 197 |
N.S. |
1 | 1.00 | 0.67 | 1.07 | 3.28 | 22.90 | 0.00 | 1.64 | 14.08 | 2.74 |
time (sec) |
N/A | 0.320 | 0.253 | 0.175 | 0.043 | 0.111 | 0.000 | 0.228 | 0.337 | 2.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 65 | 98 | 58 | 231 | 473 | 0 | 218 | 513 | 529 |
N.S. |
1 | 1.03 | 1.56 | 0.92 | 3.67 | 7.51 | 0.00 | 3.46 | 8.14 | 8.40 |
time (sec) |
N/A | 0.487 | 0.070 | 0.160 | 0.046 | 0.090 | 0.000 | 0.235 | 0.570 | 0.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 89 | 76 | 92 | 390 | 3454 | 0 | 192 | 1566 | 362 |
N.S. |
1 | 0.97 | 0.83 | 1.00 | 4.24 | 37.54 | 0.00 | 2.09 | 17.02 | 3.93 |
time (sec) |
N/A | 0.550 | 0.172 | 0.231 | 0.051 | 0.138 | 0.000 | 0.269 | 0.236 | 0.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 109 | 123 | 218 | 583 | 1563 | 260 | 534 | 217 | 138 |
N.S. |
1 | 0.96 | 1.08 | 1.91 | 5.11 | 13.71 | 2.28 | 4.68 | 1.90 | 1.21 |
time (sec) |
N/A | 0.318 | 1.000 | 0.122 | 0.059 | 0.106 | 0.307 | 0.294 | 0.254 | 0.239 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 104 | 98 | 205 | 540 | 7502 | 279 | 309 | 2074 | 155 |
N.S. |
1 | 0.97 | 0.92 | 1.92 | 5.05 | 70.11 | 2.61 | 2.89 | 19.38 | 1.45 |
time (sec) |
N/A | 0.336 | 0.198 | 0.095 | 0.139 | 0.179 | 0.269 | 0.276 | 0.280 | 2.536 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 93 | 108 | 164 | 400 | 1036 | 192 | 418 | 163 | 106 |
N.S. |
1 | 0.99 | 1.15 | 1.74 | 4.26 | 11.02 | 2.04 | 4.45 | 1.73 | 1.13 |
time (sec) |
N/A | 0.500 | 1.147 | 0.099 | 0.051 | 0.106 | 0.214 | 0.249 | 0.250 | 2.629 |
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 | 83 | 83 | 76 | 151 | 351 | 4298 | 211 | 216 | 1493 | 123 |
N.S. |
1 | 1.00 | 0.92 | 1.82 | 4.23 | 51.78 | 2.54 | 2.60 | 17.99 | 1.48 |
time (sec) |
N/A | 0.490 | 0.174 | 0.057 | 0.148 | 0.133 | 0.191 | 0.223 | 0.245 | 2.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 75 | 95 | 112 | 239 | 567 | 126 | 241 | 111 | 86 |
N.S. |
1 | 1.01 | 1.28 | 1.51 | 3.23 | 7.66 | 1.70 | 3.26 | 1.50 | 1.16 |
time (sec) |
N/A | 0.411 | 0.412 | 0.053 | 0.048 | 0.097 | 0.167 | 0.132 | 0.247 | 2.827 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 74 | 67 | 80 | 214 | 2381 | 0 | 267 | 1069 | 380 |
N.S. |
1 | 1.03 | 0.93 | 1.11 | 2.97 | 33.07 | 0.00 | 3.71 | 14.85 | 5.28 |
time (sec) |
N/A | 0.432 | 0.373 | 0.173 | 0.140 | 0.128 | 0.000 | 0.226 | 0.269 | 0.386 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 60 | 81 | 59 | 147 | 341 | 0 | 135 | 407 | 218 |
N.S. |
1 | 1.02 | 1.37 | 1.00 | 2.49 | 5.78 | 0.00 | 2.29 | 6.90 | 3.69 |
time (sec) |
N/A | 0.506 | 1.564 | 0.149 | 0.055 | 0.099 | 0.000 | 0.241 | 0.263 | 2.828 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 70 | 63 | 77 | 203 | 1686 | 0 | 274 | 712 | 327 |
N.S. |
1 | 0.97 | 0.88 | 1.07 | 2.82 | 23.42 | 0.00 | 3.81 | 9.89 | 4.54 |
time (sec) |
N/A | 0.414 | 0.307 | 0.184 | 0.142 | 0.143 | 0.000 | 0.274 | 0.268 | 3.916 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 60 | 82 | 56 | 147 | 341 | 0 | 135 | 407 | 219 |
N.S. |
1 | 1.02 | 1.39 | 0.95 | 2.49 | 5.78 | 0.00 | 2.29 | 6.90 | 3.71 |
time (sec) |
N/A | 0.498 | 0.868 | 0.170 | 0.044 | 0.102 | 0.000 | 0.297 | 23.504 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 67 | 90 | 264 | 2393 | 0 | 267 | 25 | 381 |
N.S. |
1 | 1.00 | 0.81 | 1.08 | 3.18 | 28.83 | 0.00 | 3.22 | 0.30 | 4.59 |
time (sec) |
N/A | 0.419 | 0.390 | 0.195 | 0.059 | 0.110 | 0.000 | 0.343 | 200.020 | 0.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 76 | 100 | 72 | 239 | 557 | 0 | 241 | 25 | 568 |
N.S. |
1 | 1.03 | 1.35 | 0.97 | 3.23 | 7.53 | 0.00 | 3.26 | 0.34 | 7.68 |
time (sec) |
N/A | 0.533 | 1.197 | 0.176 | 0.048 | 0.088 | 0.000 | 0.348 | 200.023 | 2.904 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 100 | 76 | 106 | 420 | 4305 | 0 | 217 | 25 | 380 |
N.S. |
1 | 0.97 | 0.74 | 1.03 | 4.08 | 41.80 | 0.00 | 2.11 | 0.24 | 3.69 |
time (sec) |
N/A | 0.574 | 0.162 | 0.240 | 0.050 | 0.172 | 0.000 | 0.427 | 200.020 | 0.314 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 108 | 128 | 179 | 410 | 1176 | 209 | 447 | 178 | 133 |
N.S. |
1 | 0.98 | 1.16 | 1.63 | 3.73 | 10.69 | 1.90 | 4.06 | 1.62 | 1.21 |
time (sec) |
N/A | 0.298 | 1.230 | 0.079 | 0.053 | 0.097 | 0.229 | 0.154 | 0.211 | 2.904 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 155 | 170 | 262 | 624 | 2133 | 308 | 721 | 261 | 188 |
N.S. |
1 | 0.97 | 1.06 | 1.64 | 3.90 | 13.33 | 1.92 | 4.51 | 1.63 | 1.18 |
time (sec) |
N/A | 0.355 | 1.585 | 0.132 | 0.063 | 0.121 | 0.330 | 0.169 | 0.231 | 2.495 |
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 | 66 | 66 | 60 | 79 | 133 | 742 | 415 | 132 | 153 | 72 |
N.S. |
1 | 1.00 | 0.91 | 1.20 | 2.02 | 11.24 | 6.29 | 2.00 | 2.32 | 1.09 |
time (sec) |
N/A | 0.322 | 0.128 | 0.098 | 0.127 | 0.175 | 4.400 | 0.183 | 0.230 | 0.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 69 | 66 | 87 | 509 | 777 | 428 | 87 | 63 | 56 |
N.S. |
1 | 1.17 | 1.12 | 1.47 | 8.63 | 13.17 | 7.25 | 1.47 | 1.07 | 0.95 |
time (sec) |
N/A | 0.346 | 0.139 | 0.148 | 0.248 | 0.119 | 3.067 | 0.164 | 0.242 | 2.341 |
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 | 46 | 52 | 44 | 49 | 82 | 118 | 306 | 96 | 119 | 46 |
N.S. |
1 | 1.13 | 0.96 | 1.07 | 1.78 | 2.57 | 6.65 | 2.09 | 2.59 | 1.00 |
time (sec) |
N/A | 0.482 | 0.028 | 0.062 | 0.123 | 0.121 | 2.507 | 0.159 | 0.222 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 54 | 47 | 72 | 215 | 486 | 253 | 65 | 40 | 38 |
N.S. |
1 | 1.17 | 1.02 | 1.57 | 4.67 | 10.57 | 5.50 | 1.41 | 0.87 | 0.83 |
time (sec) |
N/A | 0.470 | 0.022 | 0.078 | 0.152 | 0.119 | 2.132 | 0.151 | 0.221 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 47 | 35 | 44 | 58 | 82 | 146 | 61 | 79 | 43 |
N.S. |
1 | 1.12 | 0.83 | 1.05 | 1.38 | 1.95 | 3.48 | 1.45 | 1.88 | 1.02 |
time (sec) |
N/A | 0.432 | 0.018 | 0.062 | 0.049 | 0.089 | 2.019 | 0.139 | 0.236 | 2.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 65 | 71 | 57 | 484 | 240 | 63 | 39 | 37 |
N.S. |
1 | 1.00 | 1.44 | 1.58 | 1.27 | 10.76 | 5.33 | 1.40 | 0.87 | 0.82 |
time (sec) |
N/A | 0.547 | 0.064 | 0.086 | 0.141 | 0.119 | 2.100 | 0.130 | 0.241 | 2.383 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 65 | 55 | 65 | 101 | 118 | 0 | 97 | 141 | 194 |
N.S. |
1 | 1.08 | 0.92 | 1.08 | 1.68 | 1.97 | 0.00 | 1.62 | 2.35 | 3.23 |
time (sec) |
N/A | 0.539 | 0.046 | 0.151 | 0.044 | 0.123 | 0.000 | 0.142 | 0.239 | 0.389 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 71 | 67 | 89 | 329 | 784 | 0 | 89 | 227 | 402 |
N.S. |
1 | 1.18 | 1.12 | 1.48 | 5.48 | 13.07 | 0.00 | 1.48 | 3.78 | 6.70 |
time (sec) |
N/A | 0.336 | 0.137 | 0.160 | 0.175 | 0.122 | 0.000 | 0.151 | 0.263 | 2.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 82 | 60 | 88 | 159 | 747 | 0 | 133 | 661 | 313 |
N.S. |
1 | 0.96 | 0.71 | 1.04 | 1.87 | 8.79 | 0.00 | 1.56 | 7.78 | 3.68 |
time (sec) |
N/A | 0.351 | 0.127 | 0.193 | 0.042 | 0.152 | 0.000 | 0.169 | 0.353 | 2.639 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 96 | 91 | 109 | 1038 | 2368 | 0 | 147 | 550 | 519 |
N.S. |
1 | 1.17 | 1.11 | 1.33 | 12.66 | 28.88 | 0.00 | 1.79 | 6.71 | 6.33 |
time (sec) |
N/A | 0.548 | 0.453 | 0.185 | 0.261 | 0.139 | 0.000 | 0.161 | 16.547 | 2.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 84 | 69 | 91 | 217 | 1141 | 0 | 194 | 3130 | 170 |
N.S. |
1 | 1.01 | 0.83 | 1.10 | 2.61 | 13.75 | 0.00 | 2.34 | 37.71 | 2.05 |
time (sec) |
N/A | 0.596 | 0.339 | 0.115 | 0.129 | 0.180 | 0.000 | 0.236 | 0.274 | 2.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 105 | 90 | 104 | 1010 | 1950 | 0 | 195 | 228 | 1655 |
N.S. |
1 | 1.18 | 1.01 | 1.17 | 11.35 | 21.91 | 0.00 | 2.19 | 2.56 | 18.60 |
time (sec) |
N/A | 0.561 | 0.354 | 0.145 | 0.368 | 0.143 | 0.000 | 0.205 | 0.221 | 3.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 71 | 57 | 84 | 170 | 629 | 0 | 149 | 2332 | 210 |
N.S. |
1 | 0.99 | 0.79 | 1.17 | 2.36 | 8.74 | 0.00 | 2.07 | 32.39 | 2.92 |
time (sec) |
N/A | 0.556 | 0.301 | 0.089 | 0.049 | 0.120 | 0.000 | 0.191 | 0.223 | 2.914 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 99 | 86 | 100 | 614 | 2025 | 0 | 177 | 232 | 106 |
N.S. |
1 | 1.16 | 1.01 | 1.18 | 7.22 | 23.82 | 0.00 | 2.08 | 2.73 | 1.25 |
time (sec) |
N/A | 0.484 | 0.268 | 0.129 | 0.261 | 0.129 | 0.000 | 0.177 | 0.214 | 2.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 55 | 86 | 170 | 623 | 0 | 149 | 2288 | 129 |
N.S. |
1 | 1.00 | 0.81 | 1.26 | 2.50 | 9.16 | 0.00 | 2.19 | 33.65 | 1.90 |
time (sec) |
N/A | 0.363 | 0.279 | 0.087 | 0.049 | 0.092 | 0.000 | 0.162 | 0.245 | 2.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 106 | 97 | 103 | 206 | 1942 | 0 | 195 | 226 | 110 |
N.S. |
1 | 1.19 | 1.09 | 1.16 | 2.31 | 21.82 | 0.00 | 2.19 | 2.54 | 1.24 |
time (sec) |
N/A | 0.304 | 0.377 | 0.135 | 0.170 | 0.137 | 0.000 | 0.127 | 0.216 | 0.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 94 | 83 | 110 | 235 | 1148 | 0 | 195 | 1760 | 0 |
N.S. |
1 | 0.99 | 0.87 | 1.16 | 2.47 | 12.08 | 0.00 | 2.05 | 18.53 | 0.00 |
time (sec) |
N/A | 0.352 | 1.308 | 0.255 | 0.058 | 0.229 | 0.000 | 0.179 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 134 | 111 | 120 | 976 | 3725 | 0 | 336 | 1911 | 0 |
N.S. |
1 | 1.13 | 0.93 | 1.01 | 8.20 | 31.30 | 0.00 | 2.82 | 16.06 | 0.00 |
time (sec) |
N/A | 0.401 | 1.115 | 0.219 | 0.291 | 0.176 | 0.000 | 0.201 | 0.317 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 116 | 93 | 131 | 402 | 3468 | 0 | 323 | 2786 | 0 |
N.S. |
1 | 0.94 | 0.75 | 1.06 | 3.24 | 27.97 | 0.00 | 2.60 | 22.47 | 0.00 |
time (sec) |
N/A | 0.397 | 0.600 | 0.359 | 0.057 | 0.309 | 0.000 | 0.228 | 31.605 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 169 | 139 | 142 | 2345 | 8482 | 0 | 281 | 25 | 0 |
N.S. |
1 | 1.06 | 0.87 | 0.89 | 14.75 | 53.35 | 0.00 | 1.77 | 0.16 | 0.00 |
time (sec) |
N/A | 0.780 | 0.972 | 0.258 | 0.504 | 0.233 | 0.000 | 0.233 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 173 | 144 | 157 | 3354 | 7528 | 0 | 408 | 575 | 2669 |
N.S. |
1 | 1.20 | 1.00 | 1.09 | 23.29 | 52.28 | 0.00 | 2.83 | 3.99 | 18.53 |
time (sec) |
N/A | 0.436 | 0.827 | 0.219 | 1.139 | 0.218 | 0.000 | 0.329 | 0.202 | 0.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 105 | 91 | 127 | 376 | 2584 | 0 | 245 | 11531 | 416 |
N.S. |
1 | 0.96 | 0.83 | 1.17 | 3.45 | 23.71 | 0.00 | 2.25 | 105.79 | 3.82 |
time (sec) |
N/A | 0.367 | 0.725 | 0.111 | 0.075 | 0.144 | 0.000 | 0.305 | 0.270 | 0.770 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 157 | 135 | 148 | 2432 | 7757 | 0 | 384 | 580 | 2574 |
N.S. |
1 | 1.15 | 0.99 | 1.08 | 17.75 | 56.62 | 0.00 | 2.80 | 4.23 | 18.79 |
time (sec) |
N/A | 0.378 | 0.741 | 0.211 | 0.809 | 0.220 | 0.000 | 0.293 | 0.197 | 2.903 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 95 | 80 | 115 | 384 | 2611 | 0 | 245 | 10556 | 397 |
N.S. |
1 | 0.97 | 0.82 | 1.17 | 3.92 | 26.64 | 0.00 | 2.50 | 107.71 | 4.05 |
time (sec) |
N/A | 0.343 | 0.328 | 0.118 | 0.079 | 0.140 | 0.000 | 0.278 | 0.273 | 2.844 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 162 | 137 | 152 | 1472 | 7791 | 0 | 388 | 578 | 255 |
N.S. |
1 | 1.18 | 1.00 | 1.11 | 10.74 | 56.87 | 0.00 | 2.83 | 4.22 | 1.86 |
time (sec) |
N/A | 0.377 | 0.783 | 0.187 | 0.443 | 0.206 | 0.000 | 0.259 | 0.197 | 4.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 91 | 77 | 116 | 378 | 2554 | 0 | 245 | 10812 | 235 |
N.S. |
1 | 0.97 | 0.82 | 1.23 | 4.02 | 27.17 | 0.00 | 2.61 | 115.02 | 2.50 |
time (sec) |
N/A | 0.315 | 0.339 | 0.115 | 0.082 | 0.145 | 0.000 | 0.237 | 0.284 | 3.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 170 | 147 | 156 | 507 | 7496 | 0 | 409 | 575 | 260 |
N.S. |
1 | 1.20 | 1.04 | 1.10 | 3.57 | 52.79 | 0.00 | 2.88 | 4.05 | 1.83 |
time (sec) |
N/A | 0.341 | 0.209 | 0.178 | 0.231 | 0.189 | 0.000 | 0.146 | 0.204 | 3.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 134 | 117 | 161 | 498 | 4800 | 0 | 295 | 5158 | 0 |
N.S. |
1 | 0.97 | 0.85 | 1.17 | 3.61 | 34.78 | 0.00 | 2.14 | 37.38 | 0.00 |
time (sec) |
N/A | 0.394 | 1.063 | 0.647 | 0.083 | 0.359 | 0.000 | 0.272 | 0.371 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 203 | 166 | 167 | 1944 | 11865 | 0 | 437 | 4537 | 0 |
N.S. |
1 | 1.14 | 0.93 | 0.94 | 10.92 | 66.66 | 0.00 | 2.46 | 25.49 | 0.00 |
time (sec) |
N/A | 0.766 | 4.072 | 0.317 | 0.592 | 0.294 | 0.000 | 0.296 | 0.445 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 160 | 138 | 184 | 770 | 10720 | 0 | 474 | 25 | 0 |
N.S. |
1 | 0.94 | 0.81 | 1.08 | 4.50 | 62.69 | 0.00 | 2.77 | 0.15 | 0.00 |
time (sec) |
N/A | 0.709 | 1.220 | 0.905 | 0.107 | 0.579 | 0.000 | 0.373 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 248 | 194 | 189 | 4285 | 22038 | 0 | 493 | 25 | 0 |
N.S. |
1 | 1.09 | 0.85 | 0.83 | 18.79 | 96.66 | 0.00 | 2.16 | 0.11 | 0.00 |
time (sec) |
N/A | 0.816 | 2.313 | 0.378 | 1.130 | 0.377 | 0.000 | 0.379 | 200.038 | 0.000 |